Wakijo Yasuhiro

Noe-Meinongian theories admit nonexistent objects and are generally friendly to abstract objetcts like Plato's Forms. There are several different neo-Meinongian theories, and one of them is the semantic theory of G. Priest, known as “noneism”. Is it possible to interprete Plato's theory of Forms on noneism? Forms are supposed to have three characteristics about predication: predicatecorrespondence, self-predication and predicate-purity. In noneism, worlds are divided into possible, impossible, and open worlds, the first two being closed worlds and the actual world a possible world. In closed worlds, predication is incompatible with predicate-purity. For example, if something is F, it must also be F or G, so more than one predicates must apply to it. Further, predicate-purity fails in any possible world: more than one predicates apply to anything whatsoever. Moreover, in possible worlds, if Forms have predicate-correspondence, self-predication is unavoidable for some of them. Things are quite different in an open world. Since open worlds are not closed under entailment, we can hold that e.g., the Form of whiteness is white and is nothing else there: it is not true that it is colored or even that it exists; the only thing that exists in an open world is the Form of existence. We also seem to be albe to admit the Forms of a golden mountain, an exisising golden mountain, something both white and not white, etc., each Form safely having the three characteristics. This is, however, an illusion. When a matrix contains more than one free variables, infinitely many one-place predicates can be obtained from it by substitution. If they all correspond to a unique Form, it can be shown that even in an open world infinitely many predicates must apply to the same Form. Thus the predicate-purity fails. One possible responce is to modify the denotation function so that it allocates extensions not to matrices but directly to predicates, but it comes at a cost.