I agree with you that a logic is an account of truth-preserving inference. But, by this definition, fuzzy logic absolutely qualifies as a logic. The rules of inference in fuzzy logic are truth-preserving, provided we’re talking about “full” truth, i.e. we’re not in the realm of fuzziness. There are other non-classical logics, besides intuitionism, that also provide accounts of valid inference that are truth-preserving. Relevance logic, for example.
I still see those as mathematics, rather than logic, and the same goes for all other non-classical systems, such as all the modal logics. All of these are more like group theory than they are like logic, in the fundamentalist sense of “logic” I read the poll as talking about. They axiomatise certain mathematical objects, but not the general process of valid reasoning itself. That, I claim, is a problem completely solved by the classical first-order predicate calculus.
I agree with you that a logic is an account of truth-preserving inference. But, by this definition, fuzzy logic absolutely qualifies as a logic. The rules of inference in fuzzy logic are truth-preserving, provided we’re talking about “full” truth, i.e. we’re not in the realm of fuzziness. There are other non-classical logics, besides intuitionism, that also provide accounts of valid inference that are truth-preserving. Relevance logic, for example.
I still see those as mathematics, rather than logic, and the same goes for all other non-classical systems, such as all the modal logics. All of these are more like group theory than they are like logic, in the fundamentalist sense of “logic” I read the poll as talking about. They axiomatise certain mathematical objects, but not the general process of valid reasoning itself. That, I claim, is a problem completely solved by the classical first-order predicate calculus.