Logicism and Principle of Tolerance: Carnap’s Philosophy of Logic and Mathematics*

Abstract

ABSTRACT In this paper, the connection between logicism and the principle of tolerance in Carnap’s philosophy of logic and mathematics is to be presented in terms of the history of its development. Such development is conditioned by two lines of criticism to Carnap’s attempt to combine Logicism and Conventionalism, the first of which comes from Gödel, the second from Alfred Tarski. The presentation will take place in three steps. First, the Logicism of Carnap before the publication of The Logical Syntax of Language will be analyzed in its main features. Second, the relationship between Logicism and the Principle of Tolerance at the time of the publication of Logical Syntax, and thirdly, in the so-called semantical phase of Carnap’s thought will be examined. On the basis of the two preceding points, we will then critically analyze two interpretations of the possibility to maintain a philosophical position like that of Carnap nowadays.