Naturalistic Epistemology and the Harakiri of Philosophy

Abstract

Bertrand Russell, in the early part of the twentieth century, labored vigorously on a proper foundation for mathematics. One of his efforts resulted in a set theory along with a theory of types, a theory of levels of discourse. The existence of sets was made relative to the level of discourse already employed in the construction of the theory. This is the beginning of what can be termed constructive set theory, the attempt to tie talk of mathematical entities to linguistic operations of a certain kind, and hence to provide a philosophical justification for mathematics. Having embarked on this constructivist path, Russell detoured because he thought it was necessary to talk about collections of sets across levels. Consequently, he introduced his famous axiom of reducibility and committed what Hermann Weyl called the harakiri of reason. This attempt to justify mathematics resulted in suicide.