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The Hilbert program was actually a specific approach for proving consistency.Quantifiers were supposed to be replaced by $\epsilon$-terms. $\epsilon{x}A(x)$was supposed to denote a witness to $\exists{x}A(x)$, arbitrary if there isnone. The Hilbertians claimed that in any proof in a number-theoretic system$S$, each $\epsilon$-term can be replaced by a numeral, making each lineprovable and true. This implies that $S$ must not only be consistent, but also1-consistent ($\Sigma_{1}^{0}$-correct). Here we show that if the result issupposed to be provable within $S$, a statement about all $\Pi_{2}^{0}$statements that subsumes itself within its own scope must be provable, yieldinga contradiction. The result resembles G\"odel's but arises naturally out of theHilbert program itself.

The Collapse of the Hilbert Program: A Variation on the G\"odelian Theme