aristotle’s theory of modalities pisa 15_dic

Interpreting Aristotle’smodalities without determinism

Irene Binini SNS Monday Seminars, december 15th

Modal syllogistic and theory of modality

Modal syllogistic:Prior Analytics I.8-22;


Theory of modality:

Prior Analytics I.13;De Interpretatione 9; De Interpretatione 12-13;Metaphysics V 5, 12;Metaphysics IXDe Caelo I.12;Physics III, V.

«The realm of darkness» (Patzig, Aristotle’s theory of syllogism, 1986)

«[Aristotle] relies on different principles, often based on independent insightsinto the logic of modal notions» (Hintikka, 1973)

«I believe that Aristotle’s modal thought was based on different paradigms ofspeaking about necessities and that they involve various intuitions whichare not reducible to one clear-cut basic theory» (Knuuttila, 2003)

Problem:

which interpretation would fit best Aristotle’s use of modalterms and which is his understanding of modalities.

Effort of giving a univocal paradigm in which to interpretAristotelian modalities


Which interpretationfor Aristotelian modalities?

Some background:

Three modal operators

Necessity

Impossibility

Possibility

Modal operators


dunatòn (Metaphysics, De Int., De Caelo)

endechòmenon (An.Pr., De Int.)

adùnaton

anagkaion

Ambiguity of Aristotle’s notion of possibility:

Both dunatòn and endechòmenon used sometimes as

1. Possibility in a «large sense», as non impossibility

2. Possibility as contingency

• Aristotle is aware of this ambiguity

• Aristotle is (almost always) consistent in intending possibility ascontingency

• The chapters in which Aristotle provides definitions for possibility(An. Pr. I 13; Met. V 12) it is defined always as contingent

• The passages taken as evidence of possibility in a large sense are De Int. 12 and 13; An. Pr. I 3.25a37 ff.; An. Pr. I 13.32a21-29; Met. V 12.1019b27 ff. (Hintikka); Met. IX 4 (Malink)


Possibility as contingency

• Met. V 12.1019b27 ff.: «the contrary [of the impossible], the possible, isfound when it not necessary that the contrary is false»

• An. Pr. I 13.32a18-21: «I use the terms 'to be possible' and 'the possible' of that which is not necessary but, being assumed, results in nothing impossible. We say indeed ambiguously of the necessary that it is possible»

• An. Pr. I 13.32a29-32b1: «It results that all premisses in the mode of possibility are convertible into one another […] e.g. 'it is possible to belong' may be converted into 'it is possible not to belong', and 'it is possible for A to belong to all B' into 'it is possible for A to belong to no B' or 'not to all B', and 'it is possible for A to belong to some B' into 'it is possible for A not to belong to some B'»

A is possibly B A is possibly not-B

Possibility as contingency



«Necessary» as primitive concept• «The impossible is that of which the contrary is of necessity true, e.g. that the

diagonal of a square is commensurate with the side is impossible, because such a statement is a falsity of which the contrary is not only true but also necessary» (Met. V 12.1019b23-24)

• «The proposition 'it is impossible' is equivalent, when used with a contrary subject, to the proposition 'it is necessary'. For when it is impossible that a thing should be, it is necessary, not that it should be, but that it should not be, and when it is impossible that a thing should not be, it is necessary that it should be» (De Int. 13.22a38-22b6)

• «We may perhaps state that necessity and its absence are the principles of being and non-being, and that all else must be regarded as following from these» (De Int. 13.23a18 e ss.)

The equivalencesof the aristotelian system


A is possibly B A is non necessarily B and non impossibly B

A is possibly B A is possibly not B

A is impossibly B A is necessarily not B

1. Absence of a «mere logical» understanding of modalities- Possible is what that, when it is assumed, results in nothing impossible

(Met. IX 3.1047a24 ff.; Me t. IX 4.1047b11; An. Pr. I 13.32a18 ff.)

2. Hintikka’s proposal: a statistical account of modalities, in which

- Necessary is what is always actual- Impossible is what is never actual- Possible is what is «intermittently» actual

3. Another proposal: a nomological understanding of possibilities, based on his theory of potency

- Possibility means some sort of potentiality- Possibilities are the capacities, the powers of individuals- Possible is what is compatible with the principles of nature and beings


Interpreting Aristotelian Modalities:different paradigms

Hintikka noticed in Aristotle’s texts a usual overlapping of the concepts of eternity and necessity.

• Met. VI 2.1026b27-30

• Phys. II 5.196b10-13

• De gen. et corr. II 9.335a33-b4

• Met. V 5.1015b14-15

• Met. XI 8.1064b32-34

Idea: being always and being of necessity are equivalent for Aristotle


The statistical interpretation

Motivated by this observation, Hintikka sought for further evidence of Aristotle’s adherence to a systematic temporal interpretation of modal terms.Aristotle endorsed these principles:

(P1) that which never is, is impossible;(P2) which always is, is by necessity;(P3) nothing eternal is contingent.

• De Caelo I 12.281b2-25, • Met. IX 8.1050b7-20,• Top. II 11.115b17-18, • Top. VI 6.145b27, • De gen. et corr. II 9 335a33-b4, • Met. XIV 2.1088b23-25.


Statistical principles

If something has the potency of

not being, then it will not be

forever

If something is forever, then it is

of necessity

Hintikka took these passages as evidence of the fact that Aristotle, at least implicitly, assumed a form of the «principle of plenitude»:

(P) No possibility remains eternally unrealized

if something is possible, it will realize at some moment of time


The Principle of Plenitude

This interpretation of possibilities lead to the collapse between what ispossible and what is actual. It does not leave room for possibilities whichremain eternally unrealized.

Yet, it seems that elsewhere Aristotle admits these «pure», or never realizedpossibilities:

«it is possible that this cloak may be cut in half, and yet it may not be cut in half, but wear out first» (De Int. 9.19a12-14)

The admittance of unrealized possibilities has also been seen in De Int. 13.23a23-25; Met. III.6,1003a2; Met. XI.9,1065b5; XII.6,1071b13-20; Post. An.I.6,74b31 ff.

Furthermore, there are many passages, in the Aristotelian corpus, in which the author is inclined to accept an indeterminist view.


«Self-inflicted determinism»

These inconsistencies convinced many scholars that a general and unqualified version of (P) is not to be attributed to AristotleStill, it seems that without equivalences (P1)-(P3) it is hard to makesense of some passages (e.g.: De Caelo I 12; Met. IX 8…)

Idea of commentators after Hintikka (see Sorabji 1980): maintain the principle but restrict its applicability

(P) is applicable only to everlasting beings(P) Is not applied by Aristotle to transient beings (i.e. beings whichlast for a finite time)

Underlying idea: any potency is going to actualize itself, given that ithas at disposition enough time to do that (an infinite time)


Proposals for limiting Hintikka’sinterpretation

For this limitation see Sorabji 1980, Dancy 1980, Knuuttila 2003

Why this limitation of the applicability of (P) is notsatisfactory?

1) The statistical interpretation were meant to spell ut the meanings of Aristotle’s modal terms. But if“possibility” is intended as contingency, principle (P) is empty when applied to imperishable beings.

2) Sometimes principle (P) is applied by Aristotle also to transient beings (see Gaskin 1995)

Proposals for limiting Hintikka’sinterpretation


• Difficulties with Hintikka’s version of statistical interpretation: inconsistencies with Aristotle’s indeterminism

• Difficulties with Sorabji’s version of the statistical interpretation• Though, explanatory power of the statistical equivalences for

some passages

• My aim: 1) Proposal of a different paradigm in which to interpret

aristotelian modal concepts2) This paradigm ought to take in charge the explanation of

passages that Hintikka holds as evidence for (P1)-(P3), whilenot presenting the same deterministic consequences

3) This will require the admittance of principle (P) in a restrictedform


My limitation to the statistical model

Which cannot be otherwise is necessarily as it is. And from this sense of “necessary” allthe others are somehow derived(Met. V 5. 1015a33)

Therefore the necessary in the primary and strict sense is the simple; for this does not admit of more states than one, so that it cannot even be in one state and also in another; for if it did it would already be in more than one. If, then, there are any things that are eternal and unmovable, nothing compulsory or against their nature attaches to them (Met. V.5,1015b11-15).

“Potency” means a source of movement or change, which is in another thing than the thing moved or in the same thing qua other […]“Potency” having this variety of meanings, so too the 'potent' or 'capable' in one sense will mean that which can begin a movement (or a change in general, for even that which can bring things to rest is a 'potent' thing) in another thing or in itself qua other; and in one sense that over which something else has such a potency(Met. V 12.1019a15-1019b13)


Definitions of modal terms in Met. V 5-12

Change is the concept on which Aristotle grounds hisunderstanding of modalities

• Possible is said of what is subject to change or movement, what undergoes alterations and modifications

• Necessary is said of what is immutable, what does not have a principle of change

(for the connection between the concept of change and modalities see De Int. 13.23a12-16; Met. V.5,1015b14-15, VI.1,1026a11; IX.10,1052a4; XII.6,1071b5; XII.7,1073a3-13; Eth. Nic. VI.1,1139a7-8, 14; VI.3,1139b20 ff.; VI.4,1140a1; Phys.II.1,193a26-27)


Definitions of modal terms in Met. V 5,12

• Change (metabolē) and movement (kinēsis)• There can be change in different categories:

- With respect to substance: generation and corruption- With respect to quality: alteration- With respect to quantity: increase and decrease- With respect to place: local movement

• A change is a passage, undergone by a certain substratum, from being to not being(or viceversa) in a certain category

• Beings that undergo changes are material, sensible beings: matter is the thing in virtue of which a change takes place


Aristotelian theory of change

movement

Modal operators applied to things in different categories.

Aristotle’s formulations: «P is necessarily/possibly»; «P isnecessarily/possibly φ»; «Every A is necessarily B»

- Necessary beings: beings immutable with respect to their substance, i.e. ingenerated and incorrupted beings, or everlasting beings

- Contingent beings: beings subject to substantial change (generation and corruption)

- Properties belonging necessarily: the subject is immutable with respect to that quality

- Properties belonging possibly/contingently: the subject can undergoa movement of alteration with respect to that property


Change and modalities

This interpretation of Aristotelian modalities :

• is based on precise definitions given by Aristotle• preserves an idea of possibility as contingency• is compatible with the idea that necessity is a primitive

notion (priority of actuality over potentiality)• offers a metaphysical grounding some of the logical

rules used by A. in his modal system• is compatible with Aristotelian diachronic use of

modalities, and to his «modal asymmetry»: potentialities are for the present or for the future (De Caelo I 11.283b13)



I need to show:

1) that this interpretation can explain thosepassages that Hintikka took as evidence of a statistical semantics;

2) that it is not incompatible with other parts of the Aristotelian theory, and in particular thatit does not have the same dterministicconsequences the statistical semantic had.



(P1) that which never is, is impossible;(P2) which always is, is by necessity;(P3) nothing eternal is contingent.

• De Caelo I 12.281b2-25, • Met. IX 8.1050b7-20,• Met. XIV 2.1088b23-25,• De gen. et corr. II 9 335a33-b4• Top. II 11.115b17-18, • Nic Eth vi.3,1139b22-24


Statistical equivalences withoutdeterminism

Idea: what has the potency of not being, cannot always be

Aristotle does hold

(P2) which always is, is by necessity;

(P3) nothing eternal is contingent.

But only with reference to the category of substance:

(P2*) which exists forever, exists necessarily,

(P3*) What exists contingently exists at some times (and not at others)


My limitation for statistical equivalences

(P2*) Which is forever, is necessarily, • Which is eternal, is necessarily• Which is ungenerated and incorruptible, is necessarily• Which lacks a principle of substantial change, is necessarilyBut that is what “being necessarily” mean!

(P3*) What is contingently exists at some times (and not at others)• what has the potency of being (with respect to substance) exists at

some times (and not at others)• What is mutable (with respect to substance) exists at some times

(and not at others)• What is generated and corruptible exists at some times (and not at

others)

My limitation for statistical equivalences


Principles

(P2) which always is, is by necessity;

(P3) nothing eternal is contingent.

are never stated by Aristotle with respect to the othercategories:

• which always has a certain quality φ, has that property necessarily

• which always is the case, necessarily is the case

• which is always true, is necessarily true



The deterministic consequences raised by an unqualified and general endorsement of the principle (P) are not raised, given this interpretation.

Principle (P) is accepted in a limited form:If something has the potency of being and not being (i.e. is subject to substantial change), is generated and will at a certain time corrupt.

There are not generated but incorruptible beingsBut this is something that Aristotle is happy to accept!

This reading of Aristotle leaves room for potencies in other categories thatnever realize (as the potency of De Interpretatione 9’s cloak of being cut up)

What is to be done now: show that in the texts tooked as evidence by Hintikka, principle (P2)-(P3) are always limited to the category of substance



1. In De Caelo I.12,281b2-25, Aristotle proposes a famous and controversial argument:

(i) if something has the potency of being, then it also has the potency of not-being; (ii) to have a potency (or to be possible) means that it is admissible that this potency is

actualized in a certain moment of time without contradiction; (iii) something that has the potency of being is eternal.

«Anything which always exists is absolutely imperishable. It is also ungenerated, since if it was generated it will have the power for some time of not being» (DC I.12,281b25-26);

«Thus it is impossible for a thing always to exist and yet to be destructible. Nor, similarly, can it be generated» (DC I.12,281b34-282a1);

«Clearly whatever is generated or destructible is not eternal. If it were, it would be at once capable of always being and capable of not always being, but it has already been shown that this is impossible» (DC I.12,282a22-25).

The evidence for this interpretation




2. Metaphysics IX.8,1050b6 ff.

But actuality is prior in a stricter sense also; for eternal things are prior in substance to perishable things, and no eternal thing exists potentially. The reason is this. Every potency is at one and the same time a potency of the opposite; for, while that which is not capable of being present in a subject cannot be present, everything that is capable of being may possibly not be actual. That, then, which is capable of being may either be or not be; the same thing, then, is capable both of being and of not being. And that which is capable of not being may possibly not be; and that which may possibly not be is perishable, either in the full sense, or in the precise sense in which it is said that it possibly may not be, i.e. in respect either of place or of quantity or quality; 'in the full sense' means 'in respect of substance'. Nothing, then, which is in the full sense (absolutely - aplōs) imperishable is in the full sense potentially existent (though there is nothing to prevent its being so in some respect, e.g. potentially of a certain quality or in a certain place); all imperishable things, then, exist actually.

Nor can anything which is of necessity exist potentially; yet these things are primary; for if these did not exist, nothing would exist. Nor does eternal movement, if there be such, exist potentially; and, if there is an eternal mobile, it is not in motion in virtue of a potentiality, except in respect of 'whence' and 'whither' (there is nothing to prevent its having matter which makes it capable of movement in various directions). And so the sun and the stars and the whole heaven are ever active, and there is no fear that they may sometime stand still, as the natural philosophers fear they may. Nor do they tire in this activity; for movement is not for them, as it is for perishable things, connected with the potentiality for opposites, so that the continuity of the movement should be laborious; for it is that kind of substance which is matter and potency, not actuality, that causes this.

Metaphysics IX.8,1050b20 ff.



Aristotle’s argument in Met. IX 8

i. we can talk of potencies of being in all the categories, and in any category, having a certain potency implies having the contrary potency, i.e., the potency is always of the two contraries;

ii. to be absolutely potential means to have the potency of being/not being in the category of substance, i.e., to be generated and incorruptible;

iii. that the implication “nothing that is potentially not being is always” is states only for “absolute” potencies (in Ross’s translation, potencies “in the full sense”), that is to say in respect to substantial potency.

I think then we could take passage Met. IX.8 as an explicit affirmation of the use of statistical implication as applied only to substances, and not to qualities or state of things.



3. Metaphysics, is XIV 2.1088b23-25

We must inquire generally, whether eternal things can consist of elements. If they do, they will have matter; for everything that consists of elements is composite. Since, then, even if a thing exists for ever, out of that of which it consists it would necessarily also, if it had come into being, have come into being, and since everything comes to be what it comes to be out of that which is it potentially (for it could not have come to be out of that which had not this capacity, nor could it consist of such elements), and since the potential can be either actual or not,-this being so, however everlasting number or anything else that has matter is, it must be capable of not existing, just as that which is any number of years old is as capable of not existing as that which is a day old; if this is capable of not existing, so is that which has lasted for a time so long that it has no limit. They cannot, then, be eternal, since that which is capable of not existing is not eternal, as we had occasion to show in another context.



4. Nicomachean Ethics, VI.3,1139b22-24

We all suppose that what we know is not even capable of being otherwise; of things capable of being otherwise we do not know, when they have passed outside our observation, whether they exist or not. Therefore the object of scientific knowledge is of necessity. Therefore it is eternal; for things that are absolutely of necessity are all eternal; and things that are eternal are ungenerated and imperishable.

5. Top. II.11,115b17-18

It is possible for a destructible thing to escape destruction at a given time, whereas it is not possible for it to escape absolutely.



• Giving a consistent interpretation of Aristotelian modalities: an unattainabletask?

• Different intuitions regarding possibilities: a logical understanding, the connection with the theory of potency, a statistical interpretation…

• Statistical interpretation: its explanatory power and its inconsistency with Aristotle’s indeterminism

• A new paradigm based on the theory of change: to be possible means to have a principle of change or movement with respect to some category

• Evidence for this interpretation of modal terms is easily found in the definitions Aristotle gave of modalities (Met. V.5, 12)

• Compatibility of this paradigm with the logical rules of Aristotle’s modal system


Conclusions

• The validity of statistical principles is restricted to potencies in the category of substance

• Statistical implications do not hold for qualities that are always predicated of a subject, nor for states of things that are always the case. Admittance of certain unrealized possibilities are then compatible with what Aristotle says in the passages quoted by Hintikka.

• If some form of determinism is to attribute to Aristotle’s theory is the belief that any substance which is generated, won’t last eternally, because will be corrupted at a certain moment of time. But if a cloak is never cut up during all its lifetime, this won’t prevent that it would be possible for it to be.

Conclusions


• Crivelli, P. (2004). Aristotle on truth. Cambridge: Cambridge University Press.Dancy, R. M. (1980). Aristotle and the priority of actuality, in Knuuttila S. (ed.),

• Reforging the great chain of being. Dordrecht: Reidel, 73-115. • Frede, M. (1994). Aristotle’s notion of potentiality in Metaphysics Θ, in Scaltsas T., Charles D.

& Gill M. L. (eds.), Unity, Identity, and explanation in Aristotle’s Metaphysics. Oxford University Press, 173-93.

• Gaskin, R. (1995). The sea battle and the Master Argument. New York: Walter de Gruyter. • Hintikka, J. (1973). Time and necessity: Studies in Aristotle’s Theory of Modality. Oxford:

Clarendon Press. • Judson, L. (1983). “Eternity and necessity in De Caelo I.12”, Oxford studies in ancient

Philosophy 1, 217-255. • Knuuttila, S. (1993). Modalities in Medieval Philosophy, London: Routledge.

Panayides, C. (2010). “Aristotle and the principle of plenitude. The case of De Caelo A. • 12”, Filozofia 65, 49-62.

Sorabji, R. (1980). Necessity, cause and blame: Perspectives on Aristotle’s Theory. • London: Duckworth. • Waterlow, S. (1982). Passage and possibility: A Study of Aristotle’s Modal Concepts. Oxford:

Clarendon Press. • van Rijen, J. (1989). Aspects of Aristotle’s logic of modalities. Holland: Kluwer. • von Wright, G. H. (1984). Truth, knowledge and modality, Oxford: Basil Blackwell.

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