Logic and Neutrality

Timothy Williamson in the New York Times:

Here’s an idea many philosophers and logicians have about the function of logic in our cognitive life, our inquiries and debates. It isn’t a player. Rather, it’s an umpire, a neutral arbitrator between opposing theories, imposing some basic rules on all sides in a dispute. The picture is that logic has no substantive content, for otherwise the correctness of that content could itself be debated, which would impugn the neutrality of logic. One way to develop this idea is by saying that logic supplies no information of its own, because the point of information is to rule out possibilities, whereas logic only rules out inconsistencies, which are not genuine possibilities. On this view, logic in itself is totally uninformative, although it may help us extract and handle non-logical information from other sources.

The idea that logic is uninformative strikes me as deeply mistaken, and I’m going to explain why. But it may not seem crazy when one looks at elementary examples of the cognitive value of logic, such as when we extend our knowledge by deducing logical consequences of what we already know. If you know that either Mary or Mark did the murder (only they had access to the crime scene at the right time), and then Mary produces a rock-solid alibi, so you know she didn’t do it, you can deduce that Mark did it. Logic also helps us recognize our mistakes, when our beliefs turn out to contain inconsistencies. If I believe that no politicians are honest, and that John is a politician, and that he is honest, at least one of those three beliefs must be false, although logic doesn’t tell me which one.

More here.