Professor Weinberg, in his recent Abstraction, Relation, and Induction, has critically discussed the nominalistic tradition stemming from Ockham and continuing in the work of Berkeley and Hume. In this tradition there is one fundamental principle, which however divides into two parts. The first is (α) Whatever is distinguishable is distinct, and conversely. The second is (β) Whatever is distinct is separable, and conversely. Weinberg argues that both (α) and (β) are mistaken.
In this paper I propose to explore the case against nominalism. I shall suggest that Weinberg's argument against (β), though not defective in the way some recent critics believe, depends upon a hidden premiss. I shall also suggest that the argument against (β), when the needed premiss is added, is but a special case of a more general argument. The latter in no way depends upon considerations concerning relational predicates, though Weinberg does in his discussion specifically introduce such considerations. Nor is that unreasonable on his part.