Aristotle on the Non-Cause Fallacy

Abstract

When in classical formal logic the notions of deduction, valid inference and logical consequence are defined, causal language plays no role. The founder of western logic, Aristotle, identified ‘non-cause’, or ‘positing as cause what is not a cause’, as a logical fallacy (NCF). I argue that a systematic re-examination of Aristotle's analysis of NCF, and the related language of logical causality, in the Sophistical Refutations, Topics, Analytics and Rhetoric, helps us to understand his conception of (‘syllogism’). It reveals that Aristotle's syllogismhood is non-monotonic, and thus narrower than classical validity as consisting in, or coextensive with, necessary truth-preservation. It also supports the conclusion that a syllogism is a form of relevant consequence: the premisses must be causes of the conclusion in the sense that they are not only sufficient but also necessary for the conclusion to follow. Close analysis of NCF also suggests that syllogistic relevance is not a semantic matter, but a syntactic one: all premisses must be used in the chain of syllogistic deduction leading to the conclusion. Aristotelian syllogistic cannot therefore be accommodated within the framework of classical consequence—as its first interpretations ‘from a modern standpoint’ in the first half of the twentieth century attempted to do.

Acknowledgements

Many thanks to audiences in Groningen, Oxford and Cagliari, and especially to David Charles, Paolo Crivelli, Paolo Fait, Pieter Sjoerd Hasper, Francesco Paoli and an anonymous referee, for their comments on earlier drafts of this article. The preparation of the article was facilitated by the generous support of the Leverhulme Trust, who awarded me a Fellowship for the period January 2014–March 2015.

Notes

¹Compare, for example, Smith 1997, pp. xi–xxxiv; Slomkowski 1997, ch. 1.

²On the issue of the best translation for (‘syllogism’ vs. ‘deduction’), cf., for example, Barnes 1981; Mignucci 2002; Striker 2009, pp. 78–9.

³Adapting the distinction between ‘ostensive’ and ‘through (to) the impossible’ syllogisms of APr. (cf., e.g. 2.14, 62b29–32).

⁵Compare, for example, Gobbo 1997b, p. 342; contra Schreiber 2003, p. 217: ‘Aristotle nowhere in S.E. restricts Non-Cause fallacies to reductio arguments’.

⁶Compare, for example, Hamblin 1970, p. 89, 206. On this interpretation, the non-cause fallacy would be related to the well-known question of how the Socratic elenchus can reveal not only the inconsistency of the premisses, but more precisely the falsehood of one of them.

⁷For the point that and are two of the species of the genus of ‘opposites’ ( ) cf. Cat. 10, 11b17–23.

⁸Sometimes this is also referred to simply as , ‘what is posed’, or as ), ‘what was at the beginning’ (from which our ‘begging the question’ jargon: cf. Castagnoli 2012).

⁹For an interpretation along these lines, cf., for example, Sorio 2009.

¹⁰Compare Smith 1989, p. 117.

¹¹Contra Hasper's (2012) translation ‘secures in addition’ and Woods and Hansen 2001, p. 403.

¹²This raises interesting questions, which I cannot explore here, concerning the criteria of identification of ‘arguments’ within the context of dialectical practice.

¹³The passage is misinterpreted by Woods and Irvine 2004, p. 90: ‘In other places, Aristotle suggests a less technical interpretation of the fallacy, in which the trouble with R would simply be its falsity’.

¹⁴Compare Smith 1989, pp. 141–2.

¹⁵On arguments through the impossible cf. also APr. 1.44, 50a29–32; 1.29, 44; 2.11–14; APo. 1.26; Top. 8.14. On these arguments, and arguments ‘from a hypothesis’ more generally, cf. Crivelli 2011.

¹⁶For in-depth analysis of SE 6 and its relevant context, cf. Gobbo 1997a and Malink 2014.

¹⁷For the ‘compositional use’ of , cf. Fait 2004.

¹⁸Most manuscripts do not read ; it is debatable whether the phrase is a later addition on the basis of Topics 1.1 (see T7 below). In the absence of there would not be anything equivalent to the clause in the SE version of the definition of (see below).

¹⁹This is interesting from the point of view of a developmental study of the parts of the Organon, which I cannot undertake here. Brunschwig 2007, p. 293 claims that the fact that NCF in the Topics (see Section 2 below) refers to the Analytics definition of is a piece of evidence for the claim that Topics 8 was written after the Analytics, which were written, in turn, after Topics 1.

²⁰Other translations include: ‘because these things are so’ (Smith 1989; Striker 2009); ‘du fait que celles-là sont’ (Crubellier 2014); ‘par le fait que ces choses sont<le cas>’ (Brunschwig 2007); ‘in virtue of the fact that these are the case’ (Frede 1974); ‘by their being the case’ (Barnes 1980); ‘in virtue of the fact that they are there’ (Mignucci 2002).

²¹For this well-known Aristotelian tenet, cf., for example, APo. 1.2, 71b17–22; 1.13, 78b11–13.

²²Schreiber 2003, p. 107 confounds the concept of causation operative in the definition of syllogism and in NCF and that operative in the Aristotelian conception of demonstrative syllogism: ‘What Aristotle means by calling the premises “causes” (aitiai) of the conclusion is that the state of the world signified by the premises explains the state of the world signified by the conclusion’ (cf. also p. 112).

²³Compare, for example, Charlton 1992, p. 100.

²⁴For discussion of this difficult passage, cf., for example, Ross 1949, pp. 638–42; Dancy 1978, pp. 373–7; Barnes 1993, pp. 226–7; Wehrle 2000, pp. 8–11; Mignucci 2007, pp. 278–80.

²⁵The shift from the premisses to the terms used in them might be due to the fact that in ‘non-perfect’ or ‘incomplete’ syllogisms some transformations of the premisses, and thus additional propositions, are needed, at least to make the necessity evident—but these propositions will include the same terms.

²⁶Compare, for example, Lear 1980; Mignucci 2002, p. 249; Woods and Irvine 2004.

²⁷Compare, for example, Fait 2007, p. 129. We will see in Section 3 that Aristotle uses +accusative in his discussion of NCF in the Analytics. For an occurrence of +accusative in SE with reference to NCF see 8, 170a1–2, where Aristotle claims that a type of apparent refutation occurs when, in a reductio ad impossibile, the conclusion ‘does not follow because of the argument’ ( ). I take this to be compatible with the interpretation according to which what does not follow because of the full set of premisses (the logos) is the impossible conclusion.

²⁸Notice that some Greek (and Aristotelian) usages of +genitive have causal force (cf., e.g. Metaph. H3, 1043b8–10: ‘if the threshold is characterised by its position, the position is not produced by ( ) the threshold, but rather the latter by ( ) the former’). Compare also the use of to express material causation in T9 above. For the different view that Aristotle distinguishes ‘necessitation-from’ and ‘necessitation because-of’, cf. Woods 2014, p. 111.

²⁹For Aristotle's general statement of the difference between (following by) necessity and syllogism cf. APr. 1.32, 47a31–40.

³⁰The non-monotonicity at play here is not that invoked in systems adopting some form of defeasible consequence, in which the addition of new relevant information can determine that the original defeasible inference is falsified.

³¹Alexander proposes exactly the same analysis for as a clause barring redundancy in his commentary on the Topics (cf. in Top. 13.25–14.2; 568.18–23).

³²Compare, for example, McCall 1967; Smiley 1973, pp. 139–40; Frede 1974, p. 116; Barnes 1980, p. 172; Thom 1981, pp. 27–31; Cavini 1989 and 1991, p. 30; Woods and Hansen 2001; Mignucci 2002; Woods and Irvine 2004; Woods 2014. For Smiley's and Thom's approach to relevance in Aristotle see p. 19 below.

³³There is no in-depth discussion, or sometimes even mention, of this not only in Ross’ (1949) annotated edition, but also in Mignucci's (1969), Smith's (1989), Striker's (2009) and Crubellier's (2014) comments on Aristotle's definition of syllogism in their annotated translations of the Prior Analytics. Smith 2011 is agnostic on the issue.

³⁴For introductions to ‘relevant’ (or ‘relevance’) logics, cf., for example, Read 1988 and Dunn and Restall 2000. On the tension between different criteria of relevance, cf. Paoli 2007. One further complication is that most relevant logicians define logical consequence classically (and monotonically), although their systems include non-monotonic implication (I owe this point to Francesco Paoli; cf. Paoli 2007, p. 557).

³⁵The causa apparentiae, to adopt the medieval distinction, as opposed to the causa defectus or non existentiae.

³⁶Compare Fait 2007, p. 134: ‘considerare trascurabili o non decisive certe distinzioni che non necessariamente sfuggono all'attenzione’.

³⁷For an analogous point, cf. Gobbo 1997a, pp. 240–1.

³⁸Compare, for example, Pickard-Cambridge in Barnes 1984 (‘the addition’); Dorion 1995 (‘cette addition’); Fait 2007 (‘quella cosa [sc. the thing added]’); Hasper 2012 (‘it [sc. the thing added]’).

³⁹Compare SE 2, 165a38–b11.

⁴⁰For a similar suggestion cf. Schreiber 2003, p. 110: ‘in this highly condensed text, when the answerer is instructed to “say that he granted it not because it seemed true, but for the sake of argument,” Aristotle is now referring to the premise that truly does cause the impossibility’. For a different interpretation, cf. Sorio 2009.

⁴¹My proposal would require detailed comparison between reductio ad impossibile refutations and two of the alternative, non-refutative goals that according to Aristotle a questioner might pursue in dialectical exchanges, i.e. leading the interlocutor to something ‘paradoxical’ ( ) or to something false ( ) (cf. SE 3, 12, 17, 176a25–33; Cavini 1989; Gobbo 1997b). I can only mention here that Aristotle explains that those two goals can be pursued especially in dialectical exchanges in which either there is no set thesis of the answerer at all, or, even if there is one, the questioner asks many questions on subjects not relevant to that thesis (cf. SE 12).

⁴²As Herminius noted, they are listed in decreasing order of gravity (cf. Alex.Aphr. in Top. 567.8–569.8). For a useful analysis of the passage see Smith 1997, pp. 141–3.

⁴³ Contra Smith 1997, p. 36: ‘Surely that that on which the argument rests makes us overlook the cause.’

⁴⁵Compare Smith 1997, p. 146.

⁴⁶Compare Smith 1989, p. 146.

⁴⁷In Top. 8.1, 155b20-8, within a discussion of how to secure the premisses for one's argument, it is suggested that some premisses be asked just ‘to give bulk to the argument’ or ‘to conceal the conclusion’. This need not make the resulting argument non-syllogistic, by NCF, provided that its proponent does not pretend to be using these extra premisses when drawing the conclusion.

⁴⁸Aristotle refers to the Topics, but the reference is most probably to the SE passage T1.

⁴⁹According to Smith (1989, p. 211), the passage is ‘reminiscent of the efforts of modern relevance logicians to find a formal criterion (such as variable-sharing) for relevance’. Mignucci (1969, p. 678) over-generalises the implications of the examples used in T17: to avoid NCF the conclusion of the reductio must contain either the predicate or the subject term of the hypothesis. But this cannot be correct: the argument ‘All As are B, all Bs are C, all Cs are D, therefore all As are D (impossible)’ can be used as a genuine reductio of the hypothesis ‘All Bs are C’.

⁵⁰According to Smiley, given ‘the principle that the premisses of a syllogism must form a chain of predications linking the terms of the conclusion’, an Aristotelian syllogism must ‘exclude irrelevant premisses’ (1973, pp. 139–40). Compare also Smiley 1994, p. 30: ‘Aristotle’ case for the chain condition is redolent of relevance—the need for some overt connection of meaning between premises and conclusion as a prerequisite for deduction’. For a similar approach to Aristotelian relevance, cf. Thom 1981, pp. 27–31.

⁵¹Notice, however, that in A4** another premiss is also eliminated and replaced: (1**) (C is K) is used in place of (1).

⁵²This exegetical puzzle is analogous to the one raised by Aristotle's discussion of begging the question in SE/Topics and in the Analytics (cf. Castagnoli 2012).

⁵³Compare Duncombe 2014.

⁵⁴Compare Barnes 1980.

⁵⁵It is difficult to find a reading of the three clauses , and that does not make at least two of them overlap. Some editors have suggested that should be expunged as an intrusive gloss of . For this definition, and Aristotelian enthymemes, cf. Burnyeat 1994.

⁵⁶Compare, for example, Plut. Per. 36 (on Protagoras) and Gorg. Hel. and Pal.

⁵⁷For a different take on Aristotle on the ‘necessity of saying’, cf. Fait 2004.

⁵⁸Notice that the dialectical language (‘asking’) is no longer presupposing a live dialectical context here, but clearly attests to the dialectical origin of Aristotle's logical reflection.

⁵⁹For a dismissive analysis of the passage and its value see Barnes 1993, pp. 129–30.

⁶⁰For this approach, cf., for example, Boger 2004.