Does Logicism Say Something That Should Not Be Said?

Abstract

The objective of this paper is to analyze the broader significance of Frege’s logicist project against the background of Wittgenstein’s philosophy from both Tractatus and Philosophical Investigations. The article draws on two basic observations, namely (1) that  Frege’s project aims at saying something that was only implicit in everyday arithmetical practice, as the so-called recursion theorem demonstrates, and (2) that the explicitness involved in logicism does not concern the arithmetical operations themselves, but rather the way they are defined. It thus represents the attempt to make explicit not the (arithmetical) rules alone, but rather the rules governing their following, i.e. rules of second-order type. I elaborate on these remarks with short references to Brandom’s refinement of Frege’s expressivist and Wittgenstein’s pragmatist project.