Note 133 — Chapter X · SOPHISTICI ELENCHI.

Soph. El. xxxiii. p. 182, b. 37-p. 183, a. 4: ἔστι δὲ συλλογιστικὸς μὲν λόγος δριμύτατος, ἂν ἐξ ὅτι μάλιστα δοκούντων ὅτι μάλιστα ἔνδοξον ἀναιρῇ· εἷς γὰρ ὢν ὁ λόγος, μετατιθεμένης τῆς ἀντιφάσεως, ἅπαντας ὁμοίους ἕξει τοὺς συλλογισμούς· ἀεὶ γὰρ ἐξ ἐνδόξων ὁμοίως ἔνδοξον ἀναιρήσει [ἢ κατασκευάσει]· διόπερ ἀπορεῖν ἀναγκαῖον. μάλιστα μὲν οὖν ὁ τοιοῦτος δριμύς, ὁ ἐξ ἴσου τὸ συμπέρασμα ποιῶν τοῖς ἐρωτήμασι. I transcribe this text as it is given by Bekker, Waitz, Bussemaker, and Mr. Poste. The editions anterior to Bekker had the additional words ἢ κατασκευάζῃ after ἀναιρῇ in the fourth line; and M. Barthélemy St. Hilaire in his translation defends and retains them. Bekker and the subsequent editors have omitted them, but have retained the last words ἢ κατασκευάσει in the seventh line. To me this seems inconsistent: the words ought either to be retained in both places or omitted in both. I think they ought to be omitted in both. I have enclosed them in brackets in the fifth line.

This difficult passage (not well explained by Alexander, Schol. p. 320, b. 9) requires the explanations of Waitz and Mr. Poste. The note of Mr. Poste is particularly instructive, because he expands in full (p. 164) the three “similar syllogisms” to which Aristotle here briefly alludes. The phrase μετατιθεμένης τῆς ἀντιφάσεως is determined by a passage in Analyt. Priora, II. viii. p. 59, b. 1: it means “employment of the contradictory of the conclusion, in combination with either one of the premisses, to upset the other.” The original syllogism is assumed to have two premisses, each highly probable, while the conclusion is highly improbable, being the negation of a highly probable proposition. The original syllogism will stand thus: All M is P; All S is M; Ergo, All S is P: the two premisses being supposed highly probable, and the conclusion highly improbable. Of course, therefore, the contradictory of the conclusion will be highly probable — Some S is not P. We take this contradictory and employ it to construct two new syllogisms as follows:— “All M is P; Some S is not P; Ergo Some S is not M. And again, Some S is not P: All S is M; Ergo, Some M is not P. All these three syllogisms are similar in this respect: that each has two highly probable premisses, while the conclusion is highly improbable.