Logic

Me and my professor are disagreeing about the nature of logic. He claims that logic is prescribes norms for correct reasoning, and is thus normative. I claim that logic is governed by a few axioms (just like any in any other discipline, i.e. science) that one is asked to accept, and then follows deductively, free of any normative claims. My question is: which side is more sound? Thank you.

Comments

In this context, by "normative claims" I take it you mean claims that one ought to (or ought not to) do some particular thing. Can we get such claims out of principles of deductively valid inference? I think so. If you accept P, and you recognize that P implies Q, then there's a sense in which you ought to accept Q: you're logically and rationally committed to Q by propositions that you accept and recognize. If you accept Q, and you recognize that P implies Q, there's a sense in which you ought not to deduce P from those propositions alone: doing so would be fallacious.

Now, you might say that the ought and ought not in those cases is only hypothetical: "If you want your deductive reasoning to be reliable, then you ought (or ought not)...." But I think the antecedent of that conditional (the "if" part) is easy to discharge. Plenty of people do want their deductive reasoning to be reliable, and so there's a sense in which such people really ought to use modus ponens and really ought to avoid the fallacy of affirming the consequent.

In fact, it's plausible to hold that everyone who reasons deductively wants his/her reasoning to be reliable. It's hard (for me) to imagine someone who engages in deductive reasoning without caring whether the result of the reasoning can be relied on. (I'd be inclined to describe him/her as engaging in something other than deductive reasoning.) If so, then the antecedent holds for every instance of deductive reasoning, and thus the normative claims in the consequent do too.

Without disagreeing with Stephen's fine response, let me point out one other issue. You say that "logic is governed by a few axioms...and then follows deductively, without any normative claims". But there is no "following deductively" without logic: logic is about the correct norms of deductive reasoning. So this conception is flatly circular: a point made a long time ago by Quine in his paper "Truth by Convention".

I should say that there are philosophers who deny that logic is about reasoning at all. On this view, logic is about a certain relation between propositions, implication, that it aims to characterize. But then the dispute just shifts to whatever one thinks does characterize the norms of reasoning, e.g, decision theory. And, for what it's worth, my own view has always been that these philosophers have too simplistic a conception of what sorts of norms logic articulates. But that is a larger issue.

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