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Topic: Godel Incompleteness Theorem
Replies: 172   Last Post: May 2, 2013 2:49 AM

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 Jack Markan Posts: 6,964 Registered: 2/26/05
Re: Godel Incompleteness Theorem
Posted: Aug 20, 2008 4:30 PM

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

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