Tractatus 3.333: Wittgenstein on Russell’s paradox

This paper inquires into the last two paragraphs of 3.333 of Wittgenstein’s Tractatus. I argue there are two prima facie possible interpretations of these paragraphs, the ‘Allusory Interpretation’ and the ‘Stern Interpretation’. The crucial difference between these two interpretations is their answer to the question whether Wittgenstein intended to express Russell’s paradox formally, and whether he succeeded if he did intend this. These paragraphs of 3.333 have been glossed over by interpreters of Tractatus, with the exception of Max Black, in his Companion to Wittgenstein’s Tractatus (1964). Contrary to the ‘Stern Interpretation’, we shall conclude from our analysis that the formal expression in the 3rd paragraph of 3.333 does not and cannot express Russell’s paradox, which gives the ‘Allusory Interpretation’ the upper hand. We shall further dare to conclude that Black’s assertions about the last two paragraphs of 3.333 are wrong, but shall also demonstrate they point in the right direction: with some tweaking, a contradiction of Russellian flavour can be reached, which then gives the ‘Stern Interpretation’ the upper hand, in spite of the fact that Wittgenstein plausibly never thought of that particular tweaking.