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From: Newberry on 24 Jun 2010 10:57
On Jun 23, 11:19 pm, George Greene <gree...(a)email.unc.edu> wrote:
> > On Jun 23, 2:22 pm, George Greene <gree...(a)email.unc.edu> wrote:
> > >"Effectively generated" is well-defined.
> > > You just use the definition; THAT'S how you prove it.
>
> On Jun 23, 11:32 pm, Newberry <newberr...(a)gmail.com> wrote:
>
> > The issue is the definition of truth.
>
> No, DUMBASS, the issue IS NOT the definition of truth.
> ALL the definitions of truth have in common that everything that is
> provable is true (if the theory is consistent).

So prove to me that for any EFFECTIVELY GENERATED theory capable of
arithmetic and any plausible definition of truth such that everything
provable is true there are true but unprovable sentences.

 The question was
> whether
> the truths could get MORE COMPLICATED and go BEYOND that.
> It turns out that THEY CAN, so coming up with A MORE complicated
> definition of truth IS NOT going to change that!  That's only going to
> make this result MORE TRUE, under ANY definition of truth.
>
> > > "ANY conceivable" and "effectively generatable" are just NOT
> > > compatible.
> > > "Effectively generatable" puts some clear limitations on the theory.
> > > What is conceivable withOUT that constraint is going to be very broad,
>
> > Obviously I meant any conceivable within that constraint.
>
> But the whole point is, there ISN'T much of anything conceivable
> EXCEPTT TURING MACHINES, within that constraint!
> The other candidates (lambda-calculus, e.g.,) ARE PROVABLY
> equivalent!

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