Hintikka has argued1 that the term ακολουθειν, usually translated in logical contexts as ‘follow from’, is in fact less definite, sometimes possessing a wider sense of ‘going together with’, ‘accompanying’, ‘being compatible with’, ‘conforming with’, sometimes a stronger sense of ‘logically equivalent with’. These claims were originally used to clear up some difficulties in Aristotle’s De Interpretatione 12-13, but they have subsequently been employed in an attempt to obtain a consistent interpretation of Pappus’ remarks about the geometrical method of analysis and synthesis.2 It is not my intention to query the general claim that ακολουθειν and its cognates have a less definite meaning in ordinary Greek than ‘to follow logically from’. What I do wish to show, however, is that Hintikka does not give sufficient grounds for disputing the traditional understanding of this term in the discussion of modal notions in the De Interpretatione.3
In the course of his discussion Hintikka mentions five passages in chapters 12 and 13 of the De Interpretatione where he thinks a revised understanding of ακολουθειν is called for; in two of these, 21 b 35-22 a 1 and 22 b 11-14, Aristotle is to be saved from serious error by the logical compatibility interpretation, in two more, 22 b 17-22 and 22 b 22-4, he is saved from useless platitude, in the first case by the compatibility sense, in the next, a couple of lines later, by the logical equivalence reading. The fifth example Hintikka gives is in connection with the tables in chapter 13. Leaving aside the tables for the moment, the first two cases Hintikka discusses are clearly the more serious, for the traditional interpretation seems to saddle Aristotle with elementary errors. These ‘errors’ can, however, be understood, if not wholly forgiven, in a way that also allows us to see the heuristic point of the platitudes Aristotle indulges in. My interpretation thus allows Aristotle a fairly clear understanding of one of the recurrent terms employed in this discussion, and acknowledges the coherence of his overall argument. It might, I hope, also be suggestive for further investigations of the methodology of logical enquiry.
The first gross error that Aristotle appears to commit is at 21 b 35-22 a 1:
διο και ακολουθειν αν δοξαιεν αλληλαις αι δυνατον ειναι — δυνατον μη ειναι. το γαρ αυτο δυνατον ειναι και μη ειναι. ου γαρ αντιφασεις αλληλων αι τοιαυται. αλλα το δυνατον ειναι και μη δυνατον ειναι ουδεποτε αμα. αντικεινται γαρ.This is why ‘possible to be’ and ‘possible not to be’ may be thought actually to follow from one another. For it is possible for the same thing to be and not to be; such statements are not contradictories of one another. But ‘possible to be’ and ‘not possible to be’ never hold together, because they are opposites.4 Certainly the fact that two statements are not contradictories of one another is scarcely a reason for their mutually entailing each other. Hintikka says, truly, that if ακολουθειν meant mere logical compatibility the suggestion in the first line would not be based on such weak evidence. And he goes on to remark that Aristotle’s discussion a little later (22 b 36 ff) of things that can φ but cannot not φ shows that his evidence could not have supported a claim of mutual implication between δυνατον ειναι and δυνατον μη ειναι, but at most compatibility.
But Hintikka’s own reading is not without its difficulties. Aristotle has been saved from making an unsupported leap from evidence to conclusion at the cost of making none at all. It is possible for the same thing to be and not to be, and this is why it may be thought that ‘possible to be’ and ‘possible not to be’ are compatible. There needs no Stagirite to tell us this. A further oddity in Hintikka’s account is his taking it that Aristotle endorses this mutual ακολουθειν, whatever content he supposes it to have. The verbal form δοξαιεν could be used in this way, but it does not compel such a reading; indeed it has commonly been taken otherwise, as indicating a view that others perhaps have held, that may appear to be the case. Hintikka5 often claims that Aristotle did endorse a mutual equivalence here, but his only evidence in these chapters is a rough riding over a 1st. aorist optative.
The second major error Aristotle is saved from occurs at 22 b 11-12: το γαρ αναγκαιον ειναι δυνατον ειναι. ει γαρ μη, η αποφασις ακολουθησει. αναγκη γαρ η φαναι η αποφαναι. Here Aristotle seems to be relying on a general principle that if p does not imply q then it implies not-q, but Hintikka discerns this truth instead, “each given proposition must be compatible with one or the other of any pair of contradictories.”6 A slightly more charitable reading of the traditional interpretation would restrict Aristotle to the principle that if αναγκαιον ειναι does not imply δυνατον ειναι then it implies μη δυνατον ειναι. This as a principle derives no support, of course, from any more general principle that a proposition implies one or other of any given pair of contradictories, and perhaps Aristotle is unfairly hinting that it does, but is it not itself reasonable as a principle? Or, to put it in a slightly different way, could it not express part of a reasonable working hypothesis for anyone entering the field of the logic of necessity and possibility?
My suggestion is that we should see Aristotle as committed to a working hypothesis, a hard core,7 that δυνατον, αναγκαιον and their contradictories and what Aristotle calls their contraries (pairs, one with ειναι and the other with μη ειναι as subject) are directly linked logically. It is almost just the belief that there is an amenable field of study here at all. But in the light of this belief, Aristotle might feel justified in thinking that if ‘necessary to be’ does not imply ‘possible to be’ then it has got to imply ‘not possible to be’ (‘possible not to be’ being ruled out by its implausibility and the structure of the tables in chapter 13 in the light of which he is here working), since otherwise the logical links between ‘necessary’ and ‘possible’ would become too tenuous. Similarly, I think, we could see this working hypothesis suggesting the first ‘error’ — if ‘possible to be’ does not contradict ‘possible not to be’ then it had better mutually imply it, otherwise, again, the connections would be too loose. But here we have no reason to think Aristotle was taken in by this suggestion.8
Let us now turn to the other kind of argument that Hintikka employs — that Aristotle appears to be uttering platitudes which turn to significant claims under Hintikka’s revision. The platitudes in question occur between 22 b 17 and 22 b 24. Hintikka takes two parts of this passage on their own and sees no reason in Aristotle’s telling us that neither αναγκαιον ειναι nor αναγκαιον μη ειναι follow from δυνατον ειναι, or again that ουκ αναγκαιον μη ειναι does follow from it.9 To include these claims in a disconnected jumble might indeed be straining the patience of one’s audience, but we should look more carefully at the context of Aristotle’s remarks.
Chapter 12 has laboriously uncovered five contradictory pairs (the labour
being spent on the first): δυνατον - ου δυνατον, ενδεχομενον - ουκ ενδεχομενον, αδυνατον - ουκ αδυνατον, αναγκαιον - ουκ αναγκαιον, αληθες - ουκ αληθες. It has also uncovered the fact that the modal operators may be prefixed
either to ειναι or μη ειναι and that certain further logical relations may result
from this possibility. Chapter 13 begins with a sequence of such logical
relations, ακολουθησεις, asserted without argument and then
arranged for convenience in a table:
Whatever the precise thought in Aristotle’s mind concerning ακολουθειν here, the principles behind the table are clear — each column of 4 starts with an expression involving δυνατον; A1 and B1 take ειναι as subject, A2 and B2 μη ειναι; A1-1 and B1-1 are contradictories, as are A2-1 and B2-1; lines 2, 3, and 4 are said to follow from, or be equivalent with, or just accompany, line 1. But soon Aristotle recognises that all is not well with his table, at least it could be more symmetrical, since A1-4 is not the contradictory of B1-4, nor A2-4 of B2-4, and in the B columns the subject changes in the fourth line.
The series of trivialities that Hintikka rejects occurs in a passage where Aristotle suggests resolving these asymmetries by exchanging A1-4 and A2-4 — this keeps all A and B pairs contradictories, and abandons the claim that each column has the same subject all through. The argument for this re-arrangement begins with the claim that αναγκαιον ειναι implies δυνατον ειναι, i.e. B2-4 implies A1-1. (22 b 11 et seq. This claim is itself supported by the argument defended above that otherwise B2-4 would imply B1-1.) Given this supposition, as the table stood originally B2-4 would then imply A1-4, i.e. the necessary to be is not necessary to be, which is a contradiction. So, if B2-4 to A1-1 is acceptable, there is something radically wrong with the move from A1-1 to A1-4. To find out where the move from A1-1 should lead instead, Aristotle works round his table by elimination: A1-1 does not entail B2-4, nor B1-4 (the two moves Hintikka thinks too obviously wrong), so that only leaves A2-4, which is acceptable since A2-4 goes with B2-4 (the conclusion Hintikka thinks too trivial to mention.)
Given the working hypothesis I have already suggested, this elimination procedure makes perfect sense, and indeed to be persuasive requires that the lack of implications in question be obvious. These moves, trivial perhaps in themselves, fit into a coherent, and important, pattern of argument, a structure that Hintikka must perforce overlook. A further way in which Hintikka simply ignores the overall pattern of argument is his claim that at 22 b 17 an ακολουθειν of compatibility is in question — thus he translates "neither ‘necessary to be’ nor yet ‘necessary not to be’ is compatible with ‘possible to be’."10 So, according to Hintikka, Aristotle is here saying that ‘necessary to be’ is incompatible with ‘possible to be’. But as I have indicated the passage comes within a longer argument, whose supposition is precisely that ‘necessary to be’ implies ‘possible to be’. Hintikka must, therefore, fragment what is clearly a continuous argument. The implication thus supposed for this part of the argument is indeed questioned in a later passage (22 b 29 et seq.), where again Aristotle’s method is to go round his table saying if B2-4 does not imply A1-1 you must plump either for B1-1, which is absurd, or for A2-1, which is also false of the necessary to be. Again, platitudes if you like, but platitudes with a point and a basis in the working hypothesis I have tried to sketch.
I have argued that, whatever the merits of Hintikka’s proposal elsewhere, his arguments do not establish it in the chapters of De Interpretatione that he concentrates on. The serious errors Aristotle appears to make can be seen as expressions of a reasonable working hypothesis, the trivialities he permits himself have a purpose in a structure of argument that Hintikka simply ignores in order to score shallow points. If this is so, we have no need of the Hintikka-Remes explanation11 of the ambivalence attributed to Aristotle between a sense of logical compatibility and logical equivalence; indeed, if the palpable invalidity of an argument is good enough reason to revise the translation, the palpable invalidity of this move would seem sufficient reason to doubt the revised version. The wider interest of my claim, if it is well-founded, lies in what it might reveal of the methodology of logical investigation.
1
In ‘On the Interpretation of De Interpretatione 12-13’ originally published in Acta Philosophica Fennica 1962, reprinted with revisions as chapter III of his Time and Necessity (Oxford, 1973). All page references to this later version.2
J. Hintikka and U. Remes, The Method of Analysis (Dordrecht, 1974) passim, esp. ch. II.3
Thus my argument has no immediate consequences for the understanding of Pappus. It may be noted, however, that, as Hintikka and Remes show, the method of analysis Pappus seeks to charactarise is in fact largely deductive, so that it would not be wildly irresponsible to suggest that the part of his characterisation that involves an 'upward' movement through ακολουθα is somewhat misleading. Cf. Mueller’s review of Hintikka and Remes, Journal of Philosophy 73 (1976) 158-62.4
J.L. Ackrill, Aristotle’s ‘Categories’and ‘De Interpretatione’ (Oxford, 1963).5
J. Hintikka, Time and Necessity (Oxford, 1973) 48, and 53.6
Op. cit. 44.7
Cf. I. Lakatos ‘Falsification and the Methodology of Scientific Research Programmes’ in I. Lakatos & A. Musgrave (eds.), Criticism and the Growth of Knowledge (Cambridge, 1970) 91-195, esp. 133-4.8
Further minor support for my suggestion occurs early in chapter 12. At one point we are faced with a decision between δυνατον μη ειναι and μη δυνατον ειναι as the contradictory of δυνατον ειναι. The former presents various difficulties; we therefore (αρα 21 b 24) choose the latter. But if we wished to carp we should surely not allow that the natural lanaguage actually possesses the contradictory of every sentence-forming operator on sentences that it might possess, at least if we rule out the logician’s ‘it is not the case that’.9
Op. cit. 45 and 49 respectively.10
Op. cit. 45.11
Op. cit. 51-2.
© E.P. Brandon, 2002, HTML last revised 28 December 2002.
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