ABSTRACT
Philosophers and logicians who regard classes, numbers, and similar "mathematical entities" as somehow make-believe are usually referred to as "nominalists". The reason is clear if not cogent: the nominalist does not really believe that classes exist; so he avoids formulation (A). In contrast to classes, "sentences" and "words" seem relatively "concrete", so he employs formulation (B). A formalized language is given by completely specifying a grammar together with the meanings of the basic expressions. Nelson Goodman, who is the best-known nominalist philosopher, has never adopted the definition of validity as "truth of all substitution-instances". He denies that nominalism is a restriction to "physical" entities. However, while the view that only physical entities alone are real may not be what he intends to defend, it is the view that most people understand by "nominalism", and there seems little motive for being a nominalist apart from some such view.
