Abstract

On the face of it, statements like, whose truth we are readily prepared to allow, carry an "ontological commitment," in Quine's jargon, to abstract entities: Some shapes are uninstantiated. Can a nominalistic paraphrase of be provided? I take Charles Chihara to be urging a positive answer in his exciting book, with in particular meeting his precise prescription: It is possible to construct a shape predicate, in some language or other, that fails to be satisfied by anything. Not that we are supposed to have in hand an effective procedure for producing any such predicate token. Rather, we are to envisage all the different shape predicate tokens that are to be found in different possible worlds. Some of them will have a null extension in those worlds. But that is not what asks of us. Think first of some shape predicate type of which there are no tokens in the actual world. Now consider a possible world in which there are tokens of that type. Finally, we are to think of those tokens as having a zero extension in our world.