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Aristotle, Speusippus, and the method of division

Published online by Cambridge University Press:  11 February 2009

Andrea Falcon
Andrea Falcon
Affiliation:
University of Padua
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Extract

Introduction

As Aristotle himself says, A.Po. 2.13 is an attempt to provide some rules to hunt out the items predicated in what something is, namely to discover definitions. Since most of this chapter is devoted to the discussion of some rules of division (diairesis), it may be inferred that somehow division plays a central role in the discovery of definitions. However, in the following pages I shall not discuss what this role is. Nor shall I discuss what place division has in the wider discussion of definition and explanation as it emerges from A.Po. 2. 1 shall rather focus on the argument that Aristotle reports and discusses in A.Po. 2.13.97a6–22, and which our extant sources ascribe to Speusippus. As will become clear later on, this argument undermines the possibility of giving any definition, and Aristotle deals with it here because he can block it by exploiting some properties of the method of division.

Type
Research Article
Information
The Classical Quarterly , Volume 50 , Issue 2 , December 2000 , pp. 402 - 414
Copyright
Copyright © The Classical Association 2000

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References

1 A.Po. 2.13.96a13.22—3: πὼς δ δεiθηρεειυ τ υ τὼ τ στι κατηγoρμευα, υῠυλγωμευ

2 Cherniss, H., The Riddle of the Early Academy (Berkeley, Los Angeles, 1946), 42.Google Scholar

3 Isnardi Parente, M., Speusippo. Frammenti (Napoli, 1980).Google Scholar

4 Tarán, L., Speusippus of Athens. A Critical Study with a Collection of the Related Texts and Commentary (Leiden, 1981).Google Scholar

5 That Speusippus undertook division is an old, authoritative claim. The first scholar who advanced this claim was Lang in his essay on the catalogue of Speusippus’ work (Lang, P., De Speusippi Academici Scriptis [Bonn, 1911], 21–2).Google Scholar That the division which Speusippus used is dichotomic was claimed by Stenzel in the article he wrote for the entry ‘Speusippos’ in the Real-Encyclopadie der classischen Altertumwissenschaft (Stenzel, J., ‘Speusippus (2)’, RE III A, cols 1636–69 [Stuttgart, 1929]).Google Scholar A further step into this tradition was the identification of this division with the dichotomous method that Aristotle criticizes in P. A. 1.2–3. Cherniss was the first to advance this additional claim (H. Cherniss, Aristotle's Criticism of Plato and the Academy [Baltimore, 1944], 59–64, and id. [n. 2], 42). In recent years this claim has been advanced again by Taran ([n. 4], 396–406). According to him, PA. 1.2–3 is nothing but a long, detailed criticism of Speusippus’ dichotomous method of division. Although Isnardi Parente ([n. 3], 256–60) does not ascribe a dichotomous method of division to Speusippus, she has no hesitation in ascribing some method of division to Speusippus.

6 Anon., In A.Po. Librum Alterum Commentarium (CGA 13.3), 584.17.

7 A.Po. 2.13.97a7—11: κα⋯τoι ⋯δ⋯υατ⋯υ φασ⋯ τιυες εἶυαι τ⋯ς διαφoρ⋯ς εἰδυαι τς ἓκαστoυ μ εἰδoτα ἓκαστoυ ἄυευ δ τυ διαφoρυ oὐκ εἶυαιἓκαστoυεἰδυαι oὗ γρ μδιαφρει, ταὐτoυ εἶυαι τoτω o διαφρει, ἓτερoυ τoτoυ

8 Anon., In A.Po. Librum Alterum, 584.17–18: ∑πευσ⋯ππoυ τα⋯τηυ η⋯υ δ⋯ξαυ Eὓδημoςεἶυαι λ⋯γει τ⋯υ ⋯τι ⋯ρσασθαι δυατo τὼυ ⋯υτωυ μ⋯ π⋯υτα τ⋯ ⋯υτα εἰδ⋯τα.

9 Phil. 18b7–d2:καθoρυ δ⋯ ὡς oὐδες μὼυ oὐδ’ ἄυ ἓ αὐτo καθ’ αὑτo ἄυευ πυτωυ αὐτὼυ μθoι, τoὺτoυ τoυ αλoγισμευoς ὡς oυτα ἓυα κα πυτα ταὺτα ἓυ πως πoιoὺυτα μαυ π’ αὐτoῖς ὡς oσαυ γραμματικυ τχυηυ πεφσγξατo πρoσειπώυ

10 Scholars are unanimous on this point: Speusippus would have advanced his argument to support something like the strong interpretation. See Waitz, Th., Aristotelis Organon Graece 2 (Leipzig, 1844–6), 419Google Scholar; Cherniss (n. 5), 59–64;Ross, W. D., Aristotle's Prior and Posterior Analytics (Oxford, 1949), 659–60Google Scholar; Tarn, (n. 4), 388–91. Isnardi Parente ([n. 3], 256–60) goes even further and claims that Speusippus offered his argument to support a sort of παυσoφα

11 A.Po. 2.13.97a9–10:ἄυευ διασoρὼυ oὐκ εἶυαι ἓκαστoυ εἰδυαι

12 δυατoυ φασ τιυες εἶυαι τς διαφoρς εἰδυαι τς πρoς ἒκαστoυμ εἰδoτα ἓκαστoυ

13 A.Po. 2.13.97a10–11: oγρ μ διαφρει, ταὐτoυ εἶυαι τoτω, oδ διαφρει, ἒτερoυτoτoυ.

14 A.Po. 2.13.97all-14:πρτoυ μυ oυ τoὺτo ψεῠδoς oὐ γρ κατ πᾰσαυ διαφoρυἒτερoυ πoλλα γρ διαφoρα ὑπρχoυσι τoȋς αὐτoȋς τὼ εἳδει, λλ’ oὐ κατ’ oὐσαυ oὐδ καθ’ αὑτ.

15 See, for instance, Top. 7.2.152b36–153a5. An analysis of this passage is offered in Mignucci, M., ‘Puzzles about identity. Aristotle and his Greek commentators', in Wiesener, J. (ed.), Aristoteles Werk und Wirkung (Berlin, New York, 1985), 57–66.Google Scholar

16 In clause (ii) Aristotle gives his explanation for clause (i) by introducing a distinction amongst differences. I take oὐδ in 97a 13 as the negative counterpart of the epexegetic κα. According to this interpretation, in (ii) Aristotle is content to introduce only two types of differences: (a) essential differences, and (b) non-essential differences. It is nevertheless possible to read (ii) as if Aristotle is introducing the following tripartition: (a) differences in respect to the essence, i.e. essential differences;(b)per se differences; and finally (c) differences that are neither essential nor per se. Although this second interpretation is consistent with what Aristotle says elsewhere, it has at least two disadvantages. First of all, Aristotle does not need to introduce the per se differences. As a matter of fact, they add nothing to his first objection. Secondly, the per se differences would be introduced without any further clarification or explanation.

17 A.Po. 2.13.97a14—22: εἶΤά ὃΤάν λάβη ΤἀνΤικείενάΤν διάøορᾰν κάὃΤι πν μππΤει νΤάθά ἵ νΤάθά, κά ιβη ἠν θάΤρωῳ Τ ζηΤομενον νἶνάι, κάྲྀ ΤοΤο γινώσκη, οὐδνάι ἥ μ εἱδνάι ø’ ὃσων κάΤηγορονΤάιἄιιων άἱ διάøορά. øάνερν γᾰρ Τι ἃν οὓΤω βάδζων ἔιθη εἰς ΤάΤά ὧν μηκΤι ἔξει Τླྀν ιγον Τςοὐσάς. Τ δ’ ἃπάν μππΤειν εἰς Τν ειάρεσιν, ἄν ἧ νΤικεμενά ὧν μ ἔσΤι μεΤάξὺ, οὐκ άῖΤημά νγκη γཱγκη γᾰρ ἄπάν ༐ν θάΤρῳ άὐΤν εἶνάιεἵπερ κενου διάøορ σΤι.

18 Top. 4.4.141b29–34: τομυ γᾰρ εἲδους γυωριξομυου υγκη κα τυδιαØορυ γυωξεσθαι ( γᾰρ According to a position of Aristotle's in Metaph. 7.12, definition is reduced to the last difference, which records all the information conveyed by the genus and the previous differences. Let us suppose that two-footed is the last difference of man. When one knows that man is two-footed, one knows that man is an animal, that man goes on feet, and finally that man has two feet. In this case knowledge of the difference, two-footed, is also knowledge of the species, man. Later on I shall offer a brief presentation and discussion of Metaph. 7.12. Here I am content to say that in this chapter Aristotle introduces a particular rule of division. According to this rule, every difference must be a difference of a previous difference. As far as I can see, Aristotle never relies on this rule in the Topics or in the Posterior Analytics. Here Aristotle never requires that division is conducted on the basis of this particular rule. Elsewhere I claimed that the method of division as it emerges from Aristotle's use and discussion of division in the Topics and in the Posterior Analytics is not consistent with this particular rule. Cf.Falcon, A., ‘Aristotle's theory of division’, in Sorabji, R. (ed.), Aristotle and After (London, 1997), 127–41.Google Scholar

19 See note 5 for further details.

20 Taran (n. 4), 65. 2I Taran (n. 4), 65

21 Tarán (n.4),65–6.

22 Athen. 2.59d-f (T. Kock, Comicorum Atticorum Fragmenta 2, fr. 11, 287).

23 On this issue, see Merlan, P., ‘Zur Biographie des Speusippos’, Philologus 103 (1959), 198–214Google Scholar, now also in Merlan, P., Kleine philosophische Schriften (Hildesheim, New York, 1976).Google Scholar

24 Diog. Laert. 4.5.

25 Moraux, P., Les Listes anciennes des ouvrages d'Aristote (Louvain, 1951), 186.Google Scholar

26 Lang was the first scholar who advanced this possibility. See Lang (n. 5), 48. On this suggestion, see also the additional notes which M. Gigante added to the second edition of his Italian translation of Diogenes Laertius (Diogene Laerzio, Vite dei Filosofi [Bari, 19762], 579–81).

27 On the reasons for this emendation, see Lang (n. 5), 16–17; Taran (n. 4), 196; and Isnardi Parente (n. 3), 214.

28 Mutschmann, H., Divisiones Quae Vulgo Dicuntur Aristoteleae (Lipsiae, 1906).Google Scholar A translation and a commentary has recently been offered by Rossitto, C., Aristotele ed altri. Divisioni. Introduzione, traduzione e commento (Padova, 1984).Google Scholar On the formation of this corpus of divisions and its transmission, see T. Dorandi, ‘Ricerche sulla trasmissione delle Divisioni Aristoteliche’, in Algra, K. A., Van Der Horst, P W., and Runia, D. T. (edd.)Polyhistor. Studies in the History and Historiography of Ancient Philosophy Presented to Jaap Mansfeld on his Sixtieth Birthday (New York, Leiden, Koln, 1997), 145–65.Google Scholar

29 See, for instance, Cherniss (n. 2), 8Iff.; and H. J. Kramer, ‘Die Altere Akademie im Allgemeinen', in H. Flashar (ed.), Die Philosophic der Antike (Stuttgart, 1983), 6.

30 30 From Simplicius we learn that Speusippus left a division (diairesis) of names. A discussion of this testimony cannot be postponed any longer. According to Simplicius, first Speusippus divided names into TavTovv/xa and erepwvvpa, and then Tavrow/JLa into 6/xwvvixa and avvwvviux, and erepwvvfia into i'8i'a>?erfpciivvfia, TTOXVWVV/JUI, and iiapu>vvfw.. Cf. Simpl. In Cat. 38.19–24. This testimony goes back ultimately to Boethus and his commentary on the Categories. Simplicius did not have direct access to Boethus but knew his commentary indirectly, presumably through Porphyry and his major commentary on the Categories, the Ilpos FeSaXiov. (For a convenient discussion on the sources of Simplicius, see J. Barnes, ‘Homonymy in Aristotle and Speusippus', CQN.S. 21 [1971], 65–80; L. Taran, ‘Speusippus and Aristotle on homonymy and synonymy', Hermes 106 [1978], 73–99, and more recently Taran [n. 4], 406–14.) In the light of the previous discussion this can be nothing but a testimony about Speusippus'use of division. Nevertheless, Taran ([n. 4], 413–14) made an attempt to prove that this use is not neutral with respect to a particular theory of division. According to this theory, division is to be conducted by the strict application of the notions of identity and difference. Let us turn to Speusippus’ division of names. At a first stage names are divided into ravrovvixa and e'repaW/ja. But what about the second stage? In particular, what about the irepwwfuii They are divided into t&Uos erepwuvfia, iroXvuivvfui, and Trapcavvjw.. According to Taran, a third principle is here operative. Division is in fact conducted first on the basis of the notion of identity and difference, and then on the basis of the notion of similarity, in Greek SfioioTrjs. The reference to the notion of similarity is puzzling. In particular, it does not seem very helpful to describe the relationship which holds between paronyms by making appeal to the notion of similarity. DerivativenesS, a special kind of co-ordination, and ordering are clearly involved in paronymy. I do not want to enter into this further issue. I am content to claim that this particular division cannot provide evidence in favour of the attribution of a dichotomous method of division to Speusippus. Nor can it provide evidence in favour of the attribution of a particular theory of division to him. It merely confirms that Speusippus made use of division. More precisely, he made use of division in order to reach a classification of names. Division is in fact neutral with respect to the goal which may be chosen. Division may be an instrument of definition as well as of classification.