On Field’s Nominalization of Physical Theories∗

One of the most important questions of philosophy of mathematics is the ontological status of mathematical entities. In the late 70s, Quine and Putnam suggested an argument for the existence of mathematical entities. The argument is based on the idea that mathematics is not only applicable but in fact indispensable to empirical sciences; and if so, then mathematical entities are as indispensable from our best ontological picture of the world as electrons and other physical entities, to the existence of which physicists are committed. In it’s most explicit form the argument reads as follows.