Begging the Question as a Criticism of an Argument in Itself in Topics 8.11

Abstract

At Topics 8.11 161b19–33 Aristotle lists five criticisms () which may be leveled against a dialectical argument ‘in itself’ (). The five criticisms correspond in many respects to the familiar conditions Aristotle places on syllogism and refutation. However, begging the question (BTQ)—the violation of the condition that the conclusion of a syllogism be something different () from the premises—seems not to appear on the list of five criticisms . That this omission is only apparent becomes clear once it is seen that the five criticisms are not independent but rather amount to five successive filters through which an argument may be passed before its non-genuineness (as a syllogism or refutation) is exposed. This result sheds light on Aristotle's curious insistence, in the face of the heterogeneity of his examples of BTQ in Topics 8.13, that every question-begging refutation contains a premise that is ‘the same’ as the conclusion. The fact that the five criticisms expose BTQ as a defect in syllogistic reasoning (as opposed to a mere ‘dialectical’ foul) suggests we may trace the origin of Aristotle's familiar definition of syllogism to the scoring system in the game of dialectic.

Acknowledgements

Earlier drafts of this paper were read to audiences at Groningen, University of Iowa, and University of Chicago. I thank David Merry, Matt Duncombe, Leon Geerdink, Luca Castagnoli, Catarina Dutilh Novaes, Erik Krabbe, Marko Malink, Paul Thom, Greg Landini, Ali Hasan, Laura Castelli, David Bronstein, Tim Clarke, Alan Code, and David Ebrey for their many helpful questions and comments. I owe special thanks to an anonymous referee of this journal for detailed and very helpful comments on an earlier draft of this essay.

ORCID

Carrie Swanson http://orcid.org/0000-0001-8213-5942

Notes

¹Translation Smith 1997 (pp. 34–35) with modifications. Some comment is necessary here on the individuation of the five criticisms. Alexander (1981, In Arist. Top. 567, 7–569, 8) follows the reconstruction above. He reports (569, 3–8) that Herminus takes C3 and C4 to be subdivisions of a single criticism, while treating clauses (a) and (b) of C5 as the fourth and fifth criticisms, respectively. There are, however, a number of reasons for resisting the latter scheme. First, ‘’ which begins C5 above strongly marks the resumption of an enumeration, and clause (b) of C5 is introduced by no such indicator of enumeration. Next, as I shall argue below (Section 4, 37–39), there are indications elsewhere in Topics 8 for thinking that Aristotle regards the faults (a) and (b) of C5 to be very closely related.

²Cf. Topics 8.11 161a16–161b5, 161b5–10, 161b11–18, 161b34–162a3.

³As I explain in Section 7, 67–68, the process of addition and subtraction Aristotle describes here turns out to be much more restrictive than it appears.

⁴For evidence that Aristotle's phrase is shorthand for ‘a refutation is a syllogism of the contradictory’, cf. SE 1 165a2–3, 6 168a36–7, 9 170b1–2, 17 175a36–7.

⁵Cf. Castagnoli 2013 (pp. 94–99).

⁶Aristotle does say that whoever syllogizes well () ‘syllogizes the problem assigned from more acceptable and more familiar things’ (Topics 8.5 159b8–9) and that it is clear that those who try to syllogize from things more unacceptable than the conclusion ‘do not syllogize well’ (). But Aristotle does not mean by this that the questioner who invites C5 fails to syllogize at all, but only that he does not syllogize dialectically (: cf. 8.12 162b27). As I shall argue below, this fact also explains why C5, unlike C3 and C4, does not begin with the phrase ‘a syllogism comes about ()’: at C5, all conditions on the syllogism have been met; nevertheless, the questioner has failed to syllogize well due to either fault (a) or (b).

⁷Translation Smith 1997 (pp. 37–38) with substitution of ‘things’ for ‘premises’ in final line.

⁸Alexander 1981, In Arist. Top. 577, 5–579, 8.

⁹There is a familiar problem here concerning the construal of Mode 3. See problem (4) below.

¹⁰Cf. Int 8, 11; SE 30.

¹¹The difference is that in Mode 2, ‘’ (‘by itself’) goes with ‘’ (‘necessary to prove’) while ‘’ (‘together while other additional things’) goes with ‘’ (‘to be asking’); in Mode 3, ‘by itself’ goes with ‘to be asking’ while ‘together with other things’ goes with ‘necessary to prove’. The persistent confusion M2 and M3 have inspired in Aristotle's commentators runs the gamut from Alexander 1981, In Arist. Top. 577 (who rejects both as merely ‘apparent’ modes of BTQ) to Woods and Walton 1982 (p. 82). Regarding M3, the latter attribute to Aristotle a notion of complete or enumerative induction which he does not hold. On this basis, they construe both M2 and M3 as involving a ‘dependency’ account of BTQ:

What was critical in [M2] was whether the arguer had available in his pool of admissible evidence some basis for the universal premise that did not require dependency on the particular conclusion to be proved. So too in [M3], it is possible that the wrong that it comments on is that the evidence for each of the particular propositions that is put forward as a premise is somehow dependent on the universal conclusion to be demonstrated.

As we shall see, Aristotle does not subscribe to such a ‘dependency’ theory of BTQ.

¹²SE 6 168a35–36, 10 171a5–7, APr 2. 20 66b11.

¹³Cf. SE 18 on ‘false syllogism’ (); these Aristotle divides into apparent syllogisms (which appear conclusive though they are not) and syllogisms which establish a false conclusion (and which therefore must contain at least one false premise).

¹⁴Translation Smith 1997 (p. 36) with modifications.

¹⁵The second class of false reappears as the sophism of false cause when indirect proof is employed (167b21-36). However, an irrelevant conclusion may be produced by a variety of sophisms. On this point see Section 7, 68–69. The third class may be identified with the ‘pseudo-scientific’ proofs discussed in SE 8 and 11; the fourth class of false bears some resemblance to the first class of eristic syllogisms introduced at Topics 1.1 100b23-4: they genuinely syllogize but do so through premises which appear to be acceptable but are not. However, as falsehoods and merely apparently acceptable premises fall into distinct classes, Aristotle does not say enough here to allow us to make the identification with eristic syllogisms of the first type in Topics 1.1.

¹⁶I am imagining here that the questioner is utilizing the device of ‘standing off’ (, Topics 8.1 155b30) in asking for such a correlative premise: in asking whether medicine is concerned with the diseased, the questioner hopes to work his way to the premise that it is concerned with disease without alerting his opponent of this aim.

¹⁷Aristotle himself thinks these are the same class of arguments, though contentious and sophistical reasoners have in his view different aims (SE 11 171b18–33).

¹⁸On this point, I concur with Smith 1997 (pp. 148–147). As I shall suggest in Section 7, Aristotle pursues a more fine-grained articulation of the causes of the non-genuineness of sophistical refutations in SE; this claim supports my general approach to Topics 8.11, as a relatively early account on Aristotle's part of violations on the conditions on syllogism and refutation.

¹⁹Int. 6–7.

²⁰Cf. Moraux 1968 (p. 277), who suggests that Topics 8.9 160b21–22 may refer to such external judges (on the grounds that , 22 cannot refer to the questioner or answerer. It is possible, however, that the audience is referred to here); also 285 (Section v: Éloges et blâmes); Smith 1997 (pp. 138–139); Brunschwig 1967–2007 (p. 290: note 1,124). Krabbe and van Laar 2011 (pp. 212–215).

²¹In the Topics Aristotle not infrequently refers to transformations on statements such as addition () and substitution () involving subcomponents of premises (e.g. the addition of a differentia to a genus, Topics 6143b6–7; the replacement of a name for another name 149a14; cf. Int 11 21a29–30: putting ). However, it is clear that in C1 he refers to the addition and subtraction of entire premises. In Section 7, I explain why this process of addition and subtraction does not allow the substitution or replacement of one stated premise for an unstated one.

²²Krabbe and van Laar 2011 (p. 215) assert in passing that C5 (a) is designed to rule out ‘circular arguments’ on the ground that the clause says the argument ‘must be from premises more acceptable from the conclusion’. With Herminus, they identify C5 (a) and C5 (b) with Aristotle's fourth and fifth criticism, respectively, but this does not affect their point. Cf. Smith 1997 (p. 141): C5 corresponds to ‘the requirement that a demonstration be from premises “more intelligible” than the conclusion’; quoted without emendation by Brunschwig 2007, n. 2 (p. 292). But this is not what C5 (a) says, but rather that the argument that is criticized was as stated from premises more unacceptable than the conclusion. Moreover, even if in some cases of BTQ (e.g. Mode 1 involving synonymy or in certain cases of Mode 5 which I discuss below, Section 5, 45–49) a subject or predicate term in the premise is not more familiar than its correlate term in the conclusion, since the premise and conclusion are convertible, one may still BTQ when conclusion and premise are reversed. Another problem with their proposal is that Aristotle does not identify circular deductions with question-begging ones (Cf. Castagnoli 2013, pp. 109–110; Barnes 1976.) Finally, it must be borne in mind that the distinction is also in play throughout C1–C5; thus, it is most probable that C5 captures refutations wherein the questioner was forced to argue through premises conforming to C5 due to the difficulty of the thesis he was assigned to defend.

²³Cf. SE 4 165b34–8.

²⁴Cf. APr 1.12, 77b30–5.

²⁵I disagree with Fait 2013 (p. 263) that the reason the additional premise is required is because the answerer who does not know the synonymy may not see why the conclusion follows. The individual in question may or may not know the terms are synonymous; the point is that as an answerer, he is within his rights to demand that his opponent ask for the missing question which establishes this point.

²⁶Michael 1898, In SE 57.15–31, Anonymous 1884, In SE 18.8–18. The example is from the latter source, often thought to be Sophonias. Other commentators have taken the point to concern a deduction to an irrelevant conclusion. For a persuasive rejection of this reading, see Malink 2014a (pp. 14–17).

²⁷Dorion 1995 (p. 245), Fait 2007 (p. 125), and Schreiber 2003 (pp. 57–58).

²⁸Aristotle takes this sophism to depend on ‘division’ (), as opposed to ‘combination’ ().

²⁹This is the only example in SE of the fallacy of accent which Aristotle fully spells out. Other suggested examples occur at 166b4–5, 166b7, and 177b3–4.

³⁰For recent discussions of T24, see Fait 2013 (pp. 247–248) and Di Lascio 2013 (pp. 68–69).

³¹This distinction came to be known by scholastic theorizers on fallacy as that between the causa apparentiae and the causa non existentiae. For a helpful discussion, see Ebbesen 1987.

³²Aristotle is quite clear that it may be obscure to a questioner who is constructing a sophistical argument that it is in fact sophistical (Cf. SE 5 167b35–6; 16 175a10–12).

³³These observations may be congruent with the notion of a deduction as ‘an argumentative winning strategy’ of a questioner against an answerer in the dialectical arena. According to a recent defense of this notion, our standard conception of deductive reasoning as a mono-agentive process is to be explained as a result of a historical development, namely ‘the internalization of the role of the opponent: the requirement that there be absolutely no counter-arguments to particular inferential steps is now incorporated into the method itself’ Dutilh-Novaes 2015 (p. 1). Whether this account of deduction may be extended to Aristotle's notion of the syllogism is another question. One difficulty is that an Aristotelian syllogism is a much narrower notion than a deductive inference. In any case it is clear that in Aristotle's view, the (virtuous) answerer objects to a given refutation because of the nature of syllogism and refutation; it is not his view that an inference is a refutation or syllogism because the answerer does not object to it.

³⁴I discuss some further features of C1 and the method alluded to here in Section 7.

³⁵As Striker 2009 (p. 212) explains, here does not signify the reduction of all other moods of syllogism to the universal ones in the first figure, but rather the analysis of an informal argument with a view to its reformulation or completion to show that it falls into one of the syllogistic figures. For this use of , see Striker 2009. Many commentators have supposed that the informal ‘written’ arguments Aristotle refers to here are geometrical demonstrations. Cf. APr 1.24 41b13–23 and T41 Section 6 (pp. 51–55).

³⁶For example, 8.1 156a5.

³⁷Because they are not quantified, the universal propositions of Topics 8 formally resemble the ‘indeterminate’ () propositions introduced at APr 1.1 24a17–22. For an illuminating discussion, see Malink 2014b (pp. 1–33). As Slomkowski 1997 (pp. 23–24) points out, while the difference between a universal and particular premise is never explicitly articulated in the earlier treatise, it seems to boil down to this: a premise is ‘particular’ as opposed to ‘universal’ if it contains particular terms; but the latter are ambiguous between ‘specific’ and ‘individual’: a specific term is specific relative to a generic term (‘disease’ relative to ‘evil’); an ‘individual’ term signifies something than which nothing can be more specific (e.g. an individual man).

³⁸Striker 2009 (p. 52) translates the third line: ‘Again, if what is a man is necessarily an animal, and what is an animal, a substance, then what is a man is necessarily a substance.’ However, this seems to be a (modal) syllogism. On the translation above, the inference is a hypothetical syllogism. Since hypothetical syllogisms are not categorical syllogisms (APr 1.44) Aristotle's point is that the inference, while conclusive, is not a categorical syllogism.

³⁹Alexander 1883, In AnPr. 21.28–30, 344.9–345.12, 346.27–8; Philoponus 1905, In AnPr. 320.16–322.18, 323.18–27; Frede 1974 (pp. 20–23), Thom 1981 (p. 22). Cf. Striker 2009 (p. 215), and Smith 1989 (pp. 161–162) contra this position.

⁴⁰It is possible to translate ‘’ in C3 and ‘’ in C4 more neutrally as simply ‘is present’. On this construal, the point would be that in both cases, a syllogism is ‘there’—contained in the stated premises—it is just lacking a premise (C3) or contains superfluous premise(s) (C4). This reading, however, seems less suited to the context of the evaluation of refutations. (Since it will be pointless for a judge to declare ‘there is a syllogism present—hence all conditions on syllogism are met—nevertheless, not all conditions are met, for a premise is missing or superfluous’.) The reading is perhaps better suited to the context of T32 (though no form of the verb occurs there; we have only , 47a17): for there is a sense in which a categorical syllogism may ‘already be present’ in the stated premises of an informal or mathematical argument. However, in the context of T32 and T33, Aristotle is concerned with the transformation of what is not a categorical syllogism into a categorical (quantified, mediated) syllogism (e.g. ‘there is a (categorical) syllogism present in the (dialectical) syllogism’); in the Topics context by contrast there is no such item which is in this sense ‘already present’ in the stated argument. Thus, the importation of the ‘neutral’ reading of the verb into C3/C4 from ‘between the lines’ of T32 is not supported by analogy. On the contrary: since C3/C4 is a dialectical precursor to T32, it is preferable to read between the lines of the latter a more ‘dynamic’ construal of the method of completion it describes: just as a dialectical syllogism comes to be as a result of addition and subtraction in C3/C4, so a categorical syllogism comes to be as a result of reformulation by addition and subtraction in T32. Cf. Allen 1995 (p. 189): C3 criticizes arguments for being from too few of the necessary premises required to constitute a syllogism, just as C4 criticizes arguments for being from too many premises which are not necessary.

⁴¹In Section 7, I return to consider what type of argument C1 does ensnare; this turns out to be a refutation that suffers from an irreparable disconnection in its terms, on the assumption that ‘repair’ by addition and subtraction does not permit wholesale substitution of stated premises.

⁴²As I suggest in Section 7, C2 may nevertheless filter out a number of different kinds of defective refutations, since it is possible to syllogize to an irrelevant conclusion in different ways.

⁴³That is, he might agree that this was an illegitimate (because sophistical or contentious) application of the method of ‘standing off’ (), Topics 8.1 155b30 passim.

⁴⁴This construal of is proposed by Fait 2007 (p. 212; against Dorion 1995, p. 390, who supposes that the answerer concedes the premise in question on the assumption that the questioner will argue against it). In the normal scenario of ‘refutations on the side’ (), the answerer has refused to concede a premise necessary to the questioner's refutation of his thesis; in response, the questioner pauses to refute this denial in order to resume the main refutation. (Topics 2.5, 111b32–112a9; SE 17 176a23–5). In the ‘opposite scenario’ in T36, the answerer concedes a question-begging premise; to cover his mistake, he claims he assumed that his opponent would syllogize in relation to it (not against it), where this means he claims he did not suppose that the premise would be used to derive the conclusion by immediate implication. Cf. Castagnoli 2013 (pp. 104–105).

⁴⁵Translation Castagnoli 2013 (p. 104), substituting ‘syllogize’ for ‘reason’ in ll.20–1.

⁴⁶Here it may be objected that if the definition of Man that is omitted is obviously false or unacceptable (e.g. Rational biped animal is the same as Raven or Ape), clauses (b) and (c) of C3 will be satisfied; but that in such a case there is no immediate implication in M1 between the original premise and the conclusion; and so the inference cannot beg the question. But my claim is that Aristotle's examples of BTQ conform to C3; I do not claim that any inference that conforms to C3 begs the question. (On this point, see Section 7, 65–67.) Moreover, the strategy in question (‘Raven is warm-blooded; therefore, Man is warm-blooded’—or vice versa) will not produce a refutation that is even apparently valid; so it is unlikely to be used in the dialectical arena.

⁴⁷E.g. Topics 2.8, 113b15 passim; 8.1 155b29–32; Met. 5 10, 1018a20 passim.

⁴⁸Cf. Castagnoli 2013 (pp. 100, 108).

⁴⁹For the purposes of this paper, I leave open here the question whether Aristotle thinks ‘’ (‘the same’ or ‘sameness’) is ‘said in many ways’ because it has many distinct senses, or because different kinds of things may be related by the sameness relation.

⁵⁰Translation Smith 1997 (p. 6).

⁵¹Smith 1997 (p. 7).

⁵²I suggest this is why Topics 8.13 begins with the topic of ‘how’ () it is that the starting point is asked for. This topic receives separate treatment in 8.13 not because BTQ is not a defect of an argument in itself; for BTQ is caught out by C1–C5 in 8.11. Rather, 8.13 concerns the more specific problem of how and in how many ways the question is begged; this is complicated and requires separate treatment.

⁵³Unfortunately, these facts do not resolve every difficulty concerning Mode 4 (M4): chief among these is how the conclusion can be appropriately dialectical, given that the thesis it contradicts must affirm or deny one thing of one thing (Topics 1.4, 101b28–36). M4 then also raises the prior question whether Aristotle anticipates the Stoic logicians in recognizing as single truth-evaluable assertions sentences consisting of two sentences linked by a connective such as a conjunctive particle. On this controversy and its progress in the ancient and medieval commentators, see Crivelli 2004 (pp. 163–172), and Bobzien 2002, who argue pro and contra, respectively.

⁵⁴For one thing, the inference concerns the ‘dialectical topic’ of what is to be chosen and avoided (, Topics 1.11, 104b1-2); relatedly, it is not argued through the first principles of a special science.

⁵⁵The diagram is based on Ross 1949 (p. 374).

⁵⁶Malink 2014b (p. 41) suggests that Aristotle may mean to imply that the proof BTQ when either the premise is omitted or the quantifying expression ‘all’ is omitted.

⁵⁷I omit discussion as beyond the scope of the present study the other case of BTQ described in the passage, wherein the demonstrator reverses the ‘natural order’ of proof, ‘shifting the argument over to some other premises from among those which are naturally proved by what is proposed’ and ‘demonstrating the starting point by means of these’ (64b39–65a9). On the interpretative issues raised by this mode and its possible congruence with those described in T42, see Bolton 1994 (pp. 110–112), Castagnoli 2013 (pp. 105–113), Lear 1980 (pp. 82–90), Mignucci 1969 (p. 663), Smith 1989 (pp. 204–209). But cf. notes 66, 62.

⁵⁸The problem is posed in these terms by Ross 1949 (p. 463).

⁵⁹That is, they must be more familiar ‘by nature’, as opposed ‘to us’; cf. APo 1.2 71b33–72a5, Topics 6.4 141b29–34; APr 2.23, 68b35–7, Met. 7.3, 1029b3–12, Phy. 1.1.

⁶⁰Thus I take it T42 does not condemn as BTQ all demonstrations in Barbara involving the predication of genus and species in either the major or minor premise. Knowledge of the genus is prior to the species and the former is by nature more familiar than the latter (Topics 6.4 141b29–34). Thus if the scientist genuinely grasps the genus animal (and its differentiae), he may properly demonstrate that all men are mortal through the premise that men belong to this genus. BTQ may occur if the relevant genus is not known scientifically, for example, it is unclear whether all reptiles are oviparous.

⁶¹Poste 1866 (p. 183).

⁶²Barnes 1993 (pp. 209–210). The commentators evidently confused the mode of BTQ Aristotle describes in T42 with the other mode of BTQ which he says may occur in scientific demonstrations, namely ‘shifting the argument over to some other premises from among those which are naturally proved by what is proposed’ and ‘demonstrating the starting point by means of these’. Cf. APr 2.16 64b39–65a9. I have omitted treatment of this text as beyond the scope of this essay.

⁶³Cf. Topics 8.13, 163a3, 7 and 10.

⁶⁴Again: a deduction does not beg the question in Aristotle's view because it is elliptical.

⁶⁵Thus despite the reference to ‘opinion’, Aristotle's distinction has nothing immediately to do with the difference in the nature of the premises in dialectic and science ( or ‘acceptable opinions’ vs. principles).

⁶⁶Of course the final test of this account of Aristotle's distinction is whether it can accommodate the mode of BTQ in science I have not discussed, namely reversing the ‘natural order of proof’, APr 2.16 64b39–65a9. I believe the extension is possible. Let the natural order of demonstration be A then B then C. If it is argued that C then B then A, Aristotle claims that the demonstrator proves A ‘through itself’ because we have in effect [A] then B then C then B then A. Here [A] is not expressed as a premise (Castagnoli 2013, p. 110). This may seem to entail that BTQ in this mode has more in common with its dialectical than its other scientific counterparts; for we seem to reveal the question-begging nature of the proof by the addition of a missing premise. I suggest this impression is misleading; for like the other cases of BTQ in science, we do not restore the inference to the status of a demonstration by supplying [A]; moreover, [A] is not really a missing premise in the dialectical sense; it is ‘there’ in the order of nature all the while.

⁶⁷Cf. Section 6, 51–55: in the later Analytics, the quantifiers ‘all’ and ‘some’ may be added in the completion of a syllogism.

⁶⁸Such omissions could be unintentional; but Aristotle's discussion of ‘standing off’ () and ‘concealment’ () in Topics 8.1 (155b17–156a22) suggests that these were commonly intentional: the questioner is in fact advised to ask for premises which establish the necessary premises while omitting to state the latter. Of course in the case of sophistical refutation such omissions will generally be intentional.

⁶⁹The example is adapted from APr 1.4 26a8–9.

⁷⁰Section 3, 24; cf. APo 1.12 77b30–5.

⁷¹On false cause, see SE 5 167b21–36, 29 181a31–35. It is controversial whether Aristotle considers C4 the same type of argument he describes in SE as ‘’ (the one depending on positing as the cause what is not the cause). All of his examples of false cause in SE seem to involve indirect proof: the questioner syllogizes correctly to an impossible result, and attempts to reject on this basis an assumption (his opponent's thesis) which is not a cause of the impossibility. The difficult discussion of false cause in APr 2.17 is similarly focused on its occurrence in indirect proof; so too is Aristotle's passing reference to what appears to be the same sophism in T10 (where it is identified as the second mode of ‘false ’). What is unclear is why C4 as stated should not also satisfy the key condition of the fallacy: that the conclusion of the syllogism follows whether or not the redundant premise is included in the premise set. The problem is discussed in Thom 1981 (pp. 193–196).