Note 22 — Chapter VI · ANALYTICA PRIORA II.

Ibid. p. 65, a. 10: εἰ οὖν τις, ἀδήλου ὄντος ὅτι τὸ Ἀ ὑπάρχει τῷ Γ, ὁμοίως δὲ καὶ ὅτι τῷ Β, αἰτοῖτο τῷ Β ὑπάρχειν τὸ Ἀ, οὕπω δῆλον εἰ τὸ ἐν ἀρχῇ αἰτεῖται, ἀλλ’ ὅτι οὐκ ἀποδείκνυσι, δῆλον· οὐ γὰρ ἀρχὴ ἀποδείξεως τὸ ὁμοίως ἄδηλον. εἰ μέντοι τὸ Β πρὸς τὸ Γ οὕτως ἔχει ὥστε ταὐτὸν εἶναι, ἢ δῆλον ὅτι ἀντιστρέφουσιν, ἢ ὑπάρχει θάτερον θατέρῳ, τὸ ἐν ἀρχῇ αἰτεῖται. καὶ γὰρ ἄν, ὅτι τῷ Β τὸ Ἀ ὑπάρχει, δι’ ἐκείνων δεικνύοι, εἰ ἀντιστρέφοι. νῦν δὲ τοῦτο κωλύει, ἀλλ’ οὐχ ὁ τρόπος. εἰ δὲ τοῦτο ποιοῖ, τὸ εἰρημένον ἂν ποιοῖ καὶ ἀντιστρέφοι ὡς διὰ τριῶν.

This chapter, in which Aristotle declares the nature of Petitio Principii, is obscure and difficult to follow. It has been explained at some length, first by Philoponus in the Scholia (p. 192, a. 35, b. 24), afterwards by Julius Pacius (p. 376, whose explanation is followed by M. B. St. Hilaire, p. 288), and by Waitz, (I. p. 514). But the translation and comment given by Mr. Poste appear to me the best: “Assuming the conclusion to be affirmative, let us examine a syllogism in Barbara:—

All B is A. All C is B. ∴ All C is A.

And let us first suppose that the major premiss is a Petitio Principii; i.e. that the proposition All B is A is identical with the proposition All C is A. This can only be because the terms B and C are identical. Next, let us suppose that the minor premiss is a Petitio Principii: i.e. that the proposition All C is B is identical with the proposition All C is A. This can only be because B and A are identical. The identity of the terms is, their convertibility or their sequence (ὑπάρχει, ἕπεται). This however requires some limitation; for as the major is always predicated (ὑπάρχει, ἕπεται) of the middle, and the middle of the minor, if this were enough to constitute Petitio Principii, every syllogism with a problematical premiss would be a Petitio Principii.” (See the Appendix A, pp. 178-183, attached to Mr. Poste’s edition of Aristotle’s Sophistici Elenchi.)

Compare, about Petitio Principii, Aristot. Topic. VIII. xiii. p. 162, b. 34, in which passage Aristotle gives to the fallacy called Petitio Principii a still larger sweep than what he assigns to it in the Analytica Priora. Mr. Poste’s remark is perfectly just, that according to the above passage in the Analytica, every syllogism with a problematical (i.e. real as opposed to verbal) premiss would be a Petitio Principii; that is, all real deductive reasoning, in the syllogistic form, would be a Petitio Principii. To this we may add, that, from the passage above referred to in the Topica, all inductive reasoning also (reasoning from parts to whole) would involve Petitio Principii.

Mr. Poste’s explanation of this difficult passage brings into view the original and valuable exposition made by Mr. John Stuart Mill of the Functions and Logical Value of the Syllogism. — System of Logic, Book II. ch. iii. sect 2:— ”It must be granted, that in every syllogism, considered as an argument to prove the conclusion, there is a Petitio Principii,” &c.

Petitio Principii, if ranked among the Fallacies, can hardly be extended beyond the first of the five distinct varieties enumerated in the Topica, VIII. xiii.