Frege the Carnapian and Carnap the Fregean

Abstract

In this paper I examine the fundamental views on the nature of logical and mathematical truth of both Frege and Carnap. I argue that their positions are much closer than is standardly assumed. I attempt to establish this point on two fronts. First, I argue that Frege is not attempting to defend metaphysical theses. Second, I argue that Carnap, where he does differ from Frege, can be seen to do so because of mathematical results proven in the early twentieth century. The differences in their views are, then, not primarily philosophical differences. Also, it might be thought that Frege was interested in analyzing our ordinary mathematical notions, while Carnap was interested in the construction of arbitrary systems. I argue that this is not the case: our ordinary notions play, in a sense, an even more important role in Carnap’s philosophy of mathematicsPhilosophy of mathematicsthan they do in Frege’s. Finally, I address Tyler Burge’s interpretation of Frege which is in opposition to any Carnapian reading of Frege.