Logic

Hi, I'm having an argument with my pal. He argues since logic prescribes (creates a standard) what is a good/bad inference (valid/invalid) it is normative. On the other hand, I think Logic is like mathematics or physics - there are laws of logic, but they are not normative (they only describe). Can you help us settle this beef? Thank you, Miko

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I don't know that I can settle anything. The dispute you are having is one philosophers today have generally. Some people think logic is normative, in that it prescribes rules concerning how one should think, or reason; other people think logic is purely descriptive, and that it simply tells us something about the notion of implication or validity.

One reason people often given against the normative interpretation is that the norms logic provides just seem like bad ones. For example, it was once argued that, since logic tells us that A and ~A imply anything you like, then logic would be telling us that, if you reach a contradiction, you should infer that the moon is made of cheese; but, of course, what you should actually do is figure out what went wrong and give up one of the contradictory beliefs. The obvious reply, though, is that this is too simple a conception of what the norms logic prescribes are. It assumes, in particular, that if A implies B, then it is a norm that, if one thinks A, one should infer B. But maybe the norm is that, if one thinks A, then one ought either to infer B or to give up A. Logic won't tell you which one to do, but it demands you do one or the other.

A deeper concern is that reasoning itself might be more involved with probability than logic allows. In that case, the norms of reasoning would presumably come from probability theory, and classical two valued logic would have the wrong subject matter. (Let me insert a plug here for my colleague David Christensen's book Putting Logic in Its Place and suggest you read the entry on Bayesian epistemology at the Stanford Encyclopedia.) On the other hand, however, there are known ways of essentially deriving probability theories from logical theories, so two-valued logic would represent a sort of idealization to the case of absolute certainty of the norms that govern reasoning, which actually proceeds, most always, under uncertainty.

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