Functions and Operations in the Tractatus

Abstract

Wittgenstein's early criticism of Russell's theory of types involved an insight into
the limits of formal representations of mathematical reasoning that continues to find
application. I will briefly review this criticism and indicate how it helped to
motivate Wittgenstein's distinction in the Tractatus between
functions and operations. I will further suggest that Wittgenstein's remark that
formal concepts cannot be represented by a function has an application to
formalizations of the Peano Axioms within first- and second-order logic.