• Korean Journal of Logic
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• v.20 no.1
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• pp.69-96
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• 2017

Wittgenstein criticizes explicitly Russell's theory of types and, in particular, his axiom of reducibility in the Tractatus Logico-Philosophicus. What, then, is the point of Wittgenstein's criticisms of Russell's theory of types? As a preliminary study to answer this question, I will examine how Wittgenstein criticized Russell's axiom of reducibility. Wittgenstein declares that Russell's axiom of reducibility is not a logical proposition, that if it is true it will be so mere by a happy chance and that "we can imagine a world in which the axiom of reducibility is not valid." What, then, is the ground for that? I will endeavor to show that by explicating the ideas of Wittgenstein's 1913 letter to Russell, those ideas decisively influenced on Ramsey's and Waismann's model which intended to show that the axiom of reducibility is not valid.