the universal treatise (exigit ordo) - nicholas of autrecourt

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title: The Universal Treatise of Nicholas of AutrecourtMediaeval Philosophical Texts in Translation ; No. 20

author: Nicolaus.publisher: Marquette University Press

isbn10 | asin: 0874622204print isbn13: 9780874622201

ebook isbn13: 9780585371573language: English

subject Aristot le, Philosophy, Medieval.publication date: 1971

lcc: B765.N563E95 1971ebddc: 189/.4

subject: Aristotle, Philosophy, Medieval.

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The Universal Treatise of Nicholas of Autrecourt

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MEDIAEVAL PHILOSOPHICAL TEXTS IN TRANSLATION

No. 20



EDITORIAL BOARD

James H. Robb, L.S.M., Ph.D., Chairman

The Rev. Gerard Smith, S.J., Ph.D.

The Rev. Richard E. Arnold, S.J., Ph.D.

Paul M. Byrne, L.S.M., Ph.D.

The Rev. John Sheets, S.J., S.T.D.

Marquette University Press

1131 West Wisconsin Avenue

Milwaukee, Wisconsin

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Translated by

Leonard A. Kennedy, C.S.B., Ph.D.

University of Windsor

Richard E. Arnold, S.J., Ph.D.

Marquette Universi ty

Arthur E. Millward, A.M.

formerly University of Windsor

with an introduction by

Leonard A. Kennedy, C.S.B.



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Library of Congress Catalogue Card Number: 70-155364

© Copyright, 1971, The Marquette University Press

Milwaukee, Wisconsin

Printed in the United States of America

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Table of Contents

Introduction

Life and Works of Nicholas 1

The Universal Treatise 2

Prologues 3

First Treatise: The Eternity of Things 9

Indivisibles 11

The Vacuum 14

Material Substance and Quantity 16

Movement 16

Whether Everything Which Appears is 17

Whether Exactly the Same Thing Can Be Seen Clearly and

Obscurely18

Beings in the Imagination 19

The Intellect 22

Whether the Same Cause Can Produce Specifically DifferentEffects

23

Principles Used in the Translation 28

Selected Bibliography 29



The Translation of the Universal Treatise of Nicholas of Autrecourt

Prologues: I 31

II 57

First Treatise: The Eternity of Things 59

Indivisibles 71The Vacuum 87

Material Substance and Quantity 95

Movement 98

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Whether Everything Which Appears is 104

Whether Exactly the Same Thing Can Be Seen Clearly andObscurely

120

Imaginable Beings 124

The Intellect 143

Whether the Same Cause Can Produce Specifically Different Effects 146

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Introduction

Life and Works of Nicholas

Nicholas was born at Autrecourt, a vil lage in the diocese of Verdun, France, about 1300. Heis known to have l ived at the Sorbonne from 1320 to 1327, and to have received the Masterof Arts degree, the Baccalaureate in Theology and Laws, and the Licentiate in Theology.He lectured on the Sentences of Peter Lombard and also on some of the works of Aristotle.In 1338 he was made a canon of the Cathedral of Metz, this benefice being an honorary one



which helped to support him while he continued his work at the University of Paris. In1340 Pope Benedict XII summoned him to the Papal Curia at Avignon to answer chargesconcerning his teaching. His case was not concluded until 1346, under Benedict'ssuccessor, Clement VI. Nicholas was required to revoke publicly many statements he hadspoken or written; his Universal Treatise , and his letters to Bernard of Arezzo, O.F.M., hadto be burned publicly in Paris. He was deprived of his Master of Arts degree and wasdeclared unfit to be promoted to the Master of Theology degree. In 1350 he became dean

of the Cathedral at Metz.Of the works of Nicholas, two of his nine letters to Bernard are extant. These, along with aletter of Nicholas to a certain Giles, have been published by Lappe. 1 Nicholas' UniversalTreatise , and a smaller work Utrum visio creaturae rationalis beatificabilis per verbum possit intendi naturaliter , have been published by Father O'Donnell. 2 Short excerpts from otherworks by Nicholas are found in the list of his statements which were condemned. 3

Nicholas is important in the history of fourteenth-century philosophy. He is most famousfor his doctrines which bear similarities to the teachings of David Hume. 4 These doctrines,

found chiefly in Nicholas' letters to Bernard, indicate scepticism in regard to man's abilityto gain sure knowledge of substance or causes, and in regard to man's ability to proveGod's exis tence or to discover a hierarchy in beings.

1 J. Lappe, "Nicolaus von Autrecourt," Beiträge zur Geschichte der Philosophie des Mittelalters ,Band VI, Heft 2 (Münster , 1908) pp. 2*-14*, 24*-30*. The two le tters to Bernard have beentranslated into English in H. Shapiro, Medieval Philosophy (New York, 1964) pp. 509-527, and inA. Hyman and J. Walsh, Philosophy in the Middle Ages (New York, 1967) pp. 654-664.

2 J. R. O'Donnell , "Nicholas of Autrecourt," Mediaeval Studies , I (1939) 179-280.

3 H. Denifle, ed., Chartularium Universitatis Parisiensis , tom. II (Paris, 1891) 576-587.

4 H. Rashdall, "Nicholas de Ultracuria, a Medieval Hume," Proceedings of the Aristotelian Society ,N.S., 8 (1907) 1-27.

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Nicholas' most important teaching in the Universal Treatise , however, is that all things areeternal. This teaching also involves the consequence that all things repeat themselves incycles, and leads, too, to a denial of the immortality of the human soul as this immortality

had usually been understood.These doctrines were all condemned. However, it should be pointed out that Nicholasclaimed that many of the statements attributed to him were not made by him, at least not inthe form in which they were s tated. He also claimed that they had been made by way ofdiscussion and had not been asserted obstinately. He stated frequently, too, in his letters toBernard and in his Universal Treatise , that he was dealing only with what was probable, notwith what was certain.

The Universal Treatise



The Universal Treatise , usually referred to as the Exigit ordo , was composed about 1340. Ithas as its intention to call university professors, especially at Paris, to the study ofChristianity and ethics. The means to achieve this end is the discrediting of Aristotle andhis disciple Averroes (1126-1198), the study of whose writings occupied most of the timeof these professors. Attacks on Aristotle were by no means unknown; before Nicholasseveral scholastics had strongly opposed the Stagirite. Nicholas does not think that he candefinitely disprove what Aristotle and Averroes taught, but does think that he can show that

it is less probable than other doctrines. Accordingly he sets out to contradict a number ofAristotel ian tenets, and defends doctrines such as the following as being more probablethan what Aristotle and Averroes held:

(a) the universe consists of unchangeable atoms, (b) space and time are composed ofpoints and instants respectively, (c) there is a vacuum, (d) material substance and quantityare not really distinct, (e) movement is not anything real, (f) everything is as it appears, (g)the same thing cannot be seen clearly and obscurely, (h) there is not one intellect for allmen, (i) a cause can produce only one effect.

In fol lowing Nicholas through this project we shall stay close to his own order ofargumentation, hoping thereby to facilitate the work of the reader of the translation. Manydetails, of course, will be omitted.

Nicholas is not trying to establish an integrated system of his own but rather to find faultwith Aristoteli anism. For this reason the various doctrines he supports are often iso latedteachings whose compatibility is not made clear. Moreover, since Nicholas is not demon-

Page 3strating his own position but simply establishing its probabil ity, he uses arguments whichare not demonstrations and even defends positions which he beli eves to be false. He takesa set of propositions, which he need not necessarily accept as true, and defends them asmore probable than their opposites. He also answers objections against them, and drawsconclusions from them. 5

First Prologue, Part One

Nicholas thinks that the so-called "conclusions" of Aristotle and Averroes are not really

demonstrated and that opposite conclusions can just as easily be drawn from the evidence.He has seen men spend their whole lives studying the works of these men and, at the end,know only as much as another person could learn in a short while if he studied thingsrather than Aristoteli an writings. Moreover, while this li fe-long study goes on, not only i sthe study of Christian life and of ethics neglected, but these men even give bad example bytheir quarrels and their worldly lives.

Nicholas proposes, then, to find out how much certainty can be obtained about things, andto see whether Aristotle is a good guide.



First Prologue, Part Two

It may be presumptuous for someone like Nicholas to contradict the long-establishedauthority of Aristotle and Averroes. But Nicholas feels that a person is allowed to criticizewidely-held opinions if he has a special insight into things. The fact that most men thinkor act in a certain way is no guarantee that what they think is true or what they do is right.Nicholas does not claim special authority for himself, but claims that he has thought abouthis views for a long time and has consulted others about them, and thinks that they shouldbe published so that all may discuss them.

What is it that makes a man's judgment sound? It is his ability to get to the heart of thingsand his ability to relate particular instances to appropriate general rules. Judgment basedon authority is not reli able. Even if God told someone something, the person would besure i t was true, but would not have evidence that it was true, for

5 For a full treatment of Nicholas' philosophy, see J. R. Weinberg , Nicolaus of Autrecourt (Princeton, 1948). See also J. R. O'Donnell , "The Philosophy of Nicholas o f Autrecourt and HisAppraisal of Aristotle," Mediaeval Studies , IV (1942) 97-125. And, for the relation of Nicholas'

doctrine to nominalism, see E. A. Moody, "Ockham, Buridan, and Nicolaus of Autrecourt," Franciscan Studies , 7 (1947) 113-146.

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evidence is based on seeing for oneself. Therefore one should not blindly accept theauthority of Aristotle without see ing for oneself. Even Aristotle himself contradicted theauthority of his predecessors. The only criterion is natural evidence.

Nicholas remarks that the Aristotelians may have wanted to simplify things for the sake ofthe unintelligent, but does not think that this is good policy since i t has gone too far.

Nicholas now begins a discussion of his chief teaching: that all things are eternal. In orderto broach the subject, however, he must begin with a discussion of the good. For Nicholasthe universe is good, and things are disposed as they should be. As a craftsman makesthings so that they will be good and desi rable, so nature disposes things so that they willbe good. For example, stones are on the ground so that men may get at them and use them;horses are just the right height for men to ride. If things were not made according to a plan,and therefore good, there would be total chaos.

Besides being good, the beings in the universe are interconnected. Every being benefitsevery other being. Also, every being is related to a first good, for otherwise there wouldbe no explanation of how things have purposes.

Also, the whole of the universe is always perfect to the same extent. Were there to besome decrease in perfection nothing could stop it going further and further indefinitely.Besides , if there i s a first being which never changes, the goodness which it decides to putin things never changes; hence the total amount remains the same.



Nicholas puts forth these teachings about the good merely as probable. He then uses themto show that whatever exists is eternal. Whatever exists is good. Moreover, it is good forthe whole universe. Thus the withdrawal of any good would decrease the total goodness.But the total amount of goodness in the universe never changes. Therefore, everything iseternal.

Nicholas contends that his doctrine safeguards universal justice better than Aristotle's.Aristotle seems to say that, after death, men are not rewarded or punished. But, accordingto Nicholas, there are in each man spirits called sense and intellect. A man is composed ofatoms, and at death the atoms, but not these two spirits, are dispersed. In the case of a goodman the spirits continue in good condition; in the case of a bad man they continue in a poorcondition. Thus, when the spirits are joined once again to different atoms to constitute newmen, they benefit or suffer depending on how they behaved in their previous humanexistence. Or, Nicholas adds, possibly what happens is that the spirits are joined to betteror poorer atoms in their new

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human existence and benefit or suffer in this way. In any case, the requirements of justiceare met better than in Aristotle's system.

Nicholas is a little worried that his doctrine, though apparently better than Aristotle's, stillis only probable and may also be rejected. But he hopes that faith in Christian revelationconcerning the afterlife will prevent anyone being disturbed because of philosophicaluncertainty.

Nicholas is at least sure that no one can prove that some beings are not eternal, becausethere is nothing in the notion ''being" or "good" which demands that it be accompanied bythe notion of "corruptibility." On the contrary, something is more a being and more a goodif it is eternal. Nor does the notion of "many beings" demand that it be accompanied by thenotion of "corruptibility," since plurality is quite consistent with eternity.

One might argue that the notion "corruptible being" is a possible notion, not acontradictory one, and that therefore perhaps beings are not eternal. Nicholas answers that,since each being i s a good, and is demanded for the goodness of the universe, and sincethe amount of goodness in the universe never changes, the notion "corruptible being" is acontradictory notion. If someone objects that we should be able to see that the notion"corruptible being" is contradictory simply by an inspection of it without resorting to thenotion of "good", Nicholas responds that there are many notions which entailconsequences which are not obvious to us, and that "being" is one of these notions.

Nicholas now mixes a se ries of arguments in favour of his thesi s of the e ternity of thingswith a series of answers to objections against the thesis. In order to clarify somewhat thisinvolved medieval discussion, the arguments and the objections will be numbered.

Argument 1



There are no questions which cannot be answered eventually. But, if things lasted only fora certain length of time, we could not answer the question why they lasted just that longand not for a longer or shorter duration. And, if it is suggested that each being has adifferent duration, an infinite multiplicity of things will be required in order for alldurations to be represented. But it does not seem possible for there to be an infinitemultiplicity of things.

Argument 2Aristotle teaches that for the common good a man should risk death, and yet he holds that aman should love himsel f more than others. Now, if there is no afterli fe, Aristotle iscontradicting himself. But Nicholas teaches that there is a certain kind of afterlife, andhence can urge without contradiction that a man risk his life for the common good.

The point on which Nicholas opposes Aristotle is not simply the eternity of the world,since Aristotle taught that the world is eternal.

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What Nicholas teaches is that the universe is composed of atoms, each of which iseternally unchanged. The only change which occurs is change in place. This change, ofcourse, is often imperceptible to the senses. Thus Nicholas' theory is based onargumentation, not on observation. Nicholas upbraids those men who are willing tobelieve only what they sense. There are many things which are not verifiable throughsense experience and yet are true. Clock-wheels move without their movement beingperceptible. Tops can spin and seem to be resting. So Nicholas is convinced that histeaching about the eternity of things is quite probable.

Nicholas claims that Aristotelians, too, sometimes accept arguments even when they areapparently opposed to sense experience. For example, they teach that "species" come fromdistant objects to the eye, and that sound approaches successively, even though both sightand sound seem to take place instantaneously.

Objection 1

Nicholas' theory makes it difficult to judge whether one thing is nobler than another. Since

no new beings are produced, the efficient causality required to produce new beings cannotbe used as a criterion of worth.

Nicholas replies that, though the objection has some weight, the Aristotelians themselvesare not free of problems. For example, the generative power produces a substance (a child)and the intellective power produces an accident (knowledge). Now, since a substance isnobler than an accident, the generative power will be superior to the intellect. But this isabsurd.

Also, some Aristotelians say that God does not produce natural changes as efficientcause, 6 and yet they say that God is the highest being. Also, the individual is superior to



its nature, and yet the nature, not the individual, is the source of efficient causality. 7 Then,too, when a substance receives an accident, the accident seems to be superior to thesubstance, since it acts on it. But accidents are not superior to substances.

Nicholas thinks that a being can be seen to be nobler than another if it naturally pleasesmen more, or if it takes greater pleasure in its existence, as a man takes greater pleasure inhis being than a horse does in its. Another sign of superiority is evident in the case of thehuman soul. Since the natures of all things come into i t, it is of the same nature as all ofthem. Hence it is superior to a being to which this does not happen, for example, a stone.The heavenly bodies, too,

6 This is Ar istotle's teaching. See W. D. Ross, Aristotle (New York, 1959) pp. 176-177.

7 See pages 196 and 245. (All references to the Treatise refer to the pages of the Latin edition.)

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please us and seem to be noble beings; but certainty is not possible here.

Argument 3

Belief in e ternity is found in all men and is a strong impetus to good behavior. It wouldnot be right for such a belief to be i llusory.

Objection 2

When someone throws a stone, the stone in flight is different from what it was beforebeing thrown. Now, if the stone is different, there is a change in it. Thus it is not eternallythe same.

Nicholas' answer is that there is no intrinsic change in the stone. The whole process can beexplained by the local motion of unchanged particles.

Argument 4

When Socrates dies he can exist in memory. Now, it is more in keeping with the purposeof nature for something to continue in real being rather than in diminished being (as inmemory). Therefore it i s natural for Socrates to exist forever in real being.

Objection 3

It cannot be absolutely proven that something continues in being even if it is apparentlyalways visible. All one can say is that what is seen looks like what was seen in the sameplace previously. There is no guarantee that it is the same thing.

Nicholas responds that the objection is valid as far as certainty goes, but that it is veryprobable that all things are eternal if one appeals to his first argument for the eternity ofthings (that the universe always has the same amount of goodness, etc.).

Argument 5



If things were not eternal, substantial change would take place. There would then have tobe such a reality as prime matter. But the arguments given by Aristotle and Averroes forthe existence of matter are not demonstrative. One of them is founded on a comparison ofsubstantial change with accidental change. But such a comparison need not hold. The otherargument assumes that there is change from non-being; but this must be established, notassumed. And, even assuming that there is change from non-being to being, it can beaccounted for by simply positing being after non-being; it need not come from it in anyother sense.

Objection 4

Two identical objects never exist at the same time, for the existence of the second wouldbe superfluous. But they can exist successively. Now, if they existed successively, theperfection of the world would not be impaired but rather enhanced because more beingswould exist. But in this case some things would case to be, and thus would not be eternal.

Nicholas answers that there is no sense in a being ceasing to be and being replaced by an

identical being. There is no point to i t.Objection 5

Nicholas will argue later (page 203) that men have a natural desire to live forever and thattherefore they are eternal. But

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the prologue here raises the objection that some desires are never fulfil led.

Nicholas' answer is that desires which are not fulfilled here and now are always fulfilledeventually.

Averroists might claim that a man's desire for eternity is satisfied by contemplating aneternal being during his l ife, though he himsel f ceases to be at death. Nicholas claims,however, that a man desires not only eternity but also personal eternity.

Objection 6

Nicholas will teach later (page 205) that acts of the soul are eternal, the same actbelonging now to one individual, now to another. But the prologue raises the objectionthat we cannot conceive how this is possible.

Nicholas replies that he thinks that acts of the soul pass from one individual to another, butthat he cannot understand how they do so. He explains, however, that it is true of manythings that we know that they are and yet cannot understand how they happen.

Argument 6

According to Nicholas, when two things (for example, two whitenesses) appear exactly the



same to sense and to intellect, they are the same. Thus, when one appears to pass away, itreally does not pass away at all; it remains (in the other individual). The one whichapparently passes away does not even really appear to pass away; it simply ceases toappear, which is quite a different thing. Thus things are again shown to be eternal.

Objection 7

Argument 6 presumes that it is possible for one thing to be in two places at the same time.

But this i s not possible.

Nicholas retorts that the same specific nature can be in two places at the same time,although a subject numerically one cannot.

Objection 8

Nicholas will teach (pages 198 ff.) that the non-appearance of something does not prove itsnon-existence. Now, if this is so, I cannot be sure that a person, whom I see in one place,is not also in another place.

Nicholas replies that it is only when indivisibles are scattered that they exist and are notvisible. When they are gathered together to form a person, we can be quite sure that theperson is only where we see him.

Objection 9

If you cannot tell that something is non-existent because it is not visible, you cannot tellthat something is not moving because it does not seem to move.

Nicholas agrees with the substance of the objection, but adds that it is possible to tellwhether something is moving i f the right technique is used.

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Objection 10

Nicholas raises an objection against his doctrine of the good. If a person makes a mistake,his act is not good. But Nicholas has taught that whatever exists is good. Now, how can theact be both good and not good?

Nicholas' answer to this objection i s that the act is good, absolutely speaking; that is, it isbetter for it to exist than not exis t. Nicholas holds that the exis tence of whatever is isbetter than its non-existence, since otherwise everything in the universe would happen bychance.

The Beginning of the Second Prologue

The second part of the first prologue was concerned with defending the teaching containedin the body of the treatise. This second prologue i s l ike the first part of the first prologue,an explanation of why Nicholas wrote his treatise.



Nicholas finds fault with those who cannot hear a new idea, and who immediately quoteAristotle to squelch any investigation into principles, for example, the principle thatmaterial substance and quantity are really distinct. It is not right simply to quote Aristotle;one should look into the nature of things in themselves .

First Treatise:

The Eternity of ThingsNicholas has already dealt at length with this doctrine in the second part of the firstprologue, which was written after this section now under consideration. There is,accordingly, some overlapping.

What seems to oppose Nicholas' teaching about the eternity of things is that we see thingsceasing to be. Now, Nicholas says that we really do not see them cease to be; we s implycease seeing them. We cannot prove that they no longer exis t. If something i s white andthen becomes black, we cannot say that whiteness ceases to exist, just as, if the power of

movement stops functioning, we cannot say that it ceases to exist. It may be that thewhiteness was composed of particles which looked white when they were all together, butnow are dispersed and thus are no longer visible. Besides, if something white becomesblack, black things also become white; the whiteness which ceases to be in this beingcomes to be in another being. If you argue that these two whitenesses are specifically thesame but not numerically the same, your argument is not a demonstrative one. If the twowhitenesses are the same as far as sense and intellect are concerned, difference in locationis not sufficient proof of numerical difference. It might be that, just as something seems tobe in many places when mirrors are used and yet is one thing numerically, so twowhitenesses may be in different places and yet be one thing numerically.

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(This seems to contradict what Nicholas has said earlier [page 195] about individuation.The apparent conflict in Nicholas' teachings concerning individuation will be treated at theend of this introduction.)

Nicholas has now explained how things are eternal even though they seem to change. But

his explanation involves admitting the local movement of atoms. A problem now ariseswhether local movement itself is something real, distinct from the moving atoms. If it is, itcomes into being and goes out of being. Thus it is not eternal. Nicholas will explain later(page 205) that movement is not distinct from a moving object; hence it does not come tobe or cease to be.

How about light? Is it eternal? Nicholas teaches that light is a group of eternal atomswhich move very quickly because of their exceptionally penetrative quality.

Nicholas holds that things are eternal because the universe is perfect and would bedeformed if one of its parts ceased to be. But someone might say that the perfection of the



universe is produced by the species of things in it, not by individual things. Nicholas'answer is that, where certain others say that the species exists in each individual of itskind, he holds that there is only one individual of each kind. When, for example, twowhitenesses are seen, what is really seen is the same individual whiteness in twolocations.

Nicholas raises again the problem of whether a thing could not be replaced by somethingexactly like it without lessening the goodness of the universe. Of course this would notlessen the goodness of the universe from one point of view, but Nicholas thinks that itwould imply imperfection in God, who would require many acts of causation rather thanone initial one.

Nicholas then explains that his theory of the e ternal exis tence of all things is not onlyprobable, but is more probable than its opposite. He also says that the mere examination ofthe notions "things" and "eternal" will not yield a conclusion on the matter; one must resortto a study of final causality and goodness. Nicholas also admits that his theory is falsebecause it is contradicted by the Catholic faith, but he sees nothing wrong with supporting

it as more probable than its opposi te, even if it is false .Having defended his thesis, Nicholas is now ready to show that a great many of Aristotle'steachings are false or irrelevant. Aristotle taught that prime matter exists and that there ismotion other than local motion; both of these are false. Aristotle's teaching about accidentsshould be revised, too, to fit in with Nicholas' atomic theory. Also, since there is no formor matter, questions concerning them become meaningless.

Page 11Nicholas teaches that actions of the soul are eternal. A thought, for example, is merely anatom or a group of atoms of a special kind, and, if a man thinks, his thought has belongedto another man previously. Nicholas thinks that this teaching will render obsolete most ofthe third book of Aristotle's On the Soul . Some of the questions raised there will now bemeaningless, and others will have to be answered differently.

A person's thought passes from him to someone else, and so on indefinitely. Also, allthings return in long cycles to exactly where they were, so that history repeats itself.

IndivisiblesIn accordance with his atomism, Nicholas holds that space consists of points and that timeconsists of instants. Since the arguments in favor of this doctrine and the answers toobjections against it run into one another, they will be numbered for the sake of clarity.And the reader is warned that Nicholas' defense of this doctrine leads him to positionswhich seem fantastic.

Objection 1

Aristotle taught that a continuum is not composed ultimately of indivisbles, but is



infinitely divisible . One of his arguments is that, if an object crosses three indivisibles ofspace, then another object, half as fast, and starting out with it, will cross an indivisible anda half in the same time. But there cannot be half of an indivisible. Thus the continuum isnot composed of indivisibles.

Nicholas' answer to this reasoning i s that every object requires one instant to cease beingat one point and to begin to be at another point, but that it can take time resting when it isat a point. Thus, when the first object has passed three points, without resting, the secondobject has come to the first point, rested there one instant, and gone on to the second point.

Objection 2

Aristotle also argues that if a continuum is made up of indivisible points it wil l have nomagnitude. For, if a point touches a point, it coincides with it. And, if the points in themagnitude do not touch each other, there i s no continuum.

Nicholas' answer is baffling. He thinks that it is possible for points to touch each otherwithout coinciding because two points can touch with each retaining its own different

position. Yet he does not really explain how this is possible.Objection 3

Another difficulty is raised by Algazel. If two circles of different radii move togetheraround a common centre, when the large circumference has moved one point, the smallcircumference has moved through a fraction of a point. But there cannot be a fraction of apoint. Therefore a line is not composed of indivisible points.

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Nicholas answers that straight lines cannot be drawn from each point on the largercircumference to the centre. Only as many lines can be drawn as there are points on thesmaller circumference. When the larger circumference moves through so many points (asmany as there are between points from which straight lines can be drawn to the centre ofthe circle), the smaller circumference moves through one point. Thus the smallercircumference ei ther moves through a whole point or does not move at all; it does notmove through a fraction of a point.

Objection 4

Another problem in saying that a line is composed of points is saying which point is in themiddle. If the number of points is odd, the problem is easy. But, if the number is even,there is no mid-point and the l ine cannot be divided into halves.

Nicholas thinks that one half will be a little larger than the other, but that the differencewill be so small as to be neglig ible.

Argument 1



A finite continuum must be composed of indivisibles because, if it were infinitelydivisible, it would be composed of an infinite multiplicity of parts, and would thus beinfinite in magnitude. Nor can it be argued that a continuum is composed of an infinitemultiplicity of parts but that they do not make it infinite in extension because each part isinside another part; for in a continuum some parts are outside of other parts. If these partsare finite in number, they are ei ther divisible or indivisible. If they are divisible , the finalmultitude of parts will be either finite or infinite. If finite, Nicholas' contention is upheld.

If infinite, the continuum will have to be infinite in magnitude.If someone (with admittedly superhuman powers) were to divide a finite continuum into itsinfinite multiplicity of parts and put them together again, the resulting continuum would beinfinite in magnitude. But this is absurd. Thus a finite continuum is not infinitely divisible .

Objection 5

Aristotle held that a continuum is infinitely divisible only potentially, not actually, and thattherefore it can be actually finite.

Nicholas points out, however, that, without actually breaking up the continuum, theintellect can consider all its parts. If these parts are finite in number, Aristotle is wrong. Ifthey are infininte in multiplicity, the continuum is infinite in extension. And, besides, it isnot right to say that the parts are potential , for even before actual separation they aredifferent from each other. They are therefore already parts actually, not merely potentially.

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Argument 2If a finite continuum is infinitely divisible, one could keep taking away from it forever.Therefore there must have been an infinite extension before starting.

Argument 3

It can be proven that a plane is composed of points because a spherical body, touching aplane at a point, can move over the plane a point at a time. Even if it is objected that thesphere and the plane are not perfect geometrical figures, it must be admitted that the spheretraverses points at least per accidens; thus the argument holds.

Objection 6

For any rectangle taken at random, it is not possible to express the ratio of diagonal to sideas a rational fraction. But, if diagonal and side were composed of a finite number of points,this should be possible.

Nicholas sees the force of this argument, and states that the side and diagonal arecomposed of points, but of an infinite multiplicity of points. Nicholas is aware that thisposition seems to undermine the stand he has taken just previously that a continuum mustbe infinite in extent if it is infinitely divisible. But he says that his posi tion is different,



since he holds that, though the continuum is infinitely divisible, it is also composed ofindivisibles.

Nicholas thus holds that every continuum one can see has an infinite multiplicity ofindivisible parts. No matter how small a part one can see, it can always be divided. Yet(beyond our abil ity to sense i t) there are indivisible parts ultimately.

Objection 7

If moving objects rested, we would be able to see them do so.

Nicholas' answer is that we do not see them rest because we see only groups ofindivisibles and groups of points toge ther; the resting would be visible only if singleindivisibles and single points were seen.

Objection 8

Concerning the divisibility of time, Aristotle argues that, if an object moves through acertain space in an instant, a faster object would move through the same space in a fraction

of an instant. But there are no fractions of an instant. Therefore there are no instants intime; it is infinitely divisible.

Nicholas answers that the fastest object moves constantly, and that every object, when itgoes from one point to the next, does so in an instant, but that other objects are slower thanthe fastest object because they rest at the points. This gets around Arisotle 's problem.

Objection 9

Another argument for the infinite divisibility of time is that an object cannot rest in aninstant because to rest means to be the same after as before, and an instant has no after andbefore. But,

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if an object cannot rest in an instant, it cannot move in a instant. Therefore, since thingsmove, there are no instants.

Nicholas thinks, however, that an instant has duration, just as he thinks that points put

together make up a continuum. He therefore i s able to answer this objection.

Having disproved Aristotle's teaching concerning the divis ibil ity of space and time,Nicholas declares that nearly all Aristotle's conclusions in Book 6 of his Physics areinvalidated:

(a) Aristotle taught that in movement the moving object is in neither the terminus a quo northe terminus ad quem , but partly in both. For Nicholas, a moving object is never partly inboth termini; it is in one and an instant later is in the other.

(b) Aristotle was also wrong in thinking that movement is something inhering in the



moving object, as wil l be shown later (page 224).

(c) Aristotle also said that, in movement, there is no primary part which is changed, sinceeach part is divisible, and the first part of that again divisible, and so on to infinity. ButNicholas can claim that the primary parts involved in movement are the point, the instant,and the atom.

(d) Aristotle said also that all changed being is preceded by movement. But, according to

Nicholas' theory, changed being takes place without movement, since an object going froma to b is in b without passing from a to b.

(e) The beginning of Book 7 of the Physics stated that everything in motion must bemoved by something, and the proof for this assumed that whatever is in motion isdivisible . But this assumption is not established.

(f) Aristotle also claimed that, for every movement, a faster one can be found. This,Nicholas holds, is false , for the being which moves without resting is the fastest-movingthing.

The Vacuum

Another anti-Aristotelian doctrine advocated by Nicholas is that a vacuum is necessary inorder that motion take place.

Argument 1

Otherwise, when something moves, either it will have to occupy the same place assomething e lse , or all things wil l have to move and be readjusted at the same instant. Onemight say that motion takes place by the bodies bumped into becoming compressed. But

Nicholas says that such compress ion takes place only by particles coming closer to eachother than they were previously. Thus, either there is a vacuum in which they exist onlyloosely joined, or they are fully compact to start with (and the same problem remains).

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Objection 1

One teacher in Nicholas' day taught that, when a is moved into the place of b, b moves intothe place of a.

But Nicholas thinks that it will be easier for what is behind a (air, for example) to take itsplace than for what it bumps into to take its place.

Objection 2

One of Aristotle's arguments against a vacuum is that local motion in it would take placeinstantaneously, since there would be no resistance in the medium.

Nicholas points out that he does not posit a large vacuum but small vacuums among parts



of bodies . Also, according to Nicholas, all motion takes place instantaneously, althoughthis is not evident because the moving bodies res t along the way.

Objection 3

If water came out of a water-clock when a finger was pressed over the opening at the top, avacuum would be formed. But the water does not come out. This shows that a vacuum isnot possible.

Nicholas answers that poss ibly this k ind of vacuum (a large one) is not possible. But thisdoes not prove that small vacuums among the parts of bodies are not possible. Nicholasrejects the solution which says that the universe is perfectly full and that, if the water cameout, it would make the universe more full since nothing could take the place of theescaping water.

Objection 4

An inflated bladder cannot be compressed. If there were a vacuum it seems that it wouldallow the particles in it to contract and the bladder to be compressed.

Nicholas replies that there is a vacuum in ordinary air, which allows it to be contracted, butthat in the bladder the air has reached the maximum of its compressibility. Or else in thebladder there i s a vacuum separated from the particle s, but of such a nature that it cannot bepenetrated.

Argument 2

It is a fact that things grow. Now, if a person's arm grows, the additional space it occupiesis made possible only because of a vacuum. If the space were filled, the arm could not

increase in size.Aristotle interprets this increase as being due to the particles already there increasing insize. But, his position continues, since they are already full particles, they cannot increasein size. Nicholas, however, has no difficulty in answering this objection. He holds, not thatthe particles already there increase in size, but that other corporeal particles are added andfill the empty spaces.

Argument 3

A jar filled with ashes can receive as much water as if it were empty. This shows that, in a jar fi lled with water, there are spaces which can be occupied by something else .

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Argument 4

Since things grow larger, one denying that there is a vacuum will have to prove that otherthings become more compressed or that somewhere else a larger body becomes smaller in



the same proportion.

Objection 5

When a displaces b, the space is always occupied, either by a or b. Thus there is novacuum.

Nicholas replies that a vacuum is a space where there is no body or where there is a body

which can be displaced. Thus the space occupied by a is , of itse lf, a vacuum, even thoughat the moment it happens to be occupied.

Material Substance and Quantity

According to Aristotle, quantity is distinct from material substance. 8 Nicholas againcontradicts Aristotle. Total identity, he says, is imposs ible to prove posi tively, but there isa negative proof because no distinction can be proven here. For quantity and substance,when they change, always change together. And plurality is not to be assumedunnecessarily.

Similarly, number is not distinct from the things numbered.

Movement

In order to defend his position that everything is eternal, Nicholas must hold thatmovement, as a reality, does not exist, since movement, of its very nature, is transitory.What Nicholas does i s to insis t that movement is not distinct from moving objects.

In local movement there is an object in one place and at a later time it is in another place.There is nothing else involved, nothing which is successive, part of which has passed andpart of which is yet to come. A real existent cannot consist of what was and of what willbe, since both of these are non-existent.

An objection to Nicholas' posi tion is that, if someone i s going to go to Notre Dame, he isalways going there; otherwise his going there will end. If it ends, it is not eternal.

Nicholas answers that the ''going" is not a thing. Hence, when it ends, nothing ceases to be.Nicholas admits that "moving," as he has explained it, exists, but claims that it does notinvolve the beginning or termination of any positive reality.

The same is true of any kind of change. For example, when a person thinks, a thought is

present to his mind. But this same thought existed el sewhere all the time.Concerning the identity of material substance and quantity, one might object that, if theyare not distinct, they are identical. Nicholas

8 Metaphysics , V, 13.

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explains that, considered as regards what they represent outside the mind, they areidentical, but, considered as signs of concepts (that is, ways of considering things), theyare different. There is, then, a mental distinction but not a real distinction. We can havemany concepts of the same thing. For example, the length and width of a body belong tothe same body and thus are not really distinct, though they are conceptually distinct.

Whether Everything Which Appears Is

Aristotle taught that not all appearances are true. 9 This teaching also i s attacked byNicholas, who holds as the more probable opinion that everything evident to the senses istrue. If a man with a fever tastes sugar as bitter, it is bitter.

Some wish to admit this position of Nicholas but only after adding the proviso "if themedium and the sense organ are properly disposed, and if there is a proper distancebetween the sense power and its object." But Nicholas rejects this proviso , since one musttrust the senses in order to be sure the proviso i s met.

Nicholas admits that mistakes can be made when partial appearances are mistaken for full

ones, as when one thinks the sun is smaller than the earth, or when one is dreaming andmistakes for reality that which he dreams. Hence, everything evident to the senses is trueif it appears in a full light . If it were not, man would have no certitude at all.

What truth is there when the man with the fever tastes sugar as bitter? Because of his fever,he tastes something in his own sense organ which is really bitter.

Nicholas must face the problem of how a person is sure that what he senses appears to himin a full light. Nicholas thinks that man has a spontaneous conviction that what is evidentto him is true; he cannot prove such a statement as a conclusion from previously

demonstrated truths. He will be mistaken sometimes (as when he dreams) but is able lateron to correct these mistakes (as when he wakes up). As concerns evidence present to himwhen he i s awake, he trusts his spontaneous conviction. If someone is not satisfied withthis explanation, he must say that man has no full certitude.

Nicholas points out that men do not have contradictory appearances. They simply havedifferent appearances, or more or fewer appearances. Error occurs when one thinks or sayswhat actually exceeds the appearances he has. Therefore there is no poss ibili ty ofcontradictories being true at the same time.

9 Metaphysics , IV, 4-6.

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What Nicholas accepts as evident are: (1) sensible objects; (2) acts which we experience inourselves ; (3) self-evident principles; (4) conclusions depending on self-evidentprinciples. And the ultimate reason why these evidences are to be accepted is because theintellect accepts them with pleasure, while it is opposed to what it sees to be false . Wecannot prove that what is evident is true; we can only accept it as true because the intellect



finds it pleasurable. We cannot prove all things; our first truth must be accepted withoutproof, for proof involves the use of previous truths, and no truths are previous to the firsttruth.

Nicholas' position is that not many things can be known for certain. For example, asconcerns matters of experience (a magnet attracts iron), it is not possible to be sure thatwhat has happened will go on as it has in the past. Such assurance would be only opinion,not certainty.

Whether Exactly the Same Thing Can Be Seen Clearly and Obscurely

It might seem that, concerning the question of whether all appearances are true, Nicholas'answer is not really different from Aristotle's. Yet Nicholas' has a consequence whichAristotle's did not have. In defending the position that all appearances are true Nicholasdoes not hold that contradictories can be true. He does not hold, for example, that, ifsomething is seen by one man as blue and by another as white, it is both blue and white.Nevertheless he does say that the two men see different things. One sees a white thing; theother sees a blue thing. The same holds true o f clear and obscure knowledge. If an act (sayof vision) is clear at one time and obscure at another, Nicholas says that what is seen firstis something different from what is seen later. This means that the same object cannot beseen clearly and obscurely.

For Nicholas there is a proportion between an act and its object. To a certain kind of actcorresponds a certain kind of object. If an act of seeing is bright, its object is bright. If theact of seeing is dull, its object is dull. Thus there cannot be two acts by which the sameobject is seen.

Many striking conclusions follow from this posi tion:

(a) God knows what we know, He has the same kind of act of knowledge as we have. AndHe has only the certainty which we have. God's knowledge differs from ours only in thatHe knows more things.

(b) And, if Nicholas' theory is true when applied to two acts of the same power, it is just astrue when applied to acts of two different powers. Hence no two knowing powers cangrasp the same object.

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(c) Also, when an object (say whiteness) is seen, every object like i t (every whiteness l ikethe one seen) is seen. By seeing one whiteness in one place, a person sees everywhiteness everywhere in the world.

(d) Also, there cannot be two different acts of the intellect grasping the same object.Therefore every concept of a thing has a different formality or reality corresponding to itin the thing. The categories are thus really or formally distinct.



(e) If two people have different intellectual ability, they can never know the same things. Ifsomeone sees something from close up, and another from afar, they cannot see the samething. And, since God understands better than we do, He cannot know any of the thingswhich we know. (This seems to contradict what Nicholas has said in [ a]).

Beings in the Imagination

For Nicholas, imaginary beings exist just as truly as beings seen by the external senses,

but they are a different kind of reality. Objects of the imagination exist before they areimagined just as sensible objects exist before they are sensed. For an object of sense ismore closely related to the act of sensing than is an object of imagination to the act ofimagining, and, if the more closely related object does not pass away when the act ceases,then the less close ly related object will not pass away either. Also , what we imagine isknown by God always; thus it always exists.

Nicholas next deals with a number of consequences of his doctrines, or problems arisingin connection with them, or other teachings related to them:

(a) First comes a problem concerning God's knowledge. Since things are finite, they canbe known fully by a finite power. But God, being infinite, cannot know what a finite powerknows. How, then, does He know things? It seems that He knows Himself directly, andother things indirectly.

(b) There is a distinction between the object of knowledge and the act of understanding.The object is what we see, but the act of knowing in itse lf does not resemble i ts object.Besides , the object as known is less perfect than the object in itsel f, but sometimes the actof knowing i s more perfect than the object in itsel f.

(c) By objective being Nicholas means a thing as known . By subjective being he means athing in itself . There are thus many objective beings and one subjective being of eachthing. The higher the intellect, the closer the objective being is to the subjective being.

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(d) Nicholas again (see pages 194-195) argues that things are eternal because whensomething (for example, whiteness) ceases to be in one place in continues to be in anotherplace (where there is whiteness ). And the same act of see ing sees both whitenesses at thesame time.

How can whiteness cease to be in England and remain in Paris? Because its individuatingprinciple l eaves i t. But the individuating principle does not make one whiteness in anyway unlike another. It merely locates the whiteness in a certain spot. To say that thewhitenesses are in any way different is to raise insuperable difficulties. For example, if tosee one whiteness clearly is to see another clearly, as has been proven, then one can seeclearly a whiteness infinitely distant simply by looking at a whiteness nearby. Now, unlessthey were absolutely identical, this could not be. Individuation, for Nicholas, does not



necessarily bring about numerical difference.

A plurality of whitenesses is not possible because the exis tence of the second would besuperfluous. Or, if you say that two are better than one, by the same token an infinitemultiplicity would be better than a finite number. But an infinite multiplicity is notpossible. Therefore there is only one whiteness.

Nicholas' doctrine raises a serious problem. If I am in Paris looking at whiteness, by

numerically the same act, according to Nicholas, I see numerically the same whiteness inEngland. If the whiteness in Paris is destroyed, the act of seeing it remains because by thissame act I see the whiteness in England. But then there would be evidence of seeingwhiteness in Paris, even after the whiteness was destroyed. And what is evident is true. Butthis would not be true. Thus Nicholas' criterion of certitude would be invalidated.

To avoid this difficulty some say that a man see ing whiteness in Paris does not see i t inLondon because the object of knowledge must be an efficient cause of its own beingknown. But Nicholas points out that the whiteness in Paris could suffice as efficient cause.And, once it is seen, one sees immediately the whiteness in London, since i t is the samewhiteness . Besides, God could cause a person to see whiteness and he would see it; thewhiteness need not be the efficient cause of its being seen. Nicholas goes on withoutsolving this important problem.

(e) If someone says that the same object can be seen by several acts, which, for example,succeed one another, Nicholas objects that a power can produce only numerically one act.For, if it could produce more than one, why would i t produce this one rather than any other?

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It would produce all the acts at once, which is contrary to experience. So whiteness isknown always by the same act.

And, in general, from a cause comes numerically only one effect, and this effect is alwaysproduced, though not necessarily in the same place. And, since the cause always produces,the effect is e ternal.

(f) There is a problem how an accident is produced now in one substance and now inanother. Nicholas explains, however, that it is not "transported" from one substance to theother, but that it ceases to be in one substance and in the next instant is in the othersubstance.

(g) Nicholas admits that some things are corruptible in the sense that they appear here nowand elsewhere later. They are not really corruptible, of course, since they remain inexistence all the time. However, Nicholas runs into a problem in defending this doctrine.He has taught (pages 164-165) that a plurality of whitenesses is not possible because therecannot be two things of the same kind. Now, how can he reconcile this with his assertionthat individuals come and go? If individuals come and go, there must be individuals. And,



if there are individual whitenesses, there i s a plurality of whitenesses .

Nicholas' answer is that, though there is a sense in which there are many whitenesses, thereis a stronger sense in which there is only one. Nicholas has already taught that there aremany individual whitenesses and one specific nature of whiteness (pages 195, 245-46). Butnow he teaches that this is not incompatible with there being only one whitenessnumerically. Similarly, he teaches that whiteness is common to both bright whiteness anddull whiteness , the difference being that in dull whiteness it is mixed with blackness; yetsomehow the whiteness in the two cases is numerically one.

Nicholas therefore teaches that individual whitenesses require individual efficient causesto explain why they are here rather than elsewhere. Yet individuality of location, andindividuality in relation to efficient cause, are compatible with basic unity, not onlyspecific but also numerical. How can this be? Nicholas compares individuation tomovement. As movement is not anything real in a thing, so neither is individuation. that is,when a thing appears in a certain place or ceases to be in a certain place, nothing newcomes into existence or goes out of existence. The nature and its individuation are

different in concept, as are material substance and quantity, but they are not real ly distinct.(h) An interesting doctrine of Nicholas is that, since there cannot be two things alike,greater brightness is not produced by adding together equal amounts of light. And,consequently, if lights of different intensity are joined, the amount of light given off is thatof

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the light of highest intensity. Nicholas admits, however, that this seems to contradictexperience.

(i) Since there can be only one thing of a kind, every individual is identical with itsspecies. Thus individuals are required for the perfection o f the universe. (Nicholasexplains that the individual as such is required for this perfection but that its location in aparticular place is not required for this perfection except while the thing is there.)

(j) Another consequence of Nicholas' teaching about the eternity of things concerns theeternity of powers; for example, in a human being. Since a power remains eternally

unchanged, it cannot develop. Thus, when a boy grows, his powers do not really develop,as ordinarily understood. At each moment they are replaced by other, more developed,powers. Thus, the will which performs a deed immediately ceases to be, and therefore aperson is rewarded or punished for the deeds performed by a will not his own.

The Intellect

This section is directed especially against the teaching of Averroes that there is oneintellect for all men. The arguments of Nicholas, however, are unusual, not at all likethose of, say, Thomas Aquinas.



Nicholas says that men have different intel lectual capacities, and that every faculty alwaysworks according to its peak capacity, and that therefore all men do not have the sameintellect.

Nicholas takes quite seriously the statement that a power always works at peak capacity.He even says that, when a person thinks less clearly than he did an hour previously, hedoes so with a different intellect. Also , since some intel ligibles are harder to understandthan others, they will be understood by different intellects in the same person. In fact, thereare as many intellects as concepts.

A problem arises in this latter case, however, for how can an intellect compare twointell igibles if i t can understand only one of them? Nicholas thinks that, as long as bothintellects are in the same soul, the problem is settled, provided there i s a third intellectwhose object is the difference between the two intell igibles. (Nicholas seems to think thatit is possible to know the difference between two intelligibles without knowing theintelligibles.)

Why cannot men know an infinite multiplicity of things at the same time? Becausethinking is accompanied by activities of the sense powers, and these, since they involvematter, interfere with one another and thus limit the intellectual activities corresponding tothem.

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Whether the Same Cause Can Produce Specifically Different Effects

Nicholas defends the doctrine that a cause can produce only one kind of effect. The proofis that, if a cause produced an effect less noble than another effect, some of its powerwould be superfluous; and this is unfitting in a perfect universe.

A corollary is that two causes cannot produce one effect. For the higher of them willproduce a greater effect, the lesser a lesser effect; hence they cannot produce the sameeffect. And it cannot be claimed that the two causes produce an effect greater than either ofthem, since then there would be no way of proving that any effect, however exalted, isbeyond the power of any two causes.

But, if an effect cannot be produced by two causes, there seems to be no necessity for manycauses working together. The higher alone would suffice. Nicholas asserts, however, that,though two causes cannot produce the same simple effect, they can produce a complexeffect, such as Socrates, who is composed of bones, flesh, etc. One cause would producethe bones, another the flesh, and so on.

A great many conclusions follow from these doctrines.

(a) One fire cannot produce another. Since, according to previous teaching, there are notwo things exactly alike, the fires will be unlike . Suppose the fire caused is more intensethan the fire causing it. Since an effect comes from only one cause, the first fire is the only



cause of the second. But, since the second is greater than it, the first cannot be the cause ofthe second. Nicholas' posi tion is that a heating power is in some way joined to a fire andthat this heating power causes the effect. And, according as the effect is greater, the heatingpower coming into play is greater.

(b) It seems also that an animal cannot beget i ts like. It is not equal to i ts offspring, sinceno two beings are equal. It is not superior, except incidentally, since an inferior animal canbeget offspring as well as a superior one can. Nor is it inferior, since the lower cannotcause the higher. Hence the effect must be produced by some higher being.

(c) If an effect seems to depend on the condition of the material worked upon, what reallyhappens i s not that poor material makes a particular cause produce an inferior effect, butthat, because of the material, an inferior cause is at work.

(d) Averroes is wrong in holding that the same effect (mice) is caused by different causes.The effects are not really the same but are slightly different; therefore the causes aresl ightly different.

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(e) Knowledge is not caused by its object and a power of the soul, for no effect has twocauses . Nor is the object in any way the cause, since the e ffect (knowledge) is usuallysomething superior to the object.

(f) God is not the total cause of all things, since, like other causes, God has only oneeffect. And God is not the partial cause of all things, because things can have two causes

only in certain cases. Also, God produces nothing, because any creature is finite and thusout of proportion to an infinite cause.

(g) If a cause can produce only one effect, how can the will be free? For it cannot be freeunless it can produce opposi te effects. Now, there are as many wil ls as there are voli tions,

just as there are as many intellects as concepts. Thus, no vol ition is capable of producingopposite effects. Nicholas cannot see how free will is possible.

Nicholas now switches to a new topic. People who see white see i t a little differentobjectively. Yet what they see is subjectively the same. 10 So, too, white and black aresubjectively the same. For there are any number of degrees of perfection o f eyesight.When white is looked at, what is seen ranges from bright white to black. Thus the samesubjective being can give rise to such disparate objective beings. And Nicholas makes thestartling s tatement that in reality there i s only one subjective being in the universe. Thissubjective being is God.

There i s a difficulty in saying that blackness is merely the objective knowledge of whiteby a person with poor sight. For persons with good sight know blackness better thanpersons with poor sight. So blackness has, it would seem, a subjective being differentfrom the subjective being of white.



Nicholas answers, nevertheless, that there may be two orders of knowers. Those with first-order knowledge are in touch with the one subjective being, and white and black are twodifferent objective beings for them. But, for the second-order knowers, what serves as aquasi-subjective being is the objective being of the first-order knowers. These second-order knowers then know black and white as if they were two different subjective beings,but, in reality, they are not.

It seems strange to speak of one person knowing another person's knowledge, but itshould be remembered that for Nicholas knowledge is a thing, an atom or a group ofatoms. Hence, presumably it can be known.

10 For Nicholas, the objective be ing of a thing is the being it has as an object in the mind; itssubjective being is the being it has in itself, outside the mind.

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In these first-order and second-order knowers i t would seem that the first-order knower ishigher because he is close r to the subjective being of things. And yet the second-orderknower seems higher because it is harder to know knowledge than it is to know things.Nicholas answers that the second-order knower is stronger but that he i s less noblebecause the dignity of knowledge is measured by the object more than by strength.

Nicholas finishes by considering a variety of only loosely related topics:

(a) An intellect can know intuitively or abstractively. The human intellect knowsabstractively. Intuitive knowledge is different from abstractive knowledge in that it is

clearer.(b) Can a person with good vision see as wel l at a distance as a person with poor visionclose up? If so, different powers will have the same object; but this cannot be. 11 Nicholassays that in the power of sight are two powers, the power of the soul and the corporealpower that unites the spirits. The latter powers in the two men are unequal, but the formerpowers are numerically the same power. Hence there is only one power with the sameobject.

(c) The object of the intel lect is a universal. To the objective universal in the intel lectthere corresponds a subjective universal outside the mind. It may or may not be one withall other universals. It can be known more or less well in objective being.

(d) Nicholas wants to simplify logic by reducing the kinds of supposition to two: formaland material. In formal supposition, a term is taken for what it signifies, as is "human" in"Socrates i s human." In material supposi tion, a term is taken in itse lf, as in "'human' hastwo syllables." Some logicians appeal to other kinds of supposition to explain the error''Socrates is man, man is a species, therefore Socrates is a species." Nicholas, however,thinks that the error can be explained simply by saying that in the first case "man" is notconsidered in all i ts extension and in the second case i t is.



<><><><><><><><><><><><>

The Universal Treatise is incomplete. It seems, however, that not much is missing.Nicholas is lavish with references, and it would seem from the references in the extant partof the Treatise that little has been los t. It is even possible that, though Nicholas intended towrite more, he never actually did so.

The chief unity in the Treatise is a negative oneits anti-Aristotel ianism. For this reason itis difficult to put Nicholas' teachings to-

11 See page 240.

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gether as a unified whole. It is possible, however, to find some kind of posi tive unity. The

major unifying theme is Nicholas' doctrine of the good. Nicholas teaches that, since theuniverse always contains the same amount of good, everything in it always continues inexistence. Thus the universe consists of unchangeable atoms.

The first consequence of the doctrine of the good in turn serves as a minor unifying theme.For atomism fits in very well with the teaching that space consists of points, and time ofinstants.

Besides, though Nicholas admits change in quantity and change in place, he has to teachthat such changes do not produce or destroy any real being. Thus he must say that quantityis identical with material substance and that movement is simply a change in the positionof atoms. He cannot say that quantity is something o ther than material substance or thatmovement is a property inhering in the atom, for then something real would cease to be orwould come into being.

A further consequence of the eternity of things is the eternity of actions of the soul. And, ifan act of the soul (say, of vision) is eternal, it must be unchanged. Therefore it cannot varyin intensity. Thus the same object cannot be seen clearly and obscurely. Each act has itsobject eternally joined to i t.

Thus we see that the first consequence o f the doctrine of the good (atomism) itsel f hasfurther consequences (that space consists of points, that time consists of instants, thatquantity is identical with material substance, that movement is simply a change in theposition of the atoms, and that the same object cannot be seen clearly and obscurely).

Now, the second result of the doctrine of the good is that all things are as they appear.There i s no way of demonstrating that things are as they appear. The only assurance wehave is that the mind finds pleasure in this conviction, and that such pleasure would beil lusory if what is clear and evident were not true. Therefore the goodness of the universeis the only warrant for this assurance.



The third result of the doctrine of the good is that a cause has only one effect. For, if acause could produce two unequal effects, its power would be superfluous while it wascausing the lesser effect. But, if there were superfluous power in the universe, the universewould be lacking in goodness.

There is, then, some positive unity in Nicholas' doctrines. But unity is not the onlycriterion of satisfactoriness. And a serious source of dissatisfaction with Nicholas'doctrine arises from a large number

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of positions which seem unproven or false or contrary to experience, such as:

(a) The whole of the universe is always perfect to the same extent.

(b) The nature, not the individual, is the source of efficient causality.

(c) Actions of the soul are eternal, and pass from one person to another.

(d) Individuation adds nothing real to a universal nature.

(e) Moving objects rest at regular intervals.

(f) Points can join to form a continuum, and instants can join to form time.

(g) A straight line cannot be drawn from each point on the circumference of a circle to thecentre.

(h) Movement takes place by an object being in one place and at the next instant being inanother place without actually "passing" to the new place.

(i) The same thing cannot be seen clearly and obscurely, or by different persons; nor can itbe known by different powers.

(j) There are as many intellects as concepts.

(k) Objects of the imagination exist before being imagined.

(l) A cause can produce only one kind of effect.

(m) Two causes cannot produce one effect.

(n) God cannot be a cause.

(o) There is only one being (God).

Nicholas, however, does not seem disturbed by these amazing doctrines. One reason forthis, as has been said, is that he does not believe all that he advocates, but simply wantsany kind of ammunition against Aristotle. Another reason is that he does not think thatmany things can be established with certainty, and is content to defend positions even if



they are probably wrong, as long as there is some probability in their favour.

Another source of dissatisfaction with Nicholas' teaching is that it is often difficult tocoordinate what he says at different times about the same topic. Take, for example, thedoctrine of universality and individuation. He teaches (page 195) that there are individualswithin a species. He also argues (page 200) that individuation may be illusory. Later(pages 202, 245-256) he says that there is only one individual of each kind, though thisindividual can exist in many places. He then "reconciles" these apparently conflictingviews by

Page 28

holding (pages 248-251) that individuation adds nothing real to specific unity. Finally heteaches (page 262) that there i s really only one being, God. It might be possible toreconcile these views, but Nicholas does not indicate how it can be done.

Nicholas' importance in the history of medieval philosophy seems to be as a witness to afourteenth-century sceptical current. In a way it is unfair to label him a sceptic, since hethinks that a few things can be known as certain and quite a few as probable. Yetscepticism admits of degrees. If philosophical scepticism is a tendency to doubt the mind'sability to attain certainty in philosophical matters, Nicholas is somewhat of a sceptic. Heteaches that, for the most part, philosophy can arrive only at probabili ty, and that even someof its more probable teachings are false.

The Translation

Only one manuscript containing the Universal Treatise is extant, and has been edited byFather O'Donnell. 12 The manuscript contains a large number of small mistakes, many ofwhich have been corrected by the editor. Other mistakes have come to light in the processof translation, and have been indicated in the footnotes. The punctuation is also faulty, andhas frequently been ignored in the translation.

The Universal Treatise is difficult to translate for other reasons as wel l. Sentences arerambling. Some constructions are especially awkward. Ellipsis is common. There are alsouncalled-for changes in number, person, tense, voice, and mood.

The translators have shortened the involved sentences; this results, of course, in changes inconnectives. The translators have also occasionally combined double negatives intoaffirmatives. And, though they have tried to reduce, as much as possible, theunintell igibili ty or ambiguity of the text by choosing what they consider the most likelyinterpretation, difficulty in understanding, and ambiguity, sometimes remain.

The chapter headings added by Father O'Donnell have been retained. Cross-references inthe Treatise , and references to the works of previous philosophers, have been indicated inthe translation or in the footnotes (most of these footnotes are taken from the Latinedition). References to the Treatise refer to the pages (and, in the case of changes in the



text, to the lines) of the Latin edition. These pages are indicated in the translation.

12 J. R. O'Donnell, "Nicholas of Autrecourt," Mediaeval Studies , I (1939) 179-267.

Page 29

Selected Bibliography

Editions and Translations of Nicholas' Works

Denifle , H., ed. Chartularium Universitatis Parisiensis , II (Paris , 1891) 576-587.

Hyman, A., and Walsh, J. Philosophy in the Middle Ages. New York, 1967. Pp. 654-664.

Lappe, J. "Nicolaus von Autrecourt. Sein Leben, seine Philosophie, seine Schriften,"Beiträge zur Geschichte der Philosophie des Mittelalters , Band VI, Heft 2 (1908).

O'Donnell , J. R. "Nicolas of Autrecourt," Mediaeval Studies , I (1939) 179-280.Shapiro, H. Medieval Philosophy. New York, 1964. Pp. 509-527.

Studies

Gil son, E. History of Christian Philosophy in the Middle Ages. New York, 1955. Pp. 505-511.

Lappe, E. "Nicolaus von Autrecourt. Sein Leben, seine Philosophie, seine Schriften,"Beiträge zur Geschichte der Philosophie des Mittelalters , Band VI, Heft 2 (1908).

Moody, E. A. "Ockham, Buridan, and Nicolaus of Autrecourt," Franciscan Studies , VII(1947) 113-146.

O'Donnell, J. R. "The Philosophy of Nicolaus of Autrecourt and His Appraisal ofAristotle," Mediaeval Studies , IV (1942) 97-125.

Rashdall , H. "Nicholas de Ultricuria, a Medieval Hume," Proceedings of the AristotelianSociety , N.S., 8 (1907) 1-27.

Vignaux, P. "Nicholas d'Autrecourt," Dictionnaire de Théologie Catholique , XI (Paris, 1931)

561-587.Walker, L. J. "Nicolaus of Autrecourt's Refutation of Aristotelianism," Downside Review ,67 (1949) 26-42.

Weinberg, J. R. Nicolaus of Autrecourt. Princeton, 1948.

Page 31




Page 181 The beginning of the Universal Treatise of Master Nicholas of

Autrecourt, aiming to determine whether the discourses of the Peri-

patetics were demonstrative.

First Prologue, Part One

Proper procedure requires me to mention at the start what motive

led me to compose this treatise, so that the justifying reason for so

great a project might be0 known. The reason is that many things came

to my mind which, when put toge ther, I considered an unmixed good.

Moreover, further delay was displeasing to God.

First I inspected the teaching of Aristotle and his commentator

Averroes. I saw that a thousand conclusions, or quasi-conclusions,

had been demonstrated by them in abstruse matters, and especially

in those which the intel lect most wants to know. It is true that I did

not find demonstrative arguments to the contrary in all cases, but

there came to mind some by which, it seemed to me, contrary con-

clusions could be held as probably as the ones proposed by these men.

Secondly, I saw that some persons studied their doctrines for

twenty or thirty years; indeed, some until old age.

Thirdly, it became clear that one could in a short time have the

knowledge which is possible about things according to their natural

appearances and to the degree that those men seem to have had it.

Fourthly, I pondered how they all dese rted moral matters and



concern for the common good because of the log ical discourses of

Aristotle and Averroes. Indeed, among other things, there are some

reverend fathers whose heads are now growing grey, whose moral

fibre is so well attested that I would scarcely, in my considered judg-

ment, have dared claim to be worthy to si t on the ground at their

feet; and yet (it is most painful, if it be true) I have seen, although

not with a perfect view, them apparently having so spurned, alas,

the practice that is called moral that, when a friend of the truth 13

13 Nicholas himsel f. See Chartularium Universitatis Parisiensis , tom. II, p. 581.

Page 32

arose and sounded an alarm in order to arouse the slumberers from

their sleep, they sighed, indicated clearly their displeasure, and, re-

covering their breath, attacked him like men armed for mortal combat.

And what are these men doing for God? Certainly charity does

not seem fervent in them. Rather they seem subject to rivalries, jeal-

ousies, murmurings , the grasping for empty praise, and all the mis-

eries in which men are involved. Their li fe seems to differ only for

the worse from the li fe of the crowd. To have spoken thus in general

terms does not harm those I am speaking against. May my tongue

be cut off with a sword if I attack their reputation in some particular,

or if I intend to do this in what I shall write.

Let me return now to what I was saying. I saw that scarcely any

certitude about things can be acquired through their natural appear-



ances, and that what can be obtained will be obtained in a short

time if men turn their minds directly to things, as they have turned

them to the opinions of men (Aristotle and his commentator Aver-

roes). When it became clear, indeed, that man ought to place li ttle

confidence in natural appearances, I came to the conclusion that, if

those who are well- endowed in the political community knew this,

they would turn to moral matters and attach themselves strongly to

the sacred law, the Christian law, which, of all laws, has embraced

the most honorable way of li fe. They would live in charity. The per-

182 fect would direct the less perfect in his action. They would not have

matter for pride when they considered that by merely natural means

they can have li ttle certitude about things. They would purify their

hearts. Envy, avarice, and cupidity, which blind the intellect, would

depart. They would live soberly, they would live chastely. At last,

in the course of time, they would seem like divine men, so to speak,

who would not consume the whole span of their li fe in log ical dis-

course or in clarifying obscure statements of Aristotle or in quoting

the comments of Averroes. Rather, they would explain the divine

law to the people and, diffusing the rays of their goodness on every

side, so live as to appear, in the sight of the most glorious Price

of all nature, as spotless mirrors, and images of His goodness .

This is my goal, this is my aim. Perhaps it would have been more

cautious not to have expressed it, but it seems to me so divine that



ultimately it will gain the effect it dese rves, [whether] through me

or someone else. I humbly beseech the reverend fathers, under whose

wings we are protected, who are the model of all sanctity, that they

allow this work to be finished. Indeed, I really do not see how [God]

ought to grant the breath of li fe to him who would stand in the way

of this thing. Should there be need [of testing its worth], its abili ty

to last will make the matter clear.

Page 33

I declare that, neither in this treatise nor in others, do I wish to

say anything which is against the articles of faith, or against the de-

cision of the church, or against the articles the opposite of which

were condemned at Paris , etc. 14 I wish only to ask, setting aside all

posi tive law, what certainty can be obtained concerning things, and

whether the arguments of Aristotle were demonstrative.

First Prologue, Part Two

I begin my second discussion with something men syllogize about

against those who try to change popular notions and to throw new light

on conclusions that lie hidden in things. And their one statement divides

in effect into two: one involving such a man's judgment in regard to

conclusions he sets down about things; the second involving his judg-

ment in regard to the opinion he holds of his own capacity. I jo in

the discussions into one and present the argument as follows: "Those



conclusions are not true and so his judgment is not sound. Likewise,

a man seems to think higher of himself than the facts warrant if he

teaches conclusions contradictory to those long generally approved by

men of every level of understanding. But the conclusions which in

your introduction you have set down as probable , and which you

are to list in the present treatise , are of this kind, for they contradict

Aristotle and his commentator Averroes. Therefore, etc."

So that the possible answers to this argument might be seen more

distinctly, I begin by freeing myself of what seems to argue a bad

disposi tion of soul toward conduct in the ethical realm, where the

good is at issue. And to bring the truth to light, I shall set down one

rule, a moral rule which seems to me to be very useful and note-

worthy. It is as follows. There comes to a man all the concepts (con-

cerning certain questions) which come to a certain whole group

concerning those questions; and [the case is] of special interest [when

they come], so to speak, naturally from within him, not by being

received from another. Beyond these [concepts] there come [to the

individual], as though from within himself and not by being received

from another, other concepts as clear 15 as the former, and clearer.

By means of these he seems to reach things themselves better and

to bring them more intimately within himself. Every such under-

standing can set down in these questions, without heat or presump-

tion, some conclusions beyond those set down by the whole group,



indeed directly opposed to them, and with a certainty which fairly

satisfies his judgment.

14 Possibly a reference to the condemnation of 1277. See the Chartularium , tom. I (1889) 543-558. There is an English translation in J. Katz and R. Weingartner, Philosophy in the West (NewYork, 1965) pp. 533-542.

15 For ita, alii read alii ita .

Page 34

The basis for the rule is this: Anyone with a natural pre-eminence

in understanding principles has a natural pre-eminence in reaching

183 conclusions. Now, from the combination of those other concepts other

principles result, and consequently other conclusions. For it would

not be right that principles be communicated to someone and the

conclusions denied. A person, then, perceives and experiences that

many concepts occur to him about some questions. He knows also, so

far as certainty is poss ible in such matters, that he forms all those

concepts which others form, and many other concepts by which he

gains closer contact with reali ty, penetrating it, as it were. He then

sees that, as concerns the questions about which he forms as many

concepts as the whole group, he is like the whole group in capacity.

In addition, as concerns the other concepts, he is a sort of third party

of special authority. Thus he learns that he is such that the knowledge

of conclusions finds its natural abode in him above others.

This provides an aswer to a certain argument that has a great

influence on young men when they begin to see the direction men



take according to their differences and their appetites. [They see ]

that, whatever men may say, in fact the whole lo t of them abandon

concern for the intellectual virtues and ceaselessly devote themselves

to the pursuit of riches and posi tions and to doing favours for their

"carnal" friends. They consider this si tuation and see that there are

very few of the opposite persuasion. Then they experience a kind

of struggle. Thei r heads argue that they should do what is in fact

generally approved. The argument runs as follows: "Those should

be followed whose judgment is sounder; now, it is likely that the

judgment of the whole human community is sounder than that of

two or three members of that community."

Of course [the man I have described] does not use this argument,

but the rule stated above. For he sees that he has all the concepts

of the group concerning that question, and many more. So he knows

that if they were asked why they are so eager for riches, then prestige,

etc., he has many other concepts beyond these. He knows that wealth

is not a help to proper living. He knows the good that lies in the

contemplation of God and in the practice of moral virtues. Thus he

can surmise that others do not have a natural capacity, as he has,

to rejoice in this good, since divine thoughts do not constantly reach

their soul. Similarly with regard to many other things he can know

that he is exceptional, standing outside the common throng.

Anaxagoras seems to have used this rule of the privileged, accord-



ing to Aristotle's account in Book 10 of the Ethics .16 When the ob-

jection was raised against him that everybody disagreed with his

16 1179a12.

Page 35

statements, he replied that he was not surprised at this, because they

perceived only externals, as if his meaning were: "I see the concepts

of others well enough, but beyond those I have worthier ones which

set me right."

I am not invoking the protection of this rule, since I do not say

that I have all the concepts of others about the matters to be in-

vestigated below, and other concepts besides. Therefore, for my own

vindication, I lay down another, more modest rule, which is as fol-

low: "On some questions a person gets some thoughts that run coun-

ter to the general opinion. He discusses the matter with persons

whose judgment he respects. After he has stood fast for a long time

because his views have appeared and stil l appear [clear] to him,

he can and should, particularly in purely speculative matters, de-

clare his own judgment honestly, and set down his views as true, yet

so as to expose [his judgment] in those matters to examination. And

therefore, since a person like that does not have a false opinion of

his own judgment, he does not fall into the fault referred to above." 17

Now, I am such a person; and, [keeping in mind] what has been



said in the major premise , the minor can in this manner be used

under it properly.

Since a conclusion was drawn above concerning poor judgment,

I set down two criteria for recognizing whether someone's judgment

is sound. What makes one man's judgment sounder than another's

is that the proper concepts of proposi tions, whereby truth can be-

come apparent in the soul, come to his intel lect with clarity and fully

184 developed. A sign of this is that, in primary proposi tions, everyone

makes a right judgment concerning them once the soul grasps the

proper concepts of the terms which determine the truth of the prop-

osi tion, but, if the proposi tion is not obvious, the intellect will need

to do a lot of analyzing before it gets down to those concepts which

determine its truth.

Accordingly, the rule seems to be as follows: "Whenever anyone

can analyse obscure points, able to make distinctions as if by his

own power, not by habits acquired from others, when he abstracts

one concept from another, not remaining on the surface, but so to

speak piercing to the heart of things in his grasp of causes, that man's

judgment is sound." For it is evident that such a one can get right

to the proper concepts wherein the truth about the problem is con-

tained. With this rule let those well-endowed with judgment con-

sider the quali ty of the minds from which men's doctrines have come.

The second criterion is as follows: "In moral questions there are



certain rules which are posi ted universally, but, when particular cases

17 Page 182.

Page 36

are pointed out, it is often unclear whether the universal rule should

be extended to them. Here one needs a sense of equity (as Aristotle

says, 18 to whom recourse is made as to a sure guide) . Now, if it could

be known of anyone that he is well endowed with this quali ty, it

would be a sign that his judgment was sound. This reveals itsel f in

the process of getting back to motives. For a person of that sort could

not bind himself by a rule in deciding a particular case without

investigating all the possible motives of the lawgiver. When he sees

that those apply in the particular given case, he says that the rule

ought to be extended to that case. Because he can perceive the mo-

tives, he grasps the proper concepts of the terms. Therefore he can

judge soundly.''

I might have said this with respect to the argument set down

above insofar as it seemed to conclude that I have a higher opinion

of my own capacity than the truth of the matter would warrant. The

argument seemed to contain a further conclusion, that is , that the

conclusions I shall give are not true because they directly contradict

conclusions generally approved.

In the first place, one thing is clear, that such a method of argu-

ing is not the proper kind to give proof for the conclusion. Thus,



even if God simply said to a blind man, "White is the most beautiful

of colours," and the blind man knew that it was God [speaking],

nevertheless the fact [that white is the most beautiful of colours]

would not be evident to him, because he would lack the proper con-

cepts of the terms, even though he assented to this proposi tion as true.

Now, in speculative matters, our only aim is knowledge itse lf, that a

thing's appearance might come into the soul. It is not like the obedi-

ence due to the law, where the aim is not knowledge , but action.

There the lawgiver uses such arguments as may win men's assent,

for he knows that, when assent is given, action will follow. 19 But here

our only aim is proof, and so it seems unworthy to use arguments

of this kind. Nay, rather le t us seek the truth concerning the matters

at issue in sel f-evident proposi tions and in experience.

Also , if anyone hobbles himself by such maxims [that the tradi-

tional should not be contradicted], he will at once be put in a quan-

dary by my saying in turn that Aristotle's teaching is not likely to

be sound since he contradicted all his predecessors.

Likewise, by your argument you can reach only the conclusion

that "your teaching is not likely to be sound, etc." I say that, even

if your conclusion is true, the poss ibili ty of [my teaching's] being

true is not thereby el iminated, because even according to Aristotle

18 Nicomachean Ethics , V, 10; 1137b26.

19 F. H. Hourani, Averroes (London, 1961) p. 64.



Page 37

nothing prevents some false assertions from being more probable than

some true assertions. 20 And now, though I have other ways of refuta-

tion, I leave off for brevity's sake . It seems to me that there is no naturally unprejudiced person who

is bound by such maxims in investigations which are said to be made

185 according to natural appearances, but, if there were a thousand [so

bound], they would not believe a proposed conclusion to be evidently

true nor its opposite evidently false. We must also look at one point which is very important. There

could have been some reason why the reverend fathers who followed

Aristotle wanted indeed to allow the sayings of Aristotle to be held

in respect and people in general to place great confidence in them.

For they knew that not all men have a natural capacity for enjoying

the benefit of speculation; on the contrary, even if they went to pains,

they would never acquire a knowledge of a single piece of abstruse

thought. Now if these persons did not have a respect for Aristotle's

sayings , with the result that they did not believe that by studying

them they were acquiring an important science, they would despair

of [attaining] the goal of speculation and would turn to the pleasures

of the flesh. Therefore [the fathers] wanted to allow them to advance

in study in this simple fashion. Now I see that the process has gone

too much to an extreme, for dangerously few turn to the nature of



reali ty, while the majority turn to the opinions of men. Therefore,

to restore the balance, I am quite eager to show which is the true

way of investigating difficult matters.

Mention was made above of an argument that runs: "Every perfect

whole, etc." 21 It is plain that the distinction there made between the

universal and the particular, in an explanation adduced against this

argument, fails to prove that particulars do not contribute to the per-

fection of the universe. The insufficiency of the argument is made

plain by an exposition of the principles upon which the argument was

built.

One principle is that the good is present to the intellect as a

measure for quantifying beings and generally for determining the

properties they may have, so that [the intel lect] may recognize that

the beings in the universe are most justly disposed, and that things

are such as it is good for them to be, and not such as it would be

evil for them to be.

The intellect grasps this proposi tion when it considers what hap-

pens in natural objects and artifacts. In artifacts the workman has

a good as his yardstick. Hence, a house is made just as he thinks

20 Perhaps Topics , VIII, 2; 157a33.

21 Page 202. This prologue was wri tten after the treatise proper.

Page 38

it is good for it to be madeit is not made roofless, it is not made of



feathers, for all these would be contrary to the purpose on which the

goodness and desirability of this house seem to depend. If there

were no good, there would be no obvious plan for the construction

of a house, since there is no end to evil or to the negation of good.

And so there would be no more reason for building the house in one

way than in another, or in countless ways, or not at all .

Now, just as the good and the orderly arrangement is seen to

serve as a yardstick in a craft, the same seems to hold true in nature,

and even much more so, according to Aristotle's teaching, in propor-

tion to the greater strictness of principles on which being depends.

That this is so in natural objects we perceive from two considerations.

First, from a certain inductive process . The desi rabil ity of stones

seems to lie in their use for building monuments for man. Do we not

see that they are not up in the sky because they would be useless

[there]? A horse is not as tall as the sky, for then man could not

mount it. Man's front teeth are sharper for breaking up food, and his

back teeth broader for chewingthis example Aristotle uses. 22

In other things, too, the proposi tion becomes evident for the reason

that there is no limit to evil and the negation of good, as [was said]

above [when speaking] of artifacts. 23 For it would then be unintel-

ligible why [things] are made in one way rather than in another, nor

would we know how to settle the questions which arise in us naturally

when we consider how things are arranged in their inherent quantity



and quali ty. Therefore, just as the craftsman aims at the most suitable

disposi tion of his product, and one that pleases him most, similarly

we must suppose that the beings of the universe are disposed as

would please a sound intellect more.186 The second principle is that the beings of the universe are con-

nected to one another, so that one seems to be on account of another

in some way. The intellect grasps this principle when it considers the

origin of its sense of the desirability and pleasingness of things. Thus,

it is immediately seen that, if you take away from a house its abili ty

to protect from heat and rain, its goodness and desi rabil ity are taken

away. Take away man, and it is immediately seen that there is taken

away that which makes protection a good; and similarly in other

cases. The basis for the proposi tion seems to lie in the assumption

that there is some first being, because no goodness is found in beings

except in conjunction with that being which is the first good. Now,

such beings subordinate to an end do not seem to be joined to [the

first good] except through the end to which they are subordinate.

22 Physics , II, 8; 198b24.

23 This same page.

Page 39

The third principle is one that seems to follow from the preceding.

Since the universe is so interconnected, there is nothing whose ex-



istence does not benefit the entire multitude of beings. Hence this

being is for the sake of that, that for the sake of another, and so on

forever.

The fourth principle is that the universe is always perfect to the

same extent. For if there were a deterioration to some degree of im-

perfection, it could proceed to a yet worse degree, and so on indefi-

nitely forever. Likewise, assuming a first being, it seems that if all

things take place as the first being demands, and this being itsel f

never varies, then whatever it demanded at one time [it will demand]

also at another.

Philosophers have used these principles; and, having expounded

them so, I wish to use them as probable in order to show that this

particular thing which now exists exis ts always. The argument runs

as follows: "Everything whose present existence benefits and em-

bell ishes the whole multitude of some totality that is always perfect

to the same extent, exists always. But this holds true of this thing.

For, in accordance with what was said above, it exists only because

its existence is good, according to the first principle set down above. 24

It is for the good of the whole multitude of beings because the uni-

verse is an interconnected whole, according to the second and third

principles; and the universe is always perfect, according to the fourth

principle. Therefore this thing will always exist."

Likewise, on the basis of the principles set down above, it seems



that nothing in the universe, ei ther in particular or in general, can

be useless, for, if it were, then it would be better for it not to be

than to be. Therefore, since the existence of any existent thing is

good, it seems that nothing can be removed without involving a

deformity in the whole, just as in a very well -arranged house, in which

nothing would be superfluous or incomplete, one could not imagine

the removal of any item except as disfiguring the whole house. We

must believe the same about the whole multitude of beings.

Here is a further argument for the principal conclusion. When

the intellect knows some extremes between which stands a middle

posi tion [produced] by negating the extremes, if the extremes have

any consequences, the middle position will also have a consequence

midway between those consequences and [produced] by the nega-

tion. The truth of this norm will become evident in applying it to

the case at hand. Well , then, it goes as follows. There are, so to

speak, the extremes: "Some being never exists; every possible being

24 Page 185.

Page 40

always exists." And there seems to be a kind of middle position:

"There are beings that sometimes exist, sometimes do not exist." Now

the consequence of "Some being never exists" is "There will be a

total lack of good." The consequence of "Every possible being ex-

ists" will be ''There will always be a total complement of good."



Therefore the consequence of "Sometimes a being exists, sometimes

it does not exist" will be "There will not always be a total comple-

ment of good." And so the universe would not always be perfect to

the same extent. The proposi tions become evident from the fact that "being" and

"good" are interchangeable. And so from "Some being never exis ts"

will follow "A good never exists." The intellect notices that "being"

and "good" are interchangeable because the intel lect always takes

187 pleasure in the fact of "being." Hence we also feel displeasure when

we believe that a thing has become non-existent, and we would feel

it more strongly except that familiarity has made us callous.

Moreover, there is another argument for the conclusion about the

eternity of things which brings out the kind of response to this

reasoning which would be given according to Aristotle's principles

and conclusions. The argument runs as follows: "A conclusion which

can safeguard the rewarding of good men and the punishing of the

evil seems close r to the truth than one which could not so safeguard

these, since the good order of the universe seems to demand that the

good be rewarded and the evil punished, and universal justice seems

to require this. But this safeguard is lacking in Aristotle 's contention

about the decay of things. For, when each and every man becomes

completely non-existent as regards all that is proper to him, it does

not seem possible to understand how one person would have a greater



share in good than another. Hence [Aristotle] himself in the Ethics

seems to mean that the dead have in them neither good nor evil . 25

But will not this be a perverse ordering of the universe?"

Now, from what has been said about the eternity of things it will

be easy to understand wherein the good man has the advantage over

the evil . First, someone might wish to say: "Let us imagine in a

good man two spirits, of which one is called intell igence, and the

other sense . The sense-spirit is subservient, as it were, because uni-

versal and divine likenesses are not so constituted as to come to the

spiri t called intel ligence except when particular and more material

likenesses come first to the spirit called sense . Now, when one speaks

of the decay of the subject [in which these spiri ts reside], this means

only the dispersal of the atomic bodies. The spirits called intelligence

25 I, 10; 1100a12.

Page 41

and sense remain. An infinite number of times these will be in the

same excel lent condition in which they were in the good man, ac-

cording as those indivisibles will be re-assembled an infinite number

of times. In this very fact lies an advantage for a good man over an

evil man, who will recover his evil condition an infinite number of

times just as the other his good condition." Or, one might say that,

when that subject is said to decay, those two spiri ts will take up



their abode in another subject composed of more perfect atoms; and,

since the subject would be more adaptable, intell igibles would come

to [the spirits] more than before.

Before God I pray that these remarks exert no evil influence on

anyone. For although in my opinion they appear far more probable

than what Aristotle said, yet, just as for a long time Aristotle's state-

ments seemed to be probable , though now perhaps their probabil ity

will be lessened, so someone will come along and undermine the

probabil ity of these [statements of mine]. Let us also hold fast to

the law of Christ and believe that there never occurs a rewarding

of the good or a punishing of the evil except in the manner stated

in that holy law.

But to return to the main point: Any conclusion that can be

known when formulated in terms of being can be known through

the concepts of being or of the consequences of being. But the con-

clusion "Not all things are eternal" is formulated in terms of being

and cannot be known through such concepts. Therefore it cannot

be known and consequently you cannot say that that conclusion has

been demonstrated by the Peripatetics. The major premise is known. According to my opponent meta-

physics is a science embracing all fields, 26 and, because of this prop-

erty, by means of transcendental proposi tions it seeks truth concern-

ing any recondite proposi tion at all. The minor premise is clear. For



[the conclusion] cannot be known through the concept of being, be-

cause the concept of being seems rather to argue for eternity than for

deficiency and corruptibil ity. Neither [can it be known] through the

concept of good; rather, [thinking] in terms of [good] argues for

the opposite, for it is better for any being at all to be eternal than

not to be [eternal], as it seems. Neither [can it be known] through

[the concept of] plurality, because plurality and distinction in beings

are consistent with the eternity of being.

188 Nevertheless, it might seem to someone that this conclusion would

be knowable even in concepts of being, or at least that the ex-

26 Aristotle, Metaphysics , XI, 3; 1060b 31.

Page 42

istence of such a [non-eternal] being is possible. The argument runs

as follows: "Every being which does not contain an incompatibility

in its concept is possible; but there is nothing incompatible in the

concept of a corruptible being, because there is no incompatibili ty

in the concepts that something exists now and that it does not exis t

later."

The answer is as follows. What contains an incompatibility in

none of its concepts is possible. Thus the major premise is true, but

not the minor. The minor, indeed, is not true if one admits that

"corruptible being" contains an incompatibility in its concepts, that

is , if one says that "a corruptible being which is part of a whole



that is always perfect to the same extent" contains an incompatibility

and contradiction. (Keep in mind what was said above in the argu-

ment running ''Every perfect whole, etc." 27) If you should say "Every

impossibili ty in secondary concepts reduces to an impossibili ty in a

primary concept," I say that this is true when speaking of a primary

concept which it is possible for us to have insofar as reality is con-

cerned; but there is no need for the reducing always to be such that

we have an evident reduction to a primary concept which we actually

possess.

There is another argument for the main point. It is strengthened

by supposing what the adversary Averroes says in Book 2 of the

Metaphysics , that there is no question which the human intellect can

never answer. 28 This is the argument: "The conclusion that there

would be some question which the human intel lect could never an-

swer, or which might even seem unanswerable to every intel lect, does

not seem probable . Thus it is when, for instance, things are caused

in a segment of eternity. Suppose a definite duration, for instance a

hundred years. The question arises why things have not been caused

with a greater length of duration; and it does not seem that that ques-

tion can be solved. 29 It seems then that they are caused with every

degree of duration. But this seems to be impossible since, whatever

finite degree of duration be granted, there are still infinite degrees

between it and eternity. Therefore [things have been caused] with



ei ther every degree of duration (which seems to be impossible, as has

been said) or certain particular degrees [which has also been ruled

out]."

Likewise there is an argument against Aristotle , who posits that

things pass from being to non-being absolutely. For Aristotle posits

27 Page 185.

28 II, comm. 1; in Aristotelis Opera cum Averrois Commentariis (Venice , 1562-74) vol. VIII.

29 This argument is recounted by Algazel. See S. Van den Bergh, ed., Averroes' Tahafut Al-Tahafut (London, 1954) vol. I, p. 1.

Page 43

that friendly relations towards another proceed from what a man

desires for himself; 30 he also posits that for the sake of the common

good a virtuous man ought to expose himself to death. 31 Now, then,

how can these [propos itions] be reconciled so that it can be argued

in this way? Nothing in whose eyes its own existence is most highly

desi rable ought to perform an act tending to the destruction of its

own existence. But this is the case here according to him. Not so,

however, according to the conclusion that we posi t. For it gives better

reason for urging that one should die for the common good than

does his conclusion previously mentioned, since we have not posited

a change to non-being absolutely. "If these arguments. . . ." 32

Now, as for acts of the soul, in a special treatise on the soul 33

we shall investigate more close ly whether there is one intellect for

all men and, if so, whether there is numerically one act of under-



standing, or more; and so on concerning some other matters. But I

do not want at the moment to take much trouble to remove all

doubts arising about the proposed conclusion. I hope that some-

where else I shall have need to speak again about this matter; and

should there be no need, I shall write pertinent special treatises.

It should be noted that I said before 34 that when a thing is said

to be in the process of dissolution, this is nothing but the separation

of the particle s which are dispersing and parting. Although this is

clear enough in some cases, still it is not in all cases so clear to the

senses as it is when grain is separated from chaff.

189 Now, one should know that there are some men who are willing

to accept only those proposi tions that come into sense experience.

Thus, when it is said that a whiteness is disintegrating, if they saw

that minute whitenesses, like mustard seeds, were separating, they

would then believe the statement. Such men are always asking "How

is this?" and are unwilling to believe unless a man gives a sense

demonstration of it. Nevertheless, not all truths are so demonstrable

by us. Thus some men, by abstraction and analysi s, see many things

which these fellows never see, and are well aware that not all things

are of such a nature as to come in this way into sense experience.

Now, use your imagination, and you will have something like the

dispute in which men are now involved. In some country everyone

is blind from birth. Some among them are eager for knowledge and



aspire after truth. Sooner or later one [of these] will say: "You see ,

30 Nicomachean Ethics , IX, 4; 1166al ff.

31 Nichomachean Ethics , III, 6; 1115a 33.

32 These last three words are quoted from page 203. The prologue was written after the treatiseproper.

33 Page 253.34 Page 187.

Page 44

si rs, how we cannot walk straight along our way, but rather we fre-

quently fall into holes. But I do not believe that the whole human

race is under such a handicap, for the natural desi re that we have

to walk straight is not frustrated in the whole race. So I believe that

there are some men who are endowed with a faculty for se tting them-

selves straight."

Another will say: "Your supposi tion goes right against experience.

What would that faculty be? Not intell ect, for we have that, and we

stil l do not walk straight. Not taste, not smellthese senses effect

nothing."

And indeed, through his metaphysical argument based on natural

desire, he will not be able to make the other assent to what he says

because he will not be able to make something appear to his senses.

He could not do this unless he made him see , thus bestowing on

him the power of sight. Nevertheless, he himself will have certitude

through his metaphysical argument, and he will know that many



things can exist which are not naturally fitted to reach their senses ;

at least there is no incompatibil ity [here].

So I have here arguments probable enough to conclude that the

conclusion about the eternity of things is probable . Some perhaps

will withhold belief because I cannot show that those minute white-

nesses come and go like seeds; but that is no reason for a denial.

They will perhaps make the mistake of saying that I am denying

what is self-evident, as that ignorant blind man would say to his

knowledgeable fellow. Let these men take note that there are many

things which are not naturally evident to sense. Thus, as perhaps

will be said later in the treatise on indivisibles, 35 in a clock there is

a certain wheel that moves, but, no matter how fixedly one watches it,

he would not see it move. Similarly, the faster an arrow moves in

the air, the less its movement is seen. And so, it seems, its motion

could be accelerated so much that it would not be evident. For boys

play with certain toys, like a top, or a hoop with or without a string;

and, the faster these move, the less they are said to move, to the

point that, when one of them is moving very fast, it seems that it is

at rest, and the boys say that it is sleeping.

This also ought to carry special weight because, according to those

who hold Aristotle's conclusions, there are many things which cannot

be readily imagined at first sight; nevertheless men because of Aris-

totle 's pronouncements (or, le t us say, giving them more credit, be-



cause of reasons which they have not known how to fathom) have

ended by scorning imagination and clinging to reason. They say,

35 Page 196.

Page 45

indeed, that, if there is a mountain visible twenty leagues away,

this is because it causes certain realities which they call "species."

These multiply themselves through the whole intervening distance,

so that they are infinite in number and [can be produced] an infinite

number of times; and thus they go on multiplying until they reach

the sight. And the whole process takes place in an instant. In sound

190 the production is success ive and yet it seems to happen suddenly.

They also posit a memory which retains the forms of non-sensory

concepts which sometimes move [the memory] and sometimes do

not; and many such things.

Now, for our part, we do not set down that some such things [as

species] are caused by objects from scratch. We simply say that, when

an object is present to the vision, and the eye is open, etc. (under-

stand that these are simultaneous), some reali ty is now present to

the soul which previously was not present [to it], though it existed.

Nor do we say that particular atoms are released, but just that, as if

by some special motion, 36 what is there imagined is sometimes present

to this thing, sometimes not. And perhaps, if God grants, I shall

compose a special treatise on the soul, where more will be seen about



these matters. And so we shall have said that things which are called

permanent are eternal. ("Now, if the . . . , etc.") 37

If things are posited to be eternal, as above, it will not be clear

how the worth of one thing over another can be proven; for it will

not be proven from the efficient causality required to produce some

new being. It is true that a difficulty also arises for those who posit

generation and corruption, according to the mind of Aristotle. For,

according to this, the conclusion seems to be that the generative

power in man would be nobler than the active intel lective power,

since every active power whose effect is nobler seems to be nobler.

Now, this is the case; the effect of [the generative power] is a sub-

stance; the effect of [the intel lective power] is an accident. But,

according to Aristotle, every substance is nobler than any accident. 38

From this, in conjunction with the other points set down above, the

argument could be derived that natural things are eternal, because

otherwise you would be left with the absurdity that the generative

power would be nobler than the active intel lective power.

Likewise, according to them the argument of efficient causality

does not suffice [to prove nobility] because God is the noblest of

36 See pages 205 and 225.

37 A reference to page 206.

38 Metaphysics , IV, 2; 1003b17. Averroes, De Anima , II, comm. 2, in Averrois . . . Commentarium . . .in . . . De Anima . . . (Cambridge, Mass., 1953).



Page 46

beings, and yet according to them, several of them at least, he is the

efficient cause of nothing according to its natural appearances.

Likewise, the rank of individual seems nobler than the specific

nature, since it is later in generation, and things which are thus later 39

in generation seem to be prior in perfection, as Aristotle seems to say

in Book 8 of the Physics; 40 and yet it does not seem to have any

efficient causality.

Likewise, the receiving of some quali ty or accident, whatever it

may be, does not seem to be a sufficient argument [to prove nobil ity]

because every agent is nobler than the recipient [of an action] ( On

the Soul ). 41 Therefore they encounter a difficulty in solving that prob-

with certainty.

In keeping with the thought stated above about the eternity of

things, it might conjecturally be said that, just as in the case of

taste that flavor is called better which is more attractive to the taste,

and in the case of vision that color, so in the case of the intel lect that

being seems nobler and more perfect which pleases it more and in

which it naturally delights more, or which gives itsel f greater pleasure

because of its nature. Now if you compare a man to an ass or a horse,

and a horse to a stone, the one has a natural satisfaction and pleasure

in being this rather than that.

As a man knows that somehow the likenesses of all things come

to him, so he knows that somehow he seems to be all things. And, as



it is in natural sense-objects, that things move towards things of the

same nature, as fire to the fire in the concave part of the moon's orb,

and earth towards the centre, so it does not seem that those beings

which thus come to the soul would come except because of a certain

sameness of nature. This seems to give evidence about nobili ty and

perfection. That capacity does not seem to be in the stone, for which

191 reason there are no indications by which we might know it is in it.

Therefore man is nobler and more perfect than a stone. I have spoken

about sameness in nature; what I have said, I beli eve to be true; and

so the person who speaks about the earth so that paltry ideas come

to men's souls seems in some fashion himself to have a soul of the

same nature, and therefore paltry.

Concerning the heavenly bodies, with respect to shape, quantity,

motion, light, and that change in beings which seems to be a con-

sequence of changes of the heavenly bodies, we conjecture that there

is nobil ity there, and so they give us much pleasure; and we con-

jecture that they would be more pleasing and satisfying if we knew

39 Read posteriora for posterior in line 27.

40 261a13.41 III, 5; 430a18.

Page 47

everything in them. But in this case I do not see that demonstrative

reasons are possible. Nevertheless, what has been said is sufficient



to answer the question.

Therefore, things are eternal. Indeed, this can be further proved

as follows: "Nothing should be called absolutely false which binds

together the whole multitude of men with a view to communal actions

and generally to the goal of the whole human race; for this arrange-

ment of the universe would not seem to be fitting or right. But all

men, of whatever sect they be, unite in good works because of their

belief in eternity; therefore this [bel ief] ought not to be called abso-

lutely and altogether false." But now we encounter two ways of speaking. One would say that

[things] pass over to non-being and later return. And, though this

way would be, absolutely speaking, closer to the truth, yet the op-

posite is said to have been the mind of Aristotle, for in Book 5 of

the Physics he says: "Things whose substance perishes do not return

numerically the same." 42 The second way encountered would deny a

transfer to non-being, and here, as is certain, the proposi tion [that

things are eternal] would be conceded.

But against this conclusion about the eternity of things there arises

a difficult argument. When a man throws a stone, there exists in the

stone, which moves when the man's hand leaves it, ei ther something

which did not exist previously (and there [you have] the contention,

it seems) or nothing (which cannot be asse rted because the in-

divisibles which are in the stone naturally move downward).



It can be answered that there is nothing there which did not exist

previously. This is Plato's teaching, as reported by the commentator

Averroes in Book 4 of the Physics .43 According to Plato, the motion

of the stone is produced because the hand moves and the stone yields

to it, part of the air yields to the stone, that part of the air is sup-

planted by another part which moves the projectile ; and this continues

to some point determined by the amount of the air which first yielded

or by its motion in a particular pattern. Or it might be said that there

is present in the stone something that was not present before, but yet

existed, just as according to absolute truth and the Catholic faith

there are some things, angels for example, who do not have a being

circumscribed in space but only a determined location; that is , they

are present in one place in such a way as not [to be present] in

another.42 V, 4; 228a3 ff.

43 IV, comm. 68; in Aristotelis Opera cum Averrois Commentariis (Venice, 1562-74) vol. IV. Therefere nce is to Plato, Timaeus, 79.

Page 48

The principal conclusion is further proved as follows: "A thing

ought not to be posi ted to endure in diminished being rather than

in absolute being, but rather the other way round, since absolute

being is more in keeping with the intent of nature. But, when Socrates

is said to be decayed, he stil l endures materially in diminished being,



for example, in memory. Therefore, etc."

Likewise I raise an argument which perhaps will be shown not

to be valid. It would follow that, in the case of a whiteness which

we see, we would not be certain that it would have the same identity

now as before, because it is not sufficient to argue that the present

whiteness and the former whiteness are completely united in sense

experience. Now, according to [the arguments] men use, this is not

sufficient because, if I take two equal whitenesses, Socrates ' white-

ness and Plato's whiteness, these are completely united in sense ex-

perience and yet are not simply one whiteness, as [men] admit. Nor

is identity of si te or place sufficient, because in numerically the same

192 place different things can succeed one another. By such inference

I do not see that there could be another argument except by reason-

ing [this way]: "It was previously, therefore it is now, and so it has

the same identity now as previously." And this reasoning would be

proved through the arguments adduced above for the eternity of

things: "Every part of a whole that is always perfect to the same

extent always exists, etc." 44

And let no one think it ridiculous to make use of the arguments

adduced above 45 concerning the eternity of things. For they are meta-

physical, and such are most certain, as Aristotle says in the preface

to the Metaphysics .46 (Not only, as the expositors say, are they cer-

tain from the nature of the matter, but also as regards us, if there



were someone naturally fitted to use them.) Hence they depend upon

proposi tions which are not received by sense except incidentally.

Moreover, if things passed from non-being to being, it would fol-

low that there would have to be something to act as subject (which

would be matter), and something which would be form in the being;

for such is Aristotle's description of generation. 47 But there is no

necessi ty for matter to exist. For this [necessity] would result chiefly

from two arguments. The first would be Aristotle's, 48 as it seems:

"A substantial change is comparable to an accidental change, but in

the latter there must be something acting as subject to the termini of

the change. For example, if something changes from whiteness to

blackness, there is given a surface which acts as subject to both white-

44 Pages 186.

45 Pages 186 ff.

46 I, 2; 982b2.

47 Physics , I, 7; 190b1 ff.

48 Physics , I, 7; 190a33 ff.

Page 49

ness and blackness." But, admitting that in accidental change a sub-

ject is necessary, this argument requires the positing of matter only

because accidents, according to Aristotle, 49 are beings only in a rela-

tive sense, so that they can have no independent existence. It does

not follow from this that the same holds true in substantial genera-

tion. For Aristotle also, in Book 7 of the Metaphysics, 50 seems to mean



that accidents are beings only because they belong to a being.

The other argument in proof of prime matter seems to be the

Commentator's. 51 If there were no prime matter, one of two things

would follow: ei ther [something] would be changed without change,

or the change would be based upon non-being. Now, ei ther there is

change or there is not. If there is not, and it is certain that something

is changed from non-being to being, then it will have been changed

without change. If there is change, then it has as subject ei ther non-

being (and thus [you have] another unsuitabili ty) or the terminus a

quo or the terminus ad quem (and each is false because these are

the limits of the change). Therefore [there is] something besides

these, and that is called matter or subject.

It is certain that to those who posi t the eternity of things this

argument proves nothing. It assumes as known that something is

being changed from non-being to being, which would be denied it.

Nevertheless, supposing that I posi ted generation and corruption in

things, as men generally do, I would still not be positing prime mat-

ter. I would reply to the argument with the premise that by this

statement "This being is being changed in substance" I understand

merely "This being is , and previously it was not." Nor do I mean

therein something other than non-being and being; or, if something,

I would mean a relationship founded in being. If you should reply,

"This means that being is acquired through change," I would say,



"If this is true, it ought to be understood so as to mean: 'A being

which is changed is and previously it was not.'"

And [now] for the replies . Since he who says "This being is being

changed" seems always to understand something by way of subject,

I would say: "Remove that verb 'is changed', and substitute all the

appearances, and see if from them a subject is necessarily inferred."

According to [my opponents] the appearances are: a thing is which

previously was not, or a thing is not which previously was. Accord-

ing to them this is known or, more truly, inferred. But, now, on the

basis of these proposi tions a subject would never be inferred. If you

193 say, "The ancients agreed that nothing arises from nothing," 52 I should

49 Ibid.

50 VII, 1; 1028a10 ff .

51 Averroes, Physics, I, comm. 68.

52 Aristotle, Physics, I, 4; 187a27.

Page 50

reply: "If by this proposi tion the ancients meant to denote the natural

order which exists among beings (for when one being is generated,

another decays, and so nothing is generated without being preceded

by something to which the emergent being had a natural ordering

in its emerging), then their meaning would be true on that inter-

pretation. But, if by the aforementioned proposi tion they meant some-

thing else, they would be contradicted." So, granted that I posi ted

generation and corruption in things as is commonly done, yet I would



not posi t prime matter, and I used to say so before there occurred

to me the conclusion about the eternity of things.

Concerning what has been said before, a doubt is raised by re-

calling a certain argument previously touched upon to some extent,

namely, that it seems that eternity cannot be demonstrated from the

concept of plurality, since there are in nature as many things as are

possible (as was said above), 53 but corruptible things are possible

(as it seems and as was asserted above). 54 So one might argue as

follows: "Just as the existence of an individual object is possible in

nature so is that of its equal. But neither will exist at the same time

[as the other] because the other would be superfluous. Therefore,

they will exist in success ion. In this way the universe will remain

always perfect to the same extent, and it is better thus by substitu-

tions in that one may posit as large a plurality as is possible."

In this way they could answer the argument I gave above 55 for

the eternity of things, for it is known, through the reasoning given,

that some things are corruptible because they pass into non-being.

Therefore, ei ther [the corruptible things] are those things which are

always in evidence (which is false and contradicts sense experience)

or they are those things which are not always in evidence. And then

ei ther they have non-being when they are in evidence (which is

against sense experience) or they have non-being when they are not

in evidence (and this would be the contention).



To this argument, which seems to do away with the eternity of

things, I have a reply. When it is said that one must posi t a plurality,

I am ready to agree , although it ought not to be posi ted unneces-

sarily, as they themselves admit. 56 But I say that eternity does not

seem to do away with plurality because, though you imagine as many

things as you like, they can still be eternal. Concerning this point,

indeed, it was objected that we [can] imagine some individual equal

[to another]. But here I say that plurality ought not to be posi ted

except to reveal the First Being. Now, since the other is altogether53 Page 187.

54 Page 188.

55 Page 186.

56 Aristotle, On the Parts of Animals, III, 4; 665b15.

Page 51

equal, they are identical in relation to the First Being; and so to posi t

corruption would be pointless . Likewise, one individual object does

not exclude another. If you say it does, this is only because the second

would be superfluous and so the existence of one is as good as if

there were a pair of things.

It was argued that it seems that man's natural desi re for eternity

is not in vain. 57 But a counter-argument is raised, first, because we

see that many things are in vain. For example, someone has a natural

desire to be somewhere and yet he will never be there. This is no

obstacle; nay, rather it seems to confirm the proposi tion. That natural



desi re is a thing that will always be, and, though the journey to a

particular thing may not follow now, it will follow on another occa-

sion. So even now [the desire] is not in vain.

Therefore you must know that on this subject I picture [the si tua-

tion] as follows. Each thing is in the first place intended by nature for

its own sake , so that each thing has, so to speak, its own divinity and

its own goodness, and it is for this that it s intended by nature in the

first place. In the second place, as regards a secondary intention, a con-

nexion is found in some way among beings so that one is for the sake of

another. Now, then, it would seem unfitting for the secondary purpose

of the thing never to be achieved. But, if at some time it is not

194 achieved, [that] does not seem unfitting, because the first purpose for

which it was intended by nature remains. This could be said here.

Hence that desire is something which at some time will be followed

by movement towards Notre Dame.

Some, however, from the Rue Fouarre, 58 might perhaps want to

make a different rejoinder to the argument given. When it is said

"Then the natural desi re would be in vain," they might say: "Not so,

for men achieve their purpose . They contemplate eternity, for they

have it in the intellective soul, which Aristotle 59 (as they claim for

themselves) posited as eternal." But this does not hold good because

not only do men desi re eternity, but they desi re it in such a way that

each desires to achieve it in a manner proper to himself. 60 But accord-



ing to them the intellective soul is common, so as to be numerically

one in all men. 61

But a doubt is raised over the statement that the natural desi re to

go to Notre Dame (and in general with regard to other acts of the

soul) 62 is present now to one individual and now to another. There-

57 Page 203.

58 The University of Paris was located there.

59On the Soul III, 5; 430a22.

60 For alio in line 9 read modo .

61 This was taught by Averroists, of whom there were many at Paris. See E. Gilson, History of Christian Philosophy in the Middle Ages (New York, 1954) pp. 387-402, 521-527.

62 Page 205.

Page 52

fore, le t us determine that mode of presence. My opinion is that that

mode cannot easily be explained or determined. But this [difficulty] is

not peculiar to the one who posi ts eternity in things, but happens to

others also. For it is not evident, if the intellect is numerically one in

all men, what mode of presence it has with respect to each individual.

Alsoand this seems better knownit is not evident what is meant

by the statement ''An accident inheres in a subject." Hence, it is true

that the intel lect somehow seems to abstract this concept of inherence

from certain things, as when it says that skin inheres in the bones, and

afterwards it applies [the concept] to accident and subject as if imag-

ining that it belongs there, but the truth about the real si tuation is not

evident. Similarly one does not posit the inherence of intell igence.



What, then, its mode of presence is in this world, it is not easy to say.

Hence in some matters he have a concept, as it were, through a con-

cept that a thing is or if it is, but do not have a concept of its essence

or properties . It would be like a blind man's being told by a being that

cannot lie (and the blind man would know this [veracity], as was said

above) 63 that white is the most beautiful of colours, for example. The

blind man would know this to be true, and yet would not know how

to attach to his statement any meaning as regards essence or property.

So in this case we satisfactorily conclude that the act of understanding

is now present in this individual (indeed, it seems to be evident

enough), and yet we cannot describe the presence.

Another argument for the eternity of things applies especially to

those who posi t a plurality of formal causes in the same subject. 64 For,

according to them, when the whiteness in a wall is said to give place

to blackness, it does not pass away insofar as what appears is con-

cerned, because it does not appear except as regards something com-

mon to itself and to another whiteness equal to it (hence they are

completely united in sense -experience). Now, insofar as it is the same

as another whiteness, it does not pass away except as regards the sin-

gular [concerned], which is an extrinsic consideration. Therefore, since

it does not pass away as regards the being which appearedand it is

not evident that it passes to non-being as regards other beingit seems

that it does not pass to non-being in any way. It seems that those who



posit a plurality of formal causes ought easi ly to be converted to a

belief in eternity. For, according to them, when it is said "The white-

ness which was in the wall is destroyed," one ought to say that nothing

that was there has been destroyed, although nothing appears there of

what appeared there previously. However, what ought to be said

195 about this plurality of formal causes is not now among the matters

fall ing within our scope.

63 Page 184.

64 The Scotists.

Page 53

Nevertheless, incidentally, it seems to me that it may be more prob-

able to say that in the whiteness of Socrates and the whiteness of Plato

there is some one thing in reality itsel f, one thing which, iso lated from

anything subsequent to it, is of itse lf in no way differentiated in the

two; and that I call the specific nature.

That this would be the case is shown. Granted that some devise

many highly abstract arguments, I do not think that any is more prob-

able than the following: "Things that are completely identified in sense

experience and in the intel lect have a real unity. For, where the intel -

lect makes a discovery in reali ty so that it can point out that this [ob-

ject] has two existences , it then says that there is plurality there.

Where [it can point out that it has] only one, there it must assert



unity. Now, since they are completely one in sense experience and in

the intel lect, it is evident that the intel lect cannot point out this thing

twice without repetition. But this is the case. Assume two equal white-

nesses. These are completely identified in sense experience and in the

intellect."

But you will say: "The major premise is true if they are completely

identified in sense experience and in the intellect so that the intellect

has neither an a priori nor an a posteriori means of posi ting a differ-

ence. But this is not the case here; on the contrary, the intel lect

posits a difference on the basis of different locations. For it is evident

to the intel lect that one thing cannot be in several places at the same

time."

I retort with a question about the major premise which we as-

sumed before, namely, that what are in themselves completely iden-

tified in sense experience and in the intellect are in some way one thing

in reality itsel f. Either this assumed [premise] is necessarily true, or

it can be untrue. If the first, the contention [is established], because

you readily grant the minor premise . But, if the assumption can be

untrue, then we shall have no certainty that something is the same now

as previously, because unity in sense experience and in the intellect

will be inconclusive. Unity of place is inconclusive because different

things can succeed one another in the same place.

Also , no identity ought to be rejected except the one about which



your argument draws a conclusion, arguing from the difference in

location. But [this identity concerns] only a subject numerically one,

or the formal constitution of a subject which is numerically one. It is

true that such a thing cannot be in several places, but it is not true

that the specific nature cannot.

But it seems that I shall prove not only identity as regards species

between these whitenesses but an absolute identity, because the same

Page 54 kind of argument proves that this whiteness is completely the same

now as before. For it seems that the only way of showing this, as was

said above, is that in sense experience and in the intellect it is exactly

the same. 65 But this argument is inadequate to prove that a particular

whiteness is completely the same now as before. Or we might say:

"We have a way of proving identity, and because no way comes to

mind of proving diversi ty, therefore we do not posi t it." And then this

falls short of full certainty.

Here, though, we do have a means of proving diversi ty, namely,

[diversi ty] of location. Therefore we have proved identity in nature

and diversity on the individual level . That level does not come as

such into sense experience, for this whiteness is seen only according

to something common to itsel f and another whiteness equal to it.

Hence, concerning [individuality], 66 we have, as it were, a concept



that it is , but we do not have a concept of its essence or a concept of

its properties , as was said above, in the case of the blind man. 67 If

someone who could not lie (and this [veracity] were known to the

blind man) were to address him and tell him that white is the most

beautiful of colours, the blind man would have a concept of the fact

but would not have a concept of its content. Hence, if he were asked

"What do you mean?", he would say: "I don't know." Therefore, when

it is asked whether [the individual], taken as such, is nobler than the

nature, the question cannot be fully settled since the concept which

ought to be the means of settling that question lies hidden. Neverthe-

196 less, whichever may be said, I do not see that it has impossible

consequences. If it is said that [it is] nobler, on the other hand it seems not

to have a function. [But] this is not an obstacle, because neither is

the nobil ity of God dependent upon some [function] in Him different

from Himself. Thus the [individual] itsel f sets an end, and its function

is like an end because all that precedes it exists for it.

Were it said that it is less noble, there is no great difficulty in what

was said concerning things later in generation being more perfect, 68

because in our view there is no generation. And, granted that there

were, I do not see that that rule could be proved except by induction in

some instances. And such inductions, when they are not confirmed by

a cause, are like Priscian's argument: "If there is order in some, there

is order in all ." But enough of this for the present. Perhaps I shall dis-



cuss it at greater length elsewhere, for the confirming of this conclu-

sion will prepare men's minds to a great extent for the conclusion

65 Add sit eadem after omnino in line 32.

66 Read ipso for ipsa in line 41.

67 Pages 184 and 194.

68 Page 190.

Page 55

about eternity as related above. 69 For, when whiteness i s said to give

place to blackness , it does not cease appearing insofar as it was like

some other whiteness . Nevertheless, previously nothing else appeared,

and so as much appears now as did before.

[There may be] those who stil l have doubts about the argument

first adduced for the eternity of things. 70 In its minor premise it was

said that it does not follow that, if something does not appear, therefore

it does not exis t. It can be objected: "Then, if you are in one

place, 71 we would not be certain you were not in another, because it

does not follow that, if you do not appear there, you do not exist." The

answer, indeed, is that we shall be certain enough, because, while you

exist as an individual, you are not elsewhere. For, when there are

posi ted those things which an appearance will follow, the appearance

is posited as it follows them. Now, this is the case, for we do not posit

in the instance given indivis ibles which are scattered, but we posi t

that they are gathered toge ther so that they are 72 here when the indi-

vidual is here, and elsewhere [when he is elsewhere].



There is another reason, too. It is evident that you are now in one

spot. Positing this, it is evident to the intellect that you are not else-

where, because it is unintelligible that one individual would be simul-

taneously in several places. Therefore, according to this, it would not

be proved by non-appearance.

But there is still a doubt from another source: according to this, it

could not be proved that a moving object is not always in motion, be-

cause it will not follow that, because it does not appear to move,

therefore it does not move, as in [the case of] a certain clock-wheel ,

which moves without appearing to. My answer is that you are speak-

ing ei ther of an individual sense object which moves in a straight line

(and then it is known not to be moving because it appears here now

as previously, and thus is here now as previously, and so is not else-

where; as [was said] above) 73 or of one which moves with a circular

movement (then it is not entirely certain whether it is moving unless

this appears post factum; for example, if some mark were placed on

that clock-wheel, then it would be evident that the mark had changed

when movement had previously been present).

Now, an argument is raised against some bases of the above dis-

cussion. A basis was the concept of good. Now, it seems that it cannot

provide a sure argument in things because men sometimes judge the

false to be true. Thus a person's act is spoiled, and thus it would seem

better for it not to exist. I say that, even though it is evil or imperfect



69 Pages 186 ff.

70 Pages 198 ff.

71 Omit non after te in line 18.

72 Add sunt after the firs t nunc in line 24.

73 Page 191.

Page 56

in some respect, yet absolutely it is better for it to be than not be.

Consequent on that judgment are some good movements and some

good operations, the exis tence of which is better than their nonexist-

ence. Let that be our answer, even though it seem to destroy one of

the arguments given above. 74 Hence, unless we wish to say that every-

thing happens by chance, it seems to me true (according to 75 the

imperfect concepts which we now use) that there is nothing in the

universe whose existence is not better than its nonexistence. And per-

haps he to whom the false judgment is attributed ought rather to wish

to exist with this state of affairs than not exis t at all , with no actions

whatever. 76

74 Page 186.

75 Add secundum after verum in line 44.

76 Add non sit after quod in line 48.

Page 57

197 The Beginning of the Second Prologue

To Master Odo, 77 and to All Others Who Want to

Seek the Truth and Accept It



When my mind in its deliberations turned to thinking of those who

call themselves searchers of truth as it is found in natural appearance,

[I found] one matter among others which of itse lf is very displeasing

to any lover of truth. For those who would claim to proceed discursive-

ly to diverse conclusions by [reasoning from] acts which we experience

in ourselves and from principles sel f-evident from their terms agreed

so much with the mob that their final solution in their investigations

was in accord with the conclusions and words of Aristotle and his

commentator Averroes. They used these as principles, and gave them

such great credence that they considered it entirely irrational to argue

against someone denying their conclusions, as though to argue against

such a one were to argue with a half-wit. Lest I seem to seek glory in

imputing falsi ty to these I have been speaking about so that thereby

I might appear to the people as a corrector of errors, I adduce some

examples and some probable conjectures which ought to suffice in

this matter.

The first is this. When for the first time the doctors of this univer-

si ty heard that some people were asse rting it as probable that material

substance and quantity are not really distinct, 78 I heard from the elders

among them that it was unfitting to argue against such people be-

cause they denied self-evident principles . But I have a query. They

though that to be a principle ei ther simply because it was said by

Aristotle in which case the contention [is established]or because



the intel lect grasps it naturally as soon as it understands the terms,

or because it is something we experience within ourselves . But neither

[of these last] can be said, because ei ther there would then be no

question about such a proposi tion or, if there were, its solution would

be quite easy. And yet their master Aristotle, whom they wish to fol-

low so closely, said that this is a very difficult problem, and accord-

ingly lis ts it among the most difficult problems in Book 3 of his Meta-

physics , near the beginning. 79

Briefly let the argument be as follows: "One should not think it

irrational to argue with someone upholding the other side of a very

difficult problem. It would not be called very difficult unless each part

of it were difficult, ei ther in itself or by reason of the arguments ap-

77 This may be Gerard Odo. See Histoire Littéraire de la France , XXIV (1896) 349.

78 William of Ockham, Sentences , lib. IV, q. 4 (Lyons, 1494-96) f. R viii ff.

79 III, 1; 996a12 ff.

Page 58

parently leading to its solution. But, as has been said, it is a very diffi-

cult problem whether substance and quantity are really the same.

Therefore it must not be rational to judge that it is irrational to argue

against someone upholding the other side. If they have thought this

to be a principle whereas (as is clearly shown by Aristotle, whom they

follow implicitly) it is not, it is most likely that they act similarly in

other matters, so that, especially since they have no arguments and



have always used Aristotle's conclusions as principles, they will say

that men deny principles when a man merely asse rts conclusions which

are true but different from those usually held. Let each person, then,

leave these [supposed principles] aside, and take care to persuade his

soul that the true philosopher should distinguish himself from the

crowd by not accepting some things as principles merely because they

are commonplace."

There is a second example which confirms the contention stated

above. The doctors who gather to keep occupied fill books during their

deliberations and compose long courses in expounding the words of

Aristotle. But, if the precise cause of their accepting Aristotle's words

as true is an evident reason, it seems utterly superfluous for them to

198 thus set aside the consideration of things and turn to a man's words.

For no one doubts that [the purpose] could have been accomplished

in a shorter time if each person gave his reason for holding a con-

clusion.

The third example concerns teachers who settle fully scarcely one

out of ten arguments in their questions. They merely allege a statement

of Aristotle or of his Commentator for the major or minor proposi tion.

Yet, as would be evident to one looking at their books , the proposi tions

are not know from their terms, nor are they such as the intel lect spon-

taneously assents to, nor [do they concern] something which we ex-

perience in ourselves .



My mind has seen all these things and more like them, and it

thought that there was error in them and no li ttle deception. Moved

by a charitable zeal, I thought that their opinion needed help. God

knows [that I was] not [moved] by love of glory, but by the belief

that, when there is a search based on principles, truth will reign in

the soul and there will not be room for falsehood any longer.

And so I proposed, among other things, to show against these mis-

guided persons that there are some conclusions which it is certain that

Aristotle taught and which they do not call into doubt, but which

they could not know at all . In the course of this there were a great

many conclusions which will be examined, not by settling them but

questioning them.

Page 59

First Treatise:

The Eternity of Things

We must investigate the eternity of things especial ly. And first

partially under this form: "Can our intel lect state a conclusion that is

certain from the fact that some things absolutely permanent are not

eternal, those things of which it is commonly said that they are gene-

rated and decay or that they are subject to alteration and the move-

ment of growth?" The proof deals first with things in which, as it

seems, it is more obvious that there is a passage from non-being to



being and from being to non-being, as in [the case of] sensory quali -

ties. But it should be known at the outset that it can be shown in two

ways that we do not know this conclusion: "Not all things are eternal."

[We can] ei ther show that the opposite is true; or show that the only

arguments which appear sufficient to show the proposed conclusion

are not sufficient. Hence it is possible that someone might think this

an open question because the first way is ruled out but not the second.

Therefore we shall begin with the second way.

No intel lect, to which it is certain and evident that something exists

at some time, can say for certain at a later time that that thing does not

exist, unless it has some argument with the power to induce a knowl-

edge of that negative proposi tion asserting that the thing which existed

previously no longer exists. In the case of sensory qualities which exist

now, the intel lect is , or can be, certain that they exist. Therefore at a

later time it ought not to deny the thing's existence unless it has some

argument with the power to induce the knowledge of this negative

proposi tion. The major premise is known, since the intellect, as a ra-

tional power, ought not to change from the extreme of an affirmative

proposi tion to the negative extreme without an inherent reason for the

change, since there is no sel f-evident principle. For, take a proposi tion

about a thing previously existing which is said to be non-existent: "The

whiteness does not exist." My question is whether that [proposition] 80

is known to you from its terms, or is first known through experience



as something you experience in yoursel f. Not in the first way, because

it would be always known to you, and so its truth was known to you

when the opposite was a fact; even in the absence of sensation that

negative proposi tion would be known once its terms were understood.

199 Nor in the second way, for all we experience in ourselves is that, before

blackness takes over, there seems to be a cessation of the act of appear-

ing that we had, so that we no longer experience in ourselves the act

of see ing that we had before. Therefore, since [the proposi tion] is not

known as a principle, it must be as a conclusion, and so by virtue of

some argument.

80 Read illa for alia in line 41.

Page 60

But there is no argument inducing a knowledge of this negative

proposi tion that a thing, or whiteness, does not exist. For both propo-

si tions of that argument would be known ei ther from their terms or

through experience. I shall prove that it is not from their terms be-

cause, if they were known from their terms or were dependent on such,

such a proposi tion would always be understood once they were under-

stood, and thus in the absence of whiteness itsel f one would have cer-

tainty about it.

Therefore [the proposi tion] must be known through experience,

from sensory acts which we experience in ourselves. Therefore, the

proposi tion "This whiteness does not exist" is assumed on the basis of



ei ther a positive sense act or the cessation of a sense act which at first

was experienced with regard to whiteness. Not from the first, because

that would point rather to the existence of the whiteness than to its

non-existence. Therefore from the second, that is, from the cessation

of an act which at first was experienced with regard to the whiteness.

If, therefore, there is produced some suitable argument leading to the

conclusion that the whiteness which formerly existed exists no longer,

it seems to be the one stated.

This is clear also from the fact that what the intellect seems to

naturally resort to when asked about a proposi tion is what serves as

an argument for the intel lect in regard to the proposi tion. But when it

is asked if water is hot, men at once reso rt to an act of touch. When it

is asked if this wall is white, it resorts to an act of sight. And similarly

in other cases. With some young men a more adequate argument might

seem to be: "Because blackness inheres, therefore whiteness does not."

But the intel lect cannot use this as a primary argument because, if

the intellect says that on the advent of blackness whiteness is removed,

this is only because it sees that on the advent of blackness the sense

of sight loses the appearance of whiteness. Thus it seems that the argu-

ment ought to be declared the one into which all others are finally

resolved, and the one which seems to suffice by itsel f.

It would be tedious and useless to discuss all the arguments that

could be given, and it is customary enough that the argument be taken



for granted that is more probable and more suitable for the question

at issue. And if there is another, 81 he who claims he is certain of his

conclusion should propose [this argument]. Otherwise we should be

forced to wander through almost endless arguments. Similarly, it has

been proven well enough that there is no other argument, or, if there

is , that it reduces to this one as the basic argument.

Now, indeed, it is shown that the cessation of appearance is an in-

adequate argument to conclude that a thing does not exist. Let us

81 Read alium for alius in line 30.

Page 61

phrase the argument so as to make its force more apparent by argu-

ing: "Everything which previously appeared to a sense but now does

not appear, no matter what the sense fixes its attention on, no longer

exists. But this is the case with the whiteness which previously ap-

peared, but now does not appear. Therefore, etc." The inconclusive-

ness of this reasoning can be shown in three ways. The first of these

ways seems to me to be more probable than the others, even though

I do not have an evidently demonstrative conclusion. Here it is : "As

concerns the major premise , le t it be said that it does not contain

truth. For natural forms are divisible into their smallest units in such

a way that these, when divided off from the whole, could not perform

their proper action. And so, though they are visible when existing in



the whole, they are not visible when dispersed and divided or sepa-

rated. For this is true even according to the mind of Aristotle when

he says 82 that natural beings have maximum and minimum limits."

The second way would be to say that the case is analogous with

the power of movement, which sometimes performs its act and some-

200 times is at rest. When it functions, it appears. When it is at rest, it then

does not appear, but it is not therefore said to be destroyed. The

same could be said of all other powers. [If the contrary is true,] then

a man is said to be destroyed when those of his faculties are at rest

which relate to his principal function. And, when this happens in all

the parts of some region, then the world is said to be destroyed as far

as that region is concerned. So it has been countless times, and so it

will be, if the world, because of natural appearances, is said to be

destroyed.

The third way would be to say that the nature of no thing's appear-

ance is lost. For if you see whiteness in Socrates' face, blackness in his

hair, and a scar on his forehead, all these things you will see when he

is said to be destroyed. You will not see them where you saw them

before, but elsewhere: the whiteness in John, for example, the black-

ness in a horse, the scar on Peter. But you will say: "I shall see some-

thing similar and specifically the same, but not numerically the same."

The answer is that, regarding things which come exactly the same to

sense and intellect, so that the intellect, at least of itself, does not



posit a distinction, you ought not deny some degree of identity unless

because of a diversi ty of some external characteristics from which it

might be concluded. Now, these two things come exactly the same to

sense and intellect as in the case of two eggs totally alike, so that no

diversity is conceived except the diversity of location. And so, if loca-

tion is set aside, no diversity would be conceived there. Therefore, if

there is diversity, it comes from something external.

82 Physics, I, 4; 187b14 ff.

Page 62

This gives rise to the argument: ''Things in numerically diverse

places are at least numerically diverse. But these two whitenesses are

in numerically diverse places, as sight makes known. Therefore they

are numerically diverse , since the same thing cannot be in diverse

places."

Though this argument is probable, it is not conclusive. The major

premise , though denied by some who assert that the same thing can be

in diverse places, may be grantedI am not will ing, as some think, to

proceed by means of principles so at odds with sense experience. But

the minor premise is denied because, in order to prove that the white-

ness appearing in two eggs is 83 in diverse places, you cannot adduce

the argument that whiteness is in diverse places because sight sees

whiteness when it fixes its gaze on diverse places. This is invalid. For,

suppose in front of or around you several mirrors in diverse places.



According to common doctrine, if you fix your gaze in one direction,

you will see yoursel f and nothing else formally inhering in the mirror.

Similarly, if you look in another direction, you will see yoursel f. Thus

in looking in diverse directions you will see something which will not

be in numerically diverse places. So in the case under discussion the

position might be stated that here there is only something material

underneath, and that separated principles are responsible for the ac-

tions of things, as Plato claimed; 84 for example, a separated whiteness

for the action of this whiteness. (I refer to a separateness of the kind

attributed to the intell igences and also to the possible intellect accord-

ing to the Commentator.) 85 And then that material that is looked at is

only a sort of mirror in which the whiteness can be seen when the

gaze is fixed in that direction. This is how Plato understands it.

Each of these three ways is poss ible, and I do not see that any of

them would have been adequately disproved by Aristotle. However,

for the present I choose the first. But the reasoning given under the

first theory, which was chosen as more probable , does not apply to

motion, if [motion] is a thing distinct from the movable object, since,

unlike other natural beings, it does not consist of permanently exist-

ing atoms that can be dispersed. But before the end of the whole

treatise we shall investigate whether motion is distinct from the mov-

able object, and also what their relationships are. 86 For, if they are

not distinct, it is unnecessary to inquire carefully into them. We shall



also deal separately with the acts of our soul. 87

83 Put esse after ovis in line 26.

84 For example, Timaeus, 52.

85 Averroes, De Anima, III, comm. 4 and 36.

86 Page 205.

87 Pp. 223 ff.

Page 63

Thus in natural things there is only local movement. When this

201 movement results in an assembly of natural bodies which gather to-

ge ther and acquire the nature of a subject, this is called generation.

When they separate, it is called destruction. When through local move-

ment there are jo ined to a certain subject atomic particle s of such a

kind that their arrival seems unrelated both to the movement of the

subject and to what is called its natural functioning, that is called

alteration. Perhaps there is something there which connects and re-

tains the indivisibles in this union, as a magnet does with iron. The

stronger the force of this thing, the longer the subject survives as a

subject. If there were a force of this kind, it would be called the quasi -

formal principle of the thing.

What should be said about the light in a medium? What is it in

the night? It could be said that the light itse lf is nothing but certain

bodies that naturally accompany the movement of the sun or of some

other luminous body also. If in this regard it is objected 88 that light is

generated instantaneously, one must reply that, though it seems to be



generated instantaneously because it happens as if all at once, never-

theless it takes time. According to the common doctrine, sound multi-

plies itself successively in the intervening space because [it proceeds]

by a kind of local movement; yet it seems to arrive as if all at once.

So, too, it is not difficult to imagine that there are some finer and more

penetrative bodies which seem to diffuse themselves almost instantly

throughout the whole intervening space. [This will become clear]

particularly from certain considerations about movement and rest

which will be discussed 89 when this subject is treated. 90

The point of the first chapter would be that, if a well endowed

man reflects without fall ing under some misleading influence, he will

say that men of this age cannot say for sure that they know that some

thing has passed from being to non-being. From this it seems that, if

my intel lect has an alternative to suggest, it ought to claim that things,

especially permanent things, are eternal. For, if in each thing eternity

is better than [the thing's] destruction, it will be seen that the uni-

verse is more perfect if its parts, particularly its permanent parts, are

posited to be eternal, just as its being is admitted to be eternal. [There

is a connection between a thing's perfection and its being,] for, if

movement is distinct from the movable object, as is commonly thought,

perhaps one should say that its perfection, like its being, lies rather in

the negation of permanence. It may be argued as follows: "That hy-

pothesi s about the universe should be made which reveals a greater



perfection in the universe, as long as the hypothesis involves no impos-

88 Read in stando in line 13 as one word.

89 Read dicentur for dicetur in line 19.

90 Pages 206 ff.

Page 64

sibility. But the hypothesis that permanent natural things, which have

been discussed above, are eternal, reveals a greater perfection in the

universe, and involves no impossibili ty. Therefore, etc." The major

premise is known because it is not to be thought that the universe

lacks any possible perfection. If one were lacking, in the same way

[there could be lacking] two perfections, or three , or infinite perfec-

tions infinitely multiplied; and thus there would be no limit, nor

[would there be one] with regard to the rule for measuring divine

truths. The minor premise , too, appears true from what has been said

previously.

This conclusion may be further argued as follows: Things ought

to be said to decay in a way more befitting the nature of a thing. If

[this proposi tion] is considered carefully, it is known from its terms.

However, if it is considered carefully with regard to the cessation of

permanent natural things, there does not take place the total annihila-

tion of some permanent being, but there takes place the removal or

separation of small bodies, or even the withdrawal of bodies previous-

ly inhering and their replacement by others. Consider the case of



sticks that are being burned, or a lighted candle, and you will see that

there constantly occurs a certain withdrawal of bodies. Hence death,

too, as Aristotle says in his book On Death, 91 in one way befalls a man

because the enveloping heat attracts the heat that was within. So, in

things that rot, the natural heat is being released. In brief, by induction

from similar cases it is not clear that decay takes place in things in

202 another way than through the withdrawal of bodies. If in some in-

stance the process appears to take place otherwise because of the

minuteness of the bodies withdrawing, it is not therefore to be denied.

Even according to Aristotle, in Book 1 of the Meteorology, 92 there con-

stantly arise from water and earth bodies which leave their imprint in

the air; and so, when a lake has dried up, one must not think that it

passes over to non-being, but there occurs only a separation and rais-

ing-up of its component bodies.

There is still another [argument]: "Every whole that is most per-

fect because of the inclusion of every perfection and the exclusion of

every imprefection, one in which there is no deformity, ought to have

all its parts as good as possible, especially where the nature of the

thing permits. The universe is [a whole] of this kind. Therefore, etc."

The major premise is obvious because, if a city seems to be disfigured

when any house of that city falls down, much more must the whole

universe be thought to be disfigured in its totality by a deformity in a

part. The minor premise , namely, that the universe itse lf is perfect



91 470a29.

92 I, 9.

Page 65

because of the inclusion of every perfection and the exclusion of every

imperfection, seems known. Even Aristotle agrees. 93 Hence, granted

that something in the universe could in a way be called imperfect by

comparison with something else in the universe that is more perfect,

it is still true that there is nothing in the universe which is imperfect

absolutely speaking, so that it would be better for it not to exist. For

in the universe good should be set up as a standard, since it has the

nature of an end. Hence the only 94 reason you will find why a thing

is what it is , rather than its opposite, is that it is better for this thing

to exist than for its opposite; and similarly in other cases .

Those who delight in looking for ways of evading what seems truer

so far as natural appearances are concerned might reply to this argu-

ment first by saying that it is species, and not individuals , that make

up the perfection of the universe, and that species, indeed, survive

perpetually. I counter by asking what you mean by species. [You may

mean] universal concepts. But they do not seem to make up the per-

fection of the universe more than the external natures of things do.

Or you may mean by a species something absolutely one in itsel f,

really existing in all the individuals of the species . This seems more



probable. It is what might be said by those who posi t that the specific

nature really exists in individuals as absolutely one in itself so that it is

differentiated in them only by the addition of the individual differ-

ences, and so is differentiated only extrinsically.

Now I ask why in the case of two whitenesses you posit some differ-

entiating principles superimposed upon that nature absolutely one in

itsel f. It does not seem unreasonable for me to ask this . For [the two]

are completely united in the senses and in the intellect's first grasp of

[the nature], so that the intel lect would make no distinction unless

there were difference of location. But the location-argument (i.e., that

it is impossible for something numerically one to be in different places,

etc.) would be inconclusive. It is inconclusive because, according to

those who use this argument, the specific nature, which is absolutely

one in itse lf, is in several places. If they can maintain this, it can simi-

larly be maintained against them that, as this is absolutely one it itsel f,

so also is that (what is numerically one).

The argument based on generation and decay would be inconclu-

sive to those who say that, when this whiteness decays, whiteness itsel f

does not decay (except extrinsically) but simply ceases to be shared.

This could be said even if [whiteness and this whiteness ] were not

differentiated at all .

93 Perhaps On the Heavens, II, 11; 291b14.

94 Add nisi before quia in line 21.



Page 66

Coming back to the argument given above, one could make another

seemingly probable reply: "It might be said that a particular thing con-

tributes to the perfection of the universe, but contingently, in the sense

that in nature it is poss ible to produce perfections the exact equals of

203 this, so that another will replace it when it decays." I think this reply

improbable. For one thing, first of all, this replacing seems to smack of

a certain imperfection. This is true, and the spokesmen of the adver-

saries do not deny it, but openly admit it. The Commentator Averroes

in Book 2 of On the Soul 95 says that, when the divine solicitude saw

that the individual could not survive in numerical identity, it took pity

on it by bestowing upon it at least the abil ity to survive in specific

identity.

But there is an argument against this opinion. A cause which pro-

duces its effect by a single causation, to an extent sufficient for the

nature of the whole, is more perfect than one which does not produce

at all , or, if it does , produces by several acts of causation. But, according

to this opinion, God would not produce an effect as final cause by one

act of causation to a sufficient extent, nor as efficient cause except by

many acts of causation. Therefore he would not cause those effects in

the most perfect manner ei ther as final or as efficient cause. Hence it

seems better, particularly because it does not appear impossible, to

posi t one perfect effect than to posi t so many replacements. It also



seems that you cannot say, according to this, that the destruction of a

particular thing has a final cause and therefore no efficient cause what-

ever. For, since it is necessary to substitute in its place another thing

equal in perfection, it seems that it would be better, or at least good,

for [the original] thing to continue in existence.

If these arguments should not be found altogether conclusive, yet

the posi tion taken is probable , and more probable than the arguments

for the opposite conclusion. For, if those who hold opposite conclu-

sions have arguments, let them declare them; and le t the lovers of

truth make a comparison between [the two posi tions]; and I believe

that to anyone not inclined in favor of one side rather than the other

the degree of probabil ity will appear higher in the arguments I have

given. I speak in this way because, in the books of others, I have seen

in favor of recondite conclusions few arguments to which I would not

know how to give probable replies. If they say that I deny sel f-evident

principles, it is amazing how they express such falsehoods openly, for

they cannot do so without lying. Has it not, indeed, been adequately

shown above that, when blackness takes over, to say that whiteness

does not exist is neither a principle know from its terms nor something

that we initially experience in ourselves? It is also amazing how they

95 De Anima, II, comm. 34.

Page 67

consider those to be self-evident principles when virtually all Aristotle 's



predecessors, at least the more il lustrious, agreed upon their opposites .

However, making use of this opportunity, I shall devote a chapter later

to the sel f-evident proposi tion. 96 Moreover, students of philosophy

should not le t them get away with the verbosi ties behind which these

incompetent resis ters of the truth take shelter.

I adduce also an argument that seems probable , but perhaps I have

given it before. 97 (Then [see] the passage marked in the first pro-

logue; 98 then the paragraph [from] "If these arguments" down to "I

adduce also"; 99 and afterwards the passage "These arguments, then

. . . .") 100 How much will they be worth? If everyone naturally desires

something and, not having it, does not rest and, indeed, finds his ex-

is tence somewhat unsatisfying, as it were, [that thing] exists. But

everyone desires his own eternity. Therefore, etc. The major premise

seems known because such a universal desire in nature seems not in

vain; otherwise the disposi tion of the universe would seem unfitting

because there would be a universal desire for something that will never

exist. The minor premise we experience in ourselves . For everyone

wants his own eternity and naturally tends towards it. Thus, if you

set aside all positive law and declare to the generality of men that

they will cease to exist, like horses that they think cease to exist abso-

lutely in the natural course of events, they will grow sad and think

that they are le ft with only a conjurer's trick: Now it is , now it isn't

("or i est, or n'i est une ").



204 These arguments, then, I have brought forward as probable argu-

ments for the conclusion [that things are eternal]. It is certain that this

conclusion cannot be proved by an explanation of the concepts of the

terms of the conclusion (these means of proof are called formal causes,

so than one who knows by them is said to know by means of a formal

cause). Explain as much as you will , the explanation of the concepts

will not provide you with ei ther an affirmative or a negative conclu-

sion. Therefore, in considering this matter, I had to resort to a final

cause and show that it is better to say that things are eternal, and that

greater perfection is thereby attributed to the universe. And, since that

is not impossible, it should be stated; at least it deserves more assent

than its opposite.

These asse rtions are made in conformity with the natural appear-

ances in which we are now involved. I know, indeed, that the truth is ,

and that the Catholic faith holds, that not all things are eternal, nor do

I seem to contradict this, because I am saying only that this conclusion

96 This promise is not carried out.

97 Page 193.

98 The passage is not marked in the extant manuscript.

99 Page 203.100 Page 204.

Page 68

is more probable than its opposite with respect to the natural appear-

ances in which we are now involved.



From this conclusion, indeed, it can be concluded that the asse r-

tions of Aristotle in various places are false, and sometimes in certain

places there is only fiction. For what he says about prime matter is

neither relevant nor true, because his basis in that investigation is that

things pass from being to non-being, and vice versa. Observe that

Aristotle has not at all removed the reason for the ancient's hesi tation.

They did not see that it was in some way necessary to say that, for

something to be generated it would receive being after non-being, or

that for it to be destroyed it would receive non-being after being. For,

in their view, when something is said to decay, there seems to be a

certain withdrawal of atomic particles; when it is generated, there is a

gain of others in addition. So they said that nothing decays into non-

being, nor is anything generated from non-being, as is reported in Book

1 of the Physics and Book 1 of On Generation .101 This objection Aris-

totle in no wise removed. It was, no doubt, difficult for them to imag-

ine how something which previously would have had no being at all

could come into being. Aristotle says here that, though there is not a

being actually, yet there is a being potentially in the prime matter.

Granted that on this assumption there seems to be something to re-

ceive that form if it is produced, nevertheless it is still not apparent

how that can be a being which previously was not a being at all . Also ,

many things which he says about generation have been invalidated.

Also , when he says that there is no movement towards substance, but



towards other things, 102 this s imilarly has been removed by the fore-

going discussion, because, as was said above, 103 there is only local

movement, though it may be allotted different names.

Likewise, on the basis of what has been said, it is clear what must

be said about many statements which have been unintell igible. It was

asse rted that an accident inheres in a subject, 104 but the mode of in-

herence is not clear because it cannot be posited to be like the inher-

ence of skin in the bones. This gave rise to many difficulties: for

example, whether inherence concerns the accident's substance. On the

basis of the foregoing discussion it might be said that these accidents

are only certain atomic particles , and that they are not in the subject

except as a part in the whole, but a part, one must understand, that

is essential and necessary to the whole. Stil l more can these difficulties

be stated about the substance of the subject. Upon the departure of

these atoms [in the substance], what is called the functioning of the

101 Physics , I, 4; 187a30. On Generation , I, 1; 314a7 ff.

102 Physics , V, 1; 225b5 ff.

103 Page 200.

104 Averroes, Metaphysics , VII, comm. 18.

Page 69

thing, and the movement which previously appeared in the thing,

cease to appear. Upon the departure of the other atoms they do not go

away. These ought more properly to be called accidentals of the sub-



ject; yet they, too, are as a part in a whole.

Likewise, the irrelevance is evident of the debate whether

form or matter is the whole essence of a composi te, 105 or whether

205 form is the essential and primary term of generation. 106 Likewise, there

is evident the falsi ty or irrelevance of many proposi tions long employed

by some as of prime significance: for example, that every form in mat-

ter is subject to decay 107 (unless by matter you mean the atomic particles

in flux). (A heavenly body is not composed of atomic particles in flux,

and is therefore perpetual.) Likewise, there ceases the dispute whether

privation is an essential principle of natural things; 108 likewise, whether

a composi te is distinct from form and matter taken toge ther; 109 like-

wise, whether the potentiali ties of matter are infinite. 110 In short, very

many difficulties , even impossible of solution, befall those holding Aris-

totle's principles, but will be of no concern to those who will not posit

the principle about the decay of things, on which Aristotle based him-

sel f. Arguments could be formed against those men out of all the diffi-

culties besetting them.

Likewise, on the basis of what has been said, it can easily be seen

what could be said if the heavenly bodies to whose movements these

lower bodies accommodate themselves at some time return to the same

place they are in now. It can be said that the same individual which

now exists will exist again at some time. For, according to the proposed

conclusion, all atomic particles of which things are composed survive,



and so, once they are assembled, the individual will be numerically

the same as before.

If the question is raised whether the atoms are of the same kind or

are of different kinds, one must say, of different kinds. But the means

of proving the difference of kinds will perhaps become apparent

later. 111

What must be said about the acts of our soul? Certainly we have so

li ttle knowledge here that there is no question about them which the

doctors can settle. We have no sure definition (for example, of what

cognition is), which ought to have been the means of demonstration

in the aforesaid problems. Nevertheless, we can say that it can be

105 Averroes, Physics , II, comm. 31.

106 Ibid. , I, comm. 64 ff.

107 A widely held doctrine.

108 Siger of Brabant, Questions sur la Physique d'Aristote , lib. I, q. 31 (Louvain, 1941) p. 65.

109 Siger of Brabant, Questions sur la Métaphysique , lib. VII, q. 12 (Louvain, 1948) p. 375.

110 Siger of Brabant, Questions sur la Physique d'Aristote , lib. I, q. 40 (Louvain, 1941) p. 80.

111 This is not treated.

Page 70

maintained as a probabil ity, and that it is probable , that the acts of

our soul are eternal, by recapitulating some of the previous statements

above: 112 "Every perfect whole requires that its parts exist, just as, in

their way, these material beings do. In them (at least in the case of

absolutely permanent beings) nothing is new. Nevertheless, through

local movement a particular thing is at some time present to someone



to whom previously it was not present. So, through spiri tual move-

ment, [the same thing happens] there, that is , in our soul." This is

rendered intell igible by considering some things concerning the senses,

which our opponents admit, for example, that species multiply them-

selves across the whole intervening space right up to the [sense] organ.

If you understand this, you will understand my posi tion, or be well

enough prepared to understand it.

If this conclusion is true, it will dispose of almost all of Book 3 of

Aristotle's On the Soul , which gives rise to insoluble difficulties, all

providing arguments against those who posit such things. We are also

freed from the dispute about the agent intellect and the possible intel-

lect. 113 There will stil l be left many matters for consideration, for ex-

ample , whether the soul can have many intel ligibles in act (as they

are called) at the sime time. One must consider, also, the connection

of one intel ligible to another, the difference between them, and the

relationship they have to [thei r] objects. Yet one must know that the

grouping of such spiritual atomic beings sometimes turns out inharmoni-

ous, sometimes harmonious. Just as external material things, because

of disharmony or harmony in the grouping, are said sometimes to be

monstrosi ties, sometimes to be well put together, so in [the case of]

206 the soul an inharmonious grouping is called a false composi tion, a

harmonious one ([i.e.,] when it is properly related to what is in reali ty

outside) a true composi tion.



One must consider, also , the differences between cognition, compo-

si tion, judgment, assent, will ing, not will ing, and so on; also , whether

there is a distinction between the concept and the appearance of a

thing; also , in what way we are to number those beings called acts of

understanding, whether according to the natures proper to the species

or according to the number of subjects. All these matters are not yet

clarified by what has been written above.

Returning to the matter in hand, it could be said that the intel lec-

tual act now present to me will later be present to another subject, and

so on forever. When in my youth I first heard Book 3 of On the Soul ,

it occurred to me, supposing the Commentator's opinion that the intel -

lect is numerically one in all men, 114 to say instead (see how easy the

112 Page 202.

113 On the Soul , III, 5.

114 III, comm. 5.

Page 71

substitution is) that understanding can be called eternal. According

to him, although the intel lect is one as regards Socrates and Plato, yet

Socrates does not always understand when Plato does; although the

intellectual act is in the intellect which belongs to him he understands

only when the intellect is joined to him 115 (this [being joined] depends

upon an image). Now, I, too, would say that Socrates understands by

an act of understanding which is eternally in the poss ible intel lect,



and when the possible intellect actually possesses the same form as is

in the image actually existing in his cognitative power. The argument

would be as follows: "If understanding were posi ted to be subject to

decay, the reason would be because man sometimes understands and

sometimes does not. But this gives no difficulty because, even though

an act of understanding is in the intel lect, he does not understand

[with it] because it does not have the same form as in his image."

Now, if the problem about movement were se ttled, and it were

shown that movement is not distinguished from the movable object, as

far as what is outside the intel lect is concerned, and that relationships

are not distinguished from their terms, it could be universally conclud-

ed as probable that all things are eternal. But I want to defer these

matters until I have treated of indivis ibles, because some of the points

to be raised about them will prepare us for the question of movement.

Indivisibles

It seems good to examine indivisibles in this way: to give Aristotle 's

conclusion first, with his arguments; then to place beside them argu-

ments against them, which, in my opinion, lead to the opposite con-

clusion with sufficient probabil ity.

The Aristotleian conclusion, then, is that a continuum is not com-

posed of indivis ibles; rather each one, no matter how small , even so

small that it cannot be divided by sense, is infinitely divisible, and that

something smaller than it can always be obtained. 116 This is proved by

one ar ument es eciall , which was for a lon time called an "Achilles"



[that is, a conclusive argument]. Concerning it, one solemn doctor of

the Rue Fouarre has said that it would never have been discovered

and come to light if Aristotle had not existed.

According to this argument, take two moving objects, one of which

is twice as fast at the other. Then, according to the definition of a fast

object (i.e., the faster object is one that crosses a larger space in equal

time, or an equal space in a shorter time) , the object twice as fast will

move through double the space in an equal time. Posi t, with the oppo-

nent [that is , the advocate of indivisibles ], that it moves through a

115 Add coniunctus ei after est in line 16.

116 Physics , VI, 1; 231a21 ff.

Page 72

certain space in three instants. Then the argument against the oppo-

nent proceeds as follows: ''As a line is composed of points, so time is

composed of instants. Let [the faster object] move through the space

abc . Now, since the fast and the slow objects began their movement

through abc at the same time, the question is how far the slow one

207 has reached when the fast one has finished its movement in those three

instants. First of all , not to a, because then the fast one would not be

merely twice as fast, as was posi ted. Nor to c, because then it would

have moved as far as the fast one. If to b, so that it has completed its

movement through ab , then the fast one will not be twice as fast. There-



fore there is left the necessi ty of conceding that it is at a and half of b.

Thus b, which was assumed to be indivisible , wil l be divis ible."

However, with apologies to Aristotle, I say that this argument is

inconclusive. But, to refute it in keeping with the opinion that a line

is composed of points and time of instants, how are we to deal with

the superio r velocity of one movable object over another? First, I

make this negative assertion: "It must not be accepted as depending

on reaching the terminus [ad quem] when the terminus a quo is le ft

(I am not here referring to the extreme termini) for, since the space

abc is composed of indivisibles with nothing between them, the mov-

ing object is at b as soon as it leaves a, and so on forever." Secondly,

I make this affirmation: "One movable thing is faster than another

because one rests and the other does not. The fastest movable thing,

indeed, is the one which moves without resting at all. The first heaven

is like this, I believe. 117 But other movable objects rest to a certain

extent, according as they are more or less slow."

Now for the argument. If the fastest movable thing moves in three

instants through a space abc composed of three indivisibles, it has

traversed it by moving without resting. If a movable object twice as

slow moves through that space, I say that it will reach a in one instant

and res t at a for another instant; similarly it will reach b in one instant

and rest at it for one instant; similarly with c. Thus in traversing that

space it will require six instants, three of movement and three of rest.



Thus, when you ask whether the slow object will be in the middle of

the space at the time the object twice as fast has completed the whole

space, the answer is no, if you understand "the middle of the space"

materially, but yes, if you understand it formally, in relation to the

movable object. For example, in the case under consideration, I say

that, in the time taken by the fast object of the aforesaid to reach c,

the slow object has reached b, but it is not in b in the same way in

which the fast object was. For the fast object came to b and was there

only one instant, while the slow object is there two instants; at least

117 On the Heavens , II, 4; 287a24.

Page 73

[it would be] if it had to keep on going. Therefore it is the half-way

mark as far as the object is concerned, for the object has taken three

instants, and would take three [more] if it had to cross the whole space

abc . For, when the faster object has finished its movement abc , the

slow one has reached a in one instant, rested there the second instant,

and reached b in the third. If it were proceeding further, it would rest

for one instant in b, reach c in one instant, and remain there one in-

stant. In this way, it will take six instants in crossing the whole space,

and three in moving through half of it. But the half is reckoned in

terms of time rather than in terms of space considered materially. For

this reason an object twice as fast is one that moves through an equal



space in half the time. 118

Aristotle 119 has another argument, the gist of which is as follows:

"If a continuum were composed of points, ei ther the points would

touch one another or not. If not, a continuum or a 'contiguum' would

never be made from them. If they do, then ei ther a whole point touch-

es a whole point, or part [of a point] touches part [of a point]. But

part does not touch part, since then [the points] would be divisible,

which was denied orig inally. And, if a whole touches a whole, it does

not make it any larger, which is against the hypothesis ."

But the following answer could be given to this argument. "A

whole touching a whole" can be understood in a certain way, that is ,

with each part of itse lf, so that nothing of it is related to the other

mediately, but the whole of it is related immediately as a whole to it.

208 This kind of contact is not possible in bodies because one body is al-

ways related to another mediately as regards the parts farther away,

and [the bodies] do not touch except by means of the parts that are

close together. In this way a point can be said to touch another point

with its whole self, in the manner explained; but this is not true of

bodies. In another way, someone could understand that one of the wholes

is not outside the other (although this meaning is perhaps not explicit-

ly stated). I gainsay this meaning, for in this second way a whole

touching a whole would not make it larger; but in the first way it will



make it larger. Accordingly, a point has its own posi tion and its own

mode of being. Therefore, if points are put together and retain their

own positions, it is senseless to say that they will not constitute some-

thing larger.

Another argument is presented by certain other persons: "If a con-

tinuum were composed of points, the quantified would be made of the

118 This theory of movement was taught by Mutakallemin, a group of Mohammedan theologians.See Moses Maimonides, The Guide for the Perplexed , trans. M. Friedländer (London, 1919) pp.120-122.

119 Physics , VI, 1; 231a29 ff.

Page 74

non-quantified, since a continuum is quantified and a point is not quan-

tified. Now, ei ther you understand by the quantified the composi te it-

self or its extension (and then a point is not quantified, although

according to this interpretation the quantified can be made from the

non-quantified just as the composi te from what are incomposi te) or

you understand by the quantified that which has its own posi tion and

a circumscribed being (and thus I grant that a point can be said to be

quantified, and you will not then be able to conclude from this that

the quantified is made from the non-quantified)."

Again, it is amazing how Aristotle, in the immediately preceding

argument, has accepted as a self-evident principle that which required

proof. For his adversarie s said that an indivis ible added to an indivisi-

ble makes it larger, just as a line of three points is longer than one of



two. Aristotle accepted the opposite of this as a principle, but it seems

that he should not have so accepted it without having given a clearer

explanation of it.

Algazel, 120 however, brings forth some arguments for Aristotle's

proposi tion. One is: "Take a mill wheel which moves, and around its

center imagine a small and unimpress ive circle composed of four

points. Let the circumference of the mill wheel or large circle contain a

hundred points, and suppose that it moves continuously. Then I ask:

When the larger circumference passes through one point, what does

the small circle pass through? If through one point, it moves as much

as the circumference, which is false, since [the circumference] would

go through a hundred points while the small circle went through only

four. But it cannot be said that it rests , since then there would be dis-

continuity in the parts, and the parts will be broken up."

According to the conditions laid down, we must answer that, if in

the small circle there are only four points, in the large circumference

there will be only four points from which straight lines would end at

those four points of the small circle. Lines drawn from other points

would meet before they reached the center. Thus, when these points

move, the small circle will not move, but be at rest. However, when a

point moves from which a straight line terminates at a point of the

small circle, then the point of the small circle moves. If this did not

happen, that line would have to be broken. If for some reason a point



on the small circle does not [have to] move, then no line has to be

broken.

The same person argues from another point of view. 121 If a line

were composed of points, it would follow that not every line could be

120 Metaphysics , pars I, tract. I, div. I, cap. 2; ed. J. T . Muckle (Toronto, 1933) p. 13.121 This is like an argument ibid. , pp. 11-12.

Page 75

divided into two equal parts (for example, a line of an odd number of

points, say three or five). Or, if one point is said to be the dividing-

209 point, every line of an odd number of points will be divided into two

halves at will, but no line of an even number of points will permit

this kind of division.

But le t us not yet consider this discomfiting. For, although each line

seems to have two equal parts, this is ei ther because they are equal,

as in a line of an odd number of points, or because one half is larger

than the other by one point only, and they show up as equal because

a point is so small.

Now the next thing is to bring in some arguments in favor of the

conclusion we are aiming at: first, rather by raising doubts; secondly,

more by explaining the matter in question. Whatever has an infinite

multiplicity of quantified parts is infinite in extension, because, since

each part is a certain extension, and [the parts] are infinite [in num-

ber], it is unintell igible that the extension is not infinite. But this is



[how they describe] a continuum, and a particle which is seen in the

sun's ray falls into this category.

Some answer this by saying that the major premise is true if those

parts are not related as container and contained, and each is outside

any other; but that this is not the case here, for these parts are not

each outside the others.

Against this it is argued that in that continuum there are some parts

one of which is outside another. Now, the total of such parts is a

definite number or infinite . If a definite number, it cannot be said

[that there are some parts one of which is outside another] unless that

continuum is broken down into indivis ibles because, since each part is

divisible into two parts of which one is outside the other, if you say

there are 122 four such parts, you will arrive at what is indivisible or

else [the parts] will be infinite. And thus the total of such parts will be

infinite, and the contention is upheld. If, however, it were said that

the major premise mentioned above is true on the condition that that

multiplicity be of parts of some one determined quantity, this gives

no difficulty because an infinite multiplicity of parts, of which one is

totally outside another, seems to suffice for an infinite extension. There is another argument leading to the same conclusion. Let us

suppose that a per impossible hypothesis never changes the nature of

what is in question unless it changes the nature of the subject, and that

in relation to the predicate. For, when the subject remains totally un-



changed, what we are dealing with is unchanged, since there is in the

subject a cause for the inherence of the predicate in the subject itse lf.

The argument then proceeds. A continuum is now as large as would be

122 Read sunt for super in line 19.

Page 76

[a continuum] composed of its parts if (supposing the impossible)

some agent had broken it up from eternity. This is known from what

was supposed, since the agent would not have added anything to that

continuum, but would merely have broken it up. 123 Now, however,

if (supposing the impossible) some agent had broken up the continu-

um from eternity and had put toge ther a continuum out of those

parts, since you say that the parts are infinite , that [continuum] put

together would be of infinite extension also.

I say (again by way of preface) that, when someone wants to rea-

son out some problem properly, he should first form in his mind the

concepts of the terms of the conclusion. And then see whether you can

abstract from these a concept containing knowledge of the conclusion

and meanwhile take into consideration factors related to the problem.

The closer the concepts you form are to the problem at issue, the more

fitting the argument will be. Sometimes you ought to consider the

opposites of the subject and the predicate, and many such things, as

you yoursel f learn from Aristotle in Book 1 of the Prior Analytics .124

And, if you were noticing carefully, you would know that many argu-



ments, which are sometimes considered subtle because they are very

abstract, are nevertheless entirely logical and are extraneous to the

point in question, so that they are unable to give knowledge about it.

Therefore le t us form concepts about our problem, and see how

they come to the intel lect. On the part of the subject, there comes a

concept about the continuum, common to it and the "contiguum", that

210 is , "having parts with nothing between them." This [concept] comes

to the intel lect by means of sight and touch. Another concept is proper

to the continuum and is an a posteriori one. It comes to the intell ect

through movement, when the movement of one thing necessarily moves

something else. Therefore it is said that "those things which have a

single movement are continua."

The concept of a continuum finite in extension comes to the intel-

lect because something is seen outside of it. Or (which Aristotle thinks

is closer to the truth) 125 I ge t a concept of the finite because there i s

in it some definite section which, taken a certain number of times,

would produce the whole . Likewise the infinite in extension comes to

the intellect ei ther because there is nothing outside it, as the ancients

seem to have thought, or because no common measure could be ob-

tained in it by which the whole might be measured.

Another concept concerns the predicate of the suggested proposi -

tion (that [the continuum] is divisible ), which is indeed a relation.

Now, 126 a relation comes to the intel lect through knowledge of its



123 Read illud for aliud in line 33.

124 I, 27.

125 Physics , III, 6; 206b7 ff .

126 Read autem for autum in line 12.

Page 77

terms; thus one must examine the concepts of the terms. Division, in-

deed, is simply the separation of one thing from something which was

outside it, since it would not be a division if it were inside. So before

division there naturally must be in the continuum something outside

something else, and before division into infinity there must be some-

thing outside something else into infinity.

From these [concepts] it is seen that the concept of this conclusion

(that no continuum is divisible into endless ly divisible parts) can be

abstracted clearly. This is the argument: "In every being which is in-

finitely divisible there is something outside something else into infinity.

But a continuum is infinitely divisible . Therefore there is in it some-

thing outside something else into infinity." Then to continue: "Every-

thing in which there is something outside something else into infinity

is infinite in extension. But in a continuum there is something outside

something else into infinity. Therefore the continuum is infinite in

extension." The conclusion is false . Therefore one of the premises is

false . The major premise is not false , since it is not imaginable that in

something there is something outside another thing into infinity with-

out this forming something infinite in extension. Therefore the minor



premise from the first syllogism (which was the conclusion of the first

syllogism) is false . Thus one of the premises from which it follows [is

false]. The major premise is not false, as appears from what has been

said, because, in order for something to be infinitely divisible it is re-

quired, of its nature, that something be outside something else into

infinity. It remains therefore that the minor premise of the first syllo-

gism is false , which says that a continuum is infinitely divisible .

But perhaps someone might say, concerning the major premise

of the first syllogism, that in what is infinitely divisible there is some-

thing outside something else into infinity potentially, but not actually.

Thus it would not be concluded that the continuum is actually infinite

in extension. 127 But, arguing against this, it is certain that in this desig-

nated continuum an act of intel lect (indeed, even of sight) can

consider something of the continuum without considering the whole.

And it is certain that [the continuum] would be infinite in extent if,

just as there are parts in it which an act [of the intel lect] can consider

when it considers something, there were in the continuum an infinite

multiplicity of parts each of which an act of the intel lect could consider

(as much as nature allows) . But now as follows: "Those things which

an act of the intel lect considers or can consider one at a time (as much

as nature allows) are finite or infinite. If infinite, since each of them is

a certain extension and is outside another, it follows that the continuum

127 Read concluderetur for excluderetur in lines 33-34.



Page 78

is infinite in extension. If finite, they are divisible or indivisible . If di-

visible, then nothing in the nature of the case prevents an act of the

intellect from being able to consider one and not another. If indivisible ,

then the contention is established."

Also , when you say "they are potential," it is true as regards their

being separated from one another. But they are not potential in such

a way as not to be actual. For, first, an actual composi te seems to have

211 parts actually, as a potential composi te has parts potentially. Also ,

what is divided from something else precedes of its nature its division

from the other. Also , parts of the continuum are really distinct if an

act of a sense power can grasp one and not the other. Also , it is certain

that there is something in the continuum now which can be divided

from something else. Therefore the parts are ei ther finite (and thus

the contention is established, for, if they were divisible, they would

stil l have components between which division could take place) [or

infinite] (if infinite, then [there would be] an infinite extension).

Also , this actual continuum is larger than another. Since this is not

by the whole of itsel f, it is by part of itse lf. Therefore there are actual

parts. According to Aristotle in Book 9 of the Metaphysics ,128 "Act is

the [real] exis tence of a thing, not in the sense of what we call poten-

tial [existence], as I say that Mercury [exists] in the stone 129 potential-



ly." Now, indeed, by designating something in the continuum and not

the whole continuum, this definition applies .

Also , as [the parts] are said to have actual being after division, so

[they are said to have had it] before. For the intel lect ought not to

affirm of any being that it has actual being which it did not have be-

fore, since [this actuali ty] does not come to the intellect by some con-

cept by which it did not come previously. For the intel lect does not

attribute the concept of actual being which it did not attribute pre-

viously except because it 130 comes to the intel lect by some concept

concerning existence by which it did not come before. This concept

is a means by which the intel lect concludes that there is actual being.

For example, the intel lect now says that whiteness, which it previously

called potential, is actual, because its power of judging attributes the

predicate of actual being to it, after attributing potentiality to it for a

time, when it considers the previous state of the sight of a person when

he looked at the surface, and its present state. But it is now the case

that, when a division of the continuum is made, [the intel lect] has no

concept concerning existence which it did not have before. From this

[division] it has this concept which it did not have before: "This is

not with that now." But this is not the concept of existence; nor can

128 IX, 6; 1048a31.

129 Read lapide for lapidem in line 11.

130 Read ipsa for ipsum in line 17.



Page 79

this concept be abstracted from this. For it does not follow that, if

something was previously with something else, is was not a being.

Indeed the opposite [is the case]. Also, it does not appear how division

can be a means of establishing a new being.

There is also this argument for [my] contention: "It is not true to

say that, for every magnitude, a smaller one can be found. Thus mag-

nitude is not infinitely divisible ." The [validity of the] reasoning is

well known. The antecedent is explained because, to the extent that

the removal of a part makes the remaining whole smaller, to that ex-

tent its presence makes it larger. Therefore, if the lessening by removal

can go into infinity, there was an infinite extension before any lessen-

ing.

Some adduce also for this conclusion a certain reasoning which

they consider difficult. It is demonstrated in geometry that, if a spheri-

cal body is placed on a plane, it will touch the plane at only a point.

They also accept what Aristotle says in Book 6 of the Physics ,131 that,

if an indivisible moves, it traverses a distance equal to itself before it

traverses a larger distance. Thus, le t that spherical body, touching the

plane beneath it at a point, move over the plane. It is clear that it will

traverse the whole plane by traversing a distance always equal to itse lf,

that is, a point. Therefore the plane itself is composed of points.

Nor does it suffice to say, as some do, that there are no two bodies

one of which is perfectly spherical and the other perfectly level; and,



if there were such, others say that motion would not take place in the

manner stated. In answer: "All of these men say that a point in a

movable body moves with the motion of the movable body itself, and,

212 if not per se , at least per accidens . Therefore let the validity of the

argument stated above be assumed. Whether the point moves per se

or per accidens , it must first traverse a distance equal to itself before

it traverses a greater distance. And yet it does traverse that space, at

least per accidens ; therefore distances equal to itself; and thus points.

Hence it follows that a continuum is composed of indivisibles."

Some persons argue against this conclusion, and claim that they do

so demonstratively, not merely dialectically. They say that, if a con-

tinuum were composed of indivisibles, it would follow that the diago-

nal would be commensurable with the side, the contrary of which is

demonstrated in Euclid, Book 10. 132 They prove their argument by say-

ing that, if the diagonal were composed of points, it would be com-

posed of a certain number of points; and the side likewise , although

the diagonal would be composed of more points than the side, since

131 VI, 10; 241a6 ff.

132 Sir T. L. Heath, The Thirteen Books of Euclid's Elements (New York, 1956) vol. 3, p. 2.

Page 80

it is larger. Therefore, since every number has its measure, these two

numbers [of points] in the diagonal and the side are measured by



unity, since they have some common measure. And every smaller

number forms part or parts of a larger one.

I leave the full solution of this argument and of others like it (as,

for example, that mentioned above concerning the wheel 133 and others

of the sort) to certain ones who hold this conclusion about the con-

tinuum which I have presented as probable . For things which are

said to belong to the imagination agree less well with my mind than

things of the intel lect, which are said to have a greater abstractness.

For the sake of practice, however, I will give some responses (how-

ever probable they are) which are not customarily given.

First, concerning the argument about the diagonal, a certain rever-

end master says that he has arguments against that conclusion (that

the diagonal is incommensurable with the side) which are better than

the arguments Euclid had for his proposi tion. But I answer differently.

The opponents indeed accept as a principle that, if the diagonal were

composed of points, it would be composed of a finite number of points,

like a diagonal drawn on a wall or on the ground. Otherwise this

argument would be invalid. But they are wrong in accepting this as a

principle. For it is not a conclusion from the Master's [principles], nor

is it known to follow from a conclusion from them. For these stand at

the same time: a continuum is composed of points; and a continuum

marked on a wall or elsewhere, whether sensed or imagined, is com-

posed of infinite points.



Perhaps they might say, against this, that, if a point added to a

point makes it larger and causes it to have extension, and three points

are larger than two, and so on, and the points are infinite, it follows

that there would be an infinite extension there. Also , the only reason

why the continuum is said not to be divided into endless ly divisible

parts is because an infinite extension seems to result from what was

said above.

By an infinite extension you mean an extension without limits. This

[extension] I deny; nor does it follow from the points argued or from

what is posi ted, for such an infinity requires that, if some agent or

agents had been dividing it from eternity, the division would never

cease . Now, however, I do grant that, supposing that any magnitude

pointed out to sense or imagination is composed of infinite points,

nevertheless, if some agent or agents had divided it from eternity, they

would finally come to indivisibles. Or else, by an infinite extension

you mean an extension capable of infinite division in any magnitude

pointed out to sense or imagination.

133 Page 208.

Page 81

When it is said that the only reason for denying that a continuum is

divisible into parts endless ly divisible is the infinite extension which

seemed to result, it should be said that, even if there were no reason

other than the denial of the adversary's conclusion, this is no obstacle,



because what seems to result from his opinion is an extension which

is infinite because of a complete absence of limits. For they say that a

continuum is divisible into endlessly divisible parts, and that, if infinite

agents had divided it from eternity, they would never come to indi-

213 visibles; indeed, that infinitely infinite agents in infinitely infinite pe-

riods would never come [to indivisibles]. But I do not posi t "division

into infinity" in this way, as is known from what has been said.

In line with this view an answer can be given to a certain argu-

ment made above which is considered very difficult. 134 This argument

proves that, if a continuum were composed of indivisibles, a larger

circle would be equal to a smaller one. Imagine a circle, and another

circle, a small one, about its center. Now, a line can be drawn from

any point on the circumference to the center through a point on the

small circle. Or also this: a straight line can be drawn from any point

of the larger circle to one point of the small circle. Then there will be

as many points in the small circle as in the larger one, since, if there

were not as many, then straight lines could not be drawn, as was

posited.

We must say here that, although it is true that from any part (of

the circumference) demonstrable to the senses a straight line can be

drawn to some part of the smaller circle, yet it is not true that from

any point of the circumference a straight line could be drawn to some

point of the small circle. Indeed, there are some points on the circum-



ference from which no line reaches down to the center or the small

circle. Therefore, from any point, that is , from whatever we take as a

point when we draw a circle on the ground or elsewhere, a circle not

infinitely divisible, a straight line can be drawn to the center or to

some point on the small circle. But what I mean is that a line cannot

be drawn from every point on the circumference so that that line

would reach some point placed directly under it on a line exactly coin-

ciding [with the first line] (as I draw here so that it may be seen,

since perhaps I am not using geometrical terms in speaking this way).

But, if the line is drawn, [it will reach] a point of meeting, as it were

(as in the diagram). And thus from two points in the circumference

only one straight line will reach down to the small circle or the center

(as in this diagram YY). This is true also of other lines coming down.

In this way there will not be so many points in the small circle as in

the larger one.

134 Ibid.

Page 82

If, then, what has been said in these answers is true, two conclu-

sions might be made in the problem concerning the composi tion of the

continuum. First, the continuum is not composed of parts which can

always be further divided (and in this there would be a departure

from common opinion). Secondly, a continuum demonstrable to sense



or imagination is not composed of a finite number of points (and in

this a departure would be made from the opinion of all those who

have posited that a continuum is composed of indivisibles). And on

this basis [other] proposi tions are true. For example: ''For every mag-

nitude which is given or which is pointed out to sense or imagination,

there is a smaller one (at least, nothing seems to prevent this) , and

yet, along with this, it will be true to say that there is in a thing some

magnitude such that a smaller cannot be found."

Now if someone wished to say that one of our statements above is

false, 135 and that an object moving slowly does not take rests, I see no

more probable escape than to say that, just as one indivisible does not

come to sense or imagination as a finished being, so one indivisible ,

taken in itsel f, does not constitute the space to be traversed, but several

together [do]. The more swiftly or rapidly the movable object moved,

the more [indivisibles] there will be to constitute a unit of space for

it to traverse, and speed and slowness of movement would be meas-

ured accordingly. All these things need no li ttle consideration.

Coming once again to the theory of the continuum's being com-

posed of endless ly divisible parts, an implicit argument is given by

214 Aristotle in Book 6 of the Physics :136 "If the continuum is composed of

indivisibles, let there be an indivisible in a which is to pass along the

line bcd composed of three indivisibles. Either it moves (or crosses b)

and simultaneously has finished its movement (which seems utterly



unintell igible and impossible), or it moves first and has finished its

movement afterwards (which cannot be unless b is divisible), so that it

can be said that it has crossed part of b and there still remains a part

to be crossed." To solve this argument we must see what the word "moves" means,

and what the express ion "it moves through a or through b" means, and

what this means, "it crosses a or b," so that it can be seen when and

in what sense these express ions are to be allowed.

Now, as will be seen in the treatise on material substance, [discussing] whether it is distinct from quantity, 137 this word "moves" im-

plies many proposi tions. I mention now those which suffice for the

present. For it implies that there is nothing between a movable object

and something else, where previously something intervened between

135 Page 207.136 VI, 6; 237a17 ff.

137 Pp. 223 ff.

Page 83

them. Secondly, when this is true of the movable object, the parts of a

single contradiction [that the movable object moves and is stil l in the

same place] cannot be verified. From this it is clear that the statement

"something moves" is rightly described. It is true to say that "some-

thing has been acquired" and that "something is to be acquired" [in

movement]; and it will be said in the aforementioned treatise concern-



ing material substance, etc., 138 how "to be acquired'' is to be under-

stood.

Now, the statement "the movable object moves to b" implies the

first proposi tion 139 and further connotes a certain deprivation of b, and

indicates a certain relationship between the movable object and b

which arises from the fact that the movable object by moving becomes

altogether indistinguishable from b through the removal of what was

between them. I say therefore that the movable object which is in a

and has to cross the space bcd does not move to b (because there is in

b no negation of b itse lf) nor [is i t] ahead of b (because then it does

not move). (And thus there will be a "primary [when]" in movement,

although Aristotle seems to say the opposite in Book 6 of the

Physics .) 140 But, when it is in c, it moves to d (when I say "it moves"

I imply those things which concur and are involved in movement and

which I have just now explained), for it is identical in place with some-

thing when previously it was not. And, this being so with it, the parts

of the single contradiction cannot be verified, especially if it is the

fastest movable object. And it can move to c since there is a lack of

identity with c itself which it had afterwards. But will this be true in

the case given (the movable object passes b)? For, if this means that

the movable object first was not in b, is now in b, and will be in other

than b with no medium between [it and the "other than b"], then it

should indeed be admitted. If [it means that] this movable object



first moved to b, is in b, and will now remain in b, it should be denied,

since it did not first move to b, as has been said.

And from this it is clear what should be said in answer to Aristotle's

argument that "either the movable object moves through b and at the

same time has a completed motion in b, etc." I say that it does not

move to b in any way, but that it does indeed have a changed being in

b, if by "to be changed" we mean "to be different now from what one

was before." But it does not have a completed motion if by saying

that the movable object is in b we mean that some movement existed

before or that the moving object first moved to b and is in b now. But

I say that it is moving to c when it is in b. For all the proposi tions

which movement implies are true then, and not til l then.

138 Page 226.

139 For primo read prima in line 19.

140 VI, 5; 236a6 ff.

Page 84

Another answer could be given. It might be said that Aristotle

means by "movement" a success ive entity infinitely divisible into parts.

But we deny that anything so defined exis ts in the nature of things, as

will become clear in what follows. Or else he means by "movement"

215 what we have said it means ([by saying] what "it moves" does not

mean). 141 We have used this meaning above; and all appearances can

be saved according to what we said. 142

Another argument is adduced by Aristotle 143 concerning the divisi-



bili ty of time. [He says] that time is divisible into endless ly divisible

parts, and that, as a consequence, magnitude is , since these two seem

to be related in the same way to divisibil ity and indivisibil ity. That

time is such, and that it is not composed of [indivisibles], is proven

because there would be no movement. My proof will be that, if some

movable object moved through a space in an instant, a faster movable

object would move through that space in a shorter time, and as a con-

sequence there would be [a length of time] smaller than an instant.

There is another argument which confirms this and which seems

to be evident: "Resting cannot take place in an instant; therefore

similarly neither can movement. 144 It is proven that rest cannot be-

cause to rest is to be the same now as before. But in an instant there is

no before and after, since then it would be divisible."

The answer is to say that by "to move" (we are concerned with

motion in place) is meant "to move in place". What is somewhere was

elsewhere without anything in-between, and will be elsewhere without

anything in-between. We say this because that is the way it is , or how

it appears to us. Therefore, although some things are not moving (since

they are not in a place in such a way as to be elsewhere [in the next

instant] without anything in-between), sometimes we say that they

are moving, but that is hidden from us, as I said above. 145 A movable

thing which is in fact of this kind [always moving] is the first heaven,

which moves with the swiftes t motion. Of such it can be said that it



moves in an instant. When you argue that a faster movable object will

move through that space in a shorter length of time, I say that there is

no movable object faster than it. But you will say: "What of another

movable object?" I say that it moves in an instant. You will say:

"Therefore a faster movable object will move in a shorter time [shorter

than an instant].'' I answer no, for, as I have said above, 146 one mov-

able object is faster than another only because one moves continuously

and the other rests, or because one rests more than the other, so that,

141 Page 207.142 Read ea for ipsum in line 1.

143 Physics , VI, 1; 232a18 ff.

144 Aristotle, Physics , VI, 3; 234a32.

145 Page 213.

146 Page 207.

Page 85

if it moves for one instant, it will rest for another instant in a, or for

more instants in proportion to its slowness .

And, when the second objection says that a movable object cannot

rest in an instant, I say that this is false. To prove it: "To rest is to be

the same now as before. Let this be granted, explaining 'before' in this

way: when a movable object moves to a in a certain instant so that

it is in a in that instant and is still in a in the instant immediately fol-

lowing, then in that second instant it is at rest, since it is the same now

as in the previous instant." Therefore perhaps no movable object ex-



cept the first heaven ought to be said to move, unless by "to move" is

meant that something which was somewhere without something in-

between will be elsewhere without something in-between, whether

the something is real or apparent. And considering the truth further,

though it is not said to move, neither will it be said to rest. Therefore

it would not be true there to say that "this being is moving," but

perhaps that "it is changing from non- a to a." (What I have just said,

"nei ther will it be said to rest,'' ought to be understood [as having the

condition] "unless it is compared to the first heaven, which is by its

nature in motion.")

If what has been said is true, nearly all the conclusions of Book 6

of the Physics, concerning which express mention has been made, are

destroyed. That conclusion is destroyed also which says that everything

that moves is divisible . 147 Aristotle proves it in this way: "The moving

object is ei ther totally in the terminus a quo or totally in the terminus

ad quem .148 If the former, it is at rest. If the latter, it already has a

changed being and thus it is not moving. Or else it is partly in one and

partly in the other, and thus it will be divisible ."

I answer that, according to what has been said above, 149 the divi-

216 sion is not sufficient. For, in the case given above, namely, that the

movable object is in a and has to be transferred to d, it does not move

to b, but, when it is in b, then it can be said to be moving, as has been

seen. Now, according to this, b is neither the terminus a quo (indeed,



[this is] a itself, in which it rested when it was there) nor the terminus

ad quem of the movement. Aristotle was right in adopting that clause

in Book 6 of the Physics, 150 namely "that [what moves] i s at nei ther

of the members or termini"; but in that text he does not disprove [our

interpretation].

Likewise another conclusion of Aristotle 151 is ei ther equivalent to

no argument or is completely destroyed. It says that movement is di-

visible according to the division of the parts of the movable object.

147 VI, 4; 234b10 ff.

148 For certo read termino in line 44.149 Pp. 213-214.

150 See n. 139.

151 Physics, VI, 4; 234b21.

Page 86

For, if by movement he means something inhering in the movable

object, as is commonly thought, there is no such thing, as will be said

later in the treatise on material substance, etc. 152 If, however, by the

proposi tion "movement is divided according to the divisions of the

parts of the movable objects" he means the proposi tion "the movable

object in motion so moves that all its parts move," it will be true,

but then it will be a statement scarcely doubtful.

The same might be said in regard to another conclusion, which

says that that toward which movement proceeds is divisible. 153 For,

if he means that in movement (let us suppose local movement) some-



thing new is acquired which did not exist before (for example, a new

position, as some think), that will negate itsel f, for such things would

be posited gratuitously. Therefore in local movement the movable

object, as will be said later, 154 acquires a new place, that is, makes

itself locally undifferentiated from something between which and it

something was previously interposed. This does not allow the parts

of a contradiction 155 to be verified. Thus i t is true.

Likewise another conclusion is destroyed, 156 which says that in

movement, in regard to the beginning of movement, there is no pri-

mary part which is changed. (This applies to the movable object

which moves, the distance over which movement takes place, the time

in which [it takes place], and the terminus ad quem .) This argument

is based on the contention that all things are divisible into endless

divisibles, which has been denied.

Likewise another conclusion 157 is destroyed, which says that move-

ment precedes all changed being. Indeed, we have above posi ted

changed being which is not preceded by any movement in relation

to it. In the case given above, 158 if a movable object which is in a has

to be transferred to d, it is not true to say that it moves to b; yet with

respect to b it has a changed being. For Aristotle's argument is

founded on divisibil ity into endless divisibles of the things which

concur in motion, as is evident to one inspecting his text. Hence he

says that a half-way movement precedes a completely changed being,



and that a quarter-way movement precedes a half-changed being,

and so on. Notice that he grounds his argument on divisibili ty into

endless divisibles!

Another conclusion 159 also is abolished, which says that an indivis-

ible does not move. His proof is that space would then be composed

152 Page 224.

153 Aristotle, Physics , VI, 5; 236a10.

154 Page 226.

155 Page 214.

156 Aristotle, Physics , VI, 5; 236a28 ff. Also, for quia read qua in line 23.

157 Aristotle, Physics , VI, 6; 237b3.

158 Page 207.159 Aristotle, Physics , VI, 10; 241a6 ff.

Page 87

of indivis ibles (we have conceded this), and also that there is no

movement in an instant (this is disproved above). 160 Now, his argu-

ment, by which he proves that an indivisible does not move, proceeds

from insufficient grounds. He would say that it would move ei ther

when it is in the terminus a quo or when it is in the terminus ad quem ,

etc. The answer is that it has been stated above in this treatise 161 that

this is an insufficient division, because a movable object is moving

neither when it is in the terminus a quo nor when it i s in the terminus

217 ad quem, but when it is at an in-between point in respect to which

it is said to be changed. For example, when an indivisible movable

object which is in a is to be transferred to d, it is not moving when



it is in a. But, when it is in b (to which it does not move) it is mov-

ing, as I have stated above. 162

Aristotle also does not demonstrate the first conclusion of Book 7

of the Physics, 163 because he supposes that it becomes impossible for

an indivis ible to move, which he has not yet demonstrated in Book 6.

And, even supposing that that principle were true, he stil l does not

demonstrate his conclusion, as will be said elsewhere. 164

Also another conclusion of Book 6 165 [is destroyed], which says

that for every movement, considered as movement, there is a more

rapid one. For, as has been said above, 166 no movable object moves

more quickly than that which moves so as not to rest at all . Conse-

quently I argued elsewhere 167 about this against Aristotle, because

then there would not have been, nor would there be, in the realm of

nature, a most perfect individual of a certain universal [nature].

The Vacuum

We have, with probabil ity, destroyed many arguments. Now we

wish to consider certain matters on which we have some unusual

things to say on the basis of what has previously been laid down. Let

us begin the discuss ion with the question whether there is a vacuum,

after laying down a definition indicating the meaning of the name.

By the name "vacuum" we understand that in which there is no body,

but in which there can be a body. It seems that there is [a vacuum]

because otherwise it would follow that there could be no local motion

in a strai ht line, either because two bodies would coincide, or be-



cause all things would have to move and change place in a single

motion. We can be left with nothing so probable as [that there is]

a vacuum; therefore one must posit a vacuum.

160 Page 215.

161 Pp. 215-216.

162 Page 216.

163 VII, 1; 241b24 ff .

164 Pp. 223-224.

165 VI, 2; 232b20 ff.

166 Page 207.

167 Pages 206-207.

Page 88

That all those alternatives are les s suitable than positing a vacuum

seems well enough known, and it will be conceded to us that they

would follow. It is shown because, when a body changes posi tion,

ei ther the place it goes into was empty (and so the proposi tion is

affirmed) or it was occupied by a body (and then ei ther the body

remains and so the two bodies will coincide, which is one of the un-

suitable [alternatives], or it withdraws and passes to another posi tion,

and then I shall ask my former question). By progressing in this

way, you will concede ei ther that there is always a progression ad

infinitum, or that two bodies coincide; or you will concede a vacuum.

But at this point the retort is made that finally there will be a

halt because a compacting will be made. But we cannot make this

asse rtion so as to deny a vacuum, though perhaps Aristotle could on



the basis of his principles. 168 For we do not say that an object would

be compact because of the generating of some new quali ty which did

not exist before, but that it would be compact only through the with-

drawal of bodies, as in the case of wool , or because the parts come

together, that is , they are closer than before. And a body will be

rarified only because its parts are more widely separated than be-

fore; and so it is compact or rarified only through local movement of

its parts. And so another interpretation of the rarefied and the com-

pact would not help us.

There is another answer which I have heard from an influential

teacher, which may seem more probable both on Aristotle's side and

on the side of our conclusion. He imagines that, in straight local mo-

tion, things come to a halt because a kind of circle is reached. For

example, if a body existing in a moves to point b, [the body] existing

in b will also move to point a, and so things will come to a halt. But

this seems inadequate. Let us imagine around a space differences in

position: before, behind, etc. Now let this movable object move in

a straight line. It is evident that what is behind, air for example,

could arrive at that [vacated] spot before what is in front of the mov-

218 able object, and so the rear object would enter the spot. Then what

is in rear of it [would occupy its vacated place], and so there would

never be a halt, as above, unless one admits a vacuum. Likewise , a

body which is in front of a movable object seems to move only be-



cause it is struck and gives way. Now I ask: "What is at a is at b at

the same instant as what is at b is at a . And so it is not clear that this

would give way to that rather than vice versa. Then how would this

give way as if struck? Or else [what is at a is at b] at a different

instant [than what is at b is at a], and then ei ther the two bodies

168 Physics, IV, 6-9.

Page 89

coincided at that first instant or there was a vacuum." And perhaps

this argument might serve in other cases against another approach.

(What I have said about the "next instant" is to be understood in

accordance with the conclusion posi ted above, 169 that a continuum

is composed of indivisibles, and time of instants.)

Another argument might be adduced from new wine in a jar. When

it expands there is an appearance of greater quantity. However, this

is not because of the generation of a new quali ty (we have dealt

with this above) 170 or because of the addition of new bodies. It only

seems to be, because the combining parts, as if there were a certain

pressure there, would now separate and be further apart than before.

Likewise, this argument is attested by what seems more intel-

ligible in the definition of the rarefied and compact. The usual defini-

tion of the compact is that the compact is a thing whose parts lie

closer together. Hence water seems more compact than air only be-



cause its parts are closer one to another. And so in a rarefied thing

the parts somehow are separated, so that a vacuum intervenes ; that

is , the parts could be closer one to another; there is something where

body is not, yet could be. This is my explanation; for those urging

the opposite seem to frighten men by the mere name [of vacuum].

It is true that others use the designation "compact" in another

sense . They say that the compact is what is less yielding to the touch,

and the rarefied what does yield. But then this does not put an end

to one question which the intel lect naturally asks , namely, why this

body is more compact than another. Likewise they cut into the defini-

tion of other things, i.e ., solid and light. For the concept of compact

comes to the intellect solely through see ing a body, so that, as soon

as the body is seen, on the basis of what we see of its constitution

we say it is compact. But sol id comes to the intellect by means of

touch, so that a thing is called solid because it hardly yields to the

one touching it, and light conversely.

If this is what we were saying (a point I am not now deciding

fully), we would investigate how to answer the contrary proposi tions.

The first thing would be to see how the posi ting of a vacuum destroys

the objection raised above, 171 which concluded that either there would

be no local motion, or all things would move in a single motion, etc. It

must be said that this is how we shall understand the case of local

motion. For when a body moves locally in the air, parts of the air in



some way contract and come toge ther. Then it is not necessary that

such a process go on ad infinitum or that two bodies coincide. You

169 Pp. 206 ff.

170 Page 216.

171 Page 217.

Page 90

may imagine something like what would be said. Suppose that wool is

not interspersed with those minute bodies which are said to be there,

and that someone were in a room full of wool , and moved. The parts

would come closer together and draw nearer to one another.

If there were some good arguments against this conclusion, it

would seem that they would be those of Aristotle in Book 4 of the

Physics, 172 though there are but few of them (indeed, hardly any).

Aristotle adduces some arguments in Book 4 of the Physics against

those who posi t a vacuum which is drunk in, as it were; 173 but those

arguments are directed against the reasons they gave for posi ting the

vacuum rather than against the conclusion in itse lf; and we do not use

those reasons. He argues as follows (the reasoning seems very difficult

and is considered to be one of his more subtle ones, at least against

219 one way of posi ting a vacuum): "If there were [a vacuum], it would

follow that local motion would take place instantaneously. The reason-

ing is proved because the swiftness or slowness of a moving body in

relation to another is like the relationship between the media [through



which they move]. For it is clear that, the greater the resi stance of

the medium, the slower the movement becomes. Now there is no rela-

tionship between media when one is a plenum and the other a

vacuum; therefore neither [is there a relationship] of swiftness or

slowness among movements. Now, if movement through a vacuum

were in time, there would be some relationship like that between

times. Therefore it will be instantaneous."

The first thing is to see that this argument is not directed (nor did

Aristotle wish to adduce [it]) against the way of posi tioning a vacuum

that I have used. For we do not posi t a separate, pre-existing vacuum

through which movement would take place, but a vacuum among the

parts of the body. When an object has to move in place, those parts

contract and come closer toge ther. Now, if you wish to speak of the

movement of that first body which is posi ted to move through a

medium whose parts contract, though [the body] is received in a

vacuum, yet previously [the medium] was full. Other things being

equal, the faster those parts contract, the faster the body moves, just

as [fast], perhaps, as if we assumed that it moved through a pre-

existing vacuum. But though the argument is no obstacle to us from

this point of view, it is an obstacle from the point of view of the body

whose parts contract. For here the parts contract inwardly where

there was a pre-existing vacuum, and so, it seems, their movement is

instantaneous.



172 IV, 8-9.

173 IV, 9; 216b22 ff. The expression "drunk in" is found in Averroes' c ommentary on this text,comm. 79.

Page 91

It is shown in other ways that the argument is not conclusive. You

have seen above in the treatise on motion 174 whether the conclusion is

unfitting. For a movable object can be instantaneously in some place

in which it previously was not; and, if by motion you understood a

composi te of several changed things, then the motion would not take

place in one instant, but in several.

And, whatever be the case with regard to the conclusion (which

we do not say is absolutely unfitting, as above in the treatise on

motion), 175 I do say that the reasoning is not valid if it is well known

what determines the swiftness or slowness of one movable object in

relation to another (as stated above in the treatise on the continu-

um, 176 when I answered Aristotle's arguments). Hence, restating

briefly: an agent is called slower only because it rests in some way.

One must therefore consider that in motion there is a certain

essential characteristic so that, just as one part of space is before

another, so it is traversed first; and that essential characteristic cannot

be removed. One must also consider that slowness results from the

fact that the movable object rests, so that to say "One movable object

is slower than another" is the same as saying "One movable object

rests more than another." The movable object rests because of the



determination of its nature or the resi stance of the medium (which

results from the parts of the medium not contracting easi ly). Now

then, granted that there is motion in a vacuum, it does not follow

that, as concerns what was essential in movement (that one part of

space would be traversed before another), it has no relationship to the

movement made in the vacuum. And so you would stil l not conclude

that the motion accomplished through the whole space would take

place instantaneously. Likewise , neither [would you conclude] that

there would be no resting. And this is true if we said, not that the total

cause of the resting in such motion is the resis tance of the medium,

but that the resting is caused by a determination of the moving object

itself. And that theory which I have se t down about success ion, that it

depends on the order of parts in space, was the theory of Avempeche,

as it seems. 177

Other arguments are adduced to show that there is no vacuum.

They are certain natural experiments, as it were, which seem to take

place only because of the impossibili ty of a vacuum. The first 178 con-

cerns the water-clock. 179 This is a jar with an opening at the top and

at the bottom, and filled 180 with water. If a finger is held at the top,

174 Page 207.

175 Ibid.

176 Pp. 206 ff.

177 Averroes, Physics , Lib. IV, comm. 71.

178 Aristotle, Physics , IV, 6; 213a23 ff.

179 Read clepsedra for clapsedra in line 47.



180 Read repletum for repleto in line 48.

Page 92

the water will not come out, though its natural tendency is to fall. If

220 the finger is removed, the water falls . Its not falling in the first case

seems only because of repugnance to a vacuum, because there would

be a vacuum if [the water] came out. For another body could not

enter from above, since that is blocked; nor from below, because then

two bodies would be simultaneously in the same place, which is im-

possible. Say this: this argument is not opposed to the conclusion

which we hold, because we have not yet posi ted that it would be

poss ible for such a separate vacuum to exis t as would be the case

after the removal of the water.

Likewise, I have heard a subtle answer: the fact that the water

would not go out is not because of a repugnance to a vacuum. They

imagine that the whole universe has its proper measure of fullness, so

that there is as much as can enter the universe, taking into considera-

tion the welfare of beings. Now, if that body left, another could not

enter, and so ei ther the whole universe would not have been wholly

full, or two bodies would coincide. In that [problem] I now choose

the first answer.

A doubt arises in connection with the sense in which we posi t a

vacuum. Suppose a body moves locally. You say that the parts of a

body, of air, for example, which were in the place to which [the



object] moves, contract so as to occupy less space than before. But,

following this up, I ask whether anything enters the place left by [the

object]. If we say no, then we shall posi t the same kind of vacuum as

others do, a separate vacuum. If we say yes, then something would

enter, air, for example. Then, as before, we shall ask about the place

left by [the air], and so we shall not avoid another unfitting si tuation,

which we sought to escape by posi ting a vacuum. Perhaps on this

point it will be a suitable reply to say that some parts of the air which

were, as it were, behind the object somehow expand (because they

moved) so that, being less contracted, they fill the place, and this up

to a certain quantity, not, however, ad infinitum .

Likewise, though we might not have to posi t a vacuum on that

basis , yet we might posi t it for another reason, to avoid falling into

the awkwardness of having all bodies in front move when one body is

moved, 181 and also to avoid the position we have mentioned briefly, 182

that in the previous instant the parts of the space contract, which we

do not approve of. Perhaps we shall consider this point elsewhere. 183

Against what we have said about the vacuum, there is the experi-

ment with an inflated bladder which cannot be compressed. This

would not seem to be [possible] if there were a vacuum intervening,

181 Page 217.

182 In the previous paragraph.

183 This point does not seem to have been considered elsewhere.



Page 93

so that the parts would contract. Here one of two kinds [of answer]

must be given. [It might be said] that the parts of that body which is

enclosed in the bladder cannot be further compressed, at least easi ly.

Hence, though the parts of air through which motion takes place con-

tract, yet they are not so cohesive as to prevent some vacuum 184 re-

maining among them. They have the abili ty, then, to contract up to a

certain extent, and this limit does not hold as regards the contents of

the bladder. Or else it might be said that the reason for this is that

there then remained a vacuum completely separated from the rest and

such that another body would not penetrate.

The ancients adduced one argument in favour of the vacuum

hypothesis. 185 They argued as follows: "If there were no vacuum,

there would be no increase in size. The proof is that the increase takes

place only by some corporeal addition. That, then, is received ei ther in

a plenum or in a vacuum. If in a plenum, two bodies would coincide.

If in a vacuum, the hypothesis is established. Nor would it be valid to

say that [it is received] in something previously filled with some

subtle body. First, this seems only an evasion. Secondly, [the enlarged

body] in this case would not occupy more [space] than [the orig inal]

body. Now, a whole arm, interspersed with those subtle bodies, was

previously only one foot long, and now it is two feet long."

Aristotle 186 does not answer this argument, but says that those



arguments work against themselves. For, granted that there is a

221 vacuum, it stil l follows that there will be no increase, because it

follows ei ther that some part of the enlarged body will not have been

enlarged, or that increase would not take place by some corporeal

addition, or that two bodies will coincide, or that the whole body will

have been increased. The proof of the reasoning is that, if in the en-

larged body there are empty spaces, then ei ther there will be empty

spaces everywhere and so the whole will be a vacuum and nothing

will be corporeal (which is one of the inadmissible results), or some

part of the enlarged body is vacuum and some plenum, and then

ei ther the full part, even with its lack of emptiness, is increased, or it

is not. If it is granted that it is increased, I ask: by a corporeal addi-

tion or not? If not, this is another inadmissible result. If it is increased

by a corporeal addition, then since in this hypothesis that part was

completely full, there will be, according to them, two bodies in the

same place.

With all due respect to Aristotle, this argument ge ts nowhere

against them. First le t us see what "increase" means. Suppose that

184 Read vacui for vacu in line 35.

185 Aristotle, Physics , IV, 6; 213b19.

186 Ibid. , IV, 7; 214b3 ff.

Page 94

some body is composed of four indivisibles, a, b, c, d . I say that be-



tween these indivisibles there are empty spaces. Separate a and b by

one indivis ible . I say that, upon the approach of a suitable thing, the

indivisibles spread themselves, as it were, so that they stretched some-

how (like ab , with an empty space of two indivisibles), and there

they will receive within them the thing that is congruous with their

own nature, and thus increase will be effected. Such a meaning of the

proposi tion "When a body is increased, every part of it is increased"

does not at all include the primary parts of the body increased, in the

sense that an indivisible is enlarged. The meaning is that, after the

increase of any composi te part that is demonstrable to the senses , it is

true to say that it is larger than it was before the increase. For ex-

ample , a hand after growth is larger than before growth, and similarly

in other cases.

Again, the ancients argued that a jar fil led with ashes takes as

much water as if there were no ashes in it, or almost as much. The

Commentator Averroes 187 who wishes to resolve this argument says

first that he has not made the experiment. In the second place he says

that it is because some parts of the water and some parts of the ash

are destroyed. The evidence for this is that, if the ashes are later dried

out, they do not appear in so great a quantity. As for his first point, it

seems that he would not be much of a lover of truth to neglect so

easy an experiment. His second point seems an evasion, and what he

says is no obstacle because the ancients 188 would say that, if the bulk



appears less, this is because the parts are close r together than before.

The ancients had another way of arguing against those who deny

a vacuum and posi t generation in things. 189 Suppose that from a body

of lesser bulk arises a body of greater bulk. Then it must be ei ther

that there is a vacuum, or that necessarily there takes place a com-

pressing of bodies [those round about], or that, just as here a body of

greater bulk would be generated from a smaller one, so necessarily, in

another place, a body of lesser bulk would be generated from a larger

one in the same proportion. In avoiding this they grant [that there

is a vacuum]. This reasoning follows from the fact that the generated

body occupies more space than it did before.

Again, when it is asserted that a body moves locally, it is received

ei ther in a plenum or in a vacuum. If in a plenum, two bodies coin-

cide. If in a vacuum, the proposi tion is affirmed. The last of Aristotle's

expositors replies that by "to be received" is meant ei ther what pre-

cedes being received (and thus the body is received in another full

body) or the being which is received (and thus it is received in that

187 Physics, Lib. IV. comm. 56.

188 For antique read antiqui in line 32.

189 Aristotle, Physics , IV, 9; 216b21 ff.

Page 95

full body which is received); and so there is never a vacuum. Nay

rather, in accordance with what has been said, it seems that there

would be a vacuum because, while it is true that one concept of



vacuum is quasi-relative and would not be attributed to a thing except

when there is the negation of a body in it, yet it will be seen that there

222 is a vacuum in the absolute sense he speaks of, whether it be a posi -

tive or a privative being, so that, if a body were removed from any

place without having another body enter, that would be called a

vacuum in which that body formerly was. If a body should come

[there], the nature [of the vacuum] would not be destroyed. Only,

indeed, previously it was thought of [in] a relative concept as existing

under a negation of a body; now it will be thought of as existing

under the contrary. It is true that to a person speaking in this way it

would be said, unless he had something else on which to base his

imagination, that he is being led by imagination, and that the imagi-

nation is not to be trusted.

Material Substance and Quantity

[I treat] the problem of material substance and quantity in con-

nection with the statement: ''Quantity is a thing inherent in material

substance, but distinct from it." It needs to be investigated whether

they are mutually distinct. First we shall inquire into continuous and

discrete permanent quantity; then into success ive quantity.

On the first point, one conclusion is posi ted, namely, that the

intellect is not compelled by some reason to say that permanent

quantity is a thing distinct from material substance. Here one must

first inquire how a problem about total identity can be settled by



man. A problem about partial identity is settled only through a mani-

festation of some things in which [two things] agree (as two white-

nesses agree in that they penetrate sight). Similarly, total identity will

be proven only by the agreement in all the things that can be attrib-

uted to them. It follows from this and from another consideration that

[the problem] is not fully determinable by man. For the intel lect

cannot fully arrive at a conclusion which depends upon a minor

premise not fully understood. But that is the case here. For the con-

clusion here depends upon this minor premise : "Everything that is in

this thing is in that, and in the same way." But this is not fully known.

For, granted that agreement were shown in such and such details, it

does not therefore follow that there is agreement in all details, be-

cause perhaps in this thing there are some details of which you are not

aware. It is sufficient, therefore, since we cannot settle the matter com-

pletely, if, so far as is possible, on the basis of the details which are

seen to be in each thing, one shows by induction a total agreement in

Page 96

them. And so in disputes, when an opponent shows agreement in all

details which seem to be known by a man, the respondent bears the

onus of saying where there is no agreement, or else total identify [is]

concluded. This is , therefore, sufficient to make an assertion as long as



no known fact is le ft out.

In accordance with what has been said, I set down some con-

clusions. The first is that permanent quantity is not distinct from

material substance. This we prove (so far as such a matter can be

proved). Things which coincide in all the details which are recognized

to exist in them are not distinct. But quantityas concerns everything

outside the souland material substance are of this kind. The proof:

"When we think of those things that are totally inseparable so far as

pertains to all movement or change, we think of them as totally coin-

cident. Hence the understanding cannot attribute anything to the one

without being able to attribute it to the other. But this is the case here.

For, if the quantity becomes greater, so too the substance. If it is

generated, so too the substance. And so on. Therefore, they are totally

coincident." This method of proof satisfies Aristotle , in Book 4 of the

Metaphysics ,190 when he proved that being and oneness are the same

because they are generated by the same generation, etc. Obse rve that

he there takes "by the same generation" ei ther to refer to a measure

of time or simply as it stands. [If the former,] this helps to confirm

the proposi tion. [If the latter,] then the adversary would deny the

minor premise , or, rather, would say that in that case there are two

generations of which one is naturally prior to the other, just as being

is naturally prior to oneness. It should be noticed that, because plur-

ality is not to be posited unnecessarily, it is sufficient for the upholder



223 of identity to know how to reply to the arguments opposed to [his]

conclusion. Hence the onus of proof lies upon the one positing the

distinction.

In the same way it can be said that a subject and its distinctive

characteristics, so far as pertains to anything that can be considered

in the real order, are not distinct, because no kind of change can

separate them. The same can be said of fire and its heat, of water and

its coldness, and similarly of other things in relation to what have for

a long time been called the qualities of the elements. In the same way

it can be said that the number of continua, as regards what it implies

outside the intellect, is not distinct from the continua. There is also

another reason [for saying this]. Sometimes there are two proposi tions

which are rendered impossible or false for the same reasons, if they

190 IV, 2; 1003b23 ff.

Page 97

are verified without positing that the predicate entails something in-

herent in its subject and distinct from it. If one is verified without

such a distinction, the other can also be called true in the same way.

But that is the case here. For we talk of "two intel ligences," "two

continua." Now, there is no more impossibili ty involved in the one

case than in the other. For, if the concept of duali ty can be enter-

tained about two intel ligences, and granted that there is in them no

common reali ty really distinct from them, it does not seem that it



would be less possible in the case of two continua. The same can be

said of relations and of the categories in general. For when there are

two white objects, no real generation or corruption appears [either in

the things or in their duali ty] without the other being similarly

affected. If it appears in some cases, doubt will enter our statement.

However, it seems to some that the number of two continua is

distinct from the two continua, for those things are distinct which are

such that something is really in one that is not in the other. But that

is the case here. For if there are two continua and one becomes

greater by addition, ei ther . . . or else these continua are now greater

than before; and yet the duali ty is not greater than before. I say that

in one way duali ty can be taken for the concrete object for which it

stands when one says "The two continua are two," and then one

would admit that it is greater than before. In another way [it can be

taken] for what it signifies , and then it implies a concept to which,

since [the concept] is abstracted from things, it is irrelevant that they

be large or small. Hence, when the intellect conceives of a thing as

undivided in itse lf and divided off from any other, and of another

thing in like manner, and compares the one with the other, it abstracts

the concept of duali ty.

The same might be said of equali ty. One might argue that it is

distinct from the things of which it is predicated because the equality

itsel f is destroyed if one of its elements becomes larger. I answer



that it always remains while the elements remain, so far as concerns

what it stands for. [What happens is that,] for the abstraction of the

concept designated "equali ty" there were first other concepts, which

are now not held about the things. For, when the intel lect saw that,

upon the juxtaposition of these two bodies, everything in the first

body had something corresponding in the other, it abstracted from

this the concept of equality. When something new is added to one of

the bodies, so that it becomes larger while the other does not, the

former proposi tions become void. One would say, likewise , if the

argument were about the similarity obse rved between two white

things, that, when one of them becomes whiter, the similarity is lost.

Page 98

Movement

And now the question of movement. We must see whether it is

distinct from the movable object. Let us take it in the sense of local

movement. One must notice that, as someone says, 191 these names

"movement" and "motion" were invented only 192 for stylistic reasons.

224 Hence, if the proposi tions in which such names are used were broken

down into their words, many difficulties, whether nominal or real,

would disappear. Let us see, then, what is implied by the predicate of

this proposi tion: "A being moves locally." First we must see what con-

cepts come to the mind when a body appears to move locally, so that



it may appear how the concept "moving locally'' is abstracted from

them. I say that these concepts come: a body which moves; a place or

interval between which and the movable object there was previously

an interval, but there is now an absence of interval there. Likewise

the intellect realizes that the object which moves locally behaves so

that there can never be a verification of the parts of a single contra-

diction (that the original object is [still ] in the same place) . Now I

say that, when one has these concepts, one has the concept of what

"moving" is . Granted that this term is incomplex, nevertheless "it

moves" implies all those proposi tions, and the statement using this

expression 193 is the equivalent of many propositions. Hence, to say

"This being moves locally" is the same as saying all the following:

"Between this body and another there was previously an interval; now

there is an absence of interval; and, now that the body is related to

some place by an absence of interval, the parts of the contradiction

cannot be verified." 194

Next I say that by the name "movement" is not implied something

completely distinct objectively from place, absence of interval, and so

on. For by means of these , all other realities being set aside, all appearances

in things can be truly saved. From this it appears clearly

how some chatterboxes, who want to argue against a man before they

understand him, have been deceived. They argue as follows: "There

is a sel f-contradiction in the aforesaid conclusion about movement.



Since the movable object existed yesterday, and the movement did

not exist yesterday, therefore the movable object is not the movement."

I answer that they draw a true conclusion after a fashion when

they say "The movable object is not the movement." But it is not an

argument against me, for I concede what they have said. "A movable

object is a movable object" and "A movable object moves" are not one

and the same in predicate, as synonyms would be. Rather, I say that

191 William of Ockham, Summulae in libros physicorum, III, 7 (Rome, 1637) p. 54.

192 Add nisi after inventa in line 48.

193 Read qua for quibus in line 11.194 Page 214.

Page 99

this predicate "moves" implies many proposi tions, as I said above. 195

And, if one were not verified, the proposi tion which affirmed that "a

movable object moves" would not be true; and yet the other proposi -

tion would be true: ''A movable object is a movable object." But in my

conclusion on movement I mean, and meant, that this predicate

"moves" does not imply one positive thing existing in the movable

object, as is commonly imagined. I posit no such thing because it is

not necessary, as has been seen, nor even very intell igible. Nor have

I yet heard a good answer to the argument of the ancients 196 who

proved that movement does not exist because anything consisting of

non-beings is non-being. But this is what the opposition maintain; for



they imagine that movement is one success ive thing, of which one

part has passed and another is yet to come.

These notions are not very intell igible, for, in knowing the truth of

a proposi tion about the past, the intel lect's yardstick is always the

truth of a proposi tion about the present. Hence one says: "It is true

that 'Socrates was in love yesterday', since at some time it was true

that 'Socrates was in love'." A fuller explanation of this proposi tion

comes to light; for to say "This thing existed yesterday" is only saying

"This thing's existence is measured by some time before the present."

But they reply that, though the parts of movement are not in perma-

nent existence, yet they are in success ive existence, and this is enough

for its success ion. I do not clearly understand this reply unless they

mean that for a success ive being it is enough that there be a non-

being. But it does not seem intell igible that there should be some

posi tive entity and yet that it be such that of its two component parts

it is true to say that one has passed and is non-being, and the other

is yet to come and is non-being.

Because of what has been said above, 197 we are relieved of such

225 unintell igible proposi tions, since for the truth of the statement "A

movable object moves" it is not necessary to posit any such positive

thing inherent in the movable object. It is sufficient to posi t what we

have discussed above, 198 that is: a movable object which moves, a

terminus a quo, a terminus ad quem, the negation of an interval, and



that, this being so, the parts of a single contradiction cannot be veri-

fied. For, when these requirements are present, all others being re-

moved, it is true that "a movable object moves." The negation of inter-

val is to be understood as above; for when between that movable

object and a particular spot there is a negation of the interval which

previously intervened, the other requirements concurring, we say that

the movable object moves.

195 Ibid.

196 Aristotle, Physics, I, 4; 187a32 ff.

197 Page 214.

198 Ibid.

Page 100

From what was said before, it is clear that it is not necessary to

posi t that quantity is a thing inherent in material substance, as is

imagined. And this was said about all quantity, both permanent and

success ive, because it might seem that especially in dealing with them

the opposite should be said about movement.

Now, however, in accordance with the exposition above, the fol-

lowing conclusion is probable , although according to absolute truth

and the Catholic faith it is not true: that all permanent and success ive

things are eternal. And therefore the general inference can be made

safely enough that all things are eternal. There is not much need to

answer the arguments adduced on the other side because their con-

clusions are merely probable.



eternity of things) , 202 no new understanding or new knowledge, which

had not existed before, is acquired. There is posited simply a lack of

differentiation as regards subject, as it were, between the soul and

its knowledge. I say "as regards subject, as it were" because things

that cannot be sensed are not conceived by means of their own essen-

199 Ibid.

200 Omit non in line 30.

201 Page 214.

202 Page 205.

Page 101

tial concepts, as will be seen elsewhere. 203 So an explanation can be

made only according to certain superficial analogies .

If the same mistake leads you to ask me whether I have existed

always, I reply that one must say, as a result, that I have existed in the

following sense: "When stones are assembled, we call them a heap. If

they are scattered, we no longer call them a heap. Yet every true

entity that existed before exists now. These things are called thus

(that is , a heap) when there is a negation of spatial intervals between

them. So in the present case it is true that every true entity which

exists in me now has existed always and will exist always. But they will

not exist, as they do now, in the same subject. For at some time the

atoms of which my substance is composed will be dispersed. So it has

been an infinite number of times , and so it will go on being, according

to these opinions." 204



In keeping with what has been said, it has seemed that it is not

necessary to posit that movement signifies a thing existing in the

226 movable object, as is generally posi ted. Against [this]: "Movement is

rapid or slow, and yet the movable object is not rapid or slow." The

answer, in accordance with what was said above, is that, if proposi -

tions using the noun "movement" were rephrased so as to use a verb

instead of this term, one would get rid of much that seems difficult to

understand. Let us then rephrase: "Movement is rapid or slow, that is ,

a movable object moves rapidly or slowly.'' That proposi tion can be

said to be true without any such reali ty as is imagined to exist in such

a thing. For from the fact that a movable object separates itse lf from

some terminus so that fewer parts of the contradiction can be veri-

fied 205 than those which can be verified in another movable object

separating itsel f 206 locally from that terminus, it is said to move more

rapidly than the other. The fewer [the parts] that can be verified, the

more rapidly it is moving. Or speak of the rapid object as above in

the treatise on indivisibles. 207 And so the objection had no validity.

Another objection can be made: "Something is acquired through

movement. (We must not say 'through the movable object as such.')

The meaning of the first statement (something is acquired through

movement) ought to be that, when a movable object moves, it

acquires something." Now, the word "acquire" could be taken in a

proper and an improper sense. For if you mean that some new thing



is brought into being, that is false . If you mean [that it acquires]

something in as much as, by reason of the negation of an interval in-

203 Page 235.

204 Diogenes Laertius, Lives of Eminent Philosophers, IX, 30 ff.

205 Page 214.206 Read se distinguente for indistinguente in line 9.

207 Page 207.

Page 102

between, it is not separated locally, that is true. However, our oppon-

ents imagine that some form is le ft there in the located body by the

locating body. I do not see, according to what was said above, that

one should posit such trivial realities.

But someone will ask, "Since material substance and quantity are

not distinct, ought one not to admit that material substance is quan-

tity?" I say that these terms can be taken in two ways, ei ther in a pre-

cise sense as signs of things outside the mind (and in this way I would

admit that the proposi tion is true) or in another way, as signs of con-

cepts, or of things thus conceived (and in this way it is not to be con-

ceded). For to the thing considered in itse lf or as related to what are

called its functions, there is ascribed the name of substance. But to the

same thing [considered] as having one part outside another part there

is ascribed the concept of quantity. And these are different concepts.

And we must keep in mind that these concepts, as being signs of

things, or [as being] things thus conceived, sometimes are mutually



related in a certain way, as container and contained, or part and

whole, so that, when one is presented to the intel lect, in some way the

other is presented also , and, when one is removed, the other is re-

moved also . For example, if the intel lect posi ts that a particular being

does not have one part outside another part, from this Aristotle 208

concludes that it is not of infinite magnitude. If it posi ts that it has

magnitude, from this he makes the abstraction, as a part from a whole,

that it has one part outside another part. If we posi t that some being

is a man, we posit implicitly that it is an animal. Then the intellect

abstracts concept from concept until it arrives at a simple concept. By

so abstracting it finds ten simple concepts which are included in all

others. These concepts, and the things in which they are included, are

the means for all scientific investigation. These ten first concepts, or

things thus conceived, he calls the ten categories.

If by the ten categories you wish to understand something else, for

example, ten things really distinct, I would deny it absolutely. It does

not follow that, because there are ten concepts, therefore there are ten

things of which there are these concepts first. Perhaps it is true that, if

we had the most perfect concept of a thing, that concept would not

permit another concept 209 of the same thing. Then the argument

would hold that there are as many concepts as there are things. But

now we grasp things only partially, and so nothing prevents us from

having several concepts of the same thing. There is also a sense in



which we can conclude that there are as many things as concepts.

This is not in the sense in which people usually understand this, but

208 Physics, III, 6; 207a8.

209 For aliquando read alium in line 45.

Page 103

227 in this sense: "A thing is conceived of in itse lf, and that is the concept

of substance. It is conceived of as having parts, and that concept is

implied by the term 'quantity'." As you see, it is irrelevant to the first

concept that the thing has several parts; but not to the second. Thus

in a sense there are as many things as concepts, but not in such a way

that quantity implies a thing totally distinct from the first thing.

But it might seem to some that material substance and quantity

are really distinct because they are generically distinct. 210 This follows

because whatever differ generically differ in species, and whatever

differ in species are really distinct. I answer that this rule (whatever

differ in species are really distinct) is true only as regards those things

that belong to the same order of category, and then not to every one,

but only to that which is called substance. At least it does not hold in

the case of quantity. For the concepts of that order [of substance] are

taken from things as they are in themselves or as [a thing] is con-

sidered in its functions.

Let us give an example. When whiteness is presented to sight, and

the intel lect actually thinks of this, it has a concept of whiteness.



When sight beholds whiteness in a location different from the first, the

intellect forms a concept of likeness as if by a process of abstraction.

Then it abstracts, as it were, some common concept and says that the

whitenesses are of the same species because it does not perceive that

there was diversity in the sense experience or [it perceives ] as if there

had been no diversi ty. Afterwards it encounters blackness, and then it

abstracts the concept of diversi ty. Because these concepts [likeness

and diversi ty] are, as it were, essential to things, therefore things that

differ thus in the intel lect with respect to such concepts are really

different (if the intel lect can say that some things are really different).

But afterwards the intel lect considers that the same thing is seen in

two different places, and that therefore, as it were, there seem to be

there [two] things one of which is outside the other. These concepts

are, after a fashion, more external to the thing because they are ob-

tained, as it were, through comparison with what is outside it. To this

concept which has been mentioned the intel lect applies the name

"quantity". Then, things that differ thus with respect to such concepts

are not really different; rather, several concepts of this kind can be

had of the same thing without one's imagining some reality inherent

in the thing. It is true, as I have said above, 211 that the thing from

which the concept implied by this name "quantity" is abstracted must

have several parts. I say now that what differ thus generically are not



really different.

210 For medio read in eo quod in line 7.

211 Page 226.

Page 104

Similarly le t us take two things in the category of quantity which

are said to differ specifically: line and surface. I say that it is not

necessary for these to differ really, because, as has been said, quantity

is not distinct from material substance. Similarly neither are its

species. For example, length [is not distinct] from a long substance,

or width from a wide substance. A reason was given why it is not

necessary to posit diverse things on the basis of this diversity of con-

cepts, because one of them, namely the concept of quantity, was

obtained from the thing from extrinsic considerations, as it were. The

intellect does not obtain it by considering what are posited to be the

natural functions of a thing. For the same reason, nay, rather, for a

weightier reason, when both [concepts] are extrinsic, as the concepts

of length and width, a real distinction will be possible only because

it is indeed true that those parts which determine length (which is

the terminus of some width) are not those parts which determine the

width of which it is the terminus.

But it does not follow from this that there is a diversi ty of things

inherent in a substance in the sense in which men are generally

thought to understand this. For it has been said 212 that concepts [of



inherent things] are, as it were, intrinsic, in relation to things' func-

tions, and it has been said that concepts of quantity are extrinsic

because they are not obtained from things with reference to a thing's

functions. In regard to this point it has been fittingly stated by the

228 Commentator in Book 4 of the Physics 213 that quantitie s are not of the

genus of active or passive powers because the fact that a thing is

active or passive is irrelevant to the concept of quantity being

abstracted from it.

Whether Everything Which Appears Is

We must next treat of the problem whether everything which

appears is , and whether everything which appears to be true is true.

In this matter we have to consider that one who says that everything

which appears is true, at least as regards what appears to the external

senses, need only know how to answer objections [against his posi-

tion]. For a rule of general application should not be modified or

restricted unless necessi ty forces a modification. And so a person who

says this need only bear the onus of responding, this being sufficient

to make the intellect incline more to this conclusion than to its

opposite. Now, as will be seen below, 214 it is not necessary to modify

the rule in order to safeguard "everything which appears is true."

Therefore the rule must be held universally.

212 Page 227.

213 Comm. 84.

214 Page 234.



Page 105

However, although that should suffice in a way, the intel lect does

not rest content with knowing that the opposite [of a proposi tion] is

not known, but also wants to establish the proposi tion [itself] by

some probable arguments. For this reason I will introduce some

probable arguments concerning what we are looking for.

Therefore, if we have any certainty about things, I say that it is

probable that everything that appears to be is , and that everything

that appears to be true is true. Let this universal proposi tion be

understood according to the meaning which can be gathered from

statements below. I argue as follows: "The intellect is certain concern-

ing everything which is evident to it, and, ultimately, evident to it

according to an act of the senses . Now, as concerns everything which

appears in a proper sense, such appearance is only in an act of the

external senses. Otherwise it would not be said to appear in a proper

sense. Hence the intel lect judges of many things that they are such

and such, and assents to them; but they are not said to appear to it,

properly and strictly speaking, since they are not, in the final analysis ,

evident; for example, that Rome is a large city. But it would be

evident and perfectly clear to a viewer who was in Rome."

Let food which you call swee t be given to a patient with a fever;

it is perfectly evident to him, in tasting, that what he tastes is bitter.



I do not say that that food is bitter, but something else which he

tastes. Someone sees redness where you say there is whiteness; I say

that it is clear and evident to him that there is redness . And similarly

in other cases. This minor premise [that the only kind of experience

which, properly speaking, appears, belongs to the external senses ]

rests on acts of experience; I experience this within me.

Someone wishing to remove or diminish the probabil ity of the pro-

posed conclusion will say that the argument given for the major

premise (that the intellect is sure of what is evident to it in the final

analysis) is inconclusive, [and that] it is true if three things are pre-

supposed: the proper disposi tion of the medium, the organ, and the

distance between the power and the object. To the contrary: "That

response is not good which takes away from the intellect certitude

about things. Such is this response because it is not less possible that

evidence of the proper disposi tion exists without the reality (for

example, that there be ultimate evidence that the power is rightly

disposed, and yet it is not) than that there be ultimate evidence that

redness exist, and yet redness does not exist. But according to you

the latter evidence can be present without the reali ty. Therefore the

former also, and so the intellect will have all this evidence concerning

the object, the proper disposi tion of the medium and organ, and the

Page 106



right distance, and stil l the intel lect will not have certitude. Hence I

say that this conclusion is probable : that everything that appears

229 (properly and strictly speaking) is , and what appears to be true is

true." I posi t this conclusion as more probable than its opposite, not

as truer.

There are doubts against this conclusion. First, it will seem to

follow that all things are true and that all things are false. I hold that

this undesirable consequence does not follow. To prove this I say by

way of preface that not every act of a knowing faculty is the appear-

ance of an object. Thus, as has been said elsewhere previously, 215 the

intellect judges and assents concerning things which are not present

to it as appearances, even if "appearances" be taken in the wide

sense. For example, a man gives judgment and assent to the proposi -

tion that "Rome is a large city" even though he has not seen Rome.

Thus it is true that your conclusion would follow if we were saying

that everything judged to be true is true, or that everything to which

the intel lect assents is true. But this is not what we say; our statement

concerns only an act involving an appearance.

And it should be noted that sometimes it happens that the intel lect

judges about something which appears to it but does not appear com-

pletely. For example, when someone sees the sun, what appears to him

is smaller than the whole earth, as we shall say below. 216 Now, be-

cause he depends totally on what is seen, he judges that there is noth-



ing there except what is seen, and so he declares that the whole of

what is seen moving from east to west is smaller than the whole

earth. In this way the object concerning which the intel lect judges

appears to it but perhaps does not appear completely. This will be

investigated more fully elsewhere. 217 Thus there is falsehood in the

act of judging, although there is none in the act involving the

appearance.

The second doubt which comes to mind is considered by adver-

saries to be an Achil les [a conclusive argument]. In sleep it appears

to someone that he is flying through the air or that he is across the

sea fighting the Saracens. I would say by way of preface something

about things which we experience when awake. At the command of

my will there comes now a combination of objects in my mind, for

example, that my father is flying. In a certain way that combination

has the nature of an appearance, and it is true to say that the com-

bination appears to me. Yet the truth of the combination does not

appear to me. It would appear, however, if my father were present

215 Page 228.

216 Page 231.

217 Ibid.

Page 107

here and really flying, and I fixed my gaze on him with my eyes open.

Hence it follows from this kind of appearance merely that that com-



bination is within my mind in the form of likenesses . But it does not

follow that it is true, that is , that it exists as such in reali ty. For such

a conformity to external reali ty does not naturally belong to an ap-

pearance in itse lf but only when it is considered further in relation to

what is outside; 218 that is, in so far as things actually exist in them-

selves and are known by the external senses.

But you will say: "It is not merely that such a combination appears

to me in sleep, but it also appears to me to be true." The answer is

that only the combination appears, and the judgment of its truth 219

follows because other concepts which should rectify the power in its

judgment are hidden. Right judgment naturally follows these concepts

if there is an appearance [of them].

It is evident that in sleep the appearance is not clear. For, no

matter how vividly it appears to someone in sleep that he has seen a

camp, the light of heaven, etc., nevertheless everyone experiences

when awake that the appearance he gets through sight is clearer and

is different in kind, and so he is more attracted by this. For, if they

were equally clear, he would have ei ther to say nothing is certain for

him or to admit that in both appearances what appears to be true is

true. Now, in those appearances concerning which I said that things

are as they appear, the appearances are perfectly clear. For example,

when redness appears to someone looking through a red medium, it

appears so clearly that nothing appears clearer to him. Therefore



"clear and evident in the final analysis" was placed in the major

premise of the argument used to arrive at the conclusion stated.

230 Therefore, on the basis of the preceding, the conclusion proposed

seems probable, that, although acts of judging and assenting may be

false, acts of appearing (in the strict sense) are not. [It] also [seems

probable] why, whereas in other matters there is general agreement

(because such an appearance is the fundamental principle of all the

truth we know, so that certainty would be removed if [this appear-

ance] exis ted without the reali ty), yet this is not true of the act of

judging; though judgment is sometimes false , it will be able to be set

right somehow by this [further] act.

Other doubts come to mind which are easier to solve. One con-

cerns the man with a fever to whom swee t food seems bitter. I say, as

above, 220 that in the sense of taste there are some l ikenesses [in the

mind] to which there correspond in reali tyfor example, in the

218 Read exterum for extremum in line 33.

219 In line 37 read veritatis for veritatem .

220 Page 229.

Page 108

[sense] organother things of the same kind. There is also another

doubt, touched on above, 221 concerning redness being seen where the

object is said to be white. I say that there are atoms there whose like-

nesses naturally come to the soul when the organ and medium are

disposed in a certain way. There is also the problem about the sun. 222



I say that what appears is smaller than the whole earth. Thus, if you

imagine a line drawn straight from your eye to the sun, and a small

circular circumference around the point of that line in the sun, that

will indicate what is seen. It is therefore probable that whatever appears is true; that is ,

what is clear and evident in a full light. For otherwise the intellect

would be sure of nothing, since the intellect can claim to be sure only

of what is experienced directly or is reasoned to as a result of exper-

ience (as with those things which follow as a natural resul t of exper-

ience) . This is obvious, for the intellect is sure of nothing insofar as

it is in darkness, but inso far as it is in the light. Therefore what the

intellect is certain of must be either the light itsel f (as our experiences

are) or what is consequent upon the light (as what we reason to as

a natural resul t of our experiences or by way of abstraction from our

experiences).

Considering a man who says he has certainty, I ask him further

whether or not he has some light or some appearance in which light

or appearance he says he has certainty. If not, he is therefore in dark-

ness and speaks like a blind man. If there is some light or appearance,

then ei ther what he says he is certain of is the light itself or the light is

[part] of it. Then it is always experienced in itsel f or in its light, or

what he says he is certain about is consequent upon, or related to,

[what is so experienced]. For, if the light itse lf did not have some



relationship to what he says he is sure of, it would be, as it were,

completely in darkness in regard to it; and then, like a blind man, he

would not be sure of it. If it has a relationship, which one ought to

admit, this relationship might be a contingent one, indifferent to

whether [the relationship] exists or not. But then he will not be able

to say that he is certain through that light or appearance, because he

could not say he was surer of its existence than of its nonexistence.

Thus it must have a necessary relationship. And, if this is the case,

[what he says he is sure of] can be reasoned to by means of a con-

clusion, for, if something is present, all things necessarily consequent

upon it seem to be present also. As a consequence it is true that no

one can claim certainty about something unless he has the light

providing ei ther it or what it is necessarily consequent upon. Because

221 Page 228.

222 Page 229.

Page 109

of this proposi tion, I have said elsewhere 223 that no one can say that

in a body, besides the three dimensions, there is a reali ty which is the subject of them, as those say who posi t that quantity is distinct from

material substance. The reason is that that reali ty does not provide

the intel lect with any light in which the existence of that reali ty is

experienced. For we have not seen it or heard it; nor can the existence



of such a reali ty be reasoned to from what we see or from what we

sense in any other way whatever, as has been said elswhere. 224

231 According to this teaching, then, it can with probabil ity be said

that, if a man can say he is certain of something, what appears

(properly speaking and in the final analysis) is true. Let us express

this rule in other words: every act of affirmation which is formulated

in a full light, in so far as man can have a full light, is true. For every

act measuring up to its true norm is true. And an act of affirmation

formulated in a full light measures up to its true norm, that is , the full

light. For we can state nothing with certainty unless in relation to the

light or the appearance which we have. For these have the nature of

a measure and principle, as has been sufficiently seen above. 225 As has

been said above, 226 it would not be valid to say that the full light does

not of itse lf have the nature of a measure, but [only] if three things

concur, that is , the proper disposi tion of the organ and of the medium,

and the proper distance of the object. For I ask two things of one who

says this. First, how is he sure that they are required? He will not be

able to give a true means [of knowing] other than an appearance or

its light, and thus his denial of the statement will involve its admis-

sion. Secondly, I ask the one who says he has certainty, whether he

knows that those three things do concur, [that is ,] that his faculty is

properly disposed, etc. He cannot allege a true means [of knowing]

except that it appears so to him. Therefore he will always have to fall



back on what he has denied, namely, that a full appearance, without

any reservation, is always true, and that an act of affirmation based

on it is always true.

We have used the express ion "full light" because a light which is

not full does not have the nature of a measure. Hence they argue

frivolously who say: "In sleep it appears that I am running through

the camp, or that I am in heaven, and yet this is not so ." I answer: "It

did not appear to you with a full appearance, for a full appearance of

the truth of this statement is an appearance through the external

senses when you see the movement through sight."

But it should be known, because of certain other matters, that

sometimes a thing is said to be seen in its own light, and sometimes

223 Page 222.

224 Ibid.

225 Page 230.

226 Pp. 228-229.

Page 110

in the light of its image, as when a man is seen in a mirror. Now I say

that every act of affirmation which is based on light and does not

exceed it is true. Therefore, when the sun is seen, some say that sense

is deceived because [the sun] is larger than the whole earth and yet

seems to have a size of two feet [around]. It is amazing that they talk

so. If they were to think over carefully what they are saying they

would see that he [sic] is speaking in darkness , or else they would



agree with us. For they say that the whole sun is larger than the

whole earth, and they say that what they see is in its appearance only

one foot [across]. How will the fact that it appears in its entirety and

the fact that it appears to be only one foot [across] be reconciled? I

say, then, that it is seen by us in the light of its image. Thus we see

the one image which is the image of the sun; when this has been seen,

the sun is said, after a fashion, to be seen. And in that [image] one

part is not represented more than another. Hence the sun's extension

is represented there only by way of resemblance in shape, substance,

and light; it is not represented there by way of a quantity equal [to

the original]. Some want to use this fact as the basis of a specious

argument proving that quantity is really distinct from substance and

shape, but I forego a rebuttal for now. It is sufficient for me at present

that there is a true act of affirmation which refers to an image smaller

than the whole earth.

The same answer would be given concerning a stick appearing

broken in the water. I say that the appearance has to do with an

image, which is of the same nature at is appears [to be]. I would say

the same concerning a river-bank which, to a man in a ship, appears

to move. Concerning the man with a fever to whom swee t things

seem bitter, it can be said, as above, 227 that this is due to certain

really bitter things which are present in the organ of taste. So these

objections have li ttle force against my contention. Rather [what I have



said] has much more force because, according to what was said con-

232 cerning the light of an image, it would follow that no one could

speak of the true subjective 228 existence of whiteness or anything else .

For he cannot say [anything about it] except according to its appear-

ance, [and] it wil l now be said that that appearance terminates at the

image of the thing and not at something subjectively existing in a

thing outside. It must be said, of course, that it is certain that when

sight sees whiteness it sees something. Its appearance vouches for

this; and that it is outside the eye and in such and such a place. I

grant that all these things are true.

Now, when vision does not change, no matter where it turns or

what its state, and [whiteness] appears to it, it imposes that name

227 Page 230.

228 See n. 10.

Page 111

[whiteness] and says that true whiteness is there, possessing a stable

or subjective existence. 229 When this is not the case, it imposes the

name and calls that thing an image, as when a man is seen in a mirror,

or when a man sees the river-bank move but would not see it move if

he were in another spot, provided he saw it most fully. But it is

somehow not sure that there is any difference between the image and

what it calls a fixed thing; indeed, from its appearance, there is simply



a numerical difference. (In the case of touch, indeed, there does not

seem to be any reason for doubting, for it does not seem to be con-

cerned sometimes with an image, but always with a fixed thing.)

But, because of what has been said above, just as because of what

others have said, it would seem to some that certitude is destroyed:

''According to the above, to prove that something exists it would not

suffice to say that it appears to me to be true, and that therefore it is

true. For in sleep something appears which is not true. One must

accept as true what appears in a full light. Now, concerning the minor

premise of this argument, how can you have certainty? If you say

[that it is] because it appears to you without quali fication, I shall then

hold that the appearance ought to be taken without quali fication as

an argument for drawing the conclusion. If you say [that it is] because

it appears in a full light, the question 230 will return as before. For in

sleep it appears most clearly that I see some person, and yet I do not."

One way of answering this would be to say that there would be no

way of proving the conclusion, but that the concept of certitude which

is present comes as a certain natural consequence, and not as a con-

clusion. An example, among others, [is] that white and black are

different. This concept of their difference is not gotten by way of con-

clusion. For, if one said "I prove that white and black are different

because the acts of seeing are different," it would be proving 231 [the

more know] by the less known. Also the question would return con-



cerning the acts of seeing, and it would be necessary to grant the

contention at least there.

I will answer similarly in the other case, that is , as regards sleep.

I answer negatively. For it appears to me when I am awake that I can

drink, speak, hear, etc., and that this is something unchanging and

calm; and from many such appearances the concept of certi tude

arises. [But it is] not so in the other case. And perhaps, in the final

analysis , it would have to be that we do not have full certitude about

things; indeed that only the First Intel lect, which is the measure of all

intellects, has it.

229 See n. 10.

230 Namely, how can you be ce rtain that it is a full light?

231 For esse read esset in line 29.

Page 112

We might say one thing about this matter. The disagreement

which seems to happen among men does not have to do with the

appearance itse lf. Opposi tes do not appear to men. But it is true that

things not the same appear; indeed, one thing appears to one man,

another thing to another, and sometimes more things appear to one

man, fewer to another. So the disagreement concerns the act of

speaking. For example, if someone says that it is better to live in

bodily delights than to philosophize, the only thing that appears to

such a man is that bodily delights appear to him as superio r. But



another person who says the opposite is more concerned with the

work in itself as it prescinds from pleasure, and similarly with the

operation of touch, and the appearance comes that the former is

better than the latter. Thus they contradict each other in what they

say, but not in the appearances they receive. Similarly, if someone

denied the [accepted] number of categories, ordinarily one would

say to him: you are denying first principles. But another person would

answer that he is not. For it seems to the former only that that man

denies what are considered as first principles , and nothing more

appears to him. The latter considers that it is not a proposi tion sel f-

evident from its terms that there are ten categories. And what appears

to both of them is true.

233 It is only because of the poor quali ty of the intel lect that the act of

speaking would thus go beyond the limits of an appearance. For a

good intel lect is always equal to its measure, and a man has a better

intellect than others if he knows better how to lead back all his acts of

speaking to their first measure, that is , to appearances or the light

within them. When men argue, their consideration will concern knowl-

edge about one of two things, either leading back their acts of speak-

ing to their measure, or multiplying appearances. In the first case a

man wanting to lead another back [to the measure] must show him

the reasons for what he says. In the second case he must show the

appearances he has and assume the stance of his opponent completely.



What happens when assent is given when the act of speaking

exceeds the bounds of its measure and we give greater credence for a

more perfect reason, as when someone proposes that bodily delights

are preferable? The delight itself is in the appearance and, as it pre-

scinds from the action, it is good, as we have said elsewhere. 232 There-

fore, although he says this about the action, his assent nevertheless is

in accord with the appearance which concerns the pleasure. Similarly,

true things appear to people who are awake, except madmen or a man

resembling a sleeper, and they assent to truths, but they do not always

232 Page 234.

Page 113

express truths, because sometimes the act of speaking goes beyond its

limits.

A consideration of what was said above seems to lead to a contra-

diction. For, when reference is made to the same thing, it is true that

to that man the delights of touch appear greater than intel lectual

delights, and to another the contrary appears [true]. The explanation

for this will be to say that there appear to these men things which are

diverse in some way but not contradictory nor impossible. In the case

of the one saying that the delights of touch are greater than intel -

lectual delights, we shall say that what he says is true if it is referred

to what appears to him. But to complete the statement it must be

added that intel lectual delights do not occur in him with their full



being. He has only a diminished experience of them, while they

appear to the other absolutely, with no such diminution. Recall what

Aristotle says in agreement with this matter in Book 2 of the

Politics .233 Speaking of those who want to experience pleasure com-

pletely and continuously, he says that they will seek relief only in

turning to philosophy if they are able to find joy in it.

A third way of accounting for divergencies occurring among men

is a difference in assent. For, when two men have equal appearances,

assent follows in one (for example, that Rome is a large city) and not

in the other, or not so firm an assent. Suppose that one believes firmly

and the other does not. Still , the same thing appears to both (that is ,

that this is common knowledge and that there is no contradiction in

it). 234 Or perhaps this should be corrected to say that the same

appearance is followed by the same assent, but not the same belief

about this, even though it appears to be common knowledge . What

actually appears to [one of them] is that there is no necessary con-

nection, and therefore he does not beli eve firmly.

Indeed it happens sometimes that, although appearances exist and

somehow or other contribute to opposite conclusions, yet attention

dwells on one appearance and not on the other. For example, when it

is asked whether two similar whitenesses have some real unity, it

appears that, considered simply in themselves, they come as com-

pletely one to the sense , so that, if the intellect took no account of



their [different] locations, it would not tell them apart. Looking at

what appears, some declare that there is a real unity there. Others

consider that one thing cannot be in different places, and that one of

those things [can] cease to be while the other remains. Considering

this, they declare that there is no real unity there. Certain others,

indeed, declare that there is a real unity there. And certain others,

233 II, 7; 1267a10.

234 Omit non aliquo in line 34.

Page 114

considering all such appearances, say that this conclusion should be

accepted by men as neutral, that is , as surpassing man's abili ty to

decide, and that the appearance cannot be fully explained here.

234 What is the answer to this? I hold, as above, 235 that whatever

appears in a full light is true, and that contrary things cannot appear

to men in a full light. For otherwise the disputant would have to use

as his argument "whatever appears to me is true," and not "whatever

appears in a full light is true." 236 For, if he used the former, and said

that contrary things can appear, it could be deduced that contraries

would be true at the same time; which is impossible.

And here we must make an observation. For perhaps it would

seem to some that it is not much good to have knowledge of things

because it has been said that we cannot have full certainty about

them. The answer to this would be that, granted that such is the case,



there is no great obstacle. For it is certain that every object provides

some appearances and some light. It doesn't matter much, except that

our desire to know things would then remain unsatisfied.

Concerning this, also, consider that the superio rity of one man's

intel lect over another's occurs in one of the two ways mentioned

above, ei ther because the appearances of things come to him in

greater number and more quickly, or because he reflects more upon

his appearances and is less hasty in pronouncing upon them.

Just as we have said that whatever appears is true, so we must say of the will, according to a certain similarity, that whatever the appe-

tite desires is a good simply speaking, not merely an apparent good.

For, as the means of proving that something is true is the appearance

itself, so, in its own way, the means of proving that something is good

on the part of the appetite is the very act of desi ring. In order not to

leave room for doubt should there occur the objection that some want

to steal, others want to ki ll themselves, and others want bodily delights,

we shall answer those persons that the appetite is not directed to those

things in themselves , but only because of what is annexed to them, at

least in the first two cases . For, if ki ll ing or stealing were considered

apart from what precedes, accompanies , or follows them, the appetite

would never desire them. But the possession of money accompanies

theft, and certainly it is good to have money in order to stay alive.

Likewise those suffering many sorrows ki ll themselves through the



desire to escape the sorrows, which desire is good. And so on. Con-

cerning bodily delights, for example tactile ones , we shall say that the

delight is a good if considered apart from everything other than the

delight. But the latter is not good because, if it is considered apart235 Page 230.

236 Add in pleno lumine after apparet in line 5.

Page 115

from the delight, no one would desire it except for the sake of genera-

tion or some attendant benefit. And thus it appears that what is desi red

is good, just as what appears is true, as has been shown above.

Indeed, it must be considered that sometimes men accept as

evident many things which are not evident to them, as when they

mistake one thing for another. For example, someone may accept as

evident that there is no whiteness when blackness comes on the

scene; yet this is not evident to him, but the whiteness merely does

not appear to sight and it appeared previously. Others accept some

things as evident because they are much talked of. Sometimes, too,

people say that something is totally evident to them which is evident

only in part. For instance, someone states a universal proposi tion

which he has accepted only by induction from some individual cases.

Sometimes he proposes it by saying "this is evident to me;" and yet

nothing is evident to him except those singular proposi tions on which



he based the induction; nor is it even evident to him that those singu-

lars are of the same nature as far as the predicate is concerned.

In another way someone says that something is evident to him

because of an inadequate indication. For example, people claim to

know that a certain person is acting out of vainglo ry; and yet nothing

is evident to them except one indication, which is related very inci-

dentally to the conclusion. But, because their mind is given to detrac-

tion, they accept the contingent argument as if it were evident to

235 them, and were a necessary one. (All that one needs to do in order to

have evidence in an argument is to arrange it in a syllogistic form,

since that form is evident. Then, if the premises are evident to him,

the conclusion will be evident to him too, as depending on the

premises.)

There is something, also , which is not evident directly, but is

accepted because its opposite, of its very nature, cannot appear. For

example, if the world has not existed eternally, why did it begin at

one time rather than another?

The following are evident, properly speaking: sensible objects, and

the acts which we experience in ourselves . These refer to what is in-

complex. As regards what is complex, there are the principles which

are known from their terms, and conclusions depending on them.

Therefore from the above we can easi ly see what certitude means.

For, as concerns certain knowledge in regard to some proposi tionfor

this is its li teral meaningmen use this word thus: when someone has



clear and evident knowledge of the truth of a proposi tion and also

perceives that he has such clear and evident knowledge , he then says

that he is certain. Therefore certitude implies such clear knowledge of

Page 116

some proposi tion. Aristotle used such a method of investigating the

meaning of the word in Book 1 of the Posterior Analytics ,237 when he

says, "We think we know something etc." But you will ask: "What do

you mean by clear and evident knowledge?" I reply that you should

see what kind of explanation can be given here. If you ask "What do

you mean by color?", perhaps the answer will be "what is seen." And,

if you ask ''What do you mean by seeing?", the meaning of this word

could be shown to someone not knowing it by call ing attention to his

eyes, or tell ing him to fix his gaze on something or to watch me fix

my gaze. "Look," I would say to him, "this is what I call 'see ing'."

There is no better way in which it could be shown to him.

"But how about the acts of the soul, which are harder to point out?

What do you mean by 'clear knowledge ' as it is used in the proposi -

tion?" I say that I use some concepts side by side, and that finally

the acceptance of what is meant by clear and evident knowledge will

come to the intellect disposed in this way. For example, I use this

term 238 in this way, for I say that I have clear and evident knowledge



237 I, 2; 71b9.

238 Namely, clear and evident knowledge.

239 Page 228.

Page 117

degree is questioned, since it is uncertain and indeterminate, our

236 possession of truth would be an uncertain and indeterminate thing

for us.

But you will say, as was touched on above somewhat, 240 that,

according to the aforesaid, contradictories will be true at the same

time, for some persons posit contradictory conclusions. Here we shall

say that our argument would be better if we added these words:

"Which would be clear to each person, clear and evident that things

are as he asse rts." But you will say: "This is not a valid answer, for

each of them judges that it is complete ly clear and evident to him

that things are so, and he is thereby drawn to assent." Hence, if the

opposite could exist along with such [knowledge] you will then argue,

as we argued before, that we will be sure of nothing. For we say we

have certitude even of first principles only because we judge that it is

completely clear and evident that things are so. Here it must be said that, where men hold opposite conclusions,

something is clear to both, but they do not contradict on this point or

those points. But sometimes they mistake one thing for another, as was

said above. 241 There was an example of this which I have often seen



actually happen. Someone says something. Some hear him. Sometimes

one says "He said this" (whereas in reali ty he did not). Another says

"No; this is what he said." When this happens, they are then said to

contradict one another. But in reali ty opposite [pieces of evidence]

do not enter their intel lects. For it is not evident to the first man, who

says that I said something which I did not say, that I said it. What is

evident to him is that, while I was speaking, the concept of that thing

entered his mind, perhaps because of my manner of speaking or

because what I said was close to the thought he got. It is also evident

to him that I said something and that I moved my lips, but it is not

evident to him that I said [what he thought I said]. Thus he mistakes

one thing for another.

You will still say: "According to this way of answering it would

follow that the intellect could say it was certain of nothing specifically

although it could [say it was certain] of something in general. For,

according to you, the intel lect can mistake one thing for another and

thus it will judge something to be perfectly clear when it is not that

which will be clear to it but something else on which it will not pass

judgment. And, if you say that someone will have certitude but will

lack every means of proving to himself or another that he is certain, it

follows that 'this is, and it is not,' since the degree of knowledge

necessary to rule out its opposite being true is not sufficiently deter-

240 Page 229.

241 Page 234.



Page 118

minate to be known." And, in line with this, an answer could be given

to the argument I adduced above 242 to prove that everything clear

and evident to the intel lect is true, by applying to that argument the

present objection. It thus becomes clear that that conclusion has not

yet been sufficiently proven. Therefore, according to this position,

someone will be sure, but no one would say for certain that he is sure.

But I argue against this, because not only does it seem that I am

certain, when I say that every whole is greater than its part, but it

also seems that I am certain of [my certainty]. I therefore respond

differently to the above reasoning which holds that no one will be

sure of something specific in a determinate manner because he will

not be sure whether he mistakes one thing for another. I say that a

person will be sure when, after the meaning of the terms is grasped,

something is so clear and evident to him that he is drawn [to assent]

entirely and cannot backtrack, and especial ly that that is precise ly

what has come to his knowledge . For, if one person heard another,

and it was not perfectly clear that he said such and such, and some-

one asked "Can it not be that he said one thing and you understood

another?", the answer would be yes. And thus it becomes clear that

the conclusion laid down above can be held, namely, that that is true

which, by the very nature of vision, is so clear and evident to the



intel lect that the intel lect cannot backtrack. The reason for this con-

clusion is apparent: as taste does not naturally enjoy most what is

bitter, so the intellect does not naturally enjoy most what is false,

especially because falsity is the evil of the intellect.237 From what has been said a second conclusion is inferred: namely,

that that conclusion, which was proved hypothetically (on the suppo-

si tion that something is true), ought to be accepted as a principle.

For, if it were proven to be true, the premises would be assumed as

ei ther evident or true. If as evident only, then, though they would

make the conclusion evident, they would not prove it to be true. If as

true, I have a question: [it would be] ei ther in virtue of themselves

as being evident (and this would be begging the question) or because

they are true (and then it would be necessary that their truth be

shown from other premises, and so on into infinity).

The third conclusion is that there is no principle serving as founda-

tion for another principle in such a way as to prove its truth. This can

be proven in the same way as the preceding conclusion.

The fourth conclusion is that we do not seem to have full certainty

concerning things because we must assume as an argument that what

is evident is true. This is not evident; 243 nevertheless the intel lect finds

rest in that reasoning.

242 Page 228.

243 Add non after licet in line 11.



Page 119

The fifth conclusion is that, as concerns the nature of evidence,

there is no first principle. Or, rather, this conclusion 244 can be made

evident in a way, because evil does not seem to set the intellect at rest,

etc., as above.

The sixth conclusion is that no conclusion can be proven true

unless by means of evidence, that is , unless it be proven evident by

evident proposi tions.

The seventh conclusion is that something cannot be proven true

unless something is more evident than it.

The eighth conclusion is that not all proposi tions can be shown to

be evident through the first principle. 245 For, along with the first prin-

ciple, it is necessary to assume something which contains the con-

clusion actually. The minor premise does not [contain the conclusion]

as do the major premise and the first principle, that is , potentially.

The ninth conclusion is that someone could, because of custom or

some other reason, refuse to assent unhesitatingly to the point that the

first principle is true. An example of this would be a person so brought

up as to be taught that there is an omnipotent agent who can bring

about the contrary, and that evidence should not move him [to assent]

since the opposite can coexist with it, as might be shown in many

instances.

The tenth conclusion is that he could not withhold assent that it

[the first principle] was clear and evident to him.



The eleventh conclusion is that, as we agree that what is perfectly

evident is true, so, appropriately, we agree that what cannot be pre-

sented by evidence cannot be true. Thus we distinguish the possible

from the impossible.

The twelfth conclusion is that one would have full certitude if, in

addition to something being evident to him, the reasoning "this is

evident to me and therefore is true" was also evident to him.

The thirteenth conclusion is that only opinion, not certainty, is had

concerning things known by experience, in the way in which it is said

to be known that rhubarb cures cholera, or that a magnet attracts iron.

When it is proven that certitude [comes] from the proposi tion exis ting

in the mind which states that what is usually produced by a non-free

cause is its natural effect, I ask what you call a natural cause. A cause

which has produced what has happened usually, and which will stil l

produce in the future if [the cause] lasts and is applied? Then the

minor premise is not known. Even if something has been produced

usually, it is stil l not certain whether it must be produced in the

future.

244 Namely, that something is true because it is evident.245 That is, the principle of non-contradiction.

Page 120

The fourteenth conclusion is that everything evident to the external

senses is true, provided some certitude is had of such objects.



The fifteenth conclusion is that what appears in sleep is true as it

238 appears internally, that is , in forms which are likenesses. (When

awake, indeed, he experiences other evidence, and among other

objects).

The sixteenth conclusion is that, just as not every proposi tion can

be proven evident by what is called the first principle, as has been

said, and we call a proposi tion impossible only if it cannot become

evident to us, so there are some impossible things which cannot be

reso lved into the first principle in such a way that it shows evidence

of their impossibili ty. At least the matter is not certain.

The seventeenth conclusion is that, in order to know that we are

awake, or are speaking, etc., it is not necessary to know that the power is

properly disposed, since this is more hidden than the former, and it is

not clear how this could be known except by an act of sense. Also ,

even if this were known, I should still possess only evidence. If, there-

fore, I have evidence as clear under the one set of circumstances as

under the other, ei ther no one is certain or he [who does not know

that the power is properly disposed] will be.

The eighteenth conclusion is that not everything lacking the

highest degree of evidence is provable. This is clear from a statement

made above, 246 that not everything which follows the first principle

is provable by it.

Whether Exactly The Same Thing Can Be Seen Clearly and Obscurely

In order for us to see something more concerning objects which



appear, I propose the problem whether exactly the same thing can be

seen clearly and obscurely. It seems that it can. For, when two things

deal with the same object or thing acted upon, the more perfect will

always have the more perfect act with regard to that thing acted

upon. With this as preface the suggested conclusion seems to follow,

and this is accepted as certain by all , and a contradictor of this has

not been found. But the contrary seems to me to be true, as far as the

natural reason we partake of in this li fe is concerned. This is what I

shall discuss here and in what follows.

The first conclusion, therefore, is that there can never be clear and

obscure knowledge in regard to the same thing. To show this, take two

whiteness, one of which is clear, and the other dim. Let the first be

called a, the second b. Now take c, the act of seeing a, and d, the act

246 Conclusion eight.

Page 121

of seeing b. It is certain that c will be a clearer act than d, just as a is

a clearer whiteness than b, since an act is a sort of copy of the object

in the intellect. Therefore, when whiteness a is seen from afar, or is

seen as if in the darkness of fading light like that at nightfall, it is

certain that it has the dim act of seeing, d. It is then argued that, for

every instant that there is in vision an act of seeing some object, that

object is seen; and for every instant that there is in the power no act



of see ing some object, that object is not seen. But, as we have posited,

at this instant vision has the act, d, of seeing b, and not the act of

seeing a. Therefore whiteness b is seen, and not whiteness a. Or, if a

is seen, it is only because whiteness b is seen, which is somehow the

same as it, and is , as it were, evidently contained in it.

A further explanation proceeds from the same root. Suppose that

someone else sees a dim whiteness . He will have the act of seeing, d,

and the first person has the act of seeing, d. Thus, [arguing] similarly,

a power having an act equal to another power sees whatever the other

power sees , and only that, since it has only an equal act. But one sees

a dim, and not a clear, whiteness. Therefore the other will be similarly

affected.

Also, no intellect using reason, and existing under one extreme of a

contradiction, should change to the other extreme without there exist-

ing some reason for the change. At one time, when the intellect is as

though in darkness, blackness appears to it, as it judges. At another

time, in the light, whiteness appears to it. Now, it is not entitled from

239 this to say that it did not see blackness previously; it can say only

that it does not see blackness now, unless perhaps as i t is evidently

contained in whiteness. And, just as it has been said concerning sight

that clear and dim vision cannot exist in regard to the same thing, so

it may be said, mutatis mutandis , of other cognitive powers, and for

the same reasons.



From what has been said a second conclusion follows. Speaking of

the First Conceivable Being, whatever is conceived by us, the same

thing is conceived by God just as clearly as it is conceived by us. For,

if the knowledge were clearer, it would indeed be knowledge of

another thing.

And a third conclusion follows. All things are conceived equally

clearly, each according to its dimness , because, according to what has

been said, 247 each thing is conceived as much as it can be conceived,

and as clearly as it can be conceived.

And from this follows a fourth conclusion. God is not different

from man in that He knows things more clearly, but in that He has

more concepts of things.

247 Conclusion one.

Page 122

A fifth conclusion follows. The intellect and sight (or any other

sensitive power whatever), or any two powers whatever, never have

the same object, because the act of one of the powers is always

different, or is clearer, in regard to the same object. Either way there

follows a distinction on the part of the thing [known].

And a sixth conclusion is contained in this. Nothing that can be

apprehended by sight can be apprehended by the intel lect or by

another power. This is true universally of one power compared to

another.



Then a seventh conclusion can be inferred. When sight sees white-

ness, the intellect understands whiteness when the whiteness is

absent, that is , something like whiteness in some way. And it can be

said that that exis ts in reali ty before any act of the intel lect, as does

the whiteness seen. But it is never visible .

Here is the eighth conclusion. Of these two whitenesses the white-

ness seen is more perfect than the whiteness understood, because it

has more brightness. Because of this some might think that sight

knows bright whiteness because in comparing two extremes it must

know both of the extremes. Say that sight somehow knows insofar as

it has knowledge of a whiteness which is in some way like that object;

and this suffices. Here give some thought.

The ninth conclusion is that every lower degree of whiteness is

present where the brightest whiteness exis ts. For, when that spot is

looked at, every whiteness below that whiteness can be seen in turn as

the light gradually leaves. Indeed, where there is the greatest white-

ness even blackness will be more capable of being seen as the light

leaves; and so contraries co-exis t.

The tenth conclusion is that one who actually sees whiteness

actually sees absolutely every whiteness at the same time. Therefore

that whiteness will be seen, no matter where it might be. One see ing

a whiteness which is in Paris sees the one exactly like it which is in

England. I do not say that he sees it by looking at a place in England,



anything or deny anything.

The fourteenth conclusion follows from the foregoing. Under genus

and difference different things or formalities are considered, because

there are different concepts there.

The fifteenth conclusion is that there are ten categories really or

formally distinct because there are that many concepts and therefore

that many things or formalities .

The sixteenth conclusion is that, if there are two persons of whom

one has a better intel lect than the other, he will be able to say to the

other: "You have known nothing which I have known." This appears

plainly when the first conclusion is considered.

The seventeenth conclusion is that, if someone looks at close range at

something visible, and another person from a greater distance, he will

be able to say to the second: "You do not see what I see ." This will be

true even though, because their acts of sight are similar, they can

think they see the same thing. The same must be said of hearing, etc.

Let us here go back over the proof of this conclusion (that is , that

one who is near sees something different from what the one at a

distance sees). Indeed, when the argument for some conclusion re-

mains, and nothing else is present which removes the nature of the

argument, the conclusion, too, will always and everywhere be posi ted.

But this is the case for, if a bright and a dim whiteness were seen in

different subjects and judged to be different, the means of judging



would be the very appearances, not, however, the consideration of the

difference in location, for even if this is not considered, they will still

be judged to be different. Now, this basis [of judging], that is , the

change of form in appearances , concerns what is called one whiteness,

for from a distance it seems to be dimmer, from nearby brighter. And

Page 124

so, if there is also identity of location, only identity in location can be

concluded from this, not, however, identity in nature. From the preceding this corol lary would seem to be true: nothing

which is seen is understood or imagined. Similarly this: nothing which

is heard is understood. And so on. And this is convertible : nothing

which is understood is seen or heard.

This would also seem to be true: God understands nothing which

I understand. For, since he is the most perfect intel lect, he under-

stands according to the condition of his nature. Now, it has been said

in the first conclusion, [though] in different words, that what the most

perfect intel lect understands is different from what the less perfect

understands. What the Commentator Averroes says in Book 12 of the

Metaphysics 249 agrees with this opinion: that is, that what the Prime

Mover understands about God is different from what the second

mover understands. And this conclusion will be similarly convertible.

That is , I can understand none of the things which God understands.



Likewise, if a person's intellect is better than another's, the other of

the two can say: "You can understand none of the things I under-

stand." Thus God comprehends all things only in their highest degrees .

That is , he comprehends whiteness at its brightest, and comprehends

man similarly, and so on. Accordingly Aristotle 250 seems to have reas-

oned well when he said that God understands nothing of the lower

beings which we understand, since his intel lect would be demeaned

if he did. And it is certainly true because it would then follow that

241 his intel lect would be equal to ours in perfection. For, if it is more

perfect, then he will understand an object differently, as was proved

in the first conclusion.

Imaginable Beings

We must also take notice here of imaginable beings, of which it

can be said that they have a true exis tence which is prior to the act

of the imagination and persists after the act of the imagination has

passed away, just as in the case of visible and audible beings. Thus

a chimera exists. And, if anyone dreams that he is a cardinal, so will

he be. This is denied only because he is not so in visible form. But

this does not destroy the fact, for there are differences between beings

of the external sense , beings of the imagination, and beings of the

intellect. Hence, if he existed in visible form, he would no longer be

imaginable , as has been said. Therefore [imaginary beings] truly

exist, although their existence is not like that of things subject to the



external senses.

249 Comm. 44.

250 Metaphysics , XII, 9; 1074b25.

Page 125

Something similar must be said about intelligible beings. For, as

was said above, nothing intell igible is sensed, just as no sense object

is understood. But intelligible objects have their own proper and

distinct being just as do sense objects. And so it will be true that each

faculty will presuppose the existence of its own object; no faculty will

produce it. Hence, just as sense objects (for example, visible objects)

precede, and must needs precede, vision, so imaginable objects pre-

cede imagination.

What comes to mind about the nature of such imaginable and

intell igible objects seems to be true, namely, that one does not have

to say they can be generated and destroyed; likewise , that there are

many of them in the same species , and that they have no particular

determination of local existence.

It follows also from what has been said that it is false to say that

every being is intell igible. For what is perceived by the senses is not

perceived by the intellect, as was seen above, although the intellect

does perceive something which is very much like it in appearance

and similarity.

Furthermore, one must consider that, when we say "A whiteness



exists, which did not exist before," the whiteness, considering the

subject [of the statement], is grasped according to the being it has

when it is the object of the intel lect or imagination; and the predicate

joins to it every existence which is simply the being the whiteness has

when it is an object of the senses; and these two [beings] are really

distinct. And, indeed, according to this, the being of essence 251 and

the being of exis tence are really distinct. And, if the things are cor-

poreal, the proposi tion so formed is a contingent one.

If the question is raised whether the being of exis tence attributed

to an object of the imagination or intellect is distinct [from the being

of its essence], the answer would be that it is , formally, for the reason

given above, but that it is not, really and simply, because no separa-

tion is possible there, as I indicated to some extent above. 252

If the question is raised why a thing is said to exist in an absolute

sense when it exists according to the being which is grasped by the

senses , the answer to this will be that that being presupposes the

being of imagination and the being of intellect, and so it is then true

to say that the thing exists according to all its being, and thus exists

absolutely and wholly. That the object of imagination or intellect does not pass away

when their act ceases, seems probable for the following reason. If an

251 After hoc esse in line 31, replace existentiae by essentiae .

252 This page.



Page 126

object which is more close ly related to an act, or at least not less

closely related, does not pass away when the act ceases, neither will

an object which is less closely related to the act. But the fact is that

an object of the external senses is more close ly related to the act of

an external sense since it is grasped more, or not less, fully than is the

object of imagination in the act of imagining. But it is considered

certain that [the sense object] does not pass away when the act

ceases. Therefore neither does the other.

242 From what has been said it would seem that a thing, even as

concerns the being it has as an object of an external sense , does not

cease to be. For, if a thing is indestructible with respect to its less

perfect being and with respect to what is less its natural purpose ,

much more with respect to its perfect being. But, as has been said

above, 253 a thing in relation to the being it has as an object of imagi-

nation is of this kind.

Further, one should know that, as has been said in earlier pas-

sages, 254 each power in its act presupposes the existence of i ts object.

And, to the extent that the act of the power is clearer, to that extent

the object is presupposed to exist more clearly, that is, in a clearer

being. For example, vision presupposes the existence of its object in a

clearer being than does imagination. Consequently, if it is at its

clearest, its object will be presupposed to exist in its clearest being;

and that will be said to be the hi hest bein in which the ob ect exists.



Therefore, if there is some faculty which knows things constantly and

most clearly, as is believed about God, then it will have to be said that

things always exist; and one will be able to say this absolutely.

Let us draw a comparison on this point. The visual power grasps

its object more clearly than does the imagination. Suppose , per im-

possibile , that the being which is considered whiteness ceased to be

insofar as it is an object of imagination, while it still remained with

respect to the being it has as an object of vision. The whiteness would

still be said to be, simply speaking. Now, if there is a faculty which

grasps whiteness more clearly than does vision, suppose that the object

passed away in regard to the being which is apprehended by vision,

so that the being which vision knows were destroyed. Nevertheless, if

the object remains as regards what pertains to the clearer faculty, it

could still be said to be, simply speaking, though it should not be said

that it had being in every sense .

From what has gone before it is evident that that proposi tion 255 is

not altogether true which says that intuitive knowledge is of an exist-

ing thing as existing, and abstractive knowledge is not, and hence [the

253 Page 241.

254 Ibid.

255 William of Ockham, Sentences , lib. 1, Prologue, I, AA.

Page 127

latter] is indifferent to existence and nonexistence. As I said above, 256



each knowledge is of an existing thing. The difference lies in this, that

intuitive knowledge grasps the existent in a clearer being. If God knows

all things most clearly, as is believed, our intuitive knowledge could

even be called abstractive in comparison with God's knowledge , which

would be called intuitive absolutely.

And, since one object is more perfect and clearer than another,

though they be of the same thing, it does not seem, if the thing is

finite, that there would be a progression to infinity in such objects

concerning the same finite thing. For every objective being 257 seems

to fall short of the perfection which the thing has in itsel f according

to the subjective being it has. Accordingly there must be some finite

objective being beyond which, if progress were made in knowing the

thing more clearly, the thing would be known according to its sub-

jective being. And, since all this can be done by a finite power, just as

the thing in itself has finite being, ei ther God is not infinite or He will

not know such a thing according to its own nature, unless one wished

to say that the clearest being of each thing would be the one infinite

being that is God. And it seems more acceptable to the mind to say

that God knows none of the things outside Himself except insofar as

they are reflected in His essence. For example, when one sees the

brightest whiteness , he is said not to see the dim in itself, but only as

its perfection seems to be contained in the whiteness in a preeminent

manner.



Furthermore, one must consider that sometimes the thought arises

that that objective being of a thing was simply the act of understand-

ing. But this does not seem true. Let us take the example of see ing

whiteness . There is something outside to which we give this name

''whiteness", and something inside. Otherwise it should not be said

that we 258 see the whiteness which [we allege to be that] of a stone.

We experience the external whiteness by way of object, but the white-

243 ness inside by way of act. And if it be asked what that act is , there

is no better explanation than [this]: If he asked "What is whiteness?",

it would be shown by pointing 259 out "What you see here;" and

similarly vision is what you have when you say you see whiteness .

We do not know experientially that such a thing as we call knowl-

edge [i.e., the act of knowing] is a likeness of an object. For when we

contemplate the act of see ing whiteness , it is not evident to us that

it is whiteness or something like whiteness . Moreover, each likeness

seems to fall short of the perfection of the thing of which it is a like-

256 Page 229.

257 See n. 10.

258 Read nos for vas in line 47.

259 For ad digitum read addigitatum in line 2.

Page 128

ness , but the act of knowing at times seems more perfect than its

object. For it seems that knowing blackness pleases someone with

more natural pleasure accompanying a higher good than does actually



possessing it.

But, concerning what has been said about objective being, 260 i t

should be noted that by objective being I understand that being of an

object which has such a conjunction with and inseparabili ty from an

act that, wherever the act is posi ted, that objective being will be

posited also. For example, when someone is in a boat on a river and it

seems to him that the bank is moving, in whomever such an act of

see ing was posited, the object would come with that kind of being.

Likewise, the objective being is multiplied, while the subjective being

remains one, because if there are two persons, one of whom under-

stands an object more clearly than the other, what each understands is

not the same thing, as was proven above, 261 even when it seems more

probable that the thing is one in its subjective being. For when a

bright and a dull intel lect looked at anything, regardless of its unity,

what the bright intel lect conceived would be different from what the

dull one conceived, as has been shown sufficiently above. 262

Hence, to assert that a diversi ty of conceptsfor example, calling

a thing true, of such a size, good, etc.does not prove a subjective

diversi ty in the thing, be it a real or a formal diversi ty, but only in the

objective being. For in these concepts the same thing is grasped,

though according to a different objective being. For the one who says

that a thing is good, true, and eternal is looking at the same thing.

This is not so in other concepts that are altogether disparate, as in the



concepts of a man, an ass, and the like. Accordingly one can get a

means of knowing what kind of diversi ty of concepts is sufficient to

prove a subjective diversi ty in the thing.

If you ask of a thing, taken subjectively in itse lf, whether it is

eternal, true, and good, one must say that subjectively in itsel f it is not

formally eternal, that is , so as to establish eternity as a reali ty or

formality existing subjectively in itsel f; and likewise with the rest. But

it is quite true that the thing, of itself, can be understood 263 by a

certain kind of intellect according to such objective beings. For if

someone understood a thing with respect to the subjective being that

it has in itsel f, he would not affirm several predicates of it. And

though we do not know that subjective being as it is in itself, but only

according to particular objective beings, nevertheless we make affirma-

tions about these objective beings according as they represent or are

taken for that subjective being which is one in itsel f; and similarly

260 Page 242.

261 Page 240.

262 Ibid.

263 Add intelligi after possit in line 35.

Page 129

with other things. Since a clearer intel lect understands a thing in an

objective being that is more intimate to the thing, it follows that the

brightest intel lect will understand the thing most intimately, and then



it would seem true that it would understand the thing as it is in itse lf.

As for what we said about the man in the boat, 264 i t must be

known that sometimes movement has a quasi-subjective being, as

when a thing is of such a nature that it would be seen by sight or by

an intel lect considering it, so that such subjective being is , in a way,

joined to things. This is when a thing is ordinarily said to be moving;

and this is true. But sometimes [the movement] is joined rather to the

act of seeing than to the nature of the thing, as when to the man in

244 the boat it appears that the bank is moving; and then it is said to have

objective being rather than subjective.

In connexion with the material concerning acts of understanding, 265

I cite one argument to prove the eternity of things. Suppose that there

is a whiteness in Paris and one in England. I prove that, when black-

ness takes over in the subject in which was the whiteness which was

in England, the whiteness is not destroyed. First I bring in a proof of

the conclusion that through numerically the same act are seen the

whiteness in Paris and the totally similar whiteness in England. I

accept the following proposi tions. When the whiteness in Paris is seen,

it is true to say that this whiteness is seen not only by this act, because

then this whiteness could not be seen perpetually, once this act of

seeing ceased; which you deny. The second proposi tion is that this

whiteness is seen through all acts like the first one. For, as this white-

ness can be seen through an act other than this but exactly like it, for



the same reason it can be seen through any act exactly like it.

Now, since the whiteness in Paris is exactly like the whiteness in

England, it is true to say that the acts of seeing them are exactly alike.

If this is granted, then let us call the whiteness in Paris whiteness a;

that in England whiteness b; the act of seeing a, c; the act of see ing

b, d . Then a can be seen not only through c, but through any act like

c, as the second proposition says. But d is altogether like c, as was

posited above. Therefore a can be seen through d. Thus also I shall

say that it will be possible for b to be seen through act c for the same

reason. Therefore, since a is seen through act c, and similarly b

through act c, this is numerically the same act. Then it follows that the

whiteness in Paris and the whiteness in England can be seen through

numerically one act. From this follows another conclusion, that, as

often as the whiteness in Paris is seen, the whiteness in England is

seen also. 266 It is proved as follows: "At whatever instant there exists

264 Page 231.

265 Page 205.

266 Add Parisius et videtur albedo after albedo in line 25.

Page 130 in someones' sight the act of see ing some object, that object is seen.

But, at the instant at which there exists in one's sight the act of seeing

the whiteness in Paris, there exists in his sight the act of see ing the

whiteness in England, because there is numerically one and the same



act of seeing, as was proven above. 267 Therefore the whiteness in Eng-

land is seen when the whiteness in Paris is seen."

From this it can be argued to the conclusion principally aimed at,

namely, that when blackness takes over in the subject of the whiteness

in England, the whiteness in England is not destroyed. It is certain

that, when the blackness takes over, I do not thereby 268 cease to see

the whiteness in Paris . Now, then, this act of seeing is as much the act

of see ing the whiteness in England as the whiteness in Paris. But the

act is not removed with the removing of the whiteness which is in

England. Therefore it is not removed with the removing of the white-

ness in Paris . Thus, if the whiteness in Paris passed away, [the act]

would stil l remain.

But then it would follow that sight would be deceived about its

object, even when there concur the proper disposi tion of the organ

and of the medium, and the proper distance of the object. And every-

one denies this. Indeed, to say this is to destroy every principle which

gives us certainty about how things are. For we gain no certainty

about things except through the appearances we get; and these ap-

pearances would be related contingently to their objects, as has been

seen.

The true meaning of the statement is in accord with our aim. For

the whiteness is the same in Paris and in England, so that there is no

difference in the nature of the whiteness. And so, when blackness



takes over from the whiteness in England, although the whiteness

ceases to be there, yet it is not destroyed, but remains entirely in its

full being in Paris . And, as it can be said that this thing is eternal, so

it can be said of every other thing.

If you ask why it ceases to be in England, I shall say that this is

because of the local withdrawal (or quasi-local withdrawal) of a

certain principle, commonly called the individuating principle of a

245 thing, that determines a thing's being in a particular spot, and

[because] a composi te of such a principle and the nature it thus

determines cannot be in several places.

If anyone holds that the whiteness in Paris is different from that in

England, he will be led into various errors, according to the con-

clusion proved above. 269 For, supposing that he sees very clearly the

whiteness in Paris , it is true to say that he sees very clearly the white-

267 This page.

268 Add hoc after propter in line 33.

269 Page 244.

Page 131

ness in England, as was proved above. 270 Hence it would follow that,

if an object were removed to an infinite distance, it would be seen as

clearly as if it were two feet away. Let us then say that the whiteness

is altogether the same in Paris and in England.

And much more easi ly can it be said that the act of seeing whereby

Socrates and Plato see numerically one object is numerically the same



here because it does not exist elsewhere. This merits consideration.

Someone might perversely wish to obstruct the argument made

above, whereby it was proved that one who sees the whiteness in Paris

sees the whiteness in England. Answering the principle upon which

the reasoning was based, namely, that one who has the act of seeing

some object sees the object, he might say that it is true if the object is

present, but that the whiteness in England is not present. My rejo inder

is that they assert that the object is required only because it is neces-

sary for creating the act or for determining the relationship of the act

to the object. Now, in the case in hand, the presence is not required

for the first reason because it has been proved that the act of seeing

the whiteness in England is there. Nor for the second reason, for the

270 Ibid.

Page 132

presence is not required there, for even according to them, if two

white things were an infinite distance apart, the relation between

them would be just as it is now.

Furthermore, according to Averroes, in Book 3 of On the Soul ,271

whose words they accept as true, to understand is nothing else than

to receive the objects understood and to be perfected by them. And it

is certain, even according to them, that this perfection does not exist

except as regards the act, or the species of the object. Now, it has been



proved that the act of seeing the whiteness in England is present, and

by the same reasoning it can be proven that the species is present, if

the species is posited as being distinct from the act. Likewise, suppose ,

as was argued above, 272 that the act of seeing, and similarly the acts

of the other external senses , can exist in a power without an object

being known. If [an object] is brought near, and nothing more were

added to the power than was there [before], then, just as the power

246 did not know the object before, neither will it know it now. Hence it

is true that whatever has knowledge is a knowing subject, and what-

ever has knowledge of some object is a subject knowing that object.

From the preceding it seems to be proven not only that the same

whiteness is in Paris and in England, but also that a plurality of white-

nesses is not possible. This is so in all other things, as, clearly, can

become obvious from what has been said before. Also, ei ther the exist-

ence of two has the same perfection as that of one, and then the

second would be superfluous; or there is a greater perfection in two,

and then an infinity of such things would have to exist or the world

would not have complete being.

But it might seem to some that one could refute the principal

argument made above, 273 when it was said that, just as upon the

removal of the whiteness in England the act of see ing the whiteness

in Paris did not cease , so, upon the removal of [the whiteness in

Paris], the act of seeing it would not cease . It might be said that there



is no similarity because the whiteness in Paris is the efficient cause

(and somehow the conserving cause) of the act of seeing it. So, if this

object is removed, that act would cease . Therefore, it must be said

that the act does not have a contingent relationship to the object. But

this does not seem to be valid, because one who knows most clearly

would then not be in a posi tion to pass any certain judgment upon the

object. For him it is irrelevant that the object be the efficient or pre-

serving cause, since he would be said to know that object no matter

what other agent were causing the act of knowing whereby knowl-

edge was present in the faculty. Hence, if the act were caused and

271 III, 18.

272 Page 244.

273 Ibid.

Page 133 preserved by a higher agent, he would know that object and yet he

would be deceived about it; which seems to be false.

A refutation of the teaching previously mentioned can come from

another source. He concedes well enough that one who sees the white-

ness in Paris sees the whiteness in England; yet he will say that this is

consistent with the existence of two whitenesses . This is the opposite

of what we maintained. In answer: "One who knows very clearly two

whitenesses differentiated as to subject, or two continua, knows clearly

that number is inherent in them. But one who knows the whitenesses



in Paris and England does not know that number is inherent in them,

and yet he knows each one clearly, according to the proof given

above. Therefore there is no duality in them. Likewise, one who knows

some object clearly can experience that he knows that object; but one

who knows the whiteness in Paris never experiences that he knows the

whiteness in England. And if someone said that the assumptions in the

major premises of the two aforesaid arguments are true not only when

the whiteness known is known but also when it is the efficient cause

of its being known, this is not valid, or, rather, it is frivolous, if one

pays attention. For one thing, evidence for number is found only

because there is clear evidence of numerically diverse objects. For

another thing, experience of an act is found only because it takes

place, and clearly."

Furthermore, an argument can be adduced to confirm my principal

aims. First I prove that, when the object is equally close, the medium

equally disposed, and an equally strong faculty equally applied, an

object numerically the same can be seen by the same faculty only by

an act one in number. You may say that [it is seen] by several acts, so

that [the faculty] can see now by one act, then will terminate [this]

act of seeing, and will see a second time; and there will be a numeric-

ally different act of see ing. I will raise the following counter-argu-

ment: "If a faculty numerically one contained numerically several acts

of see ing with respect to numerically the same object, since those acts



are alike and equal, insofar as it contained one [it would contain]

also [any] other." Then as follows: "In things existing at some moment,

when all factors concur for the causing of some effect, that effect is

caused. But, at the moment at which this whiteness is seen by this act

of sight, there are present all the causes of another act of sight like

and equal to this one. For nothing more is needed than the faculty,

the object, proximity, etc.; and these are present. Therefore, at this

moment the other act of sight is posi ted. And so at whatever moment

247 sight saw some object, it would see it with an infinity of acts of sight."

This is confirmed, and comes virtually to the same thing. A natural

cause acting naturally and containing equally several effects produces

Page 134

ei ther none of them or all of them at once, for there is no reason for

one rather than the rest. But sight and its object are in the posi tion

of containing equally all acts of see ing this object, since all are alike;

for there is no reason for one rather than the rest. Therefore it is true

that the object is always seen by numerically one act of seeing. Now,

moreover, if someone, when he has ceased to see, afterwards sees the

object numerically the same (and, as has been said, this cannot be by

several acts of sight), it will be necessary to admit that the act of

see ing whereby the object was first seen was not absolutely destroyed,

even though it ceased to exist here. This is my contention. Or [it will



be necessary to admit] that numerically the same [act] has been re-

stored. [But] they do not admit this because they have it form Book 5

of Aristotle's Physics 274 that invariably things whose substance has

perished cannot return numerically the same. There are also some who, to obstruct the above train of argument,

say that, though those acts of seeing are equal, yet they have an order-

ing in their coming into being. The truth of the reply to this is not

evident. Hence let the major premise be rephrased as follows: "No

two effects that are altogether alike and equal can have a necessary

ordering in their production, because the agent contains them equally,

and because an order cannot originate from a final cause because the

existence of one is as good as that of the others. Likewise, it is a mark

of greater perfection to contain two like things rather than one; other-

wise two like things would never exist in nature, since one would be

superfluous. So also to contain three [is better] than [to contain] two,

and so on, ad infinitum . And so, since each faculty of itself contains an

infinite number [of its acts] (because to the degree that it contains a

particular act [it contains] every one like it) , it will therefore be

infinite."

In the matter of the conclusion principally aimed at, concerning

the eternity of things, there comes to mind another way of asse rting

it, as I have to some extent intimated in what has gone before. 275 From

causes numerically the same is always produced numerically the same



effect. This is evident to me both from a grasp of the terms and from

the analyses given above. For, if a cause numerically the same con-

tained several such effects, it would produce ei ther none, or all at the

same time, as was said above. 276 Therefore, we shall be able to say

that all things are eternal, so that, when any particular thing at all is

pointed out, it is true to say that it has always been, is now, and

always will be. For, suppose that there is light now in our hemisphere.

274 Aristotle, Physics , V, 4; 228a3. See also Averroes, Physics , IV, comm, 36.

275 Pp. 193, 203.

276 Ibid.

Page 135

I say that at night that light is not destroyed, but is produced in a

hemisphere other than ours. Hence at one time it was here, and at the

end of that time it was produced in another hemisphere. Or, if time

is composed of instants, as I have said elsewhere, 277 then at this instant

it is here, and at the next instant it is in the next hemisphere.

And so this rule is true: that a thing which is , or, rather, which

has been for all time, will go on being produced. In keeping with

this, to say that this agent produces this thing is not to say that it

causes it to be after it was not, but only to say that it causes the thing

to be. And, in keeping with this, it could be said that when some

object is seen continuously, granted that the act of see ing has been

produced, it is being produced at each instant of time, because present



causes always produce their proper effect unless something else inter-

feres. And here all the causes are present (the faculty of sight and an

object); and there is nothing interfering. The greatest [interference]

would seem to be the existence of the thing [the act], for the reason

that, as it seems, nothing which exists can be produced. And so it is

false [that the act is not constantly produced], as was said above. 278

248 Let us say, then, that, if light is something produced, a heavenly

body produces it in the intervening space as long as the body is

present. And accordingly the preservation of a thing is nothing else

than continuous production of the thing. But sometimes the preserva-

tion of a thing is simply preventing the escape of hot bodies from the

thing, the escape of which would make the thing cold, as in a room, in

which there was a fire, when the windows are closed.

In keeping with this, when it is asked whether all things are

eternal, it might be said that "They are eternal" could be understood

in two ways. For example, [it might refer to] things which are called

liable to generation and corruption, in the sense that they had one

production which receded into the past while the thing itself endured

ever after. In this sense it is not true. And so Aristotle 279 understood

that in this sense some things are corruptible. Likewise, in the sense

that their existence lasted forever in the same place or subject, it is not

true of things liable to generation and corruption. But in the sense

that they are being continuously produced whether in this place or in



speak, taken by the hand and placed in another subject. But one must

not imagine any such thing, as was said before. 283

Furthermore, one should know that some of the ancients 284 said

that all things are eternal simply because they refused to investigate

249 the causes, especially the efficient causes, of things, as if everything

281 Metaphysics , V, 21, and VII, 1.

282 Averroes, Metaphysics , V, comm. 26.

283 Possibly pp. 223-225.

284 Aristotle, Metaphysics , I, 3; 983b6 ff.

Page 137

existed of itself. In answer to these men Aristotle says that there are

some corruptible things (as we admit too), meaning things which

require an efficient cause. Also , they are corruptible in the sense that,

if a whiteness is here, and one numerically the same is produced in

England, the one in England can be said not to have existed pre-

viously. For, just as it would have needed an efficient cause if it had

not existed here before, so it also needs one now [in England]. Like-

wise, previously it was not here.

Nor are we, accordingly, compelled to say that there is some one

thing, universal or particular, which is in several places; but only that,

when this thing ceases to be here, it is produced elsewhere. It is true

to say that, when any whiteness at all is pointed out, this whiteness is

now here and is not now elsewhere, neither itself nor one exactly like

it. For, as I have said, 285 if there were several similar effects, they



would be contained simultaneously in the agent's active power, and

thus the active power would produce ei ther no effect, or all its effects

at once. Hence in my view it does not seem impossible both that there

be a perfect likeness and that there be otherness . For likeness, after a

fashion, as far as the connotation of the name is concerned, presup-

poses otherness , since nothing is like itsle f. And otherness seems con-

sis tent with perfect likeness. 286 This makes a better foundation, beyond

the reasons cited above.

There seems to be a doubt left about things not altogether similar,

for example, whether there is something common to a bright white-

ness and a dull whiteness . There might be here one way of answering

which, as it seems at first, is not based upon what was laid down

before; namely, that wherever whiteness has subjective being, 287 it is

always equally bright. If anywhere it is called dull, this is only because

of an admixture of its opposite , namely, blackness. Then it is different

from when it is seen in its subjective being. It is obstructed from its

perfect action because of the presence of its opposite, and produces a

duller object. In the case of such bright and dull objective being,

though it be admitted that there is some one thing in both of them,

yet it would not be held that one thing is in several places according

to the subjective being it has.

But if the whiteness in Paris and the whiteness in England are such

that, just as one is bright, so also is the other of itself, the question



returns. Then, as it seems, ei ther they will be numerically one white-

ness , and so it would be numerically the same, which we were trying

to prove; or there will be some one thing common to them, which we

were also trying to prove. If this were the answer, it would concede285 Page 247.

286 Omit non in line 15.

287 See n. 10.

Page 138

that there is only one whiteness in Paris and in England. But this

could be understood in two ways. One is that this whiteness would be

numerically one in such a way that [its cause] would contain one

production equivalent [to all]. This is false ; indeed it contains several

equivalent ones. Hence, suppose that God is the productive [agent]

of the whiteness here. Then he would contain the effect just as before,

for He is just as perfect as before. It does not appear impossible that

he be able to produce the effect there, that is , to cause the effect to

be there.

And then there is a doubt. This production is ei ther something

distinct from the producting agent or altogether the same. If it is the

same, then just as it was not producing there previously, neither will it

produce now. If it is distinct, then it will seem to receive its being

from the agent, and, just as the agent is one, so the production will be

one. Then, since that production would have exis ted previously, it



seems that the whiteness ought always to have been in England, since

a production numerically one lasts forever.

We shall speak here about movement, and be consistent with what

was said in other statements above, in the treatise on material sub-

stance and quantity. 288 [The question was] whether they are distinct

subjectively, that is , in their subjective being. We said there that the

word ''movement" does not imply anything distinct from permanent

things, that is , from a moving object and its terminus. And it can be

seen there concerning the possibili ty of this thing. Now, in keeping

with this, it is true that a thing is here and previously it was not.

Nevertheless, no reality is present which did not exist previously, nor

250 has one been destroyed which previously existed. Ponder that case,

and apply it appropriately in this case. Hence, it is only in accordance

with the local movement of the heavenly bodies that this whiteness is

sometimes produced here, sometimes elsewhere.

In the case of material substance and quantity, le t us readily admit

that they are different in objective being, because in that case there

are different concepts, as was said above. 289 And thus the distinction

of categories posited by Aristotle 290 will stand up. Ponder this point, if

you want to understand, because the matter needs close consideration,

and a lot of young men at this point would despair of comprehending

what has been said above in several places.

But it seems highly unintell igible and false that a stranger, who is



numerically one, as long as he is here, it being established that he is

here, could at the same time be produced elsewhere. For in him the

full manifestation of the agent, as regards the kind of manifestation

288 Pp. 222 ff.

289 Page 226.

290Categories , chap. 4.

Page 139

which has to do with this effect, seems expressed in the effect which

is here. But this argument would not be very conclusive (even if one

were to accept that [duplication] as impossible), especially as regards

an agent as perfect as the First Agent. For it is true, but only if the

agent's power is used up in making the stranger be here. Likewise,

[such a duplication] could not be found in the movement of the

heavenly bodies, for no part of them 291 is in several places at the

same time. So, in keeping with what has been said above, 292 there is

some one thing in them [two similar things], and that is a universal

not limited ultimately by an individuating principle. Nothing prevents

something of this sort from being in several places at once, which

accords even with the common opinion of those who hold that a

specific nature is one in its subjects.

And consider well that it can be held with probabil ity, although it

is not in keeping with what has been said, that wherever hotness has

being it has equally perfect being, and similarly in the case of cold-



ness , whiteness, and blackness, and so on, but that it does not every-

where perform its action equally, because of the admixture of its

opposite. And thus Aristotle 's saying in Book 3 of the Metaphysics ,293

that there is no order among individuals, will have good standing; and

the one in Book 3 of the Topics ,294 that we call something whiter

because it has a smaller admixture of blackness. However, one thing

is not whiter than another in its subjective being, 295 but only in its

objective being; for one contrary obstructs the action of another

contrary.

But two things seem to contribute to the destruction of this proba-

bility. First, that one contrary is not always equally obstructed in its

action seems to be true only because sometimes it receives a greater

admixture of its contrary, and so will then take on more of its contrary

and, in consequence, the rest of its opposite, in accordance with the

rule in the Topics .296 Likewise, some things seem to obstruct them-

selves in their function only because they previously obstruct them-

selves in the principle of the function, namely, in their essence, so that

one enfeebles the others. Likewise, it would be ridiculous to say that

in the flame of a candle there was as great an intensi ty of fire as in a

blazing furnace. For, that there is in the latter a smaller admixture of

the contrary is nevertheless due simply to the fact that it has been

expelled through the perfect inherence of its contrary. This seems to

represent the truth.



291 Read quae for qui in line 16.

292 Pp. 244-245.

293 III, 3; 999a12.

294 III, 5; 119a27.

295 See n. 10.

296 See n. 294.

Page 140

Do not suppose that something is hotter because of having more

degrees of hotness altogether equal, because that is impossible, as was

said above. 297 It is because it has one, more perfect, hotness. And so,

if two candles were taken altogether equal and alike as to matter,

form, etc. (which is not poss ible, as I intimated above), 298 I would

say that at the midpoint, where the lights would meet, there would

not be greater light, nor would that midpoint be more il luminated

than before, and this would be as true of a thousand as of two. In

keeping with this, the highly improbable result would seem to follow

that, if some altogether similar wax were taken and made into a torch,

it would not give more light than a small candle. For it seems laid

down as a rule that the assembling of several items of the same

character does not produce an effect of greater intensi ty.

251 It will be said that the preceding is impossible (that there would

be such a continuum having all its parts of exactly the same nature)

except as the thing takes on objective being. For there cannot be

several things of exactly the same nature in the universe, as I said



above. 299 Rather, according to this, the being of each thing consists of

an indivis ible, as the author 300 of The Six Principles intimates. Hence,

of each thing there will be only a point, and, just as a torch is made as

an aggregate of several things of different natures, so light is some-

thing composed of several things of different natures. But then it

would seem that the most perfect nature among them would be

sufficient. One might say: "No, because it does not have the full con-

tent of the others, even though it is more perfect than the others." Or,

if you want rather to return to opinions commonly held, do not take

the arguments adduced above insofar as they are efficacious, 301 if set in

order, to prove that there cannot be two things of the same nature in

the universe. Rather take them insofar as they prove that these things

are not contained in the active power of an agent numerically one. This

is inadmissible because, if they are totally alike, the way in which one

is contained in the active power of this agent is the same as that in

which the rest are contained, as was deduced above. 302

In keeping with this, if Socrates is white, one will now be able to

say that no one else has exactly the same colour. Or, when one sees or

understands this whiteness , he can say that no one else sees this white-

ness right now with exactly the same kind of sensation because, as has

been said, 303 there do not occur in the universe several effects exactly

297 This page.

298 Pp. 246-247.

299 Ibid.



300 Gilbert de la Porrée, Liber de Sex Principiis , ed. A. Heysse (Monasterri, 1929) p. 11.

301 Read efficaces for efficacibus in line 11.

302 Pp. 246-247.

303 Ibid.

Page 141

alike. It will follow from this that this whiteness belongs to the per-

fection of the universe, because one does not find another exactly like

it in the universe and so in a fashion the same thing is species and

individual. Hence nature is adorned by the existence of such a reali ty

which exists only because this specimen exists. If you say that indi-

viduals are not of the perfection of nature, I say that an individual is

of two kinds, a natural individual and a local individual. An example

of a natural individual is a whiteness in which are contained whiteness

and also some ultimate characteristic which makes it this [particular]

whiteness. Such a natural individual certainly belongs to the perfec-

tion of nature or of the universe. But an example of a local individual

is some particular being here in our midst in this hemisphere. It is

accordingly not of the perfection of the universe. Hence, this light is

not always in our hemisphere, but sometimes in the other, and so its

being here does not belong to the perfection of the universe, simply

speaking, but only while it is [here].

Concerning what I have said about things having active powers,

some probabil ities can be inferred. First, there are the ease and diffi-

culty, painfulness, weariness, which we experience in ourselves when



something is somewhere where previously it was not, as when some-

thing moves a small or larger stone, or when someone sees the sun

or something else. Again, something else is inferred about this. For,

as has been said, 304 when this whiteness ceases, at the moment of

ceasing it is elsewhere, and it does not always appear that it is trans-

ferred to a neighbouring place. If, therefore, this were by way of

transference, it would need an agent. And so it is satisfactory to accept

as a rather conjectural proposi tion that it is elsewhere by way of

causation, so that it is caused elsewhere in the way explained above. 305

In keeping with what has been said, you can see that resurrection

is possible. For example, if a man who exists now ceased to exist here

in our hemisphere and were caused elsewhere, and again ceased to

exist there some time later, and then were caused here, he would be

said to have risen.

It should be obse rved that the eternity of things could be under-

stood in one of two ways. One is that they would always remain in-

tegral as some composi te whole , just as they are now. For example, in

Socrates there are many reali ties of different natures jo ined toge ther,

such as flesh, bone, and breath. Now, one could take it to mean that

Socrates would be eternal in the sense that he would be always just

252 as he is now, meaning that, since Socrates is not altogether identical

with himself as boy and old man (rather, in some way he varies from

304 Page 244.



305 Page 248.

Page 142

hour to hour), it would be understood that when he ceased to be in

one condition, for example, that of boyhood, he would exis t elsewhere

in the same condition, and, later still , in another place, and so on for-

ever in a circle, until he would have existed everywhere. And [this

happens] not only from hour to hour or from day to day, but even

from moment to moment, so that, as soon as he ceased to exist in one

condition here, he would begin to exist in the same condition else-

where.

Another way of understanding eternity in things would be by way

of separation, so that Socrates would be nowhere as a composi te

whole, but his whiteness would be caused in one place, his virtue in

another, and so on, until finally, the mighty orb having come full

circle, a gathering-together would again take place. Take the more

probable of these ways.

As for my remark that the old man is not the same thing as the

boy, this is clear from the fact that no power can be changed in its

essence without being destroyed. Suppose that there are two powers

very closely related in nature. Let a be the more perfect power, b the

less perfect. Now, if a were changed in the direction of imperfection,

this would be only because b was produced. And then the truth of

the matter would be that a was destroyed and b was caused. And so



one must say that the powers of the boy are not the sameat least

not allas the powers of the mature man, because then the boy would

produce works as perfect as does the man of mature condition. [The

man], therefore, has other, more perfect powers, and [those of the

boy] are caused elsewhere. But because the powers are continuously

changing to a very closely related condition, he is always said to be

numerically the same (perhaps it would not be so if a year-old boy

were suddenly made into an old man), or else because a boy is a very

similar root which is put down, and is a necessary prerequisi te accord-

ing to the regular course of nature.

Although [the man] later has a more perfect faculty of memory

than before, yet this is with respect to objects previously seen and

remembered by the previous feeble memory. And sometimes he is

punished in old age for the misdeeds of his youth. For a person

naturally protects the being he will have in old age just as much as

his present being. And so, for fear of later punishment, he would re-

strain himself even now. And yet, from a strict point of view, it is true

to say that he is being punished who is committing no offense; and

so such fear is instill ed into his nature as will induce him to refrain

from the fault. Similarly, as concerns the death which someone fears, it

can be said that, unless it were feared, many evil s and many murders

would be committed; the dissolution of a well-made connection be-



Page 143

tween beings is an evil. Even a madman can be punished for a crime

committed before his madness , to make everyone recognize that he

will always be punished ei ther in his own person or in what is left of

him.

And, if it is asked whether a boy is a man, it can be said, in ac-

cordance with what was said before, that, if the designation is based

on the rather general appearance, he should then be designated a man

because he has an appearance like a man's, with the head above and

the feet below. But it is fitting to take the designation not from this,

but rather from the function and the inherent power. And, just as he

does not have the function, so he could be said not to have the power.

It is only as he functions that a person should be said to have a power.

So, if a child dies when he is one day old, it can be said that he had

the power neither to laugh nor to reason, although certainly he had

some remote preparations for this , just as it is in the seed. Neverthe-

less, it is customary to say that men and boys are of the same species.

Perhaps the reason for the custom is so that men may have more com-

passion upon them.

If a child has not a man's powers, it is proper to inquire whether

the power exists in a quiescent state. For example, when someone is

not moving a stone or some other heavy object, has he the power to



move the stone? It seems not, because its being would then be super-

fluous at the time. On the other hand, it seems [that he has], because

otherwise no one ought to choose a state of rest, nor should nature

naturally incline to this when a natural power tires it, since this would

involve its destruction.

And so it could well be said that [the power] persists during a

253 state of rest. And this is not something superfluous because it thereby

ensures its prese rvation in its subject. Otherwise it would be caused

elsewhere and would cease to exist here, and in its place would be a

less perfect thing. Hence, when with the concurrence of certain spiri ts

a heavenly body causes such a power, the spiri ts leave as the work

(say, of laborious motion) progresses , and in their stead come less

perfect ones. When the toil is very excessive, they withdraw com-

pletely. Sometimes, when it is light and moderate, stronger spirits

come. They certainly come to more practised subjects, as if they were

seeking a place of activity, not of rest, provided, at least, that it is

regulated activity. As has been said about this power, so le t it be un-

derstood about others.

The Intellect There might be a number of questions concerning the intellect:

first, whether the intel lect is the same for each man. It seems that it is

Page 144

not because, after a man is declared dead, it is true to say that he has



never seen 306 as clearly as some other man, never heard as clearly, and

so on. Therefore he has never needed as perfect a faculty. This excess

[of power], consequently, is something in nature which is superfluous.

Moreover, every faculty performs an operation commensurate with

its nature. If there were a degree of the faculty to which no degree of

operation corresponded, neither would there be other [degrees of

operation] less perfect, or at least not more perfect; as a result the

faculty would do nothing. Moreover, every natural faculty functions

according to the whole inborn force of its nature. Also, if it is possible and fitting to postulate a being, then in fact

it does exist. We have used this principle, mentioned above, in the

treatise on the eternity of things. 307 But an intellect corresponding to

a level of imperfect operations is possible, for it does not include a

contradiction in its concept. Moreover, it is fitting that it be postu-

lated, since it is very fitting that a level of operation correspond to

each level of the faculty so that nothing be above the maximum or

below the minimum [required for its operation].

From this it is shown clearly enough that the intel lect of Socrates

is one thing and the intellect of Plato another.

This argument can also be confirmed. If unequal operations came

from equal faculties , there would be no degree of preferment of one

faculty above another, for we measure the degrees only by means of

the operations. From this it follows that not only Socrates and Plato,



but a young man and an old man, have different intel lects, if the

young man's intellect operates more clearly than the old intellect in

all matters. Hence, just as the old man would see like a youth, so he

would understand like a youth if he had the intel lect of a youth. It

even seems that, just as someone, by understanding more clearly or

less clearly, changes from one day to the next and from one hour to

the next, and similarly in other functions, accordingly a change is pro-

duced in his faculties.

Consequently it remains to be shown whether there is one intellect

from the point of view of its containing all intell igibles . It seems that

there is not, because anyone possessing intellect would then have the

capacity for understanding all intel ligibles ; but, since there are some

who have syllogized with universals scarcely once in their li fe, the

intellect was idle in relation to the knowledge of the other intell igibles

it contained. The argument could now proceed as previously. Let us

suppose , as previously, that there are intel ligibles which do not require

unequal power [of understanding], as carrying a hundred pounds of

306 Add vidit after numquam in line 13.

307 Pp. 185-186.

Page 145

stone or a hunderd pounds of iron [do not] in the power of moving.

Then he who has the power to do one has the power to do the other,

254 since he is equally able to do ei ther. But, where a diversi ty of intel -



ligibles of themselves require unequal power (as a man desiring to get

a concept of prime matter in things) , there is required a more perfect

power because of the effect [to be achieved]. Then we must say that

there is a different intellect in these men; otherwise there would be a

superfluous degree of understanding in the man who will never under-

stand these difficult intell igibles.

Also , as was argued above, 308 faculties should correspond to their

operations, so that, just as there is a difference in perfection and

imperfection in operations, so also is there in faculties. And so, to

prevent there being 309 an excessive or deficient [power], let us posi t

degrees of perfection and imperfection in faculties to match the

operations.

It is the same with the other arguments given just above, for all

the arguments set down there hold here. And so if there is some

intell igible by which one thing is seen more clearly than another, as

it is both in itself and in relation to us, the understanding of it, accord-

ingly, takes its origin from an intellect more proper to it. This [wil l be

true] also: there were as many intel lect as there are concepts. Simi-

larly, in the case of a man blind from birth to death, even though

perhaps he had an intel lect capable of understanding things more

difficult to understand than are colors for one not deprived of sight,

it could be said that he never had an intel lect capable of understand-

ing colors. As there should be nothing superfluous or deficient in a



master's well-ordered household, so also should it be in God's creation.

But, if there are as many intel lects as concepts, there seems to be a

difficulty. It then seems that no intellect will be able to differentiate

between two things because no one intellect knows two things. I

answer that it suffices that the separated intel ligibles are understood

by intel lects connected with each other and with a [common] subject,

and also that there is an intellect able to know the difference between

the separated intel ligibles . As corporeal [parts] which are in a subject

are joined to one another in a certain order, so these intellects are

jo ined to one another in a certain natural order, and perhaps it could

be said that where these three intel lects exis t (that is , the two know-

ing the separated intell igibles, and the third intellect knowing the

difference [between them]) they are all rooted in the essence of the

soul. Give further thought here.

308 Page 253.

309 Add sit after nihil in line 7.

Page 146

Supposing these matters settled, there remains the difficulty

whether a person could know several things; and, if he could know

several, why he could not know ten as easi ly as two. It seems that this

should be the case, for, since they proceed from different intel lects,

none of them gets tired when functioning according to its nature, and



it is not evident how they can impede one another. The aswer seems

to be that, in understanding, there is a certain movement of spiri ts, as

appears from the subsequent condition, that is , fatigue and the change

of the spirits into weaker ones. The more things someone considers, the

greater and faster is the movement required, as experience testifies .

Sometimes the spirits' powers of movement do not suffice for such

great motion, and intellection ceases.

Why is such a motion of spirits necessary? The answer is difficult,

but it could be said that the reason is that we do not understand

anything except somehow with matter or with the admixture of some-

thing like matter. The image of a thing, which is like corporeal things,

is carried to the place where intellection should take place, or (per-

haps better) the cogitation prel iminary to intellection. These spirits,

some of which carry the image of one thing, and others the image of

another thing, can impede one another in their movement. Then the

image of neither thing is carried without mutilation. It is men in this

condition who judge of things defectively and imperfectly. And so, if

there were a being to which there were joined intellects which always

had present the images of things without such motion of the spiri ts,

there, indeed, could be the understanding of an infinite multitude of

things. There does not seem to be an impossibili ty in this, and this is

granted concerning the First Being.

Whether the Same Cause Can Produce Specifically Different Effects



255 From the aforesaid arguments it is clear enough whether the same

cause can produce specifically different effects. It seems that it cannot.

For, granting that one of those effects is less perfect, it is true to say

that of itsel f it does not require as perfect a cause as does the more

perfect effect, because, if it did, then from the nobil ity of effects one

could never argue to the nobil ity of causes. Furthermore, a less perfect

effect requires no more than that its cause is such as to contain it

virtually. Now, according to the common opinion of all , something

which is not more perfect than something else can contain it virtually,

as in the case of a univocal production; although, as they say, an

equivocal cause should be more perfect than its effect. Therefore,

since that effect does not need as perfect a cause as does the more

perfect effect, there will be a superfluity of perfection, proportionate

Page 147

to the degree of superiority. Therefore, that nothing be in vain, le t us

say that it is produced by a cause that befits its perfection. For the

fitting order is one in which a perfect effect is produced by a perfect

cause, a more perfect effect by a more perfect cause, and the most

perfect effect by the most perfect cause.

Likewise, as was argued above, 310 every possible entity which it

would be fitting and for the adornment of the universe to postulate

does exist. But a cause that corresponds directly to an effect is a



poss ible entity, for it does not include any contradiction in its concept,

and it is fitting to postulate it, for it seems fitting that each effect be

produced by a cause befitting it. Furthermore, it seems that a cause

which performs according to its whole inborn force performs its more

perfect effect, and, it seems, only its more perfect effect. But a natural

cause always performs according to its whole inborn force. Further-

more, a cause performs insofar as it is a certain kind of thing. Now,

since it is one, it seems to be of only one kind, just as it has one

essence. Therefore, one must say that one cause does not produce

effects specifically different, especially quite dissimilar effects. (If,

however, an imperfect effect followed a more perfect one, perhaps it

could be that the nobil ity of being ought to be measured by the first

effect.) 311

And what is it fitting to say about whether the same effect can be

produced by specifically different causes? It seems that it cannot,

because, just as the effect is one in itse lf, having one nature and one

essence, so it seems to be produced by only one cause having one

nature and one essence. Furthermore, the more perfect of two causes

must always of itself produce a more perfect effect, the less perfect

cause a less perfect effect. Therefore their effects will not agree. Like-

wise , the production of each effect is by the most suitable means

poss ible. But, that one effect be produced by one cause in the same

genus of cause and the same mode of causality seems the more suit-



able production, so that, just as it is one in itself, it may have one

cause. Nothing else seems possible, because an effect requires only

some being which contains it in active power.

Furthermore, in a way this amounts to the same thing as some

previous points. Never does the meeting of a less perfect cause with a

more perfect cause change its nature; but the more perfect cause of

itself must produce a more perfect effect, and the less perfect cause

a less perfect effect. Likewise, suppose the effect produced by a more

perfect and a less perfect cause were more perfect than the effect

produced simply by the more perfect cause. It is then not clear

310 Pp. 185-186.

311 Add esse after posset in line 26.

Page 148

whence it can have this extra degree of perfection, because it is

neither from the more perfect cause nor from the less perfect. Some-

one will say that it is from both at once. The rejo inder is that, if we

posi t that the most perfect effect is from a cause moderately perfect

and one less perfect, there would be no means of disproving this,

because, though one said that this effect exceeds the perfection of each

256 of the causes, this would not satisfy you. You will say that it exceeds

the perfection of both causes taken together.

Even if it be admitted [that two causes produce an effect greater

than that of the higher cause], let us further investigate how the



perfection of these causes taken together is to be investigated. Let us

suppose that the more perfect cause includes as much perfection as

does the less perfect, and in addition one degree more. Let us suppose

that the less perfect contains three degrees . Then, if the degrees of the

less perfect cause are added together with all the degrees of the more

perfect cause, the same thing would be taken twice, because on our

assumption the more perfect cause included the perfection of the less

perfect and something more. Now, the same thing taken twice does

not imply a greater perfection in the intensi ty of perfection, just as, if

there existed a thousand whitenesses exactly equal, they would not

posit a greater intensity of perfection in the category of whiteness .

Perhaps this argument is not conclusive, because then the world

would seem to be as perfect through the exis tence of a more perfect

cause alone as through the simultaneous existence of a more and a less

perfect. Also , ''containing" is equivocal; it means "having as much

power as." Perhaps equivocal "containing" would be involved if we

imagined that those two beings are one being. Then it would be seen

in which a man would naturally have more satisfaction, considering

each of those beings, in the being which is imagined as one (if per

impossibile that were the truth), or in the o ther which in truth is one.

Whatever may be said concerning that answer or argument, the pre-

vious ones make me think that this conclusion is more probable than

its opposite: one effect always proceeds from only the one cause. This



is true of a simple effect but not of one composed of things of different

natures. In [a complex effect] it would be otherwise, because then in

truth there are different beings there, as in Socrates there are bones,

flesh, breath, blood, etc.; and so one must posi t different causes there. From these rules, that one cause cannot have several effects speci-

fically different and that one effect can be produced by only one

cause, there are many consequences that run counter to what is usually

asse rted. From these it follows that fire is not produced from fire, nor

heat from heat. For suppose that, when there is a small fire (little

sparks, for example) , there follows an enormous and very intense fire.

Page 149

Now, one heat is naturally more perfect than another, and similarly

one fire than another, because it is never possible to allow two effects

altogether alike and equal, as was proved above. In our present ex-

ample , the first fire was less perfect, and similarly its heat. The argu-

ment proceeds as follows: "The second fire is produced by the first,

and the second heat by the first. Therefore, according to the rule

above (that one effect can be produced only by one cause), [the

second fire is produced] by the first fire alone. But the first fire, by

hypothesi s, is less perfect. Therefore, a less perfect cause will, by

itsel f, produce a more perfect effect. This is impossible. Therefore so is

that from which it followed, namely, the hypothesis made that a small



more perfect heating power is joined to it. In accordance with this, it

is false to say that light or movement heats, except insofar as they are

attended by certain heating powers.

Wind, however, seems to help the generation of fire, as in the case

of blowing with the mouth or by some artificial means, especially

when it is moderate. This is because along with such wind some

bodies withdraw which obstructed the reception of fire in a particular

312 Page 247.

313 William of Ockham, Sentences , Lib. IV, I, G.

Page 150

subject, so that a perfect fire-producing power was not jo ined to it.

But, when the wind is uncontroll ed, then also those bodies are re-

moved which disposed the subject for ignitibili ty. Above, in the

treatise on the eternity of things, 314 I said that, when fire is said to be

produced, the truth of the matter is that this is only the addition of

some hot bodies; and coldness is said to be produced through the

withdrawal of these and the addition of cold bodies, as in the case of

hot water, which, le ft to itse lf, reverts to its former nature, namely,

coldness, through the withdrawal of hot bodies and the addition of

cold bodies. In this last case, the only serious improbabil ity seems to

be that, when fire appears where previously it did not appear, it is not

evident how a local movement of hot bodies could have taken place



so quickly.

Also , with respect to the sun, we say that it does not heat, but that

certain hot bodies in the fiery sphere naturally follow the movement

of the sun. It is similar in the case of coldness, when it is said that this

planet makes cool . And so with other things in their own way. With

respect to the movement of hot bodies, it might be imagined that they

are close enough, but have been kept from their action because of a

large admixture of their opposite. But, when they gather in a place

where there is fire accompanied by a power capable of expelling cold

bodies, then [the heating power] performs its actions there.

From the rules set down above 315 that one effect proceeds from

only one cause, etc.it follows that the soul of one man, whatever

sort it might be, is not produced by another man, because it follows

that, since it is produced by him, it is produced by him alone. Now,

[the cause] is not les s noble, because a cause can never exceed its own

perfection in producing, as has been said. 316 Nor is it equally perfect,

because, as was said above, 317 there cannot be two equal effects in

one species . Therefore, it will be more perfect. But this is false ; in-

deed, it is generally found to be less perfect in regard to all powers

and functions. Therefore it is produced by some superior agent (I do

not say by the most perfect agent, unless the effect is the most perfect,

as was proved above). 318

If the man who might be called the producer is more perfect, this



is irrelevant, because in the matter of the generation of a man the

less perfect producer seems to do as well as the more perfect. As was

said of a man, so one must understand of an ass and everything else.

Consequently, there will be no univocal production, because the

cause would be ei ther less perfect (which cannot be) or equally

314 Page 201.

315 Page 255.

316 Page 256.

317 Ibid.

318 Page 255.

Page 151

perfect (which has been disproved above) 319 or more perfect (and

this is irrelevant insofar as it is the cause of the effect, as has just

been said). Nevertheless, man can indeed be one of the prerequisites

(semen, etc.) to which the human form is related. (By "man" I mean

some power inherent in man.)

In accordance with the aforesaid, one must consider that it is false

that a power produces a more perfect effect in a more perfect subject,

and a less perfect effect in a less perfect subject, because a power

258 has only one effect, as was said above, 320 and so it produces either that

or none. But it is true that, unless the subject is suitable to receive it,

it will not produce in that subject, but a less perfect power will be

jo ined with that subject for operation. For an il l-adapted subject in no

way alters the nature of the agent so as to prevent it from producing



in accordance with its nature (if it does produce).

From what has been said there appears the solution of the problem

discussed by the Commentator Averroes in Book 7 of the Meta-

physics, 321 how it is that some animals, such as mice, are generated

through putrefaction, and others, which are called by the same name,

through generation. One would have to say that "generation" in the

two cases is used equivocally, and [in the former case] takes place

through the power of a superior agent. The difference lies in the

preparation of the material, and the things which prepare it. They are

different in the two cases. And it will be said that there is also some

diversi ty in nature, even though there is a close affinity in nature.

Let us go back now to a matter mentioned before, 322 whether a

cause must be more perfect than its effect or it suffices that it be

equally perfect. The truth is that a cause as such is more perfect

because, as such, it has formal being because it causes what in itse lf

is nothing. And, when its inherent power to produce the effect as

such is described, the cause must be posi ted, but the effect need not

be. Likewise, absolutely it ought to be more perfect because, if it were

less perfect, it would not be clear how in its power it would contain

a more perfect effect. Rather, it seems well enough known that it

could not contain an equally perfect effect ei ther, because [cause and

effect] would be ei ther of the same species or of different. [If of

different], then one would be more perfect that the other. If of the



same, this cannot be, as was sufficiently proved above, 323 since there

would be no more reason for one than for the other to have had prior

319 Page 256.

320 Page 247.

321On the Generation of Animals , I, comm. 1; in Aristotelis Opera cum Averrois Commentariis (Venice ,

1562-74) VI.322 Page 257.

323 Page 247.

Page 152

being or to have had priority as the cause of the other. Therefore [the

cause] must be more perfect [than the effect.].

But it seems that this can be disputed. For if a work were eternally

unproduced, the goodness and desi rabil ity of the producing power

would cease, for all its desirability seems to derive from the work. The

answer is that the goodness of a power, strictly speaking, is not in the

work except for the purpose of demonstration. For we demonstrate

from the work the desi rabil ity and goodness of the power, but the

power has its own goodness and desirability in itsel f. Hence, assum-

ing that the work had not been produced, still it would be good for

such a being to be, since it would have been produced itsel f, although

it would not be good for it to produce this work.

Understand that every cause, considered in itself, produces its

effect with equal facil ity, because every cause is uniformly matched

with its effect. But sometimes causes are obstructed and others,

attended by effort, take their place. Thus, suppose a most perfect



heating power, joined to a most perfect fire which is brought into

contact with very cold water accompanied by a most perfect cool ing

power. My understanding is not that a reduced heat is produced by

that most perfect power, because it cannot act except after the manner

of its own nature. But these powers obstruct each other. Nevertheless,

certain other powers succeed which are not as perfect; and these pro-

duce their own effects. If the heat was more perfect and more active

in the genus of heat, then, as it were, it brings, through a certain

concomitance, a more perfect heating power.

But you will say that these second powers would obstruct each

other just as the first, and that consequently they will produce noth-

ing; and so with a third se twhich is clearly false. The difficulty

would not be present if one said that there is no production of heat

there, but only the addition and subtraction of hot and cold bodies

which obstruct one another (because, if there had been no cold bodies,

more of the hot would have been taken in, and vice versa).

But there is another answer to the difficulty. The difficulty seems

to suppose , in its way of arguing, that there are two powers, each

259 most perfect in its own genus, for example, a most perfect heating

power, and a most perfect cool ing power; and that one has obstructed

the other, and other, less perfect, powers have taken over. But this is

not the case. Rather, the powers which were present have had their

proper effect. To show this, one should know, as I intimated to some



extent above, 324 that the most perfect heating power, so far as con-

cerns its functioning, is joined with the most perfect fire, so that it

324 This page.

Page 153

functions where there is the most perfect fire, if there is fitting material

which the ignited bodies enter. The more they enter and penetrate, 325

assuming the material remains the same, the more perfect a heating

power functions. Now, when the fire and the water come into prox-

imity, the fire does not thus enter into the matter of the water because

of the coldness, or the attendant expulsive power, which repels it. It is

similar in the case of the coldness. And so the heating power then

does not function, but a less perfect power, [producing] also an

imperfect heat. In keeping with this, a discerning investigator would

not find an instance in which a cause does not always produce in

accordance with the condition of its nature, wherever it functions;

and [he would find] that a more perfect effect is produced by a more

perfect power.

It is clear from what has been said that a certain common saying

is false, namely, that the act of knowing is produced by an active

power of the soul and by an object, because, as was said above, 326

there can be only one cause of one effect. Furthermore, it is false that

the object is a cause of the act of understanding, because generally



the object can be less perfect that the act of understanding, as in the

case of relationships. And so we are left with some other power as the

active power of the act of knowing, if such beings have been

produced.

On the basis of what has been said, we hold that not all things

have been produced by the First Agent, neither as by a total producer

(because He has only one effect, proportionaate in its production to

His nature) nor as by a partial cause 327 (because such partial causes

are in play only in an effect made up of many parts, as was seen

above). 328

From the aforesaid it is clear that, if the Prime Being is of infinite

power, no effect can be produced by Him naturally. Any effect which

is produced is finite and so never needs an infinite power. A more

perfect finite power suffices for it, and so infinity in the agent would

there be superfluous. Likewise it follows that, if the Prime Being is

infinite, He could not have any magnitude, so as to partake of the

conditions of powers which exis t in magnitude, which are greater in

the whole than in a part. His power would then be divided in propor-

tion to the magnitude. And so, since the whole magnitude is finite

because one must not allow an infinite magnitudeit will follow that

that power would be finite. Likewise, He would not seem to have

325 Read et for ei in line 7.

326 Page 256.

327 Read sicut a for sit in line 24.

328 Page 256.



Page 154

magnitude except in order to cause motion or to produce some such

effect; and this He does not do, as has been said. 329

With respect to what was said 330 about a natural cause functioning

according to the condition of its nature, is this true in the case of a

free power, the will, for example? As was said above, 331 no cause can

produce more than one effect, and the acts of the soul are not pro-

duced by their objects. From this it follows that the will can issue in

no act other than willing. It seems that this is not so. In the first place,

take the el iciting of the immanent act. I can will this more intensely

or more slackly. Similarly, I can will to throw a two-foot or a three-

foot stone. (Concerning the will's not always functioning with all its

inborn capacity, many theologians say that the reasoning is poor,

because, if the First Being moved the first heaven, which has an in-

stantaneous movement, He would move it by intel lect and will , and

so He could will it to move at a certain speed.)

But the contrary seems supported by a proof given above. 332 There

260 are as many intellects as there are intell igible objects or as there are

concepts, because one cause does not produce different effects. So

here for the same reasons one would have to say that there are as

many wills as there are objects of the will . Just as it was said that no

intellect functions beyond or beneath its nature, so also neither does



the will. For if at any time it will ed beneath its own nature, it would

always will beneath its nature, because one cause does not have two

effects. So a higher degree of perfection would be superfluous in it.

So one must say that it would seem that, just as the First Intel lect can

have only the act that befits its own nature, so with its act of willing.

In keeping with this, the First Intel lect, which undertsands the noblest

object, namely, itse lf, also wills , with pleasure, the same object. As for

the remark that we can will more intense ly or more slackly, one must

say that this is not by means of the same will , but by one in the one

case, and another in the other. When someone carries a two-foot or

three-foot weight or stone, this is not by means of the same power,

but by one in the one case, another in the other.

In accordance with this, it is clear that the problem of the freedom

of the will ceases if it becomes a problem whether a will numerically

the same can choose one thing or its opposite. But there will still re-

main the following problem: "There is one will for choosing the

journey of going to church and another for refusing it. Now, it can

be asked whether it can be truly asse rted that ei ther will can be

united to me. It seems that it cannot, because there is some cause of

this union equally effective for both extremes. But this cannot be

329 This page.

330 Page 253.

331 Page 256.

332 Pp. 253-254.



Page 155

because there is no natural or free cause that is numerically the same

for opposites. For, since you say that ei ther can equally be united to

me, the cause causes one no more than the other; so it causes neither.

If, however, it is the cause of one and not of the other, then the one

of which it will not be the cause will not be united to me. If you

should say that those powers are already in that subject, although it is

not yet accepting or rejecting, still , according to this, it seems that it is

never true to say that at any moment ei ther would be able to produce

its own effect, for each one is equally capable of producing its own

effect. Therefore, ei ther both would produce, or there must be present

some cause why one has to yield."

Hence it could be argued that every single cause that has in its

power only a single effect, of which it is the sufficient cause, produces

its effect at some specific moment or time, unless something obstructs

it; otherwise it would never produce it. But this is the case with any

cause, whether natural or free. For each is determined to one effect,

as was proved above, so that it has the capacity for only one effect of

which it is the sufficient cause, because one effect can never be pro-

duced by two specifically different causes, as was proved above. 333

Therefore, if it is not obstructed, it will produce its effect. And so it is

true to say of any cause in the world that, if it should not produce its

effect, it is because it is obstructed, and not because it is free, as our



opponents imagine.

If in the case of two causes one posi ted equal factors obstructing

and favouring [the effects], it follows that neither will produce its

effect, or both will at the same time. For example, suppose that some-

one were in a circle over all of whose parts a heavenly body had equal

influence, and which was of the same nature in all its parts. Suppose

that Socrates were in the middle, seeing similar food in equal quantity

in every part of the circle. Suppose , also, that there are voli tional

powers, each of which could el icit an act of will towards one part of

the circle, so that one act of will and one volitional power [incline

him] towards one part, and another act and its power towards another,

according to the assumptions above. If one assumes that these powers

exist and are not obstructed, not even by mutually obstructive colli s-

261 ion, each would produce its effect. But in this supposed case, if the

powers existed, they would obstruct one another by collision. Even

granting that someone will to limit his motion to one place, it does not

follow that his will is free, as if it had opposite possibili ties. For that

will strictly has the capacity for that effect, as has been said; 334 it did

not have such voli tional power for moving to another place.

333 Page 256.

334 Pp. 259-60.

Page 156



You will say that, on the contrary, it had the voli tional power for

moving to any part. For since we posi t an equal distance, and the

parts alike and equal, and similarly concerning the food placed there,

the same power can perform any act, since the acts are all exactly

alike . To the extent that one act is contained in this power, so are the

rest. The reasoning seems to be true according to what was said

above. So I would say that the hypothesis is not poss ible. For, as I

have said, it is impossible for there to be two effects exactly alike and

equal in nature, as was shown above. 335

If, therefore, someone posited that the First Being is infinite in per-

fection and moved the first heaven, the meaning could only be that He

moved it naturally or through His will . If naturally, then in accordance

with the condition of His nature. And so, since the greater the power of

the mover, the swifter the movement, He could produce no movement

measurable by success ive duration. Therefore He would produce it

instantaneously; and so the reasoning of Aristotle in Book 8 of the

Physics 336 holds good.

If He moved it through His will, stil l, according to what has been

said, 337 that will is determined to an act of will commensurate with

itsel f, so that a more perfect act of will is el icited by a more perfect

will. Therefore, since the movement is finite, one can always imagine a

finite will with which the effect will be commensurate. Hence, a finite

effect never requires an infinite cause. On the contrary, if an infinite



power were involved, in respect to its infinity it would be superfluous

in as much as [the effect] can be produced by a finite power from

which this is infinitely remote.

Thus, therefore, since a power has the capacity only for an effect

commensurate with itsel f, if the First Being is infinite and does not

understand anything outside Himself (because that, being finite, can

be commensurate with a finite power), neither does He will anything

outside Himself. Nevertheless, He ought not for this reason 338 to be

said simply to be ignorant of or not to understand what is outside

Himself. For, as was proved above, 339 if two persons fix their gaze on

something, and one of them sees more clearly, they will never see

exactly the same thing. The one who has the clearer visual power will

never see exactly the same things as the one with the dull vision sees.

However, we do not say that he does not see it; for he sees the same

thing under the aspect of a clearer beinghe sees, say, a clearer white-

ness which seems to contain the dull eminently. So, also, all things are

reflected in the essence of the First Being because it is eminently all

335 Page 251.

336 VIII, 6; 259a14 ff.

337 Pp. 259-260.338 Add hoc after propter in line 28.

339 Page 240.

Page 157

being. So, when it sees itself, it is not said to be totally ignorant of



other things. This seems to be the intention of the Commentator Aver-

roes on Book 12 of the Metaphysics, 340 [when he says] that one who

knows the most perfect heat, heat in its essence, is not ignorant of heat

in other hot things.

Likewise, from the aforesaid it is clear how what the Commen-

tator says 341 about intell igences and the heaven itself is true: if any-

thing were added to or anything taken away from the heaven, the

intell igence would never move it. This is explained above. 342 This

reference is not precisely to intell igences, but it is explained that a

perfect cause can never produce the effect of a less perfect cause. For

each cause produces an effect commensurate with itse lf, and not

another, so that no cause acts ei ther beneath or above itse lf.

When, therefore, it is said that the will is related to opposites , this

must not be understood of the individual as if any particular will were

262 related to opposites. Rather, each is determined to a single thing, as

has been said. But [the statement] must be understood [of the will]

as a species. For one will is related to one object, another to its

opposite.

In connection with what was said above near the beginning of the

treatise dealing with this, 343 it was maintained that, if two persons see

or understand the same thing, and one of them has clearer vision or

understanding, they do not see the same aspect of the thing, but one

sees rather a clear whiteness where the other sees a dull whiteness.



Nevertheless, those whitenesses in their subjective being are one white-

ness. 344 What each person tries to see when they look is subjectively

the same numerically, although it comes to them according to a

different objective being. According to this way of speaking, it could

with probabil ity be maintained that whiteness and blackness are one

in subjective being. For suppose there are a hundred visions arranged

according to the more perfect and the less perfect. The highest sees a

thing, and according to its objective being gives it the name of white-

ness. The lowest will see so dimly that it will call blackness what the

highest called whiteness. And yet they are the same in subjective

being. Thus, to see what the supposi tion means, le t it be said, in this

case, that whiteness and blackness do not differ in subjective being

but differ indeed in objective being. And, if this be said, it will be

possible to say of any things at all that all things are one thing in340 XII, comm. 51.

341 Averroes, De Substantia Orbis, cap. 3; in Aristotelis Opera cum Averrois Commentariis (Venice ,156274) IX.

342 Page 255.

343 Page 238.

344 See n. 10.

Page 158

subjective being, although there is differentiation in the objective

being according to which it comes to us.

Therefore, what each objective thing seeks, and what it moves

towards, is the one subjective being which is God. And this being



understands Himself by a knowledge which is the same as Himself in

subjective being, and He contacts [Himsel f] in the subjective being

according to which He exis ts.

But there seems to be an obstacle to this position. For one who

sees clearly perceives blackness more than the man of feeble vision

perceives it. Therefore it seems that, the more blackness increased, the

more it would be seen. As a result whiteness and blackness would

never be found to be united in subjective being. It might be retorted

that sight can be extended absolutely in the genus of being, so as to

reach a perfect grasp of an object as it is in itsel f. But this is false ;

rather the thing in itsel f sometimes appears according to one such

objective being, and that comes in clearer being to one person than to

another. If there were further progress made in clarity, there would

be made an approach to a unity. Finally one would discover one sub-

jective being which would be the foundation, as it were, of these

objective beings.

But the argument returns in the following way: ''Granted that

there were one subjective being, no one would deny that one objective

being would approach closer to it than another, for example, whiteness

close r than blackness . Now, when blackness is perceived more clearly,

its objective being is that much more perfect, and consequently that

much close r to the being of whiteness . Nevertheless, the distinction

and difference is now judged better than before, and [the objective



being] seems to be receding further from whiteness."

This seems to be a serious obstacle to the aforesaid position. But

there seems to be an answer in what follows. First I imagine that

subjective being. Secondly, [I imagine] powers of sight or intellects,

say a hundred arranged according to more perfect and less perfect.

Now, when one person mentions whiteness in connection with what

he sees, another will see only a dimmer being and he will call it

black. Of these visions the first is [closer] to the subjective being.

Then I imagine intellects of another sort, whose gaze will not be

directed towards the thing's subjective being, but towards these

objective beings. Now, the objective being which one man calls black-

ness, this intellect will see , and, to the extent to which it has clearer

vision, it will see that objective being in a being close to itsel f. And,

because in its objective being it was distinguished from other objec-

263 tive beings, the more clearly it is seen, the more evident will be its

distinction from another objective being, namely, from whiteness,

Page 159

because it is an objective being with respect to the first group, but it

is a subjective being with respect to the second. Concerning those who

know in the second way, the argument proceeds that, the more

clearly they know, the more evident it will be to them that blackness



is distinguished from whiteness . It is otherwise with those who know

in the first way. Indeed, if their knowledge were extended, finally they

would arrive at one subjective being.

It is doubtful, however, whether there are certain persons whose

knowledge is of a third type, persons for whom the being which we

know would be, so to speak, a subjective being, while they themselves

would have other objective beings, and those have others, and so on

ad infinitum . It seems that this is so, because any being can be known

more clearly and les s clearly; and so their objective beings can be

known more clearly and less clearly. Those who see these see them

more clearly and les s clearly, and so on endless ly. And such beings

are only objective. But [the truth] seems contrary to this, because

there would then be an infinite progression of beings. And, if it were

said that finally there would be a halt, then that [last] objective being

would thus be imperfect, because it would be known in only one way,

and it could be comprehended only as it is in itsel f.

According to this posi tion, something amazing appears. For, in the

order of knowing subjects which you imagine for that objective being,

the lowest being will be further removed from that subjective being

in which resides the truth of the being. Similarly, the cognitive faculty

corresponding to it will be lowest in the genus of knowing powers.

And yet it seems that, the less knowable an object is , that is , the closer

to unknowabili ty, the more perfectly does the power which appre-



hends it [know it]. So this cognitive faculty which was placed lowest

will be more perfect than all the others. Likewise, the others appre-

hend [the object] only in its objective being, but this [apprehends it]

in its subjective being.

The answer in this case seems to be that there are some faculties

whose perfection or imperfection is measured by their strength, not

by the perfection of the object of their act. An example is the power to

li ft a weight. The power to li ft gold is not more perfect than the

power to li ft stones, but the more perfect power is that which is

stronger and which li fts a greater weight. Not so with other powers

[which are measured] by the nobil ity of their object, as is the case

with the cognitive powers. And so the power [we are discussing] will

not be a more perfect power, but the lowest. Even though it attains

the object in itsel f, yet that being is less perfect. Likewise, it will know

the effect (namely, that objective being) as far as it is knowable in

Page 160

itself; yet it will not know the causes of that being because then it

would be going beyond its own nature.

In the same way it could be said that God, though He knows Him-

sel f insofar as He is knowable in Himself, nevertheless does not know

in their proper form things that are beneath Him because then His

nature would be lessened, as has been said above and explained. 345



In the case of intellects that know only the objective beings of things,

there is found a progression from one to another. It is different with

another intellect or other intellects which know things in the being

which they have in themselves. Therefore, that lowest intellect will

know that final object in itself as it is, and so in its mode of knowing

it will be more perfect than the higher powers with the exception of

the first. Or you might answer (and this is better) that even in its

mode of knowing it is not more perfect, because each cognitive power

knows some objective being in itsel f and insofar as it is knowable, as

has been explained above, 346 but it does not know the objective being

of a higher [knowledge]; rather, to it that being is 347 a subjective

being, as it were.

Since every being can be intuited by an intel lect (for this is not

repugnant to the intellect as intellect), it is seen that one must postu-

264 late a twofold order of knowing subjects, and that we are in the second

order. For it is not repugnant to the most perfect cognitive power to

possess its object in a perfect manner. Now, the intel lective faculty is

more perfect, as is seen, and the manner of possessing through abstrac-

tion is not perfect, but only the manner of possessing by way of in-

tuition. 348 And this [abstraction] befits the external senses, which are

less perfect. Nor does that seem to be repugnant to the thing [known].

Another [factor] is that not every entity can be intuited by one intel -

lect, because, as was proven above, 349 one intellect can understand



only one intell igible object. Therefore there are several intellects. So,

in keeping with this, we have one order of intellects understanding

intuitively. And in our experience there is a second order of intellects

understanding abstractively. But it does not seem that there is any

intellect understanding intuitively unless one intellect understands in

one way, and another in another way, each thus understanding in-

tuitively. For, as has been said, each intel lect apprehends its first

object in itsel f insofar as it can be apprehended.

In accordance with what was said above, 350 it is certain that no

one apprehends the first subjective being (which is the first being

345 Pp. 240241.

346 Page 262.

347 Read est for et in line 46.

348 William of Ockham, Sentences, lib. I, Prologue, I, Z.

349 Page 254.

350 Page 262.

Page 161

absolutely) insofar as it can be apprehended, except the one very

being which we would posi t. And this seems to be truer. But this not-

withstanding, those two orders of intellects imagined above have still

been able to stand up, even though their difference is not found in

the intuitive and abstractive mode of knowing. Or perhaps it might

be said that the intuitive is not distinguished from the abstractive in

that there is knowledge of the object in itself, as was said, but because

the one is discursive, or quasi-discursive, the other not. But since in



animal, and so on. By collecting many such ideas he es tablishes a

definition which explains what was implicitly contained in the con-

fused being.

Those objective beings were distinguished above from the sub-

jective being 351 because they are multiplied while the thing's subjec-

tive being remains one in itsel f. For example, granted that the thing

is one in itself, if two persons look at it, of whom one has clearer

vision, he will see more clearly. The same consequence follows as was

deduced above 352 when, speaking of what is in objective being, we

said that one person will see one objective being in his sight and

351 Read subjectivo for objectivo in line 43.

352 Page 262.

Page 162

another another. Nevertheless, it seems possible to have a situation

where persons with different senses of sight will see the same thing.

265 For the one with clearer vision will at a distance see a thing less

clearly. Consequently he will be able to stand far enough away that

the one with duller vision will see equally clearly, even though their

powers differ. Thus powers that differ in intensi ty of perfection will

have the same effectwhich was disproved above. 353

Likewise, it has been proven 354 that the same power cannot pro-

duce two [different] effects. But the contrary seems to be true, since

with the same power a man will see clearly at close quarters and he



will see dimly from a distance. The answer seems to lie in the premise

that in connection with the act of seeing one must reckon with a two-

fold power. One is more corporeal, which unites the spiri ts and the

visual rays. In or by their union the species is conveyed right to the

organ of sight. Whether it be for receiving the species or for what-

ever other purpose , it is certain that such a union of spiri ts is pre-

requisi te to the act of see ing. [Only] after this should we consider the

power of the soul which el icits the act of see ing.

It would then be said that one afar off who sees a thing as clearly

as one near at hand certainly has an unequal and different power

(meaning the corporeal power that unites the spiri ts); and so its effect

is different. For when someone is farther away, if he wants to see an

object equally clearly, that much more perfect a union is needed of

the spirits and the visual rays. But, as far as concerns the power of

the soul that el icits the act, we say that it is a power of the soul

altogether one in itsel f, although it is determined by some individuat-

ing principles to be here or there. In the second example, that of the

man who with one power will see clearly or less clearly as he is close

at hand or far away, I say that it is poss ible here that there is an equal

power uniting the spiri ts, and an equal effect, namely, the union of the

spiri ts and the rays. But I say that the power of the soul that el icits

the act will not be equal then and now. And, if one thing cannot be in

several places at once, then it will be said that two persons can never



see an object equally clearly, as was asserted above.

Thought must be given to what has been said, 355 that two [causes]

can never have one effect, that a power never acts beneath or above

itself, that one power can have only one effect, and that there are as

many intel lects as there are concepts. It follows that the intel lect that

knows universals does not know particulars. Therefore, what kind of

power will tell the difference between universals and particulars? It

seems that none will because every power of the soul that tells the

353 Page 253.

354 Ibid.

355 Pp. 253255.

Page 163

difference between two things knows each of them. But the power

that knows particulars cannot know universals , because it would then

be acting above itsel f; and vice versa. I say that there is one power

of the soul, by whatever name it be called, that will tel l the difference,

and it knows only that one object of thought, namely, the difference,

while the extremes will be known by two other powers of the soul.

This satisfied Aristotle , in Book 2 of On the Soul ,356 when he

wanted to prove that there is a common sense from the fact that we

differentiate between acts of the external senses , namely, seeing and

hearing. Certainly it is right to conclude that there is another power.

For to know this difference belongs to a power other than the power



that knows the extremes. Hence, one concludes that there is not just

one power of the soul, but three , though they can be called one

faculty because they are ordered, as it were, to one thing. On the

basis of experience it is argued that the three powers of the soul will

be virtually the same power. For we know the act of seeing and the

act of hearing separately, and so there will be two powers. And we

conceive the difference [between them], and here there is another

power of the soul. Nevertheless, because these powers are close ly

related, they are taken after a fashion as one faculty. So it is said that

the power that differentiates between two extremes knows each of

266 the extremes. Similarly one speaks of only one intellect because all

intellects have the same mode of knowing, namely, an abstract mode

of knowing.

The intellect knows whiteness in itsel f, abstracted from every

location and every particular. As has been said, in the case of an

object of the external senses, the object exists before or is simultaneous

with the act, and it would not cease to exist even if, by any possibili ty

or per impossibile , [the act] ceased to exist. The same could be said

of the object of the intel lect. It is a universal, and such a universal

can be said to be everywhere and always, for it need not be in one

place rather than another, or at one time rather than another.

When that universal is in the mind of a person where previously it

was not, this does not happen by way of transference, since such a



being is not contained in space. It seems that it is by means of some

causation. Such a power could be called the poss ible intel lect, which

is accompanied by the agent intel lect which produces intel lection.

Both these faculties, since each produces something abstract, can be

called the agent intel lect. So they are one power in genus but two

powers in species . And [it seems] that the objective being in the

higher [part of the] soul, which comes to a particular interior power,

356 III, 2; 426b17 ff .

Page 164

and the universal objective being in the soul, have thus had a close

relationship to the one subjective being from which they are taken.

One is attributed to the other in predication, for example, the universal

to the particular, as when it is said that Socrates is a man; and

similarly in the case of universals , when "animal" is attributed to

"man".

If you ask whether there is some subjective universal corresponding

to the objective universal in the intellect, it might be said that

there is. If all things are not united in one subjective being, but

[instead] there is a subjective being for each species , then there would

be a subjective being corresponding to an objective universal. This

would not be multiplied in being. There is a multiplication of objective

beings in the intel lect, however; for a man of clearer and more

abstract intel lect, in understanding whiteness, holds whiteness in



clearer being in his intel lect than does another man who understands

less clearly.

It might be said that this subjective universal being is the quiddity

of particulars, the principle of their existing, the principles for understanding

them, and much [else], in agreement with Plato's posi tion.

But they would not subsist in the air, as perhaps was held because of

Plato's words, 357 against which Aristotle argued. 358 For [Plato] laid

down that they would have a being separate from particulars. Against

this, Aristotle in the preface to On the Soul 359 says that the universal

animal posited by Plato ei ther is nothing or is subsequent to singulars,

so that it will have no validity for the understanding of the singulars

themselves . This is true, granting such a separation. So universal

objective being would be attributed in predication to singular objective

being. Universal objective being would be taken for that universal

subjective being which is the quiddity of the singulars themselves.

So, in the proposi tion "Socrates is man", "man" is not taken for

Socrates as if it had a personal supposi tion, as many intimate and

false ly so. For the one who forms this proposi tion does not find that

in the predicate of the proposi tion he has Socrates as object, but only

the universal nature of man. Therefore, the reasoning "Socrates is

man, man is a species, therefore Socrates is a species" is not rebutted

by saying, as some do, that the error occurs because of the changing

supposi tion of a termfor in the first proposi tion the term "man" has



a personal supposi tion and is taken for its inferior, in the second it

h i l i ti 360

the universal treatise (exigit ordo) - nicholas of autrecourt

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