ABSTRACT
Initially, the Vienna Circle strongly endorsed logicism, but its members were well aware of the problems arising for logicism in the form it was given in Principia Mathematica. Wittgenstein’s new view of logical propositions as tautologies only threw the existing problem into sharp relief. Several of the axioms needed for the logical reduction of mathematics to logic were obviously not tautologies. This chapter reconstructs how the logical empiricists adopted a form of nonstandard logicism in which the problematic axioms are represented as antecedents of conditionals. This if-thenism was adopted until the logicist position was abandoned by the logical empiricists, especially Carnap, under the pressure of Gödel’s results. This chapter covers the development from the early reception of logicism until its abandonment in Carnap’s Logical Syntax.
