Re-examining Russell's Paralysis: Ramified Type-Theory and Wittgenstein's Objection to Russell's Theory of Judgment

Abstract

It is well known that Russell abandoned his multiple-relation theory of judgment, which provided the philosophical foundations for PM's ramified type-theory, in response to criticisms by Wittgenstein. Their exact nature has remained obscure. An influential interpretation, put forth by Sommerville and Griffin, is that Wittgenstein showed that the theory must appeal to the very hierarchy it is intended to generate and thus collapses into circularity. I argue that this rests on a mistaken interpretation of type-theory and suggest an alternative one to explain Russell's reaction.