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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Received on Sat May 26 2007 - 14:38:43 PDT