[FOM] "Proof" of the consistency of PA published by Oxford UP

[martdowd at aol.com]

the axioms
of PA are indeed *obviously true* in the natural
numbers. What better and more
convincing proof can one want?


 

 

 

Arnon,

I would call this the standard classical position.  It's worth adding that there are progressions of theories, both the "natuarally occurring" ones (Q, E;ementaty arithmetix, PA, various subsystems of second order arithmetic, etc.), and artificia iterations (Turing, Feferman), all of which are consistent in the standard classical view, with stronger ones proving the consistency of weaker ones.

- Martin Dowd



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