## Consider the following:

Let's assume it's true that "If P, then Q". The conditional claim that you imagine being inferred from this has the structure "If not-P, then not-Q". [Not quite: I don't think the negation of "we lower standards" is "we raise standards". One way in which we might fail to lower standards is to keep them fixed.] This is indeed an incorrect inference. The first conditional claims that P is a sufficient condition for Q. While the second claims that P is a necessary condition for Q. And the latter claim simply doesn't follow from the former. For instance, it's true that if Rex is a dog, then Rex is a mammal. (Being a dog is a sufficient condition for being a mammal.) But this does not imply the false claim that if Rex is not a dog, then Rex is not a mammal. (Being a dog is not a necessary condition for being a mammal.) This fallacy is sometimes called *The Fallacy of Denying the Antecedent*. ("P" is called the *antecedent* of the first conditional claim above.)

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