  The problematic finitary propositions are those that express general facts about numerals such as that, for any given numeral \(n, 1+n = n+1\). It is problematic because, as Hilbert puts it, it “is from the finitist point of view incapable of being negated”  (1926,  378). By this he means that the contradictory proposition that there is a numeral \(n\) for which \(1+n \ne n+1\) is not finitarily meaningful. “One cannot, after all, try out all numbers”  (1928,  470). For the same reason, a finitary general proposition is not to be understood as an infinite conjunction but “only as a hypothetical judgment that comes to assert something when a numeral is given” (ibid.). Even though they are problematic in this sense, general finitary statements are of particular importance to Hilbert’s proof theory, since the statement of consistency of a formal system \(S\) is of such a general form: for any given sequence of formulas \(P, P\) is not a derivation of a contradiction in \(S\).