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This article was downloaded by: [University of Toronto Libraries] On: 18 February 2013, At: 01:57 Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Inquiry: An Interdisciplinary Journal of Philosophy Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/sinq20 Aristotle's different possibilities K. Jaakko J. Hintikka a b a Society of Fellows, Harvard University, b Society of Fellows, University of Helsinki, Version of record first published: 29 Aug 2008. To cite this article: K. Jaakko J. Hintikka (1960): Aristotle's different possibilities, Inquiry: An Interdisciplinary Journal of Philosophy, 3:1-4, 18-28 To link to this article: http://dx.doi.org/10.1080/00201746008601302 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

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Page 1: Inquiry (Taylor & Francis) Volume 3 Issue 1 1960 [Doi 10.1080%2F00201746008601302] Hintikka, K. Jaakko J. -- Aristotle's Different Possibilities

This article was downloaded by: [University of Toronto Libraries]On: 18 February 2013, At: 01:57Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

Inquiry: An Interdisciplinary Journal of PhilosophyPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/sinq20

Aristotle's different possibilitiesK. Jaakko J. Hintikka a ba Society of Fellows, Harvard University,b Society of Fellows, University of Helsinki,Version of record first published: 29 Aug 2008.

To cite this article: K. Jaakko J. Hintikka (1960): Aristotle's different possibilities, Inquiry: An Interdisciplinary Journal ofPhilosophy, 3:1-4, 18-28

To link to this article: http://dx.doi.org/10.1080/00201746008601302

PLEASE SCROLL DOWN FOR ARTICLE

Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form toanyone is expressly forbidden.

The publisher does not give any warranty express or implied or make any representation that the contentswill be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses shouldbe independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims,proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly inconnection with or arising out of the use of this material.

Page 2: Inquiry (Taylor & Francis) Volume 3 Issue 1 1960 [Doi 10.1080%2F00201746008601302] Hintikka, K. Jaakko J. -- Aristotle's Different Possibilities

ARISTOTLE'S DIFFERENT POSSIBILITIES

by

K.Jaakko J. Hintikka

Society of Fellows, Harvard University, and University of Helsinki

1. The interrelations of modal notions in Aristotle. The results of our ex-amination of the varieties of ambiguity in Aristotle (see Inquiry vol. 2 (1959),pp. 137—151) can be used to analyze his notion of possibility. This notionis closely connected with the other modal notions, notably with those of ne-cessity and impossibility. Since these notions are somewhat more perspicuousthan that of possibility, it is advisable to start from them.

Aristotle knew that the contradictory (negation) of 'it is necessary that p'is not 'it is necessary that not p' but rather 'it is not necessary that p' (De Int.12, 22*4 ff.). The last two phrases are not contradictories, either, for theycan very well be true together (De Int. 13, 22bl ff.), the latter being widerin application than the former. By parity of form, 'it is not necessary thatnot p' is wider in application than 'it is necessary that p\

These relations are conveniently summed up in the following diagram(which is not used by the Stagirite):

necessary that p not necessary that p

(0 ~not necessary that not p necessary that not p

According to Aristotle, 'impossible' behaves like 'necessary' (De Int. 12,22*7 ff.). We can therefore illustrate it by means of a diagram similar to (i).In fact, the diagram will be virtually the same as the one for 'necessary',for "the proposition 'it is impossible'is equivalent, when used with a con-trary subject, to the proposition 'it is necessary'." (See De Int. 13, 22b5.)In other words, 'impossible that p' is equivalent to 'necessary that not p','impossible that not p' equivalent to 'necessary that p\ etc. We can thereforecomplete the diagram (i) as follows:

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necessary that p= not necessary that p=impossible that not p not impossible that not p

<») ; — .. 'not necessary that not p= necessary that not /? =not impossible that p impossible that p

2. The two notions of possibility. The problem is to fit the notion of pos-sibility into the schema (ii). In this respect, Aristotle was led by two in-compatible impulses. On one hand, he was naturally tempted to say that'possible' and 'impossible' are contradictories: something is possible if andonly if it is not impossible. (See e.g. De Int. 13, 22" 16—18, 32—38.) Underthis view, we get the following diagram:

not possible that not p= possible that not p =necessary that p not impossible that not p

(Hi) — :

possible that p= not possible that p=not impossible that p impossible that p

But this temptation is not the only one. In ordinary discourse, saying thatsomething is possible often serves to indicate that it is not necessary. Aris-totle catches this implication. For him, "if a thing may be, it may also notbe" {De Int. 13, 22b20; see also 22M4 ff.). Essentially the same point iselaborated in the Topica II, 7, 112bl ff. There Aristotle says that "if a neces-sary event has been asserted to occur usually, clearly the speaker has deniedan attribute to be universal which is universal and so has made a mistake."

Under this view, our diagram will have this look:

necessary that p= possible thatp= impossible that p =impossible that not p possible that not p necessary that not p

(iv) ; ; -

not impossible that p

It is seen that (Hi) and Civ) differ in that in (Hi) the range of possibilitycomprises everything that is necessary, while in (iv) possibility and neces-sity are incompatible.

It appears from De Interpretatione that Aristotle did not immediately seethat the assumptions underlying (Hi) and (iv) are incompatible. Not sur-prisingly, he ran into difficulties which he discusses in a not entirely clearway in De Int. 13, 22bll—23*7 (although I suspect that the confusion ofthe usual translations of this passage is not altogether Aristotle's fault). Heperceives clearly enough that the gist of the difficulty lies in the relation of

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possibility to necessity (De Int. 13, 22b29 ff.). And at the end he is led todistinguish two senses of 'possible' one of which satisfies (iii) and the other(iv). (De Int. 13,23*7—27.) However, Aristotle does not make any termin-ological distinction between the two. Insofar as the distinction is vital, I shallcall the notion of possibility which satisfies Uii) 'possibility proper' and thenotion which satisfies (iv) 'contingency'.

3. Homonymy v. multiplicity of applications. Now we can see why thedistinction between a diversity of applications and homonymy is vital forthis essay. We have found a clear-cut case of homonymy: the notions ofcontingency and of possibility proper have different logical properties. Theycannot be covered by a single term 'possibility' except by keeping in mindthat this word has different meanings on different occasions. Their relationis therefore one of homonymy (cf. section 10 of the first paper).

But in addition to this duality of 'contingency' and 'possibility proper', thereis a different kind of distinction. One of these two logically different notions,viz. possibility proper, covers two kinds of cases. When one says that p ispossible (in the sense of possibility proper), one sometimes could also saythat p is contingent and sometimes that p is necessary. This does not mean,of course, that the term 'possible' is ambiguous; it merely means that itsfield of application falls into two parts. It was for Aristotle therefore a typicalcase of multiplicity of applications as distinguished from homonymy (cf. sec-ion 10 of the first paper). The following diagram makes the situation clear:

necessary contingent impossible

possible

The distinction between the different applications of 'possibility proper'loomed large for Aristotle because he tended to emphasize the distinctionbetween necessity and contingency. Thus Aristotle argues in Met. X, 10 thatthe perishable and the imperishable are different in kind (sISo; and Y^V0?)-

In an earlier paper ('Necessity, Universality, and Time in Aristotle', Aj'atusvol. 20 (1957), pp. 65—90), I have argued that the distinction between con-tingency and necessity is for Aristotle equivalent to that between what isperishable and imperishable. The field of application of 'possibility proper'therefore falls into two parts which are different in kind. We have alreadyseen in sections 10 and 12 of the first paper that Aristotle viewed situationsof this kind with suspicion, although he grudgingly admitted that no logicalharm need result. This is probably one of the reasons why Aristotle in Ana-lytica Priora preferred the notion of contingency to that of possibility proper.

4. Aristotle's definition of contingency. According to the results of our

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examination of the ambiguities of Aristotelian ambiguity, we may expectthat the Stagirite usually refers to the distinction between possibility properand contingency by means of 6fiwvu(/.foc and that he always refers to thedistinction between the different cases of possibility proper (/. e. betweennecessity and contingency) by means of some other locution, e. g. Si^Os"kifz-cxi, XKTO: Suo TpoTtou? XeysTat or itok'ktx.'/G>s TiyeTai. An examination ofthe text will bear out this expectation as far as the first, the second, and thefourth expressions are concerned. Similarly, the third locution is, we shallfind, used by Aristotle in distinguishing two kinds of cases of contingency(see section 6 below).

In Aristotle's discussion of the notion of possibility, the key passage is inAn. Pr. I, 13, 32*18—21. It is referred to by Aristotle repeatedly as the def-inition of possibility (e.g. An. Pr. I, 14, 33b24; 15, 33b28; 15, 34b28; 17,37"27). The 'definition' is clear enough (I shall not discuss here why Aristotlethinks of it as a definition):

I use the terms 'possibly' and 'the possible' of that which is not neces-sary but, being assumed, results in nothing impossible.

This is clearly the notion I have called contingency. However, it is not theonly variant of possibility, for Aristotle continues:

TO -yap avayxatov ofAwvujxw; IvSs^eaOat Xl-yopz-i

That is, to say of the necessary that it is possible is to use the term 'possible'homonymously. This explanation obviously serves to motivate the quali-fication "which is not necessary" in Aristotle's definition. The use of theword 6[iuvu(Aw; shows that he knows that he is making a choice betweentwo incompatible meanings of IvSe^eaGxi (to be possible). The second mean-ing, under which even necessary things are called possible, is the notion ofpossibility which satisfies (iii) and which I have called possibility proper.

We have thus reached two important conclusions: (a) the main notion ofpossibility employed by Aristotle in An. Pr. is what I have called contin-gency; (b) Aristotle is aware of the existence of the other notion (possibilityproper) which is different from contingency to the degree that the sameterm can be applied to them only homonymously.

These results are confirmed by other passages. A glance at (iv) showsthat contingency is symmetrical with respect to negation: p is contingent ifand only if not-/? is also contingent. They are therefore convertible to eachother. Aristotle makes the same observation and applies it to syllogistic prem-ises in An. Pr. I, 13, 32"30 ff. This shows that his 'possibility as defined'

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agrees with my 'contingency'. Essentially the same point is made in An. Pr. I,17, 37*22 ff.

Aristotle's awareness of the ambiguity of possibility is also demonstratedby the development of his syllogistic. He frequently points out that the con-clusion of a certain syllogism is valid only if one does not understand pos-sibility in the sense defined (i. e. in the sense of contingency) but in a sensein which it is the contradictory of impossibility (e.g. An. Pr. I, 15,33b30—33;34b27—32; 16,35b33; 17, 36b33; 20, 39*12).

5. An analysis of An. Pr. /, 13,32"21—28. The fact that Aristotle wasaware of the different logical properties of contingency as distinguished frompossibility proper seems to me to be in agreement with what Aristotle writesimmediately after the passages I have quoted (An. Pr. I, 13, 32*21—28).This passage has been censured by the recent commentators in spite ofthe fact that it occurs in all the MSS and is recognized both by Alexanderand by Philoponus (W. D. Ross, Aristotle's Prior and Posterior Analytics,Oxford, 1949, p. 327). However, it seems to me that the passage can beunderstood as it stands by making due allowance for Aristotle's conspicuousconciseness. I shall offer a paraphrase of the passage, enclosing explanatoryadditions as well as my own comments in brackets. The superscripts referto further comments.

Aristotle has just explained his sense of IvSe^ojievov (possible) and dis-tinguished it from the homoiiymous notion of possibility proper. He goes on:

That this [=Aristotle's definition] is the meaning of'possible' is obviousfrom the opposing affirmations and denials.1 For [in the other sense of'possible'] 'it is not possible to apply', 'it is impossible to apply' and 'itis necessary not to apply' are either the same or imply each other.2

Consequently their contradictories3 'it is possible to apply', 'it is not im-possible to apply' and 'it is not necessary not to apply' are the same orimply each other. For either the affirmation or the negation alwaysapplies. [This is not correct, however, for we mean by possibility some-thing more than the absence of impossibility.4] That which is neces-sary will therefore not be possible, and that which is not necessary[nor impossible5] will be possible.

Further comments: (1) This elliptic sentence poses two questions:(a) What are these affirmations and denials affirmations and denials of?(b) What kind of opposition is Aristotle here referring to?

As regards (a), the sequel shows that Aristotle is not dealing with affir-mations and denials of possibility in the sense (of contingency) just defined-It turns out (c/. (2) below) that the affirmations and denials pertain to theother sense of possibility (possibility proper). Since Aristotle is obviously

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trying to justify his own definition, it may be concluded that he is herestarting a reductio ad absurdum argument.

As regards (b), a comparison with the occurrences of avTixsipyos laterin the passage (cf. (3)) suggests that this word — which is Aristotle's vaguestand most general term for opposition of any kind — here refers to contra-dictory opposition. The alternative would be to understand the sentence asreferring to the opposition between the two kinds of possibility; this wouldsuit my interpretation quite as well as the other reading.

(2) This is exactly what we get by accepting the other sense of evSe^o-(isvov, i.e. by not excluding necessity from the range of possibility: 'not pos-sible that p' will be equivalent to 'impossible that p ' which is (cf. diagram (ii))tantamount to 'necessarily not p\

(3) The following sentence shows that these contradictories are the av-ri-xsijisva referred to here.

(4) It was already pointed out above (in section 2) that Aristotle took thisview. See especially the reference to the Topica, loc. cit. It appears fromthe cpavspov in 32"20 that Aristotle thought of this point as being perfectlyobvious; so obvious, indeed, that he neglected to make it explicit here.

(5) The second part of the last sentence seems strange. The addition Ihave indicated is a most tempting way of making the passage correct. It isvery likely, however, that the passage is Aristotle's as it stands. He knewthat his notion of possibility (i. e. contingency) is symmetrical with respectto negation in the sense which best appears from diagram (iv). He may havethought that this symmetry justifies the transition from 'what is necessaryis not possible' to 'what is not necessary is possible'. This leads to a readingof'not necessary' as an elliptic form of'not necessary either way', i.e. 'neithernecessary nor impossible'. In the sequel, we shall find more indications thatthis was Aristotle's reading; see section 7 infra.

Here I shall only point out that my interpretation is supported by whatwe find in De Interpretatione. If it is true that'not necessary'sometimes doesduty for 'neither necessary nor impossible', it may be expected that 'notnecessarily not', i.e. 'not impossible', will sometimes mean 'neither impos-sible nor necessary'. When this is so, 'not impossible' will entail (in fact,it will be equivalent to) 'not necessary*. And this is exactly what we find inDe. Int. 13, 22b14—16, where Aristotle infers 'not necessary' from 'not im-possible'. This inference is very difficult to explain otherwise. The inferenceis based on the sequence of implications (equivalences?) set up by Aristotlein De Int. 13, 22* 16 ff., where again p j a8uva-rov slvat entails pj avayxocTovelvai.

6. A subdivision of contingency. Having made these distinctions, Aristotle

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goes on to say (in An. Pr. I, 13, 32b5 ff.) that possibility has two applications(the expression he uses is xa-ra Suo TpoTrou; Hye-roci). On one hand, it isused to describe what generally happens but falls short of being necessary;on the other hand it is used to describe the indeterminate, that which canbe 'thus or not thus' without the prevalence of either alternative. Now thedistinction plainly has nothing to do with the difference between possibilityproper and contingency. Neither of the two uses distinguished by Aristotlecovers what happens necessarily. What we have here is therefore a subdivisionof contingency. Aristotle's use of the expression XOCTOC 5<JO Tpojrous Xsysfaisuggests that he is not distinguishing two meanings of evSe^dpevov but rathertwo kinds of cases to which it can be applied (cf. section 13 of the firstpaper). This is verified by his remarks on the conversion of statements ofcontingency. He says that in both cases the possible premise can be con-verted into its opposite premise, i. e. 'p is contingent' into 'not-p is con-tingent'. This is trivial in the case of a p which is contingent because it is'indeterminate'. But Aristotle also holds that the conversion applies to con-tingency in the sense of that which 'generally happens'. This may seemmistaken: if p happens generally but not necessarily, we certainly cannotinfer that not-p happens generally. What Aristotle means is that even inthis case not-p is neither necessary nor impossible and hence contingentin the sense of his definition. If 'what happens generally but not necessarily'were one of several meanings of 'contingent', Aristotle would not be ableto say that 'contingent' always converts with its opposite. What he means isthat in each of the different cases that fall under the term 'contingent' wehave a conversion to the opposite of some case — not necessarily of thesame case — covered by the term.1 Hence, he is not dealing with differentmeanings of £vSe d(Jievov, but only with different applications of the term.'Contingent' is not homonymous although it covers different kinds of cases.

7. An analysis of An. Pr. /, 3, 25"37—25b19. Some of the passages I havejust discussed are referred to by Aristotle earlier in Analytica Priora in con-nection with the conversion of problematic (possible) premises (An. Pr. I, 3,25*37—25b19). We are now in a position to understand the context of thesereferences.

In An. Pr. I, 3, 25b18 Aristotle refers to his later discussions of the con-version of problematic premises. All the remarks on this subject later inAnalytica Priora pertain to contingent premises. This suggests that the notionAristotle has in mind in 25b18 is his 'possibility as defined' or contingency.This is confirmed by the way Aristotle explains the notion of possibilitywhich he is here dealing with: "But if anything is said to be possible be-cause it is the general rule and natural. . ." (An.Pr. I, 3, 25b14 ff.). This re-

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calls one of the different cases of contingency discussed in An. Pr. I, 13,32b5 ff. (vide supra). And when Aristotle says that this "is the strict sensewe assign to possible" (Ross's translation), he is obviously anticipating hisdefinition of contingency in 32b18—20.

I conclude, therefore, that in An.Pr. I, 3, 25b14—18 Aristotle is thinkingof contingency rather than possibility proper. Now the passage which wasjust quoted shows that this variant of possibility is contrasted to the oneemployed in the immediately preceding passage (An. Pr. I, 3, 25b8—13).We may therefore expect that this latter notion of possibility is what I havecalled possibility proper. Aristotle's examples show that this is in fact the case.In one of his examples the term 'man' necessarily does not apply to anyhorse, while in another the term 'white' does not necessarily apply to anycoat. This shows that the meaning of possibility which is used here coverscases of necessity as well as cases of contingency. (The examples are bothnegative in form because he is discussing the conversion of negativepremises.)

Although the testimony of Aristotle's examples thus unambiguously showsthat in 25b8—13 he is discussing possibility proper, one may still be puzzledby his own explanation of the variant of possibility he is using: "Whateveris said to be possible because it is necessary or because it is not necessaryadmits of conversion like other negative statements.. . ." For what onewould expect here is 'neither necessary nor impossible' instead of 'not nec-essary'. Some commentators have tried to emend the passage by insertingthe negative particle p j so as to make it read 'not necessarily not', althoughthere is no real support for such an insertion in the MSS (see Ross, op.cit.).Moreover, this insertion has the disadvantage of making the clause 'becauseit is necessary' superfluous. In any case, the emendation is quite unneces-sary, for we have already found independent reasons for suspecting thatAristotle sometimes uses 'not necessary' (T6 y/r\ avayxatov) and, by analogy,'not necessarily' (pj si; ava-pvj;) as elliptic expressions for 'neither neces-sary nor impossible' and 'neither necessarily nor impossibly', respectively(see section 5, comment (5) supra). This suspicion is now confirmed bythe fact that the same explanation works here: on my reading the quotedpassage says just what one is entitled to expect.

Here one may ask whether my reading is contradicted by the fact that inhis second example Aristotle'says that it is not necessary that 'white' appliesto any coat (TO Se ofot avayxT] CimxpxEiv). If Aristotle were consistently usingthe elliptic mode of expression, should he not use double negative oox ava-•pa] [«] uTrap^eiv, since he is here dealing with negative premises? To thisit may be answered that 'neither necessary nor impossible* is symmetrical

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with respect to negation, so that no extra p j is needed even if the ellipticmode of expression is used. Besides, one of Bekker's MSS as well as Philo-ponus do have the missing [«] (see Ross, op. cit.), so that Aristotle may verywell have been even pedantically consistent in his usage.

We may conclude that in his treatment of the conversion of negative prob-lematic premises Aristotle first discusses premises in which the notion of'possibility proper' is used and then those in which the notion of contingencyis used. In contrast, both these notions are lumped together in Aristotle'sdiscussion of the conversion of positive problematic premises (25*37—25b2).He indicates this as follows: ITTSISV] TZOWIX^GX; XsyeTai TO Iv5s^sa0at(xal yap TO ^vayxaTov xai TO p ] dvocYxaTov xal TO SUVOCTOV IvSs^soBai 5^0-(xsv).... Here the words KoWxy&s ^E^STOU suggest that he is not exclusivelyconcerned with the different meanings of Iv8e^6(i.evov. In fact, it has beenpointed out by Ross that the three cases listed in the parenthetical clausecannot possibly be as many different meanings of evSe^ojisvov. However, itseems to me that it cannot be said, either, that they are just three differentcases to which the notion of possibility can be applied. The first two areclear; we have encountered TO dvocYxaTov and TO p) dvocYxaTov before asthe two cases covered by the notion of possibility proper. The recurrencefor the fourth time of the elliptic expression TO p j dvocYxaTov (or of one ofits variants) where one expects 'neither necessary nor impossible' givesfurther support to my interpretation of this phrase. But TO SUVOCTOV cannotvery well be a third case to which the notion of possibility is applied, forthere is no third case comparable with the two already listed. Rather, we mustunderstand TO dvayxatov xal TO p] dvaY^atov as referring to the notion ofpossibility proper, and understand TO SUVOCTOV as referring to the other notionof possibility, viz. contingency. This, in fact, seems to be the way Ross under-stands the passage. Its meaning may hence be expressed somewhat asfollows: " . . . seeing that possibility has many applications (for we call pos-sible both that which is necessary or is not necessary either way and thatwhich is capable of being) . . . " .

This interpretation is supported by the fact that the context shows thatAristotle is here treating both the variants of possibility at the same time.If they are here mentioned in the same order in which they are subsequentlytreated (in the connection of the conversion of negative problematic prem-ises) we can scarcely separate Aristotle's references to the two variantsin any way different from the one just suggested.

Our interpretation also agrees with the way SUVOCTOV is used elsewherein Analytica Priora. The most important passage in which this term occursis An.Pr. I, 15, 34*6 ff. And it is indicated by Aristotle (in 34M4) that the

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arguments he there gives pertain to possibility with respect to generation.Now this variant of possibility is very likely just our contingency. For some-thing which is generated will sometimes be (viz. after having been generated)and sometimes not be (viz. before it is generated). It is therefore possiblein the very sense (in that of contingency) which we wanted to give SUVOCT6V

in An. Pr. I, 3, 25*39.8. Remarks on An. Pr. /, 13,32b25—32. What we have found in this paper

and its predecessor confirms my earlier analysis of An. Pr. I, 13, 32b25—32(in 'Necessity, Universality, and Time in Aristotle', pp. 86—88). Here I shallonly briefly outline the argument, adding such new evidence as was notmentioned in the earlier paper.

In the passage under discussion Aristotle seems to be saying that

(P) • it is possible for A to apply to all B

is ambiguous in that it may mean either

(Pi) it is possible for A to apply to everythingto which B in fact applies

or

(P2) it is possible for A to apply to everythingto which B possibly applies.

This cannot be his meaning, however. For one thing, he never seems to use(Pi), but only (P2) in his subsequent discussion of syllogisms from possiblepremises. He seems even to say that (P2) is what (P) was defined to mean(An. Pr. I, 14, 33*24—25). For another, the term Aristotle uses is Si^uic,which strongly suggests that he is not at all distinguishing two differentmeanings of (P). Rather, he is saying that (P) covers two kinds of cases, /. e.that (P) is tantamount to the conjunction of (Pi) and (P2). This suffices toexplain everything that Aristotle says and does. It may be expected thatthe variant of possibility Aristotle is using in (P2) is the one he usually em-ploys, viz. contingency. Expressed as explicitly as possible, Aristotle's pointtherefore is that (P) is equivalent to the conjunction of (Pi) and (P21), wherethe latter is(P21) it is possible for A to apply to everything

to which B applies contingently.

Now this conjunction is clearly equivalent to what we get by assuming thatthe variant of possibility used in (P2) is my 'possibility proper':

(P22) it is possible for A to apply to everythingto which B possibly applies (in the sense of

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Page 12: Inquiry (Taylor & Francis) Volume 3 Issue 1 1960 [Doi 10.1080%2F00201746008601302] Hintikka, K. Jaakko J. -- Aristotle's Different Possibilities

'possibility proper'), ί. e. to everything to which

Β applies necessarily or contingently.

This explains why Aristotle seems to deal exclusively with (P2) in his syl-

logistic theory; for what he is really dealing with is (P22) which is equivalent

to the conjunction of (Pi) and (P2i) and therefore also to (P).

Further evidence is perhaps found in An. Pr. I, 29, 45b31—32. Having

just explained how the different kinds of assertoric syllogisms are established,

Aristotle goes on to say that apodeictic (necessary) and problematic (possible)

syllogisms are established in the same way. But he adds a warning:

In the case of problematic propositions, however, we must include thoseterms which, although they do not apply, might possibly do so; for ithas been shown that the problematic syllogism is effected by meansof t h e s e . . . . (H. Tredennick's translation in the Loeb Library edition.)

Prima facie this is completely tautologous. For problematic syllogisms con-

tain by definition terms which do not apply but may apply. What can Aris-

totle mean here ? It is clear that the predicate term A of a premise like (P)

may apply possibly but not actually. But it is not equally obvious whether

the subject term Β is to be taken to apply possibly or actually; whether, in

other words, (P) is to be understood as being equivalent to (Pi) or to (P22).

Unless we assume that Aristotle's statement is pointless, we can scarcely

interpret it except as a repetition of the point which we found him making

in An. Pr. I, 13, 32b25—32, viz. as identifying (P) and (P22). Notice in parti-

cular that there is no semblance here of a distinction between two meanings.

9. Concluding remarks. We have discussed the most important passages

of An. Pr. I which turn on the distinction between the various notions of

possibility used by Aristotle. Insofar as we have been successful in applying

the results of my earlier analysis of the ambiguities of ambiguity in Aristotle,

our success conversely serves as a further confirmation of the earlier anal-

ysis. In particular, it supports what was said in section 10 of the first paper.

Aristotle's own definition of contingency (see supra section 4) establishes

a connection between contingency and possibility proper: contingent is that

which is (properly) possible but not necessary. If homonymy were tant-

amount to the absence of any common element in definition, contingency and

possibility proper would not be homonyms. The fact that Aristotle calls them

homonyms shows that there is more to his notion of homonymy than that.

N O T E1 Aristotle's awareness of the fact that a case of a concept may be converted into an-

other case of the same concept is also shown by his remarks on το είχóς in Rhet. II23, 1402a9 ff.

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