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In 4.27 and 4.42 of his  Tractatus  Wittgenstein introduces quite complicated formulas, which are equivalent to    $$2^n$$  2 n and    $$2^{2^{n}}$$  2 2 n . This paper shows, however, that the formulas Wittgenstein presents fit particularly well with the way he thinks about truth values, logical connectives, tautologies, and contradictions. Furthermore, it will be shown how Wittgenstein could have avoided truth values even more radically. In this way it is demonstrated that the reference to truth values can indeed be substituted by talking of existing and non-existing facts.

Truth Tables Without Truth Values: On 4.27 and 4.42 of Wittgenstein’s Tractatus