Modality, the semantic approach and quantum mechanics

Abstract

According to the indispensability argument, we ought to be ontologically committed to mathematical entities, given that they are indispensable to our best scientific theories. Hartry Field (1980) has famously resisted the argument, developing a program to reformulate scientific theories without quantification over mathematical objects. In particular, Field worked out in detail the nominalization of Newtonian gravitacional theory, indicating how the theory could be formulated without quantification over real numbers. Field also provided an argument why the use of modal operators doesn't providean adequate strategy to nominalize scientific theories. In this paper, I discuss Field's argument against the claim that modality can be a general surrogate for ontology. After resisting this argument, I indicate an alternative picture that makes it clear why modality can play such a role.