What are Carnap's views on the epistemology of mathematics? Did he believe in a priori justification, and if so, what is his account of it? One might think that such questions are misguided, since in the 1930s Carnap came to reject traditional epistemology as a confused mixture of logic and psychology. But things are not that simple. Drawing on recent work by Richardson and Uebel, I will show that Carnap's mature metaphilosophy leaves room for two distinct notions of a priori (...) justification: one propositional, the other doxastic. The latter is especially interesting since it comes closest to a traditional understanding of a priority. On the other hand, Carnap has little to say about doxastic justification in his writings. This lacuna can be filled by drawing on an unpublished exchange with Irving M. Copi. In it, so I will show, Carnap endorses the view that agents can come to know all mathematical truths a priori. This fact, so I will further argue, can be used to adjudicate a dispute between Ricketts and Friedman about the nature and viability of Carnap's philosophy of mathematics—specifically his reliance on infinitary methods. (shrink)

The paper analyses Frege's approach to the identity conditions for the entity labelled by him as Sinn. It starts with a brief characterization of the main principles of Frege's semantics and lists his remarks on the identity conditions for Sinn. They are subject to a detailed scrutiny, and it is shown that, with the exception of the criterion of intersubstitutability in oratio obliqua, all other criteria have to be discarded. Finally, by comparing Frege's views on Sinn with Carnap's method of (...) extension and intension and the method of intensional isomorphism, it is proved that these methods do not provide a criterion for the identity of Frege's Sinn, even for extensional contexts, that the concept of intension does not coincide, as stated by Carnap, in these contexts, with Frege's concept of Sinn, and that Carnap's claim that in oratio obliqua Frege's semantics leads to an infinite hierarchy of Sinn entities can be questioned at least hypothetically in the light of certain new historical facts. (shrink)