Aristotle on the reducibility of all valid syllogistic moods to the two universal moods of the first figure (APr A7, 29b1–25)

Abstract

In Prior Analytics A7 Aristotle points out that all valid syllogistic moods of the second and third figures as well as the two particular moods of the first figure can be reduced to the two universal first-figure moods Barbara and Celarent. As far as the third figure is concerned, it is argued that Aristotle does not want to say, as the transmitted text suggests, that only those two valid moods of this figure whose premisses are both universal statements are directly reducible to Barbara and Celarent, but rather that it is those four valid moods of this figure whose respective minor premisses are universal statements of which this is true. It is shown that in order to carry this sense the transmitted text has to be corrected by inserting just one word, which seems to have dropped out.

Notes

The German original of this paper has been published under the title ‘Aristoteles über die Reduzierbarkeit aller gültigen syllogistischen Modi auf die beiden universellen Modi der ersten Figur (An. Pr. I 7, 29b 1–25)’ in N. Avgelis and F. Peonidis (eds), Aristotle on Logic, Language and Science (Proceedings of an International Symposium organized by the Aristotle University of Thessaloniki under the auspices of the Cultural Capital of Europe Thessaloniki, 5–7 June 1997), Thessaloniki: Sakkoulas Publications, 1998, pp. 75–83 (reprinted in N. Öffenberger and M. Skarica (eds), Zur modernen Deutung der Aristotelischen Logik, vol. 8: Beiträge zum Satz vom Widerspruch und zur Aristotelischen Prädikationstheorie, Hildesheim/Zürich/New York: Georg Olms Verlag, 2000, pp. 258–265). For the English translation I am grateful to Richard Gaskin (Liverpool).

The quotations are from Robin Smith's translation, which I have slightly altered: Aristotle, Prior Analytics. Translated, with introduction, notes, and commentary, by R. Smith, Indianapolis/Cambridge: Hackett, 1989, p. 12. My alterations were prompted by Gisela Striker, ‘Perfection and Reduction in Aristotle's Prior Analytics’, in M. Frede and G. Striker (eds), Rationality in Greek Thought, Oxford: Clarendon Press, 1996, pp. 203–219. As Striker points out, ‘perfection is in principle independent of reduction to perfect syllogisms. It consists in proving the validity of a syllogistic mood by making it evident that the conclusion follows from the premisses, by a deduction that may or may not contain one of the perfect syllogisms’ (p. 209). She adds: ‘[…] reduction is also independent of perfection, since Aristotle acknowledges that some of the perfect moods can be reduced to imperfect ones’ (p. 209).

RAI consists in proving the validity of a valid syllogism by deriving from the negation of its conclusion and one of its premisses the negation of its other premiss (or a proposition which implies the negation of its other premiss) (cf. APr A7, 29a35–39). The assumption that both premisses are true and the conclusion false is thus reduced to the impossibility that one and the same premiss is both true and false.

Cf. Alexander, In APr I, ed. M. Wallies (CAG II-I), Berlin 1883: 116, 20–35; 117, 9–17.

Cf. Alexander, loc. cit. In contrast to Alexander Philoponus does not mention the difficulty; cf. In APr, ed. M. Wallies (CAG XIII-2), Berlin 1905: 116, 20–117, 22. The same is true of Smith (p. 119).

That the two moods in question, namely Datisi and Ferison, admit only of an indirect reduction to the universal first-figure moods is not true without qualification, however. It is true only under the presupposition that in reducing a given syllogistic mood to another we must use either the method of conversion or the method of reductio ad impossibile, but not both. For, if a combination of these two methods is allowed, a direct reduction of Datisi and Ferison to Celarent is possible:

I owe this observation to Ulrich Nortmann (Saarbrücken).

Cf. the immediately preceding note.

For another solution to the problem discussed in the present paper see Mario Mignucci, Aristotele, Gli Analitici Primi. Traduzione, introduzione e commento, Naples: Luigi Loffredo Editore, 1969, p. 258. In my opinion, however, Mignucci's explanation of what according to the received text Aristotle says is not very convincing. He himself concedes: ‘La spiegazione può apparire un po’ troppo macchinosa […].’ Moreover, his explanation is rendered obsolete by his recent account of Aristotle's theory of ekthesis, which I find very plausible. See M. Mignucci, ‘Expository Proofs in Aristotle's Syllogistic’, Oxford Studies in Ancient Philosophy, Supplementary Volume, 1991, pp. 9–28.