ABSTRACT
The two classical problems in the philosophy of logic are the demarcation problem and the correctness problem.1 The first is to answer the question “What is logic?” in the sense of saying what is distinctive of logical vocabulary or logical concepts. How are they to be demarcated from non-logical ones? Is second-order logic logic? Are modal operators logical operators? Is the set-theoretic epsilon logical vocabulary? The second is to say what the correct logic is: is it classical logic or intuitionism? Is it some modal logic (if so, which one?) and non-modal logic is just a fragment of it? My answer to the demarcation question is an expressive one: the expressive role distinctive of logical vocabulary is to make explicit in propositional form the broadly inferential relations in virtue of which non-logical locutions mean what they do. More specifically, in the language of Between Saying and Doing,2 it is to be both elaborated from and explicative of such inferential relations. On this account, the question of correctness lapses. No reasonably well-behaved logic is any more correct than any other (though some – such as classical logic – have other distinctive virtues such as being able to specify in their own terms the inferential roles of their own vocabulary). The right question is rather which aspects of inferential role do the various kinds of vocabulary serve to make explicit. Thus the classical two-valued conditional lets us say that an inference is good in the sense that it does not have true premises and a false conclusion. (Admittedly, this is a pretty weak endorsement of an inference, but it is still an important good-making property of inferences. Those that do not have it are bad.) The intuitionistic conditional lets us make explicit assessments of an inference as good in the sense that there is a recipe for turning a proof of its premises into a proof of its conclusion. C. I. Lewis’s hook of strict implication lets us claim that an inference is good in the sense that it is impossible for its premises to be true without its conclusion being true. And so on. I take it that there is no definite totality of dimensions along which we might want to assess the goodness of inferences, and so no definite totality of possible logical vocabulary.
