On Aug 20, 1:22 am, contact080...@jamesrmeyer.com wrote:
>For years and > years, there have been numerous texts, books, etc on Gödel?s proof, > and it has been hailed as a masterpiece of logic ? without any need > for any additional theoretical assumptions such as might be required > by theories such as ?two-sorted? language.
And we don't need to use the rubric 'two-sorted langugae', but Godel does IN FACT specify that a certain kind of variable ranges over a certain kind of object and another certain kind of variable ranges over another kind of object, etc. Whether or not Godel himself would call that a 'multi-sorted' (meta)-language, the fact is that what he sets up in the paper is a multi-sorted metalangauge.
> So isn?t it strange that once I point out a flaw that applies to > Gödel?s proof, and which applies to those texts that have filled in > Gödel?s ?omissions?, that Gödel?s proof suddenly needs propping up > with new notions that Gödel did not intimate, and which haven?t been > perceived to have been necessary for over half a century?
No, whether or not called 'multi-sorted' (actually more sorts than just two), Godel mentions EXPLICITLY in his paper that he's using (in what we call his 'meta-language') different kinds of variables for different kinds of objects.