Quine’s Other Way Out

Abstract

It is shown that, on the traditional, grammatical notion of a predicate as the remainder of a sentence once the subject term has been removed, there is no problem with Russell's Paradox, or comparable paradoxes such as Grelling's, and the Paradox of Predication. The standard formal ban on substituting predicates involving free variables into schemas where those variables would become bound is enough to prevent the standard paradoxes from developing. The re-arrangements required in the foundations of Set Theory to incorporate this insight are then discussed, and the consequences for the closely related matters Diagonalisation, and Cantor's Theorem explained.