On Aug 20, 9:30 pm, MoeBlee <jazzm...@hotmail.com> wrote: > 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. > > MoeBlee
We have varaibles that range over numbers, and varaibles that range over symbol combinations of the formal system. You can call that "two- sorted" if you like. So waht? While there has been mention of "two sorts" of varaibles, nobody has given any indication of how that overcomes the problems that I have shown that arise in Godel's proof.