Abstract
In his recent book Science Without Numbers, and in several subsequent papers,1 Hartry Field has defended an important, and in key respects highly unorthodox, variety of nominalism. In this paper, I want to do two things. First, I want to explain why I think that the position to which Field appears to me to be committed is not a tenable one. What I shall be saying in this part of my paper follows quite closely a line of argument first presented in my book Abstract Objects, which has since been further developed in an important paper by Crispin Wright.2 Then I want to consider whether there is scope for a version of nominalism that preserves what might seem especially attractive in Field's original position but avoids the problem I think that founders upon.
