 Though Cantor’s diagonal is not a proof of non-denumerability, when it is expressed in a constructive manner, as Wittgenstein himself expresses it at (RFM II, §1), “it gives sense to the mathematical proposition that the number so-and-so is different from all those of the system” (RFM II, §29). That is, the proof proves non-enumerability: it proves that for any given definite real number concept (e.g., recursive real), one cannot enumerate ‘all’ such numbers because one can always construct a diagonal number, which falls under the same concept and is not in the enumeration. “One might say”, Wittgenstein says, 