Topics Logic

Question Is there any way to justify the laws of logic without using the laws of logic?

Accepted:
November 5, 2005

Comments

This is an incredibly complicated question. One question we might want to ask is what's meant by "justifying" a law of logic. I'll do my best to ignore that question here.

It's tempting to say that one can't justify anything without using the laws of logic, but that is arguably too strong. I think my belief that there is a computer in front of me is justified by my perception of it, and I doubt that the laws of logic have to be invoked there. Moreover, it is not obvious that the laws of deductive logic have always to be invoked even when justification is somehow "inferential". Often, they will, but, again, it's not clear they always must be.

What is meant here by "laws of logic"? Do we mean such generalizations as that, if a conditional is true and its antecedent is also true, then its consequent is true? Or do we mean to count what we'd otherwise call instances of logical laws, such as "Either Dubya likes popcorn or Dubya does not like popcorn", as "laws of logic" for the purposes of the question? If we're counting the latter sort of thing, then I don't see any obvious reason to deny that there could be "non-inferential" justification of such a claim: One just sees that the thing is true. That will be all the more appealing if we consider not seeing the truth of a single sentence but appreciating the correctness of an inference.

Things are more complex as regards generalizations. I doubt there could be non-inferential justification of such generalizations, and I doubt there could be inferential justifications that did not involve deductive reasoning. But I don't have a proof. Moreover, the really central question is whether reasoning deductively counts as "using the laws of logic". In some sense, surely, it does. But we need to be careful. It might be that, in arguing for the conditional mentioned above, I shall have to reason by modus ponens. But the correctness of the argument will depend only upon the correctness of the inferences I actually make: It will not depend upon all inferences of that form's being correct, and so I am in no way appealing to what I'm trying to prove. Moreover, the correctness of the argument does not depend upon the inferences' being logically valid as opposed, say, to their being truth-preserving for some non-logical reason.

Question Is there any way to justify the laws of logic without using the laws of logic? Accepted:November 5, 2005

Question Is there any way to justify the laws of logic without using the laws of logic?

Accepted:
November 5, 2005