A DEFENSE OF LOGICISM

Abstract

We argue that logicism, the thesis that mathematics is reducible to logic and analytic truths, is true. We do so by (a) developing a formal framework with comprehension and abstraction principles, (b) giving reasons for thinking that this framework is part of logic, (c) showing how the denotations for predicates and individual terms of an arbitrary mathematical theory can be viewed as logical objects that exist in the framework, and (d) showing how each theorem of a mathematical theory can be given an analytically true reading in the logical framework.