Logic

Is logic ever wrong?

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Let's try a related question: is physics ever wrong?

The answer is pretty clearly yes in one sense. Physicists can be wrong. And if enough physicists are wrong about the answer to some physics question, then Physics as a discipline is wrong. It's happened before and will no doubt happen again. Nonetheless, it's perfectly natural to say things like "I wonder if we really have the physics of black holes right." When we talk that way, we use the word "physics" to mean "the principles that provide the true descriptions of physical systems." Those principles, of course, can't be wrong because the right principles, whatever they may be, aren't wrong.

Same goes for logic. There are logicians. They can make mistakes. And there is a discipline of Logic. It could end up in some collective error about something or other. But there's lots of room for the other sort of usage. Someone might insist that logic dictates a certain conclusion when in fact the conclusion doesn't really follow from the premises. It might not really follow even if we were all under the illusion that it does. If by "logic" we mean, more or less, the correct principles of inference correctly applied then logic in that sense can't be wrong for the trivial reason that we're using the term to mean the principles and inferences that are right whether we know it or not.

Though this sense makes sense both for logic and for physics, it strikes my ear that it's a bit more natural in the logic case, perhaps because we think of the correct logical principles as having a kind of Eternal Truth that nothing else except pure mathematics can aspire to.

Be that as it may, even if we agree that there's a sense of the world "logic" in which logic can't be wrong, there's not much mileage to be gotten from that. Logic may not lie, but liars and lunkheads have been known to cry "Logic!"

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