On Aug 22, 3:52 am, MoeBlee <jazzm...@hotmail.com> wrote:
> > So, in the instance under discussion, Z(x1) is an expression of the > formal system.
No, it's not. That's the whole point of meta-language and sub- language. A meta-language can talk about the symbol combinations of the sub-language as combinations of symbols.
But once you say that, in a meta-language, that A = BC, you are assigning an equality between A and B, you have to at the same time IGNORE any physical properties of A and BC. Otherwise you could then state that A consists of one symbol - but because you have assigned an equality between A and BC, then it would also follow that BC consists of one symbol.
So that means that assigning an equality such as Z(x1) = ?some formal combination? precludes referring to the physical attributes of either side of that equality in the same set of propositions that constitute a proof, and that means that yoiu cannot apply that equality at the same time as applying the Godel numbering system to ?some formal combination?.