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 552 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.”