17. We recognize four varieties of Opposita: (1) Contradictory; (2) Contrary; (3) Habitus and Privatio; (4) Relata. You will consider how the relation in each of these four varieties bears upon the thesis in debate.
In regard to Contradictories, you are entitled, converting the terms of the thesis, to deny the predicate of the converted proposition respecting the negation of the subject. Thus, if man is an animal, you are entitled to infer, What is not an animal is not a man. You will prove this to be an universal rule by Induction; that is, by citing a multitude of particular cases in which it is indisputably true, without possibility of finding any one case in which it does not apply. If you can prove or disprove the converted obverse of the thesis — What is not an animal is not a man — you will have proved or disproved, the thesis itself, Man is an animal. This locus is available both for assailant and respondent.[111]
[111] Ibid. viii. p. 113, b. 15-26: ἐπεὶ δ’ αἱ ἀντιθέσις τέσσαρες, σκοπεῖν ἐκ μὲν τῶν ἀντιφάσεων ἐκ τῆς ἀκολουθήσεως καὶ ἀναιροῦντι καὶ κατασκευάζοντι· λαμβάνειν δ’ ἐξ ἐπαγωγῆς, οἷον εἰ ὁ ἄνθρωπος ζῷον, τὸ μὴ ζῷον οὐκ ἄνθρωπος· ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων — ἐπὶ πάντων οὖν τὸ τοιοῦτον ἀξιωτέον.
Aristotle’s declaration, that this great logical rule can only be proved by Induction, deserves notice. I have remarked the same thing about his rules for the conversion of propositions, in the beginning of the Analytica Priora. See above, [p. 145, seq.]
In regard to Contraries, you will study the thesis, to see whether the contrary of the predicate can be truly affirmed respecting the contrary of the subject, or whether the contrary of the subject can be truly affirmed respecting the contrary of the predicate. This last alternative occurs sometimes, but not often; in general the first alternative is found to be true. You must make good your point here also by Induction, or by repetition of particular examples. This locus will serve either for the purpose of refutation or for that of defence, according to circumstances. If neither of the two alternatives above-mentioned is found correct, this is an argument against the thesis.[112]
[112] Topic. II. viii. p. 113, b. 27-p. 114, a. 6. λαμβάνειν δὲ καὶ τὰ τοιαῦτα ἐξ ἐπαγωγῆς, ἐφ’ ὅσον χρήσιμον. — σπάνιον δὲ τὸ ἀνάπαλιν ἐπὶ τῶν ἐναντίων συμβαίνει, ἀλλὰ τοῖς πλείστοις ἐπὶ ταὐτα ἡ ἀκολούθησις. εἰ οὖν μητ’ ἐπὶ ταὐτὰ τῷ ἐναντίῳ τὸ ἐναντίον ἀκολουθεῖ μήτε ἀνάπαλιν, δῆλον ὅτι οὐδὲ τῶν ῥηθέντων ἀκολουθεῖ τὸ ἕτερον τῷ ἑτέρῳ.
In regard to Habitus and Privatio, the rule is the same as about Contraries; only that the first of the two above alternatives always holds, and the second never occurs.[113] If sensible perception can be predicated of vision, insensibility also can be predicated of blindness; otherwise, the thesis fails.
[113] Ibid. p. 114, a. 7-12.
In regard to Relata, the inference holds from the correlate of the subject to the correlate of the predicate. If knowledge is belief, that which is known is believed; if vision is sensible perception, that which is visible is sensibly perceivable. Some say that there are cases in which the above does not hold; e.g., That which is sensibly perceivable is knowable; yet sensible perception is not knowledge. But this objection is not valid; for many persons dispute the first of the two propositions. This locus will be equally available for the purpose of refutation — thus, you may argue — That which is sensibly perceivable is not knowable, because sensible perception is not knowledge.[114]
[114] Ibid. a. 13-25.