[Nocturne]

pam69ur,

I agree. However, this is only a problem if you are attempting to achieve a secure proof, something which I am not particularly concerned with. In short, that a derivation may not be a proof in the sense which you mean does not mean that the same derivation is invalid, and so until someone produces an critical argument which purports to show that a language is inconsistent, I am not going to hold the mere possibility that it is inconsistent against it. In other words, the problem which seems to concern you is not inherent to mathematics, but with what you want to do with mathematics, and since I do not share the same goals I do not share the problem which afflicts you. Therefore, the result of the Godelian theorem doesn't concern me in the same way that it concerns you, since what you seek to do by mathematical argument is not something which I am interested in achieving.

If you want to argue that ZFC, or any other formal language is inconsistent then I am all ears. If, however, you simply want to rant on about how "proofs" in these languages do not provide the security which you would like then I am not interested--that is your problem, not mine.