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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."
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