Field & Fregean Platonism

Crispin Wright

pp. 73-93

in: Irvine (ed), Physicalism in mathematics, Berlin, Springer, 1990

Abstract

In this paper, I want to return to an attempt I made a few years ago in my Frege's Conception of Numbers as Objects (henceforward FCNO)¹ to bring general ideas about the nature of singular terms and singular reference to bear on the issue between mathematical platonism and its opponents. The ideas in question are at least implicit in Frege's way of proceeding in Grundlagen, and are also canvassed in various of Dummett's writings.² They have been deepened and strengthened in Hale's recent book³ and provide, it seems to me, by far the best hope for a straightforward platonistic construal of large portions of classical mathematics. My principal purpose here is to add to the reasons for confidence in them by responding to some criticisms canvassed by Field, in his critical notice of FCNO.⁴

Cited authors

Frege Gottlob

Plato