Abstract

This paper deals with the question: what does Carnap's conventionalism consist in? As Quine points out, logic is needed for inferring logic from conventions. In the same way, in order to show that mathematics is true by convention, or to provide a justification for mathematics by convention, the very mathematics must be presupposed, as Godel puts it. So, the conventionalist claim that logic and mathematics are true or justified by convention must fail. Is this predicament not a problem for Carnap's conventionalism? I shall argue it is not, for his conventionalism does not aim at justification of logic and mathematics. It is what Carnap later called "explication" that he tries to undertake with his conventionalism.