[FOM] Provability of Consistency
Timothy Y. Chow
tchow at math.princeton.edu
Tue Apr 2 14:53:01 EDT 2019
This is my final contribution to the Artemov thread.
Sergei Artemov wrote:
> A scheme is finitarily provable if each instance of S is.
It would appear to follow from the above principle that if anyone ever
proves Goldbach's conjecture by any means, then Goldbach's conjecture will
be finitarily provable.
We can write down a scheme
"exists prime p1 : exists prime p2 : p1 + p2 = E"
where in each instance of the scheme we insert a different even number E.
Under the assumption that Goldbach has been proved, every instance of the
scheme is certainly finitarily provable.
By Artemov's principle, it follows that Goldbach's conjecture is
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