Topics Logic

Question Consider the following: "If we lower the standards we lower the results, so if we raise the standards we raise the results" (in passing this is about education). I have the impression that there is a fallacy in this - even if I assume the first part of the inference, I suppose we could raise educational standards and just watch everybody fail miserably), but I cannot phrase clearly why/how this is a fallacious claim. Am I right? Is this fallacious and if so, is there a technical term for it?

Accepted:
November 12, 2011

Comments

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.)