18. You will look at the terms of the proposition, also, in regard to their Derivatives, Inflections, &c., and to matters associated with them in the way of production, preservation, &c. This locus serves both for proof and for refutation. What is affirmable of the subject, is affirmable also of its derivatives: what is not affirmable of the derivatives, is not affirmable of the subject itself.[115]
[115] Ibid. ix. p. 114, a. 26-b. 5. δύστοιχα, πτώσεις, τὰ ποιητικὰ καὶ φυλακτικά â€” δῆλον οὖν ὅτι ἑνὸς ὁποιουοῦν δειχθέντος τῶν κατὰ τὴν αὐτὴν συστοιχίαν ἀγαθοῦ ἢ ἐπαινετοῦ, καὶ τὰ λοιπὰ πάντα δεδειγμένα γίνεται. — b. 23: ὧν μὲν γὰρ τὰ ποιητικὰ ἀγαθά, καὶ αὐτὰ τῶν ἀγαθῶν, ὧν δὲ τὰ φθαρτικὰ ἀγαθά, αὐτὰ τῶν κακῶν.
19. Arguments may often be drawn, both for proof and for refutation, from matters Similar or Analogous to the subject or predicate of the thesis. Thus, if one and the same cognition comprehends many things, one and the same opinion will also comprehend many things. If to possess vision is to see, then also to possess audition is to hear. If to possess audition is not to hear, then neither is to possess vision to see. The argument may be urged whether the resemblance is real or only generally supposed. Sometimes, however, the inference will not hold from one to many. Thus, if to know is to cogitate, then to know many things should be to cogitate many things. But this last is impossible. A man may know many things, but he cannot cogitate many things; therefore, to know is not to cogitate.[116]
[116] Topic. II. x. p. 114, b. 25-36: πάλιν ἐπὶ τῶν ὁμοίων, εἰ ὁμοίως ἔχει, — καὶ ἐπὶ τῶν ὄντων καὶ τῶν δοκούντων· χρήσιμος δ’ ὁ τόπος πρὸς ἄμφω· — σκοπεῖν δὲ καὶ εἰ ἐφ’ ἑνὸς καὶ εἰ ἐπὶ πολλῶν ὁμοίως ἔχει· ἐνιαχοῦ γὰρ διαφωνεῖ.
20. There are various loci for argument, arising from degrees of Comparison — more, less, equally. One is the argument from concomitant variations, which is available both for proof and for disproof. If to do injustice is evil, to do more injustice is more evil. If an increase in degree of the subject implies an increase in degree of the predicate, then the predicate is truly affirmed; if not, not. This may be shown by Induction, or repetition of particular instances.[117] Again, suppose the same predicate to be affirmable of two distinct subjects A and B, but to be more probably affirmable of A than of B. Then, if you can show that it does not belong to A, you may argue (à fortiori) that it does not belong to B; or, if you can show that it belongs to B, you may argue (à fortiori) that it belongs also to A. Or, if two distinct predicates be affirmable respecting the same subject but with unequal degrees of probability, then, if you can disprove the more probable of the two, you may argue from thence in disproof of the less probable; and, if you can prove the less probable, you may argue from thence in proof of the more probable. Or, if two distinct predicates be affirmable respecting two distinct subjects but with unequal degrees of probability, then, if you can disprove the more probable you may argue from thence against the less probable; and, if you can prove the less probable, you are furnished with an argument in proof of the more probable.[118] If the degrees of probability, instead of being unequal, are equal or alike, you may still, in the cases mentioned, argue in like manner from proof or disproof of the one to proof or disproof of the other.[119]
[117] Ibid. b. 37-p. 115, a. 5: εἰσὶ δὲ τοῦ μᾶλλον τόποι τέσσαρες, εἷς μὲν εἰ ἀκολουθεῖ τὸ μᾶλλον τῷ μᾶλλον, — χρήσιμος δὲ πρὸς ἄμφω ὁ τόπος· εἰ μὲν γὰρ ἀκολουθεῖ τῇ τοῦ ὑποκειμένου ἐπιδόσει ἡ τοῦ συμβεβηκότος ἐπίδοσις, καθάπερ εἴρηται, δῆλον ὅτι συμβέβηκεν, εἰ δὲ μὴ ἀκολουθεῖ, οὐ συμβέβηκεν. τοῦτο δ’ ἐπαγωγῇ ληπτέον.
[118] Topic. II. x. p. 115, a. 5-14.
[119] Ibid. a. 15-24: ἐκ τοῦ ὁμοίως ὑπάρχειν ἢ δοκεῖν ὑπάρχειν, &c.
21. Another locus for argument is, that ex adjuncto. If the subject, prior to adjunction of the attribute, be not white or good, and if adjunction of the attribute makes it white or good, then, you may argue that the adjunct must itself be white or good. And you might argue in like manner, if the subject prior to adjunction were to a certain extent white or good, but became more white or more good after such adjunction.[120] But this locus will not be found available for the negative inference or refutation. You cannot argue, because the adjunction does not make the subject white or good, that therefore the adjunct itself is not white or not good.[121]
[120] Ibid. xi. p. 115, a. 26-33.