WITTGENSTEIN’S TRACTATUS 3.333 AND RUSSELL’S PARADOX
WITTGENSTEIN’S TRACTATUS 3.333 AND RUSSELL’S PARADOX

Summary/Abstract: In his ‘Tractatus logico-philosophicus’, Ludwig Wittgenstein declares that he has solved Russell’s paradox. He presents the solution in a prima facie simple formula “($f) : F(fu) . fu = Fu”. This solution is disregarded both by the Russellians and most Wittgensteinians. In this paper I try to read the above formula and translate it into a class membership language (CML). I show that this formula contradicts Russell’s logic. I investigate and compare the different forms of this formula in Wittgenstein’s manuscripts and in the different editions of the ‘Tractatus’. I also take a look at the different interpretations of this formula in literature. My position is that Wittgenstein created his own transcendental logic that can show self-referential (reflexive) sentences without reflexivity.

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