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ABSTRACT
The hypothesis of a theoretical unity between On Sophistical Refutations and Prior Analytics presents a major challenge to scholars attempting to unify the criteria of analysis. This paper examines this problem and proposes a middle ground between the perspectives of Woods and Boger to address this crucial question: If a unitary and coherent theory of deduction exists, why does not the technical apparatus of syllogistic modes for analyzing fallacies appear in SE? This paper makes useful contributions to the discussion on the internal unity of Aristotle's logical writings on around categorical syllogistics and the doctrine of sophistical refutations.
Notes
1 Regarding the proper translation of συλλογισμός, see Section 3, cf. Boger Citation2022, 23, 369.
2 Schreiber (Citation2003, 87–8) writes: ‘In SE 4 and 5, Aristotle mentions thirteen sources of fallacious reasoning. One of these, called “ignorance of what refutation is” […] although introduced in SE 5 as a source of on a par with the other twelve sources; in SE 6, it becomes an alternative way of incorporating all twelve of the other sources’ (emphasis added). Krabbe (Citation2012, 245) notes that ‘the core of his completeness proof lies in the reduction of all fallacies to ignoratio elenchi […] from which Aristotle's list of sophistical refutations can be obtained (minus ignoratio elenchi, which is no longer on a par with the other kinds of sophistical refutation)’ (emphasis added); Malink (Citation2014, 1) writes, ‘He states that these thirteen kinds can ultimately be reduced to one of them, namely to ignoration elenchi’ (emphasis added); Woods (Citation2004, 178) further supports the idea: ‘If so the idea that, except for the ignoratio elenchi – the source of refutational failure is syllogisticity – failure, could not be advanced with confidence […] it is always an error of one or other of the other twelve kinds as separated by the in–extra subdivision’ (emphasis added).
3 Thomas Aquinas Citation1954, 14; Peter of Spain Citation1972, VII 179–181.
4 It is telling that both Barnes (Citation1993) and Forster (Aristotle Citation1960) translate here for ‘ignorance’, so there no need to translate SE's principle for ‘misconception’ unless it is understood as a fallacy. Schreiber (Citation2003, 87) also refers to the principle as ‘ignorance’.
5 This statement is related to this paper's central thesis, and it will be explained in the subsequent pages.
6 It is worth mentioning that for medieval authors, fallacia serves as another term for locus sophisticus, a doctrine of Boethius closely linked to his theory of maximae propositiones, which has had great influence in medieval logic texts. For a discussion of these concepts, see Ebbesen Citation1981, 122–23; Green–Pedersen Citation1984, 39–44.
7 For example, Forster (Aristotle Citation1955) translates ἀπάτη for ‘fallacy’ in SE 7 169a23 and ‘fallacies’ for παραλογισμοί in SE 5 166b28. See Schreiber Citation2003, 173–76.
8 Woods (Citation2004, 26) ignores this issue: ‘Prior Analytics has nothing to say about refutations’.
9 Although it can be translated as ‘proposition’ in the modern sense, different from a sentence, the proper translation is ‘premise’ because a πρότασις is in fact a proposition, so as it is the conclusion, which it's not a πρότασις but a συμπέρασμα. One deduces a συμπέρασμα but assumes a πρότασις. Therefore, I disagree with Boger (Citation2022, 351) when he states: ‘two protaseis are necessary and sufficient for generating a third and different protasis’. He seems to mean here ‘proposition’. Medieval authors recognized this difference, stating that they are identical in substance as an utterance but different in concept. Thomas Aquinas (Citation1954, 18) writes: ‘est autem idem secundum substantiam, enuntiatio, propositio, interrogatio et conclusio […] propositio secundum quod sumitur ad alterius probationem; conclusio vero secundum quod ex aliis probatur’. Peter of Spain (Citation1972, VII 171): ‘enunciatio, propositio, interrogatio, et conclusio sunt idem substantia, different autem propriis rationibus’. Cf. Woods Citation2004, 30; Boger Citation2022, 221, 253, 372.
10 I disagree with Woods (Citation2004, 33) on this point: ‘It was not Aristotle’s intention to preclude plural propositions’, because this view is precisely what Aristotle tries to preclude.
11 Alexander (Aphrodisias Citation2013a, 269.25–31) quotes SE 5 167a23–7 in full for explaining these logical difficulties, cf. Ammonius Citation2013, 86.1–5.
12 See Thomas Aquinas Citation1964a, l.9 117; Boethius Citation1877, 81.1–2; Ammonius Citation2013, 85.29–30.
13 See note n° 21.
14 φαινόμϵνος ἒλϵγχος, συλλογισμὸς, in SE 1 164b25–26, 165a19, 2 165b8, 6 168a17, 169a17–18, 8 169b18–19, 169b40, 9 170b9–10, 10 171a5, 171a8, 11 171b9, 171b20, 18 176b33–34.
15 φαινομένη ἀντίφασις, SE 6 169a20–21.
16 φαινομένη πρότασις, SE 6 169a14–17, 30 181b22–24.
17 Unlike other cases, apparent demonstration (φαινομένη ἀποδϵίξις, SE 11 171b29–30, 6 168b3) is correct from a logical point of view (8 169b23, 11 171b19–21); its defect is epistemological, as it is only apparently appropriate to the object of proof (169b20–23, 170a20–35). For further discussion of this subject, see Angioni Citation2012b.
18 ‘Materiam sophisticam de quo tractatur in libro Elenchorum’ (Thomas Aquinas Citation1927, pr).
19 Thomas Aquinas Citation1954, 4; Peter of Spain Citation1972, VII 27.
20 That is also why both are studied in APr II 16, 17 and in Top VIII 13 and SE 5, 29. However, both receive less attention in SE and Top than in APr, where the same sequence of analysis is maintained: Petitio Principi is studied first in APr II 16 64b28–37 and then Non–cause as Cause in the following chapter (17 64b38–66a15).
21 ἀληθὴς συλλογισμός, SE 10 171a12. In this context, ‘True’ is used in contrast to ‘apparent’, which is not the same as a valid deduction because every syllogism is valid. Simply put, an invalid syllogism is an oxymoron. Thus, true syllogism is a concept closer to sound argument. Cf. Boger Citation2004, 116; Woods Citation2004, 30.
22 The concept of ‘expression’, in my opinion, encompasses both names (ὀνόματα) and sentences (λόγοι); this is because defect exists in names such as Homonymy, Accent and Form of speech as well as in complete sentences such as Composition, Division and Equivocation (SE 1 165a16–7, 6 168a24–27).
23 Example suggested by the reviewer.
24 The term ‘sophistical syllogism’ is found in Aristotle’s writings in SE 8 169b21, 11 171b8, alongside similar terms such as sophism (σόφισμα) and eristic syllogism (ἐριστικός συλλογισμός) in Top I 1 100b24, VIII 11 162a15–18, 12 162b5.
25 It is important to consider here that to give a remote cause as explanation, even though related, it doesn't explain the fact one wishes to explain (see APo I 13 78b29–31), in this case, apparent syllogism.
26 Commentators share the same view regarding this issue. Ross (Aristotle Citation1924, 311) notes: ‘because these identities are accidental, none of them can be generalized […] for universal propositions are essential’. See Aphrodisias Citation2013b, 376.32–377.30 and Thomas Aquinas Citation1964c, V l.11 910.
27 Bonevac (Citation2012, 92): ‘Ockham […] shares with Buridan the thought that universality is a generalization of conjunction and particularity a generalization of disjunction’.
28 Bonevac (Citation2012, 62) writes: ‘There is no theory-neutral way of defining quantification, or even of delineating the class of quantifiers. Some logicians treat determiners such as “all”, “every”, “most”, “no”, “some”, and the like as quantifiers; others think of them as denoting quantifiers’.
29 SE 5 167b1, 24 181a24, Cf. Top III 2 117a8–11, II 5 112a24–27.
30 See Schreiber Citation2003, 131.
31 An interpretation of the Consequent as a defect of modus ponens and tollens is anachronistic, because in Aristotle's case the consequent is not directly affirmed, nor the antecedent is directly denied, but it operates by means of an improper conversion of the consequence. See Slomkowski Citation1997, 4.
32 Thomas Aquinas (Citation1964b I l.22 187) generalizes the solution by saying: ‘idest quia accipiunt medium affirmative praedicatum de utroque extremorum; quod est syllogizare in secunda figura ex duabus propositionibus affirmativis; quod facit fallaciam consequentis’. It is plausible to generalize this solution because the conditional proposition of the Consequent can be reduced to a categorical based on that it is a part of the Accident.
33 Quoted by Read Citation2017, 13.
34 APr I 4 25b31–35, 25 42a31–34, 42b1–16, 28 44b6– 8, 32 47b1–10, APr II 19, 66a28–9, APo I 19 81b10, 11 94a23–25, Met Δ 1014b1–3.
35 According to Crubellier (Citation2017, 36–7) contemporary logic has dismissed the capital importance of figures in Aristotle’s thought. After the mathematized versions of Frege’s and Russell’s logic the Aristotelian concept of figure disappeared, the result of which was that the concept of logical schema (schemata) only found a correlate in the modes. But Aristotle does not have a technical expression to refer to the ‘syllogistic modes’ (τρόποι συλλογίστικοι), which was an invention of the commentary tradition to name the syllogistic combinations of three terms, because there are also non–syllogistic combinations in each figure (Correia Citation2003, 99, cf. Dutilh Novaes Citation2012, 403).