Not Every Object of Thought has Being: A Paradox in Naive Predication Theory

Abstract

Naive set theory with an unqualified axiom specifying the existence of sets is contradictory as Russell showed. So too certain theories of predication resting on plausible, intuitive principles are contradictory if those principles are not in some way qualified or if restrictions are not imposed on standard inferential steps. This can be shown by an argument analogous to that of Russell with respect to the Abstraction Axiom of naive set theory. Just as Russell's argument has philosophical import, demonstrating that not every condition or attribution determines a set ofjust those things satisfying the condition or attribution, so too an inconsistency in a certain version of naive predication theory has its philosophical interest. It suggests for instance that not every object of thought has being. To put the point bluntly with respect to a rising, contemporary interest in Meinongian and other intensionalist theories, it shows that to think of a putative object is not a guarantee that there is in some sense (perhaps other than actual existence) such an object. Professor Hector-Neri Castafieda has developed in a recent series of articles ([1], [2], [3]) a novel and philosophically interesting theory of the nature of particulars and of their relations to things true of them.' In what follows, I gather some principles and assumptions suggested by what Castafieda has written about these matters. Using these to determine at least in part one version of naive predication theory, it turns out that such a theory can be shown by ordinary inferences of standard second-order logic to be inconsistent. This is a consequence of some interest in its own right. But it is of more interest philosophically as a kind of test case for such theories of predication. In particular, it should provide a