Logic

How do we know if we are reasoning correctly? Consider, for example, this witty “proof” that a ham sandwich is better than eternal bliss: Nothing is better than eternal bliss. But, surely, a ham sandwich is better than nothing (despite Leviticus 11:7). Therefore, a ham sandwich is better than eternal bliss! Admittedly, the error in this argument may be easy to see. But, of course, in more subtle lines of reasoning it is much harder to check for bugs. How, then, can we be confident, in general, that our arguments are fallacy-free?

Comments

I've generally become pretty good at detecting fallacious reasoning, both my own and that of others. I'm not perfect, to be sure, but pretty good. So, overall, it seems that, in any given case, my chances of having committed an undetected fallacy are fairly small. How small depends upon the complexity of the reasoning. If I'm trying to prove a complicated theorem, I may have to go over the proof repeatedly, spell out all the details, etc, before I can convince myself that the proof is correct. So maybe in those cases, at least initially, the chances I'd committed a fallacy are higher than they would be otherwise. But that seems all right. It just means that, to be justifiably sure that I've not committed a fallacy in any given case, I may have to do different things: a lot in some cases, maybe nothing in others. But if I have done those things and come to the belief that my reasoning is correct, then I see no particular reason the belief should not count as knowledge.

Of course, one can push skeptical worries here, just as one can push them elsewhere. But the usual replies will equally be available.

One more point. You sometimes see people argue this way. Suppose you've given a proof. You might have made a mistake, and if you have made a mistake, then the "proof" doesn't in fact give you reason to believe its conclusion. So your evidence for the conclusion must include evidence that you haven't made a mistake, and of course that evidence is empirical---you check the proof, etc. Hence, even mathematical beliefs depend upon empirical evidence and so aren't a priori. The standard answer to this nowadays is that the evidence you have is given by the proof alone, and the evidence that your proof is correct is just evidence that you have a proof.

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