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Topic: A HARD FLAW in Godel's Proof
Replies: 7   Last Post: Dec 8, 2012 2:27 PM

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Graham Cooper

Posts: 4,295
Registered: 5/20/10
Re: A HARD FLAW in Godel's Proof
Posted: Nov 18, 2012 3:46 AM
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On Nov 18, 4:14 pm, George Greene <gree...@email.unc.edu> wrote:
> On Nov 17, 10:10 pm, "INFINITY POWER" <infin...@limited.com> wrote:
>

> > STEP 1:  DEFINE a 2 parameter predicate DERIVE(THEOREM, DERIVATION)
>
> > DERIVE(T,D) is TRUE IFF
> >   D contains a sequence of inference rules and substitutions
> >   and the final formula T in D is logically implied from the Axioms.

>
> This is NOT even what you MEANT to say.
> The WHOLE QUESTION is <<not>> whether T is or isn't logically implied by the
> axioms.
> That is HARD.  What is a SMALLER question and therefore
> EASY enough to make this doable



George I like your thinking here!



> is whether
> "the final formula T in D" is or isn't logically implied *BY*D*, by
> *THIS* derivation,
> by THIS sequence of inferences D.  Even IF THIS chain of reasoning D
> is WRONG, it could STILL be the case
> that T followed frOM THE AXIOMS, by A DIFFERENT sequence of inferences
> (different from D).
> Checking whether the final formula in the sequence is correctly
> derived BY THAT SEQUENCE
> is easy.  Checking whether there does or doesn't exist ANY old
> sequence-of-derived-inferences
> starting at some axioms and finishing with T is HARD, partly because
> the shortest such sequence might be
> MUCH MUCH longer than T.
>


OK so the T/F PREDICATE
DERIVES(T,<t1, t2, t3, t4,,,,T>)

is easy to program!
...As long as D is a given argument, for now.

STEP 2!

- - - - - - - - - - - - - -
STEP 2: DEFINE a Godel Statement.
i.e. Godel Statement named G =
ALL(M) ~DERIVE(G,M)
- - - - - - - - - - - - - -






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