[FOM] Provability of Consistency

[Timothy Y. Chow]

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 
finitarily provable.

Tim