Field's programme: some interference

Abstract

The Quine/Putnam Indispensability Argument says that, since our best scientific theories unavoidably quantify over abstract objects, and since we have good reasons for believing our best scientific theories, we have good reasons for believing in the existence of abstract objects (Putnam 1971). Field has attacked the first premiss of this argument: he suspects that scientific theories can be formulated so that they do not quantify over abstract objects (Field 1980, 1985a). He defends this claim by providing nominalistic reformulations of two physical theories: Euclidean three-dimensional geometry and Newtonian gravitational theory. Although it does not immediately follow from this that modern physical theories can be nominalistically reformulated, Field sees no reason to suppose that the techniques used in his nominalistic reformulations could not be extended and developed to cover these theories. Field says we should prefer his reformulations for two reasons. Firstly, there is simply the consideration of nominalism: the new formulations of scientific theories are not committed to abstract objects, the old formulations are.1 Secondly, Field argues that, independently of the issue of nominalism, the reformulations have superior explanatory power to the old ones (Field 1980, Ch. 5). In this paper I shall argue that (1) aside from nominalism, Field's reformulations have the same unattractive features Field pins on the platonistic ones; (2) though his reformulations are nominalist, they are nevertheless still ontologically unparsimonious; and (3) Field has failed to show that certain aspects of scientific practice can be captured in his reformulations.