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ARISTOTLE'S COMPARATIVE LOGIC: A MODEST PROPOSAL*

Published online by Cambridge University Press:  06 October 2015

Luca Gili
Affiliation:
K.U. Leuven, Fonds Wetenschappelijk Onderzoek, Vlaanderen
Giuseppe Pezzini
Affiliation:
Magdalen College, Oxford

Extract

Both W.D. Ross's and J. Brunschwig's editions of Aristotle's Topics contain the following passage:

ἔτι εἰ τοῦ αὐτοῦ τινος τὸ μὲν μᾶλλον τὸ δὲ ἧττον τοιοῦτο· καὶ εἰ τὸ μὲν τοιούτου μᾶλλον τοιοῦτο, τὸ δὲ μὴ τοιούτου, δῆλον ὅτι τὸ πϱῶτον μᾶλλον τοιοῦτο. (Γ 119 a20-2)

The passage is translated in the revised Oxford translation as follows: ‘Moreover, if in any character one thing exceeds and another falls short of the same standard; also, if the one exceeds something which possesses the character, while the other exceeds something which does not, then clearly the first thing exhibits that character in a greater degree’.

Type
Research Article
Copyright
Copyright © The Classical Association 2015 

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Footnotes

*

We thank Carlo Natali, Tobias Reinhardt, Carlos Steel and CQ's anonymous referee(s) for their comments on a previous draft of this paper. The authors are responsible for any remaining mistakes or shortcomings.

References

1 The Complete Works of Aristotle. The Revised Oxford Translation, edited by J. Barnes (Princeton, 1984), 199.

2 Aristoteles Latinus. V 1–3. Topica. Translatio Boethii, fragmentum recensioni alterius, et translatio anonyma, ed. L. Minio-Paluello (Bruxelles-Paris, 1969), 59. Cf. also the Renaissance version of Pacius: ‘si alterum sit tali re magis tale, alterum non sit tali re tale, manifestum est’, etc. (Aristotelis Stagiritae Peripateticorum Principis Organum: hoc est, libri omnes ad Logicam pertinentes, Greaece et Latine Jul. Pacius a Beriga recensuit [Hanau, 1623], 603).

3 Aristote Topiques Livres I-IV, texte établi et traduit par J. Brunschwig (Paris, 1967), 74. In his notes on this passage, at 161 of his edition, Brunschwig acknowledges that all readings in the extant manuscripts and Alexander's lemma have the same meaning; however, Brunschwig fails to acknowledge that this meaning, as it has been rendered by his translation, contains a logical mistake of a certain magnitude.

4 Aristotele, Organon, a cura di G. Colli (Torino, 1955), 472.

5 Aristoteles, Topik, übersetzt und kommentiert von T. Wagner und C. Rapp (Stuttgart, 2004), 111.

6 Most translations are equivalent to Brunschwig's and to Barnes's revised Oxford translation: see also Aristotle. Organon V. Les Topiques, édite par J. Tricot (Paris, 1950), 113 and Aristoteles. Topik. Topik, neuntes Buch oder Über sophistischen Widerlegungsschlüsse, herausgegeben, übersetzt, mit Einleitung und Anmerkungen versehen von H.G. Zekl (Darmstadt, 1997), 129; A. Zadro (Aristotele. I Topici [Napoli, 1974]) and M. Zanatta (Aristotele. Analitici Secondi, Topici, Confutazioni sofistiche [Torino, 1996]) did no better. Other translations are slightly better, in the sense that they are not logically flawed; we will discuss them later.

7 Aristotelis Organon Graece, Pars Posterior. Analytica Posteriora, Topica, edidit T. Waitz (Leipzig, 1846), 470. Waitz's main concern seems to be that the τόπος at Γ 119 a20-2 is not paralleled in the previous discussion on the ‘preferable’ (τὸ αἱϱετόν). Therefore, Waitz suggests to treat the τόπος as if it were dealing with the ‘preferable’: his paraphrase, which echoes Alexander of Aphrodisias’ commentary, makes explicit the logical flaw of the common reading of this passage. It is difficult to establish whether Waitz intentionally stressed this inconsistency; we think, however, that his reading is not completely accurate: Aristotle is not talking any longer about τὸ αἱϱετόν at Γ 119 a20-2, but he wants to make a claim on comparison in general (be it a comparison between two or more αἱϱετά or not). We thank the journal's referee for discussion on this point.

8 Comparative logics are presented in a formal way by Casari, E. in his paper ‘Comparative logics’, Synthese 73 (1987), 421–49CrossRefGoogle Scholar. In this paper Casari underlines that Aristotle was the first to develop a comparative logic. On Aristotle's own comparative logic, see Casari, E., ‘Note sulla logica aristotelica della comparazione’, Sileno 10 (1984), 131–46Google Scholar; Gutiérrez, J.M. Gambra, ‘The topoi from the greater, the lesser and the same degree: an essay on the σύγκϱισις in Aristotle's Topics ’, Argumentation 26 (2012), 413–37CrossRefGoogle Scholar.

9 The only attempt at defining the status of the τόποι in Aristotle's works has to be found in Rhet. B 26, 1403 a17-19. On the status of the τόποι see T. Reinhardt, Das Buch E der aristotelischen Topik. Untersuchungen zur Echteitsfrage (Göttingen, 2000), 46. For a map of contemporary literature on the controversial nature of the τόποι see M. Schramm, Die Prinzipien der aristotelischen Topik (Munich and Leipzig, 2004), 89–107.

10 Oliver Primavesi defended the idea that the τόποι are forms of reasoning through which, given a certain proposition which needs to be proved, we can built a dialectical syllogism. Primavesi developed his theory on the basis of the dialogical argumentation theory, which Aristotle expands in Topics Θ; cf. O. Primavesi, Die aristotelische Topik. Ein Interpretationsmodell und seine Erprobung am Beispiel von Topik B (Munich, 1996), 83–101. Even though the τόποι do not have the structure of standard syllogism, we should not forget that Aristotle thought that all sound inferences may in principle be reduced to syllogistic (cf. Prior Analytics A 23 and A 32), but it is hard to see how this may be true in the case of many τόποι. In particular, in Topics Γ Aristotle expands a series of τόποι whose status is difficult to explain for two reasons:

(a) if we take this book as a treaty on comparative logic, all the rules that Aristotle introduces are theorems of a logic which is stronger than first-order logic (comparative logic, as it has been presented by E. Casari [n. 8], is an extension of first-order logic); however, since categorical syllogistic proves only a proper subset of the theorems of first-order logic (cf. on this J. Łukasiewicz, Aristotle's Syllogistic from the Standpoint of Modern Formal Logic [Oxford, 19572], especially 77–99; A. Rini, Aristotle's Modal Proofs. Prior Analytics A8-22 in Predicate Logic [Dordrecht, 2011], 11–31), it is clear that the rules that Aristotle expands in Topics Γ cannot be reduced to syllogistic;

(b) the doctrine of the praedicabilia, which plays a crucial role in the Topics (and, according to some scholars, in Aristotle's Prior Analytics too: cf. on this M. Malink, ‘A reconstruction of Aristotle's modal syllogistic’, History and Philosophy of Logic 27 [2006], 95–141), is absent in the section on comparatives in Topics Γ.

For these two reasons, it is difficult to establish whether Aristotle was committed to the properties of the comparatives, which he expands in Topics Γ (this understanding seems to be implied by Primavesi's interpretation [this note]: if all τόποι are schemes for drawing syllogisms, they should be understood as logical rules, whose validity Aristotle was taking for granted), or whether he simply took these arguments to be dialectical arguments, whose validity was not to be taken for granted, but which should have been able to persuade an opponent in a dialectical debate (this interpretation is suggested by Reinhardt in his monograph [n. 9]). Both possibilities are compatible with the text: the τόποι are in both readings the underlying argumentative forms of dialectical debates; as a consequence, even if we think that Aristotle accepted these arguments as valid logical rules, this does not necessarily mean that he was committed to the truth of the premises of these arguments. Our impression is that Aristotle tried to expand the rules of comparison in a formal way; later, when he tried to turn his (many) logics into a system, he thought that syllogistic could have been the underlying logic of dialectic too (cf. An. Pr. A 24 a22-8). This is why Aristotle introduced syllogisms as the standard inference for dialectic too in the very first chapter of the Topics (cf. Top. A 100 a18-b23). However, this attempt at building a system was not succesful, as we have noted above, when we underlined that comparative logic cannot be reduced to syllogistic. Nevertheless, the τόποι expound properties that Aristotle was presumably endorsing, if our reconstruction is correct. However things might be, the properties of the comparative relations should make appeal to the common understanding of these relations, so that the τόποι concerning comparative relations may usefully result in a dialectical debate. In other words, even though Aristotle might have been sceptical regarding their logical truth, as Reinhardt seems to suggest, these τόποι should be accepted by most people. On the status of dialectic in the context of Aristotle's scientific research, see also W.A. de Pater, Les Topiques d'Aristote et la dialectique platonicienne (Fribourg, 1965); J.D.G. Evans, Aristotle's Concept of Dialectic (Cambridge, 1977); P. Slomkowski, Aristotle's Topics (Leiden, New York and Cologne, 1997); Wlodarczyk, M., ‘Aristotelian dialectic and the discovery of truth’, OSAPh 18 (2000), 153210 Google Scholar.

11 Aristoteles. Topik, neu übersetzt und mit einer Einleitung und erklärenden Anmerkungen versehen von E. Rolfes (Leipzig, 1919), 60. W.A. Pickard-Cambridge's translation had the same reading in its original form, before the revision by J. Barnes (cf. The Work of Aristotle translated into English, under the editorship of W.D. Ross, vol. 1 [Oxford, 1928], ad loc.). The Loeb translation by E.S. Forster is more elliptical, but, as will be shown later (cf. n. 28), is probably the most accurate, as regards both language and logic.

12 In other words, the relation ‘more than’ (as well as its reverse ‘less than’) appears to have the property of trichotomy. This aspect is extremely interesting from the logical viewpoint, and if this were what Aristotle had in mind, his remarks would no longer be trivial, or even unsound, but highly relevant.

13 The forms τοιοῦτον and τοιοῦτο are mere variants, morphologically and semantically equivalent (cf. LSJ ad loc.). Henceforth they will be referred to, without distinction, as τοιοῦτο(ν).

14 For word order a. (verb, comparative, second term of comparison) cf. e.g. Met. M 1082 b19-21: εἴτε δὲ μὴ ἔστι πλείων ἀϱιθμὸς ὁ τῆς τϱιάδος αὐτῆς ἢ ὁ τῆς δυάδος, θαυμαστόν. For word order b. (second term of comparison, comparative, verb) cf. e.g. Pol. B 1265 b7: ὥστε ἀϱιθμοῦ τινὸς μὴ πλείονα γεννᾶν. For word order d. (second term of comparison, verb, comparative) cf. e.g. Met. N 1088 b10-11: οἷον ἡ δεκὰς πολύ, [καὶ] εἰ ταύτης μή ἐστι πλεῖον. Finally, for word order e. (comparative, second term of comparison, verb) cf. e.g. [Oec.] B 1346 a16: τὸ τἀναλώματα μὴ μείζω τῶν πϱοσόδων γίνεσθαι.

15 ‘Again in another sense that which happens to something else in virtue of the latter's own nature is said to happen to it per se; while that which does not so happen is called an accident.’

16 ‘But if AB is not necessary, but BC is necessary.’

17 For the use of μή with noun, adjectives or participles (a use traditionally explained as being ‘generic’ as opposed to the ‘referential’ use of οὐ) see R. Kühner and B. Gerth, Ausführliche Grammatik der griechischen Sprache: Zweiter Teil (Hannover and Leipzig 1904), 2.197-203, especially 201-2. For a more recent and sophisticated account see E. Gerö, Negatives and Noun Phrases in Classical Greek (Frankfurt am Main, 1997), with her supplementary article in Glotta 77 (2011), 38–55. Cf. also J. Wackernagel, Lectures on Syntax, trans. D. Langslow (Oxford, 2009), 729–33, 752–4; Laird, A.G., ‘When is generic μή particular?’, AJPh 43 (1922), 124–45Google Scholar; A.C. Moorhouse, Studies in the Greek Negatives (Cardiff, 1959), 36–40. In our passage the conditional context (καὶ εἰ …) would probably be enough to account for the use of μή (on this use see Wackernagel [this note], 750–1).

18 For the view that in Greek the negative particle is immediately placed before the word that is negatived, cf. e.g. Kühner and Gerth (n. 17), 2.179; LSJ s.vv. οὐ D, μή D. For a criticism of this view as ‘misleading oversimplification’, cf. Moorhouse (n. 17), 75–6, 89–120.

19 ‘It is possible also that an argument, even though brought to a conclusion, may sometimes be worse than one which is not so concluded.’

20 ‘That which naturally has a certain quality has that quality in a greater degree than that which possesses it not naturally.’ Cf. Alex. Aphr. ad loc. (p. 276.9): τὸ ϕύσει ἀγαθὸν τοῦ μὴ ϕύσει αἱϱετώτεϱον.

21 ‘If [the principles] are not better known to him than the conclusion, he will have his knowledge only incidentally.’

22 From a semantic (and thus syntactic) point of view, the sentence with the negative particle negating only the predicate phrase (τοιούτου) μᾶλλον τοιοῦτο (‘is [ not possessing the character to a greater degree]’) is equivalent to both the one with the negative particle negating the (implied) copula ἐστι (‘is not [possessing the character to a greater degree]’) and the one with the negative particle negating the whole clause (‘ not [is possessing the character to a greater degree]’).

23 ‘Or shall we rather say that there is no one (who deals) with properties of the matter which are not separable nor yet treated as separable, but the physicist deals with all the active properties or passive affections belonging to a body of a given sort and the corresponding matters? (…) When on the other hand the qualities, though inseparable, are regarded not as properties belonging to a body of a given sort and are treated abstractly, they fall within the province of the mathematician.’

24 The ‘detachment’ of the negative particle from the word expectedly negatived (the predicate in a clause or the head in a phrase) is also to be related to a (primeval) tendency of the negative particle to be placed in an initial position: in Herodotus, for instance, in negative conditional protases the particle μή is normally found in first position (87%), often detached from the verb (57%); for these figures and a discussion of the tendency and its development in the history of Greek, see Moorhouse (n. 17), 75–6, 82–120. On the syntax and position of the negative see also Wackernagel (n. 17), 725–34, 751–4.

25 It is perhaps worth mentioning that, according to the analysis of negation in the Peripatetics, in a proposition the negative adverb always negates the copula (cf. Alex. Aphr. in An. Pr. 402.1–405.16). In our case the copula would be the implied ἐστι (μᾶλλον τοιοῦτο), which, if negated by μή, would indeed produce the meaning required by the interpretation we envisage (‘is not possessing the character to a higher degree …’; cf. above, n. 22). In other words, the explicit view of Aristotle's school on the syntactic role of negation might be compatible with our understanding of the syntactic role of μή in the text under investigation. For the peripatetic analysis of negation see Barnes, J., ‘Peripatetic negations’, OSAPh 4 (1986), 201–14Google Scholar. For Aristotle's analysis see W. Cavini, La negazione di frase nella logica greca, in W. Cavini, M.C. Donnini Macciò, M.S. Funghi, D. Manetti (edd.), Studi su papiri greci di logica e medicina (Florence, 1985), 7–126, especially 7–45.

26 ‘Furthermore, if both terms apply or do not apply to some of the middle, or if one applies to some and the other does not, or if one applies to some and the other does not apply to all, or if they are related to the middle indefinitely, there will in no case be a syllogism’.

27 As pointed out by Wallies in the preface of his edition (p. xi), manuscript P (Parisinus 1874, saec. xiii), although often corrupt, is occasionally carrier of good readings.

28 This translation is essentially the one provided by the Loeb edition, which thus seems to be one of the most correct, although it does not explicitly discuss the issue.

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