Classical logic and its rivals

Abstract

Classical logic and a given nonclassical logic are, by definition, incompatible in some sense. In some cases, this incompatibility is innocuous. In other cases, the nonclassical logic is incompatible with classical logic on a fundamental level, such that the two logics can be seen as rival theories of logical entailment and only one of them can succeed. I will explore the structure of these cases of logical rivalry by considering three examples: Dummett’s antirealism, Putnam’s response to results of quantum mechanics, and Tye’s response to vagueness. I will show that, despite the differences between these cases’ motivations and methods, they nevertheless all conform to a particular framework in challenging classical logic. Moreover, these diverse cases all characterize classical logic as the result of an unwarranted generalization from a limited and apparently privileged realm of entailment.