Re: Godel's Theorem and Model Theory
- From: Newberry <newberryxy@xxxxxxxxx>
- Date: Mon, 30 Jul 2007 07:20:59 -0700
On Jul 28, 1:46 pm, LauLuna <laureanol...@xxxxxxxx> wrote:
On Jul 26, 9:25 pm, Newberry <newberr...@xxxxxxxxx> wrote:
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.- Hide quoted text -
- Show quoted text -
It seems that you are conflating derivation in the system with
deduction in general. What G says, under the standard interpretation,
is equivalent to the statement that G cannot be derived in the system;
G does not say G is absolutely unprovable.
Where exactly did I conflate them?
Regards- Hide quoted text -
- Show quoted text -
.
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