Steps toward a constructive nominalism

We do not believe in abstract entities. No one supposes that abstract entities—classes, relations, properties, etc.— exist in space-time; but we mean more than this. We renounce them altogether. We shall not forego all use of predicates and other words that are often taken to name abstract objects. We may still write ‘ x is a dog,’ or ‘ x is between y and z ’; for here ‘is a dog’ and ‘is between … and’ can be construed as syncate-gorematic: significant in context but naming nothing. But we cannot use variables that call for abstract objects as values. In ‘ x is a dog,’ only concrete objects are appropriate values of the variable. In contrast, the variable in ‘ x is a zoölogical species’ calls for abstract objects as values (unless, of course, we can somehow identify the various zoological species with certain concrete objects). Any system that countenances abstract entities we deem unsatisfactory as a final philosophy.