Re: Godel's Theorem and Model Theory
- From: Newberry <newberryxy@xxxxxxxxx>
- Date: Thu, 26 Jul 2007 18:00:09 -0700
On Jul 26, 1:09 pm, stevendaryl3...@xxxxxxxxx (Daryl McCullough)
wrote:
Newberry says...
On Jul 26, 7:08 am, stevendaryl3...@xxxxxxxxx (Daryl McCullough)
wrote:
Newberry says...
Assume the standard model
Then T(G)
G [by T(G) <--> G]
this leads to a contradiction
Therefore the standard model is incorrect
That leaves the non-standard models
So let's assume a non-standard model
If I am not mistaken a contradiction can be derived as well
The liar strikes back
What is wrong with the above reasoning?
Well, the key statement that is wrong is the
claim "...this leads to a contradiction". No,
it doesn't. I can't say what's wrong with your
reasoning since you didn't say why you think it
leads to a contradiction.
We have derived G, which says about itself that it is not derivable.
G is constructed for a specific theory. For example, Peano
Arithmetic. For PA we can construct a sentence G such that
G is true (in the standard model of arithmetic)
<-> G is not provable in PA
That's not a contradiction.
When you say "G is true in the standard model" is it not the same as
"if we assume the standard model then G"? .
--
Daryl McCullough
Ithaca, NY- Hide quoted text -
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