Fregean Metasemantics

Abstract

How the semantic significance of numerical discourse gets determined is a metasemantic issue par excellence. At the sub-sentential level, the issue is riddled with difficulties on account of the contested metaphysical status of the subject matter of numerical discourse, i.e., numbers and numerical properties and relations. Setting those difficulties aside, I focus instead on the sentential level, specifically, on obvious affinities between whole numerical and non-numerical sentences and how their significance is determined. From such a perspective, Frege’s 1884 construction of number, while famously mathematically untenable, fares better metasemantically than extant alternatives in the philosophy of mathematics.