ABSTRACT
By a "nominalistic language" is meant a formalized language whose variables range over individual things, in some suitable sense, and whose predicate letters stand for adjectives and verbs applied to individual things. These adjectives and verbs need not correspond to observable properties and relations, but they must not presuppose the existence of such entities as classes or numbers. It has been repeatedly pointed out that such a language is inadequate for the purposes of science; that to accept such a language as the only language we are philosophically entitled to employ would require us to give up virtually all of mathematics. In truth, the restrictions of nominalism are as devastating for empirical science as they are for formal science; it is not just "mathematics" but physics as well that we would have to give up.
