On 5/26/07, Jesse Mazer <lasermazer.domain.name.hidden> wrote:
>
>
> Mohsen Ravanbakhsh wrote:
>
> >
> >Hi everybody,
> >I need to clarify. When we build this new combined system, we would be
> >immune to Godelian statements for one of them not for the whole system,
> >whatever it might be. So Jesse's argument does not hold, and of course
> the
> >new system does not contradict the Godel's theorem, it's (was!) just a
> way
> >to avoid it.
>
> But didn't you claim the combination of the two of them would be
> "complete"?
> "Complete" is supposed to mean a system will print out *every* true
> statement about arithmetic, and a Godel statement for a theorem-proving
> system is itself a true statement about arithmetic. So if the combined
> system has a Godel statement that it will never print out, and the
> combined
> system prints out every statement that the two of them can print out, then
> the combination of the two of them does not allow you to escape
> incompleteness.
>
> Jesse
>
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>
>
> >
>
Aha, there seems to be subtle point here:
My claim was: the new system would be complete regarding the statements
each one of two systems(one of them, because they're the same) can generate,
BUT building such a system would require some additional staff(!) to glue
those similar systems so they'd rely on each other, and follow the mentioned
mechanism. Those extra THINGS still should(!) cause the incompleteness of
the new system as a whole regarding the statements that consider this
coupling.
Anyway... it didn't work.
--
Mohsen Ravanbakhsh.
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Received on Sat May 26 2007 - 15:01:14 PDT