> Then think a bit harder in order to see that his proof is self- > contradictory. He assumes a complete list, enumerated by all natural > numbers. But he gets a further real that without problems can be > enumerated too. His procedure of assuming a complete list is obviously > wrong.
I believe this corresponds with Wittgenstein's criticism of the proof. It can say as much about the semantic indeterminacy of "all" as it can about the countability of real numbers.
In general, the finiteness of formulas forces issues of locally finite reference. Similarly, the semiotics of observable sign vehicles (Saussere) forces issues of local denumerability on namespaces.
Piercean semiotics, however, has no such delineation of signs and might be interpretable as admitting a continuum of names.
The proof, however, is not self-contradictory.
It is a proof by contraposition. Falsity of the consequence is taken to imply falsity of the antecedent.
If you using a different logic from the rest of us, could you please list it rules?