That has nothing to do with any of the major points of Goedel. What it sounds like is that you have put Cantors diagonalization argument in a blender with Russel.

Goedels first work of major import was (extremely rough!) a proof that propositional calculus is complete. This is to say that if a sentence P is semantically true under the definition of the PROP language, then it can be proven to be true under the rules of derivation.

Goedels second work of note was that (going on distant memory) any axiomatization of arithmetic is not both complete and consistent. This is to say you can state things that are intuitively true in arithmetic and not be able to prove them within the system syntactically. This is very important not only for the foundations of mathematics, but for mathematics in general.

So they may or may not be *really* true. (but voyager I/II still hit the cosmic bullseye, so I ain't holding my breath)

Davin L.