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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.

DOI: 10.1007/978-94-009-1902-0_6

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