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Aristotle on ‘Signifying One’ at Metaphysics Γ 4

Published online by Cambridge University Press:  01 January 2020

Michael L. Ross*
University of Dallas, Irving, TX75062-4799, USA


I Introduction

At Metaphysics Γ 3, Aristotle argues that it belongs to a single discipline, which he calls first philosophy, to investigate both substance (οὐσία) and a special class of claims which includes among its members the principle of non-contradiction (PNC). At Γ 4, after insisting that the PNC is, strictly speaking, indemonstrable, he sets forth a series of sketches of refutative arguments intended to show how it can, nonetheless, be substantiated. Traditionally, his main refutative argument has been taken to be embedded in the passage which runs from 1006a31 to b34. In that passage, he tries to show that anyone who denies the PNC and who can then be led, by means of an artfully arranged series of questions, to agree (whether willingly or grudgingly) to a few seemingly modest theses about the signification of expressions of a certain type — which Aristotle illustrates with the general term ‘man’ (ἄνθρωπος) — is thereby logically committed to the following modal claim: ‘It is necessary, then, if it is true to say that something is a man, that it be a bipedal animal' (1006b28-30).

Research Article
Copyright © The Authors 1995

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I wish to thank Professors Calvin G. Normore, Joseph J. Owens, C.Ss.R., and John M. Rist for discussing many of the issues dealt with herein and commenting on earlier drafts. I also wish to express my gratitude to the anonymous referees for the Canadian Journal of Philosophy for their comments, many of which were insightful and all of which were helpful and appreciated.


2 At Γ 3, he formulates the PNC as follows: ‘It is impossible that the same thing both belong and not belong to the same thing at the same time and in the same respect.’ Aware that this formulation may prove inadequate for certain purposes, Aristotle immediately adds: ‘ … and should we need to make any other qualifications, let them be made <as needed> to meet dialectical difficulties’ (1005b19-22). (For a similar statement of Aristotle's willingness to produce qualifications ad hoc, see his de Interpretatione 17a36-37. Plato expresses similar sentiments in his Republic 436b-437a). Aristotle's Greek is this: In this paper I follow Jaeger's edition of the Greek text, Aristotelis Metaphysica (Oxford: Oxford University Press 1957). All translations of Aristotle's texts are mine.

3 The views of Alexander of Aphrodisias (fl. 200 AD) and St. Thomas Aquinas (c. 1225-1274) are fairly representative. Both treat Aristotle's argument as holding for any being. Consequently, both hold (at least implicitly) that it works for a much wider range of expressions than just substance terms. For Alexander's position, see his In Aristotelis Metaphysica Commentaria (Hayduck, Michael ed., Commentaria in Aristotelem Graeca [hereafter, CAG], 1 [Berlin, 1891], 276.3-7Google Scholar. For Aquinas’ position, see In Metaphysicam Aristotelis Commentaria (Cathala, M.R. ed. [Turin: Marietti 1935]), IV, lect. 7, no. 613.Google Scholar

4 The most secure principle is, according to him, (apparently, uniquely) identifiable as that principle about which it is impossible to be mistaken On the assumption that the PNC does hold for everything, it is impossible, he says, to be mistaken about the PNC. Thus, he concludes, the PNC is the most secure of all principles. In Aristotle's view, being mistaken about the PNC would, were such a mistake possible, require believing at one and the same time both that something or other is the case and that it is not the case. But the PNC — for reasons I will not go into — is said to rule out the possibility of anyone adopting such a stance. Some of his argument's missing premises are explicitly stated at Γ 6, 1011b13-22.

5 For his theory, see Posterior Analytics I. For remarks bearing on the axioms, see (in the same work) I 2, especially 72a14-19, I 10, esp. 76a31-b23, and I 11, esp. 77a10-35.


7 While I would not claim that Aristotle was as alert to the distinction between asserting and, say, entertaining a proposition as was Frege, neither would I agree that he was oblivious to it. His own version of dialectic as employed in the philosophic branches of knowledge, for example, rests upon such a distinction. See Topics I 2 (101a25ff) and VIII 5 (159a25ff).

8 Aristotle even grants that the disputant might with justification balk if asked the sort of leading question which would require him to answer by saying either that something is the case or that it is not (1006a20-21).


10 Aristotle recognizes that the disputant might not concede this claim. If he does not, however, Aristotle advises that further interrogation would be pointless (1006a22- 24; cf. a13-15). In any case, Aristotle clearly thinks that he will have shown that the PNC is amenable to refutative demonstration whether or not any particular opponent of the PNC would play along or be persuaded so long as signifying something is a prerequisite for saying something. I am then in sympathy with Alan Code's suggestion that Aristotle is setting forth both an elenctic argument and a meta-elenctic argument. On the rationale for this reading of Aristotle's discussion, see pp.145ff of Code's, Metaphysics and Logic,Aristotle Today: Essays on Aristotle's Ideal of Science, Matthen, Mohan ed. (Edmonton: Academic Printing & Publishing 1987), 127-49CrossRefGoogle Scholar. It is worth noting that Aristotle has not, thus far, specified what sorts of expressions can be used to say something.

11 It should be noted that my translation of the explicans differs from other English translations — indeed from all other translations that I am aware of — in one important respect. It is standard practice among translators to treat its first clause, which I have translated as ‘if man is that,’ as the antecedent of a consequent conditional, and its second clause, which I have translated as ‘if man is anything,' as the antecedent in that consequent conditional. Thus, it is standard practice among translators to interpret the explicans according to the form P ⊃ (Q ⊃ R). In contrast, I treat the second clause as an antecedent embedded in a larger antecedent whose consequent is the final clause, which I have translated ‘[being] that will be man's [essential] being.’ Thus I read the whole complex conditional as saying that if it is the case that man is either a bipedal animal or nothing at all, then being a bipedal animal is man's essential being.


13 My use of this designation is intended neither to indicate my views on how Γ 4 should be divided nor to prejudice such issues. Aquinas, (In Aristotelis Metaphysica, IV, 7, 611)Google Scholar, Ross, W.D. (Aristotle's Metaphysics [Oxford: Clarendon Press 1924], 265-8)Google Scholar, and Kirwan, Christopher (Aristotle's Metaphysics, Books Γ, △, E 2nd ed. [Oxford: Clarendon Press 1993], 90105)Google Scholar divider Γ 4 into seven arguments. The main argument falls within Aquinas’ first (1006a28-1007a20), Ross's first (1006a28-1007b18), and Kirwan's second argument (1006a31-1007b18). Kirwan subdivides his second argument into three parts, the first of which coincides with my main argument. The main argument also falls within Dancy's, RM. (Sense and Contradiction: A Study in Aristotle [Boston: D. Reidel 1975], 28)CrossRefGoogle Scholar first refutation (1006a11-b34).

14 The following are some of the more recent —1986 to the present— discussions which, at least in part, take up this task (starting with the most recent): (1) Gottlieb, PaulaThe Principle of Non-Contradiction and Protagoras: The Strategy of Aristotle's Metaphysics IV 4, Proceedings of the Boston Area Colloquium in Ancient Philosophy, Cleary, John J. ed., 8 (1992), 183-98CrossRefGoogle Scholar; (2) Degnan, MichaelDoes Aristotle Beg the Question in His Defense of the Principle of Non-Contradiction,Proceedings of the American Catholic Philosophical Association 63 (1990) 146-59CrossRefGoogle Scholar; (3) Irwin, T.H. Aristotle's First Principles (Oxford: Clarendon Press 1988), esp. 179-88Google Scholar; (4) Lear, Jonathan Aristotle: The Desire to Understand (Cambridge: Cambridge University Press 1988), esp. 249-65CrossRefGoogle Scholar; (5) Alan Code, ‘Metaphysics and Logic'; (6) Code, AlanAristotle's Investigation of a Basic Logical Principle: Which Science Investigates the Principle of Non-Contradiction?Canadian Journal of Philosophy 16 (1986) 341-57CrossRefGoogle Scholar; (7) Cohen, S. MarcAristotle on the Principle of Non-Contradiction,Canadian Journal of Philosophy 16 (1986) 359-70CrossRefGoogle Scholar; and (8) Furth, MontgomeryA Note on Aristotle's Principle of Non-Contradiction,Canadian Journal of Philosophy 16 (1986) 371-81.CrossRefGoogle Scholar

15 Kirwan sums up the thoughts of many commentators, confessing that he finds the Main Argument an ‘extraordinarily mystifying argument’ (93). Anscombe, G.E.M. in her essay ‘Aristotle’ (in Three Philosophers [Ithaca: Cornell University Press 1961])Google Scholar, is referring to a section which includes the Main Argument when she speaks of ‘[a] long, difficult and bad-tempered passage in Metaphysics Γ’ (39).

16 Among recent commentators, the following (more or less) expressly state this claim: Anscombe, 39-43; Lear, in his Aristotle and Logical Theory (Cambridge: Cambridge University Press 1980), 109Google Scholar; Furth, ‘A Note …,’ 376-7Google Scholar; Code, ‘Metaphysics and Logic,’ 148Google Scholar; Lear, Aristotle, 257-64Google Scholar; and Gottlieb, ‘The Principle of Non-Contradiction,’ 192-5Google Scholar. In the early part of this century, Jan Lukasiewicz, whose interpretation of the Main Argument may have influenced some later commentators, contended that in Aristotle's view the PNC is ‘ … a metaphysical truth which holds primarily of substances and whose application to the world of appearances is at least dubious’ (58). Lukasiewicz's ‘Uber den Satz des Widerspruchs bei Aristoteles’ was originally published in Bulletin International de l'Academie des Sciences de Cracovie, Cl. d'histoire et de philosophie, 1910. I am following Jonathan Barnes's translation of Lukasiewicz's article, Aristotle on the Law of Contradiction,’ which is found in vol. 3 of Articles on Aristotle, 4 vols. Barnes, J. Schofield, Malcolm and Sorabji, Richard eds. (London: Duckworth 1979), 5062.Google Scholar

17 For example, Dancy thinks that, provided the argument works at all, it works for all predicates, 34 and 54. Michael V. Wedin also thinks that the argument works— or, at least, can be interpreted as working— for all predicates. (See his ‘Aristotle on the Range of the Principle of Non-Contradiction,’ Logique et Analyse [1982], 87-92.) Edward Halper, although he says that the argument works for any significant name, seems to hold the same position as Dancy, and Wedin, . (See his ‘Aristotle on the Extension of Non-Contradiction,History of Philosophy Quarterly 1 [1984] 369-80.Google Scholar) Irwin appears to hold that the argument works for any category term which can function as a subject term, 184. Although he does not explicitly say so, it looks as though Irwin holds that the argument works for any ordinary proper name which refers to an individual belonging to a category.

18 The only exception I am aware of is Dancy. He argues that, contrary to what Aristotle may have thought, the main argument (actually, what he calls the first refutation, but the difference can be ignored here) requires Fregean senses rather than essences as significates (xi-xii). Lear apparently held the former position (that the Main Argument requires significates having essences) first (Aristotle and Logical Theory, 104-9) and adopted the latter position (that it requires significates which are essences) later (Aristotle, 256-9). Charles, David argues for the former position in his recent ‘Aristotle on Names and their Signification,’ 66-7Google Scholar. His article appears in vol. 3 of Companions to Ancient Thought: Language, Everson, Stephen ed. (Cambridge: Cambridge University Press 1994) 3773.Google Scholar

19 Of recent commentators, these (more or less) expressly state this claim: Anscombe, 39-43; Furth, 376; Code, ‘Metaphysics and Logic,’ 146Google Scholar; Lear, Aristotle, 257-8Google Scholar; and Gottlieb, 192-5. Because Anscombe eschews the word ‘essence’ as an unhelpful and misleading rendering of certain of Aristotle's technical phrases (for her reasons, see 24, 34-5, and 43), it may not be immediately apparent that she shares this position. (Furth also attributes this position to her. See n.3, 376.) For the doctrine that the essences of substances are primary, see Metaphysics VII 4 (1030a29-b7) and VII 5 (1031a10-14).

20 For example, Wedin, 89; Halper, 373-9; and Irwin, 182-3.

21 These include Anscombe, 39-43; Furth, 376-7; Code, ‘Metaphysics and Logic,’ 146Google Scholar; Lear, Aristotle, 257-9Google Scholar; and Gottlieb, 192-5.

22 These include Anscombe, 39-43; Furth, 376-7; Code, ‘Metaphysics and Logic,’ 146Google Scholar; and Lear, Aristotle, 257-9Google Scholar.

23 I here emphasize the word ‘term’ to avoid a confusion which might arise should it be observed that Aristotle also holds that some complex expressions (i.e. definitions [understood more or less strictly]) signify essences. The Main Argument is designed to run on terms, not definitions — which is not to say that definitions play no role therein. For his doctrine that definitions signify essences, see, e.g, Posterior Analytics II 11 (94a34-35), Topics I 4 (101b19-22), I5 (101b38-102a1), I8 (103b9-11), V 3 (132a1-6),and VII 5 (154a31-32).

24 My claim that A2 implies A1 is consistent with and, therefore, slightly strengthened by the position taken by proponents of A2. For, of the commentators I have surveyed, all who hold/held A2 (listed in note 18) also at the same time hold/held A1, but not all who hold/held A1 (listed in note 15) also at the same time hold/held A2.

25 Thus, if neither A1 nor A2 depends on the Clinching Argument for its textual justification, attempts (such as Wedin's) to prove that the Main Argument is not so-restricted by showing how the Clinching Argument is generalizable to a wider range of beings will be ineffectual against restrictive interpretations of the whole argument based on A1 and/ or A2.

26 I have omitted the phrases ‘signifying just what’ and 'signifying of one’ an adequate treatment of either phrase would require a lengthy discussion. Nevertheless, I have a few remarks to make about the latter phrase which are germane to my discussion. At 1006b13ff, Aristotle indicates that the Main Argument presupposes that’ … “man“ signifies not only of one but also one.’ Explaining this claim, he adds— I am now paraphrasing: For we do not maintain that signifying one is the same as signifying of one, although even if they were, contrary to our position, the same [it would not help the disputant, for], ‘pale,’ ‘musical,’ and ‘man’ would then have signified one, with the result that all pale things, musical things, and humans would be one. Some commentators (including the proponents of A1) have taken Aristotle's distinction here to correlate with a distinction between terms that are essentially and/or non-accidentally predicated (e.g. ‘man’) and terms that are accidentally predicated (e.g. ‘pale’ and ‘musical’). Against these commentators’ position, I have four brief points to raise: (1) The position they take requires them to see Aristotle's distinction not simply as a distinction between signifying one and signifying of one, which is what his remarks first suggest, but as a distinction between terms that signify one (e.g. 'man’) and terms that signify of one (e.g. ‘pale’). (2) More precisely, since these commentators hold that no accidentally predicated terms signify one and since Aristotle explicitly says that “'man” signifies not only of one but also one,’ their position requires them to redraw his distinction as a distinction between terms that signify both one and of one (e.g. ‘man’) and terms that signify only of one (e.g. ‘pale’). (3) For Aristotle, no terms signify only of one. H a term signifies of one, then it is a predicate which (when functioning as such) signifies something of the one thing of which it is predicated. (For a supporting text, see Physics 186a32-33.) (4) At de Int. 18a12ff, Aristotle says that those affirmative and negative statements are accounted single which ‘signify one of one.’ The examples he gives include ‘Every man is pale,' 'Man is pale,’ and ‘Some man is pale.’ Now, if any of these sentences is a single statement, then the predicate ‘pale,’ which in all three sentences is accidentally predicated, not only signifies of one but also signifies one.

27 My use of ‘name’ is intended to cover any expression which, for Aristotle, counts as an In this paper, then, the class of names includes general terms.


29 It should be recalled that Aristotle earlier described saying something as having a public character. For in order to say something the disputant must, Aristotle says, signify something both to himself and to someone else. According to the conclusion now under discussion, the denial that names signify one undermines more than public discourse, it also undermines ‘talking to oneself.’ Aristotle's reasons for asserting this latter point are tied to his theory of cognition. Immediately after drawing the above conclusion he explains, ‘for it is not even possible to think unless thinking one.’ The Greek is this: ‘….….’ (1006b10)

30 Recent commentors who hold that S1 does represent his position include Irwin, 224;Halper,374;code,'metaphysics and logic;146; and Gottlieb,192.


32 This claim is also presupposed by Aristotle at de Interpretatione 18a12-27. Very few commentators on de Int. 18a12-27 have called attention to the presence of this claim. Here are four who have: (1) Ammonius (435/ 445-517/26 AD). See his In Aristotelis De Interpretatione Commentarius, Busse, Adolfus ed., in CAG 4.5 (Berlin, 1897), 126.21-26Google Scholar. (2) The anonymous author of a commentary written in either the late sixth or the seventh century AD. See the Anonymous Commentary on Aristotle's De Interpretatione (Codex Parisinus Graecus 2064), Tarán, Leonardo ed., Beoträge zur Klassische Philogie 95 (Meisenheim am Glan 1978), 52.6-7Google Scholar. (3) Peter Abelard (1079-1142). See his Super Aristotelem De Interpretatione, Pra, Mario Dal ed., in Pietro Abelardo: Scritti Filosofici (Rome: Fratelli Bocca 1954), 98.43-99.2.Google Scholar (4) Walter Burley (1275-c.1345). See his Questiones In Librum Perihermeneias, Brown, Stephen F. ed., in Franciscan Studies 34 (pp. 200295), n. 1.86.Google Scholar

33 Kirwan's judgment is yet more severe. Referring to the claim I represent by S1, he states that it is ‘a doctrine absurd in itself and contradicted by a34’ (94).

34 Here are a few terms which are said to signify many: ‘perceiving’ (Topics 129b33), and (S.E. 166a16), ‘being’ and ‘unity’ (S.E. 170b22; see also Physics 186b11 on ‘being’), and ‘both’ and ‘all’ (S.E. 181b20). Aristotle also mentions complex expressions which signify many. E.g. the sentence ‘[A] cloak is white’ (de Int. 18a25), the phrase ‘knowing this’ (Topics 130a20), and the phrase ‘knowing letters’ (S.E. 166a18ff).

35 It might be objected that the other general claim at work in the argument from discrete signification is not S3 but something like this:

For any term t, if t signifies many, then either (a) t has a limited number of significates or (b) it has an unlimited number.

This cannot, however, be Aristotle's point. For this claim would leave it open to the disputant both to concede that ‘man’ has a limited number of significates and to pick a number of significates large enough to render a complete assignment of names to significates either unfeasible or humanly impossible. Kirwan comes to the same conclusion, saying that’ Aristotle's argument does not in fact require that the significations of a name be finitely many, but only that there be unit significations, like points on a line … ‘ (94). Kirwan's phrase ‘unit signification’ nicely captures Aristotle's idea; however, unit significations would be better compared to Aristotle's classification of numbers (at Categories 4b20ff) as discrete quantity than to points.

36 For the Greek, see n.29 above.

37 The term ‘subordinated’ is borrowed from William Ockham (c.1285-1356), who at Summa Logicae I, c.1 (Boehner, P. Gal, G. and Brown, S. eds., Opera Philosophica, Vol. 1 [St. Bonaventure, NY: Franciscan Institute 1974])Google Scholar writes:

‘Dico autem voces esse signa subordinata conceptibus seu intentionibus animae, non quia proprie accipiendo hoc vocabulum ‘signa’ ipsae voces semper significent ipsos conceptus animae primo et proprie, sed quia voces imponuntur ad significandum illa eadem quae per conceptus mentis significantur … ‘ (italics mine).

One of the more interesting corollaries of Ockham's subordinationism is the following: Assuming that thoughts or ideas naturally signify the very items which expressions (subordinated to those ideas) conventionally signify, if an idea were to change from signifying one item to signifying another, the expression subordinated to it would simultaneously change from signifying the original item to signifying the other. (For Ockham's formulation, see his Expositio In Librum Periherminias Aristotelis, Lib. I, Prooernium,2, Gambatese, A. and Brown, S. eds., Opera Philosophica, Vol. II [St. Bonaventure, NY: Franciscan Institute 1978].)Google Scholar Bracketing off disputes over details, Aristotle's account of language, thought, and reality which he briefly states at de Int. 1, 16alff has traditionally been construed as involving this anti-Fregean corollary. The traditional subordinationist reading of de Int. 1, 16alff has, however, been indirectly challenged recently by two authors. Kretzmann, Norman (‘Aristotle on Spoken Sound Significant by Convention,’ in Ancient Logic and Its Modern Interpretations, Corcoran, J. ed. [Dordrecht-Holland: D. Reidel 1974], 331)CrossRefGoogle Scholar and Magee, John (Boethius on Signification and Mind, in Philosophia Antiqua 52, Verdenius, W.J. and Winden, J.C.M. Van eds. [Leiden: E.J. Brill 1989])CrossRefGoogle Scholar each proposes a novel interpretation of the text which undermines the subordinationist reading.

38 If it were otherwise, a single mind could be simultaneously actualized by two different acts of thinking. Cf. de Anima I.3 407a6ff. The acts of thinking here in question are in some manner non-complex. Cf. de Anima III.6 430a26ff.

39 This seems to be very close to a position held by John Duns Scotus (c.1266-1308). In his Primum Librum Perihermenias Quaestiones, Q. 2 (in Opera Omnia, I, Gregory, T. ed. [Hildesheim: Georg Olms 1968])Google Scholar, he claims that ‘… aequivocum … diversis actibus significandi significat multa.’

40 Any occasion on which P thinks just one (appropriate) thought corresponding to t will count as a single occasion. Use would not be a reliable guide for demarcating occasions. For equivocal terms are expressions which can be used just once and yet prompt (on the side of the listener) or be prompted by (on the side of the speaker) a succession of thoughts. On the difficulties of temporally correlating utterances and thoughts, see Geach, Peter Mental Acts: Their Content and Their Objects (London: Routledge & Kegan Paul 1957), 104-6.Google Scholar

41 Cf. the medieval maxim omne aequivocum reducatur ad univocum. See, for example, Aquinas, In Librum Boetii De Trinitate, Prooem., q.1, a.4, ad 4; Summa Theologiae, I.13.5, obj.l. Peter Abelard, in his Super Aristotelem De lnterpretatione illustrates one way in which a term can be reduced from equivocity to univocity. He writes: ‘Sed dicamus: latrabile animal est canis; in hoc actu canis <ex> aequivocatione reducitur ad univocationem per suum subiectum, id est latrabile animal…’ (70.33-36).

42 My case against A1 and A2 is perhaps further confirmed by evidence outside the Metaphysics. In both his de Interpretatione (18a17) and Physics (186a26-27), the adjective 'pale’ is treated as a term which signifies one. This would be disallowed if Aristotle held either A1 or A2. Kirwan, therefore, incorrectly supposes that ‘signifying one'’ … is an expression not used elsewhere by Aristotle’ (94).

43 Among recent attempts at sorting out Aristotle's remarks on signification, the most ambitious is Irwin's, T.H.Aristotle's Concept of Signification,Language and Logos: Studies in Ancient Greek Philosophy Presented to G.E.L. Owen, Schofield, Malcolm and Nussbaum, Martha eds. (Cambridge: Cambridge University Press 1982) 241-66.CrossRefGoogle Scholar

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