Topics Logic

Question Alex George wrote [http://www.amherst.edu/askphilosophers/question/1663] that we can't ask "why should we be convinced by logic" or some similar question without thereby already submitting to logical priority; i.e., because the question itself has logic embedded in it. I'm not sure I understand this claim fully. Logic studies entailment relationships; if p, then q, therefore if not q, not p. On the other hand, logic doesn't tell us how to love another person. Insight from experience might tell us that. So there are other ways of knowing things, and different sorts of things, than logic. So if someone asks why choose to listen to logic at all, when I can learn plenty of important things from other roads to knowledge, why isn't this a fair question that doesn't already involve logic?

Accepted:
June 9, 2007

Comments

It's true that logic doesn't tell us how to do certain things, like dance or play badminton. Philosophers often distinguish between knowing how to do something and knowing that something is the case. The latter kind of knowledge is often termed propositional knowledge, because what we know is that a particular proposition holds. For instance, our knowledge that London is in England is an instance of propositional knowledge; the proposition we know is proposition that London is in England.

Now let's return to the question of how to justify logical inferences. Can we hope to do so by pointing to any abilities (knowings-how) that we possess (abilities which, I grant you, are not given to us simply in virtue of our appreciating logical entailment relations)? I don't think so. Abilities, knowings-how, aren't really routes to knowledge. (They might be prerequisites for our acquisition of knowledge—for instance, if I don't have the ability to walk to the window, I might not be able to learn what's going on outside—but they won't be relevant to the justification of the proposition known.)

Perhaps there are other, non-logical, ways of knowing that something is the case. For instance, just by opening my eyes I can know that there's a foot in front of me; that perception justifies the proposition that there's a foot here. So, perhaps perception is an example of one of those other "roads to knowledge" that you talk about. And it seems true that we don't justify the use of our eyes through logic.

But is it plausible to think that we could justify logical inferences on the basis of perception?

I guess my thought was: What could justify logical inference if not some argument? And yet how can an argument do that in a non-circular fashion given that logic just is the study of what makes for a good argument?

Recent epistemology has made a lot of the distinction between justification and something else that goes by the name warrant or entitlement, though some philosophers use "warrant" as an umbrella notion that covers both justification and entitlement. And of course the distinction gets drawn in different ways. But the basic idea is that being justified in some sense involves being able to appreciate that justification, which will, in central cases, take the form of an argument: If my belief that p is justified, then what justifies it must be something I know or at least could know. In that sense, justification, as philosophers in the tradition I'm exploring use the term, is more an "internalist" notion. An agent's being entitled to a belief, on the other hand, need not involve h'er appreciating the nature of that entitlement: I could be entitled to a belief that p even though I have no idea what it is that entitles me to that belief. And so entitlement is more of an "externalist" notion.

Many philosophers have thought this distinction would help with the case of perception: I could be entitled to the perceptual belief that there is a cup in front of me even though I cannot say why. (Maybe it has to do with the reliability of my perceptual systems.) I don't quite agree with that myself, but never mind. We were supposed to be talking about logic. And in the case of logic, the crucial question really concerns not so much knowledge about logic---such as, say, the knowledge that modus ponens preserves truth---but the epistemic status of logical inferences themselves. I myself think there's nothing very hard about knowing about validity, for reasons Michael Dummett pointed out some time ago, and I think most people would now agree.

Suppose I know that p and also know that, if p, then q. I now come to believe that q. Is that new belief knowledge? Well, maybe. But first of all, it is important to add that I inferred q from my other two beliefs. If I only came to believe that q because Fred told me, then maybe it is knowledge and maybe it isn't. So one might suggest this: If I know some premises and infer some conclusion from them, and if the conclusion really does follow from the premises, then I know the conclusion. Will that do? No, it won't. Counterexample: Suppose that Fred believes all the axioms of Peano arithmetic; let the year be 1992, i.e., before the proof of Fermat's Last Theorem. Suppose Fred says, "I hereby infer Fermat's Last Theorem from the axioms of Peano arithmetic". What Andrew Weil showed is that this is a valid inference. (Actually, he didn't show you could do it in PA, but you can, so we'll credit him with that, too.) Did Fred know FLT before Weil did? I don't think so.

So there's got to me more to such an inference's being epistemically appropriate: more than just the fact that the inference is valid. What more? Well, this is where the justification--entitlement distinction might help: You could be entitled to make a certain inference, even if you were not justified in making that inference. What being entitled would involve---well, that's a tough question. But it won't involve having an argument. Supposing it did would lead to an immediate regress, since we're obviously dealing with one's right to make the very simplest kind of inference. (This is essentially what Lewis Carroll pointed out in "What the Tortoise Said to Achilles".) So it seems there has to be something else going on here, some way of being in an epistemically good state without having an "argument" for anything.