the works of aristotle - vol 8 - editor william ross

7/30/2019 The Works of Aristotle - Vol 8 - Editor William Ross

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JOHN M. KELLY LIBDAEY

University of

St. Michael s College, Toronto



OXFORD UNIVERSITYPRESS

LONDON: AMEN HOUSE, E.G. 4

EDINBURGH GLASGOW LEIPZIG

COPENHAGEN NEW YORK TORONTO

MELBOURNE CAPETOWN BOMBAY

CALCUTTA MADRAS SHANGHAI

HUMPHREY MILFORDPUBLISHER TO THE

UNIVERSITY



THE

WORKS OF ARISTOTLETRANSLATED INTO ENGLISH

UNDER THE EDITORSHIP

OF

W. D. ROSS, M.A., HON. LL.D. (EDIN.)

FELLOW OF ORIEL COLLEGE

FELLOW OF THE BRITISH ACADEMY

VOLUME VIII

METAPHYSICA

SECOND EDITION

OXFORD

AT THE CLARENDON PRESS

1928



TO

INGRAM BYWATER



PREFACE TO FIRST EDITION

WITH the permission of Messrs. Teubner I have followed in

this translation the text of W. Christ (Leipzig, 1895). All

divergences from his readings have been mentioned in the

notes, except that I have frequently left it to the rendering

itself to show that I have not followed his punctuation or his

excisions. The commentaries of Alexander and Bonitz havebeen my greatest help ;

but I owe much also to Bullinger s

notes, and to the translation of Book Z, chaps, i-xi, by

the late Mr. Richard Shute.

I wish to acknowledge my deep obligations to Mr. Bywater

and Prof. Cook Wilson, whose opinions on several difficult pas

sages

have been mostkindly placed

at

my disposal;to the mem

bers of the Oxford Aristotelian Society, for what I learnt from

them during our reading of Books M and N;to Mr. H. H.

Joachim, Fellow of Merton College, for the loan of his valuable

notes on Books Z, H, and;to Mr. C. Cannan, Secretary to

the Delegates of the University Press, and Mr. R. P. Hardie, of

Edinburgh University, whose comments on various parts of

the work have been of the greatest assistance to me;to my

co-editor Mr.J.

A. Smith, and to Dr. G. R. T. Ross, who have

read the whole book both in manuscript and in proof, and

whose suggestions I have adopted in countless passages ;and

to my wife, who has read the whole book in proof, and has

aided me very greatly in points of style.

W. D. R.

1908



PREFACE TO SECOND EDITION

THE present edition of this translation is based on the text

published with my commentary on the Metaphysics (Oxford,

1924). The translation has been carefully revised throughout,

and brought into agreement with the commentary, except in

a very few places where later reflection has led me to revive

an old or to propose a new interpretation.

My thanks are due to the officials and staff of the Clarendon

Press for the care and skill shown in the production of the

work.

W. D. R.

1928



CONTENTSCH. A.

1. The advance from sensation through memory, experience, and art, to

theoretical knowledge.

2. Characteristics of wisdom (philosophy).

3. The successive recognition by earlier philosophers of the material,

efficient, and final causes.

4. Inadequacy of the treatment of these causes.

5. The Pythagorean and Eleatic schools;the former recognizes vaguely

the formal cause.

6. The Platonic philosophy ;it uses only the material and formal causes.

7. The relation of the various systems to the four causes.

8. Criticism of the pre-Platonic philosophers.

9. Criticism of the doctrine of Ideas.

10. The history of philosophy reveals no causes other than the four.

a.

1. General considerations about the study of philosophy.

2. There cannot be an infinite series, nor an infinite variety of kinds, of

causes.

3. Different methods are appropriate to different studies.

B.

1. Sketch of the main problems of philosophy.

2. Fuller statement of the problems :

(i) Can one science treat of all the four causes ?

(ii) Are the primary axioms treated of by the science of substance,

and if not, by what science ?

(iii) Can one science treat of all substances?

(iv) Does the science of substance treat also of its attributes?

(v) Are there any non-sensible substances, and if so, of how manykinds ?

3. (vi) Are the genera, or the constituent paits, of things their first

principles ?

(vii) If the genera, is it the highest genera or the lowest ?

4. (viii) Is there anything apart from individual things?

(ix) Is each of the first principles one in kind, or in number ?

(x) Are the principles of perishable and of imperishable things the

same ?

(xi) Are being and unity substances or attributes?

5. (xii) Are the objects of mathematics substances ?

ix



CONTENTSCH.

6. (xiii) Do Ideas exist, as well as sensible things and the objects of

mathematics ?

(xiv) Do the first principles exist potentially or actually ?

(xv) Are the first principles universal or individual ?

r.

1. Our object is the study of being as such.

2. We must therefore study primary being (viz. substance), unity and

plurality, and the derivative contraries, and the attributes of being

and of substance.

3. We must study also the primary axioms, and especially the law of

contradiction.

4. Fatal difficulties involved in the denial of this law.

5. The connexion of such denial with Protagoras doctrine of relativity ;

the doctrine refuted.

6. Further refutation of Protagoras.

7. The law of excluded middle defended.

8. All judgements are not true, nor are all false;

all things are not at

rest, nor are all in motion.

A.

Philosophical Lexicon.

1. Beginning.

2. Cause.

3. Element.

4. Nature.

5. Necessary.

6. One. Many.

7. Being.

8. Substance.

9. The same. Other. Different. Like. Unlike.

10. Opposite. Contrary. Other in species. The same in species.

11. Prior. Posterior.

12. Potency. Capable. Incapacity. Possible. Impossible.

13. Quantum.

14. Quality.

15. Relative.

16. Complete.

17. Limit.

18. That in virtue of which. In virtue of itself.

19. Disposition.

20. Having or habit (eis~).

21. Affection.

22. Privation.

23. Have or hold(ex*")-

Be in -

24. From.



CONTENTSCH.

25. Part.

26. Whole. Total. All.

27. Mutilated.

28. Race or genus (yevos). Other in genus.

29. False.

30. Accident.

E.

1. Distinction of theology ,the science of being as such, from the other

theoretical sciences, mathematics and physics.

2. Four senses of being . Of these(i)

accidental being is the object

of no science.

3. The nature and origin of accident.

4. (ii) Being as truth is not primary being.

Z.

1. The study of being is primarily the study 01 substance.

2. Various opinions on the question, what things are substances ?

3. Four things are commonly held to be substantial the essence, the

universal, the genus, the substratum. The last may be conceived

as matter, form, or the concrete individual. Reasons why matter

and the concrete individual cannot be primary substance. Form

to be studied first in sensible things.

4. What is essence and to what does it belong, i. e. what things can be

defined ? Primarily substance.

5. Combinations of a subject with one of its proper attributes have no

definition nor essence.

6. Is a thing the same as its essence ? Yes, if it is a substance.

(7. Analysis of generation, whether by nature, art, or spontaneity.

8. Form is not generated, but put into matter; yet it did not previously

exist apart the agent in generation is form embodied in another

individual of the same species.

9. Why spontaneous generation sometimes takes place. The conditions

of generation in the categories other than substance.)

10. When are definitions of the parts included in the definition of the

whole ? When the parts are parts of the form.

1 1. Which parts are parts of the form, which of the concrete individual ?

12. Wherein consists the unity of an object of definition ? In the appro

priateness of the differentia to the genus.

13. A universal cannot be either the substance or an element in the sub

stance of anything (yet how else can a thing be defined ?).

14. Hence it is fatal to make Ideas substances and yet hold that they are

composed of other Ideas.

15. No individual can be defined, whether sensible or, like the Ideas,

intelligible.

xi



CONTENTSCH.

16. The parts of sensible things are only potencies. Unity and being

are not the substance of things.

17. Substance is the cause or form which puts matter into a determinate

state;

it is that in a thing which is distinct from its material

elements.

H.

1. The discussion of sensible substances continued. Their matter is

itself substance.

2. The main types of form or actuality. Definitions of matter, of form,

and of the concrete individual distinguished.

3. Form distinguished from the material elements;Antisthenes attack

on definition;definition analogous to number.

4. Remote and proximate matter;the substratum of attributes not matter

but the concrete individual.

5. The relation of matter to its contrary states.

6. What gives unity to a definition ? The fact that the genus is simply the

potency of the differentia, the differentia the actuality of the genus.

0.

1. Being as potency and actuality. Potency in the strict sense, as

potency of motion, active or passive.

2. Non- rational potencies are single, rational potencies twofold.

3. Potency defended against the attack of the Megaric school.

4. Potency as possibility.

5. How potency is acquired, and the conditions of its actualization.

6. Actuality distinguished from potency ;a special type of potency

described;

actuality distinguishedfrom movement.

7. When one thing may be called the potency or matter of another;

how things are described by names derived from their matter

or their accidents.

8. Actuality prior to potency in definition, time, and substantiality ;

nothing eternal or necessary is a mere potency.

9. Good actuality better than potency, and bad actuality worse;therefore

no separate evil principle in the universe. Geometrical truths

found by actualization of potencies.10. Being as truth, with regard to both composite and simple objects.

I.

1. Four kinds of unit;theessenceof a unit is to be a measure of quantity

or of quality ;various types of measure.

2. Unity not a substance but a universal predicate ;its denotation the

same as that of being.

3. Unity and plurality ; identity ;

likeness;

otherness; difference.

4. Contrariety is complete difference;how related to privation and

contradiction.

xii



CONTENTSCH.

5. The opposition ofJhe equal to the great and the small.

6. The opposition of the one to the many.

7. Intermediates are homogeneous with each other and with the

extremes, stand between contraries, and are compounded out of

these contraries.

8. Otherness in species is otherness 0/"the genus and is contrariety ;

its nature further described.

9. What contrarieties constitute otherness in species.

lo. The perishable and the imperishable differ in kind.

K.

1. Shorter form of B. 2, 3,

2. B. 4-6.

3. r. i, 2.

4, 5- r. 3j 4.

6. r. 5-8.

7. E. i.

8. E. 2-4.

Extracts fromPhysics

:

8. II. 5, 6, on luck.

9. III. 1-3, on potency, actuality, and movement,

10. III. 4, 5, 7, on the infinite; there is no actual infinite, and

especially no infinite body.

11. V. i, on change and movement.

12. V. 2, on the three kinds of movement.

V. 3, definitions of together in place , apart *,touch

,be

tween , contrary in place , successive ,

*

contiguous ,

continuous .

1. Substance the primary subject of inquiry. Three kinds of substance

perishable sensible, eternal sensible, and unmovable (non-

sensible).

2. Change implies not only form and privation but matter.

3. Neither matter nor form comes into being. Whatever comes into

being comes from a substance of the same kind. If form ever

exists apart from the concrete individual, it is in the case of

natural objects.

4. Different things have elements numerically different but the same

in kind; they all have form, privation, and matter. They also

have a proximate and an ultimate moving cause.

5. Again actuality and potency are principles common to all things,

though they apply differently in different cases. The principles of

all things are only analogous, not identical,

xiii



CONTENTSCH.

6. Since movement must be eternal, there must be an eternal mover,

and one whose essence is actuality (actuality being prior to

potency). To account for the uniform change in the universe,

there must be one principle which acts always alike, and onewhose action varies.

7. The eternal mover originates motion by being the primary object of

desire (as it is of thought) ; being thoroughly actual, it cannot

change or move;

it is a living being, perfect, separate from

sensible things, and without parts.

8. Besides the first mover there must be as many unmoved movers

as there are simple motions involved in the motions of the planets.

The number is probably either 55 or 47. As there is but one

prime mover, there must be but one heaven.

9. The divine thought must be concerned with the most divine object,

which is itself. Thought and the object of thought are never

different when the ooject is immaterial.

10. How the good is present in the universe both as the order of the parts

and (more primarily) as their ruler. Difficulties which attend the

views of other philosophers.

M.

1. We pass to immaterial substance. Two kinds of immaterial

substances have been believed in, mathematical objects and

Ideas. We shall discuss first the former, then the latter, then

the view that numbers and Ideas are the substance of sensible

things.

2.(i) Mathematical objects cannot exist as distinct substances either in

or apart from sensible things.

3. They can be separated only in thought. Mathematics is not entirely

divorced from consideration of the beautiful, as is sometimes

alleged.

4. (ii) Arguments which led to the belief in Ideas. Some prove too

little, others too much.

5. Even if there were Ideas, they would not explain the changes in the

sensible world.

6. (iii) Various ways in which numbers may be conceived as the substanceof things.

7. (a) If all units are associable, this gives only mathematical, not ideal

number,(b) If all units are inassociable, this gives neither mathe

matical nor ideal number, (c) If only the units in the same

number are associable, this leads to equal difficulties;units must

have no difference of kind.

8. The views of Platonists who disagree with Plato, and those of the

Pythagoreans, lead to equal difficulties. Further objections to

ideal numbers : (a) How are the units derived from the indefinite

xiv



CONTENTSCH.

dyad ? (b] Is the series of numbers infinite or finite;and if finite,

what is its limit ?(c) What sort of principle is the One ?

9. Discussion of the principles of geometrical objects. Criticism of the

generation of numbers from unity and plurality, and of spatial

magnitudes from similar principles. The criticism of ideal

numbers summed up. The upholders of Ideas make them at once

universal and individual.

10. Are the first principles of substances individual or universal ?

N.

1. The principles cannot be contraries. The Platonists in making them

contraries treated one of the contraries as matter. Various forms

of this theory. The nature of unity and plurality expounded.

2. Eternal substances cannot be compounded out of elements. The

object of the Platonists is to explain the presence of plurality in

the world, but in this they do not succeed. What justifies the

belief in the separate existence of numbers ?

3. Difficulties in the various theories of number. The Pythagoreans

ascribe generation to numbers, which are eternal.

4. The relation between the first principles and the good.

5. How is number supposed to be derived from its elements ? How is it

the cause of substances ?

6. The causal agency ascribed to numbers is purely fanciful.

xv



BOOK A

I ALL men by nature desire to know. An indication of g8oa

this is the delight we take in our senses;for even apart

from their usefulness they are loved for themselves;and

above all others the sense of sight. For not only with a

view to action, but even when we are not going to do any- 25

thing, we prefer seeing (one might say) to everything else.

The reason is that this, most of all the senses, makes us

know and brings to light many differences between things.

By nature animals are born with the faculty of sensation,

and from sensation memory is produced in some of them,

though not in others. And therefore the former are more 98

intelligent and apt at learning than those which cannot

remember;

those which are incapable of hearing sounds

are intelligent though they cannot be taught, e. g. the bee,

and any other race of animals that may be like it;and those

which besides memory have this sense of hearing can be

taught.

The animals other than man live by appearances and 25

memories, and have but little of connected

experience;but

the human race lives also by art and reasonings. Now

from memory experience is produced in men;

for the

several memories of the same thing produce finally the

capacity for a single experience. And experience seems 98ia

pretty much like science and art, but really science and art

come to men throiigh experience ;for experience made

art , as Polus says,

1

but inexperience luck.

Now art 5

arises when from many notions gained by experience one

universal judgement about a class of objects is produced.

For to have a judgement that when Callias was ill of this

disease this did him good, and similarly in the case of

Socrates and in many individual cases, is a matter of experi

ence;but to judge that it has done good to all persons of 10

1Cf. PI. Gorg. 448 c, 462 BC.



9 8ia METAPHYSICA

a certain constitution, marked off in one class, when they

were ill of this disease, e. g. to phlegmatic or bilious people

when burning with fever, this is a matter of art.

With a view to action experience seems in no respectin

ferior to art, and men of experience succeed even better

15 than those who have theory without experience. (The

reason is that experience is knowledge of individuals, art of

universals, and actions and productions are all concerned

with the individual;for the physician does not cure man,

except in an incidental way, but Callias or Socrates or

some other called by some such individual name, who20 happens to be a man. If, then, a man has the theory with

out the experience, and recognizes the universal but does not

know the individual included in this, he will often fail to

cure;for it is the individual that is to be cured.) But yet we

think that knowledge and understanding belong to art

25 rather than to experience, and we suppose artists to be

wiser than men of experience (which implies that Wisdom

depends in all cases rather on knowledge) ;and this because

the former know the cause, but the latter do not. For men

of experience know that the thing is so, but do not know

3o why, while the others know the 4

why and the cause. Hence

we think also that the master-workers in each craft are

more honourableand know in a truer sense and are wiser

98ib than the manual workers, because they know the causes of

the things that are done (we think the manual workers are

like certain lifeless things which act indeed, but act without

knowing what they do, as fire burns, but while the lifeless

things perform each of their functions by a natural tendency,

5 the labourers perform them through habit) ;

1 thus we view

them as being wiser not in virtue of being able to act, but

of having the theory for themselves and knowing the causes.

And in general it is a sign of the man who knows and of

the man who does not know, that the former can teach, and

therefore we think art more truly knowledge than experi

ence is;for artists can teach, and men of mere experience

cannot.

10 Again, we do not regard any of the senses as Wisdom;

1

98ib 2 TOVS ...

5 etfoy may be a later addition.



BOOK A. I 981*

yet surely these give the most authoritative knowledge of

particulars. But they do not tell us the why ofanything

e. g. why fire is hot; they only say that it is hot.

At first he who invented any art whatever that went

beyond the common perceptions of man was naturally

admired by men, not only because there was something I5

useful in the inventions, but because he was thought wise

and superior to the rest. But as more arts were invented,

and some were directed to the necessities of life, others

to recreation, the inventors of the latter were naturally

always regardedas wiser than the inventors of the

former,because their branches of knowledge did not aim at utility.

Hence when all such inventions were already established, ao

the sciences which do not aim at giving pleasure or at the

necessities of life were discovered, and first in the places

where men first began to have leisure.1 This is why the

mathematical arts were founded in Egypt ;for there the

priestly caste was allowed to be at leisure.

We have said in the Ethics 2 what the difference is 25

between art and science and the other kindred faculties;

but the point of our present discussion is this, that all men

suppose what is called Wisdom to deal with the first causes

and the principles of things ;so that, as has been said

before, the man of experience is thought to be wiser than 30

the possessors of any sense-perception whatever, the artist

wiser than the men of experience, the master-worker than

the mechanic, and the theoretical kinds of knowledge to

be more of the nature of Wisdom than the productive.

Clearly then Wisdom is knowledge about certain principles 982*

and causes.

2 Since we are seeking this knowledge, we must inquire of 5

what kind are the causes and the principles, the knowledgeof which is Wisdom. If one were to take the notions we

have about the wise man, this might perhaps make the

answer more evident. We suppose first, then, that the wise

man knows all things, as far as possible, although he has not

1

Reading in 98 l b 23 ov Trpurov e

2

Ii39bi4-ii4i

b8.

B 2



982a METAPHYSICA

10 knowledge of each of them in detail; secondly, that he who

can learn things that are difficult, and not easy for man to

know, is wise (sense-perception is common to all, and

therefore easy and no mark of Wisdom) ; again, that hewho is more exact and more capable of teaching the causes

is wiser, in every branch of knowledge ;and that of the

1 5 sciences, also, that which is desirable on its own account

and for the sake of knowing it is more of the nature of

Wisdom than that which is desirable on account of its

results, and the superior science is more of the nature of

Wisdom than the ancillary ;for the wise man must not be

ordered but must order, and he must not obey another, but

the less wise must obey hint.

20 Such and so many are the notions, then, which we have

about Wisdom and the wise. Now of these characteristics

that of knowing all things must belong to him wrho has in

the

highest degree

universal

knowledge;for he knows in

a sense all the instances that fall under the universal. And

these things, the most universal, are on the whole the

hardest for men to know;for they are farthest from the

25 senses. And the most exact of the sciences are those which

deal most with first principles ;for those which involve

fewer principles are more exact than those which involve

additional principles, e. g. arithmetic than geometry. Butthe science which investigates causes is also instritctive, in

a higher degree, for the people who instruct us are those

30 who tell the causes of each thing. And understanding and

knowledge pursued for their own sake are found most in

the knowledge of that which is most knowable (for he who

chooses to know for the sake of knowing will choose most

g82breadily that \vhich is most truly knowledge, and such is

the knowledge of that which is most knowable) ;and the

first principles and the causes are most knowable;for by

reason of these, and from these, all other things come to be

known, and not these by means of the things subordinate

to them. And the science which knows to what end each

5

thing

must be done is the most authoritative of the sciences,

and more authoritative than any ancillary science;and this

end is the good of that thing, and in general the supreme



BOOK A. 2 g82b

good in the whole of nature. Judged by all the tests we

have mentioned, then, the name in question falls to the same

science;this must be a science that investigates the first

principles and causes; for the good, i. e. the end, is one of

i

the causes.

That it is not a science of production is clear even from

the history of the earliest philosophers. For it is owing to

their wonder that men both now begin and at first began to

philosophize ; they wondered originally at the obvious

difficulties, then advanced little by little and stated diffi

culties about the greater matters, e.g. about the phenomena J 5

ofthe moon and those of the sun and of the stars, and about

the genesis of the universe. And a man who is puzzled

and wonders thinks himself ignorant (whence even the lover

of myth is in a sense a lover of Wisdom, for the myth is

composed of wonders) ;therefore since they philosophized

in order to escape from ignorance, evidently they were 20

pursuing science in order to know, and not for any utili

tarian end. And this is confirmed by the facts;

for it was

when almost all the necessities of life and the things that

make for comfort and recreation had been secured, that

such knowledge began to be sought. Evidently then we do

not seek it for the sake of any other advantage ;but as the 25

man isfree, we say, who

exists for his

ownsake and not for

another s, so we pursue this as the only free science, for it

alone exists for its own sake.

Hence also the possession of it might be justly regarded

as beyond human power ;for in many ways human nature

is in bondage, so that according to Simonides l God alone 30

can have this privilege ,and it is unfitting that man should

not be content to seek the knowledge that is suited to him.

If, then, there is something in what the poets say, and

jealousy is natural to the divine power, it would probably 983**

occur in this case above all, and all who excelled in this

knowledge would be unfortunate. But the divine power

cannot be jealous (nay, according to the proverb,2 l bards

tell many a lie),nor should any other science be thought

more honourable than one of this sort. For the most 5

1Fr. 3 Hiller.

2Cf. Solon, fr. 26 Killer.



983a METAPHYSICA

divine science is also most honourable; and this science

alone must be, in two ways, most divine. For the science

which it would be most meet for God to have is a divine

science, and so is any science that deals with divine objects;

and this science alone has both these qualities ;for

(i)God is

thought to be among the causes of all things and to be a

first principle, and (2) such a science either God alone can

10 have, or God above all others. All the sciences, indeed,

are more necessary than this, but none is better.

Yet the acquisition of it must in a sense end in something

which is the opposite of our original inquiries. For all

men begin, as we said, by wondering that things are as

15 they are, as they do about self-moving marionettes, or

about the solstices or the incommensurability of the diagonal

of a square with the side;for it seems wonderful to all who

have not yet seen the reason, that there is a thing which

cannot be measured even by the smallest unit. But we

must end in the contrary and, according to the proverb,1

the better state, as is the case in these instances too when

men learn the cause;

for there is nothing which would

ao surprise a geometer so much as if the diagonal turned out

to be commensurable.

We have stated, then, what is the nature of the science

we are searching for, and what is the mark which oursearch and our whole investigation must reach.

Evidently we have to acquire knowledge of the original 3

25 causes (for we say we know each thing only when we think

we recognize its first cause), and causes are spoken of in

four senses. In one of these we mean the substance, i. e.

the essence(for

the*

whyis reducible

finally

to the defini

tion, and the ultimate why is a cause and principle) ;in

30 another the matter or substratum, in a third the source of

the change, and in a fourth the cause opposed to this, the

purpose and the good (for this is the end of all generation

and change). We have studied these causes sufficiently in

our work on nature,2 but yet let us call to our aid those who

1 Cf. Leutsch and Schneidewin, Paroemiographi Graeci, i. 62, 234,

ii. 357-2

Phys. ii. 3, 7-



BOOK A. 3 98ab

have attacked the investigation of being and philosophized

about reality before us. For obviously they too speak of

certain principles and causes;to go over their views, then,

will be ofprofit

to the

present inquiry,

for we shall either 5

find another kind of cause, or be more convinced of the

correctness of those which we now maintain.

Of the first philosophers, then, most thought the prin

ciples which were of the nature of matter were the only

principles of all things. That of which all things that are

consist, the first from which they come to be, the last into

which they are resolved (the substance remaining, but

changing in its modifications), this they say is the element 10

and this the principle of things, and therefore they think

nothing is either generated or destroyed, since this sort of

entity is always conserved, as we say Socrates neither comes

to be absolutely when he comes to be beautiful or musical,

nor ceases to be when he loses these characteristics, because 15

the substratum, Socrates himself, remains. Just so they say

nothing else comes to be or ceases to be;for there must be

some entity either one or more than one from which all

other things come to be, it being conserved.

Yet they do not all agree as to the number and the

nature of these principles. Thales, the founder of this type 20

of philosophy, says the principle is water (for which reason

he declared that the earth rests on water), getting the

notion perhaps from seeing that the nutriment of all things

is moist, and that heat itself is generated from the moist and

kept alive by it (and that from which they come to be is

a principle of all things). He got his notion from this fact, 25

and from the fact that the seeds of all things have a moist

nature,and that water is the

originof the nature of moist

things.

Some l think that even the ancients who lived long before

the present generation, and first framed accounts of the

gods, had a similar view of nature;for they made Ocean 3

and Tethys the parents of creation,2 and described the oath

1

The reference is probably to Plato (Crat. 4026, Theaet. 152 E,162 D, i8oc).

2Horn. //. xiv. 201, 246.



g8ab METAPHYSICA

of the gods as being by water,1to which they give the

name of Styx ;for what is oldest is most honourable, and

the most honourable thing is that by which one swears. It

984** may perhaps be uncertain whether this opinion aboutnature is primitive and ancient, but Thales at any rate is

said to have declared himself thus about the first cause.

Hippo no one would think fit to include among these

thinkers, because of the paltriness of his thought.

5Anaximenes and Diogenes make air prior to water, and

the most primary of the simple bodies, while Hippasus of

Metapontium and Heraclitus of Ephesus say this of fire, and

Empedocles says it of the four elements (adding a fourth

earth to those which have been named) ;for these, he

says, always remain and do not come to be, except that

TOthey come to be more or fewer, being aggregated into one

and segregated out of one.

Anaxagorasof Clazomenae, who,

thougholder than

Empedocles, was later in his philosophical activity, says the

principles are infinite in number;for he says almost all the

things that are made of parts like themselves, in the manner

of water or fire, are generated and destroyed in this

i 5 way, only by aggregation and segregation, and are not

in any other sense generated or destroyed, but remain

eternally.

From these facts one might think that the only cause is

the so-called material cause;but as men thus advanced, the

very facts opened the way for them and joined in forcing

them to investigate the subject. However true it may be

20 that all generation and destruction proceed from some one

or (for that matter) from more elements, why does this

happen and what is the cause ? For at least the substratum

itself does not make itself change ;e. g. neither the wood

nor the bronze causes the change ofeither of them, nor does

the wood manufacture a bed and the bronze a statue, but

25 something else is the cause of the change. And to seek

this is to seek the second cause, as we should say, that

from which comes the

beginning

of the movement. Nowthose who at the very beginning set themselves to this kind

1Ibid. ii. 755, xiv. 271, xv. 37.



BOOK A. 3 g84a

of inquiry, and said the substratum was one,1 were not at

all dissatisfied with themselves;but some at least of those

who maintain it to be one 2 as though defeated by this 30

searchfor

thesecond

causesay

the one and nature as

a whole is unchangeable not only in respect of generation

and destruction (for this is a primitive belief, and all agreed

init), but also of all other change ;

and this view is peculiar

to them. Of those who said the universe was one, then,

none succeeded in discovering a cause of this sort, except

perhaps Parmenides, and he only inasmuch as he supposes

that there is not only one but also in some sense two causes.

But for those who make more elements 3it is more possible 5

to state the second cause, e. g. for those who make hot and

cold, or fire and earth, the elements;for they treat fire as

having a nature which fits it to move things, and water and

earth and such things they treat in the contrary way.

When these men and the principles of this kind had had

their day, as the latter were found inadequate to generate

the nature of things men were again forced by the truth 10

itself, as we said,4to inquire into the next kind of cause.

For it is not likely either that fire or earth or any such

element should be the reason why things manifest goodness

and beauty both in their being and in their coming to be,

or that those thinkers should havesupposed

it was;nor

again could it be right to entrust so great a matter to

spontaneity and chance. When one man 5said, then, that 15

reason was present as in animals, so throughout nature

as the cause of order and of all arrangement, he seemed

like a sober man in contrast with the random talk of his

predecessors. We know that Anaxagoras certainly adopted

these views, but Hermotimus ofClazomenae is credited with

expressing them earlier. Those who thought thus stated 20

that there is a principle of things which is at the same time

the cause of beauty, and that sort of cause from which

things acquire movement.

4 One might suspect that Hesiod was the first to look for

1

Thales, Anaximenes, and Heraclitus.

2

The Eleatics.3 The reference is probably to Empedocles4 a

i8.5

Anaxagoras ;cf. esp. fr. 12.



984b METAPHYSICA

such a thing or some one else who put love or desire

among existing things as a principle, as Parmenides, too,

25 does; for he, in constructing the genesis of the universe,

saysl

:

Love first of all the Gods she planned.

And Hesiod says2

:

First of all things was chaos made, and then

Broad-breasted earth, . . .

And love, mid all the gods pre-eminent,

30 which implies that

amongexisting things there must be

from the first a cause which will move things and bring

them together. How these thinkers should be arranged

with regard to priority of discovery let us be allowed to

decide later;

* but since the contraries of the various forms

of good were also perceived to be present in nature not

only order and the beautiful, but also disorder and the ugly,

985 and bad things in greater number than good, and ignoble

things than beautiful therefore another thinker introduced

friendship and strife, each of the two the cause of one of

these two sets of qualities. For if we were to follow out

the view of Empedocles, and interpret it according to its

5 meaning and not to its lisping expression, we should find

that friendship is the cause of good things, and strife ofbad.

Therefore, ifwe said that Empedocles in a sense both men

tions, and is the first to mention, the bad and the good as

principles, we should perhaps be right, since the cause of

all goods is the good itself.

10 These thinkers, as we say, evidently grasped, and to this

extent, two of the causes which we distinguished in our

work on nature4

the matter and the source of the move

ment vaguely, however, and with no clearness, but as

untrained men behave in fights ;for they go round their

15 opponents and often strike fine blows, but they do not fight

on scientific principles, and so too these thinkers do not

seem to know what they say ;for it is evident that, as a

rule, they make no use of their causes except to a small

1Fr. 13.

2

Theog. 116-120.3 The promise is not fulfilled.

*

Phys. ii. 3, 7.



BOOK A. 4 985

extent. For Anaxagoras uses reason as a deus ex machina

for the making- of the world, and when he is at a loss to tell

from what cause something necessarily is, then he drags20

reasonin,

but in all other cases ascribes events to

anything rather than to reason.

1 And Empedocles, though

he uses the causes to a greater extent than this, neither

does so sufficiently nor attains consistency in their use. At

least, in many cases he makes love segregate things, and

strife aggregate them. For whenever the universe is dis- 25

solved into its elements by strife, fire is aggregated into

one, and so is each of the other elements ; but whenever

again under the influence of love they come together

into one, the parts must again be segregated out of each

element.

Empedocles, then, in contrast with his predecessors, was

the first to introduce the dividing of this cause, not positing 30

one source ofmovement, but different and contrary sources.

Again, he was the first to speak of four material elements;

yet he does not use four, but treats them as two only ;he

treats fire by itself, and its opposites -earth, air, and water

as one kind of thing. We may learn this by study of his

verses.2

This philosopher then, as we say, has spoken of the

principles in this way, and made them of this number.

Leucippus and his associate Democritus say that the full 5

and the empty are the elements, calling the one being and

the other non-being the full and solid being being, the

empty non-being (whence they say being no more is than

non-being, because the solid no more is than the empty) ;

and they make these the material causes of things. And as 10

those who make the underlying substance one generate all

other things by its modifications, supposing the rare and

the dense to be the sources of the modifications, in the same

way these philosophers say the differences in the elements

are the causes of all other qualities. These differences, they

say, are three shape and order and position. For they 15

say the real is differentiated only by rhythm and inter-

1Cf. PI. PhaedO) 98 BC, Laws, 967 B-D.

2Cf. fr. 62.



985b METAPHYSICA

contact and turning ;and of these rhythm is shape,

inter-contact is order, and turning is position ;for A differs

from N in shape, AN from NA in order, HJ from H in

position.The

questionof

movementwhence or

howit is

to belong to things these thinkers, like the others, lazily

neglected.

20 Regarding the two causes, then, as we say, the inquiry

seems to have been pushed thus far by the early philo

sophers.

Contemporaneously with these philosophers and before 5

them, the so-called Pythagoreans, who were the first to take

up mathematics, not only advanced this study, but also

25 having been brought up in it they thought its principles

were the principles of all things. Since of these principles

numbers are by nature the first, and in numbers they

seemed to see

manyresemblances to the

thingsthat exist

and come into being more than in fire and earth and

water (such and such a modification of numbers being

30 justice, another being soul and reason, another being oppor

tunity and similarly almost all other things being numeri

cally expressiblel

) ; since, again, they saw that the

modifications and the ratios of the musical scales were

expressible in numbers ; since, then, all other things

seemed in their whole nature to be modelled on numbers,

and numbers seemed to be the first things in the whole of

g86anature, they supposed the elements of numbers to be the

elements of all things, and the whole heaven to be a musical

scale and a number. And all the properties of numbers

and scales which they could show to agree with the attri-

5 butes and parts and the whole arrangement of the heavens,

they collected and fitted into their scheme;and if there

was a gap anywhere, they readily made additions so as to

make their whole theory coherent. E.g. as the number 10

is thought to be perfect and to comprise the whole nature

ic of numbers, they say that the bodies which move throughthe heavens are

ten,but as

the visible bodiesare

only nine,

1Cf. Diels, Vorsokratiker, ed. 3, i. 303. 15-19.



BOOK A. 5 g86a

to meet this they invent a tenth the*

counter-earth . Wehave discussed these matters more exactly elsewhere.

1

But the object of our review is that we may learn from

these philosophers also what they suppose to bethe

prin

ciples and how these fall under the causes we have named. 15

Evidently, then, these thinkers also consider that number is

the principle both as matter for things and as forming both

their modifications and their permanent states, and hold

that the elements of number are the even and the odd, and

that of these the latter is limited, and the former unlimited;

and that the One proceeds from both of these (for it is both

even and odd), and number from the One;and that the 20

whole heaven, as has been said, is numbers.

Other members of this same school say there are ten

principles, which they arrange in two columns ofcognates2

limit and unlimited, odd and even, one and plurality,

right and left, male and female, resting and moving, straight 25

1 De Caelo, ii. 13; Fr. de Pythagoreis, ii. I5i3a4.o-

b 20. Cf. Diels,

ibid. 347. 3-11.2

arvo-Toi\in and o-to-roi^o? are used in a great variety ofconnexions byAristotle, but the common notion is that of things which from some point

of view may be treated as forming one line or column. The meaningsin the Metaphysics may be summarized thus :

In A. g86a23, N. ic93

b 12 the reference is to a Pythagorean classifica

tion of important general notions. The first column is the line of good

(f) (Tvoroi^ta TI TOV KaXoO, N. io93

b

12), the second the line of evil. Tothe line of good N. io93b13 adds the equal and the potencies of

certain numbers .

In r. ioo4b27, K. io66a 15, A. io72

a31 there is no explicit reference

to the Pythagorean doctrine, but Aristotle speaks of two lines,one

of which is knowable in itself, while the other is privative ,and its

*

principles are indefinite because they are privative .

In I. I054b35, 1058*13 we have a different sort of line. Terms

which in the strict sense differ are said to be either different in genusor in the same line of predication, and therefore in the same genus ;

and contraries which differ in species and not in genus are said to bein the same line of predication, o-uorot^ia rfjs Karr^yopias seems to

correspond to V\THJM rr}? Karrjyopins (lo54b29), which is said in A.

Ioi6b 33 to be coextensive with a ycvos. It is at first sight surprisingto find genus identified with category, and one is tempted to suggestthat orvtTTotxia (or o-^/ua) TTJS KaTr)yopis means one of the main divisions

of a category, within which the same sort of predicate is found. Thusnumber would be the genus within which the predicates odd and even,and various subordinate predicates, are found. Then the subordinate

predicates might be thought of as forming a column under odd and

even.

But A. io24b 12-16 shows that genus in one sense can beidentified with category. The categories are the only genera proper,since they are the only genera which are not species.



986a METAPHYSICA

and curved, light and darkness, good and bad, square and

oblong. In this way Alcmaeon of Croton seems also to

have conceived the matter, and either he got this view from

30 them or they gotit

from him; for he expressed himself

similarly to them. For he says most human affairs go in

pairs, meaning not definite contrarieties such as the Pytha

goreans speak of, but any chance contrarieties, e. g. white

and black, sweet and bitter, good and bad, great and small.

He threw out indefinite suggestions about the other con-

g86btrarieties, but the Pythagoreans declared both how many

and which their contrarieties are.

From both these schools, then, we can learn this much,

that the contraries are the principles of things ;and how

many these principles are and which they are, we can learn

from one of the two schools. But how these principles can

5 be brought together under the causes we have named has

not been clearly and articulately stated by them; they

seem, however, to range the elements under the head of

matter;for out of these as immanent parts they say sub

stance is composed and moulded.

From these facts we may sufficiently perceive the mean

ing of the ancients who said the elements of nature were

10 more than one;

but there are some who spoke of the

universe asif it

were one entity, though they were not all

alike either in the excellence of their statement or in its

conformity to the facts of nature. The discussion of them

is in no way appropriate to our present investigation of

causes, for they do not, like some of the natural philo

sophers, assume being to be one and yet generate it out of

15 the one as out of matter, but they speak in another way ;

those others add change, since they generate the universe,

but these thinkers say the universe is unchangeable. Yet

this much is germane to the present inquiry : Parmenides

seems to fasten on that which is one in definition,

a Melissus on that which is one in matter, for which reason

the former says that it is limited, the latter that it is

unlimited;

:while Xenophanes, the first of these partisans

of the One (for Parmenides is said to have been his pupil),

1Cf. Phys. 185* 32-

b3, 2o;

a15-17.



BOOK A. 5 g86b

gave no clear statement, nor does he seem to have grasped

the nature of either of these causes, but with reference to

the whole material universe he says the One is God. Now 25

these thinkers, as we said, must be neglected for the pur

poses of the present inquiry two of them entirely, as being

a little too naive, viz. Xenophanes and Melissus;but Par-

menides seems in places to speak with more insight. For,

claiming that, besides the existent, nothing non-existent

exists, he thinks that of necessity one thing exists, viz. the

existent and nothing else (on this we have spoken more 30

clearly in our work on nature),1 but being forced to follow

the observed facts, and supposing the existence of that

which is one in definition, but more than one according to

our sensations, he now posits two causes and two principles,

calling them hot and cold, i. e. fire and earth;and of these

he ranges the hot with the existent, and the other with the 987**

non-existent.

From what has been said, then, and from the wise men

who have now sat in council with us, we have got thus

much on the one hand from the earliest philosophers, who

regard the first principle as corporeal (for water and fire

and such things are bodies), and of whom some supposes

that there is one corporeal principle, others that there are

more than one, but both put these under the head of matter;

and on the other hand from some who posit both this cause

and besides this the source of movement, which we have got

from some as single and from others as twofold.

Down to the Italian school, then, and apart from it,

philosophers have treated these subjects rather obscurely, 10

except that, as we said, they have in fact used two kinds of

cause, and one of these the source of movement sometreat as one and others as two. But the Pythagoreans have

said in the same way that there are two principles, but

added this much, which is peculiar to them, that they 15

thought that finitude andinfinity were not attributes of

certain other things, e. g. of fire or earth or anything else

of this kind, but that infinity itself and unity itself were the

1

Phys. i. 3.



987a METAPHYSICA

substance of the things of which they are predicated. This

is why number was the substance of all things. On this

20 subject, then, they expressed themselves thus;and regarding

the question of essence they began to make statements anddefinitions, but treated the matter too simply. For they

both defined superficially and thought that the first subject

of which a given definition was predicable was the sub

stance of the thing defined, as if one supposed thatl

double

and 2 were the same, because 2 is the first thing of which

25 double is predicable. But surely to be double and to be

2 are not the same ;if they are, one thing will be many l

a consequence which they actually drew.2 From the earlier

philosophers, then, and from their successors we can learn

thus much.

After the systems we have named came the philosophy 6

30 of Plato, which in most respects followed these thinkers,

but had peculiarities that distinguished it from the philo

sophy of the Italians. For, having in his youth first become

familiar with Cratylus and with the Heraclitean doctrines

(that all sensible things are ever in a state of flux and there

is no knowledge about them), these views he held even in

later years. Socrates, however, was busying himself about

ethical matters and neglecting the world of nature as a whole

but seeking the universal in these ethical matters, and fixed

thought for the first time on definitions;Plato accepted his

5 teaching, but held that the problem applied not to sensible

things but to entities of another kind for this reason, that

the common definition could not be a definition of any

sensible thing, as they were always changing. Things of

this othersort, then,

he calledIdeas,

and sensiblethings,

he

said, were all named after these, and in virtue of a relation

to these;for the many existed by participation in the

10 Ideas that have the same name as they. Only the name

participation was new;for the Pythagoreans say that

things exist by*

imitation of numbers, and Plato says they

exist by participation, changing the name. But what the

1i. e. 2 will be each of several things whose definition is predicable

of it.

2

e.g. 2 was identified both with opinion and with daring.



BOOK A. 6 g87b

participation or the imitation of the Forms could be they

left an open question.

Further, besides sensible things and Forms he says there

are the objects of mathematics, which occupy an inter- 15

mediate position, differing1

from sensible things in being

eternal and unchangeable, from Forms in that there are

many alike, while the Form itself is in each case unique.

Since the Forms were the causes of all other things, he

thought their elements were the elements of all things. As 20

matter, the great and the small were principles ;as essen

tial reality, the One ; for from the great and the small, by

participation in the One, come the Numbers.

But he agreed with the Pythagoreans in saying that the

One is substance and not a predicate of something else;

and in saying that the Numbers are the causes of the

reality of other things he agreed with them;but positing 25

a dyad and constructing the infinite out of great and small,

instead of treating the infinite as one, is peculiar to him;

and so is his view that the Numbers exist apart from sensible

things, while they say that the things themselves are Num

bers, and do not place the objects of mathematics between

Forms and sensible things. His divergence from the 30

Pythagoreans in making the One and the Numbers separate

fromthings,

and his introduction of the

Forms,were due to

his inquiries in the region of definitions(for the earlier

thinkers had no tincture of dialectic), and his making the

other entity besides the One a dyad was due to the belief

that the numbers, except those which were prime,1could be

neatly produced out of the dyad as out of some plastic

material.

Yet what happens is the contrary ; the theory is not a 988*

reasonable one. For they make many things out of the

matter, and the form generates only once, but what we

1This is not quite accurate. Really it is only 2 and its powers that

could be neatly produced out of the I and the indefinite dyad ;cf.

N. 109^9-12. In Parmenides 143 C-I44A, 3 is derived from I and 2

(the number 2, not, as Aristotle says, the indefinite 2) by addition, andthe numbers higher than 3 are derived from 2 and 3 by multiplication.

Primes are not there excepted ; Plato speaks as if all the highernumbers could be got by multiplication. Nothing in the works of

Plato corresponds exactly to what Aristotle says here.



988a METAPHYSICA

observe is that one table is made from one matter, while the

man who applies the form, though he is one, makes many

5 tables. And the relation of the male to the female is

similar; for the latter is impregnated by one copulation,

but the male impregnates many females; yet these are

analogues of those first principles.

Plato, then, declared himself thus on the points in ques

tion;

it is evident from what has been said that he has used

only two causes, that of the essence and the material cause

10

(for

the Forms are the causes of the essence of all other

things, and the One is the cause of the essence of the

Forms) ;and it is evident what the underlying matter is, of

which the Forms are predicated in the case of sensible

things, and the One in the case of Forms, viz. that this is a

dyad, the great and the small. Further, he has assigned the

cause of good and that of evil to the elements, one to each

15 of the two, as we say1

some of his predecessors sought to

do, e. g. Empedocles and Anaxagoras.

Our review of those who have spoken about first prin- 7

ciples and reality and of the way in which they have

20 spoken, has been concise and summary ;but yet we have

learnt this much from them, that of those \vho speak about

4

principle and

*

causeno one has mentioned any principle

except those which have been distinguished in our work

on nature,2 but all evidently have some inkling of them^

though only vaguely. For some speak of the first prin

ciple as matter, whether they suppose one or more first

25 principles, and whether they suppose this to be a body or

to be incorporeal ;e. g. Plato spoke of the great and the

small, the Italians of the infinite, Empedocles of fire, earth,

water, and air, Anaxagoras of the infinity of things com

posed of similar parts. These, then, have all had a notion

of this kind of cause, and so have all who speak of air or

30 fire or water, or something denser than fire and rarer than

air;for some have said the prime element is of this kind.

3

1

Cf. 984b i5-i9, 32-b 10.2

Phys. ii. 3, 7.3

Cf. Diels, Vorsokratiker, ed. 3, i. 18. 8-21, 415. 32-416. 27. Thereference is probably to some follower of \naximenes.



BOOK A. 7 988a

These thinkers grasped this cause only ;but certain

others have mentioned the source of movement, e. g. those

who make friendship and strife, or reason, or love, a principle.

The essence, i. e. the substantial reality, no one has expressed distinctly. It is hinted at chiefly by thosewho believe 35

in the Forms;for they do not suppose either that the Forms g88

b

are the matter of sensible things, and the One the matter of

the Forms, or that they are the source of movement (for

they say these are causes rather of immobility and of

being at rest), but they furnish the Forms as the essence of

every other thing, and the One as the essence of the Forms. 5

That for whose sake actions and changes and movements

take place, they assert to be a cause in a way, but not in

this way, i. e. not in the way in which it is its nature to be

a cause. For those who speak of reason or friendship

class these causes as goods ; they do not speak, however,

as if anything that exists either existed or came into being

for the sake of these, but as if movements started from 10

these. In the same way those who say the One or the

existent is the good, say that it is the cause of substance,

but not that substance either is or comes to be for the sake

of this. Therefore it turns out that in a sense they both

say and do not say the good is a cause;for they do not 15

call it a cause

qua goodbut

only incidentally.All these thinkers, then, as they cannot pitch on another

cause, seem to testify that we have determined rightly both

how many and of what sort the causes are. Besides this it

is plain that when the causes are being looked for, either

all four must be sought thus or they must be sought in one

of these four ways. Let us next discuss the possible diffi- *o

culties with regard to the way in which each of these

thinkers has spoken, and with regard to his situation rela

tively to the first principles.

8 Those, then, who say the universe is one and posit one

kind of thing as matter, and as corporeal matter which has

spatial magnitude, evidently go astray in many ways. For

they posit the elements of bodies only, not of incorporeal 35

things, though there are also incorporeal things. And in

c 2,



988b METAPHYSICA

trying to state the causes of generation and destruction,

and in giving a physical account of all things, they do

away with the cause of movement. Further, they err in not

positing the substance, i.e. the essence, as the cause ofany

thing, and besides this in lightly calling any of the simple

30 bodies except earth the first principle, without inquiring

how they are produced out of one another, I mean fire,

water, earth, and air. For some things are produced out

of each other by combination, others by separation, and this

makes the greatest difference to their priority and pos-

35 teriority. For (i) in a way the property of being most

elementary of all would seem to belong to the first thing

g8ga from which they are produced by combination, and this

property would belong to the most fine-grained and subtle

of bodies. For this reason those who make fire the prin

ciple would be most in agreement with this argument.

But each of the other thinkers agrees that the element of5 corporeal things is of this sort. At least none ofthose who

named one element claimed that earth was the element,

evidently because of the coarseness of its grain. (Of the

other three elements each has found some judge on its side;

for some maintain that fire, others that water, others that

air is the element. Yet why, after all, do they not name

earth also, as most men do ? For people say all things are

10 earth. And Hesiod sayslearth was produced first of cor

poreal things ;so primitive and popular has the opinion

been.) According to this argument, then, no one would

be right who either says the first principle is any of the

elements other than fire, or supposes it to be denser than

15 air but rarer than water. But (2) if that which is later in

generation is prior in nature, and that which is concocted

and compounded is later in generation, the contrary of

what we have been saying must be true, water must be

prior to air, and earth to water.

So much, then, for those who posit one cause such as we

mentioned;but the same is true if one supposes more of

20

these,as

Fmpedocles says the matter of thingsis

fourbodies. For he too is confronted by consequences some of

1

Theog. 1 1 6.



BOOK A. 8 989

which are the same as have been mentioned, while others

are peculiar to him. For we see these bodies produced

from one another, which implies that the same body

does not

always

remain fire or earth (we have spoken about

this in our works on naturel

) ;and regarding the cause of 25

movement and the question whether we must posit one or

two, he must be thought to have spoken neither correctly

nor altogether plausibly. And in general, change of quality

is necessarily done away with for those who speak thus,

for on their view cold will not come from hot nor hot from

cold. For if it did there would be something that acceptedthe contraries themselves, and there would be some one

entity that became fire and water, which Empedocles denies.2

As regards Anaxagoras, if one were to suppose that he 3

said there were two elements, the supposition would accord

thoroughly with an argument which Anaxagoras himself

did not state articulately, but which he must have accepted

if any one had led him on to it. True, to say that in the

beginning all things were mixed is absurd both on other

grounds and because it follows that they must have existed

before in an unmixed form, and because nature does not

allow any chance thing to be mixed with any chance

thing, and also because on this view modifications and

accidents could be separated from substances (for the same

things which are mixed can be separated ) ; yet if one

were to follow him up, piecing together what he means,

he would perhaps be seen to be somewhat modern in his 5

views. For when nothing was separated out, evidently

nothing could be truly asserted of the substance that then

existed. I mean, e. g.,that it was neither white nor black,

norgrey

norany

othercolour,

but ofnecessity

colourless;

for if it had been coloured, it would have had one of these

colours. And similarly, by this same argument, it was 10

flavourless, nor had it any similar attribute;for it could

not be either of any quality or of any size, nor could it be

any definite kind of thing. For if it were, one of the

particular forms would have belonged to it, and this is

impossible, since all were mixed together ; for the par-1 De Caelo, iii. 7.

2

989* 26 oAo>? ... 30 (prjaiv is possibly a gloss.



989b METAPHYSICA

ticular form would necessarily have been already separated

15 out, but he says all were mixed except reason, and this

alone wras unmixed and pure.1 From this it follows, then,

that he mustsay

theprinciples

are the One(for

this is

simple and unmixed) and the Other, which is of such a

nature as we suppose the indefinite to be before it is defined

and partakes of some form. Therefore, while expressing

himself neither rightly nor clearly, he means something like

20 what the later thinkers say and what is now more clearly

seen to be the case.

But these thinkers are, after all, at home only in arguments about generation and destruction and movement

;

for it is practically only of this sort of substance that they

seek the principles and the causes. But those who extend

25 their vision to all things that exist, and of existing things

suppose some to be perceptible and others not perceptible,

evidently study both classes, which is all the more reason

why one should devote some time to seeing what is good in

their views and what bad from the standpoint of the inquiry

we have now before us.

The Pythagoreans treat of principles and elements

3o stranger than those of the physical philosophers (the reason

is that they got the principles from non-sensible things, for

theobjects

ofmathematics, except

those ofastronomy,

are

of the class of things without movement) ; yet their dis

cussions and investigations are all about nature;for they

99a

generate the heavens, and with regard to their parts and

attributes and functions they observe the phenomena, and use

up the principles and the causes in explaining these, which

implies that they agree with the others, the physical philo

sophers, that the real is just all that which is perceptible

5 and contained by the so-called heavens . But the causes

and the principles which they mention are, as we said,2

sufficient to act as steps even up to the higher realms of

reality, and are more suited to these than to theories about

nature. They do not tell us at all, however, how there can

be movement if limit and unlimited and odd and even are

10 the only things assumed, or how without movement and

1Fr. 12.

8

99b3i-3.



BOOK A. 8 ggoa

change there can be generation and destruction, or the

bodies that move through the heavens can do what they do.

Further, if one either granted them that spatial magnitude consists of these elements, or this were proved, still

how would some bodies be light and others have weight ?

To judge from what they assume and maintain they are 15

speaking no more of mathematical bodies than of percep

tible;hence they have said nothing whatever about fire or

earth or the other bodies of this sort, I suppose because

they have nothing to say which applies peculiarly to per

ceptible things.

Further, how are we to combine the beliefs that the

attributes of number, and number itself, are causes of what 20

exists and happens in the heavens both from the beginning

and now, and that there is no other number than this

number out of which the world is composed ? When in

one particular region they place opinion and opportunity,

and, a little above or below, injustice and decision or mixture, and allege, as proof, that, each of these is a number,

and that there happens to be already in this place a plurality 25

of the extended bodies composed of numbers, because these

attributes ofnumber attach to the various places, this being

so, is this number, which we must suppose each of these

abstractions to be, the same number which is exhibited in

the material universe, or is it another than this ? Plato says

it is different; yet even he thinks that both these bodies 30

and their causes are numbers, but that the intelligible num

bers are causes, while the others are sensible.

9 Let us leave the Pythagoreans for the present ;for it is

enough to have touched on them as much as we have done.

But as for those who posit the Ideas as causes, firstly,in 99O

b

seeking to grasp the causes of the things around us, they

introduced others equal in number to these, as if a man who

wanted to count things thought he would not be able to do

it while they were few, but tried to count them when

he had added to their number. For the Forms are practi

cally equal to or not fewer than the things,in

tryingto

5

explain which these thinkers proceeded from them to the



99ob METAPHYSICA

Forms. For to each thing there answers an entity which

has the same name and exists apart from the substances,

and so also in the case of all other groups there is a one

over

many,whether the

manyare in this world or are

eternal.

Further, of the ways in which we l

prove that the Forms

10exist, none is convincing ;

for from some no inference

necessarily follows, and from some arise Forms even of

things of which we think there are no Forms. For accord

ing to the arguments from the existence of the sciences

there will be Forms of all things of which there are sciences,

and according to the one over many argument there will

be Forms even of negations, and according to the argu

ment that there is an object for thought even when the

thing has perished, there will be Forms ofperishable things ;

15 for we have an image of these. Further, of the more accu

rate arguments, some lead to Ideas of relations, of which

we say there is no independent class, and others introduce

the*

third man .

2

And in general the arguments for the Forms destroy the

things for whose existence we are more zealous than for the

existence of the Ideas;for it follows that not the dyad

3 but

20 number is first, i. e. that the relative is prior to the abso

lute,4

besides all the otherpoints

on which certain

peopleby following out the opinions held about the Ideas have

come into conflict with the principles of the theory.

Further, according to the assumption on which our

belief in the Ideas rests, there will be Forms not only of

substances but also of many other things (for the concept is

25 single not only in the case of substances but also in the

other cases, and there are sciences not only of substance butalso of other things, and a thousand other such difficulties

confront them). But according to the necessities of the

1Aristotle speaks as a Platonist.

2Cf. Z. I039

a2, Soph. EL i;8

b36-179* 10, and Plato Farm. 132 AB,

D-ISSA.3

Sc. the*

indefinite 2 which Plato held to be one of the first prin

ciples of number.4

i.e. number, which is relative, is prior to the indefinite 2, which

Plato held to be an absolute first principle.



BOOK A. 9 990b

case and the opinions held about the Forms, if Forms can

be shared in there must be Ideas of substances only. For

they are not shared in incidentally, but a thing must share 30

in its Form as in something

1

not predicated of a subject (by*

being shared in incidentally I mean that e. g.if a thing

shares in double itself, it shares also in eternal,but

incidentally ;for eternal happens to be predicable of the

double).

Therefore the Forms will be substance;but

the same terms indicate substance in this and in the ideal

world (or what will be the meaning of saying that there is 991

something apart from the particulars the one over many P).1

And if the Ideas and the particulars that share in them have

the same form, there will be something common to these;

for why should 2 be one and the same in the perishable

2 s or in those which are many but eternal, and not the

same in the 2 itself as in the particular 2 ? But if they 5

have not the same form, they must have only the name in

common, and it is as if one were to call both Callias and

a wooden image a man,without observing any com

munity between them.2

Above all one might discuss the question what on earth

the Forms contribute to sensible things, either to those that

are eternal or to those that come into being and cease to I0

be. Forthey

cause neither

movementnor

any changein

them. But again they help in no wise either towards the

knowledge of the other things (for they are not even the

substance of these, else they would have been in them), or

towards their being, if they are not in the particulars which

share in them; though if the) were, they might be thought

to be causes, as white causes whiteness in a white object 15

by entering into its composition. But this argument, whichfirst Anaxagoras and later Eudoxus and certain others

used, is very easily upset ;for it is not difficult to collect

many insuperable objections to such a view.

But, further, all other things cannot come from the

1This seems to be an enthymeme, the conclusion to be supplied

being that the Forms, since they are substances, must be of substances.

2 With 99ob2~99i

a8 cf. M. io;8

b34-io79

b3.



99ia METAPHYSICA

20 Forms in any of the usual senses of from . And to say

that they are patterns and the other things share in them is

to use empty words and poetical metaphors. For what is

it

that works, looking to the Ideas ? And anything caneither be, or become, like another without being copied

25 from it, so that whether Socrates exists or not a man like

Socrates might come to be;and evidently this might be so

even if Socrates were eternal. And there will be several

patterns of the same thing, and therefore several Forms;

e. g. animal and two-footed and also* man himself will

be Forms of man. Again, the Forms are patterns not only

30 of sensible things, but of Forms themselves also;

i. e. the

genus, as genus of various species, will be so;therefore

the same thing will be pattern and copy.

ggib

Again, it would seem impossible that the substance and

that of which it is the substance should exist apart ; how,

therefore, could the Ideas, being the substances of things,

exist apart ? In the Phaedo lthe case is stated in this way

that the Forms are causes both of being and of becoming ;

yet when the Forms exist, still the things that share in them

5 do not come into being, unless there is something to origi

nate movement;and many other things come into being

(e.g. a house or a ring) of which we say there are no Forms.

Clearly, therefore, even the other things can both be andcome into being owing to such causes as produce the things

just mentioned.2

Again, if the Forms are numbers, how can they be

10 causes ? Is it because existing things are other numbers,

e. g. one number is man, another is Socrates, another

Callias ? Why then are the one set of numbers causes of the

other set ? It will not make any difference even if the

former are eternal and the latter are not. But if it is

because things in this sensible world (e.g. harmony) are

ratios of numbers, evidently the things between which they

are ratios are some one class of things. If, then, this the

15 matter is some definite thing,3

evidently the numbers

themselves too will be ratios of something to something

1

ioo c-E.2 With 991* 8-b 9 cf. M. io79

b 2-io8oa 8.

3

Reading in 991^ 14 &T)n TOVTO, 17 vA/;.



BOOK A. 9 ggib

else. E. g. if Callias is a numerical ratio between fire and

earth and water and air, his Idea also will be a number of

certain other underlying things ;and man-himself, whether

it is a number in a sense ornot,

will still be a numerical

ratio of certain things and not a number proper, nor will

it be a kind of number merely because it is a numerical 20

ratio.1

Again, from many numbers one number is produced, but

how can one Form come from many Forms ? And if the

number comes not from the many numbers themselves but

from the units in them, e. g. in 10,000, how is it with the

units ? If they are specifically alike, numerous absurdities

will follow, and also if they are not alike (neither the units 25

in one number being themselves like one another nor those

in other numbers being all like to all) ;for in what will they

differ, as they are without quality ? This is not a plausible

view, nor is it consistent with our thought on the matter.

Further, they must set up a second kind of number

(with which arithmetic deals), and all the objects which

are called intermediate by some thinkers;

and how

do these exist or from what principles do they proceed ?

Or why must they be intermediate between the things in 30

this sensible world and the things-themselves ?

Further, the units in 2 must each come from a prior 2;

but this is impossible.

Further, why is a number, when taken all together, one ? 992a

Again, besides what has been said, if the units are diverse

the Platonists should have spoken like those who say there

are four, or two, elements;for each of these thinkers gives

the name of element not to that which is common, e.g.

to

body,but to fire

and earth, whether there is something 5

common to them, viz. body, or not. But in fact the

Platonists speak as if the One were homogeneous like fire

or water;and if this is so, the numbers will not be sub

stances.2

Evidently, if there is a One-itselfand this is a first

1i. e. the Idea is a numerical ratio in some underlying material. It

may perhaps be called a sort of (rt?) number, but strictly it is a

numerical ratio. Thepassage, however,

is

very difficult, and thecontradiction in 11. 19, 20 almost intolerable.2Sc. but ordinary mathematical numbers. Cf. M. 1081*5-12.



gg2a METAPHYSICA

principle, one is being used in more than one sense;for

otherwise the theory is impossible.

ID When we wish to reduce substances to their principles,

we state that lines come from the short and long- (i. e. froma kind of small and great), and the plane from the broad

and narrow, and body from the deep and shallow. Yet

how then can either the plane contain a line, or the solid

a line or a plane ? For the broad and narrow is a different

15 class from the deep and shallow. Therefore, just as num

ber is not present in these, because the many and few are

different from these, evidently no other ofthe higher classes

will be present in the lower. But again the broad is not

a genus which includes the deep, for then the solid would

have been a species of plane.1

Further, from what prin

ciple will the presence of the points in the line be derived ?

20 Plato even used to object to this class of things as being

a geometrical fiction. He gave the name of principle of the

line and this he often posited to the indivisible lines. Yet

these must have a limit;therefore the argument from which

the existence of the line follows proves also the existence

of the point.

In general, though philosophy seeks the cause ofper-

25 ceptible things, we have given this up (for we say nothing

of the cause from which change takes its start), but whilewe fancy we are stating the substance of perceptible things,

we assert the existence of a second class of substances,

while our account of the way in which they are the sub

stances of perceptible things is empty talk;for

*

sharingf

,

as we said before,2 means nothing.

Nor have the Forms any connexion with what we see to

30 be the cause in the case of the arts, that for whose sake both

all mind and the whole of nature are operative,3 with this

cause which we assert to be one of the first principles ;but

mathematics has come to be identical with philosophy for

modern thinkers, though they say that it should be studied

for the sake of other things.4

1 With 992* 10-19 cf. M. 1085*9-19.2

991*20-22.3Sc. the final cause.

4Cf. Plato, Rep. vii. 531 D, 533 B-E.



BOOK A. 9 992b

Further, one might suppose that the substance which

according to them underlies as matter is too mathematical,

and is a predicate and differentia of the substance, i. e. of

the matter, rather than matter itself ; i. e. the great and thesmall are like the rare and the dense which the physical

philosophers speak of, calling these the primary differentiae 5

of the substratum;for these are a kind of excess and defect.

And regarding movement, if the great and the small are to

be movement, evidently the Forms will be moved;but if

they are not to be movement, whence did movement come ?

The whole study of nature has been annihilated.

And what is thought to be easy to show that all things

are one is not done;for what is proved by the method of 10

setting out instances1is not that all things are one but that

there is a One-itself, if we grant all the assumptions. And

not even this follows, if we do not grant that the universal

is a genus ;and this in some cases it cannot be.

Nor can it be explained either how the lines and

planes and solids that come after the numbers exist or

can exist, or what significance they have; for these canT5

neither be Forms (for they are not numbers), nor the

intermediates (for those are the objects of mathematics),

nor the perishable things. This is evidently a distinct fourth

class.2

In general, if we search for the elements of existing

things without distinguishing the many senses in which

things are said to exist, we cannot find them, especially if

the search for the elements of which things are made is con- 30

ducted in this manner. For it is surely impossible to dis

cover what acting or being acted on,or the straight ,

is made of, but if elements can be discovered at all, it is

only the elements of substances;therefore either to seek the

elements of all existing things or to think one has them is

incorrect.

And how could we learn the elements of all things ?

Evidently we cannot start by knowing anything before. 25

For as he who is learning geometry, though he may know

1 For this Platonic method cf. Z. iO3ib2i, M. io86b 9, N. iogo

a17.

2Cf. M. ic8ob 23-30, 1085*7-9.



992b METAPHYSICA

other things before, knows none of the things with which

the science deals and about which he is to learn, so is it in

all other cases. Therefore if there is a science of all things,

such as some assert to exist, he who is learning this will

3 know nothing before. Yet all learning is by means of pre

misses which are (either all or some of them) known before,

whether the learning be by demonstration or by defini

tions;for the elements of the definition must be known

before and be familiar;and learning by induction proceeds

993a

similarly. But again, if the science were actually innate, it

were strange that we are unaware of our possession of the

greatest of sciences.

Again, how is one to come to know what all things are

made of, and how is this to be made evident ? This also

affords a difficulty; for there might be a conflict of opinion,

5 as there is about certain syllables ;some say za is made out

of s and d and<z,

while others

sayit is a distinct sound and

none of those that are familiar.

Further, how could we know the objects of sense without

having the sense in question ? Yet we ought to, if the

elements of which all things consist, as complex sounds

10 consist of the elements proper to sound, are the same.

It is evident, then, even from what we have said before, 10that all men seem to seek the causes named in the Physics?-

and that we cannot name any beyond these;but they seek

these vaguely ;and though in a sense they have all been

described before, in a sense they have not been described at

15 all. For the earliest philosophy is, on all subjects, like one

who lisps, since it is young and in its beginnings. For

even Empedocles says2 bone exists by virtue of the ratio

in it. Now this is the essence and the substance of the

thing. But it is similarly necessary that flesh and each of

the other tissues should be the ratio of its elements, or that

20 not one of them should;for it is on account of this that

both flesh and bone and everything else wall exist, and not

on account of the matter, which he names, fire and

1

>7-

2

Diels, Vorsokratiker, ed. 3, fr. 96 and i. 214. 22-215. 6.



BOOK A. 10 993a

earth and water and air. But while he would necessarily

have agreed if another had said this, he has not said it

clearly.

On these questions our views have been expressed before ;

but let us return to enumerate the difficulties that might be 25

raised on these same points ;

1for perhaps we may get from

them some help towards our later difficulties.

1 The reference is to Bk. B.



BOOK a

30 THE investigation of the truth is in one way hard, in i

another easy. An indication of this is found in the fact

that no one is able to attain the truth adequately, while, on

993 the other hand, we do not collectively fail, but every one

says something- true about the nature of things, and while

individually we contribute little or nothing to the truth, bythe union of all a considerable amount is amassed. There

fore, since the truth seems to be like the proverbial door,1

5 which no one can fail to hit, in this respect it must be easy,

but the fact that we can have a whole truth and not the

particular part we aim at shows the difficulty of it.

Perhaps, too, as difficulties are of two kinds, the cause of

the present difficulty is not in the facts but in us. For as

10 the eyes of bats are to the blaze of day, so is the reason in

our soul to the things which are by nature most evident

of all.

It is just that we should be grateful, not only to those

with whose views we may agree, but also to those who have

expressed more superficial views;for these also contributed

something, by developing before us the powers of thought.

15 It is true that if there had been no Timotheus we should

have been without much of our lyric poetry ;but if there

had been no Phrynis there would have been no Timotheus.

The same holds good of those who have expressed views

about the truth;for from some thinkers we have inherited

certain opinions, while the others have been responsible forthe appearance of the former.

It is right also that philosophy should be called know-

20 ledge of the truth. For the end of theoretical knowledge

is truth, while that of practical knowledge is action (for even

if they consider how things are, practical men do not study

the eternal, but what is relative2 and in the present). Now

1Cf. Leutsch and Schneidewin, Faroemiographi Craed, ii. 678.

2

Reading in 993b 22 dAX 6 rrpos .



BOOK a. I 993b

we do not know a truth without its cause;and a thing has

a quality in a higher degree than other things if in virtue

of it the similar quality belongs to the other things as well

(e.g. fire is the hottest of things ; for it is the cause of the 25

heat of all other things) ;so that that which causes deriva

tive truths to be true is most true. Hence the principles

of eternal things must be always most true (for they are not

merely sometimes true, nor is there any cause of their

being, but they themselves are the cause of the being of

other things), so that as each thing is in respect of being, so 3

is it in respect of truth.

But evidently there is a first principle, and the causes of 994a

things are neither an infinite series nor infinitely various in

kind. For (i) neither can one thing proceed from another,

as from matter, ad infinitum (e. g. flesh from earth, earth

from air, air from fire, and so on without stopping), nor 5

can the sources of movement form an endless series (man

for instance being acted on by air, air by the sun, the sun by

Strife,1 and so on without limit). Similarly the final causes

cannot go on ad infinitum, walking being for the sake

of health, this for the sake of happiness, happiness for the

sake of something else, and so one thing always for the sake

of another. And the case of the essence is similar. For in 10

the case of intermediates, which have a last term and a term

prior to them, the prior must be the cause of the later

terms. For if we had to say which ofthe three is the cause,

we should say the first; surely not the last, for the final

term is the cause of none;nor even the intermediate, for it 15

is the cause only of one.(It

makes no difference whether

there is one intermediateor more, nor whether they are

infinite or finite in number.) But ofseries which are infinite

in this way, and of the infinite in general, all the parts down

to that now present are alike intermediates;so that if there

is no first there is no cause at all.

Nor can there be an infinite process downwards, with

a beginning in the upward direction, so that water should 20

proceed from fire, earth from water, and so always some

1 The illustration is taken from the cosmology of Empedocles.646-28

)



994a METAPHYSICA

other kind should be produced. For one thing comes

from another in two ways not in the sense in which

4

from means after (as we say from the Isthmian games

come the Olympian ), but either (i) asthe

man comes fromthe boy, by the boy s changing, or

(ii)as air comes from

35 water. By as the man comes from the boy we mean *

as

that which has come to be from that which is coming to be,

or as that which is finished from that which is being

achieved (for as becoming is between being and not being,

so that which is becoming is always between that which is

and that which is not ; for the learner is a man of science in

the making, and this is what is meant when we say that

sofrom a learner a. man of science is being made) ;on the

other hand, coming from another thing as water comes

from air implies the destruction of the other thing. This

is why changes of the former kind are not reversible, and

the boy does not come from the man (for it is not that

which comes to be something that comes to be as a result

994bof coming to be, but that which exists after the coming to

be;for it is thus that the day, too, comes from the morning

in the sense that it comes after the morning ;which is the

reason why the morning cannot come from the day) ;but

changes of the other kind are reversible. But in both cases

it is

impossible that the number of terms should be infinite.

For terms of the former kind, being intermediates,1 must

5 have an end, and terms of the latter kind change back into

one another;for the destruction of either is the generation

of the other.

At the same time it is impossible that the first cause,

being eternal, should be destroyed ;for since the process of

becoming is not infinite in the upward direction, that which

is the first thing by whose destruction something came to

be must be non-eternal. 2

1Cf.

a27 f.

2This paragraph is very obscure. Aristotle has in

aii-i9 given a

general argument which applies to all the four causes, to show that

there must always be a first cause. This, he assumes, must be

eternal. He now applies this argument to the prime material cause,

and shows that it must be indestructible. There are two difficulties in

the paragraph :

(i) It seems pointless to say that the first cause must be inde-



BOOK a. 2 994b

Further, the final caiise is an end, and that sort of end

which is not for the sake of something* else, but for whose

sake everything- else is;so that if there is to be a last term to

of this sort, the process will not be infinite ; but if there is

no such term, there will be no final cause, but those who

maintain the infinite series eliminate the Good without

knowing it (yet no one would try to do anything ifhe were

not going to come to a limit) ;nor would there be reason in

the world; the reasonable man, at least, always acts for 15

a purpose, and this is a limit;for the end is a limit.

But the essence, also, cannot be reduced to another

definition which is fuller in expression.1 For the original

definition is always more of a definition, and not the later

one;and in a series in which the first term has not the

required character, the next has not it either. Further, 2o

those who speak thus destroy science;for it is not possible

to have this till one comes to the

unanalysable

terms.

And knowledge becomes impossible ;for how can one

apprehend things that are infinite in this way ?2 For this is

not like the case of the line, to whose divisibility there is no

stop, but which we cannot think if we do not make a

stop (for which reason one who is tracing the infinitely

divisible line cannot be counting the possibilities of section),

but the whole line also must be apprehended by something 35

in us that does not move from part to part. Again, nothing

infinite can exist;and if it could, at least the notion of

infinity is not infinite.3

But(2)

if the kinds of causes had been infinite in number,

then also knowledge would have been impossible ;for we

structible because it is eternal. Ground and consequent appear to be

identical. But probably the object is to show that the first cause mustbe to its effects not as water to air but as boy to man. It developsinto them, and is not destroyed when they come into being.

(2) The clause beginning with eW seems, as is often the case in

Aristotle, to be elliptical. The meaning probably is : Since the process of becoming is not infinite in the upward direction, (there mustbe an eternal first cause, but) that which is the first thing by whosedestruction something came to be cannot be eternal.

1i. e. one can reduce the definition of man as

*

rational animal to

rational sensitive living substance,but one cannot carry on this

process ad infinituin,2

i. e. actually infinite.3

i. e. does not contain an infinite number of marks.

D 2



994b METAPHYSICA

think we know, only when we have ascertained the causes,

30 but that which is infinite by addition cannot be gone through

in a finite time.

The effect which lectures produce on a hearer depends 3

on his habits;for we demand the language we are accus-

995atomed to, and that which is different from this seems not in

keeping but somewhat unintelligible and foreign because of

its unwontedness. For it is the customary that is intelli

gible. The force of habit is shown by the laws, in which

5 the legendary and childish elements prevail over our know

ledge about them, owing to habit. Thus some people do

not listen to a speaker unless he speaks mathematically,

others unless he gives instances, while others expect him to

cite a poet as witness. And some want to have everything

done accurately, while others are annoyed by accuracy,

either because they cannot follow the connexion of thought

10 or because they regardit

as pettifoggery. For accuracy has

something of this character, so that as in trade so in argu

ment some people think it mean. Hence one must be

already trained to know how to take each sort ofargument,

since it is absurd to seek at the same time knowledge and

the way of attaining knowledge ;and it is not easy to get

even one of the two.

1 5 The minute accuracy of mathematics is not to be demandedin all cases, but only in the case of things which have no

matter. Hence its method is not that of natural science;

for presumably the whole of nature has matter. Hence we

must inquire first what nature is : for thus we shall also see

what natural science treats of [and whether it belongs to

one science or to more to investigate the causes and the

20 principles of things].1

1 This clause has probably been wrongly inserted from 995b5-6.



BOOK B

I WE must, with a view to the science which we are seek

ing, first recount the subjects that should be first discussed.

These include both the other opinions that some have held 25

on the first principles, and any point besides these that

happens to have been overlooked. For those who wish to

get clear of difficulties it is advantageous to discuss the

difficulties well;for the subsequent free play of thought

implies the solution of the previous difficulties, and it is not

possible to untie a knot of which one does not know. But 30

the difficulty of our thinking points to a4 knot in the

object ;for in so far as our thought is in difficulties, it is in

like case with those who are bound;

for in either case it is

impossible to go forward. Hence one should have surveyed

all the difficulties beforehand, both for the purposes we have

stated and because people who inquire without first stating

the difficulties are like those who do not know where they 35

have to go ; besides, a man does not otherwise know even

whether he has at any given time found what he is looking

for or not; for

theend

is

not clear to such a man, while to him 995^who has first discussed the difficulties it is clear. Further,

he who has heard all the contending arguments, as if they

were the parties to a case, must be in a better position for

judging.

The first problem concerns the subject1 which we dis

cussed in our prefatory remarks. It is this(i) whether

5

the investigation of the causes belongs to one or to more

sciences,2 and

(2)whether such a science should survey only

the first principles of substance, or also the principles on

which all men base their proofs, e. g. whether it is possible

at the same time to assert and deny one and the same thing

or not, and all other such questions ;

:i and (3)if the science 10

in question deals with substance, whether one science deals

1Sc. the four causes.

2Cf. 996** i8-b 26.

3Cf. 996

b26-997

ai5.



995b METAPHYSICA

with all substances, or more than one,1 and it more, whether

all are akin, or some of them must be called forms of Wis

dom and the others something else. And (4) this itself is

also one of the things that must be discussed whethersensible substances alone should be said to exist or others

15 also besides them, and whether these others are of one kind

or there are several classes of substances, as is supposed

by those who believe both in Forms and in mathematical

objects intermediate between these and sensible things.2

Into these questions, then, as we say, we must inquire, and

also (5) whether our investigation is concerned only with

substances or also with the essential attributes of substances.3

20 Further, with regard to the same and other and like and un

like and contrariety, and with regard to prior and posterior

and all other such terms about which the dialecticians try

to inquire, starting their investigation from probable pre

mises only, whose business is it to inquire into all these ?

25 Further, we must discuss the essential attributes of these

themselves;and we must ask not only what each of these

is, but also whether one thing always has one contrary.4

Again (6), are the principles and elements of things the

genera, or the parts present in each thing, into which it is

divided;

5 and (7) if they are the genera, are they the genera

that are predicated proximately of the individuals, or the

30 highest genera, e. g. is animal or man the first principle and

the more independent of the individual instance ?6 And

(8) we must inquire and discuss especially whether there is,

besides the matter, any thing that is a cause in itself or not,

and whether this can exist apart or not, and whether it is

one or more in number, and whether there is something

35 apart from the concrete thing (by the concrete thing I mean

the matter with something already predicated ofit),

or

there is nothing apart, or there is something in some cases

though not in others, and what sort of cases these are.7

gg6a

Again (9) we ask whether the principlesare limited in num-

1Cf. 997*15-25.

2Cf.

997

a

34-998* 19.

The reference is to Plato.3

Cf. 997;1

25-34.4

Cf. r. ioo3b

22-ioc>5

a18.

5Cf. 99S

a 2o-b 14.6

Cf. 998b14-999*23.

7Cf. 999* 24~

b24.



BOOK B. i 996

her or in kind, both those in the definitions and those in the

substratumj

1 and (10) whether the principles of perishable

and of imperishable things are the same or different;and

whether they are all imperishable or those of perishable

things are perishable.2 Further (n) there is the question

which is hardest of all and most perplexing, whether unity 5

and being, as the Pythagoreans and Plato said, are not

attributes of something else but the substance of existing

things, or this is not the case, but the substratum is some

thing else, as Empedocles says, love;as some one else

3

says, fire; while another 4 says water or air.5 Again

(12) we ask whether the principles are universal or like

individual things,6 and (13) whether they exist potentially or 10

actually7

,and further, whether they are potential or actual

in any other sense than in reference to movement;8

for

these questions also would present much difficulty. Further

(14), are numbers and lines and figures and points a kind of

substance or not, and if they are substances are they

separate from sensible things or present in them ?9 With 1 5

regard to all these matters not only is it hard to get

possession of the truth, but it is not easy even to think out

the difficulties well.

2 (i) First then with regard to what we mentioned first,

does it belong to one or to more sciences to investigate all

the kinds of causes ? How could it belong to one science 20

to recognize the principles if these are not contrary ?

Further, there are many things to which not all the prin

ciples pertain. For how can a principle of change or the

nature of the good exist for unchangeable things, since

everything that in itself and by its own nature is good is an

end, and a cause in the sense that for its sake the other 25

things both come to be and are, and since an end or pur

pose is the end of some action, and all actions imply change ?

So in the case of unchangeable things this principle could not

1

Cf. 999b24-iooo

a4.

2Cf. icooa s~iooi

a3.

3

Hippasus and Heraclitus.4

Thales (water) ;Anaximenes and Diogenes of Apollonia (air).

6

Cf. iooia

4-^25.e

Cf. ioo3a

5-i;.7Cf. ioo2b 32-ioo3

a5.

8Cf. e. 6.

9Cf. IOOIb 26-I002b

II.



996a METAPHYSICA

exist, nor could there be a good-itself. This is why in

mathematics nothing is proved by means of this kind ot

30 cause, nor is there any demonstration of this kind

because it is better, or worse;indeed no one even men

tions anything of the kind. And so for this reason some

of the Sophists, e.g. Aristippus, used to ridicule mathe

matics;for in the arts (he maintained), even in the indus

trial arts, e. g. in carpentry and cobbling, the reason always

35 given is because it is better, or worse \ but the mathe

matical sciences take no account of goods and evils.

gg6

b

But if there are several sciences of the causes, and adifferent science for each different principle, which of these

sciences should be said to be that which we seek, or which

of the people who possess them has the most scientific

5 knowledge of the object in question ? The same thing mayhave all the kinds of causes, e. g. the moving cause of

a house is the art or the builder, the final cause is the func

tion it fulfils, the matter is earth and stones, and the form

is the definition. To judge from our previous discussionJ

of the question which of the sciences should be called Wis

dom, there is reason for applying the name to each of them.

10 For inasmuch as it is most architectonic and authoritative

and the other sciences, like slave-women, may not even

contradict it, the science of the end and of the

good

is of

the nature of Wisdom (for the other things are for the sake

of the end). But inasmuch as it was described 2as dealing

writh the first causes and that which is in the highest sense

object of knowledge, the science of substance* must be of

the nature of Wisdom. For since men may know the same

15 thing in many ways, we say that he who recognizes what

a thing is by its being so and so knows more fully than hewrho recognizes it by its not being so and so, and in the

former class itself one knows more fully than another, and

he knows most fully who knows what a thing is, not he who

knows its quantity or quality or what it can by nature do

or have done to it. And further in all other cases also we

think that the knowledge of each even ofthe things of which

1Cf. A. 982*8-19.

2ib. 30-

b2.

3i. e. essence.



BOOK B. 2 996

demonstration is possiblel

is present only when we know

what the thing is, e. g. what squaring a rectangle is, viz. that 20

it is the finding of a mean;and similarly in all other cases.

And we know about becomings and actions and about every

change when we know the source ofthe movement ;and

this is other than and opposed to the end. Therefore it

would seem to belong to different sciences to investigate 25

these causes severally.2

But(2), taking the starting-points of demonstration as well

as the causes, it is a disputable question whether they are the

object of one science or of more (by the starting-pointsof

demonstration I mean the common beliefs, on which all

men base their proofs) ;e. g. that everything must be either

affirmed or denied, and that a thing cannot at the same

time be and not be, and all other such premisses: the 3

question is whether the same science deals with them as

withsubstance,

or a differentscience,

and if it is not one

science, which of the two must be identified with that which

we now seek. It is not reasonable that these topics should

be the object ofone science;for why should it be peculiarly

appropriate to geometry or to any other science to under

stand these matters ? If then it belongs to every science 35

alike, and cannot belong to all, it is not peculiar to the 997*

science which investigates substances, any more than to

any other science, to know about these topics. And, at the

same time, in what way can there be a science of the first

principles ? For we are aware even now what each ofthem

in fact is (at least even other sciences use them as familiar) ; 5

but ifthere is a demonstrative science which deals with them,

there will have to be an underlying kind, and some of them

must be demonstrable attributes and others must be axioms

(for it is impossible that there should be demonstration

about all of them) ;for the demonstration must start from

certain premisses and be about a certain subject and prove

1 The meaning is that whether the essence is known directly (as in

the case of substances) or by means of demonstration (as in the case of

attributes or of events like thunder or eclipse), knowledge of the

essence is the primary knowledge.2 With 996* i8-b 26 cf. 995

b4-6, K. 1059** 20-23 (with 996

a 2i-b I cf.

34-8).



997a METAPHYSICA

certain attributes. Therefore it follows that all attributes

10 that are proved must belong to a single class; for all

demonstrative sciences use the axioms.

But if the science of substance and the science which

deals with the axioms are different, which of them is by

nature more authoritative and prior ? The axioms are most

universal and are principles of all things. And if it is not

the business of the philosopher, to whom else will it belong

to inquire what is true and what is untrue about them ?l

15 (3) In general, do all substances fall under one science

or under more than one ? If the latter, to what sort of substance is the present science to be assigned ? On the other

hand, it is not reasonable that one science should deal with all.

For then there would be one demonstrative science dealing

with all attributes. For every demonstrative science

20investigates with regard to some subject its essential attri

butes, starting from the common beliefs.2 Therefore to

investigate the essential attributes of one class of things,

starting from one set of beliefs, is the business of one

science. For the subject belongs to one science, and the

premisses belong to one. whether to the same or to another;

so that the attributes do so too, whether they are investigated

by these sciences or by one compounded out of them.3

25(5)

4

Further,does our

investigationdeal with substances

alone or also with their attributes ? I mean for instance, if

the solid is a substance and so are lines and planes, is it the

business of the same science to know these and to know

the attributes of each of these classes (the attributes about

which the mathematical sciences offer proofs), or of a differ-

so ent science ? If of the same, the science of substance also

must be a demonstrative science ; but it is thought that there

is no demonstration of the essence of things. And if ot

another, what will be the science that investigates the attri

butes of substance ? This is a very difficult question.5

1 With 996b26-997* 15 cf. 995

b6-10, 1059** 23-6. For the answer

cf. r. 32

Cf. 996b 28.

8 With 997*15-25 cf. 995b10-13, io59

a26~9. For the answer cf. r.

1004*2-9,E. i.

4I number the problems as in ch. i.

5 With 997*25-34 cf. 995b18-20, 1059*29-34. For the answer cf.

r. I003b22-ioo5

a18.



BOOK B. 2 997a

(4) Further, must we say that sensible substances alone

exist, or that there are others besides these ? And are sub- 35

stances of one kind or are there in fact several kinds of

substances, as those say who assert the existence both of the 997Forms and of the intermediates, with which they say the

mathematical sciences deal ? The sense in which we l

say the Forms are both causes and self-dependent sub

stances has been explained in our first remarks about them;

2

while the theory presents difficulties in many ways, the 5

most paradoxical thing of all is the statement that there

are certain things besides those in the material universe, and

that these are the same as sensible things except that they

are eternal while the latter are perishable. For they say

there is a man-himself and a horse-itself and health-itself,

with no further qualification, a procedure like that of the

people who said there are gods, but in human form. For TO

they

werepositing nothing

but eternal men, nor are the

Platonists making the Forms anything other than eternal

sensible things.

Further, if we are to posit besides the Forms and the

sensibles the intermediates between them, we shall have

many difficulties. For clearly on the same principle there

will be lines besides the lines-themselves and the sensible

lines, and so with each of the other classes of things;

so 15

that since astronomy is one of these mathematical sciences

there will also be a heaven besides the sensible heaven, and

a sun and a moon (and so with the other heavenly bodies)

besides the sensible. Yet how are we to believe in these

things ? It is not reasonable even to suppose such a body

immovable, but to suppose it moving is quite impossible.

And similarly with the things of which optics and mathe- 20

matical harmonics treat;for these also cannot exist apart

from the sensible things, for the same reasons. For if there

are sensible things and sensations intermediate between

Form and individual, evidently there will also be animals

intermediate between animals-themselves and the perish

able animals. We might also raise the question, with 25

reference to which kind of existing things we must look for

1

Cf. note on A. 99ob9.

2Cf. A. 6 and 9.



997b METAPHYSICA

these sciences of intermediates. If geometry is to differ

from mensuration only in this, that the latter deals with

things that we perceive, and the former with things that are

not perceptible, evidently there will also be a science otherthan medicine, intermediate between medical-science-itself

and this individual medical science, and so with each of the

3 other sciences. Yet how is this possible ? There would have

to be also healthy things besides the perceptible healthy

things and the healthy-itself. And at the same time not

even this is true, that mensuration deals with perceptible and

perishable magnitudes ; for then it would have perished

when they perished.

But on the other hand astronomy cannot be dealing

with perceptible magnitudes nor with this heaven above

35 us. For neither are perceptible lines such lines as the

998a

geometer speaks of (for no perceptible thing is straight or

round in the way in which he defines straight and1 round

;for a hoop touches a straight edge not at a

point, but as Protagoras used to say it did, in his refutation

ofthe geometers),1 nor are the movements and spiral orbits

5 in the heavens like those of which astronomy treats, nor

have geometrical points the same nature as the actual stars.

Now there are some who say that these so-called inter

mediates between the Forms and the perceptible things

exist, not apart from the perceptible things, however, but

in these;

2the impossible results of this view would take too

10long to enumerate, but it is enough to consider even such

points as the following : It is not reasonable that this should

be so only in the case of these intermediates, but clearly

the Forms also might be in the perceptible things ;for both

statements are parts of the same theory. Further, it follows

from this theory that there are two solids in the same place,

and that the intermediates are not immovable, since they

15 are in the moving perceptible things. And in general to

what purpose would one suppose them to exist indeed, but

1

Possibly in a work Hepi TWVMa6r]piiTa>v,

for which cf. Diog.

Laert. ix. 55.2 The reference is to a school of semi-Pythagorean, semi-Platonic

thinkers.



BOOK B. 2 998*

to exist in perceptible things ? For the same paradoxical

results will follow which we have already mentioned ;there

will be a heaven besides the heaven, only it will be not apart

but in the same place;

which is still more impossible.

1

3 (6) Apart from the great difficulty of stating the case 2

truly with regard to these matters, it is very hard to say,

with regard to the first principles, whether it is the genera

that should be taken as elements and principles, or rather

the primary constituents of a thing ;e. g. it is the primary

parts of which articulate sounds consist that are thought tobe elements and principles of articulate sound, not the

common genus articulate sound;and we give the name 2 5

of elements to those geometrical propositions, the proofs

of which are implied in the proofs of the others, either of all

or of most. Further, both those who say there are several

elements of corporeal things and those who say there is

one, say the parts of which bodies are compounded andconsist are principles ;

e. g. Empedocles says fire and water 30

and the rest are the constituent elements of things, but does

not describe these as genera of existing things. Besides

this, if we want to examine the nature of anything else, we

examine the parts of which, e. g.,a bed consists and how 99&

b

they are put together, and then we know its nature.

To judge from these arguments, then, the principles of

things would not be the genera ;but ifwe know each thing

by its definition, and the genera are the principles or 5

starting-points of definitions, the genera must also be the

principles of definable things. And if to get the knowledge of

the species according to which things are named is to get

the

knowledgeof

things,the

generaare at least

starting-points of the species. And some also of those who say

unity or being,2 or the great and the small,

3are elements of 10

things, seem to treat them as genera.

But, again, it is not possible to describe the principles in

both ways. For the formula of the essence is one;but

1 With 997a34-998

a19 cf. 995

b13-18, I059

a38-

b2i. For the

answer cf. A. 6-lo, M, N.2 The reference is to the Pythagoreans and Plato (cf. 996*6).3 The reference is to Plato (cf. A. 98;

b20).



998b METAPHYSICA

definition by genera will be different from that which states

the constituent parts of a thing.1

(7) Besides this, even if the genera are in the highest

15 degree principles, should one regard the first of the generaas principles, or those which are predicated directly of the

individuals ? This also admits of dispute. For if the

universals are always more of the nature of principles,

evidently the uppermost of the genera are the principles ;

for these are predicated of all things. There will, then, be

as many principles of things as there are primary genera,

20 so that both being and unity will be principles and sub

stances;for these are most of all predicated of all existing

things. But it is not possible that either unity or being

should be a single genus of things ;for the differentiae of

any genus must each of them both have being and be one,

but it is not possible for the genus taken apart from its

25 species (any more than for the species of the genus) to be

predicated of its proper differentiae;so that if unity or

being is a genus, no differentia will either have being or be

one. But if unity and being are not genera, neither will

they be principles, if the genera are the principles. Again,

the intermediate kinds, in whose nature the differentiae are

included, will on this theory be genera, down to the indivisible

species;

but as it is, some are thought to be genera and3 others are not thought to be so. Besides this, the differ

entiae are principles even more than the genera ;and if

these also are principles, there comes to be practically an

infinite number of principles, especially if we suppose the

999a

highest genus to be a principle. But again, if unity ?s

more of the nature of a principle, and the indivisible is one,

and everything indivisible is so either in quantity or in

species, and that which is so in species is the prior, and

genera are divisible into species (for man is not the genus

5 of individual men), that which is predicated directly of the

individuals will have more unity. Further, in the case of

things in which the distinction of prior and posterior is

present, that which is predicable of these things cannot be

something apart from them(e. g.

if two is the first of

1 With 998* 2o-b 14 cf. 995** 27-9. For the answer cf. Z. 10, 13.



BOOK B. 3 999a

numbers, there will not be a Number apart from the kinds

of numbers;and similarly there will not be a Figure apart

from the kinds of figures ;and if the genera of these things

10

do not exist apart from the species, the genera of other

things will scarcely do so;for genera of these things are

thought to exist if any do). But among the individuals one

is not prior and another posterior. Further, where one

thing is better and another worse, the better is always prior ;

so that of these also no genus can exist.

From these considerations, then, the species predicated of J 5

individuals seem to be principles rather than the genera.

But again, it is not easy to say in what sense these are to

be taken as principles. For the principle or cause must

exist alongside of the things of which it is the principle,

and must be capable of existing in separation from them;

but for what reason should we suppose any such thing to

exist alongside of the individual, except that it is predicated 20

universally and of all ? But if this is the reason, the things

that are more universal must be supposed to be more of the

nature of principles ;so that the highest genera would be

the principles.1

4 (8) There is a difficulty connected with these, the hardest

of all and the most necessary to examine, and of this the 25

discussion now awaits us. If, on the one hand, there is

nothing apart from individual things, and the individuals

are infinite in number, how then is it possible to get know

ledge of the infinite individuals ? For all things that we

come to know, we come to know in so far as they have

some unity and identity, and in so far as some attribute

belongs to them universally.

But if this is necessary, and there must be something

apart from the individuals, it will be necessary that the 30

genera exist apart from the individuals, either the lowest

or the highest genera ;but we found by discussion just now

that this is impossible.2

Further, if we admit in the fullest sense that something

1 With 998bI4~999

a23 cf. 995

b29-31. For the answer cf. Z. 12.

iO38a19, and 13. With this and the previous problem cf. loco 15 21-

1060* i.2Ch. 3.



999* METAPHYSICA

exists apart from the concrete thing, whenever something-

is predicated of the matter, must there, if there is some

thing apart, be something apart from each set of individuals,

999

b or from some and not fromothers,

or from none ?l

(A)If

there is nothing apart from individuals, there will be no

object of thought, but all things will be objects of sense,

and there will not be knowledge of anything, unless we say

that sensation is knowledge.2

Further, nothing will be

eternal or unmovable;for all perceptible things perish and

5are in movement. But if there is nothing eternal, neither

can there be a process of coming to be ; for there must be

something that comes to be, i. e. from which something

comes to be, and the ultimate term in this series cannot

have come to be, since the series has a limit and since

nothing can come to be out of that which is not. Further,

if generation and movement exist there must also be a limit;

10 for no movement is infinite, but every movement has an end,

and that which is incapable of completing its coming to be

cannot be in process of coming to be;and that which has

completed its coming to be must be as soon as it has come

to be.3

Further, since the matter exists,4 because it is un-

generated, it is a fortiori reasonable that the substance or

essence, that which the matter is at any time coming to be,

should exist;

forif

neither essence nor matteris

to be,

r5 nothing will be at all, and since this is impossible there

must be something besides the concrete thing, viz. the shape

or form.

But again (B) if we are to suppose this, it is hard to say

in which cases we are to suppose it and in which not. For

evidently it is not possible to suppose it in all cases;we

could not suppose that there is a house besides the particular

20 houses. Besides this, will the substance of all the indi

viduals, e. g. of all men, be one ? This is paradoxical, for

1 The question which individuals have something apart correspond

ing to them suggests to Aristotle the further question whether any

have. Thus the end of the sentence takes a form inconsistent with the

beginning.2 The reference is to Protagoras (cf. PI. Theaet. 152 -153 A).3Sc. and thus there is a limit to its coming to be.

4Sc. before the concrete thing.



BOOK B. 4 999b

all the things whose substance is one are one. But are the

substances many and different ? This also is unreasonable.

At the same time, how does the matter become each of the

individuals,and how is the concrete

thing

these two

elements ?l

(9) Again, one might ask the following question also

about the first principles. If they are one in kind only, 35

nothing will be numerically one, not even unity-itself and

being-itself ;and how will knowing exist, if there is not to

be something common to a whole set of individuals ?

But if there is a common element which is numerically

one, and each of the principles is one, and the principles

are not as in the case of perceptible things different for

different things (e. g. since this particular syllable is the

same in kind whenever it occurs, the elements of it are also

the same in kind; only in kind, for these also, like the 30

syllable, are numerically different in different contexts), if

it is not like this but the principles of things are numeri

cally one, there will be nothing else besides the elements

(for there is no difference of meaning between numerically

one and individual;for this is just what we mean by the

individual the numerically one, and by the universal we

mean that which is predicable of the individuals). There- ioooa

fore it will be just as if the elements of articulate sound

were limited in number;

all the language in the world

would be confined to the ABC, since there could not be two

or more letters of the same kind.2

(10) One difficulty which is as great as any has been 5

neglected both by modern philosophers and by their pre

decessors whether the principles of perishable and those

ofimperishable things are the same or different. If they

are the same, how are some things perishable and others

imperishable, and for what reason ? The school of Hesiod

and all the theologians thought only of what was plausible

to themselves, and had no regard to us. For, asserting the 10

1 With 999a24-

b24 cf. 995

b31-6, io6oa 3-27,

b23-8. For the

answer cf. Z.

8, 13, 14,

A.

6-10,M. 10.

2 With 999b24-iooo

a4 cf. 996*1-2, 1060 b

28-30. For the answercf. Z. 14, A. 4, 5, M. 10.

645-28 E



ioooa METAPHYSICA

first principles to be gods and born of gods, they say that

the beings which did not taste of nectar and ambrosia

became mortal;and clearly they are using words which are

familiarto themselves, yet what they have said about the

very application of these causes is above our comprehen-

15 sion. For if the gods taste of nectar and ambrosia for their

pleasure, these are in no wTise the causes of their existence

;

and if they taste them to maintain their existence, how can

gods who need food be eternal? But into the subtleties

of the mythologists it is not worth our while to inquire

seriously ; those, however, who use the language of proof

20 we must cross-examine and ask why. after all, things which

consist of the same elements are, some of them, eternal in

nature, while others perish. Since these philosophers

mention no cause, and it is unreasonable that things should

be as they say, evidently the principles or causes of things

cannot be the same. Even the man whom one might sup-

25 pose to speak most consistently Empedocles, even he

has made the same mistake;for he maintains that strife is

a principle that causes destruction^ but even strife would

seem no less to prodtice everything, except the One;for

all things excepting God proceed from strife. At least he

says :

From which all that was and is and will be hereafter30 Trees, and men and women, took their growth,

And beasts and birds and water-nourished fish,

And long-aged gods.1

The implication is evident even apart from these words;

iooobfor if strife had not been present in things, all things would

have been one, according to him;for when they have come

together,then strife stood outermost.

2 Hence it also

follows on his theory that God most blessed is less wise

5 than all others;for he does not know all the elements

;for

he has in him no strife, and knowledge is of the like by the

like.* For by earth, he says,

we see earth, by water water,

By ether godlike ether, by fire wasting fire,

Loveby love,

and strife

by gloomystrife.

3

1Fr. 21.

2Fr. 36.

3Fr. 109.



BOOK B. 4 iooob

But and this is the point we started from this at least

is evident, that on his theory it follows that strife is as much l

the cause of existence as of destruction. And similarly

love is not specially the cause of existence;for in collecting

things into the One it destroys all other things. And at

the same time Empedocles mentions no cause of the change

itself, except that things are so by nature.

But when strife at last waxed great in the limbs of the

Sphere,And sprang to assert its rights as the time was fulfilled

Which is fixed for them in turn by a mighty oath. 1 15

This implies that change was necessary ;but he shows no

cause of the necessity. But yet so far at least he alone

speaks consistently ;for he does not make some things

perishable and others imperishable, but makes all perishable

except the elements. 2 The difficulty we are speaking of 20

now is,

whysome

thingsare

perishableand others are

not,if they consist of the same principles.

Let this suffice as proof of the fact that the principles

cannot be the same. But if there are different principles,

one difficulty is whether these also will be imperishable or

perishable. For if they are perishable, evidently these also

must consist of certain elements (for all things that perish, 25

perish by being resolved into the elements of which they

consist) ;so that it follows that prior to the principles there

are other principles. But this is impossible, whether the

process has a limit or proceeds to infinity. Further, how

will perishable things exist, if their principles are to be

annulled ? But if the principles are imperishable, why will

things composed of some imperishable principles be perish

able, while those composed of the others are imperishable ? 30

This is not probable, but is either impossible or needs much

proof. Further, no one has even tried to maintain different

principles ; they maintain the same principles for all things.

But they swallow the difficulty we stated first3as if they iooi

a

took it to be something trifling.4

1Fr. 30.

2Cf.

Diels, Vorsokratiker,

ed. 3, i.

209.

11-21.3 ioooa 5~

b 21.4 With ioooa 5-icoi

a3 cf. 996

a2-4, 1060*27-36. For the answer

cf. Z. 7-10.

E 2



iooia METAPHYSICA

(n) The inquiry that is both the hardest of all and the

5 most necessary for knowledge of the truth is whether being

and unity are the substances of things, and whether each of

them, without being anything else, is being or unity respec

tively, or we must inquire what being and unity are, with

the implication that they have some other underlying nature.

For some people think they are of the former, others think

they are of the latter character. Plato and the Pythagoreans10 thought being and unity were nothing else, but this was

their nature, their essence being just unity and being. But

the natural philosophers take a different line;

e. g. Empe-docles as though reducing it to something more intel

ligible says what unity is;for he would seem to say it is

love : at least, this is for all things the cause of their being

15 one. Others say this unity and being, of which things

consist and have been made, is fire,1 and others say it is air.

2

Asimilar view is

expressed bythose

who makethe elements

more than one;for these also must say that unity and being

are precisely all the things which they say are principles.

(A) If we do not suppose unity and being to be sub-

20 stances, it follows that none of the other universals is

a substance;for these are most universal of all, and if there

is no unity-itself or being-itself, there will scarcely be in any

other case anything apart from what are called the indi-

25 viduals. Further, if unity is not a substance, evidently

number also will not exist as an entity separate from the

individual things; for number is units, and the unit is

precisely a certain kind of one.

But (B) if there is a unity-itself and a being-itself, unity

and being must be their substance;for it is not something

else that is predicated universally of the things that are and

are one, but just unity and being. But if there is to be

30 a being-itself and a unity-itself, there is much difficulty in

seeing how there will be anything else besides these,

I mean, how things will be more than one in number. For

what is different from being does not exist, so that it

1

Hippasus and Heraclitus.3 Anaximenes and Diogenes of Apollonia.



BOOK B. 4 iooia

necessarily follows, according to the argument of Parmenides,

that all things that are are one and this is being.

There are objections to both views. For whether unity iooib

is not a substance or there is a unity-itself, number cannotbe a substance. We have already

l said why this result

follows if unity is not a substance;and if it is, the same

difficulty arises as arose2 with regard to being. For whence

is there to be another one besides unity-itself? It must be 5

not-one;but all things are either one or many, and of the

many each is one.

Further, if unity-itself is indivisible, according to Zeno s

postulate3

it will be nothing. For that which neither when

added makes a thing greater nor when subtracted makes it

less, he asserts to have no being, evidently assuming that

whatever has being is a spatial magnitude. And if it is 10

a magnitude, it is corporeal ;for the corporeal has being

in every dimension, while the other objects of mathematics,

e. g. a plane or a line, added in one way will increase what

they are added to, but in another way will not do so,4 and

a point or a unit does so in no way. But, since his theory

is of a low order, and an indivisible thing can exist in such

a way as to have a defence even against him (for the indi- 15

visible when added will make the number, though not the

size, greater), yethow can a

magnitude proceedfrom one

such indivisible or from many ? It is like saying that the

line is made out of points.

But even if one supposes the case to be such that, as 20

some say, number proceeds from unity-itself and something

else which is not one, none the less we must inquire whyand how the product will be sometimes a number and some

times a magnitude, if the not-one was inequality5

and wasthe same principle in either case. For it is not evident how

magnitudes could proceed either from the one and this

principle, or from some number and this principle.6

25

1 a24-27.

2 a3i-

bi.

5Cf. Diels, Vorsokratiker,t&. 3, i. 170. 16-38.

4e. g. a line added to another at the end makes it longer, but one

which lies beside another makes it no broader.

5 The reference is to Plato s theory (cf. M. io8l a 24).6 With iooi a

4-b25 cf. 996*4 9.

For the answer cf. Z. io4ob

16-24, I. 2.



iooib METAPHYSICA

(14) A question connected with these is whether numbers 5

and bodies and planes and points are substances of a kind,

or not. If they are not, it baffles us to say what being1

is

and what the substances of things are. For modifications

30 and movements and relations and dispositions and ratios do

not seem to indicate the substance of anything ;for all are

predicated of a subject, and none is a this . And as to the

things which might seem most of all to indicate substance,

water and earth and fire and air, of which composite bodies

ioo2a

consist, heat and cold and the like are modifications of

these, not substances, and the body which is thus modifiedalone persists as something real and as a substance. But,

on the other hand, the body is surely less of a substance

5 than the surface, and the surface than the line, and the line

than the unit and the point. For the body is bounded by

these;and they are thought to be capable of existing with

out body, but body incapable of existing without these.

This is why, while most of the philosophers and the earlier

among them thought that substance and being were iden

tical with body, and that all other things were modifications

10 of this, so that the first principles of bodies were the first

principles of being, the more recent and those who were

held to be wiser l

thought numbers were the first principles.

As we said, then, if these are not substance, there is no

substance and no being at all;for the accidents of these it

cannot be right to call beings.

15 But if this is admitted, that lines and points are substance

more than bodies, but we do not see to what sort of bodies

these could belong (for they cannot be in perceptible

bodies), there can be no substance. Further, these are all

evidently divisions of body, one in breadth, another in

20 depth, another in length. Besides this, no sort of shape is

present in the solid more than any other;so that if the

Hermes is not in the stone, neither is the half of the cube

in the cube as something determinate;therefore the surface

is not in it either;for if any sort of surface were in

it,the

surface which marks off the half of the cube would be in it

25 too. And the same account applies to the line and to the

1 The Pythagoreans and Plato are probably meant.



^BOOK B. 5 ioo2a

point and the unit. Therefore, if on the one hand body is

in the highest degree substance, and on the other hand

these things are so more than body, but these are not even

instances of substance,1

it baffles us to say what being is

and what the substance of things is. For besides what has

been said, the questions of generation and destruction con

front us with further paradoxes. For if substance, not 30

having existed before, now exists, or having existed before,

afterwards does not exist, this change is thought to be

accompanied by a process of becoming or perishing ;but

points and lines and surfaces cannot be in process either of

becoming or of perishing, when they at one time exist and

at another do not. For when bodies come into contact or

are divided, their boundaries simultaneously become one in iooab

the one case when they touch, and two in the other when

they are divided;so that when they have been put together

one boundary does not exist but has perished, and when

they have been divided the boundaries exist which before

did not exist (for it cannot be said that the point, which is

indivisible, was divided into two). And if the boundaries

come into being and cease to be, from what do they come

into being ? A similar account may also be given of the 5

now in time;for this also cannot be in process of coming

into being or of ceasing to be, but yet seems to be alwaysdifferent, which shows 2

that it is not a substance. And

evidently the same is true of points and lines and planes ;

for the same argument applies, since they are all alike 10

either limits or divisions.3

6 In general one might raise the question why after all,

besides perceptible things and the intermediates,

4

we haveto look for another class of things, i. e. the Forms which

we 5

posit. If it is for this reason, because the objects

of mathematics, while they differ from the things in this

1Sc. not to speak of their being the most real substances.

2

Reading in Ioo2b 7-8 eu/m, s owe(<os

OVK. Ab).

3 For the answer cf. M. 1-3 (esp. io9ob5-13), 6-9, N. 1-3, 5, 6.

With problems (li), (14) cf. io6oa

36-b

19.*For these cf. A. 987^14-18.

5Sc. Platonists.



ioo2b METAPHYSICA

i 5world in some other respect, differ not at all in that there

are many of the same kind, so that their first principles

cannot be limited in number (just as the elements of all the

language in this sensible world are not limited in number,but in kind, unless one takes the elements of this individual

aosyllable or of this individual articulate sound whose

elements will be limited even in number;so is it also in

the case of the intermediates;for there also the members

of the same kind are infinite in number), so that if there are

not besides perceptible and mathematical objects others

such as some maintain the Forms to be, there will be no

substance which is one in number, but only in kind, nor

will the first principles of things be determinate in number,

25 but only in kind : if then this must be so, the Forms also

must therefore be held to exist. Even if those who support

this view do not express it articulately, still this is what

they mean,and

theymust be

maintainingthe Forms

justbecause each of the Forms is a substance and none is by

accident.

30 But if we are to suppose both that the Forms exist and

that the principles are one in number, not in kind, we have

mentioned 1 the impossible results that necessarily follow.2

(13) Closely connected with this is the question whether

the elements exist potentially or in some other manner. If

in some other way, there will be something else prior to the

ioo3a

first principles ;for the potency is prior to the actual cause,

and it is not necessary for everything potential to be actual.

But if the elements exist potentially, it is possible that

everything that is should not be. For even that wrhich is

not yet is capable of being ;for that which is not comes to

be, but nothing that is incapable of being comes to be.3

5 (12) We must not only raise these questions about the

first principles, but also ask whether they are universal or

wrhat we call individuals. If they are universal, they will

not be substances;for everything that is common indicates

1

999b27-iooo

a4.

2

(15)is

a question not raisedin

ch.I

but akin to problems (4), (8),

(14).3 With ioo2b 32-1003* 5 cf. 996*10-11. For the answer cf. e. 8,

A. 6, 7.



BOOK B. 6 ioo3a

not a this but a such,but substance is a this . And

if we are to be allowed to lay it down that a common predi

cate is a this and a single thing, Socrates will be several 10

animals himself and man and animal , if each of these

indicates a this and a single thing.

If, then, the principles are universals, these results follow;

if they are not universals but of the nature of individuals,

they will not be knowable;for the knowledge of anything

is universal. Therefore if there is to be knowledge of the 15

principles there must be other principles prior to them,

namely those that are universally predicated of them. 1

1 With 1003*5-17 cf. 996*9-10, io6ob 19-23. For the answer

cf. Z. 13, 15, M. 10.



BOOK F

THERE is a science which investigates being- as being i

and the attributes which belong to this in virtue of its own

nature. Now this is not the same as any of the so-called

special sciences;for none of these others treats universally

of being as being. They cut off a part of being and investi-

25 gate the attribute of this part ;this is what the mathematical

sciences for instance do. Now since we are seeking thefirst principles and the highest causes, clearly there must

be some thing to which these belong in virtue of its own

nature. If then those who sought the elements of existing

things were seeking these same principles, it is necessary

3othat the elements must be elements of being not by accident

but just because it zs being. Therefore it is of being as

being that we also must grasp the first causes.

There are many senses in which a thing may be said to 2

4 be,but all that is is related to one central point, one

definite kind of thing, and is not said to be by a mere

ambiguity. Everything which is healthy is related to

35 health, one thing in the sense that it preserves health,

another inthe sense that

it

produces it, anotherin

thesense that it is a symptom of health, another because it is

ioo3bcapable of it. And that which is medical is relative to the

medical art, one thing being called medical because it

possesses it, another because it is naturally adapted to it,

another because it is a function of the medical art. And we

5shall find other words used similarly to these. So, too,

there are many senses in which a thing is said to be, but

all refer to one starting-point ;some things are said to

be because they are substances, others because they are

affections of substance, others because they are a process

towards substance, or destructions or privations or qualities

of substance, or productive or generative of substance, or of

things which are relative to substance, or negations of one

10 of these things or of substance itself. It is for this reason

that we say even of non-being that it is non-being. As,



BOOK T. 2 1003

then, there is one science which deals with all healthy

things, the same applies in the other cases also. For not

only in the case of things which have one common notion

does the investigation belong to one science, but also in thecase of things which are related to one common nature

;

for even these in a sense have one common notion. It is 15

clear then that it is the work of one science also to study

the things that are, qua being. But everywhere science

deals chiefly with that which is primary, and on which the

other things depend, and in virtue of which they get their

names. If, then, this is substance, it will be of substances that

the philosopher must grasp the principles and the causes.

Now for each one class of things, as there is one percep

tion, so there is one science, as for instance grammar, being20

one science, investigates all articulate sounds. Hence to

investigate all the species of being qua being is the work

of a science which is generically one, and to investigate the

several species is the work of the specific parts ofthe science.

If, now, being and unity are the same and are one thing

in the sense that they are implied in one another as prin

ciple and cause are, not in the sense that they are explained

by the same definition (though it makes no difference even 25

if we suppose them to be like that in fact this would even

strengthenour

case);for

* one man and man are the

same thing, and so are existent man and man,and the

doubling of the words in one man and one existent man

does not express anything different(it

is clear that the two

things are not separated either in coming to be or in ceas

ing to be) ;and similarly one existent man adds nothing 3

to4

existent man,so that it is obvious that the addition in

these cases means the same thing, and unity is nothing

apart from beingl

;and

if, further, the substance of each

thing is one in no merely accidental way, and similarly is

from its very nature something that is : all this being so,

there must be exactly as many species of being as of unity.

And to investigate the essence of these is the work of a

1

The argument is obscured by doubts as to the reading, but seemsto be that being and unity are not severed from the particular thingwhich is and is one, and .*. are not severed from one another.



ioo3b METAPHYSICA

35 science which is generically one I mean, for instance, the

discussion of the same and the similar and the other con

cepts of this sort;and nearly all contraries may be referred

ioo4

a

to this origin; let us take them as having been investigated

in the Selection of Contraries .

And there are as many parts of philosophy as there are

kinds of substance, so that there must necessarily be amongthem a first philosophy and one which follows this. For

5 being falls immediately into genera ;for which reason the

sciences too will correspond to these genera. For the

philosopher is like the mathematician, as that word is used ;

for mathematics also has parts, and there is a first and a

second science and other successive ones within the sphere

of mathematics.2

Now since it is the work of one science to investigate

10opposites, and plurality is opposed to unity and it belongs

to one science to

investigate

the

negation

and the

privationbecause in both cases we are really investigating the one

thing of which the negation or the privation is a negation

or privation (for we either say simply that that thing is

not present, or that it is not present in some particu

lar class;in the latter case difference is present over and

above what is implied in negation ;for negation means just

15 the absence of the thing in question, while in privation there

is also employed an underlying nature of which the priva

tion is asserted 3

): in view of all these facts, the contraries

of the concepts we named above, the other and the dis

similar and the unequal, and everything else which is

derived either from these or from plurality and unity,

must fall within the province of the science above named.

20 And contrariety is one of these concepts ;for contrariety

is a kind of difference, and difference is a kind of other

ness. Therefore, since there are many senses in which

a thing is said to be one, these terms also will have

1Cf. Fr. I478

b35-I479

a5, I497

a32-149^43-

2 With ioo4a2-9 cf. B. 995

b10-13, 997

a15-25, E. i.

8i. e.

negationis

simplythe

negationof an attribute

;in

privationsome member of a definite class is said not to have the attribute in the

form appropriate to that class. I conjecture that TO> f.vl or TO> iv\r]

should be omitted in 1004* 13-14.



BOOK T. 2 ioo4a

many senses, but yet it belongs to one science to know

them all;for a term belongs to different sciences not if it

has different senses, but if it has not one meaning and its

definitions cannot be referred to one central meaning. And 25

since all things are referred to that which is primary, as for

instance all things which are called one are referred to the

primary one, we must say that this holds good also of the

same and the other and of contraries in general ;so that

after distinguishing the various senses of each, we must then

explain by reference to what is primary in the case of each

of the predicates in question, saying how they are related

to it;for some will be called what they are called because 30

they possess it, others because they produce it, and others

in other such ways.

It is evident, then, that it belongs to one science to be able

to give an account of these concepts as well as of substance

(this was one of the questions in our book of problems),1

and that it is the function of the philosopher to be able to

investigate all things. For if it is not the function of the ioo4b

philosopher, who is it who will inquire whether Socrates

and Socrates seated are the same thing, or whether one

thing has one contrary, or what contrariety is, or how many

meanings it has ? And similarly with all other such ques

tions.

Since, then,these are essential modifications of

unity 5

qua unity and of being qua being, not qua numbers or lines

or fire, it is clear that it belongs to this science to investi

gate both the essence of these concepts and their properties.

And those who study these properties err not by leaving

the sphere of philosophy,2 but by forgetting that substance,

of which they have no correct idea, is prior to these other

things. For number qua number has peculiar attributes, I0

such as oddness and evenness, commensurability and

equality, excess and defect, and these belong to numbers

either in themselves or in relation to one another. And

similarly the solid and the motionless and that which is in

motion and the weightless and that which has weight have

other peculiar properties. So too there are certain pro- 15

1i. e. B. 995

b18-27, 997

a25-34.

2Sc. which they do not do.



ioo4b METAPHYSICA

parties peculiar to being as such, and it is about these that

the philosopher has to investigate the truth. An indication

of this may be mentioned : dialecticians and sophists

assume the same guise as the philosopher, for sophistic is

Wisdom which exists only in semblance, and dialecticians

20 embrace all things in their dialectic, and being is common

to all things ;but evidently their dialectic embraces these

subjects because these are proper to philosophy. For

sophistic and dialectic turn on the same class of things as

philosophy, but this differs from dialectic in the nature of

the faculty required and from sophistic in respect of the

35 purpose of the philosophic life. Dialectic is merely critical

where philosophy claims to know, and sophistic is what

appears to be philosophy but is not.

Again, in the list of contraries one of the two columns 1

is privative,and all contraries are reducible to being and

non-being,and to

unityand

plurality,as for instance rest

belongs to unity and movement to plurality. And nearly

30 all thinkers agree that being and substance are composed

of contraries;at least all name contraries as their first prin

ciples some name odd and even,2 some hot and cold,

3

some limit and the unlimited,4 some love and strife.

5 And

all the others as well are evidently reducible to unity and

ioosa plurality (this reduction we must take for granted 6), and the

principles stated by other thinkers fall entirely under these

as their genera. It is obvious then from these considera

tions too that it belongs to one science to examine being

qua being. For all things are either contraries or com

posed of contraries, and unity and plurality are the starting-

5 points of all contraries. And these belong to one science,

whether they have or have not one single meaning. Prob

ably the truth is that they have not; yet even if one has

several meanings, the other meanings will be related to the

primary meaning (and similarly in the case of the con

traries), even if being or unity is not a universal and the

1

Cf. note on A. 986

a

23.

2

The Pythagoreans.3 Parmenides in thek

Way of Opinion .

4 The Platonists.6

Empedocles.fi

Cf. Fr. 1 4;8b36-i479

a5-



BOOK P. 2 ioosa

same in every instance or is not separable from the particu

lar instances (as in fact it probably is not;the unity is in 10

some cases that of common reference, in some cases that of

serialsuccession).

And for this reason it does notbelong-

to the geometer to inquire what is contrariety or complete

ness or unity or being or the same or the other, but only to

presuppose these concepts and reason from this starting-

point. Obviously then it is the work of one science to

examine being qua being, and the attributes which belong

to it qua being, and the same science will examine not

only substances but also their attributes, both those above 15

named l and the concepts prior and posterior ,

*

genus

and species ,whole and part ,

and the others of this

sort.2

3 We must state whether it belongs to one or to different

sciences to inquire into the truths which are in mathematics

calledaxioms,

and into substance.Evidently,

theinquiry

20

into these also belongs to one science, and that the science

of the philosopher ;for these truths hold good for every

thing that is, and not for some special genus apart from

others. And all men use them, because they are true of

being qtia being and each genus has being. But men use 25

them just so far as to satisfy their purposes ;that

is, as far

as the genus to which their demonstrations refer extends.

Therefore since these truths clearly hold good for all things

qua being (for this is what is common to them), to him who

studies being q^ia being belongs the inquiry into these as

well. And for this reason no one who is conducting a

special inquiry tries to say anything about their truth or 30

falsity, neither the geometer nor the arithmetician. Some

natural philosophers indeed have done so, and their pro

cedure was intelligible enough ;for they thought that they

alone were inquiring about the whole of nature and about

being. But since there is one kind of thinker who is above

even the natural philosopher (for nature is only one particu

lar genus of being), the discussion of these truths also will 35

11. 12.

2 With ioo3b22-ioo5

a 18 cf. B. 995b18-27, 997*25-34. With the

whole ch. cf. K. 3.



ioosa METAPHYSICA

belong to him whose inquiry is universal and deals with

I0 5b

primary substance. Physics also is a kind of Wisdom, but

it is not the first kind. 1 And the attempts of some ofthose

who discuss the terms on which truth should be accepted,2

are due to a want of training in logic ;for they should know

these things already when they come to a special study,

and not be inquiring into them while they are listening to

lectures on it.

5 Evidently then it belongs to the philosopher, i. e. to him

who is studying the nature of all substance, to inquire also

into the principles of syllogism. But he who knows bestabout each genus must be able to state the most certain

10principles of his subject, so that he whose subject is exist

ing things qtta existing must be able to state the most

certain principles of all things. This is the philosopher,

and the most certain principle of all is that regarding which

it is impossible to be mistaken;for such a principle must

be both the best known (for all men may be mistaken

about things which they do not know), and non-hypothe-T 5 tical. For a principle which every one must have who

understands anything that is, is not a hypothesis ;and that

which every one must know who knows anything, he must

already have when he comes to a special study. Evidently

then such a

principle

is the most certain of all;

which

principle this is, let us proceed to say. It is, that the same

attribute cannot at the same time belong and not belong to

20 the same subject and in the same respect ;we must pre

suppose, to guard against dialectical objections, any further

qualifications which might be added. This, then, is the

most certain of all principles, since it answers to the defini-

^c, tion given above. For it is impossible for any one to believe the same thing to be and not to be, as some think

25 Heraclitus says. For what a man says, he does not neces

sarily believe;and if it is impossible that contrary attri

butes should belong at the same time to the same subject

(the usual qualifications must be presupposed in this pre

miss too), and if an opinion which contradicts another is

1 With ioo5aiQ-

b2 cf. K. 4.2 The reference may be to Antisthenes.



BOOK T. 3 ioosb

contrary to it, obviously it is impossible for the same man

at the same time to believe the same thing to be and not to

be;for if a man were mistaken on this point he would have 3

contrary opinions at the same time. It is for this reasonthat all who are carrying out a demonstration reduce it to

this as an ultimate belief; for this is naturally the starting-

point even for all the other axioms.1

4 There are some who, as we said,2 both themselves assert 35

that it is possible for the same thing to be and not to be,

and say that people can judge this to be the case.3

And ioo6

among others many writers about nature use this language.

But wre have now posited that it is impossible for anything v

at the same time to be and not to be, and by this means

have shown that this is the most indisputable of all prin

ciples.4 Some indeed demand that even this shall be 5

demonstrated,5 but this they do through want of education,

for not to know of what things one should demand demon

stration, and of what one should not, argues want of educa

tion. For it is impossible that there should be demonstration

of absolutely everything (there would be an infinite regress,

so that there would still be no demonstration) ;but if there 10

are things of which one should not demand demonstration,

these persons could not say what principle they maintain

to be more self-evident than the present one.

We can, however, demonstrate negatively even that this

view 6is impossible )

if our opponent will only say some

thing ;and if he says nothing, it is absurd to seek to give

an account of our views to one who cannot give an account

of anything, in so far as he cannot do so. For such a man,

as such,is

from the start no better than a vegetable. Now 15

negative demonstration I distinguish from demonstra

tion proper, because in a demonstration one might be

1 With ch. 3 cf. B. 995b6-10, 996

b26-997

a15. With

ioc>5

b8-34 cf.

K. io6i b 34-io62a2(with ioo5

b23~6 cf. io62a 31-5).

2

Apparently a loose reference to ioo5b23-5.

3 The Megaric school may be referred to.

4i.e. we have shown that since A cannot be both B and not-jB, no

one can think A is both B and not-j5 (icos

b

22-32).6 The reference may be to Antisthenes.6 That the same thing can be and not be.



ioo6a METAPHYSICA

thought to be begging the question, but if another person

is responsible for the assumption we shall have negative

proof, not demonstration. 1 The starting-point for all such

arguments is not the demand that our opponent shall say20 that something either is or is not (for this one might per

haps take to be a begging of the question), but that he shall

say something which is significant both for himself and for

another;for this is necessary, if he really is to say any

thing. For, if he means nothing, such a man will not be

capable of reasoning, either with himself or with another.

But if any one grants this, demonstration will be possible ;

2 5 for we shall already have something definite. The person

responsible for the proof, however, is not he who demon

strates but he who listens;for while disowning reason he

listens to reason. And again he who admits this has

admitted that something is true apart from demonstration

[so

that not

everything

will be*

so and not so].

First then this at least is obviously true, that the word

34 be or not be has a definite meaning, so that not every

thing will be so and not so \2

Again, if man has one

meaning, let this be two-footed animal; by having one

meaning I understand this : if man means c X\ then ifAis a man X will be what being a man means for him.

(It makes no difference even if one were to say a wordhas several meanings, if only they are limited in number

;

ioo6bfor to each definition there might be assigned a different

word. For instance, we might say that man has not one

meaning but several, one of which would have one defini

tion, viz.*

two-footed animal,while there might be also

several other definitions ifonly they were limited in number;

for a peculiar name might be assigned to each of the

5 definitions. If, however, they were not limited but one were

to say that the word has an infinite number of meanings,

obviously reasoning would be impossible ;for not to have

one meaning is to have no meaning, and if words have no

meaning our reasoning with one another, and indeed with

10 ourselves, has been annihilated;for it is

impossible

to think

1 With 11. s-i 8 cf. K. 1062*2-5.2 For so and not so cf. PI. Theaet. 183 A.



BOOK F. 4 ioo6b

of anything if we do not think of one thing ;but if this is

possible, one name might be assigned to this thing.)

Let it be assumed then, as was said at the beginning,1

that the name has a meaning and has one meaning ; it is

impossible, then, that being a man should mean precisely

not being a man,if

( man not only signifies something

about one subject but also has one significance (for we do 15

not identify having one significance with4

signifying

something about one subject ,since on that assumption

even musical and white and man would have had one

significance, so that all things would have been one ;for

they would all have had the same significance).

And it will not be possible to be and not to be the same

thing, except in virtue of an ambiguity, just as if one whom

we call* man

,others wrere to call not-man

;but the point

20

in question is not this, whether the same thing can at the

same time be and not be a man in name, but whether it can

in fact. Now if man and not-man mean nothing dif

ferent, obviously not being a man will mean nothing

different from being a man;so that

*

being a man will

be not being a man;for they will be one. For being one 25

means this being related as raiment and 4

dress are, if

their definition is one. And if being a man and being

a not-man are to be one, they must mean one thing. Butit was shown earlier

2that they mean different things.

Therefore, if it is true to say of anything that it is a man, it

must be a two-footed animal (for this was what man

meant 3

) ;and if this is necessary, it is impossible that the 30

same thing should not at that time be a two-footed animal;

for this is what being necessary meansthat it is im

possible for the thing not to be. It is, then, impossible that

it should be at the same time true to say the same thing is

a man and is not a man.

The same account holds good with regard to not being

a man,for being a man and *

being a not-man mean ioo7a

different things, since even being white and being a man

are different;for the former terms are much more opposed,

so that they must a fortiori mean different things. And1 a

2i, 31.2

11. 11-15.3

in a3if-

F 2



ioo7a METAPHYSICA

if any one says that white means one and the same thing

5 as man, again we shall say the same as what was said

before,1that it would follow that all things are one, and not

only opposites.But if this is

impossible,then

what wehave maintained will follow, if our opponent will only

answer our question.

Andif, when one asks the question simply, he adds the

10 contradictories, he is not answering the question. For there

is nothing to prevent the same thing from being both a man

and white and countless other things : but still, if one asks

whether it is or is not true to say that this is a man, our

opponent must give an answer which means one thing, and

not add that it is also white and large . For, besides other

reasons, it is impossible to enumerate its accidental attri-

15 butes, which are infinite in number;

let him, then,

enumerate either all or none. Similarly, therefore, even if

the same thing is a thousand times a man and a not-man,

he must not, in answering the question whether this is a

man, add that it is also at the same time a not-man, unless

he is bound to add also all the other accidents, all that the

subject is or is not;and if he does this, he is not observing

the rules of argument.2

20 And in general those who say this do away with sub

stance andessence.

For theymust

saythat all attributes

are accidents, and that there is no such thing as being

essentially a man or* an animal . For if there is to be

any such thing as being essentially a man this will not be

being a not-man or not being a man (yet these are

25 negations of it3

) ;for there was one thing which it meant,

and this was the substance of something. And denoting

the substance of a thing means that the essence of the thing

is nothing else. But if its being essentially a man is to be

the same as either being essentially a not-man or essentially

not being a man, then its essence will be something else.

Therefore our opponents must say that there cannot be

1 ioo6b i7.

2 With ioo6a i8-ioo;a 20 cf. K. 1062* 5-20 (with ioo6b 28-34 cf.

1062* 20-3).3Sc. and hence (on the view attacked) should be compatible with it.



BOOK T. 4 ioo7a

such a definition of anything, but that all attributes are 30

accidental;for this is the distinction between substance and

accident white is accidental to man, because though he

is

white,whiteness is not his essence. But if all statements

are accidental, there will be nothing primary about which

they are made, if the accidental always implies predication 35

about a subject. The predication, then, must go on ad in- ioo7b

finitum. But this is impossible ;for not even more than two

terms can be combined in accidental predication. For (i)

an accident is not an accident of an accident, unless it be

because both are accidents of the same subject. I mean,for instance, that the white is musical and the latter is white,

only because both are accidental to man. But(2) Socrates 5

is musical, not in this sense, that both terms are accidental

to something else. Since then some predicates are acci

dental in this and some in that sense, (a) those which are

accidental in the latter sense, in which white is accidental to

Socrates, cannot form an infinite series in the upward direc

tion;

1e. g. Socrates the white has not yet another acci

dent;for no unity can be got out of such a sum. Nor 10

again (b) will*

white have another term accidental to it,

e. g.*

musical . For this is no more accidental to that than

that is to this;and at the same time we have drawn the

distinction, that while some predicates are accidental in this

sense, others are so in the sense in which musical is acci

dental to Socrates;and the accident is an accident of an

accident not in cases of the latter kind, but only in cases of T 5

the other kind, so that not all terms will be accidental.2

There must, then, even so be something which denotes sub

stance. And if this is so, it has been shown that contra

dictoriescannot

bepredicated

at thesame time.

Again, if all contradictory statements are true of the

same subject at the same time, evidently all things will be

one. For the same thing will be a trireme, a wall, and a 20

man, if ofeverything it is possible either to affirm or to deny

1i. e. in the direction of predicates, which are naturally wider or

higher than the subject.2

Sense (i) reduces to sense (2), and in this an infinite number ofaccidents combined together is impossible ;

there must be substance

somewhere.



ioo7b METAPHYSICA

anything (and this premiss must be accepted by those who

share the views of Protagoras). For if any one thinks that

the man is not a trireme, evidently he is not a trireme;so

that he also is a trireme, if, as they say, contradictory

25 statements are both true. And we thus get the doctrine of

Anaxagoras,1that all things are mixed together ;

so that

nothing really exists. They seem, then, to be speaking of

the indeterminate, and, while fancying themselves to be

speaking of being, they are speaking about non-being ;for

it is that which exists potentially and not in complete

reality

that is indeterminate. Butthey

mustpredicate

of

every subject the affirmation or the negation of every attri-

3 bute. For it is absurd if of each subject its own negation

is to be predicable, while the negation of something else

which cannot be predicated of it is not to be predicable of

it;for instance, if it is true to say of a man that he is not

a man, evidently it is also true to say that he is either a

trireme or not a trireme. If, then, the affirmative2

can be35 predicated, the negative must be predicable too

;and if the

affirmative is not predicable, the negative, at least, will be

ioo8a more predicable than the negative of the subject itself. If,

then, even the latter negative is predicable, the negative of

*

trireme will be also predicable ; and, if this is predicable,

the affirmative will be so too.3

Those, then, who maintain this view are driven to this

conclusion, and to the further conclusion that it is not

necessary either to assert or to deny. For if it is true

5 that a thing is a man and a not-man, evidently also it will be

neither a man nor a not-man. For to the two assertions

there answer two negations, and if the former 4is treated as

asingle proposition compounded

out oftwo,

the latter also

is a single proposition opposite to the former.5

Again, either the theory is true in all cases, and a thing

is both white and not-white, and existent and non-existent,

and all other assertions and negations are similarly com-

1Fr. i.

2Sc. trireme .

8 With ico7b i8-ioo8a 2 cf. K. io62a

23-30.4Sc. that the thing is a man and a not-man.

5 With 11. 6-7 cf. K. io62a 36-b

;.



BOOK T. 4 ioo8a

patible, or the theory is true of some statements and not of 10

others. And if not of all, the exceptions will be contradic

tories of which admittedly only one is true;but if of all,

again

either the

negation

will be true wherever the asser

tion is, and the assertion true wherever the negation is, or

the negation will be true where the assertion is, but the

assertion not always true where the negation is. And (a) 15

in the latter case there will be something which fixedly

zs not, and this will be an indisputable belief;and if non-

being is something indisputable and knowable, the oppo

site assertion will be more knowable. But (6) if it is equally

possible also to assert all that it is possible to deny, one must

either be saying what is true when one separates the pre

dicates (and says, for instance, that a thing is white, arid

again that it is not-white), or not. And if(i)

it is not true 2

to apply the predicates separately, our opponent is not say

ing what he professes to say, and also nothing at all exists;

but how could non-existent things speak or walk, as he

does ? Also all things would on this view be one, as has

been already said,1 and man and God and trireme and their

contradictories will be the same. For if contradictories can 25

be predicated alike of each subject, one thing will in no

wise differ from another;for if it differ, this difference will

be something true and peculiar to it. And(ii)

ifone maywith truth apply the predicates separately, the above-

mentioned result follows none the less, and, further, it

follows that all would then be right and all would be in

error, and our opponent himself confesses himself to be in

error. And at the same time our discussion with him is 30

evidently about nothing at all;for he says nothing. For

hesays

neither

yes

nor no,but

yesand no

;and

again he denies both of these and says neither yes nor

no;

for otherwise there would already be something

definite.

Again, it when the assertion is true, the negation is false,

and when this is true, the affirmation is false, it will not be 35

possible to assert and deny the same thing truly at the same

1 ioc6b 17, ioo7a6.



ioo8b METAPHYSICA

ioo8btime. But perhaps they might say this was the very ques

tion at issue.

Again, is he in error who judges either that the thing is

so or that it is notso,

and is heright

whojudges

both ? If

he is right, what can they mean by saying that the nature

5 of existing things is of this kind ? And if he is not right,

but more right than he who judges in the other way, being

will already be of a definite nature, and this will be true,

and not at the same time also not true. But if all are alike

both wrong and right, one who is in this condition will not

be able either to speak or to say anything intelligible ; for

10 he says at the same time both yes and no . And if he

makes no judgement but*

thinks and 4

does not think,in

differently, what difference will there be between him and

a vegetable? Thus, then, it is in the highest degree evident

that neither any one of those who maintain this view nor

any one else is really in this position. For why does a

man walk to Megara and not stay at home, when he thinks

J 5 he ought to be walking there? Why does he not walk

early some morning into a well or over a precipice, if one

happens to be in his way ? Why do we observe him

guarding against this, evidently because he does not think

that fallingin is alike good and not good ? Evidently, then,

hejudges

onething

to be better and another worse. And

if this is so, he must also judge one thing to be a man and

20 another to be not-a-man, one thing to be sweet and another

to be not-sweet. For he does not aim at and judge all

things alike, when, thinking it desirable to drink water or

to see a man, he proceeds to aim at these things ; yet he

ought, if the same thing were alike a man and not-a-man.

But, as was said, there is no one who does not obviously2 5 avoid some things and not others. Therefore, as it seems,

all men make unqualifiedjudgements, if not about all things,

still about what is better and worse.1 And if this is not

knowledge but opinion, they should be all the more anxious

about the truth, as a sick man should be more anxious about

30 his health than one who is healthy ;for he who has opinions

1 With 11. 12-27 cf. K. io63a28-35.



BOOK T. 4 ioo8fc

is, in comparison with the man who knows, not in a healthy

state as far as the truth is concerned.

Again, however much all things may be so and not so,

still there is a more and a less in the nature of things;

for

we should not say that two and three are equally even, nor

is he who thinks four things are five equally wrong with

him who thinks they are a thousand. If then they are not 35

equally wrong, obviously one is less wrong and therefore

more right. If then that which has more of any quality is

nearer the norm, there must be some truth to which the 1009*

more true is nearer. And even if there is not, still there is

already something better founded and liker the truth, and

we shall have got rid ofthe unqualified doctrine which would

prevent us from determining anything in our thought. 5

5 From the same opinion proceeds the doctrine of Prota

goras, and both doctrines must be alike true or alike untrue.

For on the one hand, if all opinions and appearances are

true, all statements must be at the same time true and false.

For many men hold beliefs in which they conflict with one

another, and think those mistaken who have not the same 10

opinions as themselves;so that the same thing must both

be and not be. And on the other hand, if this is so, all

opinions must be true;for those who are mistaken and

those who are right are opposed to one another in their

opinions ;if then, reality is such as the view in question

supposes, all will be right in their beliefs.

Evidently, then, both doctrines proceed from the same 15

way of thinking. But the same method of discussion must

not be used with all opponents; for some need persuasion,

and others compulsion. Those who have been driven to

this position by difficulties in their thinking can easily be

cured of their ignorance ;for it is not their expressed argu

ment but their thought that one has to meet. But those 20

who argue for the sake of argument can be cured only by

refuting the argument as expressed in speech and in words.1

Those who really feel the difficulties have been led to

this

opinion byobservation of the sensible world,

(i) They1 With 11. 16-22 cf. K. io6s

b7-i6.



ioo9a METAPHYSICA

think that contradictories or contraries are true at the same

time, because they see contraries coming into existence out

25 of the same thing1

. If, then, that which is not cannot come

to be, the thing must have existed before as both contraries

alike, as Anaxagoras says all is mixed in all, and Demo-

critus too;

for he says the void and the full exist alike in

every part, and yet one of these is being, and the other

30 non-being.1 To those, then, whose belief rests on these

grounds, we shall say that in a sense they speak rightly and

in a sense they err. For *

that which is has two meanings,

so that in some sense a thing can come to be out of that

which is not, while in some sense it cannot, and the same

thing can at the same time be in being and not in being

but not in the same respect. For the same thing can be

35 potentially at the same time two contraries, but it cannot

actually.2 And again we shall ask them to believe that

among existing things there is also another kind of sub

stance to which neither movement nor destruction nor

generation at all belongs.

ioo9b And (2) similarly some have inferred from observation

of the sensible world the truth of appearances. For they

think that the truth should not be determined by the large

or small number of those who hold a belief, and that the

same thing is thought sweet by some when they taste it,

5 and bitter by others, so that if all were ill or all were mad,

and only two or three were well or sane, these would be

thought ill and mad, and not the others.

And again, they say that many of the other animals

receive impressions contrary to ours;and that even to the

senses of each individual, things do not always seem the

same. Which, then, of these impressions are true and10 which are false is not obvious; for the one set is no more

true than the other, but both are alike. And this is why

Democritus, at any rate, says that either there is no truth or

to us at least it is not evident.

And in general it is because these thinkers suppose

knowledge

to be sensation, and this to be a physical altera-

1 With 11. 6-1 6, 22-30 cf. K. io62b 12-24.2 With 11. 30-6 cf. K. 1062*24-33.



BOOK T. 5 ioo9b

tion, that they say that what appears to our senses must be

true;for it is for these reasons that both Empedocles and 1

5

Democritus and, one may almost say, all the others have

fallen victims to opinions of this sort. For Empedoclessays that when men change their condition they change

their knowledge ;

For wisdom increases in men according to what is before

them. 1

And elsewhere he says that

Sofar

as their nature changed, so far to them always20

Came changed thoughts into mind. 2

And Parmenides also expresses himself in the same way :

For as at each time the much-bent limbs are composed,So is the mind of men

;for in each and all men

Tis one thing thinks the substance of their limbs :

For that of which there is more is thought.:i

A saying of Anaxagoras to some of his friends is also 25

related, that things would be for them such as they sup

posed them to be. And they say that Homer also evidently

had this opinion, because he made Hector, when he was

unconscious from the blow, lie*

thinking other thoughts ,

4

which implies that even those who are bereft of thought 30

havethoughts, though

not the samethoughts. Evidently,

then, if both are forms of knowledge, the real things also

are at the same time both so and not so V5 And it is in this

direction that the consequences are most difficult. For if

those who have seen most of such truth as is possible for us

(and these are those who seek and love it most) if these35

have such opinions and express these views about the truth,

isit not natural that beginners in philosophy should lose

heart ? For to seek the truth would be to follow flying

game.

But the reason why these thinkers held this opinion is ioioa

that while they were inquiring into the truth of that which

is, they thought that which is was identical with the

1

Fr. 106.2

Fr. 108.3

Fr. 16.*

Cf. //. xxiii. 698, which does not, however, refer to Hector.6 With a

38-b33 cf. K. 1063* 35~

b7.



ioa METAPHYSICA

sensible world;

in this, however, there is largely present

the nature of the indeterminate of that which exists in the

peculiar sense which we have explained ;

1 and therefore,

while they speak plausibly, they do not say what is true

5 (for it is fitting to put the matter so rather than as Epichar-

musput it against Xenophanes2

;.And again, because they

saw that all this world of nature is in movement, and that

about that which changes no true statement can be made,

they said that ofcourse, regarding that which everywhere in

every respect is changing, nothing could truly be affirmed.

10 It was this belief that blossomed into the most extreme of

the views above mentioned, that of the professed Hera-

cliteans, such as was held by Cratylus, who finally did not

think it right to say anything but only moved his finger,

and criticized Heraclitus for saying that it is impossible to

step twice into the same river;

3for he thought one could

not do it even once.

J 5 But we shall say in answer to this argument also, that

while there is some justification for their thinking that the

changing, when it is changing, does not exist, yet it is after

all disputable ;for that which is losing a quality has some

thing of that which is being lost, and of that which is

coming to be, something must already be. And in general

if a thing is perishing, there will be present something that20 exists

;and if a thing is coming to be, there must be some

thing from which it comes to be and something by which

it is generated, and this process cannot go on ad infinitum.

But, leaving these arguments, let us insist on this, that it is

not the same thing to change in quantity and in quality.

Grant that in quantity a thing is not constant;

still it is in

25 respect of its form that we know each thing.4 And again,

it would be fair to criticize those who hold this view for

asserting about the whole material universe what they saw

only in a minority even of sensible things. For only that

region of the sensible world which immediately surrounds

1Cf. ioo9

a32.

2Fr.

252

Kaibel.

Epicharmus mayhave said that Xenophanes

views were neither plausible nor true,or that they were true but

not plausible .

3Fr. 91.

4 With 11. 22-5 cf- K . io63a 22-8.



BOOK r. 5 ioioa

us is always in process of destruction and generation ;but 3

this is so to speak not even a fraction of the whole, so

that it would have been juster to acquit this part of the

world because of the other part, than to condemn the other

because of this.1 And again, obviously we shall make to

them also the same reply that we made long ago ;

2 we

must show them and persuade them that there is something

whose nature is changeless. Indeed, those who say that 35

things at the same time are and are not, should in conse

quence say that all things are at rest rather than that they

are in movement;for there is nothing into which they can

change, since all attributes belong already to all subjects.

Regarding the nature of truth, we must maintain that not ioiob

everything which appears is true; firstly, because even if

sensation at least of the object peculiar to the sense in

question is not false, still appearance is not the same as

sensation.

Again,

it is fair to

express surprise

at our

opponents raising the question whether magnitudes are as

great, and colours are of such a nature, as they appear to 5

people at a distance, or as they appear to those close at

hand, and whether they are such as they appear to the

healthy or to the sick, and whether those things are heavy

which appear so to the weak or those which appear so to

the strong, and those things true which appear to the

sleeping or to the waking. For obviously they do not

think these to be open questions ;no one, at least, if when 10

he is in Libya he has fancied one night that he is in Athens,

starts for the concert hall. And again with regard to the

future, as Plato says,3

surely the opinion of the physician

and that of the ignorant man are not equally weighty, for

instance, on the question whether a man will get well or

not. And again, among sensations themselves the sensa- 15

tion of a foreign object and that of the appropriate object,

or that of a kindred object and that of the object of the

sense in question,4 are not equally authoritative, but in the

1 With 11. 25-32 cf. K. 1063* 10-17.2

Cf. 1009*36-8. 3 Cf. Theaetetus 178 6-179 A.4

E.g. the awareness which smell gives us of savour and of odour

respectively.



ioiob METAPHYSICA

case of colour sight, not taste, has the authority, and in

the case of flavour taste, not sight ;each of which senses

never says at the same time of the same object that it

simultaneously is so and not so.

But not even at different

20 times does one sense disagree about the quality, but only

about that to which the quality belongs. I mean, for

instance, that the same wine might seem, if either it or one s

body changed, at one time sweet and at another time not

sweet;but at least the sweet, such as it is when it exists,

25has never yet changed, but one is always right about it, and

that which is to be sweet is of necessity of such and such

a nature.1 Yet all these views destroy this necessity, leaving

nothing to be of necessity, as they leave no essence of

anything ;for the necessary cannot be in this way and also

in that, so that if anything is of necessity, it will not be both

so and not so .

3o And,in

general,if

onlythe sensible

exists,

there would

be nothing if animate things were not;for there would be

no faculty of sense. Now the view that neither the sensible

qualities nor the sensations would exist is doubtless true

(for they are affections of the perceiver), but that the sub

strata which cause the sensation should not exist even apart

35 from sensation is impossible. For sensation is surely not

the sensation of itself, but there is something beyond the

sensation, which must be prior to the sensation;for that

ionawhich moves is prior in nature to that which is moved, and

if they are correlative terms, this is no less the case.

There are, both among those who have these convictions 6

and among those who merely profess these views, some who

5 raise a difficulty by asking, who is to be the judge of the

healthy man, and in general who is likely to judge rightly

on each class of questions. But such inquiries are like

puzzling over the question whether we are now asleep or

awake. And all such questions have the same meaning.

These people demand that a reason shall be given for

everything;

2for they seek a starting-point, and they seek

1 With 11. 1-26 cf. K. io62b 33-io63aio.

2 The reference may be to Antisthenes.



BOOK T. 6 ion*

to get this by demonstration, while it is obvious from their 10

actions that they have no conviction. But their mistake is

what we have stated it to be; they seek a reason for things

for which no reason can be given ; for the starting-point of

demonstration is not demonstration.

These, then, might be easily persuaded of this truth, for

it is not difficult to grasp ;but those who seek merely 15

compulsion in argument seek what is impossible ;for they

demand to be allowed to contradict themselves a claim

which contradicts itself from the very first.1 But if not all

things are relative, but some are self-existent, not every

thing that appears will be true;for that which appears is

apparent to some one ; so that he who says all things that

appear are true, makes all things relative. And, therefore, 20

those who ask for an irresistible argument, and at the same

time demand to be called to account for their views, must

guard themselves by saying that the truth is not that what

appears exists, but that what appears exists for him to

whom it appears, andw/ien, and to the sense to which^ and

under the conditions under which it appears. And if they

give an account of their view, but do not give it in this way,

they will soon find themselves contradicting themselves.

For it is possible that the same thing may appear to be 25

honey to the sight, but not to the taste, and that, since wehave two eyes, things may not appear the same to each,

if their sight is unlike. For to those who for the reasons

named some time ago2

say that what appears is true, and 30

therefore that all things are alike false and true, for things

do not appear either the same to all men or always the same

to the same man, but often have contrary appearances at

the same time (for touch says there are two objects whenwe cross our fingers, while sight says there is one),

3to

these we shall say yes, but not to the same sense and in

the same part of it and under the same conditions and at 35

the same time,so that what appears will be with these

qualifications true. But perhaps for this reason those who ionb

argue thus not because they feel a difficulty but for the sake

1 With 11. 3-16 cf. K. 1063*7-16.a

Cf. ioo9a38-ioio

a15.

3 With 11. 31-4 cf. K. io62b 33-io63a 10.



IOIIb METAPHYSICA

of argument, should say that this is not true, but true for

this man. And as has been said x

before, they must make

5 everything relative relative to opinion and perception, so

that nothing either has come to be or will be without someone s first thinking so. But if things have come to be or

will be,2

evidently not all things will be relative to opinion.

Again, if a thing is one, it is in relation to one thing or to

a definite number of things; and if the same thing is both

half and equal, it is not to the double that the equal is corre

lative.3

If, then, in relation to that which thinks, man and

10 that which is thought are the same, man will not be that

which thinks, but only that which is thought. And if each

thing is to be relative to that which thinks, that which

thinks will be relative to an infinity of specifically different

things.

Let this, then, suffice to show (i) that the most indis

putableof all beliefs is that

contradictorystatements are

not at the same time true, and (2) what consequences follow

from the assertion that they are, and(3) why people do

15 assert this. Now since it is impossible that contradictories

should be at the same time true ofthe same thing, obviously

contraries also cannot belong at the same time to the same

thing. For of contraries, one is a privation no less than it

is a contrary and a privation of the essential nature ; and

privation is the denial of a predicate to a determinate genus.

20 If, then, it is impossible to affirm and deny truly at the same

time, it is also impossible that contraries should belong to

a subject at the same time, unless both belong to it in par

ticular relations, or one in a particular relation and one

without qualification.4

But on the other hand there cannot be an intermediate 7

between contradictories, but of one subject we must either

25 affirm or deny any one predicate. This is clear, in the first

place, if we define what the true and the false are. To say

of what is that it is not, or of what is not that it is, is false,

2Sc. without some one s first thinking so.

3Sc. but the equal to the equal, the half to the double.

4 With 11. 17-22 cf. K. io63b17-19-



BOOK r. 7 ionb

while to say of what is that it is, and of what is not that it

is not, is true;so that he who says of anything that it is, or

that it is not, will say either what is true or what is false;

but neither what is nor what is not is said to be or not to

be.1

Again, the intermediate between the contradictories

will be so either in the way in which grey is between black 3o

and white,2 or as that which is neither man nor horse is

between man and horse, (a) If it were of the latter kind,

it could not change into the extremes (for change is from

not-good to good, or from good to not-good), but as

a matter of fact when there is an intermediate it is always

observed to change into the extremes. For there is no change

except to opposites3 and to their intermediates.

(<5)

But if it 35

is really intermediate,4 in this way too there would have to be

a change to white, which was not from not-white;but as it

is, this is never seen. Again, every object of understanding ioi2a

or reason the understanding either affirms or denies this is

obvious from the definition whenever it says what is true

or false. When it connects in one way by assertion or nega

tion, it says what is true, and when it does so in another way,

what is false. Again, there must be an intermediate between 5

// contradictories, if one is not arguing merely for the sake

of argument ;so that it will be possible for a man to say

what is neither true noruntrue,

and there will be a middle

between that which is and that which is not, so that there

will also be a kind of change intermediate between genera

tion and destruction. Again, in all classes in which the

negation of an attribute involves the assertion of its con

trary, even in these there will be an intermediate;

for 10

instance, in the sphere of numbers there will be number

which is neither odd nor not-odd. But this is impossible,

as is obvious from the definition. Again, the process will

go on ad infinitum, and the number of realities will be

1Sc. by those who say there is an intermediate between contradic

tories. Hence such a statement is neither true nor false, which is

absurd.2

Though of course it differs from this case in being between con

tradictories,not contraries.

3Sc. contrary, not contradictory opposites.

4Sc. as grey is between black and white.



ioi2a METAPHYSICA

not only half as great again, but even greater. For again

it will be possible to deny this intermediate with reference

both to its assertion and to its negation,1 and this new term

will be some definite

thing;for its essence is

something15 different. Again, when a man, on being asked whether

a thing is white, says4 no

,he has denied nothing except

that it is;and its not being is a negation.

Some people have acquired this opinion as other para

doxical opinions have been acquired ;when men cannot

refute eristical arguments, they give in to the argument and

20 agree that the conclusion is true. This, then, is why someexpress this view

;others do so because they demand

a reason for everything.2 And the starting-point in dealing

with all such people is definition. Now the definition rests

on the necessity of their meaning something ;for the form

of words ofwhich the word is a sign will be its definition.3

While the doctrine of Heraclitus, that all things are and are

25 not, seems to make everything true, that of Anaxagoras,

that there is an intermediate between the terms of a contra

diction, seems to make everything false;for when things

are mixed, the mixture is neither good nor not-good, so

that one cannot say anything that is true.

In view of these distinctions it is obvious that the one- 8

30 sided theories which some people express about all things

cannot be valid on the one hand the theory that nothing

is true (for, say they, there is nothing to prevent every

statement from being like the statement the diagonal of

a square is commensurate with the side),on the other hand

the theory that everything is true. These views are practi

cally the same as that of Heraclitus;for he who says that

35l

all things are true and all are false also makes each of

1012 these statements separately, so that since they are impos

sible, the double statement must be impossible too. Again,

there are obviously contradictories which cannot be at the

same time truenor on the other hand can all statements

1i. e. if there is a term B which is neither A nor not-A, there will

be a new term C which is neither B nor not-jS*.2 The reference may be to Antisthenes.5 With ionb

23-loi2a24 cf. K. io63

b19-24.



BOOK P. 8 ioi2b

be false; yet this would seem more possible in the light of

what has been said. But against all such views we must5

postulate, as we said above,1 not that something is or is

not, but that something has a meaning, so that we must

argue from a definition, viz. by assuming what falsity or

truth means. If that which it is true to affirm is nothing

other than that which it is false to deny, it is impossible

that all statements should be false;for one side of the con- 10

tradiction must be true. Again, if it is necessary with

regard to everything either to assert or to deny it,it is

impossible that both should be false;for it is one side of

the contradiction that is false. Therefore all such views

are also exposed to the often expressed objection, that they

destroy themselves. For he who says that everything is I 5

true makes even the statement contrary to his own true,

and therefore his own not true (for the contrary statement

denies that it is true), while he who says everything is false

makes himself also false.2 And if the former person excepts

the contrary statement, saying it alone is not true, while

the latter excepts his own as being not false, none the less 20

they are driven to postulate the truth or falsity ofan infinite

number ofstatements;for that which says the true statement

is true is true, and this process will go on to infinity.

Evidently, again,those

who sayall

thingsare at rest are

not right, nor are those who say all things are in move

ment. For if all things are at rest, the same statements

will always be true and the same always false, but this

obviously changes ;for he who makes a statement, himself 25

at one time was not and again will not be. And if all

things are in motion, nothing will be true; everything

therefore will be false. But it has been shown that this is

impossible. Again, it must be that which is that changes;

for change is from something to something. But again

it is not the case that all things are at rest or in motion

sometimes, and nothing for ever;for there is something 30

which always moves the things that are in motion, and the

first mover is itself unmoved.

1Cf. ioo6a 18-22.

2 With a24-

b 18 cf. K. io63b24-35 (with

b13-18 cf. io62b 7-9).

G 2



BOOK A

4 BEGINNING means(i) that part of a thing from which i

35 one would start first, e. g. a line or a road has a beginning

ioi3ain either of the contrary directions. (2) That from which

each thing wrould best be originated, e. g. even in learning

we must sometimes begin not from the first point and the

beginning of the subject, but from the point from which we

should learn most easily. (3) That from which, as an

immanent part, a thing first comes to be, e. g. as the keel

5 of a ship and the foundation of a house, while in animals

some suppose the heart, others the brain, others some other

part, to be of this nature. (4) That from which, not as an

immanent part, a thing first comes to be, and from which

the movement or thechange naturally

first

begins,as a

child comes from its father and its mother, and a fight

10 from abusive language. (5) That at whose will that which

is moved is moved and that which changes changes, e. g.

the magistracies in cities, and oligarchies and monarchies

and tyrannies, are called apxafV and so are tne arts&

and of

these especially the architectonic arts. (6) That from which

15 a thing can first be known, this also is called the beginning

of the thing, e. g. the hypotheses are the beginnings of

demonstrations. (Causes are spoken of in an equal number

of senses;for all causes are beginnings.) It is common,

then, to all beginnings to be the first point from which

a thing either is or comes to be or is known;but of these

some are immanent in the thing and others are outside.

20 Hence the nature of a thing is a beginning, and so is the

element of a thing, and thought and will, and essence, and

the final cause for the good and the beautiful are the

beginning both of the knowledge and of the movement of

many things.

Cause means (i)that from which, as immanent 2

1 The double meaning of apxn beginning and government-

cannot be reproduced in English.



BOOK A. 2 ioi3a

material, a thing comes into being, e. g. the bronze is the 25

cause of the statue and the silver of the saucer, and so are

the classes which include these. (2) The form or pattern,

i.

e. the definition of the essence, and the classes whichin

clude this (e. g. the ratio 2 : i and number in general are

causes of the octave), and the parts included in the definition.

(3) That from which the change or the resting from change

first begins ;e. g. the adviser is a cause of the action, and 3

the father a cause of the child, and in general the maker

a cause of the thing made and the change-producing of the

changing. (4) The end, i. e. that for the sake of which a

thing is;

e. g. health is the cause of walking. For Whydoes one walk ? we say ;

that one may be healthy ;and

in speaking thus we think we have given the cause. The 35

same is true of all the means that intervene before the end,

when something else has put the process in motion, as e. g.

thinning or purging or drugs or instruments intervene

before health is reached;for all these are for the sake of

the end, though they differ from one another in that some

are instruments and others are actions.

These, then, are practically all the senses in which causes

are spoken of, and as they are spoken of in several senses

it follows both that there are several causes of the same 5

thing,

and in no accidental sense(e. g. both the art of

sculpture and the bronze are causes of the statue not in respect

of anything else but qua statue; not, however, in the same

way, but the one as matter and the other as source of the

movement), and that things can be causes of one another

(e.g. exercise of good condition, and the latter of exercise;

not, however, in the same way, but the one as end and the 10

other as source of movement). Again, the same thing is

the cause of contraries;for that which when present causes

a particular thing, we sometimes charge, when absent, with

the contrary, e. g. we impute the shipwreck to the absence

of the steersman, whose presence was the cause of safety 5

and both the presence and the privation are causes as 15

sources of movement.

All the causes now mentioned fall under four senses

which are the most obvious. For the letters are the cause



ioi3b METAPHYSICA

of syllables, and the material is the cause of manufactured

things, and fire and earth and all such things are the causes of

bodies, and the parts are causes of the whole, and the hypo-20 theses are causes of the conclusion, in the sense that they are

that out of which these respectively are made;but of these

some are cause as the siibstratum (e. g. the parts), others as

the essence (the whole, the synthesis, and the form). The

semen, the physician, the adviser, and in general the agent,

25 are all soiirces of change or of rest. The remainder are

causes as the end and the good of the other things ;for that

for the sake of which otherthings

are tends to be the best

and the end of the other things ;let us take it as making

no difference whether \ve call it good or apparent good.

These, then, are the causes, and this is the number of

their kinds, but the varieties of causes are many in number,

though when summarized these also are comparatively few.

30 Causes are spoken of in many senses, and even of those

which are of the same kind some are causes in a prior andothers in a posterior sense, e. g. both the physician and

the professional man are causes of health, and both the ratio

2:1 and number are causes of the octave, and the classes

that include any particular cause are always causes of the

particular effect. Again, there are accidental causes and

35 the classes which include these;

e. g. while in one sense

the sculptor causes the statue, in another sense*

Poly-

clitus causes it, because the sculptor happens to be

ioi4aPolyclitus ;

and the classes that include the accidental

cause are also causes, e. g. man or in general animal

is the cause of the statue, because Polyclitus is a man, and

man is an animal. Of accidental causes also some are more

5

remote or nearer thanothers, as,

forinstance,

if the white

and *

the musical were called causes of the statue, and not

only Polyclitus or man . But besides all these varieties

of causes, whether proper or accidental, some are called

causes as being able to act, others as acting ;e. g. the cause

of the house s being built is a builder, or a builder who is

10 building. The same variety of language will be found with

regard to the effects of causes ; e. g. a thing may be called

the cause of this statue or of a statue or in general of an



BOOK A. 2 ioi4a

image, and of this bronze 1 or of bronze or of matter in

general ;and similarly in the case of accidental effects.

Again, both accidental and proper causes may be spoken of

incombination

;

e.

g. we may saynot

Polyclitusnor the

sculptor ,but *

Polyclitus the sculptor .

Yet all these are but six in number, while each is spoken 15

of in two ways ;for (A) they are causes either as the indi

vidual, or as the genus, or as the accidental, or as the genus

that includes the accidental, and these either as combined,2

or as taken simply ;and (B) all may be taken as acting or

as having a capacity. But they differ inasmuch as the act- 20

ing causes, i. e. the individuals, exist, or do not exist, simul

taneously with the things of which they are causes, e. g.

this particular man who is healing, with this particular man

who is recovering health, and this particular builder with

this particular thing that is being built;but the potential

causes are not always in this case;for the house does not

perish at the same time as the builder.325

3 Element means(i) the primary component immanent

in a thing, and indivisible in kind into other kinds;

e. g.

the elements of speech are the parts of which speech con

sists and into which it is ultimately divided, while they are

no longer divided into other forms of speech different in

kind from them. If they are divided, their parts are of the 30

same kind, as a part of water is water (while a part of the

syllable is not a syllable). Similarly those who speak of

the elements of bodies mean the things into which bodies

are ultimately divided, while they are no longer divided into

other things differing in kind;and whether the things of

this sort are one ormore, they

call these elements. The 35

so-called elements of geometrical proofs, and in general the

elements of demonstrations, have a similar character;

for

the primary demonstrations, each of which is implied in

many demonstrations, are called elements of demonstra- ioi4b

1 For this way of speaking cf. Phys. II. I94a33.

2Sc. the

particular propercause with the

particular accidental,or

the general proper with the general accidental.J With this chapter cf. Phys. I94

b23-I95

b 21.



ioi4b METAPHYSICA

tions;and the primary syllogisms, which have three terms

and proceed by means of one middle, are of this nature.

(2) People also transfer the word element from this

meaningand

applyit to that

which, beingone and

small,5 is useful for many purposes ;

for which reason what is small

and simple and indivisible is called an element. Hence

come the facts that the most universal things are elements

(because each of them being one and simple is present in

a plurality of things, either in all or in as many as possible *),

and that unity and the point are thought by some to be

first principles. Now, since the so-called genera are

universal and indivisible (for there is no definition of them),10 some say the genera are elements, and more so than the

differentia, because the genus is more universal;for where

the differentia is present, the genus accompanies it, but

where the genus is present, the differentia is not always so.

It is common to all the meanings that the element of each

15 thing is the first component immanent in each.

*

Nature means (i) the genesis of growing things the 4

meaning which would be suggested if one were to pro

nounce the v infyva-is long.

2

(2) That immanent part of a

growing thing, from which its growth first proceeds. (3) The

source from which the primary movement in each natural

20 object is present in it in virtue of its own essence. Those

things are said to grow which derive increase from some

thing else by contact and either by organic unity, or by

organic adhesion as in the case of embryos. Organic unity

differs from contact;for in the latter case there need not

be anything besides the contact, but in organic unities

there is

somethingidentical in both

parts,which makes

3 5 them grow together instead of merely touching, and be one

in respect of continuity and quantity, though not ofquality.

(4)*

Nature means the primary material of which any

natural object consists or out of which it is made, which is

1

TJon 7r\i(TTois shows that A. is not thinking of the strict universals

of science but of the rough generalizations of dialectic. Cf. the use of

o-TOLXfiov in the Topics , and Diels, Elementum, p. 29.2This (i. e. growth )

is the etymological sense of(frvo-is.

to grow ,has v long in most of its forms.



BOOK A. 4 ioi4b

relatively unshaped and cannot be changed from its own

potency, as e. g. bronze is said to be the nature of a statue

and of bronze utensils, and wood the nature of wooden

things ;

and so in all other cases ; for when a product is 3

made out of these materials, the first matter is preserved

throughout. For it is in this way that people call the

elements of natural objects also their nature, some naming

fire, others earth, others air, others water, others something

else of the sort, and some naming more than one of these,

and others all of them. (5)Nature means the essence of 35

natural objects, as with those who say the nature is the

primary mode of composition, or as Empedocles1

says :

Nothing that is has a nature, ioi5a

But only mixing and parting of the mixed,

And nature is but a name given them by men.

Hence as regards the things that are or come to be by

nature, though thatfrom which they naturally come to beor are is already present, we say they have not their nature

yet, unless they have their form or shape. That which 5

comprises both of these2exists by nature, e. g. the animals

and their parts ;and not only is the first matter nature

(and this in two senses, either the first, counting from the

thing, or the first in general ;e. g. in the case of works in

bronze, bronze is first with reference to them, but in general

perhaps water is first, if all things that can be melted are

water), but also the form or essence, which is the end of the 10

process of becoming. (6) By an extension ofmeaning from

this sense of nature every essence in general has come to

be called a nature,because the nature of a thing is one

kind of essence.

From what has been said, then, it is plain that nature in

the primary and strict sense is the essence of things which

have in themselves, as such, a source of movement;for the 15

matter is called the nature because it is qualified to receive

this, and processes of becoming and growing are called

nature because they are movements proceeding from this.

And nature in this sense is the source of the movement of1Fr. 8.

2Matter and form.



ioi5a METAPHYSICA

natural objects, being present in them somehow, either

potentially or in complete reality.

20 We call necessary (i) (a) that without which, as a con- 5

dition, a thing1

cannot live;

e. g. breathing and food are

necessary for an animal;for it is incapable of existing with

out these; (6) the conditions withoutwhich goodcannot be or

come to be, or without which we cannot get rid or be freed

of evil;

e. g. drinking the medicine is necessary in order

25 that we may be cured of disease, and a man s sailing to

Aeginais

necessaryin order that he

may gethis

money.(2) The compulsory and compulsion, i. e. that which im

pedes and tends to hinder, contrary to impulse and pur

pose. For the compulsory is called necessary (whence the

necessary is painful, as Evenus l

says : For every necessary

30 thing is ever irksome),and compulsion is a form of neces

sity, as Sophocles2

says : But force necessitates me to this

act. And necessity is held to be something that cannot be

persuaded and rightly, for it is contrary to the movement

which accords with purpose and with reasoning. (3) We

say that that which cannot be otherwise is necessarily as it

35 is. And from this sense of necessary all the others are

somehow derived;for a thing is said to do or suffer what

ioi5b

is necessary in the sense of compulsory, only when it can

not act according to its impulse because of the compelling

force, which implies that necessity is that because of which

a thing cannot be otherwise;and similarly as regards the

conditions of life and of good ;for when in the one case

5 good, in the other life and being, are notpossible without cer

tain conditions, these are necessary, and this kind of cause

is a sort ofnecessity. Again,

demonstration is a neces

sary thing because the conclusion cannot be otherwise, if

there has been demonstration in the unqualified sense;and

the causes of this necessity are the first premisses, i.e. the

fact that the propositions from which the syllogism proceeds

cannot be otherwise.

Now some things owe their necessity to something other

10 than themselves ; others do not, but are themselves the

1Fr. 8 Killer.

2Electra 256.



BOOK A. 5 ioisb

source of necessity in other things. Therefore the necessary

in the primary and strict sense is the simple ;for this does

not admit of more states than one, so that it cannot even be

in one state and also in another ; for if it did it would already

be in more than one. If, then, there are any things that are

eternal and unmovable, nothing compulsory or against their 15

nature attaches to them.

6 One means (i) that which is one by accident, (2) that

which is one by its own nature, (i) Instances of the acci

dentally one are Coriscus and what is musical , and musical

Coriscus (for it is the same thing to say4

Coriscus and what

is musical,and 4

musical Coriscus),

and what is musical

and what is just ,and ;

musical Coriscus and just Coriscus .

For all of these are called one by virtue of an accident, what 20

is just and what is musical because they are accidents of

one substance, what is musical and Coriscus because the

one is an accident of the other;and similarly in a sense

( musical Coriscus is one with4

Coriscus because one of the

parts of the phrase is an accident of the other, i. e. musical 25

is an accident of Coriscus;and * musical Coriscus is one

with just Coriscus because one part of each is an accident

of one and the same subject. The case is similar if the

accidentis

predicated of a genus or of any universal name,e. g. if one says that man is the same as musical man

;for 3

this is either because musical is an accident of man, which

is one substance, or because both are accidents of some

individual, e. g. Coriscus. Both, however, do not belong to

him in the same way, but one presumably as genus and

included in his substance, the other as a state or affection

of the substance.

The things, then, that are called one in virtue ofan accident, 35

are called so in this way. (2) Of things that are called one

in virtue of their own nature some (a) are so called because

they are continuous, e. g. a bundle is made one by a band, ioi6a

and pieces of wood are made one by glue ;and a line, even

if it is bent, is called one if it is continuous, as each part of

the body is, e. g. the leg or the arm. Of these themselves,

the continuous by nature are more one than the continuous



ioi6a METAPHYSICA

5 by art. A thing is called continuous which has by its own

nature one movement and cannot have any other;and the

movement is one when it is indivisible, and it is indivisible

in respect oftime. Those things are continuous bytheir

ownnature which are one not merely by contact

;for if you put

pieces of wood touching one another, you will not say these

are one piece of wood or one body or one continuum ofany

other sort. Things, then, that are continuous in any way10 are called one, even if they admit of being bent, and still

more those which cannot be bent;

e. g. the shin or the

thigh is more one than the leg, because the movement of

the leg need not be one. And the straight line is more one

than the bent;but that which is bent and has an angle we

call both one and not one, because its movement may be

15 either simultaneous or not simultaneous;but that of the

straight line is always simultaneous, and no part of it which

has magnitude1rests while another moves, as in the bent line.

(b) (i) Things are called one in another sense because their

substratum does not differ in kind;

it does not differ in

the case of things whose kind is indivisible to sense.

The substratum meant is either the nearest to, or the

20 farthest from, the final state. For, on the one hand, wine

is said to be one and water is said to be one, qua indivisible

inkind

;

and, on the other hand, all juices,e.

g.oil and

wine, are said to be one, and so are all things that can be

melted, because the ultimate substratum of all is the same;

for all of these are water or air.

(ii)Those things also are called one whose genus is one

25 though distinguished by opposite differentiae these too

are all called one because the genus which underlies the

differentiae is one (e. g. horse, man, and dog form a unity,

because all are animals), and indeed in a way similar to that

in which the matter is one.2 These are sometimes called

one in this way, but sometimes it is the higher genus that

is said to be the same(if they are infimae species of their

30 genus) the genus above the proximate genera ;e. g. the

1 Any point may remain fixed while the line rotates round it;but

a point has no magnitude.2

Cf. (b) (i) above.



BOOK A. 6 ioi6a

isosceles and the equilateral are one and the samefigure

because both are triangles ;but they are not the same

triangles.1

(c) Two things are called one, when the definition whichstates the essence of one is indivisible from another defini

tion which shows us the other (though in itself every

definition is divisible).Thus even that which has increased 35

or is diminishing is one, because its definition is one, as, in

the case of plane figures, is the definition of their form. In ioi6b

general those things the thought of whose essence is indi

visible, and cannot separate them either in time or in place

or in definition, are most of all one, and of these especially

those which are substances. For in general those things

that do not admit of division are called one in so far as they

do not admit of it;

e. g. if two things are indistinguishable 5

qua man, they are one kind of man;if qua animal, one kind

of animal;

if qua magnitude, one kind of magnitude.

Now most things are called one because they either do or

have or suffer or are related to something else that is one,

but the things that are primarily called one are those whose

substance is one, and one either in continuity or in form

or in definition;

for we count as more than one either

things that are not continuous, or those whose form is not 10

one,or those

whosedefinition is not one.

While in a sense we call anything one if it is a quantity

and continuous, in a sense we do not unless it is a whole,

i. e. unless it has unity of form;

e. g. if we saw the parts of

a shoe put together anyhow we should not call them one

all the same (unless because of their continuity) ;we do 15

this only if they are put together so as to be a shoe and to

have already a certain single form. This is why the circle is

of all lines most truly one, because it is whole and complete.

(3) The essence ofwhat is one is to be some kind ofbegin

ning of number;for the first measure is the beginning, since

that by which wre first know each class is the first measure

1

Horse, man, and dog are one, because all are animals. But if we

are to call them one something^ we cannot call them one (kind of)

animal, but must go to the higher genus and call them one (kind of)

living thing.



ioi6b METAPHYSICA

20 of the class;the one, then, is the beginning of the knowable

regarding each class. But the one is not the same in all

classes. For here it is a quarter-tone, and there it is the

vowel or the consonant;

and there is another unit of weightand another of movement. But everywhere the one is

indivisible either in quantity or in kind. Now that which

25is indivisible in quantity is called a unit if it is not divisible

in any dimension and is without position, a point if it is not

divisible in any dimension and has position, a line if it is

divisible in one dimension, a plane if in two, a body it

divisible in quantity in all i. e. in three dimensions. And,

reversing the order, that which is divisible in two dimensions

is a plane, that which is divisible in one a line, that which is

30 in no way divisible in quantity is a point or a unit, that

which has not position a unit, that which has position a

point.

Again, some things are one in number, others in species,

others in genus, others by analogy ;in number those whose

matter is one, in species those whose definition is one, in

genus those to which the same figure of predication applies,1

by analogy those which are related as a third thing is to

35 a fourth. The latter kinds of unity are always found when

the former are;

e. g. things that are one in number are also

one in species, while things that are one in species are not

ioi7a

all one in number;but things that are one in species are all

one in genus, while things that are so in genus are not all

one in species but are all one by analogy ;while things that

are one by analogy are not all one in genus.

Evidently many will have meanings opposite to those

ofl one

;some things are many because they are not con-

5 tinuous, others because their matter either the proximate

matter or the ultimate is divisible in kind, others because

the definitions which state their essence are more than one.

Things are said to be (i)in an accidental sense, (2) by 7

their own nature.

(i)In an accidental sense, e.g., we say

*

the righteous

doer is musical , and the man is musical , and the musician

1Sc. the same category. Cf. note on A. 986

a23.



BOOK A. 7 ioi7a

is a man, just as we say the musician builds

,because the 10

builder happens to be musical or the musician to be a builder;

for here one thing is another means one is an accident of

another . So in the cases we have mentioned;for when

we say the man is musical and the musician is a man,

or he who is pale is musical or*

the musician is pale ,the 15

last two mean that both attributes are accidents of the same

thing ;the first that the attribute is an accident of that

which ts;while

*

the musical is a man means that musical

is an accident of a man. (In this sense, too, the not-pale is

said to be, because that of which it is an accident ts.) Thuswhen one thing is said in an accidental sense to be another,

this is either because both belong to the same thing, and 20

this w, or because that to which the attribute belongs z>,or

because the subject which has as an attribute that of which

it is itself predicated, itself is.

(2) The kinds of essential being are precisely those that

are indicated by the figures of predication ;l for the senses

of being are just as many as these figures. Since, then,

some predicates indicate what the subject is, others its 25

quality, others quantity, others relation, others activity or

passivity, others its where,others its when

, being has

a meaning answering to each of these. For there is no

difference between the man is recovering and *

the man

recovers,nor between the man is walking or cutting

and the man walks or cuts;and similarly in all other 30

cases.

(3) Again, being and is mean that a statement is

true, not being that it is not true but false, and this alike

in the case of affirmation and of negation ;e. g.

*

Socrates

is musical means that this is

true,

or Socrates is not-

pale means that this is true;but the diagonal of the

square is not commensurate with the side means that it is

false to say it is.

(4) Again, being and that which is mean that some 35

of the things we have mentioned are potentially, others ioi7b

in complete reality.2 For we say both of that which sees

1 i. e. the categories. Cf. note on A. 986* 23.

2

Omitting prjTov in 1017^ I.



ioi7b METAPHYSICA

potentially and of that which sees actually, that it is seeing ,

and both of that which can actualize its knowledge and ot

5 that which is actualizing it,that it knows, and both of that to

wr

hich rest is already present and of that which can rest, thatit rests. And similarly in the case ofsubstances

;we say the

Hermes is in the stone, and the half of the line is in the line,

and we say of that wThich is not yet ripe that it is corn.

When a thing is potential and when it is not yet potential

must be explained elsewhere.1

I0 We call substance(i)

the

simple bodies,i. e. earth and 8

fire and water and everything of the sort, and in general

bodies and the things composed of them, both animals and

divine beings, and the parts of these. All these are called

substance because they are not predicated of a subject but

everything else is predicated of them. (2) That which,

15 being present in such things as are not predicated of a sub

ject, is the cause of their being, as the soul is of the beingof an animal. (3) The parts which are present in such

things, limiting them and marking them as individuals, and

by whose destruction the whole is destroyed, as the body is

by the destruction of the plane, as some 2

say, and the plane

20 by the destruction of the line;and in general number is

thought by some 2to be of this nature

;for if it is destroyed,

they say, nothing exists, and it limits all things. (4) The

essence, the formula of which is a definition, is also called

the substance of each thing.

It follows, then, that substance has two senses, (A) the

ultimate substratum, which is no longer predicated of any

thing else, and (B) that which, being a this,

is also

25

separable

3 and of this nature is the

shapeor form of each

thing.

The same means (i)that which is the same in an acci- 9

dental sense, e. g. the pale and the musical are the same

because they are accidents of the same thing, and a man

and musical because the one is an accident of the other;

and the musical is a man because it is an accident ot

30 the man. (The complex entity is the same as either of the

1e. 7.

2 The Pythagoreans and Plato.3

Cf. H. 1042* 29.



BOOK A. 9 ioi7b

simple ones and each of these is the same as it;for both

1

the man and the musical are said to be the same as the

musical man,and this the same as they.) This is why all

of these statements are made not universally ; for it is not

true to say that every man is the same as the musical (for35

universal attributes belong to things in virtue of their own

nature, but accidents do not belong to them in virtue of

their own nature) ;but of the individuals the statements ioi8

a

are made without qualification. For 4

Socrates and musi

cal Socrates are thought to be the same;but

*

Socrates

is not predicable of more than one subject, and therefore we

do not say every Socrates as we say*

every man .

Some things are said to be the same in this sense, others

(2)are the same by their own nature, in as many senses as

that which is one by its own nature is so;for both the 5

things whose matter is one either in kind or in number,

and those whose essence is one, are said to be the same.

Clearly, therefore, sameness is a unity of the being either

of more than one thing or of one thing when it is treated as

more than one, i. e. when we say a thing is the same as

itself;for we treat it as two.

Things are called other if either their kinds or their 10

matters or the definitions of their essence are more than

one;

and in general

(

other has meanings opposite to thoseof the same .

Different is applied (i)to those things which though

other are the same in some respect, only not in number but

either in species or in genus or by analogy ; (2) to those

whose genus is other, and to contraries, and to all things

that have their otherness in their essence.

Those things are called like which have the same attri- 15

butes in every respect, and those which have more attributes

the same than different, and those whose quality is one;

and that which shares with another thing the greater number

or the more important of the attributes (each of them one

of two contraries) in respect of which things are capable of

altering, is like that other thing.1 The senses of unlike

are opposite to those of like .

1Such attributes are hot and cold, wet and dry, rough and smooth,

645-28]-[



ioi8a METAPHYSICA

20 The term opposite is applied to contradictories, and to 10

contraries, and to relative terms, and to privation and

possession, and to the extremes from which and into which

generation and dissolution take place;

and the attributesthat cannot be present at the same time in that which is

receptive of both, are said to be opposed, either themselves

or their constituents. Grey and white colour do not belong

at the same time to the same thing ;hence their constituents

are opposed.1

2 5 The term contrary is applied (i) to those attributes

differing in genus which cannot belong at the same time to

the same subject, (2) to the most different of the things in

the same genus, (3)to the most different of the attributes

in the same recipient subject, (4)to the most different of the

30 things that fall under the same faculty, (5) to the things

whose difference is greatest either absolutely or in genus or

in species. The other things that are called contrary are

so called, some because they possess contraries of the above

kind, some because they are receptive of such, some because

they are productive of or susceptible to such, or are pro

ducing or suffering them, or are losses or acquisitions, or

35 possessions or privations, of such. Since one and being

have many senses, the other terms which are derived from

these, and therefore same,

*

other,

and contrary,

mustcorrespond, so that they must be different for each category.

The term other in species is applied to things which

being of the same genus are not subordinate the one to the

ioi8bother, or which being in the same genus have a difference,

2

or which have a contrariety in their substance;and con

traries are other than one another in species (either all

contraries or those which are so called in the primary

sense:5

),and so are those things whose definitions differ in

5tiie infima species of the genus (e. g.

man and horse are

hard and soft, white and black, sweet and bitter. The more important

pairs of contraries, in Aristotle s view, are the first two.1 We cannot say grey and white are opposites, but we say the consti

tuents of grey (black and white) are opposites.2 This definition is wider than the previous one, since it includes

species subordinate one to the other.3

Cf.a25-31 in distinction from 31-35.



BOOK A. 10

indivisible in genus, but their definitions are different), and

those which being- in the same substance have a difference.1

The same in species has the various meanings opposite to

these.

II The words prior and posterior are applied (i) to

some things (on the assumption that there is a first, i. e.

a beginning, in each class) because they are nearer some 10

beginning determined either absolutely and by nature, or

by reference to something or in some place or by certain

people ;e. g. things are prior in place because they are

nearer either to some place determined by nature (e. g. the

middle or the last place), or to some chance object ;and

that which is farther is posterior. Other things are prior

in time;some by being farther from the present, i. e. in 1 5

the case of past events (for the Trojan war is prior to the

Persian, because it is farther from the present), others by

being nearer the present, i. e. in the case of future events

(for the Nemean games are prior to the Pythian, if we treat

the present as beginning and first point, because they are

nearer the present). Other things are prior in movement;

for that wrhich is nearer the first mover is prior (e. g. the 20

boy is prior to the man) ;and the prime mover also is

a beginning absolutely. Others are prior in power ;for

that which exceeds in power, i.e. the more powerful, is

prior ;and such is that according to whose will the other

i. e. the posterior must follow, so that if the prior does not

set it in motion the other does not move, and if it sets it in

motion it does move;and here will is a beginning. Others 25

are prior in arrangement ;these are the things that are

placed at intervals in reference to some one definite thing

1 No satisfactory explanation of this clause has been proposed.Alexander suggests that Aristotle may mean that individuals with the

same specific essence differ in individual essence; but in ordinary

language (which alone Aristotle is examining in A) these would not be

called erep f idd. He also suggests that the reference may be to bodies

such as earth and water which are eYepa e idfi without being contrarylike fire and water; but these could hardly be said to be ev 177 avrf/

ovo-iq. Asclepius suggests more plausibly that the reference may be to

different elements in the essence of complex substances, e.g. to heat

and cold in the essence of man. Cf. vovs and amOr^is in the humansoul. But probably the reference is to attributes present at different

times in the same substance.

H 2



ioi8b METAPHYSICA

according to some rule, e.g. in the chorus the second man

is prior to the third, and in the lyre the second lowest string

is prior to the lowest;for in the one case the leader and in

the other themiddle string

is thebeginning.

30 These, then, are called prior in this sense, but (2) in

another sense that which is prior for knowledge is treated

as also absolutely prior ;of these, the things that are prior

in definition do not coincide with those that are prior in rela

tion to perception. For in definition universals are prior, in

relation to perception individuals. And in definition also

the accident is prior to the whole, e. g. musical to musi-

35 cal man,for the definition cannot exist as a whole without

the part ; yet musicalness cannot exist unless there is some

one who is musical.

(3) The attributes of prior things are called prior, e. g.

straightness is prior to smoothness;for one is an attribute

of a line as such, and the other of a surface.

1019 Some things then are called prior and posterior in this sense,

others(4)

in respect of nature and substance, i. e. those which

can be without other things, while the others cannot be with

out them, a distinction which Plato used.1

(Ifwe consider

5 the various senses of being ,

2

firstly the subject is prior, so

that substance is prior; secondly, according as potency orcom

plete reality is taken into account, different things are prior,for some things are prior in respect of potency, others in re

spect of complete reality, e. g.in potency the halfline is prior

to the whole line, and the part to the whole, and the matter to

the concrete substance, but in complete reality these are pos-

10 terior;for it is only when the whole has been dissolved that

they will exist in complete reality.) In a sense, therefore,

all things that are called prior and posterior are so called

with reference to this fourth sense;for some things can

exist without others in respect of generation, e. g. the

whole without the parts, and others in respect of dissolu

tion, e.g. the part without the whole. And the same is

true in all other cases.

1 The reference is to an oral utterance of Plato, or perhaps to the

Platonic AicupeVay. Cf. Divisiones Aristoteleae, ed. Mutschmann,

pp. xvii, xviii.2

Cf. ch. 7.



BOOK A. 12 1019*

12 Potency means (i) a source of movement or change, 15

which is in another thing than the thing moved or in the

same thing qua other;

e. g. the art of building is a potency

which is not in the

thingbuilt, while the art of

healing,which is a potency, may be in the man healed, but not in

him qua healed. Potency then means the source, in

general, of change or movement in another thing or in the

same thing qua other, and also (2)the source of a thing s 20

being moved by another thing or by itself qua other. For

in virtue of that principle, in virtue of which a patient

suffers anything, we call it capable of suffering;

and this

we do sometimes if it suffers anything at all, sometimes not

in respect of everything it suffers, but only if it suffers a

change for the better. (3) The capacity of performing this

well or according to intention;for sometimes we say of

those who merely can walk or speak but not well or not

as they intend, that they cannot speak or walk. So too 35

(4) in the case of passivity. (5) The states in virtue of

which things are absolutely impassive or unchangeable, or

not easily changed for the worse, are called potencies ;for

things are broken and crushed and bent and in general

destroyed not by having a potency but by not having one 30

and by lacking something, and things are impassive with

respect to such processes if they are scarcely and slightly

affected by them, because of a potency and because they

can do something and are in some positive state.

*

Potency having this variety of meanings, so too the

potent or*

capable}in one sense will mean that which

can begin a movement (or a change in general, for even

that which can bring things to rest is a potent thing)

in anotherthing

or in itself

quaother

;

andin

one sense 35that over which something else has such a potency ;

and in ioi9b

one sense that which has a potency of changing into some

thing, whether for the worse or for the better (for even that

which perishes is thought to be 4

capable of perishing, for

it would not have perished if it had not been capable of it;

but, as a matter of fact, it has a certain disposition and

cause and principle which fits it to suffer this ; sometimes it 5

is thought to be of this sort because it has something,



ioi9b METAPHYSICA

sometimes because it is deprived of something ;but if

privation is in a sense*

having orf

habit, everything will

be capable by having something, so that things are capable

both

by having

a

positive

habit andprinciple,

andby

having the privation of this, if it is possible to have a

privation ;and if privation is not in a sense habit

,

10 capable is used in two distinct senses); and a thing

is capable in another sense because neither any other thing.

nor itself qua other, has a potency or principle which can

destroy it. Again, all of these are capable either merely

because the thing might chance to happen or not to happen,or because it might do so well. This sort of potency is

found even in lifeless things, e. g.in instruments

;for we say

one lyre can speak, and another cannot speak at all, if it

has not a good tone.

15 Incapacity is privation of capacity i.e. of such a prin

ciple as has been described either in general or in the case

of something that would naturally have the capacity, or

even at the time when it would naturally already have it;

for the senses in which we should call a boy and a man and

a eunuch incapable of begetting are distinct. Again, to

either kind of capacity there is an opposite incapacity

20 both to that which only can produce movement and to that

which canproduce

it well.

vSome things, then, are called dSvvara in virtue of this

kind of incapacity, while others are so in another sense;

i. e. both SVVCLTOV and aSvvarovaare used as follows. The

impossible is that of which the contrary is of necessity true,

e. g. that the diagonal of a square is commensurate with the

25 side is impossible, because such a statement is a falsity of

which the contrary is not only true but also necessary ; that

it is commensurate, then, is not only false but also of

necessity false. The contrary of this, the possible, is found

when it is not necessary that the contrary is false, e. g. that

a man should be seated is possible ;for that he is not

30 seated is not of necessity false. The possible, then, in one

sense, as has been said, means that which is not of necessity

1

Aristotle passes now to Swarov and dbuvarov in the sense of possible

and impossible .



BOOK A. 12 1019

false;in one, that which is true

;in one, that which may be

true. A potency or power1

in geometry is so called

by a change of meaning. These senses of capable or

possible involve no reference to potency. But the senses 35

which involve a reference to potency all refer to the primary

kind of potency ;and this is a source of change in another iO2o

a

thing or in the same thing qua other. For other things

are called capable ,some because something else has such

a potency over them, some because it has not, some because

it has it in a particular way. The same is true ofthe things

that are

incapable.

Therefore the

proper

definition of the

primary kind of potency will be a source of change in 5

another thing or in the same thing q2ia other .

13 Quantum means that which is divisible into two or

more constituent parts of which each is by nature a one

and a this . A quantum is a plurality if it is numerable,

a magnitude if it is measurable. Plurality means that ">

which is divisible potentially into non-continuous parts,

magnitude that which is divisible into continuous parts ;

of magnitude, that which is continuous in one dimension is

length, in two breadth, in three depth. Of these, limited

plurality is number, limited length is a line, breadth a sur

face, depth a solid.

Again,some

things

are called

quanta

in virtue of their

own nature, others incidentally ;e. g. the line is a quantum 15

by its own nature, the musical is one incidentally. Of the

things that are quanta by their own nature some are so

as substances, e. g. the line is a quantum (for a certain kind

of quantum is present in the definition which states what it

is),and others are modifications and states of this kind of

substance, e. g. much and little, long and short, broad and 20

narrow, deep and shallow, heavy and light, and all other such

attributes. And also great and small, and greater and smaller,

both in themselves and when taken relatively to each other,

are by their own nature attributes of what is quantitative ;

but these names are transferred to other things also. Of 2 5

things that are quanta incidentally, some are so called in

1 The reference is to squares and cubes.



ioaoa METAPHYSICA

the sense in which it was said that the musical and the white

were quanta, viz. because that to which musicalness and

whiteness belong is a quantum, and some are quanta in the

way in which movement and time are so;for these also are

30 called quanta of a sort and continuous because the things

of which these are attributes are divisible. I mean not that

which is moved, but the space through which it is moved;

for because that is a quantum movement also is a quantum,

and because this is a quantum time is one.

Qualitymeans

(i)the differentia of the

essence,e.

g. 14man is an animal of a certain quality because he is tvvo-

35 footed, and the horse is so because it is four-footed;and a

circle is a figure of particular quality because it is without

iO2Obangles, which shows that the essential differentia is a

quality. This, then, is one meaning of quality the differ

entia of the essence, but (2) there is another sense in which

it applies to the unmovable objects of mathematics, the

sense in which the numbers have a certain quality, e. g. the

composite numbers which are not in one dimension only,

5 but of which the plane and the solid are copies (these are

those which have two or three factors) ;and in general that

which exists in the essence of numbers besides quantity is

quality ;for the essence of each is what it is once, e. g. that

of 6 is not what it is twice or thrice, but what it is once;

for 6 is once 6.

(3)All the modifications of substances that move

(e. g.

10 heat and cold, whiteness and blackness, heaviness and light

ness, and the others of the sort) in virtue of which, when

they change, bodies are said to alter. (4) Quality in

respectof

virtue and vice and, in general, of evil and good.Quality, then, seems to have practically two meanings, and

one of these is the more proper. The primary quality is the

15 differentia of the essence, and of this the quality in numbers

is a part ;for it is a differentia of essences, but either not of

things that move or not ofthem qua moving. Secondly, there

are the modifications ofthings that move,<?ua moving,and the

differentiae ofmovements. Virtue and vice fall among these

modifications;for they indicate differentiae of the move-



BOOK A. 14 io2ob

ment or activity, according to which the things in motion 20

act or are acted on well or badly ;for that which can be

moved or act in one way is good, and that which can do so

in another the contrary way is vicious. Good and evil

indicate quality especially in living things, and among these

especially in those which have purpose.2 5

Things are relative(i)as double to half, and treble to

a third, and in general that which contains something else

many times to that which is contained many times in some

thing else, and that which exceeds to that which is exceeded;

(2)as that which can heat to that which can be heated, and

that which can cut to that which can be cut, and in general

the active to the passive ; (3) as the measurable to the 30

measure, and the knowable to knowlege, and the per

ceptible to perception.

(i) Relative terms of the first kind are numerically

related eitherindefinitely or definitely, to numbers them

selves or to i. E.g. the double is in a definite numerical

relation to i, and that which is many times as great is in

a numerical, but not a definite, relation to i, i. e. not in this 35

or in that numerical relation to it;

the relation of that io2ia

which is half as big again as something else to that some

thing is a definite numerical relation to a number;that

H ~\~ I

which is - - times something else is in an indefinite rela

tion to that something, as that which is many times as

great is in an indefinite relation to i;the relation of that

which exceeds to that which is exceeded is numerically

quite indefinite;for number is always commensurate, and 5

4 number is not predicated of that which is not commen

surate, but that which exceeds is,in relation to that which

is exceeded, so much and something more;and this some

thing is indefinite;for it can, indifferently, be either equal

or not equal to that which is exceeded. All these relations,

then, are numerically expressed and are determinations

of number, and so in another way are the equal and the like

and the same. For all refer tounity.

Thosethings

are 10

the same whose substance is one;

those are like whose



io2ia METAPHYSICA

quality is one;those are equal whose quantity is one

;and

i is the beginning and measure of number, so that all these

relations imply number, though not in the same way.

15 (2) Thingsthat are active or

passive implyan active or

a passive potency and the actualizations of the potencies ;

e. g. that which is capable of heating is related to that which

is capable of being heated, because it can heat it, and,

again, that which heats is related to that which is heated

and that which cuts to that which is cut, in the sense that

they actually do these things. But mimerical relations are

not actualized except in the sense which has been else-

20 where *stated

;actualizations in the sense of movement

they have not. Of relations which imply potency some

further imply particular periods of time, e. g.that which has

made is relative to that which has been made, and that

which will make to that which will be made. For it is in

this way that a father is called the father of his son;for the

one has acted and the other has been acted on in a certain

25 way.2

Further, some relative terms imply privation of

potency, i. e.*

incapable and terms of this sort, e.g.*

in

visible .

Relative terms which imply number or potency, there

fore, are all relative because their very essence includes in

its

nature a reference to something else, not because something else involves a reference to it

;but

(3)that which is

30 measurable or knowable or thinkable is called relative

because something else involves a reference to it. For4

that which is thinkable implies that the thought of it is

possible, but the thought is not relative to that of which

it is the thought ;for we should then have said the same

thing twice. Similarly sight is the sight of something, not4

of that of which it is the sight (though of course it is true

io2ibto say this) ;

in fact it is relative to colour or to something

else of the sort. But according to the other way of speak

ing the same thing would be said twice, the sight is of

that of which it is.

1 The reference may be to the H(p\ (Sewi/ and theIle/ji rfys-

ru>v

2i.e. there need not be any present relation to justify the use of the

relative form of words in this case;there is always the past relation.



BOOK A. 15 io2ib

Things that are by their own nature called relative are

called so sometimes in these senses, sometimes if the classes

that include them are of this sort; e.g. medicine is a rela- 5

tive term because its genus, science, is thought to be arelative term. Further, there are the properties in virtue

of which the things that have them are called relative, e. g.

equality is relative because the equal is, and likeness

because the like is. Other things are relative by accident;

e. g. a man is relative because he happens to be double of

something and double is a relative term;or the white is 10

relative, if the same thing happens to be double and white.

16 What is called complete is(i) that outside which it is

not possible to find any, even one, of its parts ;e. g. the

complete time of each thing is that outside which it is not

possible to find any time which is a part proper to it.

(2)That which in respect of excellence and goodness cannot 15

be excelled in its kind;

e. g. we have a complete doctor or

a complete flute-player, when they lack nothing in respect of

the form of their proper excellence. And thus, transferring

the word to bad things, we speak of a complete scandal

monger and a complete thief; indeed we even call them

good, i. e. a good thief and a good scandal-monger. And 20

excellence is acompletion

;for each

thingis

completeand

every substance is complete, when in respect of the form

of its proper excellence it lacks no part of its natural

magnitude. (3) The things which have attained their end,

this being good, are called complete; for things are complete

in virtue of having attained their end. Therefore, since the 25

end is something ultimate, we transfer the word to bad

things and say a thing has been completely spoilt, and completely destroyed, when it in no wise falls short of destruc

tion and badness, but is at its last point. This is why

death, too, is by a figure of speech called the end, because

both are lastthings. But the ultimate purpose is also an

end. Things, then, that are called complete in virtue of 3

their own nature are so called in all these senses, some

because in respect of goodness they lack nothing and can

not be excelled and no part proper to them can be found out-



io2ib METAPHYSICA

side them, others in general because they cannot be exceeded

in their several classes and no part proper to them is out-

io22aside them

;the others presuppose these first two kinds, and

are called complete because they either make or have something of the sort or are adapted to it or in some way or

other involve a reference to the things that are called com

plete in the primary sense.

Limit means (i) the last point of each thing, i.e. the 17

first point beyond which it is not possible to find any part,

5 and the first point within which every part is ; (2) the form,

whatever it may be, of a spatial magnitude or of a thing

that has magnitude ; (3) the end of each thing (and of this

nature is that towards which the movement and the action

are, not that from which they are, though sometimes it is

both, that from which and that to which the movement is,

i. e. the final cause) ; (4)the substance of each thing, and

the essence of each;for this is the limit of knowledge ;

10 and if of knowledge, of the object also. Evidently, there

fore,4

limit has as many senses as beginning ,and yet

more;for the beginning is a limit, but not every limit is a

beginning.

That in virtue of which has several meanings : 18

J 5(i)

the form or substance of each thing, e.g. that in virtue

of which a man is good is the good itself, (2) the proximate

subject in which it is the nature of an attribute to be found,

e.g. colour in a surface. That in virtue of which

, then,

in the primary sense is the form, and in a secondary sense

the matter of each thing and the proximate substratum of

each. In general that in virtue of which will be found20 in the same number of senses as

;

cause;for we say in

differently (3)*

in virtue of what has he come ? or for

what end has he come ?;and (4)

*

in virtue of what has he

inferred wrongly, or inferred ? or* what is the cause ofthe

inference, or of the wrong inference ? Further (5) KaO ol

is used in reference to position, e. g. at which he stands

1Aristotle here mentions the original local sense of KCI& o. No

English word or phrase has quite the same ambiguity.



BOOK A. 18 io22a

or*

along which he walks;

for all such phrases indicate

place and position.

Therefore in virtue of itself must likewise have several

meanings. The following belong to a thing in virtue of 25

itself: (i) the essence of each thing, e.g. Callias is in

virtue of himself Callias and what it was to be Callias;

(2) whatever is present in the what,e. g. Callias is in virtue

of himself an animal. For animal is present in his

definition;

Callias is a particular animal.(3) Whatever

attribute a thing receives in itself directly or in one of its

parts ;e.

g.a surface is white in virtue of itself, and a man 3

is alive in virtue of himself; for the soul, in which life

directly resides, is a part of the man. (4) That which has

no cause other than itself;man has more than one cause-

animal, two-footed but yet man is man in virtue of himself.

(5) Whatever attributes belong to a thing alone, and in so 35

far as

they belongto it

merely byvirtue of itselfconsidered

apart by itself.

19 Disposition means the arrangement of that which has 1022

parts, in respect either of place or of potency or of kind;

for there must be a certain position, as even the word dis

position shows.

204

Having1

means (i) a kind of activity of the haver andof what he has something like an action or movement.

For when one thing makes and one is made, between them 5

there is a making ;so too between him who has a garment

and the garment which he has there is a having. This sort

of having, then, evidently we cannot have;for the process

will go on to infinity, if it is to be possible to have the

having of what we have. (2) Having orl

habit means 10

a disposition according to which that which is disposed is

either well or ill disposed, and either in itself or with refer

ence to something else;

e. g. health is a habit;for it is

such a disposition. (3) We speak of a habit if there is

a portion of such a disposition ;and so even the excellence

of the parts is a habit*

of the whole thing.

1 The word e|ts does duty for having ,habit

,and permanent

state .



io22b METAPHYSICA

15 Affection*

means( i) a quality in respect of which a thing 21

can be altered, e. g. white and black, sweet and bitter, heavi

ness and lightness, and all others of the kind. (2) The

actualization of these the already accomplished altera

tions. (3) Especially, injurious alterations and movements,

20 and, above all, painful injuries. (4) Misfortunes and pain

ful experiences when on a large scale are called affections.

We speak of privation (i) if something has not one of 22

the attributes which a thing might naturally have, even if

this thing itself would not naturally have it;

e. g. a plant is

said to be deprived of eyes. (2) If, though either the

thing itself or its genus would naturally have an attri-

25 bute, it has it not;

e. g.a blind man and a mole are in

different senses deprived of sight ;the latter in contrast

with its genus,1 the former in contrast with his own normal

nature.(3)

If,

though

it wouldnaturally

have the attribute,

and when it would naturally have it, it has it not;for blind

ness is a privation, but one is not blind at any and every

age, but only if one has not sight at the age at which one

30 would naturally have it. Similarly a thing is called blind

if it has not sight in the medium in which, and in respect of

the organ in respect of which, and with reference to the

object with reference to which, and in the circumstances in

which, it would naturally have it. (4) The violent taking

away of anything is called privation.

Indeed there are just as many kinds of privations as there

are of words with negative prefixes; for a thing is called

unequal because it has not equality though it would natur

ally have it, and invisible either because it has no colour at

35 all or because it has a poor colour, and apodous either

because it has no feet at all or because it has imperfect feet.

Again, a privative term may be used because the thing has

J023a

little of the attribute (and this means having it in a sense

imperfectly), e. g.kernel-less

;or because it has it not

easily or not well (e. g. we call a thing uncuttable not only

if it cannot be cut but also if it cannot be cut easily or

well) ;or because it has not the attribute at all

;for it is

1i.e.* animal .



BOOK A. 22 1023

not the one-eyed man but he who is sightless in both eyes

that is called blind. This is why not every man is good or 5

bad, just or unjust ,

but there is also an intermediate state.

23To have or hold means many things : (i)

to treat

a thing according to one s own nature or according to one s

own impulse ;so that fever is said to have a man, and 10

tyrants to have their cities, and people to have the clothes

they wear. (2) That in which a thing is present as in

something receptive of it is said to have the thing ;e. g. the

bronze has the form of the statue, and the body has the

disease. (3) As that which contains hold the things con

tained;for a thing is said to be held by that in which it is as

in a container;

e.g. we say that the vessel holds the liquid 15

and the city holds men and the ship sailors;and so too

that the whole holds the parts. (4) That which hinders a

thing from moving or acting according to its own impulse

is said to holdit,

as pillars hold the incumbent weights, and

as the poets make Atlas hold the heavens,1

implying that 20

otherwise they would collapse on the earth, as some of

the natural philosophers also say.2

In this way also that

which holds things together is said to hold the things it

holds together, since they would otherwise separate, each

accordingto its own

impulse.*

Being in something has similar and corresponding

meanings to holding or having .

35

24 To come from something means (i) to come from

something as from matter, and this in two senses, either in

respect of the highest genus or in respect of the lowest

species ;e. g. in a sense all

things

that can be melted come

from water, but in a sense the statue comes from bronze.

(2)As from the first moving principle ;

e. g. what did the 30

fight come from ? From abusive language, because this

was the origin of the fight. (3) From the compound of

matter and shape, as the parts come from the whole, and the

verse from the Iliad, and the stones from the house; (in

every such case the whole is a compound of matter and

1Cf. Hes. Theog. 517.

&

Cf. De Caelo 284* 20-26.



io23a METAPHYSICA

shape,) for the shape is the end, and only that which attains

35 an end is complete. (4)As the form from its part, e. g.

man from two-footed and syllable from letter;for this

is a different sense from that in which the statue comes

ic23bfrom bronze

;for the composite substance comes from the

sensible matter, but the form also comes from the matter of

the form. Some things, then, are said to come from some

thing else in these senses;but (5) others are so described if

one ofthese senses is applicable to a part of that other thing ;

e.

g.

the child comes from its father and mother, andplants

come from the earth, because they come from a part of

5 those things. (6) It means coming after a thing in time,

e. g. night comes from day and storm from fine weather,

because the one comes after the other. Of these things

some are so described because they admit of change into

one another, as in the cases now mentioned;some merely

because they are successive in time, e. g. the voyage took

place from the equinox, because it took place after the

10 equinox, and the festival of the Thargelia comes from the

Dionysia, because after the Dionysia.

Part means (i) (a) that into which a quantum can in 25

any way be divided;for that which is taken from a quan

tum qua quantum is always called a part of it, e. g. two is

I5called in a sense a part of three. It means (), of the parts

in the first sense, only those which measure the whole;

this is why two, though in one sense it is, in another is not,

called a part of three.(2)

The elements into which a kind

might be divided apart from the quantity are also called parts

of it;for which reason we

say

the

species

are

parts

of the

genus. (3) The elements into which a whole is divided,

or of which it consists the whole meaning either the

20 form or that which has the form;

e. g. of the bronze sphere

or of the bronze cube both the bronze i. e. the matter in

which the form is and the characteristic angle are parts.

(4) The elements in the definition which explains a thing

are also parts of the whole ; this is why the genus is called

a part of the species, though in another sense the species is

3 5 part of the genus.



BOOK A. 26 i023b

|a6A whole means (i) that from which is absent none of

the parts of which it is said to be naturally a whole, and (2)

that which so contains the things it contains that they form

a unity; and this in two senses either as being each sever

ally one single thing, or as making up the unity between

them. For (a) that which is true of a whole class and is

said to hold good as a whole (which implies that it is a kind

of whole) is true of a whole in the sense that it contains 3

many things by being predicated of each, and by all of

them, e.g. man, horse, god, being severally one single

thing, because all are living things. But (b) the continuous

and limited is a whole, when it is a unity consisting of

several parts, especially ifthey are present only potentially,1

but, failing this, even if they are present actually. Of these

things themselves, those which are so by nature are wholes

in a higher degree than those which are so by art, as we 35

said2in the case of unity also, wholeness being in fact a sort

of oneness.

Again (3),of quanta that have a beginning and a io24

a

middle and an end, those to which the position does not

make a difference are called totals, and those to which it

does, wholes. Those which admit of both descriptions

are both wholes and totals. These are the things whose

nature remains the sameafter

transposition,but

whose formdoes not, e. g. wax or a coat

; they are called both wholes 5

and totals;for they have both characteristics. Water and

all liquids and number are called totals, but the whole

number or the whole water one does not speak of, ex

cept by an extension of meaning. To things, to which quaone the term total is applied, the term all is applied

when they are treated as separate ; this total number, all 10

these units.

27 It is not any chance quantitative thing that can be said to

be mutilated;

it must be a whole as well as divisible.

For not only is two not mutilated if one of the two ones

is taken away (for the part removed by mutilation is never

1i. e. if they are only distinguishable, not distinct.

2Cf. ioi6a 4.

845-28 J



io24a METAPHYSICA

equal to the remainder), but in general no number is thus

mutilated;for it is also necessary that the essence remain

;

15 if a cup is mutilated, it must still be a cup ;but the number

is no longer the same. Further, even if things consist of

unlike parts, not even these things can all be said to be

mutilated, for in a sense a number has unlike parts (e. g.

two and three) as well as like;but in general of the things

to which their position makes no difference, e. g. water or

fire, none can be mutilated;to be mutilated, things must be

such as in virtue of their essence have a certain position.

20Again, they must be continuous

;for a musical scale con

sists of unlike parts and has position, but cannot become

mutilated. Besides, not even the things that are wholes

are mutilated by the privation of any part. For the parts

removed must be neither those which determine the essence

nor any chance parts, irrespective of their position ;e. g.

acup

is not mutilated if it is boredthrough,

butonly

if the

25 handle or a projecting part is removed, and a man is muti

lated not if the flesh or the spleen is removed, but if an

extremity is, and that not every extremity but one which

when completely removed cannot grow again. Therefore

baldness is not a mutilation.

The termc

race or genus is used(i)

if generation of 28

30 things which have the same form is continuous, e. g.*

while

the race of men lasts means while the generation of them

goes on continuously .

(2)It is used with reference to

that which first brought things into existence;for it is thus

that some are called Hellenes by race and others lonians,

because the former proceed from Hellen and the latter frorr

Ion as their first begetter. And the wordis

used in refer-35 ence to the begetter more than to the matter, though people

also get a race-name from the female, e. g. the descendants

of Pyrrha&

.

1

(3) There is genus in the sense in which

iO24b

plane is the genus of plane figures and solid of solids ;

for each of the figures is in the one case a plane ofsuch and

such a kind, and in the other a solid of such and such a

kind ; and this is what underlies the differentiae. Again1Aristotle thinks that the male supplies the efficient and the formal,

the female the material cause of generation.



BOOK A. 28 io24b

(4),in definitions the first constituent element, which is in

cluded in the what,

is the genus, whose differentiae the 5

qualities are said to be. Genus then is used in all these

ways, (i)in reference to continuous generation of the same

kind, (2) in reference to the first mover which is of the

same kind as the things it moves, (3) as matter;for that to

which the differentia or quality belongs is the substratum,

which we call matter.

Those things are said to be other in genus whose 10

proximate substratum is different, and which are not

analysed the one into the other nor both into the same

thing (e. g. form and matter are different in genus) ;and

things which belong to different categories of being (for

some of the things that are said to be signify essence,

others a quality, others the other categories we have before

distinguishedl

) ;these also are not analysed either into one 1 5

another or into some one thing.

29 The false means (i)that which is false as a thing, and

that (a) because it is not put together or cannot be put

together, e. g. that the diagonal of a square is commen

surate with the side or*

that you are sitting ;for one of 20

these is false always, and the other sometimes;

it is in these

two senses thatthey

are non-existent.(6)

There arethings

which exist, but whose nature it is to appear either not to

be such as they are or to be things that do not exist, e. g.

a sketch or a dream;for these are something, but are not

the things the appearance of which they produce in us.

We call things false in this way, then, either because they 25

themselves do not exist, or because the appearance which

results from them is that of something that does not exist.

(2)A false account is the account ofnon-existent objects,

in so far as it is false. Hence every account is false when

applied to something other than that of which it is true;

e. g. the account of a circle is false when applied to a

triangle. In a sense there is one account of each thing, i. e.

the account of its essence, but in a sense there are many,

since the thing itself and the thing itself with an attribute 30

1

ioi7a24-27.

I 2



io24b METAPHYSICA

are in a sense the same, e. g. Socrates and musical Socrates

(a false account is not the account of anything, except in

a qualified sense). Hence Antisthenes was too simple-

minded when he claimed that nothing could be described

except by the account proper to it, one predicate to one

subject ;from which the conclusion used to be drawn that

there could be no contradiction, and almost that there could

be no error. But it is possible to describe each thing not

35 only by the account of itself, but also by that of something

else. This

maybe done

altogether falsely indeed,but there

is also a way in which it may be done truly ;e.

g. eight

may be described as a double number by the use of the

definition of two.

io25a These things, then, are called false in these senses, but

(3) a false man is one who is ready at and fond of such

accounts, not for any other reason but for their own sake,

and one who is good at impressing such accounts on other

5 people, just as we say things are false, which produce a false

appearance. This is why the proof in the Hippias that the

same man is false and true is misleading. For it assumes

that he is false who can deceive J

(i.e. the man who knows

and is wise) ;and further that he who is willingly bad is

10 better.2 This is a false result of induction for a man who

limps willingly is better than one who does so unwillingly

by*

limping Plato means mimicking a limp ,for if

the man were lame willingly, he would presumably be

worse in this case as in the corresponding case of moral

character.

4

Accident means (i)that which attaches to something 30

and can be truly asserted, but neither of necessity nor

15 usually, e.g. if some one in digging a hole for a plant has

found treasure. This the finding of treasure is for the

man who dug the hole an accident;for neither does the one

come of necessity from the other or after the other, nor, if a

man plants, does he usually find treasure. And a musical man

20

might

be pale ;but since this does not

happen

of necessity

nor usually, we call it an accident. Therefore since there

1

Hippias Minor 365-9.2

Ib. 371-6.



BOOK A. 30 1025

are attributes and they attach to subjects, and some ofthem

attach to these only in a particular place and at a particular

time, whatever attaches to a subject, but not because it was

this subject, or the time this time, or the place this place,

will be an accident. Therefore, too, there is no definite cause

for an accident, but a chance cause, i. e. an indefinite one.

Going to Aegina was an accident for a man, if he went not 25

in order to get there, but because he was carried out of his

way by a storm or captured by pirates. The accident has

happened or exists, not in virtue of the subject s nature,

however, but of something else ; for the storm was the

cause of his coming to a place for which he was not sailing,

and this was Aegina.4 Accident has also (2)

another meaning, i. e. all that 30

attaches to each thing in virtue of itself but is not in its

essence, as having its angles equal to two right angles

attaches to the triangle. And accidents of this sort may be

eternal, but no accident of the other sort is. This is

explained elsewhere.1

1 An. Post. i. 75a18-22, 39-41, ;6

b 11-16.



BOOK E

i025b WE are seeking the principles and the causes of the I

things that are, and obviously of them qzta being. For,

while there is a cause of health and of good condition, and

the objects of mathematics have first principles and

5 elements and causes, and in

general every

science which is

ratiocinative or at all involves reasoning deals with causes

and principles, more or less precise, all these sciences mark

off some particular being some genus, and inquire into

io this, but not into being simply nor qiia being, nor do they

offer any discussion of the essence of the things of which

they treat;but starting from the essence some making it

plain to the senses, others assuming it as a hypothesis

they then demonstrate, more or less cogently, the essential

attributes of the genus with which they deal. It is obvious,

therefore, that such an induction yields no demonstration of

15 substance or of the essence, but some other way of exhibit

ing it. And similarly the sciences omit the question whether

the genus with which they deal exists or does not exist,

because it belongs to the same kind of thinking to show

what it is and that it is.

And since natural science, like other sciences, is in fact

about one class of being, i.e. to that sort of substance

30 which has the principle of its movement and rest present in

itself, evidently it is neither practical nor productive. For

in the case ofthings

made theprinciple

is in the maker it

is either reason or art or some faculty, while in the case of

things done it is in the doer viz. will, for that which is

25done and that which is willed are the same. Therefore, if

all thought is either practical or productive or theoretical,

physics must be a theoretical science, but it will theorize

about such being as admits of being moved, and about sub-

stance-as-defined for the most part only as not separable

from matter. Now, we must not fail to notice the mode of

being of the essence and of its definition, for, without this,



BOOK E. i i025b

inquiry is but idle. Of things defined, i. e. of whats, 3

some are like* snub

,and some like concave . And these

differ because snub is bound up with matter (for what is

snub is a concave nose), while concavity is independentof

perceptible matter. If then all natural things are analogous

to the snub in their nature e. g. nose, eye, face, flesh, bone,ic26

a

and, in general, animal; leaf, root, bark, and, in general,

plant (for none of these can be defined without reference to

movement they always have matter), it is clear how we

must seek and define the what in the case of natural

objects, and also that it belongs to the student of nature to 5

study even soul in a certain sense, i. e. so much of it as is

not independent of matter.

That physics, then, is a theoretical science, is plain from

these considerations. Mathematics also, however, is theo

retical;but whether its objects are immovable and separ

able from matter, is not at present clear; still, it is clear

that some mathematical theorems consider them qua

immovable and qua separable from matter. But if there I0

is something which is eternal and immovable and separable,

clearly the knowledge of it belongs to a theoretical science,

not, however, to physics (for physics deals with certain

movable things) nor to mathematics, but to a science prior

to both. Forphysics

deals withthings

which exist

separately but are not immovable, and some parts of mathematics

deal with things which are immovable but presumably do

not exist separately, but as embodied in matter;

while r 5

the first science deals with things which both exist

separately and are immovable. Now all causes must be

eternal, but especially these;for they are the causes that

operate on so much of the divine as appears to us.

1

Theremust, then, be three theoretical philosophies, mathematics,

physics, and what we may call theology, since it is obvious

that if the divine is present anywhere, it is present in things20

of this sort. And the highest science must deal with the

highest genus. Thus, while the theoretical sciences are

more to be desired than the other sciences, this is more to

be desired than the other theoretical sciences. For one1

i. e. produce the movements of the heavenly bodies.



io26a METAPHYSICA

might raise the question whether first philosophy is univer

sal, or deals with one genus, i. e. some one kind of being ;

25 for not even the mathematical sciences are all alike in this

respect, geometry and astronomy deal with a certain par

ticular kind of thing, while universal mathematics applies

alike to all. We answer that if there is no substance other

than those which are formed by nature, natural science will

be the first science;but if there is an immovable substance,

3 the science of this must be prior and must be first philo

sophy, and universal in this way, because it is first. And

it will belong to this to consider being qua being both

what it is and the attributes which belong to it qua being.1

But since the unqualified term being has several mean- 2

ings, ofwhich one was seen 2to be the accidental, and another

35 the true( non-being being the false), while besides these

there are the figures of predication (e. g. the what \ quality,

quantity, place, time, and any similar meanings which being

iO26b may have), and again besides all these there is that which

4

is potentially or actually : since4

being has many mean

ings, we must first say regarding the accidental, that there

can be no scientific treatment of it. This is confirmed by

5 the fact that no science practical, productive, or theoretical

troubles itself aboutit.

For on the one hand he whoproduces a house does not produce all the attributes that

come into being along with the house;for these are in

numerable;the house that has been made may quite well

be pleasant for some people, hurtful to some, and useful to

others, and different to put it shortly from all things

that are;

j and the science of building does not aim at pro-

10 ducing any of these attributes. And in the same way the

geometer does not consider the attributes which attach thus

to figures, nor whether *

triangle is different from triangle

whose angles are equal to two right angles . And this

happens naturally enough ;for the accidental is practically

1 With ch. i cf. B. 955b10-13, 997** 15-25, K. 7.

2

Cf. A. 7.3 For the point of the last clause cf. 11. 12, 17, below. The question

as to the identity or difference of various things was popular with the

Sophists.



BOOK E. 2 I0261

a mere name. And so Plato l was in a sense not wrong in

ranking sophistic as dealing with that which is not. For the 15-

arguments of the sophists deal, we may say, above all with

the accidental; e. g. the question whether musical

and

lettered are different or the same, and whether musical

Coriscus and Coriscus are the same, and whether every

thing which is. but is not eternal, has come to be,with the

paradoxical conclusion that if one who was musical has

come to be lettered, he must also have been lettered and

have come to be musical, and all the other arguments of 20

this sort ; the accidental is obviously akin to non-being.

And this is clear also from arguments such as the following :

things which are in another sense come into being and pass

out of being by a process, but things which are accidentally

do not. But still we must, as far as we can, say further,

regarding the accidental, what its nature is and from what 25

cause it proceeds ;for it will perhaps at the same time

become clear why there is no science of it.

Since, among things which are, some are always in the

same state and are of necessity (not necessity in the sense

of compulsion but that which we assert of things because

they cannot be otherwise), and some are not of necessity

nor always, but for the most part, this is the principle and 3

this the cause of the existence of the accidental;for that

which is neither always nor for the most part, we call acci

dental. For instance, if in the dog-days there is wintry

and cold weather, we say this is an accident, but not if there

is sultry heat, because the latter is always or for the most

part so, but not the former. And it is an accident that 35

a man is pale (for this is neither always nor for the most

part so), but it is not by accident that he is an animal. Andthat the builder produces health is an accident, because it is iO27

a

the nature not of the builder but of the doctor to do this,

but the builder happened to be a doctor. Again, a con

fectioner, aiming at giving pleasure, may make something

wholesome, but not in virtue of the confectioner s art;and

therefore we say it was an accident,and while there is

a sense in which he makes it, in the unqualified sense he1

Cf. Sophistes 237 A, 254 A.



io27a METAPHYSICA

5 does not. For to other things answer faculties productive

of them, but to accidental results there corresponds no

determinate art nor faculty ;for of things which are or

come to be by accident, the cause also is accidental. There

fore, since not all things either are or come to be of neces

sity and always, but the majority of things areyftr the most

\vpart, the accidental must exist;for instance a pale man is

not always nor for the most part musical, but since this

sometimes happens, it must be accidental (if not, every

thing will be of necessity). The matter, therefore, which

is capable of being otherwise than as it usually is, must be

15 the cause of the accidental. And we must take as our

starting-point the question whether there is nothing that is

neither always nor for the most part. Surely this is im

possible. There is, then, besides these something which is

fortuitous and accidental. But while the usual exists, can

nothing be said to be always, or are there eternal things?

This must be considered later,1 but that there is no science

20 of the accidental is obvious;for all science is either of that

which is always or of that which is for the most part. (For

howrelse is one to learn or to teach another ? The thing

must be determined as occurring either always or for the

most part, e. g. that honey-water is useful for a patient in a

fever is^true for the most part.) But that which is contrary

to the usual law science will be unable to state, i. e. when

the thing does not happen, e. g.4 on the day ofnew moon

;

25 for even that which happens on the day of new moon

happens then either always or for the most part ;but the

accidental is contrary to such laws. We have stated, then,

what the accidental is, and, from what cause it arises, and

that therejs no science which deals with it.

That there are principles and causes which are generable 3

and destructible without ever being in course of being

30 generated or destroyed, is obvious. For otherwise all

things will be of necessity, since that which is being gene

rated or destroyed must have a cause which is not acci

dentally its cause. Will A exist or not ? It will if B

1Cf. A. 6-8.



BOOK E. 3 io27a

happens ;and if not, not. And B will exist if C happens.

And thus if time is constantly subtracted from a limited

extent of time, one will obviously come to the present.

This man, then, will die by violence, //"he goes out; and 1027

he will do this if he gets thirsty ;and he will get thirsty if

something else happens ;and thus we shall come to that

which is now present, or to some past event. For instance,

he will go out if he gets thirsty ;and he will get thirsty if

he is eating pungent food;and this is either the case or

not;so that he will of necessity die, or of necessity not die. 5

And similarly if one jumps over to past events, the same

account will hold good ;for this I mean the past condition

is already present in something. Everything, therefore,

that will be, will be of necessity ;e. g. it is necessary that he

who lives shall one day die;for already some condition has

come into existence, e. g. the presence of contraries in the

samebody.

But whether he is to die

by

disease or

by

10

violence is not yet determined, but depends on the happen

ing of something else. Clearly then the process goes back

to a certain starting-point, but this no longer points to

something further. This then will be the starting-point

for the fortuitous, and will have nothing else as cause of

its coming to be. But to what sort of starting-point and

what sort of cause we thus refer the fortuitous whether to 15

matter or to the purpose or to the motive power, must be

carefully considered.1

4 Let us dismiss accidental being ;for we have sufficiently

determined its nature. But since that which is in the sense

of being true, or is not in the sense of being false, depends

1 The doctrine of the chapter seems to be as follows. Events in

general occur as the necessary result of a series of causes. E. g. death

is the necessary result of the presence of contrary elements in every

living body. But there are certain events which, while beginninga causal nexus, are not the result of a causal nexus. We can never

say of them, their conditions are being fulfilled, and they are comingto be. At one time they are not, and at another time they are.

Therefore they come to be. But they never are coming to be. Theevents A. seems to be thinking of are those which he would ascribe to

free will, e.g. a man s eating pungent food. Once he does this, hisdeath in some determinate way is certain

;till he does

it, only his

death is certain.



io27b METAPHYSICA

on combination and separation, and truth and falsity to

gether depend on the allocation of a pair of contradictory20judgements (for the true judgement affirms where the sub

ject and predicate really are combined, and denies where

they are separated, while the false judgement has the opposite ofthis allocation

;it is another question, how it happens

that we think things together or apart ; by together and4

apart I mean thinking them so that there is no succession

2 5 in the thoughts but they become a unity) ;for falsity

and

truth are not in things it is not as if the good were true,

and the bad were in itself false but in thought ;while with

regard to simple concepts and l whats falsity and truth do

not exist even in thought : this being so, we must consider

laterl what has to be discussed with regard to that which is

or is not in this sense. But since the combination and the

3 separation are in thought and not in the things, and that

which is in this sense is a different sort of

l

being from the

things that are in the full sense (for the thought attaches

or removes 2either the subject s what or its having

a certain quality or quantity or something else), that

which is accidentally and that which is in the sense of being

true must be dismissed. For the cause of the former is

indeterminate, and that of the latter is some affection of the

iO28a thought, and both are related to the remaining genus of

being, and do not indicate the existence of any separate

class of being. Therefore let these be dismissed, and let us

consider the causes and the principles of being itself, qua

being. [It was clear in our discussion of the various

5 meanings of terms, that being has several meanings.]3

1 Cf. . 10. 2 Reading in 1. 338 With chs. 2-4 cf. K. io64

bI5~io65

a26.



BOOKZ

J THERE are several senses in which a thing may be said 10

to be,as we pointed out previously in our book on the

various senses of words;

lfor in one sense the being

meant is4 what a thing is or a

*

this,and in another sense

it means a quality or quantity or one of the other things

that are predicated as these are. While being hasall

these senses, obviously that which *

is primarily is the

what,which indicates the substance of the thing. For T 5

when we say of what quality a thing is, we say that it is

good or bad, not that it is three cubits long or that it is

a man;but when we say what it is, we do not say white

or hot or three cubits long ,but a man or

*

a god .

And all other things are said to be because they are, someof them, quantities of that which is in this primary sense,

others qualities of it, others affections of it, and others some

other determination of it. And so one might even raise 20

the question whether the words to walk,

to be healthy ,

4

to sit imply that each of these things is existent, and

similarly in any other case of this sort;for none of them is

either self-subsistent or capable of being separated from

substance, but rather, if anything, it is that which walks or

sits or is healthy that is an existent thing. Now these are 35

seen to be more real because there is something definite

which underlies them(i.

e. the substance or individual),

which is implied in such a predicate ;for we never use the

word [

goodor

sittingwithout

implyingthis.

Clearlythen it is in virtue of this category that each of the others also

is. Therefore that which is primarily, i.e. not in a qualified

sense but without qualification, must be substance.3o

Now there are several senses in which a thing is said to

be first; yet substance is first in every sense (i) in defini

tion. (2) in order of knowledge, (3)in time. For (3) of the

other categories none can exist independently, but only

1

Cf. A.7.



io28a METAPHYSICA

35 substance. And (i)in definition also this is first; for in

the definition of each term the definition of its substance

must be present. And (2) we think we know each thing

most fully, when we know what it is, e. g. what man is or

what fire is, rather than when we know its quality, its

io28bquantity, or its place ;

since we know each of these pre

dicates also, only when we know what the quantity or the

quality is.

And indeed the question which was raised of old and is

raised now and always, and is always the subject of doubt,

viz. what being is, is just the question, what is substance ?

For it is this that some lassert to be one, others more than

5one, and that some 2

assert to be limited in number, others;

unlimited. And so we also must consider chiefly and pri

marily and almost exclusively what that is which ts in this

sense.

Substance is thought to belong most obviously to bodies; 2

and so we say that not only animals and plants and their

10parts are substances, but also natural bodies such as fire and

water and earth and everything of the sort, and all things

that are either parts of these or composed of these (either of

parts or of the whole bodies), e.g. the physical universe

and its

parts,stars and

moonand sun. But whether these

alone are substances, or there are also others, or only some

J 5 of these, or others as well, or none of these but only some

other things, are substances, must be considered. Some 4

think the limits of body, i.e. surface, line, point, and unit,

are substances, and more so than body or the solid.

Further, some do not think there is anything substantial

besides sensible things, but others think there are eternal

substances which are more in number and more real;

e. g.

Plato posited two kinds of substance the Forms and the

20 objects of mathematics as well as a third kind, viz. the

substance of sensible bodies. And Speusippus made still

more kinds of substance, beginning with the One. and

assuming principles for each kind of substance, one for

1 The schools of Miletus and Elea.2 The Pythagoreans and Empedocles.3

Anaxagoras and the Atomists.4 The Pythagoreans.



BOOK Z. 2 io28b

numbers, another for spatial magnitudes, and then another

for the soul;and by going- on in this way he multiplies the

kinds of substance. And some l

say Forms and numbers 25

have the same nature, and the other things come after

them lines and planes until we come to the substance of

the material universe and to sensible bodies.

Regarding these matters, then, we must inquire which of

the common statements are right and which are not right,

and what substances there are, and whether there are or

are not any besides sensible substances, and how sensible

substances exist, and whether there is a substance capable 3

of separate existence (and if so why and how) or no such

substance, apart from sensible substances;and we must first

sketch the nature of substance.

3 The word substance is applied, if not in more senses,

still at least to four main objects ;for both the essence and

the universal and the genus are thought to be the substance

of each thing, and fourthly the substratum. Now the sub- 35

stratum is that of which everything else is predicated, while

it is itself not predicated of anything else. And so we must

first determine the nature of this;for that which underlies 1029*

a thing primarily is thought to be in the truest sense its

substance. And in one sense matter is said to be of the

nature of substratum, in another, shape, and in a third, the

compound of these. (By the matter I mean, for instance,

the bronze, by the shape the pattern of its form, and by the

compound of these the statue, the concrete whole.) There- 5

fore if the form is prior to the matter and more real, it will

be prior also to the compound of both, for the same reason.

We have now outlined the nature ofsubstance, showing

that it is that which is not predicated of a stratum, but of

which all else is predicated. But we must not merely state

the matter thus;

for this is not enough. The statement

itself is obscure, and further, on this view, matter becomes

substance. For if this is not substance, it baffles us to say 10

what, else is. When all else is stripped offevidently nothing but

matter remains. For while the rest are affections, products,

1 The school of Xenocrates.



io29a METAPHYSICA

and potencies of bodies, length, breadth, and depth are

quantities and not substances (for a quantity is not a sub-

15 stance), but the substance is rather that to which these

belong- primarily. But when length and breadth and depth

are taken away we see nothing left unless there is something

that is bounded by these;so that to those who consider

the question thus matter alone must seem to be substance.

20 By matter I mean that which in itself is neither a particular

thing nor of a certain quantity nor assigned to any other of

the

categories bywrhich

beingis determined. For there is

something of which each of these is predicated, whose

being is different from that of each of the predicates (for

the predicates other than substance are predicated of sub

stance, while substance is predicated of matter). Therefore

the ultimate substratum is of itself neither a particular thing

nor of a particular quantity nor otherwise positively charao

25 terized ; nor yet is it the negations of these, for negations

also will belong to it only by accident.

If we adopt this point of view, then, it follows that matter

is substance. But this is impossible ;for both separability

and thisness are thought to belong chiefly to substance.

And so form and the compound of form and matter would

30 be thought to be substance, rather than matter. The sub

stance compounded of both, i.e. of matter and shape, may

be dismissed;for it is posterior and its nature is obvious.

And matter also is in a sense manifest. But we must

inquire into the third kind of substance;for this is the most

perplexing.

Some of the sensible substances are generally admitted

to besubstances,

so that we must look first

amongthese.

iO2gb

3 For it is an advantage to advance to that which is more

knowable. For learning proceeds for all in this way

through that which is less knowable by nature to that

5which is more knowable

;and just as in conduct our task is

to start from what is good for each and make what is with

out qualification good good for each, so it is our task to

start from what is more knowable to oneself and makewhat^ is knowable by nature knowable to oneself. Now

what is knowable and primary for particular sets of people



BOOK Z. 3 i029b

is often knowable to a very small extent, and has little or

nothing of reality. But yet one must start from that which 10

is barely knowable but knowable to oneself, and try to know

what is knowable without qualification, passing, as has been

said, by way of those very things which one does know.

4 Since at the startx we distinguished the various marks i

by which we determine substance, and one of these was

thought to be the essence, we must investigate this. And 13

. first let us make some linguistic remarks about it. The

essence of each thingis

whatit is said

to \>tpropterse.

2

For being you is not being musical, since you are not by

your very nature musical. What, then, you are by yourT 5

very nature is your essence.

Nor yet is the whole of this the essence of a thing ;not

that which is propter se as white is to a surface, because

being a surface is not identicalwith being white. But again

the combination of both being a white surface is not

the essence of surface, because surface itself is added.

The formula, therefore, in which the term itself is not

present but its meaning is expressed, this is the formula 20

of the essence of each thing. Therefore if to be a white

surface is to be a smooth surface,3to be white and to be

smooth are one and the same.4

But since there are also compounds answering to the

other categories5

(for there is a substratum for each category,

e. g. for quality, quantity, time, place, and motion), we must 35

inquire whether there is a formula of the essence of each of

them, i. e. whether to these compounds also there belongs

an essence, e. g. to white man .

6 Let the compound be

1

I028b33-6.

2It seems convenient here to translate thus the phrase translated in

A. 18 as;

in virtue of itself.3

Cf. De Sensu 442b

1 1 (on Democritus, whose doctrine, this is).4

i. e. this identification does not give the essence of surface (for

surface is repeated) but it gives the essence of white,since this is

not repeated but replaced by an equivalent.5

i. e. compounds of substance with the other categories.GXfvKos (iv0pu*7ros means a pale as opposed to a dark man, not a white

man as opposed to a negro (cf. H. io44b

25, I. ic-58b

34, K. io68a 17).

But as Aristotle has already in this chapter used Xeu/coi/ in the generalsignificance of white

,I have thought it best to preserve this trans

lation here and in chs. 5 and 6.

045-28



io29b METAPHYSICA

denoted by cloak . What is the essence of cloak ? But,

it may be said, this also is not & propter se expression. We

reply that there are just two waysin which a predicate may3 fail to be true of a subject propter se, and one of these

results from the addition, and the other from the omission,

of a determinant. One kind of predicate is not propter se

because the term that is being defined is combined with

another determinant, e.g. if in defining the essence of white

one were to state the formula of white man;the other

because in thesubject

another determinant is combined

with that which is expressed in the formula, e. g. if cloak

meant white man,and one were to define cloak as white

;

iO3Oawhite man is white indeed, but its essence is not to be

white.

But is being-a-cloak an essence at all ? Probably not. For

the essence is precisely what something is;but when an attri

bute is asserted of a subject other than itself, the complex is

not precisely what some *

this is, e. g. white man is not

5 precisely what some 4

this is, since thisness belongs only to

substances. 1 Therefore there is an essence only of those

things whose formula is a definition. But we have a defini

tion not where we have a word and a formula identical in

meaning (for in that case all formulae or sets of words

would be definitions;for there will be some name for any

set of words whatever, so that even the Iliad will be

a definition2

),but where there is a formula of something

10primary ;

and primary things are those which do not imply

the predication of one element in them of another element.

Nothing, then, which is not a species of a genus will

have an essence

only specieswill have it, for these are

thought to imply not merely that the subject participates

in the attribute and has it as an affection,3or has it by

accident;but for everything else as well, if it has a name,

15 there will be a formula of its meaning viz. that this

1 The point is that \(v<6v is one thing, avdpu-rros another, while faovand SITTOVI/ are not distinct things but diirow is only a form of G>OV.

Thus avQpnnos XCVKOS is not an individual type and cannot be defined,while (MOV SLTTOW is an individual type and can be defined.

2Sc. of the word Iliad .

3Cf. I037

b14-21 for the interpretation of this.



BOOK Z. 4 iQ30a

attribute belongs to this subject ;or instead of a simple

formula we shall be able to give a more accurate one;but

there will be no definition nor essence.

Or has definition,like 4

what a thing is, several mean

ings ?* What a thing is in one sense means substance and

the this,in another one or other of the predicates, quan- 2o

tity, quality,and the like. For as is belongs to all things,

not however in the same sense, but to one sort of thing

primarily and to others in a secondary way, so too what

a thing is belongs in the simple sense to substance, but

in a limited sense to the other categories. For even of

a quality we might ask what it is, so that quality also is

a what a thing is \--not in the simple sense, however, but 25

just as, in the case of that which is not, some say,1

empha

sizing the linguistic form, that that which is not is not ts

simply, but ts non-existent;so too with quality.

We must no doubt inquire how weshould

expressour

selves on each point, but certainly not more than how the

facts actually stand. And so now also, since it is evident what

language we use, essence will belong, just as what a thing

is does, primarily and in the simple sense to substance,

and in a secondary way to the other categories also, not 30

essence in the simple sense, but the essence of a quality or

of a quantity. For it must be either by an equivocation

that we say these are, or by adding to and taking from the

meaning of*

are (in the way in which that which is not

known may be said to be known 2

),the truth being that

we use the word neither ambiguously nor in the same

sense, but just as we apply the word medical by virtue of 35

a reference to one and the same thing, not meaning one

and the same thing, nor yet speaking ambiguously ;for iO3Ob

a patient and an operation and an instrument are called

medical neither by an ambiguity nor with a single meaning,

but with reference to a common end. But it does not

matter at all in which of the two ways one likes to describe

the facts;this is evident, that definition and essence in the 5

primary and simple sense belong to substances. Still they

belong to other things as well, only not in the primary1

Cf. PI. Soph. 237, 256 ff.2

i. e. it is known to be unknown.

K 2



io3ob METAPHYSICA

sense. For if we suppose this it does not follow that there

is a definition of every word which means the same as any

formula;

it must mean the same as a particular kind of

formula;and this condition is satisfied if it is a formula of

something which is one, not by continuity like the Iliad or

10 the things that are one by being bound together, but in one

of the main senses of * one,which answer to the senses of

4

is;now *

that which is in one sense denotes a this,in

another a quantity, in another a quality. And so there can

be a formula or definition even ofwhite man,but not in the

sense in which there is a definition either of white or of

a substance.

It is a difficult question, if one denies that a formula with 5

15 an added determinant xis a definition, whether any of the

terms that are not simple but coupled will be definable.

For we must explain them by adding a determinant. E. g.

there is the nose, and concavity, and snubness, which is

compounded out of the two by the presence of the one in

the other, and it is not by accident that the nose has the

attribute either of concavity or of snubness, but in virtue of

20 its nature;nor do they attach to it as whiteness does to

Callias, or to man (because Callias, who happens to be

a man, is white), but as male*

attaches to animal and4

equal to quantity, and as all so-called4

attributes propter

se attach to their subjects.2 And such attributes are those

in which is involved either \hzformula or the name of the

subject of the particular attribute, and which cannot be ex-

25 plained without this;

e. g. white can be explained apart

fromman,

but not female

apart

from animal. Therefore

there is either no essence and definition of any of these

things, or if there is, it is in another sense, as we have said.3

But there is also a second difficulty about them. For if

snub nose and concave nose are the same thing, snub and

30 concave will be the same thing ;but if snub and concave

are not the same (because it is impossible to speak of snub-

1Cf. io29

b30.

2 In the sense of <a& avro explained in An. Post. i. 73* 37-b3-

3 a ^



BOOK Z. 5 io3ob

ness apart from the thing of which it is an attribute propter

se, for snubness is concavity-in-a-nose), either it is im

possible to say snub nose or the same thing will have

been said twice, concave-nose nose ; for snub nose will be

concave- nose nose. And so it is absurd that such things

should have an essence;

if they have, there will be an 35

infinite regress ;for in snub-nose nose yet another

* nose

will be involved.

Clearly, then, only substance is definable. For if the iO3ia

other categories also are definable, it must be by addition

of a determinant, e. g. the qualitative is defined thus, and so

is the odd, for it cannot be defined apart from number;nor

can female be defined apart from animal. (When I say*

by

addition I mean the expressions in which it turns out that

we are saying the same thing twice, as in these instances.)

And if this is true, coupled terms also, like odd number,5

will not be definable (but this escapes our notice because

our formulae are not accurate). But if these also are de

finable, either it is in some other way or, as we said,1

definition and essence must be said to have more than one

sense. Therefore in one sense nothing will have a defini- 10

tion and nothing will have an essence, except substances,

but in another sense other things will have them. Clearly,

then, definition is the formula of the essence, and essence

belongs to substances either alone or chiefly and primarily

and in the unqualified sense.

6 We must inquire whether each thing and its essence are 15

the same or different. This is of some use for the inquiry

concerning substance;for each thing is thought to be not

different from its substance, and the essence is said to be

the substance of each thing.

Now in the case of accidental unities the two would be

generally thought to be different, e.g. white man would 20

be thought to be different from the essence of white man.

For if they are the same, the essence of man and that of

white man are also the same;for a man and a white man

are the same thing, as people say, so that the essence of

1

1030ai;-

bi3.



io3ia METAPHYSICA

white man and that of man would be also the same. But

perhaps it does not follow that the essence of accidental

unities should be the same as that of the simple terms. For

the extreme terms are not in the same way identical with the

25 middle term. But perhaps this might be thought, to follow,

that the extreme terms, the accidents, should turn out to

be the same, e. g. the essence of white and that of musical;

but this is not actually thought to be the case.1

But in the case of so-called self-subsistent things, is a

thing necessarily

the same as its essence ? E.g.

if there are

some substances which have no other substances nor entities

3 prior to them substances such as some assert the Ideas to

be ? If the essence of good is to be different from good-

itself, and the essence of animal from animal-itself, and the

iO3ibessence of being from being-itself, there will, firstly,

be

other substances and entities and Ideas besides those which

are asserted, and, secondly, these others will be prior

substances, if essence is substance. And if the posterior

substances and the prior are severed from each other, (a)

there will be no knowledge of the former,2 and

(/?)the

5 latter3

will have no being. (By*

severed I mean, if the

good-itself has not the essence of good, and the latter has

not the property of being good.) For (a) there is know-

1 The argument used in 11. 21-4 is :

If essence of white man = white man,then since white man = man,and man = essence of man,. . essence of white man = essence of man.

This is absurd, and Aristotle infers that essence of white man does

not = white man.

He next (11. 24-5) hints that this reductio ad absurdum fails because,

while white man is (on the hypothesis under discussion) absolutelyidentical with the essence of white man, as well as man with the essence

of man, white man is identical with man only per accidens. But, he

urges (11. 25-8), it might at least seem to follow from the identification

of an accidental unity with its essence that the accidental extremes,essence of white and essence of musical, are identical :

-

Musical man = essence of musical man.

Man = musical man.

White man = man.

Essence of white man = white man.

. .essence of white man = essence of musical man.. . essence of white = essence of musical.

Which is absurd.2 The Ideas or things-themselves.

3 The essences.



BOOK Z. 6 io3ib

ledge of each thing only when we know its essence. And

(/3)the case is the same for other things as for the good ;

so that if the essence of good is not good, neither is the

essence of reality real, nor the essence of unity one. Andall essences alike exist or none of them does

;so that if 10

the essence of reality is not real, neither is any ofthe others.

Again, that to which the essence of good does not belonglis

not good. The good, then, must be one with the essence of

good, and the beautiful with the essence of beauty, and so

with all things which do not depend on something else but

are self-subsistent and primary. For it is enough if they

are this, even ifthey are not Forms;or rather, perhaps, even

if they are Forms. (At the same time it is clear that if 15

there are Ideas such as some people say there are, it will

not be substratum that is substance;for these must be sub

stances, but not predicable of a substratum;for if they were

they would exist only by being participated in.2

)

Each thing itself, then, and its essence are one and the

same in no merely accidental way, as is evident both

from the preceding arguments and because to know each 20

thing, at least, is just to know its essence, so that even by

the exhibition of instances it becomes clear that both must

be one.

(But of an accidental term, e. g. the musical or*

the

white,since it has two meanings, it is not true to say that

it itself is identical with its essence;for both that to which

the accidental quality belongs, and the accidental quality,

are white, so that in a sense the accident and its essence are 2 5

the same, and in a sense they are not;for the essence of

white is not the same as the man 3 or the white man, but it

is thesame

asthe

attributewhite.)

The absurdity of the separation would appear also if one

were to assign a name to each of the essences;for there

would be yet another essence besides the original one, e. g. to 3

the essence of horse there will belong a second essence.4

1i.e. the Idea of good (1. 5).

2i. e. as immanent in particulars.

sSc. who is white.

4Sc. and so ad

infinitum.As an infinite

processis

absurd, whytake the first step that commits you to it why say that the essence of

horse is separate from the horse ?



io3ib METAPHYSICA

Yet why should not some things be their essences from the

start, since essence is substance ? But indeed not only are

a thing and its essence one, but the formula of them is also

iO32

a

the same, as is clear even from what has been said ; for it is

not by accident that the essence of one, and the one, are

one. Further, if they are to be different, the process will

go on to infinity; for we shall have (i) the essence of one.

and (2) the one, so that to terms of the former kind the

same argument will be applicable.1

5 Clearly, then, each primary and self-subsistent thing is

one and the same as its essence. The sophistical objections

to this position, and the question whether Socrates and to

be Socrates are the same thing, are obviously answered by

the same solution;for there is no difference either in the

standpoint from which the question would be asked, or in

10 that from which one could answer it successfully. We have

explained, then,

in what sense eachthing

is the same as its

essence and in what sense it is not.

Of things that come to be, some come to be by nature, 7

some by art, some spontaneously. Now everything that

comes to be comes to be by the agency of something and

from something and comes to be something. And the

somethingwhich I

sayit comes to be

maybe found in

anycategory ;

it may come to be either a this or of some size

or of some quality or somewhere.

15 Now natural comings to be are the comings to be of those

things which come to be by nature;and that out of which

they come to be is what we call matter;and that by which

they come to be is something which exists naturally ;and

the something which they come to be is a man or a plant or

one of the things of this kind, which we say are substances

20 if anything is all things produced either by nature or by

art have matter;for each of them is capable both of being

and of not being, and this capacity is the matter in each

and, in general, both that from which they are produced is

nature, and the type according to which they are produced

1i. e. if the essence of one is different from the one, the essence of

the essence of one is different from the essence Qf one.



BOOK Z. 7 io32a

is nature (for that which is produced, e. g. a plant or an

animal, has a nature), and so is that by which they are pro

duced the so-called formal nature, which is specifically

the same (though this is in another individual) ; for manbegets man.

Thus, then, are natural products produced ;all other 25

productions are called makings . And all makings pro

ceed either from art or from a faculty or from thought.1

Some of them happen also spontaneously or by luck 2

just

as natural products sometimes do;for there also the same 30

things sometimes are produced without seed as well as from

seed. Concerning these cases, then, we must inquire later,3

but from art proceed the things of which the form is in the

soul of the artist. (By form I mean the essence of each iO32b

thing and its primary substance.) For even contraries have

in a sense the same form;for the substance of a privation

is the opposite substance, e. g. health is the substance of

disease (for disease is the absence of health) ;and health is 5

the formula in the soul or the knowledge of it. The healthy

subject is produced as the result of the following train

of thought : since this is health, if the subject is to be

healthy this must first be present, e. g. a uniform state of

body, and if this is to be present, there must be heat;and the

physician goes on thinkingthus until he reduces the matter

to a final something which he himself can produce. Then

the process from this point onward, i. e. the process towards 10

health, is called a*

making . Therefore it follows that in

a sense health comes from health and house from house,

that with matter from that without matter;for the medical

art and the building art are the form of health and of the

house, and when I speak of substance without matter I meanthe essence.

Of the productions or processes one part is called think-I5

ing and the other making, that which proceeds from the

starting-point and the form is thinking, and that which pro

ceeds from the final step of the thinking is making. And

*

Cf. E. I025b22.

For the theory of these cf. Phys. ii. 5, 6.

3Cf.

b23-30,

a b



io32b METAPHYSICA

each of the other, intermediate, things is produced in the

same way. I mean, for instance, if the subject is to be

healthy his bodily state must be made uniform. What

then does being made uniform imply ? This or that. And20 this depends on his being made warm. What does this

imply ? Something else. And this something is present

potentially ;and what is present potentially is already in

the physician s power.

The active principle then and the starting-point for the

process of becoming healthy is, if it happens by art, the

form in the soul, and if spontaneously, it is that, whatever

it is, which starts the making,1for the man who makes by

25 art, as in healing the starting-point is perhaps the produc

tion ofwarmth (and this the physician produces by rubbing).

Warmth in the body, then, is either a part of health or is

followed (either directly or through several intermediate

steps) by something similar which is a part of health;

andthis, viz. that which produces the part of health, is the

limiting-point,2 and so too with a house (the stones are

the limiting-point here) and in all other cases.

30 Therefore, as the saying goes, it is impossible that any

thing should be produced if there were nothing existing

before. Obviously then some part of the result will pre

exist of necessity ;for the matter is a part ; for this is

present in the process and it is this that becomes some-

i033a

thing. But is the matter an element even in \hzformula ?

We certainly describe in both ways3 what brazen circles

are;we describe both the matter by saying it is brass, and

the form by saying that it is such and such a figure ;and

figure is the proximate genus in which it is placed.The

brazen circle, then, has its matter in itsformula.

5 As for that out of which as matter they are produced,

some things are said, when they have been produced, to be

not that but thaten;

e. g.the statue is not gold but

1Sc. not the thinking, cf. 11. 15-17.

2i. e. the minimum necessary basis.

3

From the proportion established, warmth:

health::

stones:

house,and from the next paragraph, it would appear that warmth is treated

as the matter which when specialized in a particular way becomes

health.



BOOK Z. 7 i033a

golden.1 And a healthy man is not said to be that from which

he has come. The reason is that though a thing comes both

from its privation and from its substratum, which we call its

matter (e. g. what becomes healthy is both a man and an 10

invalid), it is said to come rather from its privation (e. g. it

is from an invalid rather than from a man that a healthy

subject is produced). And so the healthy subject is not

said to be an invalid, but to be a man, and the man is said

to be healthy. But as for the things whose privation is

obscure and nameless, e. g. in brass the privation of a par

ticular shape or in bricks and timber the privation of

arrangement as a house, the thing is thought to be pro- 15

duced front these materials, as in the former case the

healthy man is produced from an invalid. And so, as

there also a thing is not said to be that from which it comes,

here the statue is not said to be wood but is said by a verbal

changeto be wooden 2

,not brass but brazen, not

gold

but

goldenJ

,and the house is said to be not bricks but bricken

(though we should not say without qualification,if we 20

looked at the matter carefully, even that a statue is pro

duced from wood or a house from bricks, because coming to

be implies change in that from which a thing comes to be,

and not permanence). It is for this reason, then, that we

use this way of speaking.

8 Since anything which is produced is produced by some

thing (and this I call the starting-point of the production),

and from something (and let this be taken to be not the priva- 25

tion but the matter;

for the meaning we attach to this

has alreadya been explained), and since something is pro

duced(and

this is either a

sphere

or a circle or whatever

else it may chance to be), just as we do not make the sub

stratum (the brass), so we do not make the sphere, except

incidentally, because the brazen sphere is a sphere and we

make the former. For to make a this is to make a this 30

out of the substratum in the full sense of the word.4

(Imean

1Aristotle uses the example of stone, but unfortunately we do not

say stonen ,

2

Omitting 01 uXoi> in 1. 1 8.3

Cf. 1032* 17.4

i. e. including form as well as matter (cf. lO29a3).



io33a METAPHYSICA

that to make the brass round is not to make the round or

the sphere, but something else, i. e. to produce this form in

something different from itself. For if we make the form,

we must make it out of something else;for this was

i033bassumed. 1

E.g. we make a brazen sphere ;and that in the

sense that out of this, which is brass, we make this other,

which is a sphere.) If, then, we also make the substratum

itself, clearly we shall make it in the same way, and thepro-

5 cesses ofmaking will regress to infinity. Obviously then the

formalso,

2or whatever we

oughtto call the

shape presentin the sensible thing, is not produced, nor is there any production of

it, nor is the essence produced ;for this is that

which is made to be in something else either by art or bynature or by some faculty. But that there is a brazen sphere,

this we make. For we make it out of brass and the sphere ;

10 we bring the form into this particular matter, and the result

is a brazen sphere. But if the essence of sphere in general

is to be produced, something must be produced out of

something. For the product will always have to be

divisible, and one part must be this and another that;

I mean the one must be matter and the other form. If,

then, a sphere is the figure whose circumference is at all

points equidistant from the centre, part of this will be

J 5 the medium in which the thing made will be, and part

will be in that medium, and the whole will be the

thing produced, which corresponds to the brazen sphere.

It is obvious, then, from what has been said, that that

which is spoken of as form or substance is not produced,

but the concrete thing which gets its name from this is

produced,and that in

everything whichis

generatedmatter

is present, and one part of the thing is matter and the

other form.

Is there, then, a sphere apart from the individual spheres

20 or a house apart from the bricks ? Rather we may say

that no this would ever have been coming to be, if this

had been so, but that the form means the such,and is

not a this a definite thing ; but the artist makes, or the

1 a25.

2Sc. as well as the matter.



BOOK Z. 8 i033b

father begets, a such out of as

this;and when it has

been begotten, it is a*

this such V And the whole this,

Callias or Socrates, is analogous to this brazen sphere ,

but man and animal to brazen sphere in general. Obvi- 2 5

ously, then, the cause which consists of the Forms (taken in

the sense in which some maintain the existence of the

Forms, i. e. if they are something apart from the individuals)

is useless, at least with regard to comings-to-be and to

substances;and the Forms need not, for this reason at

least, be self-subsistent substances. In some cases indeed

it is even obvious that the begetter is of the same kind as 30

the begotten (not, however, the same nor one in number,

but in form), i.e. in the case of natural products (for

man begets man), unless something happens contrary to

nature, e. g. the production of a mule by a horse. (And

even these cases are similar;for that which would be found

to be common to horse andass,

the

genusnext above

them,has not received a name, but it would doubtless be both, 1034

a

in fact something like a mule.) Obviously, therefore, it is

quite unnecessary to set up a Form as a pattern (for we

should have looked for Forms in these cases if in any ;for

these are substances if anything is so) ;the begetter is

adequate to the making of the product and to the causing

of the form in the matter. And when we have the whole, 5

such and such a form in this flesh and in these bones, this

is Callias or Socrates;and they are different in virtue of

their matter (for that is different),but the same in form

;for

their form is indivisible.

9 The question might be raised, why some things are pro

duced spontaneously as well as by art, e. g. health, whileothers are not, e. g. a house. The reason is that in some i0

cases the matter which governs the production in the

making and producing of any work of art, and in which

a part of the product is present, some matter is such as to

be set in motion by itself and some is not of this nature,

and of the former kind some can move itself in the particular

1i. e. the artist, or the father, turns a mere piece of matter into

a qualified piece of matter.



io34a METAPHYSICA

way required, while other matter is incapable of this;

for many things can be set in motion by themselves but not

J 5 in some particular way, e.g. that of dancing. The things,

then, whose matter is of this sort, e. g. stones, cannot be

moved in the particular way required,1

except by some

thing else, but in another way they can move themselves

and so it is with fire. Therefore some things will not exist

apart from some one who has the art of making them,

while others will;for motion will be started by these things

20 which have not the art but can themselves be movedby

other things which have not the art or with a motion starting

from a part of the product.2

And it is clear also from what has been said that in a sense

every product of art is produced from a thing which

shares its name (as natural products are produced), or

from a part of itself which shares its name(e. g. the house

is produced from a house, q^ta produced by reason ; for the

art of building is the form of the house), or from some

thing which contains a part of it, if we exclude things

25 produced by accident;for the cause of the thing s producing

the product directlyper se is a part of the product. The

heat in the movement 3caused heat in the body, and this is

either health, or a part of health, or is followed by a part of

health or by health itself. And so it is said to cause health,

because it causes that to which health attaches as a con

sequence.

30 Therefore, as in syllogisms, substance 4is the starting-

point of everything. It is from what a thing is that

syllogisms start;and from it also we now find processes of

productionto start.

5

Things which are formed by nature are in the same case

as these products of art. For the seed is productive in the

same way as the things that work by art;

for it has the

form potentially, and that from which the seed comes has

iO34bin a sense the same name as the offspring only in a sense,

1Sc. for building.

2 i. e. an element of it pre-existing in the things themselves (cf.

3Sc. of the rubber s hand.

4i. e. essence.

5Cf. TO eldos, 1. 24.



BOOK Z. 9 i034b

for we must not expect parent and offspring always to

have exactly the same name, as in the production of

1 human being from human being ;for a woman also

can be produced by a man unless the offspring be an

imperfect form;which is the reason why the parent of

a mule is not a mule. 1 The natural things which (like

the artificial objects previously considered2

)can be produced 5

spontaneously are those whose matter can be moved even

by itself in the way in which the seed usually moves it;

those things which have not such matter cannot be pro

duced except from the parent animals themselves.

But not only regarding substance does our argument

prove that its form does not come to be, but the argument

applies to all the primary classes alike, i. e. quantity, quality,

and the other categories. For as the brazen sphere comes I0

to be, but not the sphere nor the brass, and so too in the

caseof

brassitself,

if it

comesto

be,it is its concrete

unitythat comes to be (for the matter and the form must always

exist before), so is it both in the case of substance and in

that of quality and quantity and the other categories like

wise;for the quality does not come to be, but the wood ot

that quality, and the quantity does not come to be, but the 15

wood or the animal of that size. But we may learn from

these instances a peculiarity of substance, that there mustexist beforehand in complete reality another substance

which produces it, e. g. an animal if an animal is produced ;

but it is not necessary that a quality or quantity should

pre-exist otherwise than potentially.

10 Since a definition is a formula, and every formula has 20

parts,and as the formula is to the

thing,so is the

partof

the formula to the part of the thing, the question is already

being asked whether the formula of the parts must be

present in the formula of the whole or not. For in some

cases the formulae of the parts are seen to be present, and

in some not. The formula of the circle does not include

that of the segments, but that of the syllable includes that 35

of the letters ; yet the circle is divided into segments as the

1Cf. 1033*33.

2

cf.*9-3 2.



io34b METAPHYSICA

syllable is into letters. And further if the parts are prior to

the whole, and the acute angle is a part of the right angle

and the finger a part of the animal, the acute angle will be

3o prior to the right angle and the finger to the man. Butthe latter are thought to be prior ;

for in formula the parts

are explained by reference to them, and in respect also of

the power of existing apart from each other the wholes are

prior to the parts.

Perhaps we should rather say that4

part is used in

several senses. One of these isl

that which measures

another thing in respect of quantity . But let this sense be

set aside;

let us inquire about the parts of which substance

IO35aconsists. If then matter is one thing, form another, the

compound of these a third, and both the matter and the

form and the compound are substance, even the matter is in

a sense called part of a thing, while in a sense it is not, but

onlythe elements of which the formula of the form consists.

E.g. of concavity flesh (for this is the matter in which it is

5 produced) is not a part, but of snubness it is a part ;and

the bronze is a part of the concrete statue, but not of the

statue when this is spoken of in the sense of the form. (For

the form, or the thing as having form, should be said to be

the thing, but the material element by itself must never be

said to be so.) And so the formula of the circle does not

10 include that of the segments, but the formula of the syllable

includes that of the letters;for the letters are parts of the

formula of the form, and not matter, but the segments are

parts in the sense of matter on which the form supervenes ;

yet they are nearer the form than the bronze is when

roundness is produced in bronze. But in a sense not even

every kind of letter will be present in the formula of the

15 syllable, e. g. particular waxen letters or the letters as move

ments in the air;for in these also we have already some

thing that is part of the syllable only in the sense that it is

its perceptible matter. For even if the line when divided

passes away into its halves, or the man into bones and

muscles and flesh,it does not follow that

theyare

composed of these as parts of their essence, but rather as

20 matter;and these are parts of the concrete thing, but not



BOOK Z. 10 i035a

also of the form, i. e. of that to which the formula refers;

wherefore also they are not present in the formulae. In

one kind of formula, then, the formula of such parts will

be present, but in another it must not be present, wherethe formula does not refer to the concrete object. For it

is for this reason that some things have as their constituent

principles parts into which they pass away, while some have

not. Those things which are the form and the matter taken 2 5

together, e. g. the snub, or the bronze circle, pass awayinto these materials, and the matter is a part of them

;but

those things which do not involve matter but are without

matter, and whose formulae are formulae of the form only,

do not pass away, either not at all or at any rate not in

this way. Therefore these materials are principles and 30

parts of the concrete things, while of the form they are

neither parts nor principles. And therefore the clay statue

is resolved into clay and the ball into bronze and Callias

into flesh and bones, and again the circle into its segments ;

for there is a sense of circle in which it involves matter.

For circle is used ambiguously, meaning both the circle. iO35b

unqualified, and the individual circle, because there is no

name peculiar to the individuals.

The truth has indeed now been stated, but still let us state

it

yet

moreclearly, taking up

the

question again.The

parts of the formula, into which the formula is divided, are 5

prior to it, either all or some of them. The formula of the

right angle, however, does not include the formula of the

acute, but the formula of the acute includes that of the right

angle ;for he who defines the acute uses the right angle ;

for the acute is less than a right angle . The circle and

the semicircle also are in a like relation;

for the semicircleis defined by the circle

;and so is the finger by the whole 10

body, for a finger is such and such a part of a man .

Therefore the parts which are of the nature of matter, and

into which as its matter a thing is divided, are posterior ;

but those which are of the nature of parts of the formula,

and of the substance according to its formula, are prior,

either all or some of them. And since the soul of animals

(for this is the substance of a living being) is their substance 15



io35b METAPHYSICA

according to the formula, i. e. the form and the essence of

a body of a certain kind (at least we shall define each part,

if we define it well, not without reference to its function,

and this cannot belong to it without perception 1), so that

the parts of soul are prior, either all or some of them, to

the concrete animal,and so too with each individual

20 animal;and the body and its parts are posterior to this,

the essential substance, and it is not the substance but

the concrete thing that is divided into these parts as its

matter : this being so, to the concrete thing these are in

a sense prior, but in a sense they are not. For they cannot

even exist if severed from the whole;for it is not a finger

in any and every state that is the finger of a living thing, but

25 a dead finger is a finger only in name. Some parts are

neither prior nor posterior to the whole, i. e. those which

are dominant and in which the formula, i. e. the essential

substance,is

immediately present, e. g. perhaps the heart orthe brain

;for it does not matter in the least which of the

two has this quality. But man and horse and terms which

are thus applied to individuals, but universally, are not sub

stance but something composed of this particular formula

30 and this particular matter treated as universal;and as

regards the individual, Socrates already includes in him

ultimate individual matter ; and similarly in all other cases.

* A part may be a part either of the form(i.

e. of the

essence), or of the compound of the form and the matter, or

of the matter itself. But only the parts of the form are

parts of the formula, and the formula is of the universal;

1036* for*

being a circle is the same as the circle, and being

a soul the same as the soul. But when we come to the

concrete thing, e. g. this circle, i. e. one of the individual

circles, whether perceptible or intelligible (I mean by intel

ligible circles the mathematical, and by perceptible circles

5 those ofbronze and of wood), of these there is no definition,

but they are known by the aid of intuitive thinking or of

perception ;and when they pass out of this complete realiza

tion it is not clear whether they exist or not;

but theyare

always stated and recognized by means of the universal for-

1 And therefore not without soul.



BOOK Z. 10 1036

mula. But matter is unknowable in itself. And some matter

is perceptible and some intelligible, perceptible matter being10

for instance bronze and wood and all matter that is change

able, and intelligible matter being that which is presentin perceptible things not qzia perceptible, i. e. the objects of

mathematics.

We have stated, then, how matters stand with regard to

whole and part, and their priority and posteriority. But

when any one asks whether the right angle and the circle

and the animal are prior, or the things into which they are 15

divided and of which they consist, i.e. the parts,we must meet

the inquiry by saying that the question cannot be answered

simply. For if even bare soul is the animal or 1the

living thing, or the soul of each individual is the individual

itself, and being a circle is the circle, and being a right

angle and the essence of the right angle is the right angle,

then the whole in one sense must be called posterior to the

part in one sense, i. e. to the parts included in the formula

and to the parts of the individual right angle (for both the 20

material right angle which is made of bronze, and that

which is formed by individual lines, are posterior to their

parts) ;while the immaterial right angle is posterior to the

parts included in the formula, but prior to those included

in the particular instance, and the question must not beanswered simply. If, however, the soul is something

different and is not identical with the animal, even so some

parts must, as we have maintained, be called prior and 2 5

others, must not.

II Another question is naturally raised, viz. what sort of

partsbelong

to the form and what sort not to the form, but

to the concrete thing. Yet if this is not plain it is not

possible to define any thing ;for definition is of the universal

and of the form. If then it is not evident what sort of parts

are of the nature of matter and what sort are not, neither 30

will the formula of the thing be evident. In the case of

things which are found to occur in specifically different

materials, as a circle may exist in bronze or stoneor

wood,

1Sc. to put it more widely so as to include the vegetable world.

L 2



io36a METAPHYSICA

it seems plain that these, the bronze or the stone, are no

part of the essence of the circle, since it is found apart from

35 them. Of things which are not seen to exist apart, there

1036** is no reason why the same may not be true, just as if all

circles that had ever been seen were of bronze;for none

the less the bronze would be no part of the form;but it is

hard to eliminate it in thought. E. g. the form of man is

always found in flesh and bones and parts of this kind;are

5 these then also parts of the form and the formula ? No,

they are matter;but because man is not found also in other

matters we are unable to perform the abstraction.

Since this is thought to be possible, but it is not clear

when it is the case, some peoplel

already raise the question

even in the case of the circle and the triangle, thinking that

it is not right to define these by reference to lines and to

10 the continuous, but that all these are to the circle or the

triangle as flesh and bones are to man, and bronze or stoneto the statue

;and they reduce all things to numbers, and

they say the formula of line is that of two . And of

those who assert the Ideas some 2 make * two the line-itself,

15 and others make it the Form of the line;for in some cases

they say the Form and that of which it is the Form are the

same, e. g. two and the Form of two;but in the case of

line they say this is no longer so.

It follows then that there is one Form for many things

whose form is evidently different (a conclusion which con

fronted the Pythagoreans also) ;and it is possible to make

one thing the Form-itself of all, and to hold that the others

are not Forms;but thus all things will be one.

We havepointed

out, then, that the

question

of defini

tions contains some difficulty, and why this is so. And so

to reduce all things thus to Forms and to eliminate the

matter is useless labour;for some things surely are a par

ticular form in a particular matter, or particular things in

a particular state. And the comparison which Socrates the

younger3 used to make in the case of animal 4

is not

1

Aristotle is thinking of Pythagoreans.2 This probably includes Plato himself.

3Cf. PI. Theaet. 147 D ; Soph. 218 B

;Pol. 257 C

; Epp. 358 D.

4Cf.

a34~

b7-

20



BOOK Z. ii ios6b

sound;for it leads away from the truth, and makes one

suppose that man can possibly exist without his parts, as

the circle can without the bronze. But the case is not

similar ; for an animal is something perceptible, and it is

not possible to define it without reference to movement

nor, therefore, without reference to the parts being in

a certain state. For it is not a hand in any and every 30

state that is a part of man, but only when it can fulfil

its work, and therefore only when it is alive;

if it is not

alive it is not a part.

Regarding the objects of mathematics, why are the

formulae of the parts not parts of the formulae of the

wholes;

e. g. why are not the semicircles included in

the formula of the circle ? It cannot be said,l

because

these parts are perceptible things ;for they are not. But

perhaps this makes no difference;

for even some things 35

which are notperceptible

must have matter;indeed there

1037**is some matter in everything which is not an essence and

a bare form but a*

this . The semicircles, then, will not

be parts of the universal circle, but will be parts of the

individual circles, as has been said before l

;for while one

kind of matter is perceptible, there is another which is

intelligible.

It is clear also that the soul is the primary substance and 5

the body is matter, and man or animal is the compound of

both taken universally ;and Socrates or Coriscus

,if

even the soul of Socrates may be called Socrates,2 has two

meanings (for some mean by such a term the soul, and

others mean the concrete thing), but if Socrates or4

Coriscus means simply this particular soul and this par

ticular body, the individual is analogous to the universal in

its composition.3

Whether thereis, apart from the matter of such sub- 10

stances, another kind of matter, and one should look for

some substance other than these, e. g. numbers or some

thing of the sort, must be considered later.4 For it is for

1

1035* 3o-b 3. 2 Cf. I036a 16-17, H - i43b 2-4.3

i.e. as man = soul -f body, Socrates = this soul + this body.4

Cf. M, N.



i037a METAPHYSICA

the sake of this that we are trying- to determine the nature

of perceptible substances as well, since in a sense the inquiry15 about perceptible substances is the work of physics, i. e. ot

second philosophy ;for the physicist must come to know

not only about the matter, but also about the substance ex

pressed in the formula, and even more than about the other.

And in the case of definitions, how the elements in the

formula are parts of the definition, and why the definition

is one formula (for clearly the thing is one, but in virtue of

20 what is the

thing one, althoughit has

parts ?),

this must

be considered later.1

What the essence is and in what sense it is independent,

has been stated universally in a way which is true of every

case,2 and also why the formula of the essence of some

things contains the parts of the thing defined, while that of

others does not. And we have stated that in the formula

25 of the substance the material parts will not be present (for

they are not even parts of the substance in that sense, but

of the concrete substance;but of this there is in a sense

a formula, and in a sense there is not;

for there is no

formula of it with its matter, for this is indefinite, but there

is a formula of it with reference to its primary substance

e. g.in the case of man the formula of the soul

,for the

substance is the indwelling form, from which and the

matter the so-called concrete substance is derived;

3e. g.

30 concavity is a form of this sort, for from this and the nose

arise snub nose and snubness) ;

but in the concrete

substance, e. g. a snub nose or Callias, the matter also will

be present.4 And we have stated that the essence and the

iO37

b

thingitself are in some cases the same

;i. e. in the case of

primary substances, e. g. curvature and the essence of curva

ture, if this is primary. (By a*

primary substance I mean

one which does not imply the presence of something in

something else, i. e. in something that underlies it which

acts as matter.) But things which are of the nature of

matter, or of wholes that include matter, are not the same

5 as their essences, nor are accidental unities like that of

1Cf. z. 12, H. 6.

2 Ch. 4.& Chs. 10, ii.

4 Ch. 5.



BOOK Z. ii io37b

Socrates and *

musical;

for these are the same only by

accident.1

12 Now let us treat first of definition, in so far as we have

not treated of it in the Analytics2

;for the problem stated

in them 3is useful for our inquiries concerning substance.

I mean this problem : wherein can consist the unity of 10

that, the formula of which we call a definition, as for

instance, in the case of man,*

two-footed animal;for let

this be the formula of man. Why, then, is this one, and

not many, viz.

4

animal and*

two-footed ? For in thecase of man and *

pale there is a plurality when one term 15

does not belong to the other, but a unity when it does

belong and the subject, man, has a certain attribute;for

then a unity is produced and we have the pale man . In

the present case, on the other hand,4 one does not share in

the other;the genus is not thought to share in its differ

entiae (for then the same thing would share in contraries ;

for the differentiae by which the genus is divided are con- 20

trary). And even if the genus does share in them, the

same argument applies, since the differentiae present in

man are many, e. g. endowed with feet, two-footed, feather-

less. Why are these one and not many? Not because

they are present in one thing ;for on this principle a unity

can be made out of all the attributes ofa thing. But surely

all the attributes in the definition must be one;

for the 25

definition is a single formula and a formula of substance, so

that it must be a formula of some one thing ;for substance

means a one and a this,as we maintain.

We must first inquire about definitions reached by the

method of divisions. There is

nothingin the definition

except the first-named genus and the differentiae. The 30

other genera are the first genus and along with this the

differentiae that are taken with it, e.g.

the first may be

1

animal,the next

* animal which is two-footed,and again

1

animal which is two-footed and featherless,and similarly

if the definition includes more terms. And in general it iO38a

1

Ch. 6.2

Cf. An. Post. ii. 3-10, 13.3

Cf. ib. 97*29.4That of

*

animal and two-footed .



io38a METAPHYSICA

makes no difference whether it includes many or few

terms, nor, therefore, whether it includes few or simply

two;and of the two the one is differentia and the other

genus; e. g. in

*

two-footed animal4

animal is genus, andthe other is differentia.

5 If then the genus absolutely does not exist apart from

the species-of-a-genus, or if it exists but exists as matter

(for the voice is genus and matter, but its differentiae make

the species, i. e. the letters, out of it), clearly the definition

is the formula which comprises the differentiae.

But it is also necessary that the division be by the differentia

ofthe differentia ;e. g. endowed with feet is a differentia

10 of animal; again the differentia of animal endowed with

feet must be of it qua endowed with feet. Therefore we

must not say, if we are to speak rightly, that of that which

is endowed with feet one part has feathers and one is

featherless (if we do this we do it through incapacity) ;we

must divide it only into cloven-footed and not-cloven;for

these are differentiae in the foot;

cloven-footedness is

15 a form of footedness. And the process wants always to goon so till it reaches the species that contain no differences.

And then there will be as many kinds of foot as there are

differentiae, and the kinds of animals endowed with feet

will be equal in number to the differentiae. If then this is

so, clearly the last differentia will be the substance of the

20 thing and its definition, since it is not right to state the

same things more than once in our definitions;

for it is

superfluous. And this does happen ;for when we say

1 animal endowed with feet and two-footed we have said

nothing other than4

animal having feet, having two feet;

and if we divide this by the proper division, we shall be

saying the same thing more than once as many times as

there are differentiae.

35 If then a differentia of a differentia be taken at each step,

one differentia the last will be the form and the sub

stance;but if we divide according to accidental qualities,

e. g. if we were to divide that which is endowed with feet

into the white and the black, there will be as many differ

entiae as there are cuts. Therefore it is plain that the



BOOK Z. 12 ioa8a

definition is the formula which contains the differentiae, or,

according to the right method, the last of these. This 30

would be evident, if we were to change the order of such

definitions, e. g. of that of man, saying animal which is

two-footed and endowed with feet;

for endowed with

feet is superfluous when*

two-footed has been said. But

there is no order in the substance;for how are we to think

the one element posterior and the other prior ? Regarding

the definitions, then, which are reached by the method of

divisions, let this suffice as our first attempt at stating their 3s

nature.

13 Let us return to the subject of our inquiry, which is iO38b

substance. As the substratum and the essence and the

compound of these are called substance, so also is the

universal. About two of these we have spoken ;both about

the essence l and about the substratum,2 of which we have

said 3 that it underlies in two senses, either being a4 this 5

which is the way in which an animal underlies its attri

butes or as the matter underlies the complete reality.

The universal also is thought by some to be in the fullest

sense a cause, and a principle ;therefore let us attack the

discussion of this point also. For it seems impossible that

any universal term should be the name of a substance. For

firstly the substance of each thing is that which is peculiar

to it, which does not belong to anything else;

but the 10

universal is common, since that is called universal which is

such as to belong to more than one thing. Of which indi

vidual then will this be the substance ? Either of all or of

none;but it cannot be the substance of all. And if it is to

be thesubstance of one,

this

onewill

bethe

othersalso

;

for things whose substance is one and whose essence is one

are themselves also one.

Further, substance means that which is not predicable of 15

a subject, but the universal is predicable of some subject

always.

But perhaps the universal, while it cannot be substance

in the way in which the essence is so, can be present in this ;

1Chs. 4-6, 10-12.

2Ch. 3.

3

io29a2-3, 23-4.



ios8b METAPHYSICA

e. g.*

animal can be present in man and horse . Then

clearly it is1 a formula of the essence. And it makes

no difference even if it is2 not a formula of everything that

20 is in the substance ; for none the less the universal will

be the substance of something, as* man is the substance of

the individual man in whom it is present, so that the same

result will follow once more;

for the universal, e. g.4 animal

,will be the substance of that in which it is present

as something peculiar to it. And further it is impossible

and absurd that the this,

i. e. the substance, if it consists

25 of parts, should not consist of substances nor of what is

a this,but of quality ;

for that which is not substance,

i. e. the quality, will then be prior to substance and to the

4

this . Which is impossible ;for neither in formula nor

in time nor in coming to be can the modifications be

prior to the substance;for then they will also be separ

able fromit.

Further, Socrates will contain a substance

present in a substance 3,so that this will be the substance

30 of two things. And in general it follows, if man and

such things are substance, that none of the elements in

their formulae is the substance of anything, nor does it

exist apart from the species or in anything else;

I mean,

for instance, that no animal exists apart from the parti

cular kinds of animal, nor does any other of the elements

present in formulae exist apart.

If, then, we view the matter from these standpoints, it is

35 plain that no universal attribute is a substance, and this is

plain also from the fact that no common predicate indicates

iO39a a this

,but rather a such . If not, many difficulties

follow and especially the third man .

4

The conclusion is evident also from the following con

sideration. A substance cannot consist of substances present

in it in complete reality ;for things that are thus in com-

5 plete reality two are never in complete reality one, though

if they are potentially two, they can be one (e.g. the

double line consists of two halves potentially ;for the

1

Reading in 1. 19 m .

2

Reading in 1.

3

Reading in 1. 29 ovaia ova-ia.*

Cf. A. 99Ob

17.



BOOK Z. 13 1039

complete realization of the halves divides them from one

another) ;therefore if the substance is one, it will not con

sist of substances present in it and present in this way,

which Democritus describes rightly ; he says one thing can

not be made out of two nor two out ofone;for he identifies 10

substances with his indivisible magnitudes. It is clear there

fore that the same will hold good of number, if number is

a synthesis of units, as is said by some 1;for two is either

not one, or there is no unit present in it in complete

reality.

But our result involves a difficulty.If no substance can 15

consist of universals because a universal indicates a such,

not a this,and if no substance can be composed of

substances existing in complete reality, every substance

would be incomposite, so that there would not even be

a formula of any substance. But it is thottght by all and

wasstated

long ago

2

thatit is

either only, or primarily,substance that can be defined

; yet now it seems that not 20

even substance can. There cannot, then, be a definition of

anything ;or in a sense there can be, and in a sense there

cannot. And what we are saying will be plainer from what

follows.3

14 It is clear also from these

very

facts whatconsequenceconfronts those who say the Ideas are substances capable

of separate existence, and at the same time make the Form 2 5

consist of the genus and the differentiae. For if the Forms

exist and animal is present in* man and *

horse,

it is

either one and the same in number, or different. (In

formula it is clearly one;for he who states the formula will

go through the same formula in either case.) If then there 30

is a man-in-himself who is a this and exists apart, the

parts also of which he consists, e. g.* animal and two-

footed,must indicate thises

,and be capable of separate

existence, and substances;therefore animal

,as well as

man,must be of this sort.

Now(i)

if the animal in the horse and in man is

1Thales is said to have defined number as a system of units .

2Cf. 1031*11-14.

3Cf. Z. 15, H. 6.



i039a METAPHYSICA

one and the same, as you are with yourself, (a) how will the

one in things that exist apart be one, and how will this

animal escape being- divided even from itself?

Further, (6) if it is to share in two-footed and*

many-footed

,an impossible conclusion follows

;for contrary

attributes will belong at the same time to it although it is

one and a this . If it is not to share in them, what is the

relation implied when one says the animal is two-footed or

5 possessed of feet ? But perhaps the two things are put

together and are*

in contact,or are mixed . Yet all

these expressions are absurd.

But (2) suppose the Form to be different in each species.

Then there will be practically an infinite number of things

whose substance isi animal

;for it is not by accident that

* man has animal for one of its elements. Further, many

things will be animal-itself . For(i)

the animal in each

10 species will be the substance of the species;

for it is after

nothing else that the species is called;if it were, that other

would be an element in man,

i. e. would be the genus of

man. And further, (ii)all the elements of which man is

composed will be Ideas. None of them, then, will be the

Idea of one thing and the substance of another; this is

impossible. The animal, then, present in each species of

animals will be animal-itself. Further, from what is this

4

animal in each species derived, and how will it be derived

15 from animal-itself ? Or how can this animal,whose

essence is simply animality, exist apart from animal-itself?

Further, (3)in the case of sensible things both these con

sequences and others still more absurd follow. If, then,

these consequences are impossible, clearly there are not

Forms of sensible things in the sense in which some maintain

their existence.

20 Since substance is of two kinds, the concrete thing and 15

the formula(I mean that one kind of substance is the for

mula taken with the matter, while another kind is the

formulain

its generality), substances in the former senseare capable of destruction (for they are capable also of

generation), but there is no destruction of the formula in



BOOK Z. 15 io39b

the sense that it is ever in course of being destroyed (for

there is no generation of it either;the being of house is

not generated, but only the being of this house), but with- 25

out generation and destruction formulae are and are not ;

for it has been shown lthat no one begets nor makes

these. For this reason, also, there is neither definition

of nor demonstration about sensible individual substances,

because they have matter whose nature is such that they

are capable both of being and of not being ;for which 30

reason all the individual instances of them are destructible.

If then demonstration is of necessary truths and definition

is a scientific process, and if, just as knowledge cannot be

sometimes knowledge and sometimes ignorance, but the

state which varies thus is opinion, so too demonstration and

definition cannot vary thus, but it is opinion that deals with

that which can be otherwise than as it is, clearly there can 1040**

neither be definition of nor demonstration about sensible

individuals. For perishing things are obscure to those who

have the relevant knowledge, when they have passed from

our perception ;and though the formulae remain in the

soul unchanged, there will no longer be either definition or

demonstration. And so when one of the definition- 5

mongers defines any individual, he must recognize that his

definition may always be overthrown ; for it is not possible

to define such things.

Nor is it possible to define any Idea. For the Idea is,

as its supporters say, an individual, and can exist apart ;

and the formula must consist of words;and he who defines 10

must not invent a word (for it would be unknown), but the

established words are common to all the members of a

class;these then must apply to something besides the thing

defined;

e. g. if one were defining you, he would say an

animal which is lean or pale ,or something else which

will apply also to some one other than you. If any one

were to say that perhaps all the attributes taken apart may

belong to many subjects, but together they belong only to

this one, we must reply first that they belong also to both 15

the elements;

e. g,l

two-footed animal belongs to animal

1Ch. 8.



i040a METAPHYSICA

and to the two-footed. (And in the case ofeternal entities1

this is even necessary, since the elements are prior to and

parts of the compound ; nay more, they can also exist

apart, if*

man can exist apart. For either neither or both20 can. If, then, neither can, the genus will not exist apart

from the various species ;but if it does, the differentia will

also.) Secondly, we must reply that animal and two-

footed are prior in being to*

two-footed animal;

and

things which are prior to others are not destroyed when

the others are.

Again, if the Ideas consist of Ideas (as they must, since

elements are simpler than the compound), it will be further

necessary that the elements also of which the Idea consists,

e. g. animal and two-footed,should be predicated of

25 many subjects. If not, how will they come to be known ?

For there will then be an Idea which cannot be predicated

ofmoresubjects

than one. But this is notthought possible

every Idea is thought to be capable of being shared.

As has been said,2

then, the impossibility of defining

individuals escapes notice in the case of eternal things,

especially those which are unique, like the sun or the moon.

30 For people err not only by adding attributes whose removal

the sun would survive, e. g. going round the earth or

night-hidden (for from their view it follows that if it

stands still or is visible,3

it will no longer be the sun;but

it is strange if this is so;for the sun means a certain

sitbstance] ;but also by the mention ofattributes which can

belong to another subject ;e. g. if another thing with the

stated attributes comes into existence, clearly it will be

iO4oba sun

;the formula therefore is general. But the sun was

supposed to be an individual, like Cleon or Socrates. After

all, why does not one of the supporters ofthe Ideas produce

a definition of an Idea ? It would become clear, if they

tried, that what has now been said is true.

5 Evidently even of the things that are thought to be sub- 16

stances, most are only potencies, both the parts ofanimals

(fornone of them exists separately ;

and when they are

1i. e. the Ideas.

2Cf. 1. 17.

3Sc. at night.



BOOK Z. 16 i040b

separated, then too they exist, all of them, merely as matter)

and earth and fire and air;for none of them is a unity, but

as it were a mere heap, till they are worked up and some

unity is made out of them. One might most readily suppose 10

the parts of living1

things and the parts of the soul nearly

related to them to turn out to be both, i.e. existent in com

plete reality as well as in potency, because they have sources

of movement in something in their joints ;for which reason

some animals live when divided. Yet all the parts must

exist only potentially, when they are one and continuous by

nature, not by force or by growing into one, for such a 15

phenomenon is an abnormality.

Since the term unity is used like the term being ,and

the substance of that which is one is one, and things whose

substance is numerically one are numerically one, evidently

neither unity nor being can be the substance of things, just

as

beingan element or a

principle

cannot be the substance,

but we ask what, then, the principle is, that we may reduce 20

the thing to something more knowable. Now of these

concepts being and unity are more substantial than

principle or element or cause,but not even the

former are substance, since in general nothing that is com

mon is substance;for substance does not belong to anything

but to itself and to that which has it, of which it is the

substance. Further, that which is one cannot be in many 25

places at the same time, but that which is common is present

in many places at the same time;so that clearly no universal

exists apart from its individuals.

But those who say the Forms exist, in one respect are

right, in giving the Forms separate existence, if they are

substances ; but in another respect they are not right,

because they say the one over many is a Form. The reason30

for their doing this is that they cannot declare what are the

substances of this sort, the imperishable substances which

exist apart from the individual and sensible substances.

They make them, then, the same in kind as the perishable

things (for this kind of substance we know) man-himself

and horse-itself, adding to the sensible things the word

itself. Yet even if we had not seen the stars, none the io4ia



io4ia METAPHYSICA

less, I suppose, would they have been eternal substances

apart from those which we knew;so that now also if we

do not know what non-sensible substances there are, yet it

is doubtless necessary that there should be some. Clearly,

then, no universal term is the name of a substance, and no

5 substance is composed of substances.

Let us state what, i. e. what kind of thing, substance 17

should be said to be, taking once more another starting-

point ;for perhaps from this we shall get a clear view also

ofthat substance which exists apart from sensible substances.

Since, then, substance is a principle and a cause, let us pur-

10 sue it from this starting-point. The why is always sought

in this form why does one thing attach to some other ?

For to inquire why the musical man is a musical man, is

either to inquire as we have said why the man is musical,

or it is something else. Now why a thing is itself is

15 a meaningless inquiry (for (to give meaning to the question

why )the fact or the existence of the thing must already

be evident e. g. that the moon is eclipsed but the fact

that a thing is itself is the single reason and the single

cause to be given in answer to all such questions as whythe man is man, or the musician musical \

lunless one were

to answer because each

thing

is

inseparable

from itself,

and its being one just meant this; this, however, is com

mon to all things and is a short and easy way with the

20question). But we can inquire why man is an animal of

such and such a nature. This, then, is plain, that we are not

inquiring why he who is a man is a man. We are inquiring,

then, why something is predicable of something (that it is

predicable must be clear ; for if not, the inquiry is an

inquiry into nothing). E. g. why does it thunder ? This

is the same as why is sound produced in the clouds ?

2 5 Thus the inquiry is about the predication of one thing of

another. And why are these things, i. e. bricks and stones,

a house ? Plainly we are seeking the cause. And this is

the essence (to speak abstractly), which in some cases is the

1Sc. and therefore in this case, when the fact is known, there is no

question as to the why .



BOOK Z. 17 i04ia

end, e. g. perhaps in the case of a house or a bed, and in

some cases is the first mover;for this also is a cause. But 3

while the efficient cause is sought in the case of genesis

and destruction, the final cause is

sought

in the case of being

also.

The object of the inquiry is most easily overlooked where

one term is not expressly predicated of another(e. g. when

we inquire* what man is

),because we do not distinguish and iO4i

b

do not say definitely that certain elements make up a certain

whole. But we must articulate our meaning before we

begin to inquire; if not, the inquiry is on the border-line

between being a search for something and a search for

nothing. Since we must have the existence of the thing as

something given, clearly the question is why the matter is

some definite thing ;e. g. why are these materials a house ?

Because thatwhich was the essence ofa house is present. And 5

why is this individual thing, or this body having this form, a

man ? Therefore what we seek is the cause, i. e. the form, byreason of which the matter is some definite thing ;

and this

is the substance of the thing. Evidently, then, in the case

of simple terms no inquiry nor teaching is possible ;our 10

attitude towards such things is other than that of inquiry.

Since * that which is compounded out of something so

that the whole is one, not like2a heap but like a syllable,

now the syllable is not its elements, ba is not the same as b

and , nor is flesh fire and earth (for when these are separated

the wholes, i. e. the flesh and the syllable, no longer exist,

but the elements of the syllable exist, and so do fire and 15

earth) ;the syllable, then, is something not only its ele

ments (the vowel and the consonant) but also something

else,and the flesh is not

onlyfire and earth or the hot and

the cold, but also something else : if, then, that something

must itself be either an element or composed of elements,

(i) if it is an element the same argument will again apply ;ao

for flesh will consist of this and fire and earth and some

thing still further, so that the process will go on to infinity.

1Not even the protasis of the sentence beginning io4i

b n is ever

completed;

theparenthesis beginning 17

Se<7iAXa/3^,

1.

12,is so

longthat the original construction is forgotten.2

Omitting ai/ in 1. 12.

645-28 M



i04ib METAPHYSICA

But(2)

if it is a compound, clearly it will be a compoundnot of one but of more than one (or else that one will be

the thing itself), so that again in this case we can use the

same argument as in the case of flesh or of the syllable.

35 But it would seem that this*

other is something, and not

an element, and that it is the cause which makes this thing

flesh and that a syllable. And similarly in all other cases.

And this is the sitbstance of each thing (for this is the

primary cause of its being) ;and since, while some things

are not substances, as many as are substances are formed

inaccordance with

a nature of their

ownand

byaprocess

3 of nature, their substance would seem to be this kind of

nature V which is not an element but a principle. An

element, on the other hand, is that into which a thing is

divided and which is present in it as matter;

e. g. a and b

are the elements of the syllable.

1

Sc. the formal cause. Cf. A. ioi4b36 in contrast with ib. 27.



BOOK H

I WE must reckon up the results arising from what has been 1042*

said, and compute the sum of them, and put the finishing

touch to our inquiry. We have said that the causes, princi- 5

pies,and elements ofsubstances are the object ofour search.

1

And some substances are recognized by every one, but some

have been advocated by particular schools. Those gener

ally recognized are the natural substances, i.e. fire, earth,

water, air, &c., the simple bodies; secondly, plants and

their parts, and animals and the parts of animals;and 10

finally the physical universe and its parts ;while some

particular schools say that Forms and the objects of mathe

matics are substances.2 But there are arguments which

lead to the conclusion that there are other substances, the

essence and the substratum. Again, in another way the

genus seems more substantial than the various species, and

the universal than the particulars.3 And with the universal 15

and the genus the Ideas are connected;

it is in virtue of the

same argument that they are thought to be substances.

And since the essence is substance, and the definition is

a formula of theessence,

for this reason we have discussed

definition and essential predication.4 Since the definition

is a formula, and a formula has parts, we had to consider

also with respect to the notion of part ,what are parts of 20

the substance and what are not, and whether the parts of the

substance are also parts of the definition.5

Further, too,

neither the universal nor the genus is a substance;

6 we

must inquire later into the Ideas and the objects of mathematics

;

7for some say these are substances as well as the

sensible substances.

But now let us resume the discussion of the generally

recognized substances. These are the sensible substances, 25

and sensible substances all have matter. The substratum is

1

Cf. z. i.

2

Cf. z. 2.

3

Cf. Z. 3. io28b

33-6.4Cf. Z. 4-6, 12, 15.

6Cf. Z. 10, ii.

6Cf. Z. 13, 14, 16. I04o

bi6-i04i

a5.

7Cf. M and N.

M 2



io4 2a METAPHYSICA

substance, and this is in one sense the matter (and by matter

I mean that which, not being- a this actually, is potentially

a*

this),and in another sense the formula or shape (that

which being athis

can be separately formulated),and

30 thirdly the complex of these two, which alone is generated

and destroyed, and is, without qualification, capable of

separate existence;

for of substances completely expres

sible in a formula some are separable and some are not.

But clearly matter also is substance;for in all the oppo

site changes that occur there is something which underlies

the changes, e. g. in respect of place that which is now here

35 and again elsewhere, and in respect of increase that which

is now of one size and again less or greater,and in respect

of alteration that which is now healthy and again diseased;

iO42b and similarly in respect of substance there is something that

is now being generated and again being destroyed, and

nowr lunderlies the process as a

l

this and again2

underlies

it in respect of a privation of positive character. And in this

change the others are involved. But in either one or two

5 of the others this is not involved;for it is not necessary if

a thing has matter for change of place that it should also

have matter for generation and destruction.

The difference between becoming in the full sense and

becoming in a qualified sense has been stated in our physicalworks.

3

Since the substance which exists as underlying and 2

as matter is generally recognized, and this is that which

10 exists potentially, it remains for us to say what is the sub

stance, in the sense of actuality, of sensible things. Demo-

critus seems to think there are three kinds of difference

between things ;the underlying body, the matter, is one

and the same, but they differ either in rhythm, i. e. shape,

or in turning, i. e. position, or in inter-contact, i. e. order.4

15 But evidently there are many differences;

for instance,

some things are characterized by the mode of composition

1 Sc. in the case of destruction. 2 Sc. in the case of generation.8

Cf. Phys. 22 Sa12-20, De Gen. et Corr. 317* 17-31.

4Cf. A. 98s

b13-19.



BOOK H. a i042b

of their matter, e. g. the things formed by blending, such as

honey-water ;and others by being bound together, e. g.

a bundle;and others by being glued together, e. g. a book

;

and others by being nailed together, e. g. a casket;

andothers in more than one of these ways ;

and others by

position, e. g. threshold and lintel (for these differ by being

placed in a certain way) ;and others by time, e. g. dinner 2o

and breakfast;and others by place, e. g. the winds

;and

others by the affections proper to sensible things, e. g. hard

ness and softness, density and rarity, dryness and wetness;

and some things by some of these qualities, others by them

all, and in general some by excess and some by defect.

Clearly, then, the word is has just as many meanings ; 25

a thing is a threshold because it lies in such and such a posi

tion, and its being means its lying in that position, while

being ice means having been solidified in such and such

a way. And the being of some things will be defined by

all these qualities, because some parts of them are mixed,

others are blended, others are bound together, others are 3

solidified, and others use the other differentiae;

e. g. the

hand or the foot requires such complex definition. Wemust grasp, then, the kinds of differentiae (for these will

be the principles of the being of things), e.g. the things

characterized bythe

more andthe

less, or by the denseand the rare, and by other such qualities ;

for all these are

forms of excess and defect. And anything that is charac- 35

terized by shape or by smoothness and roughness is

characterized by the straight and the curved. And for

other things their being will mean their being mixed, and 1043**

their not being will mean the opposite.

It is clear, then, from these facts that, since its substance is

the cause of each thing s being, we must seek in these

differentiae what is the cause of the being of each of these

things. Now none of these differentiae is substance, even

when coupled with matter, yet it is what is analogous to sub

stance in each case;and as in substances that which is 5

predicated of the matter is the actuality itself, in all other

definitions also it is what most resembles fullactuality.

E. g. if we had to define a threshold, we should say wood



io43a METAPHYSICA

or stone in such and such a position ,and a house we should

define as*

bricks and timbers in such and such a position (or

a purpose may exist as well in some cases), and if we had to

define ice we should say water frozen or solidified in such10 and such a way ,

and harmony is such and such a blending

of high and low;and similarly in all other cases.

Obviously, then, the actuality or the formula is different

when the matter is different;for in some cases it is the

composition, in others the mixing, and in others some other

of the attributes we have named. And so, of the people

who go in for defining, those who define a house as stones,

15 bricks, and timbers are speaking of the potential house, for

these are the matter;but those who propose

1 a receptacle

to shelter chattels and living beings ,or something of the

sort, speak of the actuality. Those who combine both of

these speak of the third kind of substance, which is com

posed

of matter and form (for the formula that

gives

the

differentiae seems to be an account of the form or actuality,

20 while that which gives the components is rather an account

of the matter); and the same is true of the kind of defi

nitions which Archytas used to accept ; they are accounts

of the combined form and matter. E.g. what is still weather ?

Absence ofmotion in a large expanse of air; air is the matter,

and absence of motion is the actuality and substance. What25 is a calm ? Smoothness of sea

;the material substratum is

the sea, and the actuality or shape is smoothness. It is

obvious then, from what has been said, what sensible sub

stance is and how it exists one kind of it as matter, another

as form or actuality, while the third kind is that which is

composed of these two.

We must not fail to notice that sometimes it is not clear 3

30 whether a name means the composite substance, or the

actuality or form, e.g. whether house is a sign for the

composite thing, a covering consisting of bricks and stones

laid thus and thus \ or for the actuality or form, a covering ,

and whether a line is twoness in

length

or twoness,and

35 whether an animal is a soul in a body or a soul;for

1

Reading in 1. 17



BOOK H. 3 i043a

soul is the substance or actuality of some body.* Animal

might even be applied to both, not as something definable

by one formula, but as related to a single thing. But

this question,

1

while important for another purpose,is

of no importance for the inquiry into sensible substance;

for the essence certainly attaches to the form and the actu- iO43b

ality. For soul and *

to be soul are the same, but to be

man and man are not the same, unless even the bare soul

is to be called man;and thus on one interpretation the thing

is the same as its essence, and on another it is not.

If we examine2

we find that the syllable does not consist 5

of the letters +juxtaposition, nor is the house bricks +juxta

position. And this is right ;for the juxtaposition or

mixing does not consist of those things of which it is the

juxtaposition or mixing. And the same is true in all other

cases; e.g. if the threshold is characterized by its posi

tion, the position is not constituted by the threshold, but

rather the latter is constituted by the former. Nor is man 10

animal + biped, but there must be something besides these,

if these are matter, something which is neither an element

in the whole nor a compound, but is the substance;but this

people eliminate, and state only the matter. If, then, this is

the cause of the thing s being, and if the cause of its being is

its substance,3

they

will not bestating

the substance itself.

(This, then, must either be eternal or it must be destruc-15

tible without being ever in course of being destroyed, and

must have come to be without ever being in course of

coming to be. But it has been proved and explained else

where 4that no one makes or begets the form, but it is the

individual that is made, i. e. the complex of form and

matter that is generated. Whether the substances ofdestructible things can exist apart, is not yet at all clear

;

except that obviously this is impossible in some cases in 20

the case of things which cannot exist apart from the in

dividual instances, e. g. house or utensil. Perhaps, indeed,

neither these things themselves, nor any of the other things

1Sc. whether the name means the form or the concrete

thing.2Aristotle returns to the subject discussed in ch. 2.

3Cf. A. 1017^14-15.

*Cf. Z. 8.



io43b METAPHYSICA

which are not formed by nature, are substances at all;

for

one might say that the nature in natural objects is the only

substance to be found in destructible things.)

Therefore thedifficulty which used to be raised by the

school ofAntisthenes and other such uneducated people has

25 a certain timeliness. They said that the*

what cannot be

defined (for the definition so called is a long rigmarolel

)

but of what sort a thing, e. g. silver, is, they thought it

possible actually to explain, not saying what it is, but that

it is like tin. Therefore one kind of substance can be

defined and formulated, i. e. the composite kind, whether it

30 be perceptible orintelligible ;

but the primary parts of

which this consists cannot be defined, since a defmitory

formula predicates something of something, and one part

of the definition must play the part of matter and the other

that of form.

It is also obvious that, if substances are in a sense

numbers, they are so in this sense and not, as some say,2

as numbers of units. For a definition is a sort of number;

35 for (i) it is divisible, and into indivisible parts (for defini-

tory formulae are notinfinite"),

and number also is of this

nature. And (2) as, when one of the parts of which

a number consists has been taken from or added to the

number,it

is no longer the same number, but a different

one, even if it is the very smallest part that has been taken

ic>44

a

away or added, so the definition and the essence will no

longer remain when anything has been taken away or

added. And(3)

the number must be something in virtue

of which it is one, and this these thinkers cannot state,

what makes it one, if it is one (for either it is not one but a

sort of heap, or if it is, we ought to say what it is that

5 makes one out of many) ;and the definition is one, but

similarly they cannot say what makes it one. And this is

a natural result;

for the same reason is applicable, and

substance is one in the sense which we have explained, and

not, as some say, by being a sort of unit or point ;each is

1Sc. and therefore cannot give the essence, which is simple. For

the contemptuous meaning of paKpos \6yos cf. N.ic>9i

a7.

2 The Pythagoreans and Platonists (cf. M. 6, 7),8

Reading in 1. 35 arreipoi. &rreipos is a misprint.



BOOK H. 3 1044*

a complete reality and a definite nature. And (4) as

number does not admit of the more and the less, neither does 10

substance, in the sense of form, but if any substance does, it

is only the substance which involves matter. Let this, then,suffice for an account of the generation and destruction of

so-called substances in what sense it is possible and in

what sense impossible and of the reduction of things to

number.

4 Regarding material substance we must not forget that 15

even if all

thingscome from the same first cause 1

or have

the same things for their first causes, and if the same

matter serves as starting-point for their generation, yet

there is a matter proper to each, e. g. for phlegm the sweet

or the fat, and for bile the bitter, or something else; though

perhaps these come from the same original matter. And 20

there come to be several matters for the same thing, when

the one matter is matter for the other ; e. g. phlegm comesfrom the fat and from the sweet, if the fat comes from the

sweet;and it comes from bile by analysis of the bile into

its ultimate matter. For one thing comes from another

in two senses, either because it will be found at a later

stage, or because it is produced if the other is analysed into

its original constituents. When the matter is one, different35

things may be produced owing to difference in the moving

cause;

e. g. from wood may be made both a chest and a bed.

But some different things must have their matter different;

e. g. a saw could not be made of wood, nor is this in the

power of the moving cause;for it could not make a saw of

wool or of wood. But if, as a matter of fact, the same thing

can be made of different material, clearly the art, i. e. the 30

moving principle, is the same;for if both the matter and

the moving cause were different, the product would be so

too.

When one inquires into the cause of something, one

should, sincel

causes are spoken of in several senses, state

all the possible causes. E. g. what is the material cause of

man ? Shall

we say the menstrual fluid?

Whatis

the 35

1

Sc. material cause.



io44a METAPHYSICA

moving cause ? Shall we say the seed ? The formal cause ?

His essence. The final cause ? His end. But perhaps the

iO44blatter two are the same. It is the proximate causes we must

state. Whatis the

material cause?

We must namenot

fire or earth, but the matter peculiar to the thing.

Regarding the substances that are natural and generable,

if the causes are really these and of this number and we

5 have to learn the causes, we must inquire thus, if we are to

inquire rightly. But in the case of natural but eternal

substances another account must be given. For perhaps

some have no matter, or not matter of this sort but only

such as can be moved in respect of place. Nor does matter

belong to those things which exist by nature but are not

substances;their substratum is the substance. E. g. what

ic is the cause of eclipse ? What is its matter ? There is none;

the moon is that which suffers eclipse.1 What is the

moving cause which extinguished the light ? The earth.

The final cause perhaps does not exist. The formal principle

is the definitory formula, but this is obscure if it does not

include the cause.2

E. g. what is eclipse ? Deprivation of

light.But if we add 4

by the earth s coming in between ,

15 this is the formula which includes the cause. In the case

of sleep it is not clear what it is that proximately has this

affection. Shall we say that it is the animal?

Yes, butthe

animal in virtue of what, i. e. what is the proximate subject ?

The heart or some other part. Next, by what is it produced?

Next, what is the affection that of the proximate subject,

not of the whole animal ? Shall we say that it is immobility

of such and such a kind ? Yes, but to what process in the

20 proximate subject is this due ?

Since some things are and are not, without coming to be 5

and ceasing to be, e. g. points, if they can be said to be, and

in general forms (for it is not white that comes to be, but

the wood comes to be white, if everything that comes to be

comes from something and comes to be something), not all

25 contraries can come from one another, but it is in different

1i. e. the substratum of a substance is bare matter, but the sub

stratum of an attribute is a determinate substance such as the moon.2Sc. the efficient cause.



BOOK H. 5 i044b

senses that a pale man comes from a dark man, and pale

comes from dark. Nor has everything matter, but only

those things which come to be and change into one an

other. Those things which, without ever being in courseof changing, are or are not, have no matter.

There is difficulty in the question how the matter of each

thing is related to its contrary states. E. g. if the body is 30

potentially healthy, and disease is contrary to health, is it

potentially both healthy and diseased ? And is water poten

tially wine and vinegar ? We answer that it is the matter

of one in virtue of its positive state and its form, and of the

other in virtue of the privation of its positive state and the

corruption of it contrary to its nature. It is also hard to

say why wine is not said to be the matter of vinegar nor

potentially vinegar (though vinegar is produced fromit), 35

and why a living man is not said to be potentially dead.

In fact they are not, but the corruptions in question are

accidental, and it is the matter of the animal that is itself 104 5a

in virtue of its corruption the potency and matter of a corpse,

and it is water that is the matter of vinegar. For the corpse

comes from the animal, and vinegar from wine, as night

from day. And all the things which change thus into one

another must go back to their matter;

e. g. if from a corpse

is

producedan

animal,the

corpsefirst

goesback to its

matter, and only then becomes an animal;and vinegar first 5

goes back to water, and only then becomes wine.

6 To return to the difficulty which has been stated1with

respect both to definitions and to numbers, what is the

cause of their unity ? In the case of all things which have

several parts and in which the totality is not, as it were,

a mere heap, but the whole is something besides the parts,

there is a cause;for even in bodies contact is the cause of 10

unity in some cases, and in others viscosity or some other

such quality. And a definition is a set of words which is

one not by being connected together, like the Iliad, but by

dealing with one object. What, then, is it that makes man

one; why is he one and not many, e.g. animal + biped,

1Cf. Z. 12, H. io44

a 2-6.



io45a METAPHYSICA

15 especially if there are, as some say, an animal-itself and

a biped-itself ? Why are not those Forms themselves the

man, so that men would exist by participation not in man,

nor in one Form, but in two, animal and biped, and in

general man would be not one but more than one thing,

animal and biped ?

20Clearly, then, if people proceed thus in their usual manner

of definition and speech, they cannot explain and solve the

difficulty. But if, as we say, one element is matter and an

other is form, and one is potentially and the other actually,

25 the question will no longer be thought a difficulty. For

this difficulty is the same as would arise if round bronze

were the definition of cloak;

lfor this word would be

a sign of the defmitory formula, so that the question is,

what is the cause of the unity of round and bronze ?

The difficulty disappears, because the one is matter, the

30other form.

What, then,causes this that which was

potentially to be actually except, in the case of things which

are generated, the agent ? For there is no other cause of

the potential sphere s becoming actually a sphere, but this

was the essence of either.2 Of matter some is intelligible,

some perceptible, and in a formula there is always an

35 element of matter as well as one of actuality ;e. g. the

circle is a plane figure.

3

But of the things which have no

matter, either intelligible or perceptible, each is by its

iO45b nature essentially a kind of unity, as it is essentially a kind

of being individual substance, quality, or quantity (and so

neither existent nor one is present in their defini

tions), and the essence of each of them is by its very nature

a kind of unity as it is a kind of being and so none of

these has any reason outside itself for being one, nor for

5 being a kind of being ;for each is by its nature a kind

of being and a kind of unity, not as being in the genus

being or one nor in the sense that being and unity

can exist apart from particulars.

1Cf. Z. I029

b28, de Int. i8a 19.

2i. e. it was the essence of the

potential

ball to become an actual

ball, and of the actual ball to be produced from a potential ball.

3Aristotle does not give the whole definition, but only the genus, or

material element.



BOOK H. 6 i045b

Owing to the difficulty about unity some speak of par

ticipation ,and raise the question, what is the cause of

participation and what is it to participate ;and others speak

of communion , as Lycophron says knowledge is a com- 10

munion of knowing with the soul;and others say life is

a composition or connexion of soul with body. Yet

the same account applies to all cases;for being healthy, too,

will on this showing be either a communion or a con

nexion or a composition of soul and health, and the fact

that the bronze is a triangle will be a composition of

bronze and triangle, and the fact that a thing is white will 15

be a*

composition of surface and whiteness. The reason

is that people look for a unifying formula, and a difference,

between potency and complete reality. But, as has been

said,1the proximate matter and the form are one and the

same thing, the one potentially, and the other actually.

Therefore it is like asking what in general is the cause of

unity and of a thing s being one;for each thing is a unity,

20

and the potential and the actual are somehow one. There

fore there is no other cause here unless there is something

which caused the movement from potency into actuality.

And all things which have no matter are without qualifi

cation essentially unities.

1Cf.

a23-33.



BOOK

WE have treated l of that which is primarily and to which i

all the other categories of being are referred i. e. of sub

stance. For it is in virtue of the concept of substance that

30 the others also are said to be quantity and quality and the

like;for all will be found to involve the concept of sub

stance, as we said in the first part of our work.2 And since

being is in one way divided into individual thing, quality,

and quantity, and is in another way distinguished in respect

of potency and complete reality, and of function, let us now

35 add a discussion of potency and complete reality. And first

let us explain potency in the strictest sense, which is, hovv-

I046aever, not the most useful for our present purpose. For

potency and actuality extend beyond the cases that involve

a reference to motion. But when we have spoken of this

first kind, we shall in our discussions of actuality3

explain

the other kinds of potency as well.

We have pointed out elsewhere 4that potency and the

5 word can have several senses. Of these we may neglectall the potencies that are so called by an equivocation.

For some are called so by analogy, as in geometry we say

one thing is or is not a4

power of another by virtue of the

presence or absence of some relation between them. But

all potencies that conform to the same type are originative

10 sources of some kind, and are called potencies in reference

to one primary kind of potency, which is an originative

source of change in another thing or in the thing itself qua

other. For one kind is a potency of being acted on, i. e.

the originative source, in the very thing acted on, of its

being passively changed by another thing or by itself qua

other; and another kind is a state of insusceptibility to

changefor the worse and to destruction by another thing

1Cf. ZH.

2Cf. z. i.

3Cf. 0. 1048* 27-

b6.

4Cf. A. 12.



BOOK 0. i i046a

or by the thing itself qua other by virtue ot an originative

source of change. In all these definitions is implied the 15

formula of potency in the primary sense. And again these

so-called

potencies

are

potencies

either of

merely acting

or

being acted on, or of acting or being acted on well, so that

even in the formulae of the latter the formulae of the prior

kinds of potency are somehow implied.

Obviously, then, in a sense the potency of acting and of

being acted on is one (for a thing may be capable either 20

because it can itself be acted on or because something else

can be acted on by it), but in a sense the potencies aredifferent. For the one is in the thing acted on

;it is because

it contains a certain originative source, and because even

the matter is an originative source, that the thing acted on is

acted on, and one thing by one, another by another;for that

which is oily can be burnt, and that which yields in a par

ticular way can be crushed;

J and similarly in all other cases. 25

But the other potency is in the agent, e. g. heat and the art of

building are present, one in that which can produce heat

and the other in the man who can build. And so, in so far

as a thing is an organic unity, it cannot be acted on by

itself; for it is one and not two different things. And1

impotence and impotent stand for the privation which

is contrary to potency of this sort, so that every potency 3

belongs to the same subject and refers to the same process

as a corresponding impotence. Privation has several senses;

for it means (i) that which has not a certain quality and (2)

that which might naturally have it but has not it, either

(a)in general or

(b) when it might naturally have it, and

either (a) in some particular way, e. g. when it has not it

completely,or

(/?)

when it has not it at all.

Andin certain

cases if things which naturally have a quality lose it by 35

violence, we say they have suffered privation.

2 Since some such originative sources are present in soul

less things, and others in things possessed of soul, and in

soul, and in the rational part of the soul, clearly some iO46b

1i. e. the event would not happen ifthe passive factor were different.

What is oily cannot necessarily be crushed, nor what is yielding burnt.



i046b METAPHYSICA

potencies will be non-rational and some will be accom

panied by a rational formula. This is why all arts, i.e. all

productive forms of knowledge, are potencies ; they are

originativesources of

changein another

thingor in the

artist himself considered as other.

And each of those which are accompanied by a rational

5 formula is alike capable of contrary effects, but one non-

rational power produces one effect;

e. g. the hot is capable

only of heating, but the medical art can produce botli

disease and health. The reason is that science is a rational

formula, and the same rational formula explains a thing andits privation, only not in the same way ;

and in a sense it

applies to both, but in a sense it applies rather to the

10 positive fact. Therefore such sciences must deal with

contraries, but with one in virtue of their own nature and

with the other not in virtue of their nature;for the rational

formula applies to one object in virtue of that object s

nature, and to the other, in a sense, accidentally. For it is

by denial and removal that it exhibits the contrary; for the

contrary is the primary privation, and this is the removal

15 of the positive term. Now since contraries do not occur

in the same thing, but science is a potency which depends

on the possession of a rational formula, and the soul

possesses an originative source of movement;

therefore,while the wholesome produces only health and the calorific

only heat and the frigorific only cold, the scientific man

20 produces both the contrary effects. For the rational for

mula is one which applies to both, though not in the same

way, and it is in a soul which possesses an originative

source of movement;

so that the soul will start both

processes from the same originative source, having linked

them up with the same thing.1 And so the things whose

potency is according to a rational formula act contrariwise

to the things whose potency is non-rational;

for the

products of the former are included under one originative

source, the rational formula.

25 It is obvious also that the potency ofmerely doing a thing

or having it done to one is implied in that of doing it or

1i. e. with the rational formula.



BOOK 0. 2 i046b

having it done well, but the latter is not always implied in

the former : for he who does a thing well must also do it,

but he who does it merely need not also do it well.

3 There are some who say, as the Megaric school does, that

a thing* can act only when it is acting, and when it is not

acting it cannot act, e.g. that he who is not building can-30

not build, but only he who is building, when he is building ;

and so in all other cases. It is not hard to see the absurdi

ties that attend this view.

For it is clear that on this view a man will not be a

builder unless he is building (for to be a builder is to be

able to build), and so with the other arts. If, then, it is 35

impossible to have such arts if one has not at some time

learnt and acquired them, and it is then impossible not to

have them if one has not sometime lost them (either by for- 1047*

getfulness or by some accident or by time;for it cannot be

by the destruction of the object^ for that lasts for ever), a

man will not have the art when he has ceased to use it, and

yet he may immediately build again ;how then will he have

got the art ?2 And similarly with regard to lifeless things ;

nothing will be either cold or hot or sweet or perceptible 5

at all if people are not perceiving it;so that the upholders

of this view will have to maintain the doctrine of Pro

tagoras.

3

But, indeed, nothingwill even have

perceptionif

it is not perceiving, i.e. exercising its perception. If, then,

that is blind which has not sight though it would naturally

have it, when it would naturally have it and when it still

exists, the same people wall be blind many times in the day

and deaf too.

Again, if that which is deprived of potency is incapable, 10

that which is not happening will be incapable of happen

ing ;but he who says of that which is incapable of happen

ing either that it is or that it will be will say what is untrue;

for this is what incapacity meant. Therefore these views

1 The object of knowledge is always a form, which is eternal. Thematter which makes things perishable is no object for knowledge.

2 The protasis here states facts, the apodosis states a conclusion

which follows from the Megaric theory, and the final question states

a difficulty which follows from the apodosis.3

Cf. r. 5, 6.

645-28 N



io47a METAPHYSICA

15 do away with both movement and becoming. For that

which stands will always stand, and that which sits will

always sit, since if it is sitting it will not get up ;for that

which,as

weare

told,cannot

get upwill be

incapableot

getting up. But we cannot say this, so that evidently

potency and actuality are different (but these views make

potency and actuality the same, and so it is no small thing

20 they are seeking to annihilate), so that it is possible that a

thing may be capable of being and not be, and capable ot

not being and yet be, and similarly with the other kinds of

predicate ; it may be capable of walking and yet not walk,

or capable of not walking and yet walk. And a thing is

capable of doing something if there will be nothing im-

25 possible in its having the actuality of that of which it is

said to have the capacity. I mean, for instance, if a thing is

capable of sitting and it is open to it to sit, there will be

nothing impossible in its actually sitting ;and similarly if

it is capable of being moved or moving, or of standing or

making to stand, or of being or coming to be, or of not

being or not coming to be.

30 The word actuality ,which we connect with complete

reality , has, in the main, been extended from movements to

other things ;for actuality in the strict sense is thought to

be identical with movement. And sopeople

do notassign

movement to non-existent things, though they do assign

some other predicates. E.g. they say that non-existent

things are objects of thought and desire, but not that they

35 are moved;and this because, while ex hypotkesi \hey do not

actually exist, they would have to exist actually if they

iO47b were moved. For of non-existent things some exist poten

tially ; but they do not exist^ because they do not exist in

complete reality.

It what we have describedlis identical with the capable or

,

convertible with it, evidently it cannot be true to say*

this

5 is capable of being but will not be \ which would imply that

the things z>/capableof being would on this showing vanish.

Suppose, for instance, that a man one who did not take

Cf. 1047*24-26.



BOOK 0. 4 i047b

account of that which is incapable of being- were to say

that the diagonal of the square is capable of being1 measured

but will not be measured, because a thing may well be

capable

of

being

or

comingto be, and

yet

not be or be

about to be. But from the premisses this necessarily follows,

that if we actually supposed that which is not, but is cap- 10

able of being, to be or to have come to be, there will be

nothing impossible in this;

but the result will be im

possible, for the measuring of the diagonal is impossible.

For the false and the impossible are not the same;that you

are standing now is false, but that you should be standingis not impossible.

At the same time it is clear thatif,

when A is real, Bmust be real, then, when A is possible, B also must be 15

possible. For ifB need not be possible, there is nothing

to prevent its not being possible. Now let A be supposed

possible. Then, when A was possible, we agreed that

nothing impossible followed ifA were supposed to be real ;

and then B must of course be real. But we supposed B to 20

be impossible. Let it be impossible, then. If, then, B is

impossible, A also must be so. But the first was supposed

impossible ;therefore the second also is impossible. If,

then, A is possible, B also will be possible, if they were so

related that if A is real, B must be real. If, then, A and^

being thus related,1 B is not possible on this condition,

2 A 25

and B will not be related as was supposed.3 And if when

A is possible, B must be possible, then ifA is real, B also

must be real. For to say that B must be possible, ifA is

possible, means this, that ifA is real both at the time wrhen

and in the way in which it was supposed capable of being

real, Balso

mustthen

andin that

waybe real.

3o

5 As all potencies are either innate, like the senses, or come

by practice, like the power of playing the flute, or by learn

ing, like artistic power, those which come by practice or byrational formula we must acquire by previous exercise but

1Sc. so related that if the reality of A implies the reality of B the

possibility

of Aimplies

thepossibility

of B."

Sc. if A is possible.3

Sc. so related that the reality of A implies the reality of B.

N 2



io47b METAPHYSICA

this is not necessary with those which are not of this nature

and which imply passivity.

35 Since that which is*

capable is capable of something and

iO48

aat

some time andin

someway (with all the other qualificationswhich must be present in the definition), and since some

things can produce change according to a rational formula

and their potencies involve such a formula, while other things

are non-rational and their potencies are non-rational, and

the former potencies must be in a living thing, while the

5 latter can be both in the living and in the lifeless;as regards

potencies of the latter kind, when the agent and the patient

meet in the way appropriate to the potency in question, the

one must act and the other be acted on, but with the former

kind of potency this is not necessary. For the non-rational

potencies are all productive of one effect each, but the

rational produce contrary effects, so that if they produced

their effects necessarily they would produce contrary effects

10 at the same time;but this is impossible. There must, then,

be something else that decides;

I mean by this, desire

or will. For whichever of two things the animal desires

decisively, it will do, when it is present, and meets the

passive object, in the way appropriate to the potency in

question. Therefore everything which has a rational

potency, when it desires that for which it has a potencyand in the circumstances in which it has the potency, must

5 do this. And it has the potency in question when the

passive object is present and is in a certain state;

if not it

will not be able to act. (To add the qualification if no

thing external prevents it is not further necessary ;for it has

the potency on the terms on which this is a potency of act

ing, and it is this not in all circumstances but on certain

conditions, among which will be the exclusion of external

20 hindrances;for these are barred by some of the positive

qualifications.)And so even if one has a rational wish, or an

appetite,to do two things or contrary things at the same time,

one will not do them;for it is not on these terms that one has

the

potencyfor them, nor is it a potency of doing both at

the same time, since one will do the things which it is a potency

of doing, on the terms on which one has the potency.



BOOK 0. 6 1048*

6 Since we have treated 1 of the kind of potency which is 25

related to movement, let us discuss actuality what, and

what kind of thing, actuality is. For in the course of our

analysis it will also become clear, with regard to the poten

tial, that we not only ascribe potency to that whose nature

it is to move something else, or to be moved by something

else, either without qualification or in some particular way,

but also use the word in another sense, wrhich is the reason of

the inquiry in the course ofwhich we have discussed these pre- 3

vioussenses also.

Actuality, then,is the existence ofa

thingnot in the way which we express by potentially ;

we say that

potentially, for instance, a statue of Hermes is in the block of

wood and the half-line is in the whole, because it might be

separated out, and we call even the man \vho is not studying

a man of science, if he is capable of studying; the thing that

stands in contrast to each of these exists actually. Our mean- 35

ing can be seen in the particular cases by induction, and wemust not seek a definition of everything but be content to

grasp the analogy, that it is as that which is building is to that

which is capable of building, and the wr

aking to the sleep- 1048

ing, and that which is seeing to that which has its eyes

shut but has sight, and that which has been shaped out of

the matter to the matter, and that which has been wrought

up to the unwrought. Let actuality be defined by one

member of this antithesis, and the potential by the other. 5

But all things are not said in the same sense to exist

actually, but only by analogy as A is in B or to B, C is

in D or to D;for some are as movement to potency, and

the others as substance to some sort of matter.

But also the infinite and the void and all similar things

are said to exist potentially and actually in a different sense 10

from that which applies to many other things, e. g. to that

which sees or walks or is seen. For of the latter class these

predicates can at some time be also truly asserted without

qualification ;for the seen is so called sometimes because it

is being seen, sometimes because it is capable of being seen.

But the infinite

does notexist

potentiallyin the sense that

it will ever actually have separate existence;

it exists

1Cf. e. 1-5.



io48b METAPHYSICA

15 potentially only for knowledge. For the fact that the pro

cess of dividing never comes to an end ensures that this

activity exists potentially, but not that the infinite exists

separately.

Since of the actions which have a limit none is an end but

all are relative to the end, e. g.the removing of fat, or fat-

20 removal, and the bodily parts themselves when one is

making them thin are in movement in this way (i. e. with

out being already that at which the movement aims), this is

not an action or at least not a complete one (for it is not

an end) ;but that movement in which the end is present is

an action. E.g. at the same time we are seeing and have

seen, are understanding and have understood, are thinking

and have thought (while it is not true that at the same time

we are learning and have learnt, or are being cured and

25 have been cured). At the same time we are living well

and have lived well, andare

happyand

havebeen

happy.If not, the process would have had sometime to cease, as

the process of making thin ceases : but, as things are, it

does not cease;we are living and have lived. Of these

processes, then, we must call the one set movements, and

the other actualities. For every movement is incomplete

making thin, learning, walking, building ;these are move-

so ments, and incomplete at that. For it is not true that

at the same time a thing is walking and has walked, or is

building and has built, or is coming to be and has come to

be, or is being moved and has been moved, but what is

being moved is different from what has been moved, and

what is moving from what has moved. But it is the same

thing that at the same time has seen and is seeing, or is

thinking and has thought. The latter sort of process, then,

I call an actuality, and the former a movement.

35 What, and what kind of thing, the actual is, may be

taken as explained by these and similar considerations.

But we must distinguish when a thing exists potentially and 7

whenit does not

;

for it is not at

anyand

everytime.

1049* E.g. is earth potentially a man ? No but rather when it

has already become seed, and perhaps not even then. It is



BOOK 0. 7 1049*

just as it is with being healed ;not everything can be healed

by the medical art or by luck, but there is a certain kind of

thingwhich is capable of it, andonly this is potentiallyhealthy.

And (i)the delimiting mark of that which as a result of 5

thought comes to exist in complete reality from having

existed potentially is that if the agent has willed it it comes

to pass if nothing external hinders, while the condition on

the other side viz. in that which is healed is that nothing

in it hinders the result. It is on similar terms that we have

what is potentially a house;if nothing in the thing acted on

i. e. in the matter prevents it from becoming a house, and 10

if there is nothing which must be added or taken away or

changed, this is potentially a house;and the same is true

of all other things the source ofwhose becoming is external.

And(2)

in the cases in which the source of the becoming is

in the very thing which comes to be, a thing is potentially

allthose things which

it

will be of itself if nothing external hinders it. E. g. the seed is not yet potentially

a man;for it must be deposited in something other than

itself and undergo a change. But when through its own 15

motive principle it has already got such and such attributes,

in this state it is already potentially a man;while in the

former state it needs another motive principle, just as earth

is not yet potentially a statue (for it must first change in

order to become brass).1

It seems that when we call a thing not something else but

thaten e. g. a casket is not wood but wooden,and 20

wood is notl

earth but4

earthen,and again earth will illus

trate our point if it is similarly not something else but* thaten

that other thing is always potentially (inthe full sense of

that word) the thing which comes after it in this series.

E.g. a casket is not earthen nor earth,but wooden

;

for this is potentially a casket and this is the matter of a

casket, wood in general of a casket in general, and this par

ticular wood of this particular casket. And ifthere is a first

thing, which is no longer, in reference to something else,

1 The classes marked by (i) and (2) are the works of art and of

nature respectively, but at the end (2) is illustrated by an examplefrom (i).



i049a METAPHYSICA

25 calledl

thaten,this is prime matter

; e.g. if earth is airy

and air is not4

fire butl

fiery ,fire is prime matter, which is

not a this . For the subject or substratum is differentiated

by being a this or not being one; i.e. the substratum of

modifications is, e.g.,

a man, i. e. a body and a soul, while the

30 modification is musical or pale . (The subject is called,

when musiccomes tobe present init, not music but musical

,

and the man is not(

paleness but4

pale ,and not ambula-

tion or movement but walking or*

moving ,which is

akin to the thaten.)

Wherever this is so, then, the ulti

mate subject is a substance ; but when this is not so but the

35 predicate is a form and a this,the ultimate subject is

matter and material substance. And it is only right that

6 thaten should be used with reference both to the matter

iO49band to the accidents

;for both are indeterminates. 1

We have stated, then, when a thing is to be said to exist

potentially and when it is not.

From our discussion of the various senses of*

prior ,

2it 8

5 is clear that actuality is prior to potency. And I mean by

potency not only that definite kind which is said to be

a principle of change in another thing or in the thing itself

regarded as other, but in general every principle of move

ment or of rest. For nature also is in the same genus as

10 potency ;for it is a principle of movement not, however,

in something else but in the thing itself gtia itself. To all

such potency, then, actuality is prior both in formula and

in substantiality; and in time it is prior in one sense, and

in another not.

(i) Clearlyit is

priorin formula

;for that which is in the

primary sense potential is potential because it is possible

1Aristotle points out that there are two kinds of derivative predi

cates those derived from the matter of thesubject,

like wooden,

and those formed from the accidents of the subject, like musical .

Matter and accidents have this in common, that they are indetermi

nate matter having (relatively) no character and accidents not being

confined to one special subject as essential predicates are. He mentions

at the same time that there are two kinds of substratum the bare

matter which underlies form or essence, and the complete individual

which underlies accidents. Cf. Z. iO38b

5.2

Cf. A. ii.



BOOK 0. 8 io49b

for it to become active;

e. g. I mean by capable of build

ing that which can build, and by capable of seeing that 15

which can see, and by visible that which can be seen.

And the same account applies to all other cases, so that the

formula and the knowledge of the one must precede the

knowledge of the other.

(2)In time it is prior in this sense : the actual which is

identical in species though not in number with a potentially

existing thing is prior to it. I mean that to this particular man

who now exists

actually

and to the corn and to the

seeing20

subject the matter and the seed and that which is capable of

seeing, which are potentially a man and corn and seeing,

but not yet actually so, are prior in time;but prior in time

to these are other actually existing things, from which they

were produced. For from the potentially existing the

actually existing is always produced by an actually existing

thing, e. g. man from man, musician by musician ; there is 25

always a first mover, and the mover already exists actually.

We have said in our account of substance 1 that everything

that is produced is something produced from something

and by something, and that the same in species as it.

This is why it is thought impossible to be a builder if

one has built nothing or a harper if one has never played 3

the harp ; for he who learns to play the harp learns to play

it by playing it, and all other learners do similarly. Andthence arose the sophistical quibble, that one who does not

possess a science will be doing that which is the object of

the science;for he who is learning it does not possess it.

But since, of that which is coming to be, some part must 35

have come to be, and, of that which, in general, is chang

ing, some part must have changed (this is shown in the

treatise on movement 2

),he who is learning must, it would

seem, possess some part of the science. But here too, then,

it is clear that actuality is in this sense also, viz. in order of

generation and of time, prior to potency.

But (3)it is also prior in substantiality; firstly, (a] because

the

thingsthat are

posteriorin

becomingare

priorin form

and in substantiality (e. g. man is prior to boy and human 5

1Cf. Z. 7, 8.

2Cf. Phys. vi. 6.



iosoa METAPHYSICA

being to seed;for the one already has its form, and the other

has not), and because everything that comes to be moves to

wards a principle, i. e. an end (for that for the sake of which

a thing is, is its principle, and the becoming is for the sakeof the end), and the actuality is the end, and it is for the

10 sake of this that the potency is acquired. For animals do

not see in order that they may have sight, but they have

sight that they may see. And similarly men have the art

of building that they may build, and theoretical science that

they may theorize;but they do not theorize that they may

have theoretical science, except those who are learning by

practice ;and these do not theorize except in a limited

15 sense, or because they have no need to theorize. Further,

matter exists in a potential state, just because it may come

to its form;and when it exists actually

r

,then it is in its

form. And the same holds good in all cases, even those in

which the end is a movement. And so, as teachers think

they have achieved their end when they have exhibited the

pupil at work, nature does likewise. For if this is not the

20 case, we shall have Pauson s Hermes over again, since it will

be hard to say about the knowledge, as about the figure in

the picture, whether it is within or without. 1 For the

action is the end, and the actuality is the action. And so

even the word4

actuality is derived from action , and

points to the complete reality.

And while in some cases the exercise is the ultimate

thing (e.g. in sight the ultimate thing is seeing, and no

25 other product besides this results from sight), but from

some things a product follows (e. g. from the art of build

ing there results a house as well as the act of building),

yet none the less the act is in the former case the end and

in the latter more of an end than the potency is. For the

act of building is realized in the thing that is being built, and

comes to be, and is, at the same time as the house.

30 Where, then, the result is something apart from the

exercise, the actuality is in the thing that is being made,

e.

g.

the act of

building

is in the

thing

that is

being

built

1 The reference is apparently to a tricky painting in which the

figure was painted so as to stand out in high relief.



BOOK 0. 8 iosoa

and that of weaving in the thing that is being woven, and

similarly in all other cases, and in general the movement is

in the thing that is beingmoved ;butwherethere is noproduct

apart from the actuality, the actuality is present in the agents, 35

e. g. the act of seeing is in the seeing subject and that oftheo

rizing in the theorizing subject and the life is in the soul (and

therefore well-being also;for it is a certain kind of

life). iO5Ob

Obviously, therefore, the substance or form is actuality.1

According to this argument, then, it is obvious that actuality

is

priorin substantial

beingto

potency;and as we have

said,2 one actuality always precedes another in time right

back to the actuality of the eternal prime mover. 5

But (b) actuality is prior in a stricter sense also;for

eternal things are prior in substance to perishable things,

and no eternal thing exists potentially. The reason is this.

Every potency is at one and the same time a potency of the

opposite ; for, while that which is not capable of being

present in a subject cannot be present, everything that is 10

capable of being may possibly not be actual. That, then,

which is capable of being may either be or not be;the

same thing, then, is capable both of being and of not being.

And that which is capable of not being may possibly not

be;and that which may possibly not be is perishable,

either in the full sense, or in the precise sense in which it is

said that it possibly may not be, i.e. in respect either of 15

place or of quantity or quality ;in the full sense means

in respect of substance . Nothing, then, which is in the

full sense imperishable is in the full sense potentially existent

(though there is nothing to prevent its being so in some

respect, e. g. potentially of a certain quality or in a certain

place) ;all imperishable things, then, exist actually. Nor

can anything which is of necessity exist potentially; yet

these things are primary ;for if these did not exist, nothing

would exist. Nor does eternal movement, if there be such, 20

exist potentially ; and, if there is an eternal mobile, it is not

in motion in virtue of a potentiality, except in respect of4 whence and* whither

(thereis

nothingto

preventits

having

1This follows from the whole section a

4~b 2

;cf. esp.

a15, 16.

17-29.



iosob METAPHYSICA

matter which makes it capable of movement in various

directions). And so the sun and the stars and the whole

heaven are ever active, and there is no fear that they may

sometime stand still, as the natural philosophers fear they

may.1 Nor do they tire in this activity ;

for movement is

25 not for them, as it is for perishable things, connected with

the potentiality for opposites, so that the continuity of

the movement should be laborious;for it is that kind of

substance which is matter and potency, not actuality, that

causes this.

Imperishable things2 are imitated by those that are in

volved in change, e. g. earth and fire. For these also are

ever active;for they have their movement of themselves

30 and in themselves.3 But the other potencies, according to

our previous discussion,4 are all potencies for opposites ;

for

that which can move another in this way can also move it

not in this

way,

i. e. if it acts

according

to a rational formula;

and the same non-rational potencies will produce opposite

results by their presence or absence.

35 If, then, there are any entities or substances such as the

dialecticians6

say the Ideas are, there must be something

much more scientific than science-itself and something more

1051* mobile than movement-itself;for these will be more of the

nature of actualities, while science-itself and movement-itself are potencies for these.

Obviously, then, actuality is prior both to potency and to

every principle of change.

That the actuality is also better and more valuable than 9

the good potency is evident from the following argument.5

Everythingof

which we saythat it

can do something,is

alike capable of contraries, e. g. that of which we say that it

can be well is the same as that which can beill, and has

1e. g. Empedocles (cf. De Caelo, 284* 24-6).

2Sc. the heavenly bodies.

3i.e. they are both movers and moved. 4

Cf. b 8-i2.5 The Platonists are meant; cf. A. 987

b3i.

6 The Idea, being the universal apart from its special manifestations,will be a potentiality, and will therefore be inferior to the correspond

ing particulars e. g. the Idea of science will be inferior to particularacts of scientific thought.



BOOK 0. 9 iosia

both potencies at once;for the same potency is a potency

of health and illness, of rest and motion, of building and

throwing down, of being built and being thrown down.

The capacity for contraries, then, is present at the same 10

time;but contraries cannot be present at the same time, and

the actualities also cannot be present at the same time, e. g.

health and illness. Therefore, while the good must be one

of them, the capacity is both alike, or neither;the actuality,

then, is better. Also in the case of bad things the end or 15

actuality must be worse than the potency ;for that which

4 can is both contraries alike. Clearly, then, the bad does

not exist apart from bad things ;for the bad is in its nature

posterior to the potency.1 And therefore we may also say

that in the things which are from the beginning, i. e. in

eternal things, there is nothing bad, nothing defective, 2o

nothing perverted (for perversion is something bad).2

B D C

It is by an activity also that geometrical constructions3 are

discovered;for we find them by dividing. If the figures

had been already divided, the constructions would have been

obvious;

but as it is they are present only potentially.

1Sc. while the eternal and substantial must be better than the

potency.2 The paragraph seems to be directed against Plato

;cf. Rep. 402 C,

476 A, Theaet. i;6E, Laws 896 E, 8980.3 The figures required for the two theorems are as above.



iosia METAPHYSICA

Why are the angles of the triangle equal to two right

angles ? Because the angles about one point are equal to two

25 right angles. If, then, the line parallel to the side had been

already drawn upwards,the reason would have been evident

to any one as soon as he saw the figure. Why is the angle

in a semicircle in all cases a right angle ? If three lines

are equal the two which form the base, and the perpen

dicular from the centre the conclusion is evident at a

glance to one who knows the former proposition. Obvi

ously, therefore, the potentially existing constructions are

30 discovered by being brought to actuality ; the reason is that

the geometer s thinking is an actuality ;so that the potency

proceeds from an actuality ;and therefore it is by making

constructions that people come to know them (though the

single actuality is later in generation than the corresponding

potency).

The terms being and non-being are employed firstly 10

35 with reference to the categories, and secondly with refer

ence to the potency or actuality of these or their non-

iO5ibpotency or non-actuality, and thirdly in the sense of true and

false. This depends, on the side of the objects, on their

being combined or separated, so that he who thinks the

separatedto

be separated and the combinedto be

combinedhas the truth, while he whose thought is in a state contrary

5 to that of the objects is in error. This being so, when is

what is called truth or falsity present, and when is it not ?

We must consider what we mean by these terms. It is not

because we think truly that you are pale, that you are pale,

but because you are pale we who say this have the truth.

If, then, some things are always combined and cannot be

10 separated, and others are always separated and cannot be

combined, while others are capable either of combination

or of vSeparation,4

being is being combined and one, and

not being is being not combined but more than one.

Regarding contingent facts, then, the same opinion or the

same statement comes to be false and true, and it is possible

15 for it to be at one time correct and at another erroneous;but

regarding things that cannot be otherwise opinions are not



BOOK 0. 10 iosib

at one time true and at another false, but the same opinions

are always true or always false.

But with regard to incomposites^ what is being or not

being, and truth or falsity ?

A thing of this sort is not

composite, so as to* be when it is compounded, and not

to be if it is separated, like that the wood is white or 2o

1

that the diagonal is incommensurable;nor will truth and

falsity be still present in the same way as in the previous

cases. In fact, as truth is not the same in these cases, so

also being is not the same;but (a) truth or falsity is as

follows contact and assertion are truth (assertion not being

the same as affirmation), and ignorance is non-contact.25

For it is not possible to be in error regarding the question

what a thing is, save in an accidental sense;and the same

holds good regarding non-composite substances (forit is

not possible to be in error about them). And they all

exist

actually,

notpotentially

;for otherwise

theywould

have come to be and ceased to be; but, as it is, being itself

does not come to be (nor cease to be) ;for if it had done

so it would have had to come out of something. About 30

the things, then, which are essences and actualities, it is not

possible to be in error, but only to know them or not to

know them. But we do inquire what they are, viz. whether

they are of such and such a nature or not.

(b) As regards the*

being that answers to truth and the

non-being that answers to falsity, in one case there is truth

if the subject and the attribute are really combined, and

falsity if they are not combined;in the other case, if the 35

object is existent it exists in a particular way, and if it does

not exist in this way it does not exist at all.1 And truth io52

means knowing these objects, and falsity does not exist,

nor error, but only ignorance and not an ignorance which

is like blindness;for blindness is akin to a total absence of

the faculty of thinking.

It is evident also that about unchangeable things there

can be no error in respect of time, if we assume them to be

unchangeable. E. g. if we suppose that the triangle does

1i. e. we have not here A and B, which may or may not be com

bined, but A, which if it exists at all exists as A.



i052a METAPHYSICA

not change, we shall not suppose that at one time its angles

are equal to two right angles while at another time they

are not (for that would imply change). It is possible, how

ever, to suppose that one member of such aclass

hasa certain attribute and another has not

;e. g. while wre

may suppose that no even number is prime, we may

suppose that some are and some are not. But regarding

a numerically single number not even this form of error is

10 possible ;for we cannot in this case suppose that one in

stance has an attribute and another has not, but whether

our judgement be true or false, it is implied that the fact is

eternal.



BOOK I

I WE have said previously, in our distinction of the various 15

meanings of words,1that one has several meanings ;

the

things that are directly and of their own nature and not acci

dentally called one may be summarized under four heads,

though the word is used in more senses, (i) There is the

continuous, either in general, or especially that which is con

tinuous by nature and not by contact nor by being tied to

gether ;and of these, that has more unity and is prior, whose 20

movement 2is more indivisible and simpler. (2) That which

is a whole and has a certain shape and form is one in a still

higher degree;and

especiallyif a

thingis of this sort

bynature, and not by force like the things which are unified by

glue or nails or by being tied together, i. e. if it has in itself

the cause of its continuity. A thing is of this sort because its 25

movement is one and indivisible in place and time;so that

evidently if a thing has by nature a principle of movement

that is of the first kind(i.

e. local movement) and the first

in that kind (i. e. circular movement), this is in the primarysense one extended thing. Some things, then, are one in

this way, qua continuous or whole, and the other things that

are one are those whose definition is one. Of this sort are the 30

things the thought of which is one, i.e. those the thought of

which is indivisible;and it is indivisible if the thing is

indivisible in kind or in number. (3)In number, then, the

individual is indivisible, and (4) in kind, that which in

intelligibility and in knowledge is indivisible, so that that

which causes substances to be one 3 must be one in the

primary sense.l One \ then, has all these meanings the

naturally continuous and the whole, and the individual and 35

the universal. And all these are one because in some cases

1

A. 6.2Nature is defined (A. ioi5

ai3) as the essence of things which

have in themselves, as such, a source of movement .

8Sc. the form.

845-28 O



i052a METAPHYSICA

the movement, in others the thought or the definition is

indivisible.

iO52b

But it must be observed that the questions, what sort of

things are said to be one, and what it is to be one and whatis the definition of it, should not be assumed to be the same.

4 One has all these meanings, and each of the things to

5 which one of these kinds of unity belongs will be one;but

4

to be one will sometimes mean being one of these

things, and sometimes being something elsel which is even

nearer to the meaning of the word one while these other

things approximate to its application. This is also true of

4

element or4

cause,if one had both to specify the things

of which it is predicable and to render the definition of the

10 word. For in a sense fire is an element (and doubtlessalso the

indefinite or something else of the sort is by its own nature

the element), but in a sense it is not;for it is not the same

thing

to be fire and to be an element, but while as a

particular thing with a nature of its own fire is an element, the

name 4

element means that it has this attribute, that there

is something which is made of it as a primary constituent.

15 And so with cause and one and all such terms. For

this reason, too,4

to be one means to be indivisible, being

essentially a"

this"

and capable of being isolated either in

place, or in form or thought ; or perhaps*

to be wholeand indivisible

;but it means especially to be the first

measure of a kind,and most strictly of quantity ;

for it is

from this that it has been extended to the other categories.

20 For measure is that by which quantity is knowrn;

and

quantity qua quantity is known either by a one or by

a number, and all number is known by a one . There

fore all quantity qua quantity is known by the one, and

that by which quantities are primarily known is the one it

self; and so the one is the starting-point of number qua

number. And hence in the other classes too measure

25 means that by which each is first known, and the measure

of each is a unit in length, in breadth, in depth, in weight,

in

speed. (Thewords 4

weightand 4

speed

are common

to both contraries2

;for each of them has two meanings

1Cf. I052

b16-19.

2Sc. heavy and light, fast and slow.



BOOK I. i 1052

weight means both that which has any amount ofgravity

and that which has an excess ofgravity, and speed both

that which has any amount of movement and that which

has an excess of movement;

for even the slow has a 30

certain speed and the comparatively light a certain

weight.)

In all these, then, the measure and starting-point is some

thing one and indivisible, since even in lines we treat as

indivisible the line a foot long. For everywhere we seek

as the measuresomething

one and indivisible;and this is

that which is simple either in quality or in quantity. Now 35

where it is thought impossible to take away or to add,

there the measure is exact (hence that of number is

most exact;for we posit the unit as indivisible in every iO53

a

respect) ;but in all other cases we imitate this sort of

measure. For in the case of a furlong or a talent or of

anything comparatively large any addition or subtraction

might more easily escape our notice than in the case of

something smaller;so that the first thing from which, as 5

far as our perception goes, nothing can be subtracted, all

men make the measure, whether of liquids or of solids,

whether of weight or of size;and they think they know

the quantity when they know it by means of this measure.

And indeed they know movement too by the simple move

ment and the quickest ;for this occupies least time. And 10

so in astronomy a one of this sort is the starting-point

and measure(for they assume the movement of the heavens

to be uniform and the quickest, and judge the others by

reference toit),

and in music the quarter-tone (because it is

the least interval), and in

speech

the letter. And all these

are ones in this sense not that one is something predic-

able in the same sense of all of these, but in the sense we

have mentioned.

But the measure is not always one in number some

times there are several; e.g. the quarter-tones (not to the [5

ear, but as determined by the ratios) are two, and the articu

late

sounds by which we measure are more than one, andthe diagonal of the square and its side are measured by two

quantities, and all spatial magnitudes reveal similar varieties

O 2



io53a METAPHYSICA

of unit.1

Thus, then, the one is the measure of all things,

because we come to know the elements in the substance by

dividing the things either in respect of quantity or in

20 respect of kind. And the one is indivisible just because

the first of each class of things is indivisible. But it is not

in the same way that every one is indivisible, e. g. a foot

and a unit;

the latter is indivisible in every respect,

while the former must be placed among things which are

undivided to perception, as has been said already2

only to

perception, for doubtless every continuous thing is divisible.

The measure is always homogeneous with the thing

25 measured;the measure of spatial magnitudes is a spatial

magnitude, and in particular that of length is a length, that

of breadth a breadth, that of articulate sound an articulate

sound, that of weight a weight, that of units a unit. (For

we must state the matter so, and not say that the measure

of numbersis

a number;

we ought indeed to saythis if

wewere to use the corresponding form of words, but the

claim does not really correspond it is as if one claimed

30 that the measure of units is units, and not a unit;number

is a plurality of units.}

Knowledge, also, and perception, we call the measure of

things for the same reason, because we come to know some

thing by them while as a matter of fact they are measured

rather than measure other things. But it is with us as ifsome

one else measured us and we came to knowhow big we are by

seeing that he applied the cubit-measure to such and such

35 a fraction of us. But Protagoras says man is the measure

of all things ,

3as if he had said the man who knows or

IO53

b l

t^e man w^ perceives ;and these because they have

respectively knowledge and perception, which we say are

the measures of objects. Such thinkers are saying nothing,

then, while they appear to be saying something remark

able.

1 Alexander thinks this means that a line may be measured either

by the ideal measure (e. g. the standard yard) or by the particular

imperfect measure (the yard-wand, which slightly differs from the

standard yard). This sense does not agree with the context, andno doubt the meaning is that incommensurables must be measured by

different units.2

Cf. I052b33, io53

a5.

3Fr. I.



BOOK I. i io53b

Evidently, then, unity in the strictest sense, if we define

it according to the meaning of the word, is a measure, and 5

most properly of quantity, and secondly of quality. And

some things will be one if they are indivisible in quantity,

and others if they are indivisible in quality ;and so that

which is one is indivisible, either absolutely or qiia one.

2 With regard to the substance and nature of the one we

must ask in which of two ways it exists. This is the very 10

question that we reviewedJin our discussion of problems,

viz. what the one is and how we must conceive of it, whetherwe must take the one itself as being a substance (as both

the Pythagoreans say in earlier and Plato in later times), or

there is, rather, an underlying nature and the one should

be described more intelligibly and more in the manner of

the physical philosophers, of whom one says the one is love, 15

another says it is air, and another the indefinite.2

If, then, no universal can be a substance, as has been said 3

in our discussion of substance and being, and if being itself

cannot be a substance in the sense of a one apart from the

many (for it is common to the many), but is only a predi

cate, clearly unity also cannot be a substance;for being 20

and unity are the most universal of all predicates. There

fore, on the onehand, genera

are not certain entities and

substances separable from other things ;and on the other

hand the one cannot be a genus, for the same reasons for

which being and substance cannot be ge era.

Further, the position must be similar in all the kinds ot

unity. Now unity has just as many meanings as being ;

so that since in the sphere of qualities the one is something 25

definite some particular kind of thing and similarly in the

sphere of quantities, clearly we must in every category ask

what the one is, as we must ask what the existent is, since

it is not enough to say that its nature is just to be one or

existent. But in colours the one is a colour, e. g. white,

and then the other colours are observed to be produced out

1B.

iooi

a

4-

b

25.2 The three thinkers referred to are Empedocles, Anaximenes,Anaximander.

3Z. 13.



io53b METAPHYSICA

30 of this and black, and black is the privation of white, as

darkness of light.Therefore if all existent things were

colours, existent things would have been a number, indeed,

but of what ? Clearly of colours ;

and the one wouldhave been a particular one

,i. e. white. And similarly if

all existing things were tunes, they would have been a

35 number, but a number of quarter-tones, and their essence

would not have been number;and the one would have

been something whose substance was not to be one but to

iO54abe the quarter-tone. And similarly if all existent things

had been articulate sounds, they would have been a number

of letters, and the one would have been a vowel. And if

all existent things were rectilinear figures, they would have

been a number of figures, and the one would have been the

triangle. And the same argument applies to all other

5 classes. Since, therefore, while there are numbers and a

one both in affections and in

qualities

and in

quantities

and

in movement, in all cases the number is a number of

particular things and the one is one something, and its sub

stance is not just to be one, the same must be true of

substances also;for it is true of all cases alike.

10 That the one, then, in every class is a definite thing, and

in no case is its nature just this, unity, is evident;but as in

colours the one-itself which we must seek is one colour, so

too in substance the one-itself is one substance. That in a

sense unity means the same as being is clear from the facts

that its meanings correspond to the categories one to one,

15and it is not comprised within any category (e. g. it is

comprised neither in what a thing is nor in quality, but

is related to them just as being is) ;that in one man

nothing more is predicated than in man (just as being is

nothing apart from substance or quality or quantity) ;and

that to be one is just to be a particular thing.

20 The one and the many are opposed in several ways, of 3

which one is the opposition of the one and plurality as

indivisible and divisible ; for that which is either divided or

divisible is called a plurality, and that which is indivisible

or not divided is called one. Now since opposition is of



BOOK I. 3 io54a

four kinds, and one of these two terms is privative in mean

ing, they must be contraries, and neither contradictory nor 25

correlative in meaning.1 And the one derives its name and

its explanation from its contrary, the indivisible from the

divisible, because plurality and the divisible is more per

ceptible than the indivisible, so that in definition plurality is

prior to the indivisible, because of the conditions of percep

tion.

To the one belong, as we indicated graphically in our 30

distinction of the contraries,2 the same and the like and the

equal, and to plurality belong the other and the unlike and

the unequal.* The same has several meanings ; (i) we

sometimes mean the same numerically ; again, (2) we call

a thing the same if it is one both in definition and in num

ber, e. g. you are one with yourself both in form and in

matter;and again, (3)

if the definition of its primary 35

essence is one;

e.

g. equal straightlines are the

same,and

iO54

b

so are equal and equal-angled quadrilaterals ;there are

many such, but in these equality constitutes unity.

Things are like if, not being absolutely the same, nor

without difference in respect of their concrete substance, they

are the same in form; e.g. the larger square is like the smaller, 5

and unequal straight lines are like; they are like, but not

absolutely the same. Other things are like, if, having the

same form, and being things in which difference of degree

is possible, they have no difference of degree. Other things,

if they have a quality that is in form one and the same

e. g. whiteness in a greater or less degree, are called like i

because their form is one. Other things are called like if

the qualities they have in common are more numerous than

those in which they differ either the qualities in general or

the prominent qualities ;e. g. tin is like silver, qua white,

and gold is like fire, qua yellow and red.

Evidently, then, other and unlike also have several

meanings. And the other in one sense is the opposite of

the same (so that everything is either the same as or other 15

1 Two of the kinds, contrariety and privation, are not mutually ex

clusive, for contrariety is the relation between a form and its complete

privation. Cf. r. ioo4b2;, I. io55

b 26.2

Cf. r. ioo4a2.



io54b METAPHYSICA

than everything else). In another sense things are other

unless both their matter and their definition are one (so that

you are other than your neighbour). The other in the third

sense is

exemplified

in the

objects

of mathematics.1 Other

or the same can therefore be predicated ofeverything with

regard to everything else but only ifthe things are one and

existent, for other is not the contradictory of*

the same;

20 which is why it is not predicated of non-existent things

(while not the same is so predicated). It is predicated

of all existing things ;for everything that is existent and

one is by its very nature either one or not one with

anything else.

The other, then, and the same are thus opposed. But

difference is not the same as otherness. For the other and

that which it is other than need not be other in some

definite respect (for everything that is existent is either

25 other or the same), but that which is different is different

from some particular thing in some particular respect, so

that there must be something identical whereby they differ.

And this identical thing is genus or species ;for everything

that differs differs either in genus or in species,2in genus if

the things have not their matter in common and are not

generated out of each other (i.e. if they belong to different

figuresof

predication),

3 and inspecies

if

theyhave the same

3o genus ( genus meaning that identical thing which is essen

tially predicated of both the different things).

Contraries are different, and contrariety is a kind of differ

ence. That we are right in this supposition is shown byinduction. For all of these too are seen to be different

;

35 they are not merely other, but some are other in genus,

iO55a

and others are in the same line of predication,3

and there

fore in the same genus, and the same in genus. We have

distinguished4elsewhere what sort of things are the same or

other in genus.

Since things which differ may differ from one another 4

more or less, there is also a greatest difference, and this

1Cf.

a35-

b3.

2See note on io5;

b36.

8 See note on A. 986*23.*

A. 9.



BOOK 1. 4 io55a

I call contrariety. That contrariety is the greatest differ- 5

ence is made clear by induction. For things which differ

in genus have no way to one another, but are too far

distant and are not comparable ; and for things that differ

in species the extremes from which generation takes place

are the contraries, and the distance between extremes and

therefore that between the contraries is the greatest.

But surely that which is greatest in each class is complete. 10

For that is greatest which cannot be exceeded, and that is

complete beyond which nothing can be found. For the com

plete difference marks the end of a series (just as the other

things which are called complete are so called because they

have attained an end), and beyond the end there is nothing ;

for in everything it is the extreme and includes ajl else, and 15

therefore there is nothing beyond the end, and the complete

needs nothing further. From this, then, it is clear that con

trarietyis

completedifference

;

and as contraries are so

called in several senses, their modes of completeness will

answer to the various modes of contrariety which attach to

the contraries.

This being so, it is clear that one thing cannot have

more than one contrary (for neither can there be anything 20

more extreme than the extreme, nor can there be more

than two extremes for the one interval), and, to put the

matter generally, this is clear if contrariety is a difference

and if difference, and therefore also the complete differ

ence, must be between two things.

And the other commonly accepted definitions of con

traries are also necessarily true. For not only is (i) the

complete difference the greatest difference (for we can get 25

no difference beyond it of things differing either in genusor in species ;

for it has been shown Tthat there is no

difference between anything and the things outside its

genus, and among the things which differ in species the

complete difference is the greatest) ;but also (2) the things

in the same genus which differ most are contrary (for the

complete

difference is thegreatest

difference betweenspecies

of the same genus) ;and (3) the things in the same receptive

1Cf. a

6. But how can we reconcile this with io54b27-30, 35 ?



i055a METAPHYSICA

30 material which differ most are contrary (for the matter is

the same for contraries) : and (4) of the things which fall

under the same faculty the most different are contrary (for

onescience deals with one class of

things, and in these the

complete difference is the greatest).1

The primary contrariety is that between positive state

and privation not every privation, however (for priva

tion has several meanings), but that which is complete.

35 And the other contraries must be called so with reference

to these, some because they possess these, others because

they produce or tend to produce them, others because they

are acquisitions or losses of these or of other contraries.

Now if the kinds of opposition are contradiction and priva-

iO55btion and contrariety and relation, and of these the first is

contradiction, and contradiction admits of no intermediate,

while contraries admit of one, clearly contradiction and

contrariety are not the same. But privation is a kind of

contradiction ; for what suffers privation, either in general

or in some determinate way, is either that which is quite

5 incapable of having some attribute or that which, being of

such a nature as to have it, has it not;

here we have

already a variety of meanings, which have been distin

guished2 elsewhere. Privation, therefore, is a contradiction

or incapacity whichis

determinate or taken along with the

receptive material. This is the reason why, while contra

diction does not admit of an intermediate, privation some-

10 times does;

for everything is equal or not equal, but not

everything is equal or unequal, or if it is, it is only within

the sphere of that which is receptive of equality. If, then,

the comings-to-be which happen to the matter start from

the contraries, and proceed either from the form and the

possession of the form or from a privation of the form or

shape, clearly all contrariety must be privation, but presum-

15 ably not all privation is contrariety (the reason being that

that which has suffered privation may have suffered it in

several ways) ;for it is only the extremes from which

changes proceed that are contraries.

And this is obvious also by induction. For every con-

1

Punctuating in 11. 32-3 p.ia, Iv . . . /neyiVr^).2A. 22.



BOOK I. 4 io55b

trariety involves, as one of its terms, a privation, but not

all cases are alike; inequality is the privation of equality

and unlikeness of likeness, and on the other hand vice is the

privation of virtue. But the cases differ in a way already 20

described;

1in one case we mean simply that the thing has

suffered privation, in another case that it has done so either

at a certain time or in a certain part (e. g. at a certain age or

in the dominant part), or throughout. This is why in some

cases there is a mean (there are men who are neither good

nor bad), and in others there is not (a number must be either

odd or even). Further, some contraries have their subject 25

defined, others have not. Therefore it is evident that one

of the contraries is always privative ;but it is enough if this

is true of the first i. e. the generic contraries, e. g. the

one and the many ;for the others can be reduced to these.

5 Since one thing has one contrary, we might raise the 30

question how the one is opposed to the many, and the

equal to the great and the small. For if we use the word4 whether only in an antithesis such as whether it is white

or black,or whether it is white or not white (we do not

ask whether it is a man or white),

unless we are pro

ceeding on a prior assumption and asking something such 35

aswhether

it

was Cleon or Socrates that came butthis is not a necessary disjunction in any class of things ;

yet even this is an extension from the case of opposites ;for

opposites alone cannot be present together ;and we assume

this incompatibility here too in asking which of the two

came;

for if they might both have come, the question iO56a

would have been absurd;but if they might, even so this

falls just as much into an antithesis, that of the one or

many ,i. e. whether both came or one of the two : if,

then, the question whether is always concerned with

opposites, and we can ask whether it is greater or less or

equal ,what is the opposition of the equal to the other 5

two ? It is not contrary either to one alone or to both;for

why should it be contrary to the greater rather than to the

less ? Further, the equal is contrary to the uneqiiaL There-



io56a METAPHYSICA

fore if it is contrary to the greater and the less, it will be

contrary to more things than one. But if the unequal means

the same as both the greater and the less together, the equal

10 will beopposite

to both(and

thedifficulty supports

those

who say the unequal is a two 1

),but it follows that one

thing is contrary to two others, which is impossible. Again,

the equal is evidently intermediate between the great and

the small, but no contrariety is either observed to be inter

mediate, or, from its definition, can be so;for it would not

be complete2if it were intermediate between any two things,

but rather it always has something intermediate between its

own terms.

J 5 It remains, then, that it is opposed either as negation or

as privation. It cannot be the negation or privation of one

of the two;for why of the great rather than of the small ?

It is, then, the privative negation of both. This is whywhether is said with reference to both, not to one of the

two (e. g. whether it is greater or equal or whether it is

20equal or less

) ;there are always three cases. But it is not

a necessary privation ;for not everything which is not

greater or less is equal, but only the things which are of

such a nature as to have these attributes.

The equal, then, is that which is neither great nor small

but is

naturallyfitted to be either

greator small

;and it is

opposed to both as a privative negation (and therefore is

also intermediate). And that which is neither good nor

2 5 bad is opposed to both, but has no name;for each of these

has several meanings and the recipient subject is not one;

but that which is neither white nor black has more claim to

unity. Yet even this has not one name, though the colours

of which this negation is privatively predicated are in a waylimited

;for they must be either grey or yellow or some-

3 thing else of the kind. Therefore it is an incorrect criticism

that is passed by those who think that all such phrases are

used in the same way, so that that which is neither a shoe

nor a hand would be intermediate between a shoe and

a hand, since that which is neither good nor bad is inter

mediate between the good and the bad as if there must

1This is a Platonic doctrine

;cf. N. io8;

b7.

2Cf. 1055* 16.



BOOK I. 5 ios6a

be an intermediate in all cases. But this does not necessarily

follow. For the one phrase is a joint denial of opposites 35

between which there is an intermediate and a certain natural

interval;but between the other two there is no differ- ios6

b

ence l

;for the things, the denials of which are combined,

belong to different classes, so that the substratum is not one.

6 We might raise similar questions about the one and the

many. For if the many are absolutely opposed to the one,

certain impossible results follow. One will then be few 2,5

whether few be treated here as singular or plural ;for the

many are opposed also to the few. Further, two will be

many, since the double is multiple and double derives its

meaning from * two;therefore one will be few

;for what

is that in comparison with which two are many, except

one, which must therefore be few ? For there is nothing

fewer.

Further,

if the much and the little are in

plurality

10

what the long and the short are in length, and whatever is

much is also many, and the many are much (unless, indeed,

there is a difference in the case of an easily-bounded con

tinuum),3 the little (or few) will be a plurality. Therefore

one is a plurality if it is few; and this it must be, if two are

many. But perhaps, while the many are in a sense said

to be also

4

much, it is with a difference ; e. g. water is much 15

but not many. But *

many is applied to the things that

are divisible;in one sense it means a plurality which is

excessive either absolutely or relatively (while few is

similarly a plurality which is deficient), and in another

sense it means number, in which sense alone it is opposed

to the one. For we say*

one or many , just as if one were 20

to say4

one and ones or white thing and white things ,

or to compare the things that have been measured with the

measure. It is in this sense also that multiples are so called.

1Cf. 105 s

a6, 2.6.

2 The Greek is o\iyov 77 oX/ya, which, it might seem, should be trans

lated a little or a few . But the singular oXiyov is used only because

of the difficulty of predicating the plural oX/-ya of one . On the other

hand, TTO\V and rroXXa are used in the really distinct senses of muchand many . oXiyov has been translated few in this chapter exceptwhere it is opposed to TTO\V and must be translated

*

little .

3i. e. a fluid. Cf. 1. 16.



ios6b METAPHYSICA

For each number is said to be many because it consists of

ones and because each number is measurable by one;and

it is many as that which is opposed to one, not to the few.

25 In thissense, then,

even two is

many not, however,in the

sense of a plurality which is excessive either relatively or

absolutely ;it is the first plurality. But without qualifi

cation two is few;

for it is the first plurality which is

deficient (for this reason Anaxagoras was not right in

leaving the subject with the statement 1 that all things

were together, boundless both in plurality and in smallness

3 where for*

and in smallness he should have said and in

fewness;for they could not have been boundless in few

ness), since it is not one, as some say, but two, that make

a few.

The one is opposed then to the many in numbers as

measure to thing measurable;and these are opposed as

are the relatives which are not from their very nature

relatives. We have distinguished2 elsewhere the two senses

35 in which relatives are so called: (i) as contraries; (2)

as

knowledge to thing known, a term being called relative

because another is relative to it. There is nothing to

prevent one from being fewer than something, e. g. than

two;for if is few

T

er, it is not therefore few. Plurality is as

it were the class to which number belongs;

for numberis

plurality measurable by one, and one and number are in

a sense opposed, not as contrary, but as we have said some

5 relative terms are opposed ;for inasmuch as one is measure

and the other measurable, they are opposed. This is whynot everything that is one is a number

;i. e. if the thing is

indivisible it is not a number. But though knowledge is

similarly spoken of as relative to the knowable, the relation

does not work out similarly ;for while knowledge might

be thought to be the measure, and the knowable the thing

10 measured, the fact is that all knowledge is knowable, but not

all that is knowable is knowledge, because in a sense know

ledge is measured by the knowable. Plurality is contrary

neither to the few (the many being contrary to this as

excessive plurality to plurality exceeded), nor to the one in

1Fr. i.

2A. 1021*26-30.



BOOK I. 6 ios7a

every sense; but in one sense these are contrary, as has

been said, because the former is divisible and the latter

indivisible, while in another sense they are relative as 15

knowledge is to knowable, if plurality is number and the

one is a measure.

7 Since contraries admit of an intermediate and in some

cases have it, intermediates must be composed of the con

traries. For (i) all intermediates are in the same genus as ao

thethings

between whichthey

stand. For we call those

things intermediates, into which that which changes must

change first;e. g. if we were to pass from the highest string

to the lowest by the smallest intervals, we should come

sooner to the intermediate notes, and in colours if we were

to pass from white to black, we should come sooner to 35

crimson and grey than to black;and similarly in all other

cases. But to change from one genus to another genus is

not possible except in an incidental way, as from colour to

figure. Intermediates, then, must be in the same genus both

as one another and as the things they stand between.

But (2) all intermediates stand between opposites of some 30

kind;

for only between these can change take place in

virtue of their own nature (so that an intermediate is im

possible between things which are not opposite ;for then

there would be change which was not from one opposite

towards the other). Of opposites, contradictories admit of

no middle term;

for this is what contradiction is an 35

opposition, one or other side of which must attach to any

thing whatever, i. e. which has no intermediate. Of other

opposites, some are relative, others privative, others con

trary. Of relative terms, those which are not contrary have

no intermediate;the reason is that they are not in the same

genus. For what intermediate could there be between

knowledge and knowable ? But between great and small io57b

there zs one.

(3) If intermediates are in the same genus, as has been

shown, andstand

between contraries, they mustbe

composed of these contraries. For either there will be a genus

including the contraries or there will be none. And if(a)



io57b METAPHYSICA

there is to be a genus in such a way that it is something

5 prior to the contraries, the differentiae which constituted

the contrary species-of-a-genus will be contraries prior to

the species ; for species are composed of the genus and thedifferentiae. (E. g. if white and black are contraries, and

one is a piercing colour and the other a compressing

colour,1these differentiae piercing and compressing

10 are prior ;so that these are prior contraries of one an

other.) But, again, the species which differ contrarywise are

the more truly contrary species.2 And the other species,

i. e. the intermediates, must be composed of their genus and

their differentiae. (E. g. all colours which are between white

and black must be said to be composed of the genus, i. e.

15 colour, and certain differentiae. But these differentiae will

not be the primary contraries; otherwise every colour

would be either white or black. They are different, then,

from the primary contraries;and therefore they will be

between the primary contraries;the primary differentiae

are piercing and compressing .)

Therefore it is(d)

with regard to these contraries which

do not fall within a genus that we must first ask of what

20 their intermediates are composed. (For things which are

in the same genus must be composed of terms in which the

genus is not an element, or else be themselves incomposite.

3

)

Now contraries do not involve one another in their com

position, and are therefore first principles ;but the inter

mediates are either all incomposite, or none of them. But

there is something compounded out of the contraries, so that

there can be a change from a contrary to it sooner than to

25 the other contrary ;for it will have less of the quality in

1Cf. PI. Tim. 67 E ff.

8I now make the parenthesis end at Trportpa (1. n) and treat aXXa

fjtrjvas beginning a new argument.

8Aristotle has first (ei /xV, 1. 4) considered the case of contraries in

a genus, and shown that they involve prior contraries which are not

in the genus, but when added to the genus constitute its species. These

are the primary contraries, and it is primarily of them that we must

ask, Of what are their intermediates composed? The sentence,

11. 20-22, in which he reverts to contraries in a genus must be paren

thetical. A species in a genus must either contain an element (sc. the

differentia) which does not itself contain the genus, or (which is incom

patible with its being a species) be an unanalysable term.



BOOK I. 7 i057b

question than the one contrary and more than the other.

This also,1then, will come between the contraries. All the

other intermediates also, therefore, are composite \for that

which has more of a quality than one thing and less than

another is compounded somehow out of the things than

which it is said to have more and less respectively of the

quality. And since there are no other things prior to the

contraries and homogeneous with the intermediates, all 30

intermediates must be compounded out of the contraries.

Therefore also all the inferior classes, both the contraries

and their intermediates, will be compounded out of the

primary contraries.2

Clearly, then, intermediates are (i)

all in the same genus and (2) intermediate between con

traries, and (3) all compounded out of the contraries.

8 That which is other in species is other than something 35

in something, and this must belong to both 3

;e. g. if it is

an animal other in species, both are animals. The things,

then, which are other in species must be in the same genus.

For by genus I mean that one identical thing which is

predicated of both and is differentiated in no merely acci

dental way, whether conceived as matter or otherwise. iO58a

For not only must the common nature attach to the differ

ent things, e. g. not only must both be animals, but this

very animality must also be different for each (e. g. in the

one case equinity, in the other humanity), and so this

common nature is specifically different for each from what it

1i. e. this intermediate differentia comes between the extreme

differentiae, as the intermediate species comes between the extreme

species.2 This seems to mean that each extreme as well as each intermediate

species is compounded out of both the extreme differentiae. E. g. white

would have to be to some extent compressing as well as piercing .

But this is not in itself a likely doctrine, and it can hardly be said to be

proved in the present passage ;the meaning probably is that each

extreme species contains one differentia as a logical element, the other

element being the genus ;while each intermediate contains both the

differentiae.3

It might seem that the respect in which things differ is just whatdoes not belong to both. But Aristotle s meaning is this : If A differs

from>,

it must be a different something, and this something is the

genuscommon to both. Horse and man are different animals. And

when two things differ in their essence, they differ just in that in which

(in another sense of in) they agree. Difference in a genus makes

the genus itself other(ic>58

a7-8). Cf. io54

b25-28.



ios8a METAPHYSICA

5 is for the other. One, then, will be in virtue of its own

nature one sort of animal, and the other another, e. g. one

a horse and the other a man. This difference, then, must

be an otherness of the genus. For I give the name of

1

difference in the genus to an otherness which makes the

genus itself other.

This, then, will be a contrariety (as can be shown also by10 induction). For all things are divided by opposites, and it

has been proved that contraries are in the same genus1

.

For contrariety was seen 2to be complete difference

;and

all difference in species is a difference from somethingin something ;

so that this is the same for both and is their

genus. (Hence also all contraries which are different in

species and not in genus are in the same line of predica-

IKk tion,3 and other than one another in the highest degree

for the difference is complete ,and cannot be present

along with one another.) The difference, then, is a con

trariety.

This, then, is what it is to be *

other in species to have

a contrariety, being in the same genus and being indivis

ible4(and those things are the same in species which have

no contrariety, being indivisible5

); we say being indi

visible,for in the process of division contrarieties arise

20 even in the intermediate stages before we come to the

indivisibles.4

Evidently, therefore, with reference to that

which is called the genus, none of the species-of-a-genus

is either the same as it or other than it in species (and

this is fitting ;for the matter is indicated by negation,

6 and

the genus is the matter of that of which it is called the

genus, not in the sense in which we speak of the genus or

family of the Heraclidae, but in that in which the genus is

an element in a thing s nature 7

),nor is it so with reference

25to things which are not in the same genus, but it will differ

in genus from them, and in species from things in the same

1

Ch. 4.

2

io55ai6.

3Cf. I054

b35 and note on A. 986* 23.

4Sc. individuals or infimae species.

5

Sc. individuals.6

i. e. by eliminating the form which characterizes the concrete thing.7

Cf. A. io24a3i-6,

b4-6.



BOOK I. 8 ios8a

genus. For a thing s difference from that from which it

differs in species must be a contrariety ;and this belongs

only to things in the same genus.

g One might raise the question, why woman does not differ

from man in species, when female and male are contrary and 3

their difference is a contrariety ;and why a female and

a male animal are not different in species, though this

difference belongs to animal in virtue of its own nature,

and not as paleness or darkness does;both female and

male belong to it qua animal. This question is almostthe same as the other, why one contrariety makes things

different in species and another does not, e. g. with feet 35

and with wings do, but paleness and darkness do not.

Perhaps it is because the former are modifications peculiar

to the genus, and the latter are less so. And since one

element is definition and one is matter, contrarieties which io58b

are in the definition make a difference in species, but those

which are in the thing taken as including its matter do not

make one. And so paleness in a man, or darkness, does

not make one, nor is there a difference in species between

the pale man and the dark man, not even if each of them

be denoted by one word. For man is here being con- 5

sidered on his material side, and matter does not create

a difference;for it does not make individual men species

of man, though the flesh and the bones of which this man

and that man consist are other. The concrete thing is

other, but not other in species, because in the definition

there is no contrariety. This lis the ultimate indivisible

kind. Callias is definition + matter;the pale man, then, is 10

soalso, because

it is theindividual

Callias that is

pale;

man, then, is pale only incidentally. Neither do a brazen

and a wooden circle, then, differ in species ;and if a brazen

triangle and a wooden circle differ in species, it is not

because of the matter, but because there is a contrariety in

the definition. But does the matter not make things other I5

in species, when it is other in a certain way, or is there

a sense in which it does ? For why is this horse other than

1i. e. that in whose definition no contrarieties are included.

P 2



io58b METAPHYSICA

this man in species, although their matter is included with

their definitions ? Doubtless because there is a contrariety

in the definition. For while there is a contrariety also

betweenpale

man and darkhorse,

and it is acontrariety

in

30species, it does not depend on the paleness of the one and

the darkness of the other, since even if both had been pale,

yet they would have been other in species. But male and

female, while they are modifications peculiar to4

animal,

are so not in virtue pf its essence but in the matter, i. e. the

body. This is why the same seed becomes female or male

by being acted on in a certain way. We have stated, then,

25 what it is to be other in species, and why some things differ

in species and others do not.

Since contraries are other in form, and the perishable 10

and the imperishable are contraries (for privation is a deter

minate incapacity), the perishable and the imperishable

must be differentin

kind.

1

Now so far we have spoken of the general terms them-

3o selves, so that it might be thought not to be necessary that

every imperishable thing should be different from every

perishable thing in form, just as not every pale thing is

different in form from every dark thing. For the same

thing can be both, and even at the same time if it is

a universal (e. g. man can be both pale and dark), and if it

is an individual it can still be both;for the same man can

35 be, though not at the same time, pale and dark. Yet pale

is contrary to dark.

But while some contraries belong to certain things by

accident (e. g. both those now mentioned and many

others), others cannot, and among these are perishable and

1 To translate ytvos and ei<W as genus and species makes non

sense of the argument of this chapter. They have therefore been

rendered kind and form . The only trace of the technical distinc

tion is found in the last sentence of the chapter, and there it is not

justified by what precedes. It looks as if the first part of the chapterhad been written before the distinction was drawn, and io59

a10-14

(or perhaps only 1. 14) added under the supposition that a genericdifference between the perishable and the imperishable had been

proved. For the absence of distinction between yews and fl&os cf. A.

1071*25 with 27, Cat. 8b 27 with 9a

14, Hist. An. i. 49Ob 16 with 17,

Pol. iv. 1290^33 with 36. To read eifift in io5&b 28 is useless in view

of 1059* 10-14.



BOOK I. 10 io59a

imperishable . For nothing is by accident perishable. For 1059**

what is accidental is capable of not being present, but

perishableness is one of the attributes that belong of neces

sity to the things to which they belong ; or else one and

the same thing may be perishable and imperishable, if 5

perishableness is capable of not belonging to it. Perishable-

ness then must either be the essence or be present in the

essence of each perishable thing. The same account holds

good for imperishableness also;

for both are attributes

which are present of necessity. The characteristics, then,

in respect of which and in direct consequence of which one

thing is perishable and another imperishable, are opposite,

so that the things must be different in kind.

Evidently, then, there cannot be Forms such as some i

maintain, for then one man l would be perishable and an

other 2

imperishable. Yet the Forms are said to be the

same in form with the individuals and notmerely

to have

the same name;

but things which differ in kind 3are

farther apart than those which differ in form.

1 The sensible individual.2 The ideal man.

3 As the perishable and the imperishable have been shown to do.



BOOK K

THAT Wisdom is a science of first principles is evident i

from the introductory chapters,1in which we have raised

objections to the statements of others about the first prin-

20ciples ;

but one might ask the question whether Wisdom is

to be conceived as one science or as several. If as one, it

may be objectedthat

one science alwaysdeals

withcon

traries, but the first principles are not contrary. If it is

not one, what sort of sciences are those with which it is to

be identified ?2

Further, is it the business of one science, or of more than

one, to examine the first principles of demonstration ? If of

2 5 one, why of this rather than of any other? If of more,

what sort of sciences must these be said to be ?3

Further, does Wisdom investigate all substances or not ?

If not all, it is hard to say which;but if, being one, it

investigates them all, it is doubtful how the same science

can embrace several subject-matters.4

Further, does it deal with substances only or also with

3 their attributes ? If in the case of attributes demonstration

is possible,5in that of substances it is not. But if the two

sciences are different, what is each of them and which is

Wisdom ? If we think of it as demonstrative, the science of

the attributes is Wisdom, but if as dealing with what is

primary, the science of substances claims the title.6

But again the science we are looking for must not be

supposedto deal with the causes

which havebeen mentioned

35 in the Physics? For (A) it does not deal with the final

cause (for that is the nature of the good, and this is found

in the field of action and movement; and it is the first

mover for that is the nature of the end but in the case

of things unmovable there is nothing that moved them

1Cf. Bk. A. 3-10.

2Cf. B. 996

a i8-b 26.

3 Cf. B. 996b 26-997* 15.4 Cf. B. 997 a 15-25.

5

Reading in 1. 31 an-ada^is (<TTIV.

6Cf. B. 997

a25-34.

1 The material, formal, efficient, and final causes (Pkys. ii. 3).



BOOK K. i i059a

first),

1 and (B)in general it is hard to say whether per

chance the science we are now looking for deals with

perceptible substances or not with them, but with cer

tain others. If with others, it must deal either with the

Forms or with the objects of mathematics. Now (a) evi

dently the Forms do not exist. (But it is hard to say, even

if one suppose them to exist, why in the world the same is

not true of the other things of which there are Forms, as of

the objects of mathematics. I mean that these thinkers 5

place the objects of mathematics between the Forms and per

ceptible things, as a kind of third set of things apart both

from the Forms and from the things in this world;

but

there is not a third man or horse besides the ideal and the

individuals. If on the other hand it is not as they say, with

what sort of things must the mathematician be supposed to

deal ? Certainly not with the things in this world;for 10

none of these is the sort of

thing

which the mathematical

sciences demand.) Nor (6) does the science which we

are now seeking treat of the objects of mathematics;

for

none of them can exist separately. But again it does

not deal with perceptible substances;for they are perish

able.2

In general one might raise the question, to what kind of 15

science it belongs to discuss the difficulties about the matterof the objects of mathematics. Neither to physics (because

the whole inquiry of the physicist is about the things that

have in themselves a principle of movement and rest), nor

yet to the science which inquires into demonstration and

science;for this is just the subject which it investigates.

It remains then that it is the philosophy which we have set 20

before ourselves that treats of those subjects.

One might discuss the question whether the science we

are seeking should be said to deal with the principles which

are by some called elements;

all men suppose these to be

present in composite things. But it might be thought that

the science we seek should treat rather of universals;for 25

every definition and every science is of universals and not

of infimae speciesf so that as far as this goes it would deal

1Cf. B. 996

a 2i-b i.2

Cf. B. 997* 34-998* 19.3

Cf. B. 998b

15.



io59b METAPHYSICA

with the highest genera. These would turn out to be being

and unity ;for these might most of all be supposed to con

tain all things that are, and to be most like principles

30 because they are first by nature;for if they perish all other

things are destroyed with them;for everything is and is one.

But inasmuch as, if one is to suppose them to be genera,

they must be predicable of their differentiae, and no genus

is predicable of any of its differentiae, in this way it would

seem that we should not make them genera nor principles.

Further, if the simpler is more of a principle than the less

35simple, and

the ultimatemembers of

thegenus

aresimpler

than the genera (for they are indivisible, but the genera

are divided into many and differing species), the species

might seem to be the principles, rather than the genera.

But inasmuch as the species are involved in the destruction

of the genera, the genera are more like principles ;for that

which involves another in its destruction is a principle of

io6oa

it. 1 These and others of the kind are the subjects that

involve difficulties.

Further, must we suppose something apart from indi- 2

vidual things, or is it these that the science we are seeking

5 treats of? But these are infinite in number. Yet the things

that are apart from the individuals are genera or species ;

but the science we now seek treats of neither of these. Thereason why this is impossible has been stated.

2

Indeed, it

is in general hard to say whether one must assume that

there is a separable substance besides the sensible sub

stances (i.e. the substances in this world), or that these are

10 the real things and Wisdom is concerned with them. For

we seem to seek another kind of substance, and this is our

problem, i. e. to see if there is something which can exist

apart by itself and belongs to no sensible thing. Further,

if there is another substance apart from and corresponding

to sensible substances, which kinds of sensible substance

must be supposed to have this corresponding to them ?

15 Why should one suppose men or horses to have it, more

thaneither

the otheranimals or

evenall lifeless

things?

1Cf. B. 998*20-999*23.

2

io59b24-38.



BOOK K. 2 io6oa

On the other hand to set up other and eternal substances

equal in number to the sensible and perishable substances

would seem to fall beyond the bounds of probability. But

if the principle we now seek is not separable from corporeal

things, what has a better claim to the name than matter ?

This, however, does not exist in actuality, but exists in 20

potency. And it would seem rather that the form or shape

is a more important principle than this;but the form is

perishable,1 so that there is no eternal substance at all

which can exist apart and independent. But this is para

doxical;for such a principle and substance seems to exist

and is sought by nearly all the most refined thinkers as some- 25

thing that exists;for how is there to be order unless there

is something eternal and independent and permanent ?2

Further, if there is a substance or principle of such a

nature as that which \ve are now seeking, and if this is one

for all things, and the same for eternal and for perishable

things, it is hard to say why in the world, if there is the same

principle, some of the things that fall under the principle are 30

eternal, and others are not eternal;this is paradoxical. But

if there is one principle of perishable and another of eternal

things, we shall be in a like difficulty if the principle of

perishable things, as well as that of eternal, is eternal;

for

why,if the

principleis

eternal,are not the

thingsthat fall

under the principle also eternal ? But if it is perishable

another principle is involved to account for it, and another

to account for that, and this will go on to infinity.3

35

If on the other hand we are to set up what are thought

to be the most unchangeable principles, being and unity,

firstly,if each of these does not indicate a this or sub

stance, how will they be separable and independent ? Yet io6ob

we expect the eternal and primary principles to be so. But if

each of them does signify a this or substance, all things

that are are substances;for being is predicated of all things

(and unity also ofsome) ;but that all things that are are sub- 5

stance is false. Further, how can they4 be right who say that

1

It must be remembered that A. is only stating common opinions

and the consequent difficulties.2

Cf. B. 999a24-

b24.

sCf. B. ioooa 5-iooi

a3.

4 The Pythagoreans and Plato.



io6ob METAPHYSICA

the first principle is unity and this is substance, and generate

number as the first product from unity and from matter,

10 and assert that number is substance ? How are we to

think of two,

and each of the othernumbers composed

of

units, as one ? On this point neither do they say anything

nor is it easy to say anything. But if we are to suppose

lines or what comes after these(I mean the primary sur

faces) to be principles, these at least are not separable sub

stances, but sections and divisions the former of surfaces,

the latter of bodies (while points are sections and divisions

J 5 of lines) ; and further they are limits of these same things;

and all these are in other things and none is separable.

Further, how are we to suppose that there is a substance of

unity and the point ? Every substance comes into being

by a gradual process, but a point does not;for the point

is a division.1

20 A further difficulty is raised by the fact that all know

ledge is of universals and of the such,but substance

is not a universal, but is rather a this a separable

thing, so that if there is knowledge about the first prin

ciples, the question arises, how are we to suppose the first

principle to be substance ?2

Further, is there anything apart from the concrete thing

(by which I mean the matter and that which is joined with2 5

it),or not ? If not, we are met by the objection that all

things that are in matter are perishable. But if there is

something, it must be the form or shape. Now it is hard

to determine in which cases this exists apart and in which

it does not;for in some cases the form is evidently not

separable, e. g. in the case of a house.3

Further, are the principles the same in kind or in num-

3 ber ? If they are one in number, all things will be the

same. 4

Since the science of the philosopher treats of being qua 3

being universally and not in respect of a part of it, and

1

being has many senses and is not used in one only,it

follows thatifthe word

is

used equivocally andin

virtueof

1

Cf. B. iooi a 4-ioo2b

ii.2

Cf. B. 1003* 5-17.3

Cf. B. 999a24-

b24.

4Cf. B. 999

b24-1000* 4.



BOOK K. 3 io6ob

nothing common to its various uses, being does not fall

under one science (for the meanings of an equivocal term do

not form one genus) ;but if the word is used in virtue of 35

something common, being will fall under one science. Theterm seems to be used in the way we have mentioned, like

medical and *

healthy . For each of these also we use in

many senses. Terms are used in this way by virtue of some io6ia

kind of reference, in the one case to medical science, in

the other to health, in others to something else, but in

each case to one identical concept. For a discussion and

a knife are called medical because the former proceeds from

medical science, and the latter is useful to it. And a thing 5

is called healthy in a similar way ;one thing because it is

indicative of health, another because it is productive of it.

And the same is true in the other cases. Everything that

is, then, is said to be in this same way ;each thing that is

is said to be because it is a modification ofbeing q^la being

or a permanent or a transient state or a movement of it,or

something else of the sort. And since everything that is TO

may be referred to something single and common, each of

the contrarieties also may be referred to the first differences

and contrarieties of being, whether the first differences of

being are plurality and unity, or likeness and unlikeness, or

some other differences ; let these be taken as already dis

cussed.1

It makes no difference whether that which is be re- 15

ferred to being or to unity. For even if they are not the same

but different, at least they are convertible;for that which is

one is also somehow being, and that which is being is one.

But since every pair of contraries falls to be examined byone and the same science, and in each pair one term is the

privative of the other- though one might regarding some 20

contraries raise the question, how they can be privately

related, viz. those which have an intermediate, e. g. unjust

and just in all such cases one must maintain that the

privation is not of the whole definition, but of the infima

species. E. g. if the just man is by virtue of some per

manent disposition obedient to the laws \2 the unjust man 25

1

Cf. Fr. I478b35-1479* 5, M97

a32-149^43-

2Cf. [PL] Zte/. 411 E.



io6ia METAPHYSICA

will not in every case have the whole definition denied of

him, but may be merely4

in some respect deficient in obedi

ence to the laws,and in this respect the privation will

attach to him;and

similarly

in all other cases.

As the mathematician investigates abstractions (for before

30 beginning his investigation he strips off all the sensible quali

ties, e. g. weight and lightness, hardness and its contrary, and

also heat and cold and the other sensible contrarieties, and

leaves only the quantitative and continuous, sometimes in

one, sometimes in two, sometimes in three dimensions, and

35 the attributes of these qiia quantitative and continuous, anddoes not consider them in any other respect, and examines

the relative positions of some and the attributes of these,

io6iband the commensurabilities and incommensurabilities of

others, and the ratios of others;but yet we posit one and

the same science of all these things geometry), the same

is true with regard to being. For the attributes of this in so

5 far as it is being, and the contrarieties in it qua being, it is

the business of no other science than philosophy to investi

gate ;for to physics one would assign the study of things

not qzta being, but rather qua sharing in movement;while

dialectic and sophistic deal with the attributes of things that

are, but not of things qita being, and not with being itself

10 in so far as it is

being;therefore it remains that it is the

philosopher who studies the things we have named, in so

far as they are being. Since all that is is said to be in virtue

ofsomething single and common, though the term has many

meanings, and contraries are in the same case (for they are

referred to the first contrarieties and differences of being),

15 and things of this sort can fall under one science, the diffi

culty we stated at the beginningl

appears to be solved, I

mean the question how there can be a single science ot

things which are many and different in genus.

Since even the mathematician uses the common axioms 4

only in a special application, it must be the business of first

philosophy to examine the principles of mathematics also.

1

I059a20-23. Cf. r. 2. The question raised in 1059* 29-34 has

also incidentally been answered.



BOOK K. 4 io6ib

That when equals are taken from equals the remainders

are equal, is common to all quantities, but mathematics ao

studies a part of its proper matter which it has detached,

e.g. lines or angles or numbers or some other kind of

quantity not, however, qua being but in so far as each of

them is continuous in one or two or three dimensions;but 25

philosophy does not inquire about particular subjects in so

far as each of them has some attribute orother>

but specu

lates about being, in so far as each particular thing is.

Physics is in the same position as mathematics;for physics

studies the attributes and the principles of the things that

are, qua moving and not qita being (whereas the primary 30

science, we have said, deals with these, only in so far as the

underlying subjects are existent, and not in virtue of any

other character) ;and so both physics and mathematics

must be classed as parts of Wisdom.1

5 There is a principle in things, about which we cannot be

deceived, but must always, on the contrary, recognize the35

truth, viz. that the same thing cannot at one and the same

time be and not be, or admit any other similar pair of oppo- io62a

sites.2 About such matters there is no proof in the full

sense, though there is proof ad hominem. For it is not

possible

to infer this truth itself from a more certain

principle, yet this is necessary if there is to be completed proof

of it in the full sense.3 But he who wants to prove to the

5

asserter of opposites that he is wrong must get from him an

admission which shall be identical with the principle that

the same thing cannot be and not be at one and the same

time, but shall not seem to be identical;for thus alone can

his thesis be demonstrated to the man who asserts that oppo- 10

site statements can be truly made about the same subject.

Those, then, who are to join in argument with one another

must to some extent understand one another;

for if this

does not happen how are they to join in argument with one

another ? Therefore every word must be intelligible and

indicate something, and not many things but only one;and 15

1Cf. r. ioos

ai9-

b2, K. 1059*23-26.

2Cf. r. ioo5

b8-34.

3Cf. r. ioc6a 5-18.



io62a METAPHYSICA

if it signifies more than one thing, it must be made plain to

which of these the word is being applied. He, then, who

says this is and is not denies what he affirms, so that

what the word signifies, he says it does not signify; and

this is impossible. Therefore if this is signifies some

thing, one cannot truly assert its contradictory.1

Further, if the word signifies something and this is

20 asserted truly,2this connexion must be necessary ;

and it is

not possible that that which necessarily is should ever not

be;

it is not possible therefore to make the opposed

affirmations and negations truly of the same subject/

1

Further, if the affirmation is no more true than the negation,

he who says man will be no more right than he who says

254 not-man . It would seem also that in saying the man is

not a horse one would be either more or not less right than

in saying he is not a man, so that one will also be right in

saying that the same person is a horse;for it was assumed

to be possible to make opposite statements equally truly.

It follows then that the same person is a man and a horse,

or any other animal. 4

30 While, then, there is no proof of these things in the full

sense, there is a proof which may suffice against one who

will make these suppositions. And perhaps if one had

questioned

Heraclitus himself in this

wayone

might

have

forced him to confess that opposite statements can never

be true of the same subjects. But, as it is, he adopted this

35 opinion without understanding what his statement involves.5

But in any case if what is said by him is true, not even this

io62bitself will be true viz. that the same thing can at one and

the same time both be and not be. For as, when the state

ments are separated, the affirmation is no more true than the

negation, in the same way the combined and complex

5 statement being like a single affirmation the whole taken

as an affirmation will be no more true than the negation.6

Further, if it is not possible to affirm anything truly,

this itself will be false the assertion that there is no true

1Cf. r. ioo6a i8-ioo7

a2o.

2

Sc. of that of which the word is asserted.3

Cf. r. ioo6b 28-34.4

Cf. r. ioo;b 18-1008*2.

6Cf. r. ioos

b23-26.

6Cf. r. ioo8a 6-7.



BOOK K. 5 io62b

affirmation.1 But if a true affirmation exists, this appears

to refute what is said by those who raise such objections10

and utterly destroy rational discourse.

6 The saying of Protagoras is like the views we have mentioned

;he said that man is the measure of all things,

2

meaning simply that that which seems to each man also

assuredly is. If this is so, it follows that the same thing 15

both is and is not, and is bad and good, and that the

contents of all other opposite statements are true, because

often a particular thing appears beautiful to some and the

contrary of beautiful to others, and that which appears to

each man is the measure. This difficulty may be solved by20

considering the source of this opinion. It seems to have

arisen in some cases from the doctrine of the natural

philosophers, and in others from the fact that all men have

not the same views about the same things, but a particular

thing appears pleasantto some and the

contraryof

pleasantto others.

3

That nothing comes to be out of that which is not, but

everything out of that which is, is a dogma common to 2 5

nearly all the natural philosophers. Since, then, white

cannot come to be if the perfectly white and in no respect

not-white existed before, that which becomes white must

come from that which is not white ; so that it must come to

be out of that which is not (so they argue), unless the same

thing was at the beginning white and not-white. But it is 3

not hard to solve this difficulty ;for we have said in our

works on physics4in what sense things that come to be

come to be from that which is not, and in what sense from

that which is.5

But to attend equally to the opinions and the fancies of

disputing parties is childish;for clearly one of them must be

mistaken. And this is evident from what happens in respect 35

of sensation;for the same thing never appears sweet to some

and the contrary of sweet to others, unless in the one case 1063**

1Cf. r. ioi2b 13-18. Fr. i.

3

Cf. r. ioo9

a

6-i6, 22-30.4

Phys. i. 7-9, De Gen. et Corr. i. 3l7b14-319^.

5Cf. r. 1009* 30-36.



io63a METAPHYSICA

the sense-organ which discriminates the aforesaid flavours

has been perverted and injured. And if this is so the one

party must be taken to be the measure, and the other must

5 not. And I

say

the same of

goodand bad, and beautiful

and ugly, and all other such qualities. For to maintain the

view we are opposing is just like maintaining that the

things that appear to people who put their finger under

their eye and make the object appear two instead of one

must be two (because they appear to be of that number) and

again one (for to those who do not interfere with their eye

the one object appears one).1

10 In general, it is absurd to make the fact that the things

of this earth are observed to change and never to remain

in the same state, the basis of our judgement about the

truth. For in pursuing the truth one must start from the

things that are always in the same state and suffer no

15 change. Such are the heavenly bodies;for these do not

appear to be now of one nature and again of another, but

are manifestly always the same and share in no change.2

Further, if there is movement, there is also something

moved, and everything is moved out of something and into

something ;it follows that that which is moved must first

be in that out of which it is to be moved, and then not be in

20 it, and move into the other and come to be in it, and that

the contradictory statements are not true at the same time, as

these thinkers assert they are.

And if the things of this earth continuously flow and

move in respect of quantity if one were to suppose this,

although it is not true why should they not endure in

respect of qualify ? For the assertion of contradictory

statements about the same thing seems to have arisen

35 largely from the belief that the quantity of bodies does not

endure, which, our opponents hold, justifies them in saying

that the same thing both is and is not four cubits long.

But essence depends on quality, and this is of determinate

nature, though quantity is of indeterminate.3

Further, when the doctor orders people to take some

1Cf. r. ioiob i-26, ioii a

3i-4.2

Cf. r. ioioa 25-32.3

Cf. r. 1010*22-25.



BOOK K. 6 io63a

particular food, why do they take it ? In what respect is 30

4

this is bread truer than this is not bread ? And so it

would make no difference whether one ate or not. But as

a matter of fact they take the food which is ordered,

assuming that they know the truth about it and that it is

bread. Yet they should not, if there were no fixed constant

nature in sensible things, but all natures moved and flowed

for ever.1

Again, if we are always changing and never remain the 35

same, what wonder is it if to us, as to the sick, things never

appear the same ? (For to them also, because they are not 1063

in the same condition as when they were well, sensible

qualities do not appear alike; yet, for all that, the sensible

things themselves need not share in any change, though

they produce different, and not identical, sensations in the

sick. And the same must surely happen to the healthy if 5

the aforesaid2

change takes place.) But if we do not

change but remain the same, there will be something that

endures.3

As for those to whom the difficulties mentioned are

suggested by reasoning, it is not easy to solve the diffi

culties to their satisfaction, unless they will posit something

and no longer demand a reason for it;for it is only thus 10

that all

reasoningand all

proofis

accomplished;

if

theyposit nothing, they destroy discussion and all reasoning.

Therefore with such men there is no reasoning. But as for

those who are perplexed by the traditional difficulties, it is

easy to meet them and to dissipate the causes of their per

plexity. This is evident from what has been said.4

It is manifest, therefore, from these arguments that con- 15

tradictory statements cannot be truly made about the same

subject at one time,5nor can contrary statements, because

every contrariety depends on privation. This is evident if

we reduce the definitions of contraries to their principle.6

Similarly, no intermediate between contraries can be

predicated of one and the same subject, of which one of the

Cf. r. ioo8b

12-27.

2

Cf. io63a

35.3

Cf. r. ioo9a38-

b33.

4In io62b 2o-io63

b7.

5Cf. r. ioo9

a16-22, ioii a

3-i6.6

Cf. r. ioii b15-22.

645-28 O



io63b METAPHYSICA

jo contraries is predicated. If the subject is white we shall be

wrong in saying it is neither black nor white, for then it

follows that it is and is not white;for the second of the

two terms we have put together

lis

true of it, and thisis

the contradictory of white.2

We could not be right, then, in accepting the views

25 either of Heraclitus 3 or of Anaxagoras. If we were, it

would follow that contraries would be predicated of the

same subject ;for when Anaxagoras says that in everything

there is a part of everything, he says nothing is sweet any

more than it is bitter, and so with any other pair of con

traries, since in everything everything is present not poten-

30 daily only, but actually and separately. And similarly all

statements cannot be false nor all true, both because ot

many other difficulties which might be adduced as arising

from this position, and because if all are false it will not be

true to say even this, and if all are true it will not be false

35 to say all are false.4

Every science seeks certain principles and causes for each 7

1064 of its objects e.g. medicine and gymnastics and each of

the other sciences, whether productive or mathematical.

For each of these marks off a certain class of things for

itself and busies itself about this as about something exist

ing and real, not however qua real; the science that does

this is another distinct from these. Of the sciences men-

5 tioned each gets somehow thel what in some class of

things and tries to prove the other truths, with more or less

precision. Some get the what through perception, others

by hypothesis ;so that it is clear from an induction of this

sort that there is no demonstration of the substance or

1 what .

10 There is a science of nature, and evidently it must be

different both from practical and from productive science.

For in the case of productive science the principle of move

ment is in the producer and not in the product, and is either

an art or some other faculty. And similarly in practical

1 Sc. not white and not black .

2Cf. r. ioii b

23-iol2a24.

3Cf. io62a

3i-b2.

4Cf. r. ioi2a

24-bi8.



BOOK K. 7 io64a

science the movement is not in the thing done, but rather

in the doers. But the science of the natural philosopher 15

deals with the things that have in themselves a principle

of movement. It is clear from these facts, then, that natural

science must be neither practical nor productive, but theoreti

cal (for it must fall into some one of these classes).And

since each of the sciences must somehow know the what

and use this as a principle, we must not fail to observe 20

how the natural philosopher should define things and how

he should state the definition of the essence whether as akin

to snub or rather to concave . For of these the defini

tion of snub includes the matter of the thing, but that of

concave is independent of the matter;for snubness is 2 5

found in a nose, so that we look for its definition without

eliminating the nose, for what is snub is a concave nose.

Evidently then the definition of flesh also and of the eye

and of the otherparts

mustalways

be stated without

eliminating the matter.

Since there is a science of being qua being and capable

of existing apart, we must consider whether this is to be

regarded as the same as physics or rather as different.

Physics deals with the things that have a principle of 30

movement in themselves;mathematics is theoretical, and

is a science that deals with things that are at rest, but its

subjects cannot exist apart. Therefore about that which

can exist apart and is unmovable there is a science different

from both of these, if there is a substance of this nature

(I mean separable and unmovable), as we shall try to prove 35

there is.1 And if there is such a kind of thing in the world,

here must surely be the divine, and this must be the first

and most dominant principle. Evidently, then, there are io64b

three kinds of theoretical sciences physics, mathematics,

theology. The class of theoretical sciences is the best, and

of these themselves the last named is best;for it deals with

the highest of existing things, and each science is called 5

better or worse in virtue of its proper object.

One might raise the question whether the science of

being qua being is to be regarded as universal or not.

1Cf. A. 6, 7.

Q2



1064 METAPHYSICA

Each of the mathematical sciences deals with some one

determinate class of things, but universal mathematics ap

plies alike to all. Now if natural substances are the first of

10 existing things, physics must be the first of sciences ; but if

there is another entity and substance, separable and un-

movable, the knowledge of it must be different and prior

to physics and universal because it is prior.1

15 Since being in general has several senses, of which one 8

is being by accident,we must consider first that which

is in this sense. Evidently none of the traditional sciencesbusies itself about the accidental. For neither does archi

tecture consider what will happen to those who are to use

20 the house (e. g. whether they will have a painful life in it

or not), nor does weaving, or shoemaking, or the con

fectioner s art, do the like;

but each of these sciences

considers only what is peculiar to it, i. e. its proper end.

And as for the argument that when he who is musical

becomes lettered he will be both at once, not having been

25 both before;and that which is, not always having been,

must have come to be;

therefore he must have at once

become musical and lettered,

this none of the recognized

sciences considers, but only sophistic ;for this alone busies

itself about the accidental, so that Plato is not far \vrong

when he says2that the sophist spends his time on non-

being.

3o That a science of the accidental is not even possible \vill

be evident if we try to see what the accidental really is.

We say that everything either is always and of necessity

(necessity not in the sense of violence, but that which we

35 appeal to in demonstrations), or is for the most part, or is

neither for the most part, nor always and of necessity, but

merely as it chances;

e. g. there might be cold in the dog-

days, but this occurs neither always and of necessity, nor

io65afor the most part, though it might happen sometimes. The

accidental, then, is what occurs, but not always nor of

necessity, nor for the most part. Now we have said what

the accidental is, and it is obvious why there is no science

1Cf. E. I,

K. I059a26-29.

2Cf. Sophistes 254 A.



BOOK K. 8 io6sa

of such a thing; for all science is of that which is always

or for the most part, but the accidental is in neither of 5

these classes.

Evidently there are not causes and principles of the acci

dental, of the same kind as there are of the essential;for

if there were, everything"would be of necessity. If A is

when B is, and B is when C is, and if C exists not by

chance but of necessity, that also of which C was cause ro

will exist of necessity, do\vn to the last causatum as it is

called (but this was supposed to be accidental). Therefore

all things will be of necessity, and chance and the possibility

of a thing s either occurring or not occurring are removed

entirely from the range of events. And if the cause be

supposed not to exist but to be coming to be, the same

results will follow; everything will occur of necessity. 15

For to-morrow s eclipse will occur if A occurs, and A if B

occurs, and B if C occurs;and in this

wayif we subtract

time from the limited time between now and to-morrow we

shall come sometime to the already existing condition.

Therefore since this exists, everything after this will occur 20

of necessity, so that all things occur of necessity.

As to that which is in the sense of being true or of

being by accident, theformer depends on a combination in

thought and is an affection of thought (which is the reason

why it is the principles, not of that which is in this sense,

but of that which is outside and can exist apart, that are

sought) ;and the latter is not necessary but indeterminate

(I mean the accidental) ;and of such a thing the causes are 25

unordered and indefinite.1

Adaptation to an end is found in events that happen by

nature or as the result of thought. It is luck when one

of these events2

happens by accident. For as a thing may

exist, so it may be a cause, either by its own nature or by

accident.15 Luck is an accidental cause at work in such 3

events adapted to an end as are usually effected in accor

dance with purpose. And so luck and thought are concerned

1Cf. E. 2-4.

2Sc. which happen usually by nature or as the result of thought.

3Cf. Pliys. ii. I96

b21-25.



io65a METAPHYSICA

with the same sphere ;for purpose cannot exist without

thought. The causes from which lucky results might

happen are indeterminate ; and so luck is obscure to human

calculation and is a cause by accident, but in the unqualified

35 sense a cause of nothing.1

It is good or bad luck when

io6sbthe result is good or evil

;and prosperity or misfortune

when the scale of the results is large.2

Since nothing accidental is prior to the essential, neither

are accidental causes prior. If, then, luck or spontaneity is

a cause of the material universe, reason and nature are

causes before it.:3

5Some things are only actually, some potentially, some 9

potentially and actually, what they are, viz. in one case

a particular reality, in another, characterized by a particular

quantity, or the like.4 There is no movement apart from

things ;for change is always according to the categories

of being, and there is nothing common to these and in noone category. But each of the categories belongs to all its

10 subjects in either of two ways (e. g. this-ness for one

kind of it is*

positive form,and the other is

*

privation ;

and as regards quality one kind is white and the other

black,and as regards quantity one kind is complete

and the other*

incomplete ,and as regards spatial move

ment one is upwards and the other downwards,or one

thing is light and another heavy ) ;so that there are as

many kinds of movement and change as of being. ThereJ 5

being a distinction in each class of things between the

potential and the completely real, I call the actuality of the

potential as such, movement. That what we say is true, is

plainfrom the

followingfacts. When the buildable

,in

so far as it is what we mean by buildable V5exists actually,

it is being built, and this is the process of building. Simi

larly with learning, healing, walking, leaping, ageing, ripen-

20 ing.G Movement takes place when the complete reality itself

exists, and neither earlier nor later.7 The complete reality,

1Cf. Phys. ii. I97

a5-14.

2Cf. Phys. ii. I97

a25-27.

3

Cf. Phys. ii. 198* 5-13.

4

Cf. Phys. iii. 200^26-28.6i. e. not as so much matter, but as matter capable of being made

into a building.fi

Cf. Phys. iii. 2OOb 32-201* 19.7

Cf. Phys. iii. 2oi b6, 7.



BOOK K. 9 io6sb

then, of that which exists potentially, when it is completely

real and actual, not q2ia itself, but qua movable, is movement.

By qua I mean this : bronze is potentially a statue;but

yet it is not the complete reality of bronze qzia bronze that

is movement. For it is not the same thing to be bronze 25

and to be a certain potency. If it were absolutely the same

in its definition, the complete reality of bronze would have

been a movement. But it is not the same. (This is evident

in the case of contraries;for to be capable of being well

and to be capable of being ill are not the same for if they

were, being well and being ill would have been the sameit is that which underlies and is healthy or diseased, whether 30

it is moisture or blood, that is one and the same.) And

since it is not the same, as colour and the visible are not

the same, it is the complete reality of the potential, and as

potential, that is movement. That it is this, and that move

ment takes place when the complete reality itself exists, and 35

neither earlier nor later, is evident. For each thing is io668

capable of being sometimes actual, sometimes not, e. g. the

buildable qua buildable;and the actuality of the buildable

qua buildable is building. For the actuality is either this

the act of building or the house. But when the house

exists, it is no longer buildable;the buildable is what is

beingbuilt. The

actuality,then, must be the act

of building^5

and this is a movement. And the same account applies to

all other movements.

That what we have said is right is evident from what all

others say about movement, and from the fact that it is not

easy to define it otherwise. For firstly one cannot put it in

any other class. This is evident from what people say.i

Some call it otherness and inequality and the unreal ;

2

none of these, however, is necessarily moved, and further,

change is not either to these or from these any more than

from their opposites. The reason why people put move

ment in these classes is that it is thought to be something

1 The argument is that the house cannot be the eW/ryeia of the

buildable, for when the house exists the buildable has ceased to exist;

therefore its eV/ryeia must be \\\& process of building.2 The Pythagoreans and Platonists are meant; cf. PI. Soph. 256 D,Tim. 57Eff.



io66a METAPHYSICA

indefinite, and the principles in one of the two columns of

15 contrarieslare indefinite because they are privative, for

none of them is either a this or a such or in any of the

othercategories.

And the reason

whymovement is

thought to be indefinite is that it cannot be classed either

with the potency of things or with their actuality ;for

neither that which is capable of being of a certain quantity,

nor that which is actually of a certain quantity, is of neces-

20sity moved, and movement is thought to be an actuality,

but incomplete ;the reason is that the potential, whose

actuality it is, is incomplete. And therefore it is hard to

grasp what movement is;

for it must be classed either

under privation or under potency or under absolute actu

ality, but evidently none of these is possible. Therefore

25 what remains is that it must be what we said both actu

ality and the actuality we have described which is hard to

detect but capable of existing.2

And evidently movement is in the movable;for it is the

complete realization of this by that which is capable of

causing movement. And the actuality of that which is

capable of causing movement is no other than that of the

movable. For it must be the complete reality of both.

For while a thing is capable of causing movement because

30it can do

this,it is a

moverbecause it is active

;

but it is on

the movable that it is capable of acting, so that the actuality

of both is one, just as there is the same interval from one

to two as from two to one, and as the steep ascent and the

steep descent are one, but the being of them is not one;

the case of the mover and the moved is similar.3

35 The infinite is either that which is incapable of being 10

traversed because it is not its nature to be traversed (this

corresponds to the sense in which the voice is invisible),

or that which admits only of incomplete traverse or scarcely

admits of traverse, or that which, though it naturally

admits of traverse, is not traversed or limited; further, a

thing may be infinite in respect of addition or of subtrac-

1 Cf. note on A. 986** 23.&

With io65b 22-io66a 27 cf. Phys. iii. 2oi a

27-202* 3.3

Cf. Phys. iii. 2O2a 13-21.



BOOK K. 10 io66b

tion, or both. The infinite cannot be a separate, indepen- io66b

dent thing. For if it is neither a spatial magnitude nor a

plurality, but infinityitself is its substance and not an acci

dent of it, it will be indivisible ; for the divisible is either

magnitude or plurality. But if indivisible, it is not infinite,

except as the voice is invisible;but people do not mean 5

this, nor are we examining this sort of infinite, but the in

finite as untraversable.1

Further, how can an infinite exist

by itself, unless number and magnitude also exist by them

selves, since infinity is an attribute of these ?2

Further,

if the infinite is an accident of something else, it cannot be

qua infinite an element in things, as the invisible is not an 10

element in speech, though the voice is invisible.3 And

evidently the infinite cannot exist actually. For then any

part of it that might be taken would be infinite (for to be

infinite and *

the infinite are the same, if the infinite is

substance and not

predicated

of a subject). Therefore it is

either indivisible, or if it is partible, it is divisible into in

finites;but the same thing cannot be many infinites (as a 15

part of air is air, so a part of the infinite would be infinite,

if the infinite is a substance and a principle). Therefore it

must be impartible and indivisible. But the actually infinite

cannot be indivisible;for it must be of a certain quantity.

Therefore infinity belongs to its subject incidentally. Butif so, then (as we have said 4

)it cannot be it that is a prin- 3o

ciple, but that of which it is an accident the air or the

even number.5

This inquiry is universal;but that the infinite is not

among sensible things, is evident from the following argu

ment. If the definition of a body is that which is bounded

by planes , there cannot be an infinite body either sensible

or intelligible ;nor a separate and infinite number, for 25

number or that which has a number is numerable. 5 Con

cretely, the truth is evident from the following argument.

The infinite can neither be composite nor simple. For (a)

it cannot be a composite body, since the elements are limited

1 Cf. Phys. iii. 2O4a 3-14.2 Cf. Phys. iii. 204* 17-19.

3Cf. Phys. iii. 2O4

a14-17.

41. 9.

5Cf. Phys. iii. 2O4

a20-32.

6Cf. Phys. iii. 2O4

a34~

b8.



io66b METAPHYSICA

in multitude. For the contraries must be equal and no one

of them must be infinite;for if one of the two bodies falls

30 at all short of the other in potency, the finite will be de

stroyed bythe infinite.

And that each should be infiniteis impossible. For body is that which has extension in all

directions, and the infinite is the boundlessly extended, so

that if the infinite is a body it will be infinite in every direc

tion. Nor (d) can the infinite body be one and simple

35 neither, as some say,1

something apart from the elements,

from which they generate these2

(for there is no such body

apart from the elements ; for everything can be resolved

into that of which it consists, but no such product of

io67aanalysis is observed except the simple bodies), nor fire nor

any other of the elements. For apart from the question

how any of them could be infinite, the All, even if it is

finite, cannot either be or become any one ofthem, as Hera-

5 clitus says3

all things sometime become fire. The same

argument applies to this as to the One which the natural

philosophers posit besides the elements.4 For everything

changes from contrary to contrary, e. g. from hot to cold.5

Further, a sensible body is somewhere, and whole and

part have the same proper place, e. g. the whole earth

and part of the earth. Therefore if (a) the infinite body is

homogeneous, it will be unmovable or it will be always10 moving. But this is impossible ;

for why should it rather

rest, or move, down, up, or anywhere, rather than anywhere

else ? E. g. if there were a clod which were part of an in

finite body, where will this move or rest ? The proper place

of the body which is homogeneous with it is infinite. Will

the clod occupy the whole place, then ? And how ? (This

is impossible.) What then is its rest or its movement ? It

will either rest everywhere, and then it cannot move;or it

15 will move everywhere, and then it cannot be still. But (b]

if the All has unlike parts, the proper places of the parts

are unlike also, and, firstly,the body of the All is not

one except by contact, and, secondly, the parts will be

either finite or infinite in variety of kind. Finite they can-

1 Anaximander is meant.2

Cf. Phys. iii. 2O4b10-24.

3Fr. 30, 64, 66, 90.

4 For this argument cf. io66b 35~io67a

I.

5Cf. Phys. iii. 204* 32-205* 7.



BOOK K. 10 io67a

not be;for then those of one kind will be infinite in quan

tity and those of another will not(if

the All is infinite),

e.g. fire or water would be infinite, but such an infinite

element would be destruction to the contrary elements. 1

But if the parts are infinite and simple, their places also 20

are infinite and there will be an infinite number of elements;

and if this is impossible, and the places are finite, the All

also must be limited.2

In general, there cannot be an infinite body and also a

proper place for bodies, if every sensible body has either

weight or lightness. For it must move either towards the 25

middle or upwards, and the infinite either the whole or

the half of it cannot do either;for how will you divide

it ? Or how will part of the infinite be down and part up,

or part extreme and part middle ? Further, every sensible

body is in a place, and there are six kinds of place,3 but

these cannot exist in an infinite

body.In

general,

if there 30

cannot be an infinite place, there cannot be an infinite body ;

(and there cannot be an infinite place,} for that which is in a

place is somewhere, and this means either up or down or in

one of the other directions, and each of these is a limit.4

The infinite is not the same in the sense that it is a single

thing whether exhibited in distance or in movement or in

time, but the posterior among these is called infinite in

virtue of its relation to the prior ;i.e. a movement is called 35

infinite in virtue of the distance covered by the spatial

movement or alteration or growth, and a time is called

infinite because of the movement which occupies it.5

ii Of things which change, some change in an accidental 1067

sense, like that in which the musical

maybe said to walk,

1

Cf. Phys. iii. 205* 10-25. Cf. also io66b 28-34, from which it appearsthat the argument is as follows. If a finite number of kinds is to makean infinite whole, at least one kind must be infinite in extent. Theycannot all be infinite, for they limit one another. But if one is infinite

and another finite, the former destroys the latter and there ceases to be

the variety of kinds within the whole which is at present presupposed.Aristotle omits to mention that the supposition of a finite kind co

existing with an infinite kind is in itself absurd, because the finite

limits the infinite. But this would only make his case stronger.2 Cf. Phys. iii. 205* 29-32.3Sc. up and down, right and left, before and behind.

4Cf. Phys. iii. 20^24-206^ 7.

5Cf. Phys. iii. 2o;

b21-25.



io67b METAPHYSICA

and others are said, without qualification, to change, because

something* in them changes, 1. e. the things that change in

parts ;the body becomes healthy, because the eye does.

But there is something which is by its own nature moved5 directly, and this is the essentially movable. The same

distinction is found in the case of the mover;for it causes

movement either in an accidental sense or in respect of a

part of itself or essentially. There is something that

directly causes movement;and there is something that is

moved, also the time in which it is moved, and that from

which and that into which it is moved. 1 But the forms and

the affections and the place, which are the terminals of the

10 movement of moving things, are unmovable, e.g. know

ledge or heat;

it is not heat that is a movement, but heat

ing.2

Change which is not accidental is found not in all

things, but between contraries, and their intermediates, and

between contradictories. We may convince ourselves of

this by induction.3

15 That which changes changes either from positive into

positive, or from negative into negative, or from positive

into negative, or from negative into positive. (By positive

I mean that which is expressed by an affirmative term.)

Therefore there must be three changes ;for that from

20

negative into negative is not change, because (since theterms are neither contraries nor contradictories) there is no

opposition.4 The change from the negative into the posi

tive which is its contradictory is generation absolute

change absolute generation, and partial change partial

generation ;and the change from positive to negative is

destruction absolute change absolute destruction, and

25 partial change partial destruction. If, then, that which is

not has several senses,5 and movement can attach neither

to that which implies putting together or separating,6 nor

1Cf. Phys. v. 224

a 2i-b i.

2Cf. Phys. v. 224

b 11-16.*

Cf. Phys. v. 224b28-30.

4

1067^ 20-21. I now read ovre yap . . . Icrnv as a parenthesis givingthe justification for OVK dvTidfo-is and idiomatically thrown forward.

8Cf. E. I026a 33-

b2, I027

bi8-i9.

6i. e. to that which is not in the sense of the judgement which is

false .



BOOK K. ii io67b

to that which implies potency and is opposed to that which

is in the full sensel

(true, the not-white or not-good can be

moved incidentally, for the not-white might be a man;but

that which is not a particular thing at all can in no wise be

moved), that which is not cannot be moved (and ifthis is so, 30

generation cannot be movement;for that which is not is

generated ;for even if we admit to the full that its genera

tion is accidental, yet it is true to say that not-being is

predicable of that which is generated absolutely).2

Simi

larly rest cannot belong to that which is not. These con

sequences, then, turn out to be awkward, and also this, 35

that everything that is moved is in a place, but that which

is not is not in a place ;for then it would be somewhere.

Nor is destruction movement;for the contrary of move

ment is movement or rest, but the contrary of destruction

is generation. Since every movement is a change, and the io68a

kinds of change are the three named above,3 and of these

those in the way of generation and destruction are not

movements, and these are the changes from a thing to its

contradictory, it follows that only the change from positive

into positive is movement. And the positives are either 5

contrary or intermediate (for even privation must be

regarded as contrary), and are expressed by an affirmative

term, e. g. naked or toothless

4

or black.

12 If the categories are classified as substance, quality,

place, acting or being acted on, relation, quantity, there must

be three kinds of movement of quality, of quantity, of

place. There is no movement in respect of substance 10

(because there is nothing contrary to substance), nor of

relation (for it is possible that if one of two things in rela

tion changes, the relative term which was true of the other

thing ceases to be true, though this other does not change

1i. e. a thing cannot be moved when it does not exist actually, but

exists potentially.2

i. e. even if the not-being (privation) which is the starting-point of

generation can exist only as an accident of prime matter, still not-

being is the starting-point of absolute generation (i.e. generation of a

substance, not of a quality).3 In io6;b 19.4

Toothless is more obviously negative in form than the corre

sponding Greek word.



io68a METAPHYSICA

at all, so that their movement is accidental), nor of agent

and patient, or mover and moved, because there is no

15 movement of movement nor generation of generation, nor,

in general, change of change. For there might be movement of movement in two senses; (i) movement might be

the subject moved, as a man is moved because he changes

from pale to dark, so that on this showing movement,

too, may be either heated or cooled or change its place or

increase. But this is impossible ;for change is not a sub-

20 ject. Or (2) some other subject might change from change

into some other form of existence (e. g. a man from disease

into health). But this also is not possible except incident

ally. For every movement is change from something into

25 something. (And so are generation and destruction; only,

these are changes into things opposed in certain ways

while the other, movement, is into things opposed in

another

way.

1

)A

thing changes,then, at the same time

from health into illness, and from this change itself into

another. Clearly, then, if it has become ill, it will have

changed into whatever may be the other change concerned

(though it may be at rest2

), and, further, into a determinate

change each time;and that new change will be from some-

30 thing definite into some other definite thing ;therefore it

will be the opposite change, that of growing well. Weanswer that this happens only incidentally ;

e. g. there is a

change from the process ofrecollection to that of forgetting,

only because that to which theprocess attaches is changing,

now into a state of knowledge, now into one of ignorance.

Further, the process will go on to infinity, if there is to be

change of change and coming to be ofcoming to be. What

35 is true of the later, then, must be true of the earlier;

e. g. if

the simple coming to be was once coming to be, that which

io68b comes to be something was also once coming to be

;there

fore that which simply comes to be something was not yet

in existence, but something which was coming to be coming

to be something was already in existence. And this was

1

Change between contraries is movement, change between contra

dictories is generation or destruction.2 This is possible, though excluded by the theory in question.



BOOK K. 12 io68b

once coming1

to be, so that at that time it was not yet

coming to be something else. Now since of an infinite

number of terms there is not a first, the first in this series

will not exist, and therefore no following term will exist.

Nothing, then, can either come to be or move or change. 5

Further, that which is capable of a movement is also capable

of the contrary movement and rest, and that which comes

to be also ceases to be. Therefore that which is coming

to be is ceasing to be when it has come to be coming to

be;for it cannot cease to be as soon as it is coming to be

coming to be, nor after it has come to be;for that which is

ceasing to be must be} Further, there must be a matter TO

underlying that which comes to be and changes. What

will this be, then, what is it that becomes movement or

becoming, as body or soul is that which suffers alteration ?

And, again, what is it that they move into ? For it must

be themovement

orbecoming of something from some

thing into something. How, then, can this condition be

fulfilled ? There can be no learning of learning, and there

fore no becoming of becoming.2

Since there is not movement either of substance or of15

relation or ofactivity and passivity, it remains that move

ment is in respect of quality and quantity and place ;for

each of these admits of contrariety. By quality I mean not

that which is in the substance (for even the differentia is a

quality), but the passive quality, in virtue of which a thing

is said to be acted on or to be incapable of being acted on.3

The immobile is either that which is wholly incapable of 20

being moved, or that which is moved with difficulty in a

long time or begins slowly, or that which is of a nature to

be moved and can be moved but is not moved when and

where and as it would naturally be moved. This alone amongimmobiles I describe as being at rest

;for rest is contrary

1If that which comes to be comes to be coming to be, it also ceases

to be. When ? Not when it is only coming to be coming to be, for then

it is not and . . cannot cease to be;nor after it has come to be, for then

also that which comes to be is not and . . cannot cease to be. /. It

is

ceasing

to be, at the

verytime when it is

comingto be Which is

absurd.2 W7

ith io67b 4-io68

b15 cf. Phys. v. 225* 3-226** 16.

5Cf. Phys. v. 226a 23-29.



io68b METAPHYSICA

25to movement, so that it must be a privation in that which is

receptive ofmovement?-

Things which are in one proximate place are together in

place, and things which are in different places are apart:

things whose extremes are together touch : that at which

a changing thing, if it changes2

continuously according to

its nature, naturally arrives before it arrives at the extreme

3ointo which it is changing, is between? That which is most

distant in a straight line is contrary in place. That is

successive which is after the beginning (the order being

determined by position or form or in some other way) and

has nothing of the same class between it and that which it

succeeds, e.g. lines in the case of a line, units in that of a

unit, or a house in that of a house. (There is nothing to

prevent a thing of some other class from being between.)

35 For the successive succeeds something and is something

later;

* one does not succeed two,nor the first

dayof

io6gathe month the second. That which, being successive,

touches, is contiguous. (Since all change is between oppo-

sites, and these are either contraries or contradictories, and

there is no middle term for contradictories, clearly that

which is between is between contraries.4)

The continuous

5 is a species of the contiguous. I call two things continuous

when the limits ofeach, with which they touch and by which

they are kept together, become one and the same, so that

plainly the continuous is found in the things out of which

a unity naturally arises in virtue of their contact. And

plainly the successive is the first of these concepts (for the

successive does not necessarily touch, but that which touches

10 is successive;and if a thing is continuous, it touches, but if

it touches, it is not necessarily continuous ;and in things in

which there is no touching, there is no organic unity) ;

therefore a point is not the same as a unit;

for contact

belongs to points, but not to units, which have only suc

cession : and there is something between two of the former,

but not between two of the latter.5

1

Cf.Phys. v. 226

b

io-i6.2io68b 29 omit TO.

3Cf. Phys. v. 226b 21-25.

4 This sentence should probably come after the first in this para

graph.5

Cf. Phys. v. 226b 32-227* 31.



BOOK A

i THE subject of our inquiry is substance;for the principles

and the causes we are seeking are those of substances.

For if the universe is of the nature of a whole, substance is

its first part ;and if it coheres merely by virtue of serial 20

succession, on this view" also substance is first, and is suc

ceeded by quality, and then by quantity. At the same

time these latter are not even being in the full sense, but

are qualities and movements of it, or else even the not-

white and the not-straight would be being ;at least we say

even these are, e. g.*

there is a not-white V Further, none

of the categories other than substance can exist apart. And 25

the early philosophers also in practice testify to the primacy

of substance;for it was of substance that they sought the

principles and elements and causes. The thinkers of the

present2

day tend to rank universals as substances (for

genera are universals, and these they tend to describe as

principles and substances, owing to the abstract nature of

their inquiry) ;but the thinkers of old ranked particular

things as substances, e. g. fire and earth, not what is common to both, body.

There are three kinds of substance one that is sensible 3

(of which one subdivision is eternal and another is perish

able;the latter is recognized by all men, and includes e. g.

plants and animals), of which we must grasp the elements,

whether one or many ;and another that is immovable, and

this certain thinkers assert to be capable of existing apart,

some dividing it into two, others identifying the Forms and 35

the objects of mathematics, and others positing, of these

two, only the objects of mathematics.3 The former two

kinds of substance are the subject of physics (for they

1 This is an implication of the ordinary type of judgement, x is not

white .

2 The Platonists.3 The three views appear to have been held respectively by Plato,

Xenocrates, and Speusippus.

645-28 R



io69b METAPHYSICA

io6gb

imply movement) ;but the third kind belongs to another

science, if there is no principle common to it and to the

other kinds.

Sensible substance is changeable. Now if change proceeds from opposites or from intermediates, and not from

all opposites (for the voice is not-white(, but it does not

5 therefore change to white}), but from the contrary, there

must be something underlying which changes into the con

trary state;for the contraries do not change. Further, 2

something persists, but the contrary does not persist ;there

is, then, some third thing besides the contraries, viz. the

matter. Now since changes are of four kinds either in

respect of the what or of the quality or of the quantity

10 or of the place, and change in respect of thisnessJ

is

simple generation and destruction, and change in quantity

is increase and diminution, and change in respect of an

affection is alteration, andchange

ofplace

is motion,

changes will be from given states into those contrary to

them in these several respects. The matter, then, which

15 changes must be capable of both states. And since that

which *

is has two senses, we must say that everything

changes from that which is potentially to that which is

actually, e. g. from potentially white to actually white, and

similarly in the case of increase and diminution. Thereforenot only can a thing come to be, incidentally, out of that

which is not, but also all things come to be out of that

33 which is, but is potentially, and is not actually. And this

is the One of Anaxagoras ;for instead of *

all things

were togetherc

and the Mixture of Empedocles and

Anaximander and the account given by Democritus it is

better to say all things were together potentially but not

actually . Therefore these thinkers seem to have had some

notion of matter. Now all things that change have matter,

25 but different matter;and of eternal things those which are

not generable but are movable in space have matter not

matter for generation, however, but for motion from one

place to another.

One might raise the question from what sort of non-being

1

Reading in I. 1 1 TO ro 8f.2

Anaxagoras, fr. I.



BOOK A. 2 io6gb

generation proceeds ;for non-being has three senses.

1

If,

then, one form of non-being exists potentially, still it is not

by virtue of a potentiality for any and every thing, but

different things come from different things ;nor is it satis

factory to say that all things were together ;for they 30

differ in their matter, since otherwise why did an infinity of

things come to be, and not one thing ? For reason2

is

one, so that if matter also were one, that must have come

to be in actuality which the matter was in potency.:i The

causes and the principles, then, are three, twobeing

the

pair of contraries of which one is definition and form and

the other is privation, and the third being the matter.

3 Note, next, that neither the matter nor the form comes 35

to be and I mean the last matter and form. For every

thing that changes is something and is changed by some

thing and into something. That by which it is changed iO7oa

is the immediate mover ;that which is changed, the matter;

that into which it is changed, the form. The process, then,

will go on to infinity, if not only the bronze comes to be

round but also the round or the bronze comes to be;

therefore there must be a stop.

Note, next, that each substance comes into being out of

somethingthat shares its name.

(Natural objects

and 5

other things both rank as substances.) For things come

into being either by art or by nature or by luck or by

spontaneity. Now art is a principle of movement in some

thing other than the thing moved, nature is a principle

in the thing itself (for man begets man 4

),and the other

causes are privations of these two.

1 Alexander points out thataTrop^o-fie

. . . 6V refers to 1. 20. Thethree senses are probably the non-being that answers to the categoriesof being, the false, and the potential (cf. N. io89

a26-28).

2Sc. the voiis of Anaxagoras doctrine, summarized by D. L. (II. 3.

l) in the words, irdvra xprjfiara rjv 6/j.oiietra 6 vovs eXOav aura

Su/cdo-fi^o-ev.3Sc. an undifferentiated unity.

4 This is not a good instance of what A. says about nature, for the

principle of generation is not in the child but in the father. Thedefinition of nature applies better to other natural functions, such as

growth. The note ai Spano? yap av6pu>7rov yfwa is hastily thrown inbecause A. is thinking mainly of his favourite thesis of ycvco-is ex

. Hence Alexander says TOVTO crvvexf? earn TCO /uera ravraOTl fKCKJTT] K (TVVtOVV[J.OV y L V T (1 L O V (T I a.

R 2



io7oa METAPHYSICA

There are three kinds of substance the matter, which is

10 a*

this in appearance (for all things that are characterized

by contact and not by organic unity are matter and sub-

i

9 stratum,e.

g. fire, flesh,head

;

for these are all

matter, andthe last matter is the matter of that which is in the full

1 1 sense substance T

) ;the nature, which is a this or positive

state towards which movement takes place ;and again,

thirdly, the particular substance which is composed of these

two, e. g. Socrates or Callias. Now in some cases the

4

this does not exist apart from the composite substance,

e.g. the form of house does not so exist, unless the art of

15 building exists apart (nor is there generation and de

struction of these forms, but it is in another way that the

house apart from its matter, and health, and all ideals of art,

exist and do not exist) ;but if the this exists apart from

the concrete thing, it is only in the case of natural

objects. And so Plato was not far wrong when he said

that there are as many Forms as there are kinds of natural

object (if there are Forms distinct from the things of this

21earth). The moving causes exist as things preceding the

effects, but causes in the sense of definitions are simultaneous

with their effects. For when a man is healthy, then health

also exists;and the shape of a bronze sphere exists at the

same timeas

the bronze sphere. (But we must examine25 whether any form also survives afterwards. For in some

cases there is nothing to prevent this;

e. g. the soul maybe of this sort not all soul but the reason; for presumably

it is impossible that all soul should survive.) Evidently

then there is no necessity, on this ground at least, for the

existence of the Ideas. For man is begotten by man, a given

man by an individual father ; and similarly in the arts ; for

30 the medical art is the formal cause of health.

The causes and the principles of different things are in 4

a sense different, but in a sense, if one speaks universally

and analogically, they are the same for all. For one might

raise the question whether the principles and elements are

1I adopt Alexander s suggestion that olov . .. reAevrma

(11. 19-20)

should be placed after {nr-jKfipevov (1. u).



BOOK A. 4 io7oa

different or the same for substances and for relative terms,

and similarly in the case of each of the categories. But it 35

would be paradoxical if they were the same for all. For

then from the same elements will proceed relative terms

and substances. What then will this common element be ? io7ob

For(i) (a) there is nothing common to and distinct from sub

stance and the other categories, viz. those which are predi

cated;but an element is prior to the things of which it is

an element. But again (6)substance is not an element in

relative terms, nor is any of these an element in substance.

Further, (2)how can all things have the same elements ?

For none of the elements can be the same as that which 5

is composed of elements, e. g. b or a cannot be the same

as ba. (None, therefore, of the intelligibles,1

e. g. being or

unity, is an element;for these are predicable of each of

the compounds as well.) None of the elements, then, will

be either a substance or a relative term;

butit

must be oneor other. All things, then, have not the same elements.

Or, as we are wont to put it,in a sense they have and in 10

a sense they have not;

e. g. perhaps the elements of per

ceptible bodies are, zsform, the hot, and in another sense

the cold, which is the privation ; and, as matter, that

which directly and of itself potentially has these attributes;

and substances comprise both these and the things com

posed of these, of which these are the principles, or any unity

which is produced out of the hot and the cold, e. g. flesh or

bone;for the product must be different from the elements. 15

These things then have the same elements and principles

(though specifically different things have specifically differ

ent elements) ;but all things have not the same elements

in this sense, but only analogically ;i. e. one might say that

there are three principles the form, the privation, and the

matter. But each of these is different for each class;

e. g.20

in colour they are white, black, and surface, and in day and

night they are light, darkness, and air.

Since not only the elements present in a thing are causes,

but also

something external,i.e. the

moving cause, clearly1

This is apparently almost a technical name for the abstract termswhich are found in all the categories alike.



io7ob METAPHYSICA

while*

principle and element are different both are causes,

and principle is divided into these two kinds 1: and that

which acts as producing movement or rest is a principle

25 and a substance. Thereforeanalogically

there are three

elements, and four causes and principles ;but the elements

are different in different things, and the proximate moving

cause is different for different things. Health, disease,

body; the moving cause is the medical art. Form, dis

order of a particular kind, bricks;the moving cause is the

30 building art. And since the moving cause in the case ol

natural things is for man, for instance, man, and in the

products ofthought the form or its contrary, there will be in

a sense three causes, while in a sense there are four. For

the medical art is in some sense health, and the building

art is the form of the house, and man begets man;

2

further, besides these there is that which as first of all

35 things moves all things.

Some things can exist apart and some cannot, and it is 5

io7iathe former that are substances. And therefore all things

have the same causes,3

because, without substances, modi

fications and movements do not exist. Further, these causes

will probably be soul and body, or reason and desire and

body.

And in yet another way, analogically identical things are

5 principles, i. e. actuality and potency ;but these also are

not only different for different things but also apply in

different ways to them. For in some cases the same

thing exists at one time actually and at another potentially,

e. g. wine or flesh or man does so. (And these too fall

under the above-named causes.4 For the form exists

actually, if it can exist apart, and so does the complex

of form and matter, and the privation, e. g. darkness or

10 disease;but the matter exists potentially ;

for this is that

1i.e. the principles which are elements and those which are not.

2i. e. the efficient cause is identical with the formal.

3i. e. the causes of substance are the causes of all things.

4i. e. the division into potency and actuality stands in a detinite

relation to the previous division into matter, form, and privation.r<>

e| a/z0oty is not strictly in point, but is suggested by the frequent

division of ova-ia into v\rj, eldos, and ro e aptyolv.



BOOK A. 5 1071*

which can become qualified either by the form or by the

privation.) But the distinction of actuality and potentiality

applies in another way to cases where the matter of cause

and of effect is not the same, in some of which cases the

form is not the same but different;

e. g.the cause of man

is (i) the elements in man (viz. fire and earth as matter, and

the peculiar form), and further (2) something else outside,

i.e. the father, and (3) besides these the sun and its oblique 15

course, which are neither matter nor form nor privation of

man nor of the same species with him, but moving causes.1

Further, one must observe that some causes can be ex

pressed in universal terms, and some cannot. The proximate

principles of all things are the this which is proximate in

actuality, and another which is proximate in potentiality.2

The universal causes, then, of which we spoke:i do not

exist. For it is the individual that is the originative prin- 20

ciple

of the individuals. For while man is the

originativeprinciple of man universally, there is no universal man, but

Peleus is the originative principle of Achilles, and your

father of you, and this particular b of this particular ba,

though b in general is the originative principle of ba taken

without qualification.

Further, if the causes of substances are the causes of all

things, yet different things have different causes and elements,as was said

4;the causes of things that are not in the same 25

class, e. g. of colours and sounds, of substances and quan

tities, are different except in an analogical sense;and those

of things in the same species are different, not in species,

but in the sense that the causes of different individuals are

1Aristotle distinguishes two ways in which things may be related as

&vvafj.is and eWpyeia. (i) The same thing is <Wa/iei what it later comesto be evepyei a. But (2) one thing may be called Svvanis and another

eWpyeui though they have nothing in common. Here duvams and eWp-

yeia almost = cause and effect, and dvvafjus is the duvajus Kara Kivrjcriv

\eyofjievr) (transeunt potentiality or rather power) spoken of in (3. i.

The movement of the sun in the ecliptic is the cause of generation and

decay (Phys. ii. I94b

13, De Gen. et Corr. ii. 356* 3i-b9) and is thus

a transeunt dvvapis of each man who is born.2

e. g. the proximate causes of a child are the individual father (whoon Aristotle s view is the efficient and contains the formal cause) and

the germ contained in the individual mother (which is the material

cause).3

In 1. 17.4In io;o

b17.



io7i* METAPHYSICA

different, your matter and form and moving cause being

different from mine, while in their universal definition they

3o are the same. And if we inquire what are the principles or

elements of substances and relations and qualities whetherthey are the same or different clearly when the names of

the causes are used in several senses the causes of each are

the same, but when the senses are distinguished the causes

are not the same but different, except that in the following

senses the causes of all are the same. They are (i) the

same or analogous in this sense, that matter, form, priva

tion, and the moving cause are common to all things ; and

(2) the causes of substances may be treated as causes of all

things in this sense, that when substances are removed all

35 things are removed; further, (3) that which is first in

respect of complete reality is the cause of all things. But

in another sense there are different1

first causes, viz. all

the contraries which are neither generic nor ambi

guous terms;

2

and, further, the matters of different things

io7ibare different. We have stated, then, what are the principles

of sensible things and how many they are, and in what

sense they are the same and in what sense different.

Since there were 8three kinds of substance, two of them 6

physical and one unmovable, regarding the latter we must

assert that it is necessary that there should be an eternal

5unmovable substance. For substances are the first of exist

ing things, and if they are all destructible, all things are

destructible. But it is impossible that movement should

either have come into being or cease to be (for it must

always have existed), or that time should. For there could

not be a before and an after if time did not exist. Move

ment also is continuous, then, in the sense in which time is;

for time is either the same thing as movement or an attri-

10 bute of movement. And there is no continuous movement

except movement in place, and of this only that which is

circular is continuous.

1First is now taken in the sense of proximate ,

not of* ultimate

as in TO

TrpcoTov(i>T(\e\(ia.

zSc. but taken as individual qualities. All things include f 8os and

<TTcpr)<ris,but each thing has a distinct ddos and oWpgo-if of its own.

8Cf. io69

a3o.



BOOK A. 6 ioyib

But if there is something which is capable of moving

things or acting on them, but is not actually doing so, \there will not necessarily be movement

;for that which has

a potency need not exercise it. Nothing, then, is gained

even if we suppose eternal substances, as the believers in

the Forms do, unless there is to be in them some principle 15

which can cause change ; nay, even this is not enough, nor

is another substance besides the Forms enough ;for if it is

not to act, there will be no movement. Further, even if it

acts,this will not be

enough,if its essence is

potency;

for

there will not be eternal movement, since that which is

potentially may possibly not be. There must, then, be

such a principle, whose very essence is actuality. Further, 20

then, these substances must be without matter;for they

must be eternal, if anything is eternal. Therefore they

must be actuality.

Yet there is a difficulty ; for it is thought that everything

that acts is able to act, but that not everything that is able

to act acts, so that the potency is prior. But if this is so, 25

nothing that is need be;for it is possible for all things to

be capable of existing but not yet to exist.

Yet if we follow the theologians who generate the world

from night,1or the natural philosophers who say that

*

all

things were together ,

2 the same impossible result ensues.

For how will there be movement, if there is no actually

existing cause ? Wood will surely not move itself the

carpenter s art must act on it;nor will the menstrual blood 30

nor the earth set themselves in motion, but the seeds must

act on the earth and the semen on the menstrual blood.

This is

whysome

supposeeternal

actuality

e.

g. Leucip-pus

3 and Plato 4;for they say there is always movement.

But why and what this movement is they do not say, nor,

if the world moves in this way or that, do they tell us the

cause of its doing so. Now nothing is moved at random,

but there must always be something present to move it;

1

Cf. Hesiod, Op. et D. 17, Theog. 116 ff., Orpheus fr. 12, Diels,Musaeus fr. 14, Epimenides fr.

5,Acusilaus fr. i, 3, Aristoph. Av. 693.

2

Anaxagoras, fr. I.

3Cf. De Caelo, iii. 3oo

b8.

4Cf. Timaeus, 30 A.



io7ib METAPHYSICA

35 e.g.

as a matter of fact a thing moves in one way by nature,

and in another by force or through the influence of reason

or something else. (Further, what sort of movement is

primary ? This makes a vast difference.) But again for

Plato, at least, it is not permissible to name here that which

iO72a he sometimes supposes to be the source of movement that

which moves itself;]

for the soul is later, and coeval with

the heavens, according to his account.2 To suppose potency

prior to actuality, then, is in a sense right, and in a sense

not;and we have specified these senses.

3 That actuality

5 is prior is testified by Anaxagoras (for his reason is

actuality) and by Empedocles in his doctrine of love and

strife, and by those who say that there is always movement,

e. g. Leucippus. Therefore chaos or night did not exist for an

infinite time, but the same things have always existed (either

passing through a cycle of changes or obeying some other

law),

since

actuality

is

prior

to

potency.If, then, there is

a constant cycle, something must always remain,4

acting in

J the same way. And if there is to be generation and de

struction, there must be something else5 which is always

acting in different ways. This must, then, act in one way

in virtue of itself, and in another in virtue of something else

either of a third agent, therefore, or of the first. Now it

must be in virtue of the first. For otherwise this againcauses the motion both of the second agent and of the third.

15 Therefore it is better to say the first . For it was the

cause of eternal uniformity ;and something else is the

cause of variety, and evidently both together are the cause

of eternal variety. This, accordingly, is the character which

the motions actually exhibit. What need then is there to

seek for other principles ?

Since (i) this is a possible account of the matter, and (2) 7

if it were not true, the world would have proceeded out

of night and 4

all things together6 and out of non-being,

20 these difficulties may be taken as solved. There is, then,

1Cf. Phaedrus, 245 C; Laivs, 894 E.

2Cf.

Timaeus, 346.

3Cf.

io;i

b22-26.

4i. e. the sphere of the fixed stars.

Gi. e. the sun. Cf. De Gen. et Corr. ii. 336* 23 ff.

6

Anaxagoras, fr. i.



BOOK A. 7 i072a

something which is always moved with an unceasing motion,

which is motion in a circle;and this is plain not in theory

only but in fact. Therefore the first heaven 1 must be

eternal. There is therefore also something which moves it.

And since that which is moves and moved is intermediate,

there is something which moves without being moved,

being eternal, substance, and actuality. And the object of 25

desire and the object of thought move in this way ; they

move without being moved. The primary objects of desire

and ofthought

are the same. For theapparent good

is the

object of appetite, and the real good is the primary object

of rational wish. But desire is consequent on opinion

rather than opinion on desire;

for the thinking is the

starting-point. And thought is moved by the object of 30

thought, and one of the two columns of opposites2

is in

itself the object of thought ;and in this, substance is first,

and in substance, that which is simple and exists actually.

(The one and the simple are not the same;for one means

a measure, but simple means that the thing itself has

a certain nature.) But the beautiful, also, and that which is

in itself desirable are in the same column;and the first in 35

any class is always best, or analogous to the best.3

That a final cause may exist among unchangeable en- iO72b

tities is shown by the distinction of its meanings. For the

final cause is (a) some being for whose good an action is

done, and (b) something at which the action aims;and of

these the latter exists among unchangeable entities though

the former does not. The final cause, then, produces motion

as being loved, but all other things move by being moved.

1

i. e. the outer sphere of the universe, that in which the fixed stars

are set.

2Cf. note on A. 986*23.

3Sc. where there is no best in the strict sense. The argument for

the identity of the primary forms of TO opfKrov and TO VOI]TOV is not very

clearly stated, but seems to be as follows. The opfKrov is the Ka\6i>.

(In parenthesis it is stated that desire depends on thought rather than

thought ondesire.) The positive side of the list ot contraries is the

object of thought, and the first term on this side (which must be the

primary object of thought) is simple actual substance. But the objectof desire, which we have seen to be the Ka\of, is on the same side of the

list, and therefore the first member of that list (the primary object of

thought) must be the primary object of desire.



io72b

METAPHYSICA

Now if something is moved it is capable of being otherwise

5 than as it is. Therefore if its actuality is the primary form

of spatial motion, then in so far as it is subject to change,

in this respect it is capable of being otherwise, in place,

even if not in substance. But since there is somethingwhich moves while itself unmoved, existing actually, this

can in no way be otherwise than as it is. For motion in

space is the first of the kinds of change, and motion in

a circle the first kind of spatial motion;and this the first

10 mover produces?- The first mover, then, exists of necessity ;

and in so far as it exists by necessity, its mode of being is

good,2 and it is in this sense a first principle. For the

necessary has all these sensesthat which is necessary

perforce because it is contrary to the natural impulse, that

without which the good is impossible, and that which can

not be otherwise but can exist only in a single way.

On such aprinciple, then, depend

theheavens and the

world of nature. And it is a life such as the best which we

15 enjoy, and enjoy for but a short time (for it is ever in this

state, which we cannot be), since its actuality is also

pleasure. (And for this reason3are waking, perception, and

thinking most pleasant, and hopes and memories are so

on account of these.) And thinking in itself deals with

that which is best in itself, and that which is thinking

in the fullest sense with that which is best in the fullest

sense. And thought thinks on itself because it shares the

20 nature of the object of thought ;for it becomes an object

of thought in coming into contact with and thinking

its objects, so that thought and object of thought are the

same. For that which is capable of receiving the object of

thought, i. e. the essence, is thought. But it is active when

it possesses this object. Therefore the possession rather

than the receptivity is the divine element which thought

seems to contain, and the act of contemplation is what is

1If it had any movement, it would have the first. But it produces

this and therefore cannot share in it;for if it did, we should have to

look for something that is prior to the first mover and imparts this

motion to it.2

i. e. it is necessary in the sense of/jn] ev^f\6^vov aXXcos e

^ft",and is

. . good.3

Sc. because they are activities or actualities.



BOOK A. 7 io72b

most pleasant and best. If, then, God is always in that

good state in which we sometimes are, this compels our

wonder;and if in a better this compels it yet more. And 25

God ts in a better state. And life also belongs to God;for

the actuality of thought is life, and God is that actuality; and

God s self-dependent actuality is life most good and eternal.

We say therefore that God is a living being, eternal, most

good, so that life and duration continuous and eternal

belong to God;for this is God.

Those whosuppose,

as thePythagoreans

l andSpeusip- 30

pus2do, that supreme beauty and goodness are not present

in the beginning, because the beginnings both of plants and

of animals are causes, but beauty and completeness are in

the effects of these,3 are wrong in their opinion. For the 35

seed comes from other individuals which are prior and

complete, and the first thing is not seed but the complete

being ; e. g. we must say that before the seed there is io73a

a man, not the man produced from the seed, but another

from whom the seed comes.

It is clear then from what has been said that there is

a substance which is eternal and unmovable and separate

from sensible things. It has been shown also that this 5

substance cannot have any magnitude, but is without parts

and indivisible (for it produces movement through infinite

time, but nothing finite has infinite power; and, while every

magnitude is either infinite or finite, it cannot, for the above

reason, have finite magnitude, and it cannot have infinite 10

magnitude because there is no infinite magnitude atall).

But

it has also been shown that it is impassive and unalterable;

for all the other

changes

are

posterior

to4

change

of place.

8 It is clear, then, why these things are as they are. But

we must not ignore the question whether we have to

suppose one such substance or more than one, and if the

latter, how many ;we must also mention, regarding the

15

opinions expressed by others, that they have said nothing

about the number of the substances that can even be clearly

1

Cf. io75a

36.2

Cf. Z. io2Sb2i, N. I09i

a

34, io92a

u.;

i. e. the animal or plant is more beautiful and perfect than the

seed.4

i. e. impossible without.



io73a METAPHYSICA

stated. For the theory of Ideas has no special discussion

of the subject ;for those who speak of Ideas say the Ideas

are numbers, and they speak of numbers now as unlimited,

20 now1

as limited by the number 10; but as for the reason

why there should be just so many numbers, nothing is said

with any demonstrative exactness. We however must dis

cuss the subject, starting1 from the presuppositions and

distinctions we have mentioned. The first principle or

primary being is not movable either in itself or accident-

25 ally, but produces the primary eternal and single movement.

But since that which is moved must be moved by something,

and the first mover must be in itself unmovable, and eter

nal movement must be produced by something eternal and

a single movement by a single thing, and since we see that be

sides the simple spatial movement of the universe, which we

3o say the first and unmovable substance produces, there are

otherspatial

movements those of the

planetswhich are

eternal (for a body which moves in a circle is eternal and

unresting ;we have proved these points in the physical

treatises2

),each of these movements also must be caused by

a substance both unmovable in itself and eternal. For the

nature of the stars3

is eternal just because it is a certain kind

35 ofsubstance, and the mover is eternal and prior to the moved,

and that which is prior to a substance must be a substance.

Evidently, then, there must be substances which are of the

same number as the movements of the stars, and in their

nature eternal, and in themselves unmovable, and without

magnitude, for the reason before mentioned.4

iO73b That the movers are substances, then, and that one of

these is first and another second according to the same

order as the movements of the stars, is evident. But in the

number of the movements we reach a problem which must

be treated from the standpoint of that one of the mathe

matical sciences which is most akin to philosophy viz. of

5 astronomy ;for this science speculates about substance

1 The reference is to Plato Ccf. Phys. 2c6b 32).2

Cf.

Phys.viii.

8, 9;

DeCaelo,

i.

2,ii.

3-8.3 This is to be understood as a general term including both fixed

stars and planets.4

Cf. 11. 5-n.



BOOK A. 8 io73b

which is perceptible but eternal, but the other mathema

tical sciences, i.e. arithmetic and geometry, treat of no

substance. That the movements are more numerous than

the bodies that are moved is evident to those who have

given even moderate attention to the matter;for each of

the planets has more than one movement. But as to the 10

actual number of these movements, we now to give some

notion of the subject quote what some of the mathema

ticians say, that our thought may have some definite number

to grasp ; but, for the rest, we must partly investigate for

ourselves, partly learn from other investigators, and if those 1 5

who study this subject form an opinion contrary to what we

have now stated, we must esteem both parties indeed, but

follow the more accurate.

Eudoxus supposed that the motion of the sun or of the

moon involves, in either case, three spheres, of which the

first is the sphere of the fixed stars, and the second moves

in the circle which runs along the middle of the zodiac, and 20

the third in the circle which is inclined across the breadth

of the zodiac;but the circle in which the moon moves is

inclined at a greater angle than that in which the sun moves

And the motion of the planets involves, in each case, four

spheres, and of these also the first and second are the same

as the first

two mentioned above (for the sphereof

the fixed 25

stars is that which moves all the other spheres, and that

which is placed beneath this and has its movement in the

circle which bisects the zodiac is common toall),

but the

poles of the third sphere of each planet are in the circle

which bisects the zodiac, and the motion of the fourth

sphere is in the circle which is inclined at an angle to the

equator of the third sphere ; and the poles of the third sphere 30

are different for each of the other planets, but those of

Venus and Mercury are the same.

Callippus made the position of the spheres the same as

Eudoxus did, but while he assigned the same number as

Eudoxus did to Jupiter and to Saturn, he thought two 35

more spheres should be added to the sun and two to the

moon, if one is to explain the observed facts;and one more

to each of the other planets.



io73b METAPHYSICA

But it is necessary, if all the spheres combined are to

explain the observed facts, that for each of the planets

there should be other spheres (one fewer than those hither

to assigned) which counteract those already mentioned and

bring- back to the same position the outermost sphere of

the star which in each case is situated below 1the star in

5 question ;for only thus can all the forces at work produce

the observed motion of the planets. Since, then, the spheres

involved in the movement of the planets themselves are-

eight for Saturn and Jupiter and twenty-five for the others,

and of these only those involved in the movement of the

lowest-situated planet need not be counteracted, the spheres

which counteract those of the outermost two planets will

be six in number, and the spheres which counteract those

I0 of the next four planets will be sixteen : therefore the

number of all the spheres both those which move the

planetsand those which counteract these will be

fifty-five.And if one were not to add to the moon and to the sun the

movements we mentioned,2the whole set of spheres will be

forty-seven in number.

Let this, then, be taken as the number of the spheres,

15 so that the unmovable substances and principles also may

probably be taken as just so many ;the assertion of neces

sity must be left to more powerful thinkers. But if there

can be no spatial movement which does not conduce to the

moving of a star, and if further every being and every

substance which is immune from change and in virtue of

itself has attained to the best must be considered an end,

20 there can be no other being apart from these we have

named, but this must be the number of the substances.

For if there are others, they will cause change as being

a final cause of movement;but there cannot be other

movements besides those mentioned. And it is reasonable

to infer this from a consideration of the bodies that are

25 moved ;for if everything that moves is for the sake of that

which is moved, and every movement belongs to something

1i. e. inwards from, the universe being thought of as a system of

concentric spheres encircling the earth.2In I073

b35, 38-1074*4.



BOOK A. 8 i074a

that is moved, no movement can be for the sake of itself or

of another movement, but all the movements must be for

the sake of the stars. For if there is to be a movement for

the sake of a movement, this latter also will have to be

for the sake of something else;so that since there cannot be

an infinite regress, the end of every movement will be one 30

of the divine bodies which move through the heaven.1

(Evidently there is but one heaven. For if there are

many heavens as there are many men, the moving principles,

of which each heaven will have one, will be one in form but

in number many. But all things that are many in number

have matter;

for one and the same definition, e. g. that

of man, applies to many things, while Socrates is one.2 But 35

the primary essence has not matter;

for it is complete,

reality. So the unmovable first mover is one both in defini

tion and in number;

so too, therefore, is that which is

movedalways

andcontinuously

;

therefore there is one

heaven alone.)3

Our forefathers in the most remote ages have handed iO74b

down to their posterity a tradition, in the form of a myth,

that these bodies are gods and that the divine encloses the

whole of nature. The rest of the tradition has been added

later in mythical form with a view to the persuasion of the

multitude and to its legal and utilitarian expediency ; they 5

say these gods are in the form of men or like some of the

other animals, and they say other things consequent on and

similar to these which we have mentioned. But if one were

to separate the first point from these additions and take

it alone that they thought the first substances to be gods,

one must regard this as an inspired utterance, and reflect 10

that, while probably each art and each science has often

1 The argument is : Each unchangeable perfect substance is an end

and must cos6/>eKrdz> produce a distinct motion. But every motion is

ultimately for the sake of a<f)(p6fj.(t>ov,

and as we have enumerated the

motions necessary for the fapdpcva, there can be no more motions and

therefore no more unchangeable perfect substances.2

i. e. the \6yos is common to all men, so that it must be matter

which gives Socrates his uniqueness,3 This paragraph appears to be an early fragment embedded in

a chapter written rather late in Aristotle s life, ovroi in b3 refers back

to rooi/(frepofjLevcov 6ei<av

(ra)/Lidra)j/in a

30.



io74b METAPHYSICA

been developed as far as possible and has again perished,

these opinions, with others, have been preserved until the

present like relics of the ancient treasure. Only thus far,

then, is the opinion of our ancestors and of our earliest

predecessors clear to us.

15 The nature of the divine thought involves certain pro- 9

blems;for while thought is held to be the most divine of

things observed by us, the question how it must be situated in

order to have that character involves difficulties. For if it

thinks ofnothing,what is there here ofdignity ? It is just like

one who sleeps. And if it thinks, but this depends on

something else, then (since that which is its substance is not

the act of thinking, but a potency) it cannot be the best

20 substance;for it is through thinking that its value belongs

to it. Further, whether its substance is the faculty of thought

or the act of thinking, what does it think of ? Either of itselt

or of something else; and if of something else, either of the

same thing always or ofsomething different. Does it matter,

then, or not, whether it thinks of the good or ofany chance

25 thing ? Are there not some things about which it is incredible

that it should think? Evidently, then, it thinks ofthat which is

most divine and precious, and it does not change ;for change

wouldbe

changefor the

worse,and this would be

alreadya movement. 1

First, then, if thought is not the act of

thinking but a potency, it would be reasonable to suppose

that the continuity of its thinking is wearisome to it.

Secondly, there would evidently be something else more

30 precious than thought, viz. that which is thought of. For both

thinking and the act ofthought will belong even to one who

thinks of the worst thing in the world, so that if this ought

to be avoided (and it ought, for there are even some things

which it is better not to see than to see), the act of thinking

cannot be the best of things. Therefore it must be of itself

that the divine thought thinks (since it is the most excellent

of things), and its thinking is a thinking on thinking.

35 But evidently knowledge and perception and opinion

and understanding have always something else as their

1Sc. while vovs is ex hypothesi unmovable.



BOOK A. 9 i074b

object, and themselves only by the way. Further, if think

ing and being thought of are different, in respect of which

does goodness belong to thought ? For to be an act of think

ing and to <e an object of thought are not the same thing.

We answer that in some cases the knowledge is the object. In

the productive sciences it is the substance or essence of the

object, matter omitted, and in the theoretical sciences the

definition or the act of thinking is the object. Since, then,

thought and the object of thought are not different in the

case of things that have not matter, the divine thought and

its object will be the same, i. e. the thinking will be one

with the object of its thought.

A further question is left whether the object ofthe divine 5

thought is composite ;for if it were, thought would change

in passing from part to part of the whole. We answer that

everything which has not matter is indivisible as human

thought,

or rather the

thoughtof

composite beings,

is in

a certain period of time (forit does not possess the good at

this moment or at that, but its best, being something different

from it, is attained only in a whole period of time), so 10

throughout eternity is the thought which has itself for its

object.

IO We must consider also in which of two ways the natureof the universe contains the good and the highest good,

whether as something separate and by itself, or as the order

of the parts. Probably in both ways, as an army does;

for its good is found both in its order and in its leader,

and more in the latter; for he does not depend on the 15

order but it depends on him. And all things are ordered

together somehow, but not all alike, both fishes and fowls

and plants ;and the world is not such that one thing has

nothing to do with another, but they are connected. For

all are ordered together to one end, but it is as in a house,

where the freemen are least at liberty to act at random, but 20

all things or most things are already ordained for them,

while the slaves and the animals do little for the common

good, and for the most part live at random;for this is the

sort of principle that constitutes the nature of each. I mean,

S 2



io75a METAPHYSICA

for instance, that all must at least come to be dissolved into

their elements,1 and there are other functions similarly in

which all share for the good of the whole.

25 We must not fail to observe how many impossible or

paradoxical results confront those who hold different views

from our own, and what are the views of the subtler thinkers,

and which views are attended by fewest difficulties. All make

all things out of contraries. But neither all things nor*

out

of contraries is right ;nor do these thinkers tell us how all

the things in which the contraries are present can be made

3 out of the contraries;for contraries are not affected by one

another. Now for us this difficulty is solved naturally bythe fact that there is a third element.

2 These thinkers how

ever make one of the two contraries matter;this is done

for instance by those who make the unequal matter for the

equal, or the many matter for the one.3

But this also is

refuted in the same way; for the one matter which underlies

any pair of contraries is contrary to nothing. Further, all

things, except the one, will, on the view we arecriticizing,

35 partake of evil;for the bad itself is one of the two elements.

But the other school 4 does not treat the good and the bad

even as principles ; yet in all things the good is in the

highest degree a principle. The school we first mentioned

is right in saying that it is a principle, but how the good is

a principle they do not say whether as end or as mover or

as form.

IO75 Empedocles5also has a paradoxical view

;for he identi

fies the good with love, but this is a principle both as

mover (for it brings things together) and as matter (for it is

part of the mixture). Now even if it happens that the same

5 thing is a principle both as matter and as mover, still the

being, at least, of the two is not the same. In which respect

then is love a principle ? It is paradoxical also that strife

1Sc. in order that higher forms of being may be produced by new

combinations of the elements.2

i. e. the substratum.3 The reference is to Platonists.

The reference is to the Pythagoreans and Speusippus ;cf. A. 1072

b3I6

Cf. A. 985* 4.



BOOK A. 10 i075b

should be imperishable ;the nature of his

*

evil is just

strife.

Anaxagoras makes the good a motive principle ;for his

reason moves things. But it moves them for an end, whichmust be something other than it, except according to our

way of stating the case; for, on our view, the medical art is

in a sense health. It is paradoxical also not to suppose 10

a contrary to the good, i. e. to reason. But all who speak

of the contraries make no use of the contraries, unless we

bring their views into shape. And why some things are

perishable and others imperishable, no one tells us;for they

make all existing things out of the same principles. Further,

some make existing things out of the non-existent;and T 5

others to avoid the necessity of this make all things one.

Further, why should there always be becoming, and what

is the cause of becoming ? this no one tells us. And those

whosuppose

twoprinciples

must

supposeanother, a

superiorprinciple, and so must those who believe in the Forms; for

why did things come to participate, or why do they parti

cipate, in the Forms? And all other thinkers 1are con- 20

fronted by the necessary consequence that there is something

contrary to Wisdom, i.e. to the highest knowledge ;but we

are not. For there is nothing contrary to that which is

primary;

for all contraries have matter, and things thathave matter exist only potentially ;

and the ignorance which

is contrary to any knowledge leads to an object contrary to

the object of the knowledge2

;but what is primary has

no contrary.

Again, if besides sensible things no others exist, there 25

will be no first principle, no order, no becoming, no

heavenly bodies, but each principle will have a principle

before it, as in the accounts of the theologians and all the

natural philosophers. But if the Forms or the numbers

are to exist, they will be causes of nothing ;or if not that,

at least not of movement. Further, how is extension, i. e.

1 The special reference is to Plato;

cf. Rep. 477.2

If there were an ignorance contrary to philosophy, it would havean object contrary to TO

TT/JWTOI;, which is the object of philosophy. But

TOnpa>Tov

has no contrary.



io75b METAPHYSICA

a continuum, to be produced out of unextended parts ?

For number will not, either as mover or as form, produce

30 a continuum. But again there cannot be any contrary that

is

also essentially a productive or moving principle;

for it

would be possible for it not to be.1 Or at least its action would

be posterior to its potency. The world, then, would not

be eternal. But it is;one of these premisses, then, must be

denied. And we have said how this must be done.2

Further, in virtue of what the numbers, or the soul and the

35 body, or in general the form and the thing, are one of this

no one tells us anything ; nor can any one tell, unless he

says, as we do, that the mover makes them one. And

those who sayamathematical number is first and go on to

generate one kind of substance after another and give

iO76adifferent principles for each, make the substance of the

universe a mere series of episodes (for one substance has

no influence on another by its existence or non-existence),

and they give us many governing principles ;but the world

refuses to be governed badly.

The rule of many is not good ;one ruler let there be.

4

1Since contraries must contain matter, and matter implies potentiality

and contingency.2

Cf. I07ibi9, 20.

8

Speusippus is meant;

cf. Z. io28 b2i, N. iO9o

b13-20.

4 Cf. Iliad) ii. 204.



BOOK M

WE have stated what is the substance of sensible things,

dealing in the treatise on physics with matter, and later2

with the substance which has actual existence. Now since 10

our inquiry is whether there is or is not besides the sensible

substances any which is immovable and eternal, and, if

there is, what it is, we must first consider what is said

byothers, so that, if there is anything which they say wrongly,

we may not be liable to the same objections, while, if there

is any opinion common to them and us, we shall have no

private grievance against ourselves on that account; for 15

one must be content to state some points better than one s

predecessors, and others no worse.

Two opinions are held on this subject; it is said that the

objects of mathematics i. e. numbers and lines and the like

are substances, and again that the Ideas are substances.

And since (i) some recognize these as two different classes

the Ideas and the mathematical numbers, and (2) some 20

recognize both as having one nature, while (3) some others

say that the mathematical substances are the only sub

stances,15

we must consider first 4 the objects of mathematics,

not qualifying them by any other characteristic not ask

ing, for instance, whether they are in fact Ideas or not, or

whether they are the principles and substances of existing

things or not, but only whether as objects of mathematics 25

they exist or not, and if they exist, how they exist.

Then after this we must separately consider5

the Ideas

themselves in a general way, and only as far as the accepted

mode of treatment demands;

for most of the points have

been repeatedly made even by the discussions outside our

school, and, further, the greater part of our account must

finish by throwing light on that inquiry, viz. when we 30

1

Phys. i.

&

Met. ZH0.3

Plato, Xenocrates, and the Pythagoreans and Speusippus,respectively, are meant.

4Cf. chs. 2, 3.

5Cf. chs. 4, 5.



io76a METAPHYSICA

examine l whether the substances and the principles ot

existing things are numbers and Ideas;for after the dis

cussion of the Ideas this remains as a third inquiry.

If the objects of mathematics exist, they must exist either

in sensible objects, as some say, or separate from sensible

35 objects (and this also is said by some) ;or if they exist in

neither of these ways, either they do not exist, or they

exist only in some special sense. So that the subject of

our discussion will be not whether they exist but how they

exist.

That it is impossible for mathematical objects to exist in 2

sensible things, and at the same time that the doctrine in

question is an artificial one, has been said already in our

discussion of difficulties2

;we have pointed out that it is

IO76 impossible for two solids to be in the same place, and also

that according to the same argument the other powers and

characteristics also3 should exist in sensible

thingsand

none of them separately. This we have said already. But,

further, it is obvious that on this theory it is impossible for

5 any body whatever to be divided;for it would have to be

divided at a plane, and the plane at a line, and the line at

a point, so that if the point cannot be divided, neither can

the line, and if the line cannot, neither can the plane nor

the solid. What difference, then, does it make whethersensible things are such indivisible entities, or, without

10 being so themselves, have indivisible entities in them ? The

result will be the same;

if the sensible entities are divided

the others will be divided too, or else not even the sensible

entities can be divided.

But, again, it is not possible that such entities should

exist separately. For if besides the sensible solids there

are to be other solids which are separate from them and

prior to the sensible solids, it is plain that besides the

15 planes also there must be other and separate planes and

points and lines;for consistency requires this. But if these

exist, again besides the planes and lines and points of the

1

Cf. chs. 6-9.

2

Cf. B. 998a

;-i9.8 Which nevertheless the theory in question represents as Ideas

apart from sensible things.



BOOK M. 2 1076*

mathematical solid there must be others which are separate.

(For incomposites are prior to compounds ;and if there

are, prior to the sensible bodies, bodies which are not

sensible, by the same argument the planes which exist by 20

themselves must be prior to those which are in the motion

less solids. Therefore these will be planes and lines other

than those that exist along with the mathematical solids to

which these thinkers assign separate existence;

for the

latter exist along with the mathematical solids, while the

others are prior to the mathematical solids.) Again, there

fore, there will be, belonging to these planes, lines, and 25

prior to them there will have to be, by the same argument,

other lines and points ;and prior to these points in the

prior lines there will have to be other points, though there

will be no others prior to these. Now(i)the accumulation

becomes absurd;

for we find ourselves with one set of

solids apart from the sensible solids;three sets of planes 30

apart from the sensible planes those which exist apart

from the sensible planes, and those in the mathematical

solids, and those which exist apart from those in the

mathematical solids;

four sets of lines, and five sets of

points. With which of these, then, will the mathematical

sciences deal ? Certainly not with the planes and lines and

points

in the motionless solid;for science

alwaysdeals with 35

what is prior. And(2)

the same account will apply also to

numbers;for there will be a different set of units apart from

each set of points,and also apart from each set ofrealities, from

the objects of sense and again from those of thought ;so that

there will be various classes of mathematical numbers.

Again, how is it possible to solve the questions which we

have already enumerated in our discussion of difficulties

l

?

For the objects of astronomy will exist apart from sensible IO77a

things just as the objects of geometry will;but how is it

possible that a heaven and its parts or anything else

which has movement should exist apart ? Similarly also

the objects of optics and of harmonics will exist apart ;

for there will be both voice and sight besides the sensible or 5

individual voices and sights. Therefore it is plain that the

1B. 997^ 12-34.



io77a METAPHYSICA

other senses as well, and the other objects of sense, will

exist apart ; for why should one set of them do so and

another not ? And if this is so, there will also be animals

existing apart, since there will be senses.

Again, there are certain mathematical theorems that are

10 universal, extending beyond these substances. Here then

we shall have another intermediate substance separate both

from the Ideas and from the intermediates,1 a substance

which is neither number nor points nor spatial magnitude

nor time. And if this is impossible, plainly it is also

impossible that \hzformer entities should exist separate

from sensible things.

And, in general, conclusions contrary alike to the truth

15 and to the usual views follow, if one is to suppose the

objects of mathematics to exist thus as separate entities.

For because they exist thus they must be prior to sensible

spatialmagnitudes,

but in truth they must be posterior ;

for the incomplete spatial magnitude is in the order of

generation prior, but in the order of substance posterior,

as the lifeless is to the living.

20 Again, by virtue of what, and when, will mathematical

magnitudes be one ? For things in our perceptible world

are one in virtue of soul, or of a part of soul, or of something

else that is reasonable enough;

2

when these are not present,

the thing is a plurality, and splits up into parts. But in the

case of the subjects of mathematics, which are divisible and

are quantities, what is the cause of their being one and

holding together ?

Again, the modes of generation of the objects of mathe

matics show that we are right. For the dimension first

25 generated is length, then comes breadth, lastly depth, and the

process is complete. If, then, that which is posterior in

the order ofgeneration is prior in the order of substantiality,

the solid will be prior to the plane and the line. And in

this way also it is both more complete and more whole,

because it can become animate. How, on the other hand,

1 A Platonic expression for ra padyuanmi, which were regarded as

intermediate between Ideas and sensible things.2

Reading in 1. 22 euAoyw.



BOOK M. 2 io77a

could a line or a plane be animate ? The supposition passes 30

the power of our senses.

Again, the solid is a sort of substance;for it already has

in a sense completeness. But how can lines be substances ?

Neither as a form or shape, as the soul perhaps is, nor as

matter, like the solid;for we have no experience of any

thing that can be put together out of lines or planes or

points, while if these had been a sort of material substance, 35

we should have observed things which could be put to

gether out of them.

Grant, then, that they are prior in definition. Still not all iO77b

things that are prior in definition are also prior in substan

tiality. For those things are prior in substantiality which

when separated from other things surpass them in the

power of independent existence, but things are prior in

definition to those whose definitions are compounded out of

their definitions;and these two properties are not co-ex

tensive. For if attributes do not exist apart from their sub- 5

stances (e.g. a mobile or a pale ), pale is prior to the pale

man in definition, but not in substantiality. For it cannot

exist separately, but is always along with the concrete thing;

and by the concrete thing I mean the pale man. There

fore it is plain that neither is the result of abstraction prior

nor that which is produced by adding determinants posterior

;for it is by adding a determinant to pale that we 10

speak of the pale man.

It has, then, been sufficiently pointed out that the objects

of mathematics are not substances in a higher degree than

bodies are, and that they are not prior to sensibles in being,

but only in definition, and that they cannot exist some

where apart. But since it was not possible for them to

exist in sensibles either,1

it is plain that they either do 15

not exist at all or exist in a special sense and therefore

do not exist without qualification. For exist has many

3 senses. For just as the universal propositions of mathematics

deal not with objects which exist separately, apart from ex

tended magnitudes and from numbers, but with magnitudes

and numbers, not however qita such as to have magnitude or

1Cf. I076

a38-

b u.



io77b METAPHYSICA

20 to be divisible,1

clearly it is possible that there should also

be both propositions and demonstrations about sensible

magnitudes, not however qua sensible but qua possessed

of certain definite qualities.

2

For as there are many propositions about things merely considered as in motion, apart

25 from what each such thing is and from their accidents, and

as it is not therefore necessary that there should be either

a mobile separate from sensibles, or a distinct mobile entity

in the sensibles, so too in the case of mobiles there will

be propositions and sciences, which treat them however

not qua mobile but only qua bodies, or again only q^la

30 planes, or only qua lines, or qua divisibles, or qua indivi

sibles having position, or only qua indivisibles. Thus since

it is true to say without qualification that not only things

which are separable but also things which are inseparable

exist (for instance, that mobiles exist), it is true also to say

withoutqualification

that theobjects

of mathematics exist,

and with the character ascribed to them by mathematicians.

And as it is true to say of the other sciences too, without

qualification, that they deal with such and such a subject

35 not with what is accidental to it(e. g. not with the pale, if

the healthy thing is pale, and the science has the healthy

as its subject), but with that which is the subject of each

io78ascience with the healthy if it treats its object qua healthy,

with man if qua man : so too is it with geometry ;if its

subjects happen to be sensible, though it does not treat

them qua sensible, the mathematical sciences will not for

that reason be sciences of sensibles nor, on the other

5 hand, of other things separate from sensibles. Many

properties attach to things in virtue of their own nature

as possessed of each such character;

e. g. there are attri

butes peculiar to the animal qiia female or qua male (yet

there is no female nor male separate from animals) ;

so that there are also attributes which belong to things

merely as lengths or as planes. And in proportion as we

1Cf. E. 1026*25, M. io;7

a9.

2i. e. as universal mathematics abstracts from the distinctions

between different kinds of /za^/zartKa, so geometry abstracts from the

sensible characteristics of magnitudes and attends only to their spatial

relations.



BOOK M. 3 1078

are dealing with things which are prior in definition and

simpler, our knowledge has more accuracy, i. e. simplicity,ro

Therefore a science which abstracts from spatial magnitude

is more precise than one which takes it into account ; and

a science is most precise if it abstracts from movement, but

if it takes account of movement, it is most precise if it deals

with the primary movement, for this is the simplest ;and

of this again uniform movement is the simplest form.

The same account may be given of harmonics and optics ;

for neither considers its objects qua sight or qua voice, but [ 5

qua lines and numbers;but the latter are attributes proper

to the former. And mechanics too proceeds in the same

way. Therefore if we suppose attributes separated from

their fellow-attributes and make any inquiry concerning

them as such, we shall not for this reason be in error, any

more than when one draws a line on the ground and calls

it a footlong when

it is

not;

forthe

error is notincluded

ao

in the premisses.

Each question will be best investigated in this way by

setting up by an act of separation what is not separate, as

the arithmetician and the geometer do. For a man quaman is one indivisible thing ;

and the arithmetician supposed

one indivisible thing, and then considered whether any attri

bute belongs to a man qua indivisible. But the geometer 35

treats him neither qita man nor qzta indivisible, but as

a solid. For evidently the properties which would have

belonged to him even if perchance he had not been indivi

sible, can belong to him even apart from these attributes.1

Thus, then, geometers speak correctly ; they talk about

existing things, and their subjects do exist;

for being has 3

two forms it exists not only in complete reality but also

materially.

Now since the good and the beautiful are different (for

the former always implies conduct as its subject, while the

beautiful is found also in motionless things), those who

assert that the mathematical sciences say nothing of the

beautiful or the good2are in error. For these sciences say

1Sc. indivisibility and humanity.

2 The reference is apparently to Aristippus ;cf. B. 996*32.



io78a METAPHYSICA

35 and prove a great deal about them;

ifthey do not expressly

mention them, but prove attributes which are their results

or their definitions, it is not true to say that they tell us

nothing about them. The chief forms of beauty are order

iO78b and symmetry and definiteness, which the mathematical

sciences demonstrate in a special degree. And since these

(e. o-. order and definiteness) are obviously causes of many

things, evidently these sciences must treat this sort of causa

tive principle also(i.

e. the beautiful) as in some sense

5 a cause. But we shall speak more plainly elsewhere l about

these matters.

So much then for the objects of mathematics;we have 4

said that they exist and in what sense they exist,2 and in

what sense they are prior and in what sense not prior/

Now, regarding the Ideas, we must first examine the

10 ideal theory itself, not connecting it in any way with the

nature of numbers, but treating it in the form in which

it wras originally understood by those who first maintained

the existence of the Ideas. The supporters of the ideal

theory were led to it because on the question about the

truth of things they accepted the Heraclitean sayings which

15 describe all sensible things as ever passing away, so that if

knowledge or thoughtis to

havean

object, there must besome other and permanent entities, apart from those which

are sensible;for there could be no knowledge of things

which were in a state of flux. But when Socrates was

occupying himself with the excellences of character, and

in connexion with them became the first to raise the

problem of universal definition (for of the physicists Demo-

20 critus only touched on the subject to a small extent, and

defined, after a fashion, the hot and the cold;while the

Pythagoreans had before this treated of a few things, whose

definitions -e. g. those of opportunity, justice, or marriage4

they connected with numbers;but it was natural that

Socrates should be seeking the essence, for he was seeking to

syllogize, and what a thing is is the starting-point of syllo-1

Apparently an unfulfilled promise.2Chs. 2, 3.

*

io;7a17-20, 24-

bii.

4Cf. Diels, Vorsokratiker^ ed. 3, i. 346. 27-347. 11.



BOOK M. 4 1078*

gisms; for there was as yet none ofthe dialectical power which 25

enables people even without knowledge of the essence to

speculate about contraries and inquire whether the same

science deals with contraries ; for two things may be fairly

ascribed to Socrates inductive arguments and universal

definition, both of which are concerned with the starting-

point of science) : but Socrates did not make the universals 3

or the definitions exist apart ; they, however, gave them

separate existence, and this was the kind of thing they

called Ideas. Therefore it followed for them, almost by the

same argument, that there must be Ideas of all things that

are spoken of universally, and it was almost as if a man

wished to count certain things, and while they were few

thought he would not be able to count them, but made 35

more of them and then counted them;for the Forms are, one

may say, more numerous than the particular sensible things,

yetit was in

seekingthe causes of these that

they pro- 1079*ceeded from them to the Forms. For to each thing there

answers an entity which has the same name ] and exists apart

from the substances, and so also in the case of all other

groups there is a one over many, whether these be of this

world or eternal.

Again, of the ways in which it is proved that the Forms

exist, none is convincing; for from some no inference 5

necessarily follows, and from some arise Forms even of

things of which they think there are no Forms. For

according to the arguments from the sciences there will be

Forms of all things of which there are sciences, and accord

ing to the argument of the one over many there will be

Forms even of negations, and according to the argument 10

that thought has an object when the individual object has

perished, there will be Forms of perishable things ;for we

have an image of these. Again, of the most accurate argu

ments, some lead to Ideas of relations, of which they say

there is no independent class, and others introduce the

third man Y*

1

Reading in 1. 2 OUWW/JLOV TL (with A. 990^6).2

Cf. Z. 1039* 2, Soph. El. I78b36-i79

a10, and Plato, Parmenides,

132 AB, 0-133 A.



io79a METAPHYSICA

And in general the arguments for the Forms destroy

things for whose existence the believers in Forms are more

15 zealous than for the existence of the Ideas;for it follows

that not the dyad but number is first, and that prior to

number is the relative, and that this is prior to the absolute 1

besides all the other points on which certain people, by

following out the opinions held about the Forms, came

into conflict with the principles of the theory.

Again, according to the assumption on which the belief

20 in the Ideas rests, there will be Forms not only of sub

stances but also of many other things ;for the concept is

single not only in the case of substances, but also in that

of non -substances, and there are2sciences of other things

than substance;and a thousand other such difficulties

confront them. But according to the necessities of the case

25 and the opinions about the Forms, if they can be shared in

there must be Ideas of substancesonly.

Forthey

are not

shared in incidentally, but each Form must be shared in as

something not predicated of a subject. (By being shared

in incidentally I mean that if a thing shares in4

double

itself, it shares also in eternal,but incidentally ;

for the

30 double happens to be eternal.) Therefore the Forms will

be substance. But the same names indicate substance in

this and in the ideal world (or what will be the meaning of

saying that there is something apart from the particulars

the one over many ?).

:i And if the Ideas and the things that

share in them have the same form, there will be something

common : for why should 2 be one and the same in the

35 perishable 2 s, or in the 2 s which are many but eternal,4

and not the same in the 2 itself as in the individual 2 ?

io?9b But if they have not the same form, they will have only the

1i. e. the relative in general is more general than, and therefore (on

Platonic principles) prior to, number. Number is similarly prior to the

dyad. Therefore the relative is prior to the dyad, which yet is held to

be absolute.2

Reading rrjs ovcrins eiVt in 1. 23.3 This seems to be an enthymeme, the conclusion to be supplied

being that the Forms, since they are substances, must be 0/substances.4

Sc. the abstract (eternal) 2 s of which we can say e.g. 2 + 2 = 4,

i. e. TO. /zerau, which like the Ideas are eternal, but like sensible things

are many.



BOOK M. 4 io79b

name in common, and it is as if one were to call both Callias

and a piece of wood a man,without observing any com

munity between them.1

But if we are to suppose that in other respects the common definitions apply to the Forms, e.g. that plane figure

and the other parts of the definition apply to the circle- 5

itself, but4 what really is

2 has to be added, we must inquire

whether this is not absolutely meaningless. For to what

is this to be added ? To centre or to plane or to all

the parts of the definition ? For all the elements in the

essence are Ideas, e. g.l

animal and two-footed .

3Further,

there must be some Idea answering to plane above, some 10

nature which will be present in all the Forms as their

genus.

5 Above all one might discuss the question what in the world

the Forms contribute to sensible things, either to those that

are eternal or to those that come into being and cease to

be; for they cause neither movement nor any change in

them. But again they help in no wise either towards the \$

knowledge of other things (for they are not even the sub

stance of these, else they would have been in them), or

towards their being, if they are not in the individuals which

share in them; though if they were, they might be thought

to be causes, as white causes whiteness in a white object by

entering into its composition. But this argument, which 20

was used first by Anaxagoras, and later by Eudoxus in

his discussion of difficulties and by certain others, is very

easily upset ;for it is easy to collect many and insuperable

objections to such a view.

But, further,all other

thingscannot come from the Forms

in any of the usual senses of from . And to say that they 25

are patterns and the other things share in them is to use

empty wrords and poetical metaphors. For what is it that

works, looking to the Ideas ? And any thing can both be

and come into being without being copied from something

1 With ic78b34-io79

b3 cf. A. 99O

b2-99i

a8.

2 Reading ro 6 6 errn in 1. 6 (cf. Io86b 27) with P. Shorey (Class.Phil. xx. 271-3).

3Sc. in the essence of man.



io79b METAPHYSICA

else, so that, whether Socrates exists or not, a man like

30 Socrates might come to be. And evidently this might be

so even if Socrates were eternal. And there will be several

patterns of the same thing, and therefore several Forms ;

e.g. animal and two-footed,and also

l man -himself,

will be Forms of man. Again, the Forms are patterns not

only of sensible things, but of Forms themselves also;

i. e.

the genus is the pattern of the various forms-of-a-genus ;

therefore the same thing will be pattern and copy.

35 Again, it would seem impossible that substance and that

io8oa whose substance it is should exist apart ; how, therefore,

could the Ideas, being the substances of things, exist apart ?

In the Pkaedo 1 the case is stated in this way that the

Forms are causes both of being and of becoming. Yet

though the Forms exist, still things do not come into being,

unless there is something to originate movement;and

manyother

thingscome into

being (e. g.a house or a

ring)5 of which they say there are no Forms. Clearly therefore

even the things of which they say there are Ideas can both

be and come into being owing to such causes as produce

the things just mentioned,2 and not owing to the Forms.

But regarding the Ideas it is possible, both in this way and

10 by more abstract and accurate arguments, to collect many

objections like those we have considered.

Since we have discussed these points, it is well to consider 5

again the results regarding numbers which confront those

who say that numbers are separable substances and first

15causes of things. If number is an entity and its substance

is nothing other than just number, as some say, it follows

that either (i) there is a first in it and a second, each beingdifferent in species, and either (a) this is true of the units

without exception, and any unit is inassociable with any

20 unit, or(6) they are all without exception successive, and

any of them are associable with any, as they say is the case

with mathematical number ; for in mathematical number no

one unit is in any way different from another. Or(c) some

units must be associable and some not ;e. g. suppose that 2

1ico D.

2 With io79b 2-io8ca S cf. A. 99i

a 8- b9.



BOOK M. 6 io8oa

is first after i, and then comes 3 and then the rest of the

number series, and the units in each number are associable, 25

e. g. those in the first 2 are associable with one another, and

those in the first 3 with one another, and so with the other

numbers ; but the units in the 2-itself are inassociable

with those in the 3-itself ;and similarly in the case of the

other successive numbers. And so while mathematical 30

number is counted thus after i, 2 (which consists of

another i besides the formeri),

and 3 (which consists of

another i besides these two), and the other numbers simi

larly, ideal number is counted thus after i, a distinct 2

which does not include the first i, and a 3 which does not

include the 2, and the rest of the number series similarly.

Or(2)

one kind of number must be like the first that was 35

named,1 one like that which the mathematicians speak

of, and that which we have named last2 must be a third

kind.

Again, these kinds of numbers must either be separable

from things, or not separable but in objects of perception io8ob

(not however in the way which we first considered,3 but in

the sense that objects of perception consist of numbers

which are present in them) either one kind and not an

other, or all of them.

These are of necessity the only ways in which the numbers 5

can exist. And of those who say that the i is the begin

ning and substance and element of all things, and that

number is formed from the i and something else, almost

every one has described number in one of these ways ; only

no one has said all the units are inassociable. And this has

happened reasonably enough ;for there can be no way TO

besides those mentioned. Some 4 say both kinds of number

exist, that which has a before and after5

being identical

with the Ideas, and mathematical number being different

from the Ideas and from sensible things, and both being

separable from sensible things ;and others G

say mathe-

111. 15-20.

2

11.23-35.3

Cf. io;6a 38-h

u.4

Plato is meant.5

i. e. in which the numbeis differ in kind.6

Speusippus is meant.

T 2



io8ob METAPHYSICA

15 matical number alone exists, as the first of realities, separate

from sensible things. And the Pythagoreans, also, believe

in one kind of number the mathematical; only they say it

is not separate but sensible substances are formed out of it.

For they construct the whole universe out of numbers

only not numbers consisting- of abstract units; they suppose

20 the units to have spatial magnitude. But how the first i

was constructed so as to have magnitude, they seem unable

to say.

Another thinker l

says the first kind of number, that of

the Forms, alone exists, and some 2say mathematical

number is identical with this.

The case of lines, planes, and solids is similar. For some

think that those which are the objects of mathematics are

35 different from those which come after the Ideas;

3 and of

those who express themselves otherwise some speak of the

objects of mathematics and in a mathematical

wayviz.

those wrho do not make the Ideas numbers nor say that

Ideas exist;

4 and others speak of the objects of mathe

matics, but not mathematically ;for they say that neither is

every spatial magnitude divisible into magnitudes, nor do

30 any two units taken at random make 2.5 All who say the i

is an element and principle of things suppose numbers to

consist of abstract units, except the Pythagoreans ; but they

suppose the numbers to have magnitude, as has been said

before.6

It is clear from this statement, then, in how many

ways numbers may be described, and that all the ways have

35 been mentioned;and all these views are impossible, but

some perhaps more than others.

First, then,let

us inquireif the units are

associable or inas- 7io8i

asociable, and if inassociable, in which of the two ways we dis

tinguished.7 For it is possible that any unit is inassociable

with any, and it is possible that those in the 2 -itself are

inassociable with those in the 3 -itself \ and, generally, that

those in each ideal number are inassociable with those in

1 Some unknown Platonist.2Xenocrates is meant.

3 This refers to Plato; cf. A. 992^ 13-18.4

Speusippus is meant.5 Xenocrates is meant.

R

1. 19.7

Cf. io8oa 18-20, 23-35.



BOOK M. 7 ic8ia

other ideal numbers. Now (i)if all units are associable and 5

without difference, we get mathematical number only one

kind of number, and the Ideas cannot be the numbers. For

what sort of number will man-himself or animal-itselfor anyother Form be ? There is one Idea of each thing, e. g. one

of man-himself and another one of animal-itself; but the i

similar and undifferentiated numbers are infinitely many, so

that any particular 3 is no more man-himselfthan any other

3. But if the Ideas are not numbers, neither can they exist

at all. For from what principles will the Ideas come ? It is

number that comes from the i and the indefinite dyad, and 15

the principles or elements are said to be principles and

elements of number, and the Ideas cannot be ranked as

either prior or posterior to the numbers.

But (2) if the units are inassociable, and inassociable in

the sense that any is inassociable with any other, number of

this sort cannot be mathematical number;for mathematical

number consists of undifferentiated units, and the truths 20

proved of it suit this character. Nor can it be ideal number.

For 2 will not proceed immediately from i and the indefi

nite dyad, and be followed by the successive numbers, as

they say 2, 3, 4 for the units in the ideal 2 are generated

at the same time, whether, as the first holder of the theoryl

said, from unequals (coming into being when these wereequalized) or in some other way since, if one unit is to 25

be prior to the other, it will be prior also to the 2 com

posed of these;

for when there is one thing prior and

another posterior, the resultant of these will be prior to one

and posterior to the other.2

Again, since the i -itself is first,and then there is a parti- 30

cular i which is first among the others and next after the

i -itself, and again a third which is next after the second

and next but one after the first i, so the units must be

prior to the numbers after which they are named when we

1Plato.

2 The theory of ideal number holds that 2 comes next after the

original i, which with the indefinite 2 is the source of number. But

if all units are different in species, one of the units in 2 is prior to theother and . . to 2, and comes next after the original I. Similarlybetween 2 and 3 there will be the first unit in 3, and so on.



io8ia METAPHYSICA

count them ; e. g. there will be a third unit in 2 before 3

exists, and a fourth and a fifth in 3 before the numbers 4 and

35 5 exist. Now none of these thinkers has said the units are

inassociablein this

way, but according totheir

principlesit

is reasonable that they should be so even in this way, though

io8ibin truth it is impossible. For it is reasonable both that

the units should have priority and posteriority if there is

a first unit or first i, and also that the 2 s should if there is

a first 2;for after the first it is reasonable and necessary

5 that there should be a second, and if a second, a third, and

so with the others successively. (And to say both things

at the same time, that a unit is first and another unit is

second after the ideal i, and that a 2 is first after it, is

impossible.) But they make a first unit or i, but not also

a second and a third, and a first 2, but not also a second and

a third.

10 Clearly, also, it is not possible, if all the units are in

associable, that there should be a 2-itself and a 3 -itself;

and so with the other numbers. For whether the units

are undifferentiated or different each from each, number

must be counted by addition, e. g.2 by adding another i to

15 the one, 3 by adding another i to the two, and 4 similarly.

This being so, numbers cannot be generated as they gene

rate them, from the 2 and thei

;

for 2 becomes part of 3,

20 and 3 of 4, and the same happens in the case of the suc

ceeding numbers, but they say 4 came from the first 2 and

the indefinite 2, which makes it two 2 s other than the

2-itself1

;if not, the 2-itself will be a part of 4 and one

other 2 will be added. And similarly 2 will consist of the

25 i -itself and another i;but if this is so, the other element

cannot be an indefinite 2 ; for it generates one unit, not, as

the indefinite 2 does, a definite 2.

Again, besides the 3-itself and the 2-itself how can there

be other 3*3 and 2 s ? And how do they consist of prior

30 and posterior units ? All this is absurd and fictitious, and

there cannot be a first 2 and then a3-itself. Yet there must,

if the i and the indefinite dyad are to be the elements. But

1 The indefinite 2 being bvorroios produces two 2 s by operating on

the ideal 2, and it is these two 2 s which are distinct from the ideal 2.



BOOK M. 7 io8ib

if the results are impossible, it is also impossible that these

are the generating principles.

If the units, then, are differentiated, each from each, these

results and others similar to these follow of necessity. But 35

(3) if those in different numbers are differentiated, but those

in the same number are alone undifferentiated from one

another, even so the difficulties that follow are no less.

E.g. in the lo-itself there are ten units, and the 10 is com- io8aa

posed both of them and of two5*8.

But since the lo-itself

is not any chance number nor composed ofany chance 5*3

or, for that matter, units the units in this 10 must differ.

For if they do not differ, neither will the 5*3 of which the 5

10 consists differ; but since these differ, the units also will

differ. But if they differ, will there be no other 5 s in the

10 but only these two, or will there be others? If there

are not, this is paradoxical ;and if there are, what sort of

10 will consist of them ? For there is no other 10 in the 10

10 but itself. But it is actually necessary on their view that

the 4 should not consist ofany chance 2 s;for the indefinite

2, as they say, received the definite 2 and made two 2 s;

for its nature was to double what it received.

Again, as to the 2 being an entity apart from its two units, 15

and the 3 an entity apart from its three units, how is this pos

sible ? Either by one s sharing in the other, as pale manis different from pale and man (for it shares in these),

or when one is a differentia of the other, as man is

different from animal and two-footed .

Again, some things are one by contact, some by inter- 2o

mixture, some by position ;none of which can belong to

the units of which the 2 or the 3 consists;but as two men

are not a unity apart from both, so must it be with the

units. And their being indivisible will make no difference

to them;

for points too are indivisible, but yet a pair of 25

them is nothing apart from the two.

But this consequence also we must not forget, that it

follows that there are prior and posterior 2 s, and similarly

with the other numbers. For let the 2 s in the 4 be simul

taneous; yet these are prior to those in the 8, and as the 2 30

generated them, they generated the 4 s in the 8-itself.



io82a METAPHYSICA

Therefore if the first 2 is an Idea, these 2 s also will be

Ideas of some kind. And the same account applies to the

35 units;for the units in the first 2 generate the four in 4, so

that all the units come to be Ideas and an Idea will be

composed of Ideas. Clearly therefore those things also

of which these happen to be the Ideas will be composite,

e. g. one might say that animals are composed of animals,

if there are Ideas of them.

io82b

In general, to differentiate the units in any way is an

absurdity and a fiction;and by a fiction I mean a forced

statement made to suit a hypothesis. For neither in quantity

5nor in quality do we see unit differing from unit, and

number must be either equal or unequal all number but

especially that which consists of abstract units so that if

one number is neither greater nor less than another, it is

equal to it;but things that are equal and in no wise

differentiated we take to be the same when we are speaking

of numbers. If not, not even the 2 s in the lo-itself will be

10 undifferentiated, though they are equal ;for what reason

will the man who alleges that they are not differentiated be

able to give ?

Again, if every unit + another unit makes two, a unit

from the 2-itself and one from the 3-itself will make a 2.

Now(a)

this will consist of differentiated units;

and(/3)

will

it be prior to the 3 or posterior ? It rather seems that it

15 must be prior ;for one of the units is simultaneous with

the 3, and the other is simultaneous with the 2. And we,

for our part, suppose that in general i and T, whether the

things are equal or unequal, is 2, e. g. the good and the bad,

or a man and a horse;but those who hold these views say

that not even two linits are 2.

20 If the number of the 3-itself is not greater than that ot

the 2, this is surprising ;and if it is greater, clearly there is

also a number in it equal to the 2, so that this is not different

from the 2-itself. But this is not possible, if there is a first

and a second number. 1

Nor will the Ideas be numbers. For in this particular

point they are right who claim that the units must be

1i. e. if there is a difference of kind between the numbers.



BOOK i\l. 7 io82b

different, if there are to be Ideas;as has been said before.

1 2 5

For the Form is unique ;but if the units are not different,

the 2 s and the 3*8 also will not be different. This is also

the reason why they must say that when we count thus

i,2 we do not proceed by adding to the given number

;

for if we do, neither will the numbers be generated from 30

the indefinite dyad, nor can a number be an Idea;for then

one Idea will be in another, and all the Forms will be parts

of one Form. And so with a view to their hypothesis their

statements are right, but as a whole they are wrong ;for

their view is very destructive, since they will admit that this

question itself affords some difficulty whether, when we 35

count and say i, 2, 3, we count by addition or by separate

portions. But we do both;and so it is absurd to reason

back from this problem to so great a difference of essence.

8 First of all it is well to determine what is the differentia1083**

of a number and of a unit, if it has a differentia. Units

must differ either in quantity or in quality ;and neither of

these seems to be possible. But number qua number differs

in quantity. And if the units also did differ in quantity,

number would differ from number, though equal in number 5

of units. Again, are the first units greater or smaller, and

do the later ones increase or diminish ? All these are irra

tional suppositions. But neither can they differ in quality.

For no attribute can attach to them;for even to numbers I0

quality is said to belong after quantity. Again, quality

could not come to them either from the i or from the dyad ;

for the former has no quality, and the latter gives quantity ;

for this entity is what makes things to be many. If the

facts are really otherwise, they should state this quite at 15

the beginning and determine ifpossible, regarding the

differentia of the unit, why it must exist, and, failing this,

what differentia they mean.

Evidently then, if the Ideas are numbers, the units can

not all be associable, nor can they be inassociable in either

of the two ways.2 But neither is the way in which some 20

others speak about numbers correct. These are those who

1

1081*5-17.2

Cf. io8oa 18-20, 23-35.



io83a METAPHYSICA

do not think there are Ideas, either without qualification or

as identified with certain numbers, but think the objects of

mathematics exist and the numbers are the first of existing

things, andthe i -itself is the

starting-pointof them. It is

paradoxical that there should be a i which is first of I s, as

25 they say, but not a 2 which is first of 2 s, nor a 3 of 3 s;

for the same reasoning applies to all. If, then, the facts with

regard to number are so, and one supposes mathematical

number alone to exist, the i is not the starting-point (for

30 this sort of i must differ from the other units;and if this is

so, there must also be a 2 which is first of 2 s, and similarly

with the other successive numbers). But if the i is the

starting-point, the truth about the numbers must rather be

what Plato used to say, and there must be a first 2 and 3,

and the numbers must not be associable with one another.

3 But ifon the other hand one supposes this, many impossible

results, as we have said,1follow. But either this or the

other must be the case, so that if neither is, number cannot

exist separately.

io83b

It is evident, also, from this that the third version2

is the

worst, theview ideal and mathematical number is the same.

For two mistakes must then meet in the one opinion, (i)

5 Mathematical number cannot be of this sort, but the holder

ofthis

view has to spinit

out by making suppositions

peculiar to himself. And (2) he must also admit all the

consequences that confront those who speak of number in

the sense of Forms .

The Pythagorean version in one way affords fewer diffi

culties than those before named, but in another way has

10 others peculiar to itself. For not thinking of number as

capable of existing separately removes many of the im

possible consequences ;but that bodies should be composed

of numbers, and that this should be mathematical number,

is impossible. For it is not true to speak of indivisible

spatial magnitudes ;and however much there might be

magnitudes of this sort, units at least have not magnitude ;

1 5 and how can a magnitude be composed of indivisibles ?

But arithmetical number, at least, consists of units, while

1Cf. ioSob 37-io83

a17.

2 That of Xenocrates;

cf. io8ob 22.



BOOK M. 8 io83b

these thinkers identify number with real things ;at any rate

they apply their propositions to bodies as if they consisted

of those numbers.

If, then, it is necessary, if number is a self-subsistent real

thing, that it should exist in one of these ways which have 20

been mentioned,1 and if it cannot exist in any of these,

evidently number has no such nature as those who make it

separable set up for it.

Again, does each unit come from the great and the small,

equalized, or one from the small, another from the

great

?

(a) If the latter, neither does each thing contain all the ele- 25

ments, nor are the units without difference;for in one there

is the great and in another the small, which is contrary in

its nature to the great. Again, how is it with the units in

the 3-itself ? One of them is an odd unit. But perhaps it

is for this reason that they give i -itself the middle place in

odd numbers.

2

(6) But if each of the two units consists of 30

both the great and the small, equalized, how will the 2,

which is a single thing, consist of the great and the small ?

Or how will it differ from the unit ? Again, the unit is prior

to the 2;for when it is destroyed the 2 is destroyed. It

must, then, be the Idea of an Idea since it is prior to an

Idea, and it must have come into being before it. From 35

what, then ? Not from the indefinite dyad, for its function

was to double.

Again, number must be either infinite or finite;for these

thinkers think of number as capable of existing separately,

so that it is not possible that neither of those alternatives

should be true. Clearly it cannot be infinite ;for infinite

number is neitherodd nor even,but the generation ofnumbers

is always the generation either of an odd or of an even

number;in one way, when i operates on an even number, an

odd number is produced ;in another way, when 2 operates, 5

the numbers got from i by doubling are produced ;in

another way, when the odd numbers operate, the other

even numbers are produced. Again, if every Idea is an

Idea ofsomething,

and the numbers are

Ideas,

infinite

2Cf. Diels, Vorsokratiker, ed. 3, i. 346. 17-22.



io84a METAPHYSICA

number itself will be an Idea of something, either of some

sensible thing or of something else. Yet this is not

possible in view of their thesis any more than it is

reasonable initself,

at least if

they arrangethe Ideas as

they do.

10 But ifnumber infinite, how far does it go ? With regard

to this not only the fact but the reason should be stated.

But if number goes only up to 10, as some say,1

firstly the

Forms will soon run short;

e. g. if 3 is man-himself, what

15number will be the horse-itself ? The series of the numbers

which are the several things-themselves goes up to 10. It

must, then, be one of the numbers within these limits; for

it is these that are substances and Ideas. Yet they will run

short;for the various forms of animal will outnumber them.

At the same time it is clear that if in this way the 3 is

man-himself, the other 3 s are so also (for those in identical

ao numbers are similar), so that there will be an infinite num

ber of men;

if each 3 is an Idea, each of the numbers will

be man-himself, and if not, they will at least be men. And

if the smaller number is part of the greater (being number

of such a sort that the units in the same number are associ-

able), then if the 4-itself is an Idea of something, e.g. of

horse or of white,man will be a part of horse, if man

25is 2. It is

paradoxicalalso that there should be an Idea of

10, but not of 1 1, nor of the succeeding numbers. Again,

there both are and come to be certain things of which there

are no Forms; why, then, are there not Forms of them

also ? We infer that the Forms are not causes. Again, it

is paradoxical if the number-series up to 10 is more of a

30 real thing and a Form than 10 itself. There is no genera

tion of the former as one thing, and there is of the latter.

But they try to work on the assumption that the series of

numbers up to 10 is a complete series. At least they

generate the derivatives e. g. the void, proportion, the odd,

and the others of this kind within the decade. For some

things, e. g. movement and rest, good and bad, they assign

35 to the originative principles, and the others to the numbers.

This is why they identify the odd with i;for if the odd

1This includes Plato (cf. Phys. 2o6b 32) and probably Speusippus.



BOOK M. 8 io84a

implied 3, how would 5 be odd? ]

Again, spatial magnitudes

and all such things are explained without going beyond a

definite number;

e. g. the first, the indivisible, line,2 then io84

b

the 2, &c. ; these entities also extend only up to io.3

Again, if number can exist separately, one might ask

which is prior i, or 3 or 2 ? Inasmuch as the number is

composite, i is prior, but inasmuch as the universal and the

form is prior, the number is prior ;for each of the units is 5

part of the number as its matter, and the number acts as

form. And in a sense the right angle is prior to the acute,

because it is determinate and in virtue of its definition;

but in a sense the acute is prior, because it is a part and the

right angle is divided into acute angles. As matter, then,

the acute angle and the element and the unit are prior, but in io

respect of the form and of the substance as expressed in the

definition, the right angle, and the whole consisting of the

matter and the form, are

prior;for the concrete

thing

is

nearer to the form and to what is expressed in the definition,

though in generation it is later. How then is i the starting-

point ? Because it is not divisible, they say ;but both the

universal, and the particular or the element, are indivisible.

But they are starting-points in different ways, one in15

definition and the other in time. In which way, then, is i

the starting-point ? As has been said, the right angle is

thought to be prior to the acute, and the acute to the right,

and each is one. Accordingly they make i the starting-

point in both ways. But this is impossible. For the uni

versal is one as form or substance, while the element is one

as a part or as matter. For each of the two is in a sense 20

one in truth each of the two units exists potentially (at

least if the number is a unity and not like a heap, i. e. if

different numbers consist of differentiated units, as they say),

but not in complete reality ;and the cause of the error

they fell into is that they were conducting their inquiry at

1i. e. to account for the oddness of odd numbers they identify the

odd with the i, which is a principle present in all numbers, not with

the 3, which on their theory is not present in other numbers.

2 Cf. A. 992*22.3

Cf. N. io9ob21-24. i answers to the point (the indivisible line

),

2 to the line, 3 to the plane, 4 to the solid, and 1+2 + 3+4= io.



io84b METAPHYSICA

the same time from the standpoint of mathematics and from

25 that of universal definitions, so that(i) from the former

standpoint they treated unity, their first principle, as a

point;for the unit is a

point

withoutposition. They put

things together out of the smallest parts, as some others 1 also

have done. Therefore the unit becomes the matter of num

bers and at the same time prior to 2;and again posterior, 2

3 being treated as a whole, a unity, and a form. But (2)

because they were seeking the universal2

they treated the

unity w ich can be predicated of a number, as in this

sense also3

a part of the number. But these characteristics

cannot belong at the same time to the same thing.

If the i -itself must be unitary4

(for it differs in nothing

from other I s except that it is the starting-point), and the

2 is divisible but the unit is not, the unit must be liker the

35 i -itself than the 2 is. But if the unit is liker it, it must be

liker to the unit than to the 2;therefore each of the units

in 2 must be prior to the 2. But they deny this;at least

io85athey generate the 2 first. Again, if the 2-itself is a unity

and the 3 -itself is one also, both form a 2. From what, then,

is this 2 produced ?

Since there is not contact in numbers, but succession, g

viz. between the units between which there is nothing, e. g.

K betwreen those in 2 or in 3, one might ask whether these suc

ceed the i -itself or not, and whether, of the terms that

succeed it, 2 or either of the units in 2 is prior.

Similar difficulties occur with regard to the classes of things

posterior to number, the line, the plane, and the solid.

For some 5construct these out of the species of the great

10 and small ;e. g. lines from the

4

long and short , planes

from the broad and narrow,masses from the deep and

shallow;which are species of the great and small . And

the originative principle of such things which answers to

1Sc. the atomists.

2

Inserting TO before in 1. 31.3

i. e. they treated the unity which is predicable of a number, as well

as the unit in a number, as a part of the number.4

Reading conjecturally in 1. 33 p-ovaSiKov for povo5 This probably includes Plato himself.



BOOK M. 9 1085*

the ildifferent thinkers describe in different ways. And

in these also the impossibilities, the fictions, and the contra- 1 5

dictions of all probability are seen to be innumerable. For

(i) the geometrical classes are severed from one another,

unless the principles of these are implied in one another in

such a way that the broad and narrow is also long and

short (but if this is so, the plane will be a line and the solid

a plane ;

2

again, how will angles and figures and such

things be explained ?).And

(ii)the same happens as in 20

regard to number;for long and short

, &c., are attributes

of magnitude, but magnitude does not consist of these, any

more than the line consists of straight and curved,or

solids of smooth and rough .

3

(All these views share a difficulty which occurs with re

gard to species-of-a-genus, when one posits the universals,

viz. whether it is animal-itself or something other than 25

animal-itself that is in the particular animal. True, if the

universal is not separable from sensible things, this will

present no difficulty ;but if the i and the numbers are

separable, as those who express these views say, it is not

easy to solve the difficulty, if one may apply the words not

easy to the impossible. For when we apprehend the unity

in 2, or in general in a number, do we apprehend a thing- 30

itself or something else ?)

Some, then, generate spatial magnitudes from matter of

this sort, others4 from the point and the point is thought

by them to be not i but something like i and from other

matter like plurality, but not identical with it;about which

principles none the less the same difficulties occur. For if35

the matter is one, line and plane and solid will be the same;

for from the same elements will come one and the same

thing. But if the matters are more than one, and there is io85b

one for the line and a second for the plane and another for

the solid, they either are implied in one another or not, so

1i. e. that which is to the geometrical forms as the primary i is

^according to the Platonic theory) to numbers.2

With 1085* 7-19 cf. A. 992a

10-19.&

Cf. A. 992b1-7, N. io88 a

15-21.4

Speusippus is probably meant.



io85b METAPHYSICA

that the same results will follow even so;for either the plane

will not contain a line or it will be a line.

Again, how number can consist of the one and plurality,

5

they

make no attempt to

explain;but however

they

ex

press themselves, the same objections arise as confront

those who construct number out of the one and the in

definite dyad.1 For the one view generates number from the

universally predicated plurality, and not from a particular

plurality ;and the other generates it from a particular

plurality, but the first;for 2 is said to be a first plural-

10 ity.

Therefore there is practically no difference, but the

same difficulties will follow, is it intermixture or position

or blending or generation ? and so on. Above all one

might press the question if each unit is one, what does it

come from ? Certainly each is not the one-itself. It must,

then, come from the one-itself and plurality, or a part of

15 plurality. To say that the unit is a plurality is impossible,

for it is indivisible; and to generate it from a part of

plurality involves many other objections ;for (a) each of

the parts must be indivisible (or it will be a plurality and

the unit will be divisible) and the elements will not be the

20 one and plurality ;for the single units do not come from

plurality and the one. Again, (/?)the holder of this view

doesnothing

but

presupposeanother number

;for his

plurality of indivisibles is a number. Again, we must

inquire, in view of this theory also,2 whether the number

is infinite or finite. For there was at first, as it seems,

2- a plurality that was itself finite, from which and from the

one comes the finite number of units. And there is an

other plurality that is plurality-itself and infinite plurality ;

which sort of plurality, then, is the element which co-operates with the one ? One might inquire similarly about the

point, i. e. the element out of which they make spatial

magnitudes. For surely this is not the one and only point ;

at any rate, then, let them say out of what each of the other

30 points is formed. Certainly not of some distance + the

point-itself. Nor again can there be indivisible parts of

a distance, as the elements out of which the units are said

1i. e. probably Plato and Xenocrates.

aCf. io83

b36.



BOOK M. 9 io85b

to be made are indivisible parts of plurality ;for number

consists of indivisibles, but spatial magnitudes do not.1

All these objections, then, and others of the sort make it

evident that numberand spatial magnitudes cannotexist apart 35

from things. Again, the discord about numbers between the

various versions is a sign that it is the incorrectness of the io86a

alleged facts themselves that brings confusion into the

theories. For those who make the objects of mathematics

alone exist apart from sensible things,2

seeing the diffi

culty about the Forms and their fictitiousness, abandoned

ideal number and posited mathematical. But those who 5

wished to make the Forms at the same time also numbers, but

did not see, if one assumed these principles, how mathe

matical number was to exist apart from ideal,3 made ideal

and mathematical number the same in words, since mfactmathematical number has been destroyed; for they state 10

hypotheses peculiarto themselves and not those of mathe

matics. And he who first supposed that the Forms exist and

that the Forms are numbers and that the objects of mathe

matics exist,4

naturally separated the two. Therefore it

turns out that all of them are right in some respect, but on

the whole not right. And they themselves confirm this, for

their statements do not agree but conflict. The cause is that 15

their hypotheses and their principles are false. And it is

hard to make a good case out of bad materials, according

to Epicharmus5

: as soon as tis said, tis seen to be

wrong.

But regarding numbers the questions we have raised and

the conclusions we have reached are sufficient (for while he

who is already convinced might be further convinced by a

longer discussion, one not yet convinced would not come 20

any nearer to conviction) ; regarding the first principles and

the first causes and elements, the views expressed by those

who discuss only sensible substance have been partly

1 The point cannot have for an element of it (a) a distance, for this

would destroy the simplicity of the point ;or (b) part of a distance, for

any part of a distance must be a distance.

Speusippus is meant. 3 Xenocrates is meant.4

Plato. 5Fr. 14, Diels, Vorsokratiker.



io86a METAPHYSICA

stated in our works on nature,1 and partly do not belong

to the present inquiry ;but the views of those who assert

25 that there are other substances besides the sensible must be

considered next after those we have beenmentioning.

Since, then, some say that the Ideas and the numbers are

such substances, and that the elements of these are elements

and principles of real things, we must inquire regarding

these what they say and in what sense they say it.

Those who posit numbers only, and these mathematical,

30 must be considered later 2;but as regards those who believe

in the Ideas one might survey at the same time their wayof thinking and the difficulty into which they fall. For

they at the same time make the Ideas universal and again

treat them as separable and as individuals. That this is

35 not possible has been argued before.3 The reason why

those who described their substances as universal combined

these two characteristics in one thing, is that they did

not make substances identical with sensible things. They

thought that the particulars in the sensible world were in

io86ba state of flux and none of them remained, but that the

universal was apart from these and something different.

And Socrates gave the impulse to this theory, as we said

in our earlier discussion,4

by reason of his definitions, but

he did not

separateuniversals from individuals

;and in this

5 he thought rightly, in not separating them. This is plain

from the results ;for without the universal it is not possible

to get knowledge, but the separation is the cause of the

objections that arise with regard to the Ideas. His suc

cessors, however, treating it as necessary, if there are to be

any substances besides the sensible and transient substances,

that they must be separable, had no others, but gave sepa-

10 rate existence to these universally predicated substances, so

that it followed that universals and individuals were almost

the same sort of thing. This in itself, then, would be one

difficulty in the view we have mentioned.

Let us now mention a point which presents a certain IO

1

Phys. i. 4-6 ; De Caelo, iii. 3-4 ; De Gen, et Corr. i. i.?

Speusippus is meant; cf. N. 1090*7-15, 2o-b 2o.8

B. ioo3a7-17.



BOOK M. 10 io86b

difficulty both to those who believe in the Ideas and to those

who do not, and which was stated before, at the beginning, I5

among the problems.1

If we do not suppose substances to

be separate, and in the way in which individual things are

said to be separate, we shall destroy substance in the sense

in which we understandc

substance;but if we conceive

substances to be separable, how are we to conceive their

elements and their principles ?

If they are individual and not universal, (a) real things 20

will be just of the same number as the elements, and(d)

the

elements will not be knowable. For (a) let the syllables in

speech be substances, and their elements elements of sub

stances;then there must be only one ba and one of each of

the syllables, since they are not universal and the same in 25

form but each is one in number and a *

this and not a kind

possessed of a common name (and again they suppose that

the just whatathing

is2

is ineach case one). And

if

the

syllables are unique, so tooare the parts ofwhich they consist;

there will not, then, be more as than one, nor more than

one of any of the other elements, on the same principle on 30

which an identical syllable cannot3exist in the plural number.

But if this is so, there will not be other things existing

besides the elements, but only the elements. (6) Again,

the elements will not be even knowable ; for they are not

universal, and knowledge is of universals. This is clear

from demonstrations and from definitions;for we do not

conclude that this triangle has its angles equal to twro right

angles, unless every triangle has its angles equal to two 35

right angles, nor that this man is an animal, unless every

man is an animal.

But if the principles are universal, either the substances

composed of them are also universal, or non-substance will io87a

be prior to substance;for the universal is not a substance,

but the element or principle is universal, and the element

or principle is prior to the things of which it is the prin

ciple or element.

1B. 999

b 24-ioooa4, ioo3

a5-i;.

2i.e. the Idea

;cf. I079

b6.

3

Omitting aXXo>i> in 1. 30 ;there is no trace of it in ps.-Alexander.

U 2



io87a METAPHYSICA

5 All these difficulties follow naturally, when they make

the Ideas out of elements and at the same time claim that

apart from the substances which have the same form there

areIdeas,

asingle separate entity. But if,

e.g.,

in the case

of the elements of speech, the as and the s may quite well

be many and there need be no ^-itself and ^-itself besides

the many, there may be, so far as this goes, an infinite

ic number of similar syllables. The statement that all know

ledge is universal, so that the principles of things must also

be universal and not separate substances, presents indeed,

of all the points we have mentioned, the greatest difficulty,

but yet the statement is in a sense true, although in a sense

1 5 it is not. For knowledge, like the verb to know,means

two things, of which one is potential and one actual. The

potency, being, as matter, universal and indefinite, deals

with the universal and indefinite;but the actuality, being

definite, deals with a definite object, being a this,

it

deals with a this . But per accidens sight sees universal

colour, because this individual colour which it sees is

20 colour;and this individual a which the grammarian in

vestigates is an a. For if the principles must be universal,

what is derived from them must also be universal, as in

demonstrations l

;and if this is so, there will be nothing

capable of separateexistence i. e.

no substance. Butevidently in a sense knowledge is universal, and in a sense

25 it is not.

1Sc. universal premisses do not give singular conclusions.



BOOK N

I REGARDING this kind of substance, what we have said

must be taken as sufficient. All philosophers make the

first principles contraries : as in natural thing s, so also in 30

the case of unchangeable substances. But since there can

not be anything prior to the first principle of all things, the

principle cannot be the principle and yet be an attribute of

something else. To suggest this is like saying that the

white is a first principle, not qiia anything else but qua

white, but yet that it is predicable of a subject, i. e. that its

being white presupposes its being something else;this is 35

absurd, for then that subject will be prior. But all things

which are generated from their contraries involve an under

lying subject ;a subject, then, must be present in the case

of contraries, if anywhere. All contraries, then, are always io87b

predicable of a subject, and none can exist apart, but just

as appearances suggest that there is nothing contrary to

substance, argument confirms this. No contrary, then, is

the first principle of all things in the full sense;the first

principleis

somethingdifferent.

But these thinkers make one of the contraries matter,

some T

making the unequal which they take to be the 5

essence of plurality matter for the One, and others 2

making plurality matter for the One. (The former gene

rate numbers out of the dyad of the unequal, i. e. of the

great and small, and the other thinker we have referred to

generates them out of plurality, while according to both it

is generated by the essence of the One.) For even the philo

sopher who says the unequal and the One are the elements,

and the unequal is a dyad composed of the great and small, 10

treats the unequal, or the great and the small, as being one,

and does not draw the distinction that they are one in

definition, but not in number. But they do not describe

rightly even the principles which they call elements, for

1Plato is meant.

2

Speusippus is probably referred to.



io87b METAPHYSICA

some 1 name the great and the small with the One and treat

15 these three as elements of numbers, two being matter, one

the form;while others

2 name the many and few, because

the great and the small are more appropriate in theirnature to magnitude than to number

;and others 3 name

rather the universal character common to these that

which exceeds and that which is exceeded . None of

these varieties of opinion makes any difference to speak

of, in view of some of the consequences ; they affect only* the abstract objections, which these thinkers take care to

avoid because the demonstrations they themselves offer are

abstract, with this exception, that if the exceeding and

the exceeded are the principles, and not the great and the

small, consistency requires that number should come from

the elements before 2 does;for number is more universal

than 2, as the exceeding and the exceeded are more uni-

25 versal than the great and the small. But as it is, they say

one of these things but do not say the other. Others

oppose the different and the other to the One,4 and others

oppose plurality to the One. 5 But if, as they claim, things

consist of contraries, and to the One either there is nothing-

contrary, or if there is to be anything it is plurality, and the

unequal is contrary to the equal, and the different to the same,

30 and the other to the thing itself, those who oppose the One to

plurality have most claim to plausibility, but even their view

is inadequate, for the One would on their view be a few;for

plurality is opposed to fewness, and the many to the few.

The one evidently means a measure. And in every

case there is some underlying thing with a distinct nature

35 of its owr

n, e. g. in the scale a quarter-tone, in spatial

magnitude a finger or a foot or something of the sort, in

rhythms a beat or a syllable ;and similarly in gravity it is

io88aa definite weight ;

and in the same way in all cases, in

qualities a quality, in quantities a quantity (and the measure

is indivisible, in the former case in kind, and in the latter to

the sense) ;which implies that the one is not in itself the

1 This includes Plato.2Unidentifiable Platonists.

3

Perhaps Pythagoreans.4

Probably certain Pythagoreans are referred to.

5

Probably Speusippus is meant.



BOOK N. i io88

substance of anything-. And this is reasonable;

for4

the

one means the measure of some plurality, and number 5

means a measured plurality and a plurality of measures.

(Thus it is natural that one is not a number ; for the

measure is not measures, but both the measure and the one

are starting-points.) The measure must always be some

identical thing predicable of all the things it measures, e. g.

if the things are horses, the measure is horse,and if they

are men, man . If they are a man, a horse, and a god, the 10

measure is perhaps*

living being ,and the number of them

will be a number of living beings. If the things are* man

and pale and walking ,these will scarcely have a num

ber, because all belong to a subject which is one and the

same in number, yet the number of these will be a number

of kinds or of some such term.

Those who treat the unequal as one thing, and the dyad 15

as an indefinite

compoundof

great

and small,say

what is

very far from being probable or possible. For (a) these

are modifications and accidents, rather than substrata, of

numbers and magnitudes the many and few of number,

and the great and small of magnitude like even and odd,

smooth and rough, straight and curved. Again, (b) apart 20

from this mistake, the great and the small, and so on, must

be relative to something; but what is relative is least of

all thingsl a kind of entity or substance, and is posterior

to quality and quantity ;and the relative is an accident

of quantity, as was said, not its matter, since something 25

with a distinct nature of its own must serve as matter

both to the relative in general and to its parts and kinds.

For there is nothing either great or small, many or few, or,

in general, relative to something else, which without having

a nature of its own is many or few, great or small, or

relative to something else. A sign that the relative is least

of all a substance and a real thing is the fact that it alone 30

has no proper generation or destruction or movement, as

in respect of quantity there is increase and diminution, in

respect of quality alteration, in respect of place locomotion,

in respect of substance simple generation and destruction.

1

Omitting r&vK.arriyopi.u>v

in 1. 23 as a gloss.



io88a METAPHYSICA

In respect of relation there is no proper change ; for, with

out changing, a thing will be now greater and now less or

35 equal, if that with which it is compared has changed in

io88b

quantity. And(c) the matter of each

thing,

and therefore of

substance, must be that which is potentially of the nature in

question ;but the relative is neither potentially nor actually

substance. It is strange, then, or rather impossible, to make

not-substance an element in, and prior to, substance;for

all the categories are posterior to substance. Again, (d)

elements are not predicated of the things of which they are

5 elements, but many and few are predicated both apart andtogether of number, and long and short of the line, and

both broad and narrow apply to the plane. If there is

a plurality, then, of which the one term, viz. few, is always

predicated, e.g.2 (which cannot be many, for if it were

many, i would be few), there must be also one which is

10 absolutely many, e. g. 10 is many (ifthere is no number

which is greater than 10), or 10,000. How then, in view of

this, can number consist of few and many ? Either both

ought to be predicated of it, or neither;but in fact only

the one or the other is predicated.

We must inquire generally, whether eternal things can 2

15 consist of elements. If they do, they will have matter;for

everything that consists of elements is composite. Since,

then, even ifa thing exists for ever, out of that of which it con

sists it would necessarily also, if it had come into being, have

come into being,1 and since everything comes to be what it

comes to be out of that which is it potentially (forit could not

have come to be out of that which had not this capacity,

nor could it consist of such elements), and since the poten-

20 tial can be either actual or not, this being so, however

everlasting number or anything else that has matter is, it

must be capable of not existing, just as that which is any

number of years old is as capable of not existing as that

which is a day old;

if this is capable of not existing, so is

that which has lasted for a time so long that it has no limit.

1

Punctuating in 11. l6, 17 ft KCU ati eon, K.ai}d eyevero, e< TOVTOV

yiyvfadai.



BOOK N. 2 1088*

They cannot, then, be eternal, since that which is capable

of not existing is not eternal, as we had occasion to show in

another context.1

If that which we are now saying is 25

true universally that no substance is eternal unless it is

actuality and if the elements are matter that underlies

substance, no eternal substance can have elements present

in it, of which it consists.

There are some 2 who describe the element which acts with

the One as an indefinite dyad, and object to the unequal ,

reasonably enough, because of the ensuing difficulties;but 3

they have got rid only of those objections which inevitably

arise from the treatment of the unequal, i.e. the relative, as

an element;those which arise apart from this opinion must

confront even these thinkers, whether it is ideal number, or

mathematical, that they construct out of those elements.

There are many causes which led them off into these 35

explanations,and

especiallythe fact that

theyframed the

1089*

difficulty in an obsolete form. For they thought that all

things that are would be one (viz. Being itself),if one did

not join issue with and refute the saying of Parmenides: 3

For never will this be proved, that things that are not are.

They thought it necessary to prove that that which is not

is; for only thus ofthat which is andsomething else could 5

the things that are be composed, if they are many.

But, first, if being has many senses (for it means some

times substance, sometimes that it is of a certain quality,

sometimes that it is of a certain quantity, and at other times

the other categories), what sort of one, then, are all the

things that are, if non-being is to be supposed not to be ?

Is it the substances that are one, or the affections and 10

similarly the other categories as well, or all together so that

the this and the such and the*

so much and the other

categories that indicate each some one class of being will

all be one ? But it is strange, or rather impossible, that the

coming into play of a single thing4 should bring it about

that part of that which is is a this, part a * such

, part

a so much,

part

a here .

1

Cf. 0. io5ob7 ff.,

De Caelo, i. 12.2

Probably Xenocrates is meant.3Fr. 7.

4i. e. non-being.



io89a METAPHYSICA

15 Secondly, of what sort of non-being and being do the

things that are consist? For non-being also has many

senses, since being has;and not being a man means

notbeing

a certainsubstance,

notbeing straight

notbeing

of a certain quality, not being three cubits long not

being of a certain quantity. What sort of being and non-

being, then, by their union pluralize the things that are ?

20 This thinker 1 means by the non-being, the union of which

with being pluralizes the things that are, the false and the

character of falsity. This is also why it used to be said

that we must assume something that is false, as geometersassume the line which is not a foot long to be a foot long.

But this cannot be so. For neither do geometers assume

anything false (for the enunciation is extraneous to the in-

25 ference), nor is it non-being in this sense that the things

that are are generated from or resolved into. But since

4

non-being taken in its various cases2 has as many senses

as there are categories, and besides this the false is said not

to be, and so is the potential, it is from this that generation

proceeds, man from that which is not man but potentially

30 man, and white from that which is not white but potentially

\vhite, and this whether it is some one thing that is gene

rated or many.

The question evidently is, how being,in the sense of the

siibstances\ is many; for the things that are generated

are numbers and lines and bodies. Now it is strange to

inquire how being in the sense of the what is many, and

35 not how either qualities or quantities are many. For surely

the indefinite dyad or4

the great and the small is not a

reason why there should be two kinds of white or many

io89bcolours or flavours or shapes ; for then these also would be

numbers and units. But if they had attacked these other

categories, they wrould have seen the cause of the plurality

in substances also;for the same thing or something analo

gous is the cause. This aberration is the reason also why

5 in seeking the opposite of being and the one, from which

with being and the one the things that are proceed, they

posited the relative term (i.e. the unequal), which is neither

1 Plato;

cf. Soph. 237 A, 240.2

Cf. 11. 16-19.



BOOK N. 2

the contrary nor the contradictory of these, and is one kind

ofbeing"

as what and quality also are.

They should have asked this question also, how relative

terms are many and not one. But as it is, they inquire howthere are many units besides the first i, but do not go on to 10

inquire how there are many unequals besides the unequal.

Yet they use them and speak of great and small, many and

few (from which proceed numbers), long and short (from

which proceeds the line), broad and narrow (from which

proceeds the plane), deep and shallow (from which pro

ceed solids) ;and they speak of yet more kinds of relative

term. What is the reason, then, why there is a plurality of

these ?

It is necessary, then,as we say, to presuppose for each thingT 5

that which is it potentially ;and the holder of these views

further declared what that is which is potentially a*

this

and a substance but is not in itself

beingviz. that it is the

relative (as if he had said the qualitative ),which is neither

potentially the one or being, nor the negation of the one

nor of being, but one among beings. And it was much 20

more necessary, as we said,1if he was inquiring how beings

are many, not to inquire about those in the same category-

how there are many substances or many qualities but how

beings as a whole are many ; for some are substances, somemodifications, some relations. In the categories other than

substance there is yet another problem involved in the exist

ence ofplurality. Sincethey are notseparable from substances, 25

qualitiesand quantities aremanyjust because their substratum

becomes and is many ; yet there ought to be a matter for

each category ; only it cannot be separable from substances.

But in the case of thises \ it is possible to explain how the

this is many things, unless a thing is to be treated as both

a*

this and a general character.2 The difficulty arising 3

from the facts about substances is rather this, how there are

actually many substances and not one.

But further, if the this and the quantitative are not the

same, we are not told how and

why

the things that are are

1 a34-

2

Which, Aristotle thinks, the Platonists assert the Idea to be.



io89b METAPHYSICA

many, but how quantities are many. For all number

35 means a quantity, and so does the unit,unless it means a

measure or the quantitatively indivisible. If, then, the

quantitativeand the what are

different, weare not told

iO9Oa whence or how the what is many ;

but if any one says

they are the same, he has to face many inconsistencies.

One might fix one s attention also on the question,

regarding- the numbers, what justifies the belief that they

exist. To the believer in Ideas they provide some sort of

5 cause for existing things, since each number is an Idea, and

the Idea is to other things somehow or other the cause of

their being; for let this supposition be granted them. But

as for him who does not hold this view because he sees the

inherent objections to the Ideas (so that it is not for this

reason that he posits numbers), but who posits mathema-

10 tical number,1

why must we believe his statement that such

number exists, and of what use is such number to other

things ? Neither does he who says it exists maintain that

it is the cause of anything (he rather says it is a thing

existing by itself), nor is it observed to be the cause ofany

thing ;for the theorems of arithmeticians will all be found

15 true even of sensible things, as was said before.2

As for those, then, who suppose the Ideas to exist and to 3

be numbers, by their assumption in virtue of the method

of setting out each term apart from its instances of the

unity of each general term they try at least to explain

somehow why number must exist. Since their reasons,

however, are neither conclusive nor in themselves possible,

one must not, for these reasons at least, assert the existence

20 of number.

Again,the

Pythagoreans,because

theysaw

many attributes of numbers belonging to sensible bodies,

supposed real things to be numbers not separable num

bers, however, but numbers of which real things consist.

But why ? Because the attributes of numbers are present

in a musical scale and in the heavens and in many other

25 things.3

Those, however, who say that mathematical num-

1

Speusippus is meant.2

Cf. M. 3, esp. io77b17-22.

3Cf. A. 989** 29-99o

a29.



BOOK N. 3 io90a

her alone exists 1 cannot according to their hypotheses say

anything of this sort, but it used to be urged that these

sensible things could not be the subject of the sciences.

But we maintain that they are, as we said before. 2 And it

is evident that the objects of mathematics do not exist

apart ;for if they existed apart their attributes would not

have been present in bodies. Now the Pythagoreans in this 3

point are open to no objection ;but in that they construct

natural bodies out of numbers, things that have lightness

and weight out of things that have not weight or lightness,

they seem to speak of another heaven and other bodies,

not of the sensible. But those who make number separ- 35

able3 assume that it both exists and is separable because

the axioms would not be true of sensible things, while the

statements of mathematics are true and greet the soul;

4

and similarly with the spatial magnitudes of mathematics.

It is

evident, then,both that the rival

theory

5will

saythe

iogo

b

contrary of this, and that the difficulty we raised just now,

why if numbers are in no way present in sensible things

their attributes are present in sensible things, has to be

solved by those who hold these views.

There are some who, because the point is the limit and 5

extreme of the line, the line of the plane, and the plane of

the solid, think there must be real things of this sort. Wemust therefore examine this argument too, and see whether

it is not remarkably weak. For(i)

extremes are not sub

stances, but rather all these things are limits. For even 10

walking, and movement in general, has a limit, so that

on their theory this will be a this and a substance. But

that is absurd. Not but what(ii)

even if they are substances,

they will all be the substances of the sensible things in this

world;for it is to these that the argument applied. Why

then should they be capable of existing apart ?

Again, if we are not too easily satisfied, we may, regard

ing all number and the objects of mathematics, press this

difficulty, that they contribute nothing to one another, the 15

1

Speusippusis meant. 2

Cf. M.3.

3 The Platonists.4 This seems to be a quotation from some poet or writer of poetical

prose.5Sc. of the Pythagoreans ;

cf. 11. 20-25. &29-



iogob METAPHYSICA

prior to the posterior ;for if number did not exist, none

the less spatial magnitudes would exist for those who

maintain the existence of the objects of mathematics only,1

and if

spatial magnitudesdid not

exist, soul and sensiblebodies would exist. But the observed facts show that

20 nature is not a series of episodes, like a bad tragedy. As

for the believers in the Ideas, this difficulty misses them;

for they construct spatial magnitudes out of matter and

number, lines out of the number 2, planes doubtless out of

3, solids out of 4, or they use other numbers, which

makes no difference. But will these magnitudes be Ideas,

25 or what is their manner of existence, and what do they

contribute to things ? These contribute nothing, as the

objects of mathematics contribute nothing. But not even

is any theorem true of them, unless we want to change the

objects of mathematics and invent doctrines of our own.

30 But it is not hard to assume any random hypotheses and

spin out a long string of conclusions. These thinkers,2

then, are wrong in this way, in wanting to unite the

objects of mathematics with the Ideas. And those who

first posited two kinds of number, that of the Forms and

that which is mathematical, neither have said nor can say

how mathematical number is to exist and of what it is

35 to consist. For they placeit

betweenideal

andsensible

number. If(i)

it consists of the great and small, it will

be the same as the other ideal number (he3 makes

spatial magnitudes out of some other small and great4

).

iogia And if

(ii)he names some other element, he will be making

his elements rather many. And if the principle of each of

the two kinds of number is a i, unity will be something

common to these, and we must inquire how the one is

these many things, while at the same time number, accord

ing to him, cannot be generated except from one and an

indefinite dyad.

5 All this is absurd, and conflicts both with itself and with

the probabilities,and we seem to see in it Simonides long

1

Speusippus is meant.2

11. 20-32 seem to refer to Xenocrates.3

Sc. Plato.

4Cf. I090

b2I, 22.



BOOK N. 3 i09ia

rigmarole1

;for the long rigmarole comes into play, like

those of slaves, when men have nothing sound to say. And

the very elements the great and the small seem to cry

out against the violence that is done to them ; for they 10

cannot in any way generate numbers other than those got

from i by doubling.

It is strange also to attribute generation to things that

are eternal, or rather this is one of the things that are

impossible. There need be no doubt whether the Pytha

goreans attribute generation to them or not;for they say 15

plainly that when the one had been constructed, whether

out of planes or of surface or of seed or of elements which

they cannot express, immediately the nearest part of the

unlimited began to be constrained and limited by the limit.

But since they are constructing a world and wish to speak

the language of natural science, it is fair to make some

examination of their physical theories, but to let them off

from the present inquiry ;for we are investigating the ao

principles at work in unchangeable things, so that it is

numbers of this kind whose genesis we must study.

4 These thinkers say there is no generation of the odd

number, which evidently implies that there is generation of

the even;and some present the even as produced first from

unequals the great and the small when these are equal

ized. The inequality, then, must belong to them before 25

they are equalized. If they had always been equalized,

they would not have been unequal before;

for there is

nothing before that which is always. Therefore evidently

they are not giving their account of the generation of

numbers merely to assist contemplation of their nature.2

A difficulty, and a reproach to any one who finds it no

difficulty, are contained in the question how the elements 3

and the principles are related to the good and the beautiful;

the difficulty is this, whether any of the elements is such

a thing as we mean by the good itself and the best, or this

is not so, but these are later in origin than the elements.

Thetheologians

seem to

agreewith some thinkers of the

1Sim. Ceius, Fr. 189. Bergk.

2Cf. De Caelo, i. 279* 32-280* 10.



io9ia METAPHYSICA

35 present day,1 who answer the question in the negative, and

say that both the good and the beautiful appear in the

nature of things only when that nature has made some

progress. (This they

do to avoid a real objection which

confronts those who say, as some do, that the one is a first

iogibprinciple. The objection arises not from their ascribing

goodness to the first principle as an attribute, but from

their making the one a principle and a principle in the

sense of an element and generating number from the one.)

The old poets agree with this inasmuch as they say that

5 not those who are first in time, e. g. Night and Heaven2

orChaos 3 or Ocean 4

, reign and rule, but Zeus.5 These poets,

however, are led to speak thus only because they think of

the rulers of the world as changing \for those of them

who combine the two characters in that they do not use

mythical language throughout, e. g. Pherecydes and some

10 others, make the original generating agent the Best, and

so do the Magi, and some of the later sages also, e. g. both

Empedocles and Anaxagoras, of whom one made love an

element, and the other made reason a principle. Of those

who maintain the existence of the unchangeable substances

some say the One itself is the good itself; but they thought

its substance lay mainly in its unity.

15 This, then, is the

problem,

which of the two

ways

of

speaking is right. It would be strange if to that which is

primary and eternal and most self-sufficient this very quality

self-sufficiency and self-maintenance belongs primarily

in some other way than as a good. But indeed it can be

for no other reason indestructible or self-sufficient than

because its nature is good. Therefore to say that the first

20 principle is good is probably correct;

but that this prin

ciple should be the One or, if not that, at least an element,

and an element of numbers, is impossible. Powerful ob

jections arise, to avoid wrhich some have given up the

theory6

(viz. those who agree that the One is a first

1

Speusippus is meant; cf. A. 1072* 31.2 The reference is to the Orphic cosmogony.3

Cf. Hes. Theog. 116.

4

Cf. Horn. //. xiv. 201.5

Cf. A. ic7ib 26.

6i. e. Speusippus gave up the identity of the One with the Good.



BOOK N. 4 i09ib

principle and element, but only of mathematical number).

For on this view all the units become identical with species 25

of good, and there is a great profusion of goods. Again,

if the Forms are numbers, all the Forms are identical with

species of good. But let a man assume Ideas of anything

he pleases. If these are Ideas only of goods, the Ideas will

not be substances;but if the Ideas are also Ideas of sub

stances, all animals and plants and all individuals that share

in Ideas will be good.

These absurdities follow, and it also follows that the 30

contrary element, whether it is plurality or the unequal,

i.e. the great and small, is the bad-itself. (Hence one

thinker 1avoided attaching the good to the One, because it

would necessarily follow, since generation is from contraries,

that badness is the fundamental nature of plurality ;while

others 2

say inequality is the nature of the bad.) It follows, 35

then, that all

things partakeof the bad

except

one the

One itself, and that numbers partake of it in a more un

diluted form than spatial magnitudes, and that the bad is 1092*

the space in which the good is realized,3 and that it par

takes in and desires that which tends to destroy it;for

contrary tends to destroy contrary. And if, as we were

saying,4the matter is that which is potentially each thing,

e. g. that of actual fire is that which is potentially fire, thebad will be just the potentially good.

All these objections, then, follow, partly because they 5

make every principle an element, partly because they make

contraries principles, partly because they make the One

a principle, partly because they treat the numbers as

the first substances, and as capable of existing apart, and

as Forms.

5 If, then, it is equally impossible not to put the good

among the first principles and to put it among them in this

way, evidently the principles are not being correctly de- 10

scribed, nor are the first substances. Nor does any one

conceive the matter correctly if he compares the principles

1

Speusippus.2Plato and Xenocrates.

3Cf. PI. Tim. 52 A, B.

4io88b I.



io92a METAPHYSICA

of the universe to that of animals and plants, on the groundthat the more complete always comes from the indefinite and

incomplete which is what leads this thinker 1

to say that

this is also true of the first

principlesof

reality,so

that ther 5 One itself is not even an existing thing. This is incorrect,

for even in this world of animals and plants the principles

from which these come are complete ;for it is a man that

produces a man, and the seed is not first.

It is out of place, also, to generate place simultaneously

with the mathematical solids (for place is peculiar to the

individual things, and hence they are separate in place ;

20 but mathematical objects are nowhere), and to say that

they must be somewhere, but not say what kind of thing

their place is.

Those who say that existing things come from elements

and that the first of existing things are the numbers, should

have first distinguished the senses in which one thing comes

from another, and then said in which sense number comes

from its first principles.

By intermixture? But (i) not everything is capable of

2 5 intermixture, and (2) that which is produced by it is differ

ent from its elements, and on this view the one will not

remain separate or a distinct entity ;but they want it to

be so.

By juxtaposition, like a syllable? But then(i) the

elements must have position ;and (2) he who thinks of

number will be able to think of the unity and the plurality

apart ;number then will be this a unit and plurality, or the

one and the unequal.

Again, coming from certain things means in one sense

that these are still to be found in the product, and in another

30 that they are not;in which sense does number come from

these elements ? Only things that are generated can come

from elements which are present in them. Does number

come, then, from its elements as from seed ? But nothing

can be excreted from that which is indivisible. Does it

come from its contrary, its contrary not persisting ? But

all things that come in this way come also from something1

Speusippus ;cf. A. io;2

b30-34.



BOOK N. 5 iog2a

else which does persist.1

Since, then, one thinker2

places 35

the i as contrary to plurality, and another3

places it as

contrary to the unequal, treating the i as equal, number iog2b

must be being1

treated as coming from contraries. Thereis, then, something else that persists, from which and from

one contrary the compound is or has come to be. Again,

why in the world do the other things that come from con

traries, or that have contraries, perish (even when all of the

contrary is used to produce them), while number does not ?

Nothing is said about this. Yet whether present or not 5

present in the compound the contrary destroys it, e. g.

strife destroys the mixture 4

(yet it sho2ild not;for it is

not to that that it is contrary).5

Once more, it has not been determined at all in which

way numbers are the causes of substances and of being

whether (i) as boundaries (as points are of spatial magni

tudes). This is how Eurytus decided what was the number 10

of what (e. g. one of man and another of horse), viz. by

imitating the figures of living things6 with pebbles, as

some people bring numbers into the forms of triangle and

square. Or (2) is it because harmony is a ratio of numbers,

and so is man and everything else ? But how are the 15

attributes white and sweet and hot numbers ? Evidently

itis

not the numbers that are the essence or the causes ofthe form

;for the ratio is the essence, while the number is

the matter. E, g. the essence of flesh or bone is number

only in this way, three parts of fire and two of earth .

T

And a number, whatever number it is, is always a number

of certain things, either of parts of fire or earth or of units;

but the essence is that there is so much of one thing to so 20

much of another in the mixture ; and this is no longer

a number but a ratio of mixture of numbers, whether these

are corporeal or of any other kind.

1Cf. A. io69

b3~9, Phys. \. 7.

2

Speusippus.3

Plato.4

Cf. Empedocles, Fr. 17.5 a

I7~b 8 seem to refer mainly to Speusippus.

6

Eurytus may have used (pvrd in this wider sense, as Plato some

times does. The ordinary Aristotelian sense plants would be difficult

here.7

Cf. Empedocles, Fr. 96.

645-28 X 2



io92b METAPHYSICA

Number, then, whether it be number in general or the

number which consists of abstract units, is neither the cause

as agent, nor the matter, nor the ratio and form of things.

25 Nor, of course, is it the final cause.

One might also raise the question what the good is that 6

things get from numbers because their composition is

expressible by a number, either by one which is easily

calculable or by an odd number. For in fact honey-water

is no more wholesome if it is mixed in the proportion of

three times three, but it would do more good if it were in no

particular ratio but well diluted than if it were numerically

3o expressible but strong. Again, the ratios of mixtures are

expressed by the adding of numbers, not by mere numbers;

e. g. it is three parts to two,not three times two . For

in any multiplication the genus of the things multiplied

must be the same;therefore the product 1x2x3 must be

measurable by i, and 4 x 5 x 6 by 4, and therefore all pro

ducts into which the same factor enters must be measur-

35 able by that factor. The number of fire, then, cannot be

2x5x3x6, and at the same time that of water 2x3.IO93

aIf all things must share in number, it must follow that

many things are the same, and the same number must belong

to onething

and to another. Is number the cause, then,

and does the thing exist because of its number, or is this

not certain ? E. g. the motions of the sun have a number,

5and again those of the moon, yes, and the life and prime

of each animal. Why, then, should not some of these

numbers be squares, some cubes, and some equal, others

double ? There is no reason why they should not, and

indeed they must move within these limits, since all things

were assumed to share in number. And it was assumed

that things that differed might fall under the same number.

10 Therefore if the same number had belonged to certain

things, these would have been the same as one another,

since they would have had the same form of number;

e. g.

sun and moon would have been the same. But why need

these numbers be causes ? There are seven vowels, the

scale consists of seven strings, the Pleiades are seven, at



BOOK N. 6 logs3

seven animals lose their teeth (at least some do, though

some do not), and the champions who fought against 15

Thebes were seven. Is it then because the number is the

kind of number it is, that the champions were seven or the

Pleiad consists of seven stars ? Surely the champions were

seven because there were seven gates or for some other

reason, and the Pleiad we count as seven, as we count the

Bear as twelve, while other peoples count more stars in

both. Nay, they even say that E, IF, and Z are concords, 20

and that because there are threeconcords,

the double con

sonants also are three. They quite neglect the fact that

there might be a thousand such letters;for one symbol

might be assigned to PP. But if they say that each of

these three is equal to two of the other letters, and no other

is so, and if the cause is that there are three parts of the

mouth and one letter is in each applied to sigma, it is for

this reason that there are only three, not because the concords are three

;since as a matter of fact the concords are 25

more than three, but of double consonants there cannot be

more. These people are like the old-fashioned Homeric

scholars, who see small resemblances but neglect great

ones. Some say that there are many such cases, e. g. that

the middle strings are represented by nine and eight1

,and 30

that the epic verse has seventeen syllables, which is equal

in number to the two strings, and that the scansion is, in

the right"

half of the line nine syllables, and in the left eight. iO93b

And they say that the distance in the letters from alpha to

omega is equal to that from the lowest note of the flute to

the highest, and that the number of this note is equal

to that of the whole choir of heaven. It may be suspected 5

that no one could find difficulty either in stating such

analogies or in finding them in eternal things, since they

can be found even in perishable things.

But the lauded characteristics of numbers, and the con

traries of these, and generally the mathematical relations,

as some describe them, making them causes of nature,

1 The ratios corresponding to the fourth and the fifth are respectively8 to 6 and 9 to 6.

2i. e. first.



io93b METAPHYSICA

10 seem, when we inspect them in this way, to vanish;for

none of them is a cause in any of the senses that have been

distinguished in reference to the first principles.1 In a sense,

however, they makeit

plainthat

goodness belongs to

numbers, and that the odd, the straight, the square, the

potencies of certain numbers, are in the column 2 of the

beautiful. For the seasons and a particular kind of number

15 go together ;and the other agreements that they collect

from the theorems of mathematics all have this meaning.3

Hence they are like coincidences. For they are accidents,

but the things that agree are all appropriate to one another,

and one by analogy. For in each category of being an

analogous term is found as the straight is in length, so is

20 the level in surface, perhaps the odd in number, and the

white in colour.

Again, it is not the ideal numbers that are the causes of

musical phenomena and the like (for equal ideal numbers

differ from one another in form;for even the units do) ;

so

that we need not assume Ideas for this reason at least.

These, then, are the results of the theory, and yet more

25 might be brought together. The fact that our opponents

have much trouble with the generation of numbers and can

in no way make a system of them, seems to indicate that

the objects of mathematics are not separable from sensible

things, as some say, and that they are not the first

principles.

1Cf. A. I, 2.

2Cf. note on A. 986*23.

3Sc. that numerical relations are found in things, but are not the

cause of anything that happens.



INDEX

oa 93b = loooa

a privative, its meanings 22" 32.

Abstraction 36b

3, 23, 6i a29 ;

)( qualification 982a

27, 30* 33,

77b

10.

Accident, accidental A. 30, E. 2, 3,

K.8, 7aI5,2i-

b16, 13

b34-i4

a20,

1 5b

1 7, 1 7a7, 27

b33 ;

not knowable

26b 3, 64b

30, 65a

4 ;its cause

matter 27a

13; twofold 3ib22;

the same by accident 37b 6

;

nothing accidentally perishable

59a

i; )(

essential 65* 6.

Action, concerned with individuals

981* 17 ; )( motion 48b 21.

Actuality (eYepyfia) 0. 6-9, K. 9 ;

)( potency 3a

I, 7b28, 69

b16, 7i

a

6,b 22

;coni. substance, form,

definition, essence 42b

10, 43a18,

25,28, 30, 5<D

a16,

b2, 5i

b3i,7i

a

8; )( matter 43a6, 45

a35 7i

b2i,

76* 10;

differs with different

matter 43a 12

;the actual identi

cal with the potential 45b 21

;coni.

complete reality (eVreXeâa) 47a

30, 5oa 22

; )( knowledge 48b15 ;

)(motion 48

b 28;coni. action 5o

a

22;God s actuality pleasure 72

b

16; actual, syn. individual I4a21.

Aegina I5a25.

Affection, modification, attribute

(rrddos), its meanings A. 21;

)( substance 983b

10, g85b

11,

38b

28, 7ia2; coni. states 986

a

17, 2oa 19; coni. accidents,

movements 98c;b

3, 7ia 2

; )( sub

stratum 49a29 ; essential, proper

4b6, 58

a37,

b22, 78

a16

; changein respect of 69

b12.

Alcmaeon 986a

27.

All (Traira), coni. total 24a

8.

Alteration 989a

27, 42a

36, 69b

12,

88a 32.

Analogy43

a5, 48

a37,

b7,

89

b4,

93b

19; the same by i6b 32, i8a

18-21, 988a

17, 28, 3o-b21,

99ia

1 6, 9a27, i2a 26, 63

b25-30,

b20-32, 7i

b27, 72

a5, 20, 75

b

79b

20, 9ib

ii ; quoted 7

b

25,

9 25, 56b

2

15, 28b 5, 69b3i.

Anaximander 69b 22

;referred to

988a30, 52

b10, 53

b16, 66b 35.

Anaximenes 984a

5 ;referred to

984a27, 988

a30, 996

a9, i

a15,

53b

16.

Antisthenes 24b32 ;

referred to 5b

2-5(?),6a5(?),u

a7(?), I2a 2i;

his school 43b 24.

Appearance (âiveadai, âvraala) Y.

5, 6, 98ob26, 7o

a10. v. Image.

Archytas 43a21.

Aristippus 996a32 ;

referred to 78a

3i-b6.

Aristotle, references to An. Post.

25a

34, 37b8; Phys. 983** 33,

98sa

12, 986b

30, 988a

22, 993*

ii,42b8(?), 49

b36, 59

a34, 62b

3i(?), 73a 32(?), 76a 9, 8 a 23

(?) ;De Caelo 986

aI2(?), 989**

24, 73a

32(?), 86a 23 (?), 88b

24 (?) ;De Gen. et Corr. 42* 8

(?),

62b 3i (?),86a23(?); Met. A.995

b

5, 996b

8, 14, 997b

4, 59a

19 5B -

993a26, 4

a32, 53

b10, 76

bI, 77*

i, 86a 34(?),bi55 A. 26a 34 ,

28a

4,b7, 56

b355 Z.

1 6, 45 a7(?) 5

b

17, 76a

9; H.

494, 52a

15, 55a

2,

4, 18, 20, 43b

32, 49b 27, 53

13, i7, , 26,

Anaxagoras 984a

11-16,b

IS, 985**

, 39a22(?),

45b27, 76

a9; 9. i7 9, 2i a 20,

27b29, 76

a9, 88b 24(?) ;

A. 27a

19, 64a

36; M. 37* i 3 (?), 42a

22 (?), 9oa

15, 28; N. 37a

i 3 (?),

42a 22 (?), 86

a30 ;

Eth. Nic. 98 ib

25 ;lost works 986

a 12 (?), 4a

2,b

34, 2i a20(?), 54

a30, 6i a

15.

Arithmetic 982a28, 5

a31, 9o

a14 ;

arithmetical number 83b 16.

Art 98ob 28

;comes by experience

98ia3; )( science 98i

b 26; )( ex-



INDEX

perience 981* 25,b8, 31 ; genera

tion by nature, art, spontaneityZ. 7-9, 7o

a6, 17; by reason, art,

faculty 25b 22

;

= form 34a24, 70*

15; comes by learning 46b37, 47

b

33;

architectonic arts 13* 14.

Assertion, syn. affirmation 8a 4-b

i,

62a 24 ; )( affirmation, syn. con

tact 5ib24.

Associable numbers M. 6-8.b

33, 997 16, 35,

2.

Astronomy 98gb

998a

5, 53a 10

Athens iob 10.

Atlas 23a 20.

Atomists referred to 28b 5, 84b

27.

Attribute )( substance 995b 20, 3 a 25.

v. Affection.

Axioms 26, 5a20,

b33, 90* 36.

Beautiful, syn. good I3a22, 9i

a31 ;

)( good 78* 3i-b

5 ;an original

principle 72b32.

Becoming, .v. Generation.

Being (ov) A. 7, I9a

4, 28a lo, 3oa

j

21, 42b25, 45

b32, 6i a

8, 78a

30,j

89a7 ;

not a genus 998b 22, 45 b 6;

and unity I. 2, 986b

15, 9g8b

22,

ia5-

bi, 3

b22, 4o

bi6, 45

b6, 53

b

25 ; being qua being, in general,

without qualification )( particu

lar being r. i -2, E. i,6ob 3 1

;acci

dental being E. 2, 3, I7a7 ; being

as truth E. 4, e. 10, 65a 21

;in

full sense 27b

31, 5ib

i; primary

being,substance 28a

14, 30; beingof a thing 29a22, $2

b11, 75

b5 ;

being not the substance of things

ia5~

bi, 4o

b1 8

; completely real

)(material 78

a30; non-being is

non-being 3b 10

; subject of so

phistic 26b 14 ;as falsity E. 4, 0.

lo;source of becoming 62b 26,

69b

1 8;three kinds 69

b27 ;

am

biguous 89a

1 6; proof of its reality

(Platonists) 89a

2.

Between, v. Intermediate.

Broad and narrow (Platonists) 992a

12, 88b 8.

Callias 981* 8, 33b

24, 34a6.

Callippus 73b

32.

Categories 4a

29, 1 7a

23, 24b

13,

26a 36,27b3i, 28a

13, 33, 29*23,

34b

10, 5ia35, 55

ai, s8

a14, 7o

b

i, 88* 23, 89a

27,b24.

Cause A. 2, I3a

16, 26a 17 ; philo

sophy a study of first causes 98ib

28;of all causes ? 995

b6, 996

a

1 8; primary g83

a25, 3

a31 ;

proximate 44b

i;four causes 983

a

26, 7ob 26

;formal = final 44

bI

;

= efficient 7ob 26

;causes not

infinite in number a. 2, 74a

29;

cause of accident accidental 27a

8, 65a 6

; generable without being

generated E. 3. v. End, Essence,

Final, Form, Formula, Matter,

Motive, Principle.

Change, by something to something

984a

22, 69b

36 ;from opposite

to opposite or intermediate n b

34, 57a

21, 31, 69b3; contraries

do not change 69b 7 ; coni. non-being, substratum, matter, potency ioa 15, 42

a33, 69

b14, 24;

four kinds 42a32, 69

b9, cf. 72

b8

;

changeable substance 69* 3.

Complete A. 16, 23a34 ;

def. 55a

1 1;

said to proceed from incomplete

72b34, 92

a13.

Compound,composite (o-vvOfros) 23a

31,b

i, 29b

23, 43a

30, 75a

8, 88b

15-

Concrete (o-^oXo?) 995b35, 999

a33,

29a

5, 35b22, 37

a26, 30, 77

b8.

Contact 2a 34, I4b

22, 68b 27, 7oa

10, 82a20, 85

a3 ;

coni. intuitive

thought 5ib

24, 72b 21.

Contiguous 69a

i.

Continuous, def. 69a

5 ; by nature,

art, force i6 a 4, 23b34, 4o

b15 ;

in

one,two,

three dimensions 6i a

33;continuity )( form l6b 9.

Contradiction, law of F. 3-6, K.5,

6;no intermediate r. 7, 55

bj,

69* 35 )( privation, contrariety

55a38-

Contrary I. 4, 5, 7, i3b

12, i8a 25,

54a25,

b31, 58

b26, 92

a 2;con

traries said to be principles of

being 986a22,

bi, 4

b30, 7s

a28,

87

a

30;

knowledge of them one996

a20, 6i a

19, 78b26; reducible

to one principle 4a

i,b27; con

trariety )( difference, otherness,

contradiction, privation, 4a20, 54

b

32, 55b

I;one of two contraries

always privative 4b

27, n b18,

55b

14, 27, 6i a19, 63

b17; con

traries incompatible n b17, 63

b

26;coni. negation I2a g ;

contra

riety in substance i8b 3 ; contraries have same form 32

b2

;not

produced from, compounded of,



INDEX

affected by one another 44b2

5, 57b

22, 69^ 7, 75a30; contrariety

=

greatest, complete, difference 5 5a

4, 1 6, 58* II;one term one con

trary 55

a

19;contraries relative

56b

36 ;intermediate composed

of contraries I. 7 ;which contra

rieties make difference of speciesT. 9 ; prime contrarieties in being6i a

12,b

5, 13 ;sensible con

trarieties 6i a32 ;

in place 68b 30 ;

)( opposite 69b4 ;

contraries in

volve matter 75b22, 87

bi.

Coriscus I5b17-32, 26b 18, 37

a7.

Counter-earth 86* 12.

v) 3<D

bCoupled term

(a-v

1 6, 3ia

6, 43a

4-

Cratylus 987a32, loa 12.

Definition (6piarp.6st opos) Z. 10-12,

H.6, 3ia2, 43

a 21; starting-point

of discussion I2a 22,b7; coni.

essence 3oa

7, 3ian, 44

aI

;not

of the concrete and sensible 36a

2, 39b28 ; of the universal 36

a28;

why one Z. 12, H. 6; definition|

by division 37b 28

;scientific 39

b

32 ;no Idea definable 4O

a 8;

coni. number 43b

34, 45a

7. v.

Formula.

Democritus 5-20, 9a27,

b n

Dialectic 32, 23, 4 17,

J5> 39 9? 42 II, 09 22, 78 20;

referred to 29b 21.

Demonstration 992b31 ; principles

of993b 28, 996b 26, 5b 9, ii, 13,

18, 22, 62a 3 ;not everything de

monstrable 997a

7, 6a 8, iia13;

essence not demonstrable 25b14,

64a

9 ;sensible things not de

monstrable 39b 28

;demonstra

tion of necessary truths 39b31 ;

absolute and ad hominem 62* 2;

demonstrative science 997a5-30.

Destructible, destruction, perish

able 994b 6, oa 6, 22, 27, b25, 27 a

29, 42a30, 43

b15, 44

b36, 59

ai,

67b24, 69

a31,

bu, 7o

a15.

Differentia, difference 985b

13,

23, 4a

14, 2oa 33, 35,b

2, 15,

42b

15, 58a

7; its meanings i8a

12; )( otherness, contrariety 4

a

21, 54b

23, 55a

4, 1 6, 58* u ; j

opposite, prior, contrary differen

tiae i6a

25, 57b

5,ii

; generic,

specific i8a 26, 54b 28

;kinds of

42b

32; definition by 43* 19;

what makes it I. 9 ;matter does

not make it 58b6; first differ

ences 6i b 14; of numbers, units

M. 8;

three differences

(Democritus) 985

b13, 42

b 12.

Diogenes 984a

5 ;referred to 996

a

8, ia

15.

Dionysia 23b 10.

Disposition A. 19.

Divine, the 26a 20, 64* 37 ;not

jealous 983a 2

;encloses the uni

verse 74b3 ;

visible divine bodies

26* 1 8;

the divinest knowledge

9?3a

5-

Division, mathematical 994b

23, 2a

19,b

3, 10, 48b

1 6, 6ob 14, 19;

logical 37b 28.

Dyad (two), indefinite 987b

26, 33,

988a

13, 8i a14, 22,

b21, 32, 82 a

I3,b

3o, 83b36, 8 5

b7, 87

b7, 88b

28, 89a35, 9i

a5 ;

ideal 36b14, 8ia

23,b27, 82b

9, 12, 20, 22;the

first number 999a8, 85

b10, 88 b

9.

29, 986b

Egypt 98ib

23.

Eleatics referred to

10, 28b 4, 75b

15.

Element A. 3, M. 10, 989* 4, 992b

18,

ia

1 8, 59b23, 88

b4 ;

whether only

potential 2 b 33 ;coni. principle,

four elements (Empedocles) 984a

8, 985a32, 998

a30 ;

of Ideas 987b

19.

Empedocles 984a

8, 985** 2-10,

2i-b 4, 988a

1 6, 27, 989a20-30,

993a

17, 996a

8, 998* 30,a24-

b20, i

a12, 69

b21, 72

a6, 75

b2,

9ib ii

; quoted oa 29,b

2, 6, 14,

9b

17, I4b

37 ;referred to 984

b

5, 994a

7, 4b

33, 28 b5, 5o

b24,

53b

15, 92b

7-

End, syn. final cause 994b

9, 16,

3a

33, 59a 37, 74a 3; c ni -

shape 23a

34 ;coni. actuality

5ia

1 6.

Epicharmus ioa 6, 86a 16.

Equal, def. 2i a12, 56

a22, 82b 7 ;

how opposed to great and small

I. 5 ; syn. one (Plato) 75a33.

Equivocal, equivocation 3a

34, 3oa

32, 35b

25, 46a6, 6ob 33, 86b 27.

Eristic I2a 19.

Error )( ignorance 52a 2.

Essence( rjv flvai) Z. 4-6, 8, 993*

1 8, 994bi7,25

b28,3S

bi4, 45

b3J



INDEX

coni. definition 3Oa 6

;coni. form

33b

5-

Eternal 987b

16, I5b

14, 5ob

7, 51*

20;eternal sensible substance 69

a

3i,b25; necessity of an eternal

substance A. 6 ; time eternal

7ib

7; eternal things, whether

composite 8bb 14 ; ungenerated

9ia

12.

Eudoxus 99ia

17, 73b

17, 79b

21.

Eurytus 92b 10.

Even (Pythagoreans) 986* 18, 99oa

9; (Plato) 9ia24.

Evenus I5a29.

Evil, none apart from particular

bad things 5i a 17; none amongeternal things 5i

a20; said to be

a first principle 75a

35, 9ib34 ;

caused by strife (Empedocles)

984b32.

Excess and defect 992b

6, 4b

12,

42b

25, 35, 52b30, 57

a13, 8;

b18.

Experience 98ob 28

;coni. science,

art 98ia

I,b

31 ;

=knowledge

of individual facts

g8i

a

15.

Falsity, def. n b25; its meanings,

A. 29; non-being in sense of

falsity E. 4, e. 10; )( impossi

bility 47b

14; a first principle

(Plato) 89a

20.

Female sex, coni. matter 24a

35 ;

not a species I. 9.

Final cause (ov eWa) 31, 994

9, I3

a

2i, 33,

b

26, 44a

36, 5

a

8,

59a36, 72

b2. v. .Z^/.

First, its meanings 28a 31. v.

Primary.

Form, things referred to by namingtheir form 35

a8

;more real than,

cause of, matter 29a

5 ;coni.

essence 32b

I, 33b

5, 35b32 ; syn.

shape 999b

16, i5a

5, i7b25, 33

b

5, 44b22, 52

a23, 6oa 22,

b 26;

=

art 34a 24, 7oa 15 ; not generated

34b

7, 42a

30, 4 3b

17, 44b

21,

69b

35, 7oa15; coni. definition,

formula i6b 9, 35a21, 36

a28,

b5,

42a28, 43

a19, 44

b12, 69

b33, 84

b

10; syn. substance 32

bi, 4i

b8,

5ob

2, 84b 10

;

= final cause 44b

i; = efficient 7ob30 ; syn. posi

tive state 44b

33 ; )( becoming

5oa4 ; )( matter 5o

a15, 7o

ai,

84b 10; )( privation 44b 33, 7ob

11;

its parts Z. 10, 11. v. Shape,

Species.

Forms (Platonic), v. Ideas.

Formula, definition, account (\6yos)

987b

31, i6a 33,b

9, 28a 34,42*

28, 43aI9,47

b34> 5

b33 I prin

ciples in the 996a

I;formula of

the essence is one 998b 12; )(

word 6b i, 3oa

7 ;formula )(

definition (opio-^os-j 3oa

7, 14, 37b

II; parts of Z. 10, n, i6a 35,

23b

23, 33a

2; prior in i8b 31,

28a 3 2, 38b27,49

bii, 54

a28,77

b

i, 78a 10

; )(concrete individual,

matter 39b

20, 58b

10, 18, 64a23,

74a

34 ; separable in 42a

29 ;

coni. science 46b

7, 59b 26

;

analysis of 63b 18;cause as de

finition 7oa 22

; primary in de

finition, in time &4b

15 ;one in

definition, in number 87b

12.( From

,its meanings A. 24, 99i

a19,

994a22, 44

a23, 92

a23.

Full (Democritus) 985b

5, 9a28.

Generation, production, becoming,is of the concrete

thingZ.

8, 98ia

17, 34b

7, 42a

30, 43b

17, 44b

2i,

69b

35* ?oa

5; posterior in

generation, prior in nature, form,

substance 9&9a

15, 5oa4, 77

a 26;

two types 994a 22

;from non-

being, matter, privation, con

traries, the potential 994a27, 32*

20, 33a

9> 55bn,62

b26, 69

b18,

88b 17, 9ib

34; of something

from something by something999

b6, ioa 20, 3 2

a13,

b3i, 33

a

24, 44b24, 49

b 28; by nature, art,

spontaneity Z. 7, 9 ; )( making 32a

26; the product must be divisible

33b

12, 49b

35; from a memberof the same species 34

a21, 49

b

29, 7oa

5 ;absolute and partial

42b

7, 67b22, 69

b10, 88 a

33.

Genus A. 28, 54b

30, 57a

27,b

38,

59 b 27; proximate, ultimate 995 b

29, 998b

15, 999a

31, 23a

27,

34a

I, 37b

3<^ 59b27; whether

genera are first principles 998a

21, I4b

11, 42a

14, 69a

27;

part of species 23b

24 ;coni.

definition, differentia, species Z.

12, 998b

5, i3-999a

23, Mb9,

i6ft

24,b

32, 23a27,

b18, 37

b19,

39a

26, 54b

27, 57b

7, 59b36 ;

being and unity not genera 998b

22, 45b 6

;is matter of species

24b

8, 38a

6; other in genus



INDEX

24b9; )( universal 28b 34; not

substantial Z. 13, 42* 21, 53b 21

;

otherness of the genus $8a

7.

Geometry 983* 20, 992a

21, 997b

27, 998a

i, 5a

ii, 31, 5ia

21, 6ib

3, 78a25, 89

a 22.

God, a first principle 983a 8

;is life

72b

14 ;identified with the One

by Xenophanes 986b

24 ; godsin human form 997

b10, 74

b5 ;

the

stars held to be gods 74b

2.

Good, syn. final cause 983a

31,

59a

36; syn. beautiful I3a

22,

91a30 ; )( apparent good I3

b27 ;

how a first principle 75a 12, 38 ;

)( beautiful 78a

31; whether

discussed by mathematics 78a3 1

;

how related to first principles

9ia30, 92^ 9 ;

Idea of 996a

28.

Great and small, how opposed to

equal I.5 ; (Plato) 987

b20, 26,

988* 26, 992a

12, 998b

10, 83b23,

32 ;kinds of 992

an, 85

a9.

Habit, having, state (cgis) A. 20,

986* 17, I5b

34, 44b

32, 46a

13,

70a 12

; )( privation 55b13.

Harmonics 997b

21, 77* 5, 78* 14.

Have, hold, its meanings A. 23.

Hearing 98ob

23.

Heaven, only one 74a31.

Hellen24a33.

Hellenes 24a33.

Heraclidae 58a24.

Heraclitus 984a

7, 987a33, 5

b25,

ioa ii, 13, I2a 24, 34, 62a 32,63b

24, 78b

14; referred to 984a27,

989a

2, 996a

8, ia

15.

Hermes 2a 22, I7b

7, 48a33, 5o

a

20.

Hermotimus 94b19.

Hesiod g84b

23, 989a

10, oa 9 ;re

ferred to 983b27, 23

a19, 9i

b 6;

quoted 984

b

27.Hippasus 984

a7 ;

referred to 996a

8, ia

15.

Hippo 984a

3.

Homer 9b

28; quoted 76a4; re

ferred to 983b30, 9t

b 6;Homeric

scholars 95a27.

Homoeomerous 984a

14.

Hot, the (Parmenides) 987** I.

Hypothesis )( necessary principle

5

b

IS-

Ideas (Platonic) A. 6, 9, B.6, Z. 6,

M, M. 4, 5, 988b

i,997b

2, ia

4,

28b 20, 33b

27, 36b

13, 42a

ii,

59a

10, 7oa

27, 73a

I7 75b

18,

76a3 i,83

b34, 86a 31,

b14, 9

a

16,b20, 9i

b 28;elements of 987

b

19; of negations 99ob

13, 79a

9 ;

of relations 99ob

16, 79a12; of

manufactured objects 99 ib

6, 6ob

28, 7oa

14 ;coni. numbers 99 i

b

9, 76a20, 8ob 12, 22,8i

a21, 83

b

3, 86a 4, 88b 34, 9b

33, 35, 9ib

26; participate 99o

b28, 40* 27 ;

eternal sensibles 997b

12; as

causes 33b 26

;how related 39

b

4 ;indefinable 4o

a 8;transcen

dent 40a 9, 86a 33 ; universal 42a

15, 86a 33 .

Ignorance )( falsity, error 52a2.

Iliad, an artificial unity 3Oa

9,b9

45a

13-/

Image (fyavraa p.o) 99ob

14, 79a

ii.

v. Appearance.Imitation (Pythagoreans) 987

b n.

Imperishable I. 10, 4ob3i.

Impossible I9b 22

; )(false 47

b14.

In ,its meanings 23a 24.

Inassociable numbers M. 6-8.

Incapacity, impotence, its mean

ings I9b

15, 46a29.

Incomposite entities 5ib

17, 27.

Increase 42a

35 ; )( diminution

6o.bn, 88a 31.

Individual (aro^12

; (naff eKaarov acton con

cerned with individuals 98 ia

17 ;

is there anything apart from

individuals ? 999a

26, 6oa 3 ; syn.

numerically one 999b

33 ;are

the first principles individual ?

M. 10, 3a

7, 7ia20; syn. actual

I4a 21

; prior in order of perception i8b 33- v. This.

Indivisible (udiaipeTov) I. i;

in

quantity, in kind 999a

2, i4a27,

l6a

19,

21;

(iiTOfjiov) lines, magnitudes 992a

22, 83b

13, 84b

i;

species, form 998b

29, 34a

8,

58a

18; indivisible in genusi8b 6.

Induction )( demonstration, defini

tion 992b

33, 48a

36 ;used 25

b

15, 54b33, 55

a6,

b17, 5

a9 64*

9 ;Socratic 78

b28.

Infinite, the a. 2, K. 10;as sub

stance and principle 987

a

16,

995b

29,

9, 4b33 ; composed of great and

small 987b 26

;causes not infinite

in number a. 2, 74* 29 ;not



INDEX

thinkable 994b

22, 30, 999a

27 ;

by addition 994b30 ;

how potential 48

b9 ; has no separate exis

tence 48b14 ;

infinite regress 994a

3, 8, 20,b

4, ob 28, 6a 9, ica 22,

I2a

12,b

22, 22b

9, 30b

35, 32*

3, 33b

4, 41b

22, 6oa 36, 7oa

2,

74a

29; no infinite magnitude

73a

10; whether number is in

finite 83b

36 ; principles infinite

in number (Anaxagoras) 984a

13.

Intelligible )( sensible 99oa

31,

999b

2, 36a

3, 10, 45* 34.

Intermediate, def. 57a

21, 68b 27;no intermediate between contra

dictories r. 7, 55 b i, 69a 3 ; composed of contraries 1. 7 ; (Plato)

987b

1 6.

Intuition (vorjo-is), coni. perception,

definition 36* 6. v. Thinking.Ion 24

a34.

lonians 24a33.

Italian school 987a

10-31, 988a26.

Itself, used to signify Ideas 4ob34.

|

Knowledge, science (eVaa-T^/), de-j

sired by all 98oa 21

; springs i

from sensation o.8oa 28

; )( artj

98 ib 26

; theoretical, productive,j

practical 982a

i, 993b

20, 25b

21,

46b

3 ; pure, applied, superior,

ancillary o,S2a

14, 30,b

4, 27,

996b 10

;its highest object 982

b

I, 996b

13; the divinest know

ledge 983

a

5 ; is of causes 983a

25, 993b

23, 994b

29, 25b 6

;not

of the sensible or accidental Z. 15,

987a

34, 26b 3, 27a

20, 64b

30,

65a

5, 77b35 ; knowledge of con

traries one 996a

20, 6i a19, 78

b

26;

is of species, form 998b

7,

3ib

6; )( sensation 999b

3; of

universals, individuals 3a

14, 59b

26, 6ob20, 86b 6, 87

a15 ;

one

science to one genus 3b n, 55 a

31 ; )( opinion 8b 27, 30, 39b32 ;

prior in l8b 30, 28a 32 ;ratio-

cinative 25b 6

;not of matter

36a 8 ;

coni. definition, formula

28a32, 46

b7, 59

b 26; )( actuality

48b

15 ;how a measure of ob

jects 57a

9 ;its two meanings

87a

15-

Leucippus 985b 4, y

referred to 84b

27.

Libya iob u.

32, 72 a7;

Like, def. i8a 15, 2i a11, 54

b3;

said to be known by like ob5.

Limit, its meanings A. 17; of bodies

2b 10, 6ob 16; (Pythagoreans)

987a

15, 99oa

8, 4b

32.

Line 2a

5, i6b

26, 36b 12, 43a33;

perceptible lines 998a

i;not com

posed of points ib18

;indivisible

line9p2

a22, 84

bi.

Logic (dva\VTid) 5b

4.

Love (epos) (Parmenides) 984b

24,

988a

34; ((piXia, (j>i\oTr)s) (Em-

pedocles) g85a

3, 24, 988a

33,

ob n.

Luck (TVXI) 98ia

5, 984b

14, 32a29,

5-a 30- generation by nature, art,

spontaneity, luck Z. 7, 49a

3,

7oa

6.

Lycophron 45b

10.

Magi 9ib

10.

Making )( production 32a

26; )(

thinking 32b

15.

Male and female I. 9.

Many)( one I. 3, 6

; )( much56

b

15 ;matter of the one 75

a33;

and few (Platonists) 87b

16.

Mathematics 98ib23,985

b24, 992

a

32, 996a29,4

a9, 26a 7, 9, 12, 19,

6i a28,

b32, 64

a32, 77

bi,78

a33;

mathematical objects )( sensible

989b32, 99o

a15, 36

a4l )( Ideas

B. 6, 28b 20, 76* 20, 83a23, 9o

b

26; many of one species 2b 14;

whether substances M. 1-3, 42

a

n, 69a35 ;

not separable 59b13;

mathematical matter 992b

2, 59b

16; language 995a

6, 8ob 26;

parts of mathematics 4a

7 ;

mathematical sciences )( productive 64

ai

;mathematical number

M. 6, 76a20, 86a 5.

Matter H.3, 4, 983* 7-94

a18, I5

a

7, I7a

5, 42a

26, 58b

6, 14; def.

29a 20 , syn. substratum 983 a 29,

985b

10, 988au, 992

bi, 22a

18,

24b8,42

a26, 32,

b9, 6i

b22, 7o

an;

a principle 983b7,986

a17,46* 23 ;

)( definition, form, complete re

ality, actuality 986b

20, 29a

5,

35a

8, 38b6,4i

b7, 43

a6, 45

a35,

5oa

15, 7oa

i, 7ib

21, 74a34, 76

a

9, 78a30, 84

b9 ;

coni. female sex

24a35 I genus matter of species

24b 8, 38a 6;coni. motion 26a 3;

cause of accident 27a13 ;

whether

substance Z. 3, 42a27, 49

a36, 77

a



INDEX

36 ; necessary, to explain generation and change 32* 17, 42* 32,

44b27, 69

b3 ;

unknowable in it

self 36* 8; perceptible )( intelli

gible36*

9,b

35, 45

a

34;

indefi

nite 37a27, 49

bi

;coni. potency

39b

29, 42* 27,b

9, 49a23, 50*

15, 6oa 20, 69b

14, 7obI2,7i

a10,

88b i, 92a

3; indestructible 42*

30 ;matter for locomotion, gene

ration, &c. 42a

34,b

6, 69b 26

;

actuality varies with it 43a 12

;

proximate matter 44a17; )( sub

stratum 44b9 ; proximate matter

=shape 45

b 18;

of mathematical

objects 992b

2, 59b 16

;different

things have different matter 69b

25 ;individual in appearance 7o

a

10;involved in contraries 75

b

22, 87b

i.

Measure, def. of unity $2b

18, 87b

33 ; exact, homogeneous with

thing measured, indivisible 52b

36 ) 53a

25, 88a2; how know

ledge is a measure 57a

9 ;

manthe measure of all things (Prota

goras) 53a36, 62b 14, 19, 63

a4.

Megaric school 46b29; referred to

5b35 (?).

Melissus 986b

19.

Memory 98oa

29.

Middle, excluded r. 7.

Mixture, intermixture 989b

2, 42b

29, 82a 2i, 92a

24.

Monists 986b 21.

Motion, spatial (< >pa) 6gb

12, 26,

72b

5 ;the first kind of change

72b

8, 73a12; simple 73

a29 ;

of

the planets A. 8.

Motive cause A. 3, 4, 983a30, 984

a

27, 988b

27, 996b

6, I3b9,24;

necessity of 991b

5, 8oa 4 ; priorto the moved iob 37, 7o

a 21;

unmoved prime mover A. 7, i2 b

31 ;fire a motive cause 984b 6;

the self-mover (Plato) 72a

i.

Movement(KIVTJO-IS), coni. sensation,

matter 989b

32, 26a 3, 36b29 ;

)( rest 4b

29, ioa 36, I2b 23, 25b

20, 49b

7 ;coni. activity, action

20b 20, 22a7,

b5, 23

a 18;coni.

nature 25b 20

; )( action 48b 18

;

)( actuality 48b

28; eternal 7ib

7, 33 ; simple, continuous, un

resting, uniform movement 53a

9, 7ib

9, 72a2i,78

a13.

Music of the spheres gS6&

2, 93b

4.

Mutilated A. 27.

Myth 982b

18, 983b29,995

a4, oa

9,

I8,7ib27,74

bi,4,75

b26,9i

a34.

Nature,

its

meanings

A. 4 ; )( habit,

spontaneity, luck, thought 98 ib4,

32a

12, 65a

27, 7ob

30, 7ib

35 ;

)( generation 989** 15 ;not the

whole of reality 5a

34 ; syn.

matter I4b

33, 24a4; )( force I5

b

15, 52a23, 7i

b35 ;

= that which

contains its principle of motion

in itself I4b

18, 25b

20, 49b

8,

7oa

7; by nature )( to us 29b

7 )(art

32

a

12, 7o

a

7, 17;syn. form, complete reality, posi

tive state 32a

24, 44a

9, 7oa

1 1;

the only substance in destructible

things 43b23 ; )( potency 49

b 8;

natural objects,bodies, substances

I4b

19, 32, 28b 10, 42a

7, 7oa

5,

90a32 ; )(

unnatural 33b33.

Necessity, def. 6b 32 ;its meanings

26b 28, 64b

33 ; necessary, its

meanings A. 5, 72b

II ; )( usual,accidental 25

a15, 1

8, 20, 26b 28,

27b

8, 64b33-65

a3 ; objects of

demonstration necessary truths

39b

3i-

Negation )( privation 4a12; coni.

contrariety 1 2a9, 46

b13; privative

negation 56a

17, 29 ;Ideas of

negation 99ob

13, 79a10.

Nemean games i8b 18.

Non-rational potencies 46b 2, 48a

4, 5b

33-

Number M. 6-9, N. 1-3, 5, 6, 2Oa 13,

39ai2, 53

a3o, 57

a3,85

b22,8S

a5;

numerical ratio 985b32, 99i

b13,

J7>

J 9, 993a

i7>ib3o, 53

ai6,6i

bi,

92b

14, 31 ;said to be limited by

ten 986a9, 73

a20, 84

a12, 32; ele

ments, attributes, generation of

number 986a17, 4

b10, 84

a3,

b28,

87 b 15, 89b 12, 9oa 2i, 9i a 23, 29 ;

numbers as principles, substances

985b

26, 986a

16, 987a19,

b24, i

a

25,b26, 36

bI2,76

a3i, 8oa 13, 83

a

23, 9oa

4, 23, 92b

16, 26; primenumbers 987*^34, 52

a8, 8i a

5; sen

sible )( intelligible, ideal 99oa31,

9ob36 ;

coni. Ideas 99 ib

9, 76a20,

8ob 12, 22, 8i a7, 21, 83

b3, 86a 6,

88b 34,9oa

1 6,b33, 37, 9 i

b26;

wherein does its unity consist?

992a

i, 44a

3, 45a8; numerical

unity 999b26, 33, i6b 31, i8a 13,



INDEX

33b3i,39

a28, 54

a34, 6ob 29 , 87

b

12: unity the origin and measure

of number i6b 18, 2i a13, 52

b24,

88a 6; quality, differentia of number M. 6-8, 2o b

3; coni. definition

43

b

34, 45

a

8 ; associable )( in-associable M. 6-8 : mathematical,arithmetical number 76

a20, 8oa

21, 30,b

13, 8ia

6, 83b

3, 16, 86a

5, 9b33i 35, 9i

b24 ;

related as

prior and posterior, 8ob 1 2;num

ber composed of abstract units

Sob 19, 30, 82 b6, 83

b17, 92

b

20 infinite or finite ? 83b

36 ;

powers of two 84* 6; )( definition

87b 12; one not a number 88a6

;numerical succession 85

a4 ;

square, cube 93a

7.

Ocean 983b30, 9i

b6.

Odd (Pythagoreans) 986a

1 8, 99oa

9, 9la23.

One I. 1-3 ;its meanings A. 6, 52

a

15; one over many 99<D

b7, 13,

99la

2, 4ob29; unity and being

I. 2, 998b 22, i a5, 3 b 22, 4ob 16,

45b 6

;not a genus 998

b22, 45

b

6;= indivisible 999

a2, 4i

a19;

in quantity, species, number, ge

nus, by analogy 999a

2,b

25, 32,

I6b 3 i, i8a i 3 , 33b3 i, 39

a28, 54

a

34, 6ob 29, 87b 12

; unity of common reference, of succession, of

common predicability, of signifi

cance3

a

33,5a

10, 6b

15;one in

continuity, form, definition i6b 9;

origin and measure of numberi6b 18, 52

b24 ;

the one not sub

stance I. 2, 4ob

1 8; unity of num

ber and of definition Z. 12, H. 6,

992a

i, 44a3 ;

the one a measure

52b

1 8, 87b33 ;

one and many I.

3, 6, 87b

28; )( simple 72a32;

the many, matter of the one 75a

33 ; one by contact, intermixture,&c. 82a 20; primary one 83

a25; in

what sense a starting-point 84b

1 8; one in definition, in number 87b

J2; i not a number 88a 6; (Pytha

goreans) 986a

19, 987a

1 8, 27, ia

10; (Eleatics) 986

b15, i

a33;

(Plato) M. and N. passim, 987"^

21, 992a

8, ius; (Anaxagoras)

989 17.

Opinion )( knowledge 8b 28, 30,

39b

33-

Opposition, its kinds A. 10, 54a

23,

14,b

5,

i 55a38,57

a33;changetoopposites

n b34, 57

a3i 69

b4; opposite

differentia i6a 25 ; potency of

opposites 5ob

8, 30; opposite )(

contrary 69b

4.

Order 984b

17, 985

b

14 ; not in substance 38

a33.

Orphic cosmogony referred to 9ib

5.

Other, def. i8a 9 ;its meanings 54

b

14 ;in species 1. 8, 9, i8a 38 ;

in

genus 24 9 ;otherness of the ge

nus 58a7 ;

otherness )( difference

54b23; (Pythagoreans) 87

b 26.

Parmenides 984b

3, 986biS~987

a2,

l a 32 ; quoted 984b 25, 9b 21, 89a

3 ;referred to 4

b32.

Part, its meanings A. 25, 34b32 ;

parts of definition, of concrete

thing Z. 10, ii.

I Participation 987b

13,

30a

13, 3ib

i8, 37bi8/45

ai8,

b8,

79b

1 8;Ideas participable 99O

b

28, 40a27, 79

a25.

Pauson 5oa

20.

Perceptible, v. Settsible.

Perception, v. Sensation.

Perishable, v. Destructible.

Persian war i8b 16.

Petitio principii 6a 17, 20.

Pherecydes 9ib

9.

Philosophy is knowledge desirable

for its own sake, most accurate,

communicable, most divine and

honourable A. 2;

starts from

wonder 982b

12; turned into

mathematics 992a32 ;

is know

ledge of the truth 993b 20

;treats

of the axioms r. 3, K. 4, 995b 8

;

treats of being as being r. i, 2,

K. 3 ;has distinct parts 4

a2, 26a

18; )( dialectic, sophistic 4b17 ;

theoretical, practical, &c. E. i;

first philosophy 26a24 ;

the philo

sopher fond of myth 982b

18 ; canspeculate about anything 4

a34.

Phrynis 993b

16.

I Physics, natural philosophy, philo

sophers 986b

14, 989b3o, 99o

a3,

7,992b4,995

ai8,i

ai2,s

a31, 34,

bi, 6a 2, 25

b19, 26, 26a 4, 12,

37a

14, 1 6, 59b

1 6, 6i b6, 28, 62b

22, 26,

7 8b19

Place 92a i7; changeof42 a 34,69b i3.

i Planets A. 8.

Plato A. 6, 9, 988a

26, 990* 30, 996a

36, 7ib

27, 75b

27,



INDEX

6, ia

9, I9a

4, 28b 19, 53b

13, 83a

32 : referred to Z. 14, M. and N.

passim (esp. 76a

19, 77an, 8ob

11, 24, 8i a24, 84

a13, 85

a9,

b7,

86a ii, 87b

5, 13, 9ia

i,b35,92

b

i), 983b

27, 995b

16, 997b i,

998b

9, ib

19, 2a ii,b

13, i7b

19,

28b 19, 3oa26, 3i

a30, 33

b19, 34

a

2, 36b

14, 39a 26 -b 19, 5o

b35,

5ia

17-21, 59a

10,b

3, 6ob 6,

69a34, 7o

a27, 7i

b15, 73

a17, 20,

75b

19-28 ;his works quoted,

Hippias Mi?ior 25a6, Laws 72

a

I (?), Phaedo 99 ib3, 8o

a2, Phae-

drus72

aI

(?), Republic 992*33, Sophistes 26b 14, 64

b29,

89a

20, Theaetetus lob 12, 7Y-

maeus 57b

8, 7ib32, 72

a2, 92

ai.

Platonists referred to M. and N.

passim, 99ob

9, 997b

3, 998a

7,

2b 14, 4b

32, 28b 24, 3ia

31, 36b

13, 4ob

2, 43b34, 45

a16, 5o

b35,

56a

10, 66a ii, 6ga26, 75

a32.

Plurality 57a

3, 87b

6, 9ib34; def.

2o

a

8, 54

a

22; )( unity 4

a

10, 87

b

28;

first plurality 85b

9.

Point 992a

19, i6b 26, 6ob 18, 85b

27.

Polus98ia

4.

Polyclitus I3b35~i4

a15.

Position 985 15, i6 b26, 22b 2, 4

b

19, 77b

30.

Possible 0. 4, I9b 28.

Potency, power, potentiality, def. A.

12, 0. 1-9 ; whether the elements j

exist potentially 2b 33; potencyor actuality prior? 0. 8, 3

ai

; )( ac-|

tuality 7b

28, 69b

15, 7ia

6,b23 ;

j

power in geometry I9b

33, 46a7 ;

j

)( reason, art, nature 25*22, 27a

6, 33b

8, 49b

8, 64a

13 ;coni.

matter 42a

27,b

10, 5oa

15, 6oa

21, 14, 7o 12, 7ia

10,

92a

3 ; irrational, rational 0. 2,

47b 3i 5ob 33; the potentialand the actual are one 45

b 21;in

what sense the infinite and the

void exist potentially 48b9 ;

whena thing exists potentially 0. 7

primary potency 49b13 ;

the eter

nal not potential 5ob7 ; potency

is of opposites 5ob

8, 30, 5ia

6,

7ib

19.

Practical knowledge 993b

21, 25b

21, 25.

Primary 3oa

10, 37b

3, 75b24; syn.

self-subsistent3ib14 ;

substance

32b 2

;coni. categories 34

b9. v.

First.

Prime numbers 987b

34.

Principle, beginning, starting-point,

originative source (apx^), its

meanings A. I;material

9>3

b7,

24, 984a

6, 986a

17, 987a4, 46

a

23 ; efficient 984a27, 46

a14,

b3,

49b

6, 7oa7,

b25; final so

a7;

formal 69a28, 76

a24, 8ob 6, 32 ;

God a first principle 983** 8;con

trary principles 986a

22,b

I, 4b

31, 75a

28, 87a30; principles of

demonstration 993b

28, 996b

26,

5

b

9, 11, 13,1

8, 22,6a

5,62 a

3;a first principle necessary a. 2;

whether genera are first princi

ples 998a 21

;whether one in

kind or in number A. 4-5, 999b

24, 6ob 29 ;whether the same for

things perishable and imperishable oa 6

;whether potential or

actual 2b 32 ; whether universal

or individual M. 10, 3a

7, 6ob 20,

6g

a

26-30, 7i

a

20; of being assuch r.

i, E. i;

the simple a

principle 59b34 ; )( element 4i

b

31, 7b23 ;

in what sense unityis a starting-point 84

b18; the

principles, how related to the

good 9ia

30, 92a

ii; infinity of

principles (Anaxagoras) 984a13;

ten (Pythagoreans) 986a 22.

Prior, its meanings A. n;

in

generation, nature 989a

15 ; in

knowledge, definition, perceptionl8b 30 ;

in formula, time, genera

tion, 38b

27 ;in formula, sub

stantiality, time 49b

1 1;in gene

ration, form, substantiality 5Oa4 ;

in definition 54a

28, 78a

9; in

definition, substantiality 77b

i;

no Idea of a class which includes

prior and posterior members

999a 6 ; numbers related as prior

and posterior 8ob 12.

Privation 4a

12, igb

7, 58b27 ;

its

meanings A. 22, 46a

31 ; one of

two contraries privative 4b27, i i

b

1 8, 55b

14, 27, 6i a20, 63

b17 ;

)( state, form I9b

7, 44b

32, 55b

13, 7ob12; primary 46

b14; per

fect 55a

35 ; )( negation, con

trariety 4a

12, 55a33; privative

negation 56a 17, 29.

Production, v. Generation.

Productive knowledge 982* I,b

II,



INDEX

25b

21, 25 ; )( mathematical

64a

i.

Proof, negative (t\eyxos )6a 18.

Protagoras r. 5, 6, K. 6, 998** 3, ;b

22, 47a

6, 53a

35; referred to

999

b

3-

Pythagoreans 985^ 23~986b

8, 987**

13-27, ii, 23, 31, 989 29-990a

29 , 996a

6, ia 10 36*18, 53

bi2,

72b31, 78

b21, 8ob 16, 31, 8s

b 8-

19, 9oa

20-35, 9 ia 1 3) referred

to 99Sb

9, 2a

ii, 4b

31, I 7b

i 9 ,

20, 28 b5, 1 6, 36

b8, 43

b34, 6ob 6,

66au, 75

a36,

b28, 76

a2i, 87

b

I7(?), 26, 9ob

2.

Pythian games i8b

18.

Qua, def. 65b

23.

Quality A. 14, 28a 15, 68b 18; of

number 2ob 3 ;definite 63* 27 ;

change of 6gb 10

; posterior to

quantity 83a n.

Quantum, quantity, A. 13 ;attri

butes of 2oa 19; known by a

measure 52b

20; indefinite 63a

28; change of 69b 10; prior to

quality 83a

1 1;motion and time

incidentally quantitative 2Oa 29.

Ratio (Actyos) 98$b

32, 991b

13, 17,

I9 993a

I7>

ib3, 53

a16, 6i b I,

92 14,31.

Reality, realization, complete (eWe-

AeV") 7b

28; )( matter 38b

6,

78

a

30;

separates 39

a

7; coni.

substance 44a9 ; )( actuality 47

a

30, 5oa

23.

Reason, thought, mind (vovs) A. 7,

9, 7oa

26; in nature 984b

15;human 993

bn, 75

a7; )( art,

faculty 2fj

b 22;acts by contact

72b21; divinest of things 74

b16;

(Anaxagoras) 984b

15, 9&9b

15,

17, 69b3i ; (Parmenides) 9

b23.

Relation A. 15, 56b

34, 89b

6, 14;Ideas of 99o

b16, 79

a 12;rela

tive )( absolute 99ob

20; least

substantial of the categories 88a

22, 30.

Same, the 995b

21, 2ia n

;its

meanings A. 9, 54a32 ;

in speciesi8 b 7, 49

b1 8, 29, 58

a 18; by

accident 37b

6.

Scale 985 b 31, 986a 3 ; seven notesin the scale 93

a14.

Science, v. Knowledge.

Sensation, sense, perception (ai-

[email protected])IOb 32, 63 4 ) (aio OrjO is)

sight our most precious sense

98oa23 ;

sensation the source of

memory 98oa 28

; )(wisdom 98 i

b

10; )( knowledge 999

b

3 ;

not a

physical alteration 9b13 ; special

sensation always true iob 2;con

flict of sensations iob4, ll

a25 ;

coni. intuition 36a

6.

Sensible, perceptible 987a

33, 997b

12, ioa 3, 42a25, 69

a30,

b3, 78

b

16; )(

mathematical 989b

31,

99oa

15 ;no knowledge of sensi

ble things Z. 15, 987a34; )( in

telligible, ideal 99oa

31, 999b

2,

36a

3> 9, 45a

34, 9b

35 5are

there non-sensible substances ?

997a

34, 2 b 12, 59a

39; coni.

movement989" 31, 36

b28; con

trarieties 6i a32.

Sense-organ 63a

2.

Separable, capable of existing apart

I7b25 28, 26a 9, 28a 34,

a b a9, 59" 3>

6oa 8& 7

b30, 86a 33 ;

in formula )( without qualification

42a29 ; actually )(

for knowledge

48b

15.

Separate (verb) 989* 3, 4ob28, 78

b

3 i,86b

4-

Seven (Pythagoreans) 93a

13.

i Shape, coni. end 23a

34 ;coni.

formula 42a 28

;coni. actuality

43a

25, 28, 31;=

proximatematter

45

b

18;

coni. form

999

b

16, I5a

5, i7b

25, 33b

5, 52a22,

6oa 22,b 26.

Sight, the most precious sense

98oa23.

iSimonides 982

b30, 9i

a7.

Simple, coni. necessary I5b

12;

coni. principle 59b

35 ; )( one

72a32 ;

bodies 984* 6; concepts,

substance 2;b

27, 4ib

9, 72a

32 ;

movement 53

a

8, 73

a

29; generation 69

b10, 88a

33.

Snub Z. 5, 25b

31.

Socrates987" 1-4, 78

b17-31, 86b 3.

I Socrates the younger 36b25.

Solon referred to 983a

3.

Sophistic 4b

1 8;

concerned with

non-being 26b 14 ; sophistical

objections 32a6, 49

b33-

i Sophists 996a32, 4

b17, 26b 15.

i

Sophocles I5a 3o.

i Soul, partly falls within scope of

physics 2oa 5 ;substance of living



INDEX

material 10, I, 42b

9,

essence

35b22,

things 35b

14, 43a

35 ;

= its

essence 36a

i, 43b2; )( soulless

things 46a36 ; )( reason, not all

soul can survive death 7oa

26.

Species 998b7 ;

indivisible 9gSb

29, j

34a 8; one in species 999a 2, i6b I

31, i8b 7, 49b

18, 29, s8a 18

; partj

of genus 999a4, 23

b 18. 25; otherj

in species I. 8, 9, i8a

38, 54b 28

;I

genus part of species 23b

24 ;

genus matter of species 24b

8, 38a

6; species composed of genus |

and differentiae 39a26, 57

b7.

Speusippus 28b 2l, 72b3i ;

referred

to 69a36, 75

a33, 36,

b37, 76

a2i,

8ob 14, 26, 84a

13, 8sa

32, 86a 2,j

29, 87b

6, 27, 9oa

7, 25,b

17, 9ia

|

34,b23, 32, 92

a ii-b 8.

Spheres of the stars A. 8.

Spontaneity, coni. luck, )( nature, |

art984b

14, 3 2a

13,b23, 34

a10,

b4, 7o

a7.

Stars A. 8;their nature 73

a34.

State, v. Habit.

Strife

(Empedocles)oa

27.Styx 983

b32.

Substance Z and H passim ;its

meanings A. 8, A. I;

= ultimate

subject 983b

10, 2a 3, 7a

31, I7b

13, I9a

5, 29a

8, 38b

15, 42a 26

;

)( modification, accident 983b

10,j

10, 7a

31, 38b

28, 7ia

I;

44a

15, 49a36, 77

a35 ;

are num

bers substances? 987

a

19, i

b

26,

76a30; sensible substance 997

a|

34, 42a25, 69

a30,

b3 ;

= form, I

b21, 993

a18, 32

bI,

29, 38b

14, 4ib

9, sob

[

2;are there non-sensible sub-

stances ? 997a

34, 59a

39 ;uni-

versals not substance Z. 13, 3a

7,|

53 16, 6ob 21, 87a

2; primary

being 28a 14, 30 ; prior in defini-

tion, knowledge, time 28a

32 ;

alone separable 28a34 ;

four no-\

tions of it 28b 33 ;whether mat-

|

ter is substance Z. 3 ;material

substance 42a27, 49

a36, 77

a36 ;

syn. individual 3oa

19; primary

32b 2

;

=matter, form, and con-

j

crete thing 35a

i, 7ob13 ; )(

con-j

crete thing 35b

22, 37a

29; )(j

genus 42a21, 53

b 21; being not

j

the substance of things 40 18 ;

unity not the substance I. 2, 4ob

]

1 8;a principle and cause 4i

a9, ]

b30, 43

a 2; generally recognized

substances 42a 6

;natural 42* 8,

7oa

5 ;mathematical objects as

substances M. 1-3, 42a

1 1, 69a35;

coni. actuality, complete reality,

42 b 10, 43a 23, 35, 44a 9, 5ob 2,

72a

25 ; prior in substantiality

49b n, 5o

a4, 77

b 2; incompo-

site 5ib

27; concrete 54b

4;

eternal, unmovable substance A.

6; why are there many sub

stances? 89b

31.

Substratum, def. 28b 36 ;two mean

ings 38b

5, 49a 28 ; syn. matter

983*30, 985

b10, 992

bi, 22a 1 8,

7oa ii

; proximate, ultimate i6a

20, 23, I7b

24, 24b 10

; )(matter

44b

9.

Successive, def. 68b 31 ;succession

)( common reference 5a n

;suc

cession in numbers 85a4.

Syllogism, starts from the what*

34a

31, 78b

24; primary syllo

gisms I4b

2.

Ten, limit of the number-series

986a

8, 73a

20, 84a 12

;ten prin

ciples (Pythagoreans) 986a22.

Tethys 983b30.

Thales 983b20, 984

a2

;referred to

984*27,996*91 39a 12

(?).

Thargelia 23b n.

Thaten 33a

7, 49a19,21.

Theology 26a 19, 64b

3.

Theoretical knowledge E. i, 993b

20.

Thinking, thought (v6r)(ris) )( mak

ing 32b

15 ;coni. definition 52

a

29>

bi> 75

a3 5 )( faculty of

thought A. 7, 9; )( desire 72a26;

its primary object 72a27.

Third man 99ob

17, 39a

2, 59b

8,

79a

13.

This I7b

25, 30a

4, 7oa

10. v.

Individual.

Thought (four), v. Reason.

Time, incidentally quantitative 2Oa

29 ; prior in 28a 32, 38b

27, 49b

ii;eternal 7i

b7.

Timotheus 993b

15.

Total (irav) )( whole, all 24a

I, 8.

Trojan war i8b 16.

Truth 993a30,

b20, 9

aI,

b 2;def.

0. 10, n b25 ; absolute, relative

n b 3 ; being as truth E. 4, 0. 10,

65a2i.

Two, v. Dyad.



INDEX

Unequal, the 8;b

5, 88b 32, 89b

]

615, 9ib35 ; inequality i

b23.

Unit, def. i6b 25, 89b

35 ; pointwithout position 84

b 26; specific-

ally the same, associable M. 6-8, \

99ib

24; specifically different, \

inassociable M. 6-8, 992a 3 ;

differentia of 83a2

; unitary numbers 8ob 19, 30, 82 b

6.

Universal 42a

15, 6ga

26, 86a 32 ;

def. 23b

29, 38b II

;not sub-

|

stance Z. 13, 3a

7, 53bi6,6o

b21,

j

87a 2

;whether the first princi-

j

pies are M. 10, 3a

7, 6ob 19, 7ia

j

20; object of knowledge 3a

14,

36a

28, 59b

26, 6ob 20, 87a 16

;

essential (naff avrd) I7b35 ; prior

in definition i8b 32 ; )( genus28 b 34.

Universe, not episodic 76a

I.

Unlike, its meanings i8a 19.

Void 48b

9 ; (Democritus)

9a

28.5,

What 25b31, 26a 36, 28a i7, 3o

a17;

parts of the22a 27; starting-pointof syllogism 34

a3i, 78

b24.

Whole I3b 22, 52a 22;

its meanings A. 26

; )( total 24*1.

Wisdom, philosophy (o-o</>i a) A. I;

with what principles it deals A. 2,

K. i, 2, 995b

12, 996b9 ;

with

first causes 98ib28.

Xenocrates referred to 28b 24, 69a

35, 76a20, 8ob 22, 28, 83

b2, 85

b

7, 86a 5, 8bb

28, 9o

b

20-32, 9i

b

Xenophanes 986b21-27, Ioa 6.

Zeno ib7.

Zeus 9ib

6.



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