Chapter 33.—False Inferences May Be Drawn from Valid Reasonings, and Vice Versa.

51.  In this passage, however, where the argument is about the resurrection, both the law of the inference is valid, and the conclusion arrived at is true.  But in the case of false conclusions, too, there is a validity of inference in some such way as the following.  Let us suppose some man to have admitted:  If a snail is an animal, it has a voice.  This being admitted, then, when it has been proved that the snail has no voice, it follows (since when the consequent is proved false, the antecedent is also false) that the snail is not an animal.  Now this conclusion is false, but it is a true and valid inference from the false admission.  Thus, the truth of a statement stands on its own merits; the validity of an inference depends on the statement or the admission of the man with whom one is arguing.  And thus, as I said above, a false inference may be drawn by a valid process of reasoning, in order that he whose error we wish to correct may be sorry that he has admitted the antecedent, when he sees that its logical consequences are utterly untenable.  And hence it is easy to understand that as the inferences may be valid where the opinions are false, so the inferences may be unsound where the opinions are true.  For example, suppose that a man propounds the statement, “If this man is just, he is good,” and we admit its truth.  Then he adds, “But he is not just;” and when we admit this too, he draws the conclusion, “Therefore he is not good.”  Now although every one of these statements may be true, still the principle of the inference is unsound.  For it is not true that, as when the consequent is proved false the antecedent is also false, so when the antecedent is proved false the consequent is false.  For the statement is true, “If he is an orator, he is a man.”  But if we add, “He is not an orator,” the consequence does not follow, “He is not a man.”

CAPUT XXXIII. In falsis sententiis conclusiones verae esse possunt, et in veris falsae.

51. Sed in hoc loco de resurrectione cum ageretur, et regula connexionis vera est, et ipsa in conclusione sententia. In falsis autem sententiis, connexionis veritas est isto modo: faciamus aliquem concessisse, Si animal est cochlea, vocem habet; hoc concesso, cum probatum fuerit vocem cochleam non habere, quoniam consequenti ablato illud quod praecedit aufertur, concluditur non esse animal cochleam. Quae sententia falsa est, sed ex concesso falso vera est conclusionis connexio. Veritas itaque sententiae per seipsam valet; veritas autem connexionis ex ejus cum quo agitur, opinione vel concessione consistit. Ideo autem, ut supra diximus, infertur vera connexione quod falsum est, ut eum cujus errorem corrigere volumus, poeniteat concessisse praecedentia, quorum consequentia videt esse respuenda. Jam hinc intelligere facile est, sicut in falsis sententiis veras, sic in veris sententiis falsas conclusiones esse posse. Fac enim aliquem proposuisse, Si justus est ille, bonus est, et esse concessum; deinde assumpsisse, Non est autem justus; quo item concesso, intulisse conclusionem, Non est igitur bonus. Quae tamen etsi vera sint omnia, non est tamen vera regula conclusionis. Non enim sicut ablato consequenti aufertur necessario quod praecedit, ita etiam ablato praecedenti aufertur necessario quod consequitur. Quia verum est, cum dicimus, Si orator est, homo est: ex qua propositione si assumamus, Non est autem orator; non erit consequens cum intuleris, Non est igitur homo.