[FOM] Potential infinity

[Timothy Y. Chow]

On Mon, 9 Mar 2015, Arnon Avron wrote:
> As I have hinted in my previous posting, for seeing the validity of the 
> axioms of PA a potential understanding of the collection of the natural 
> numbers suffices.

Can you be more formal about this point?  What I mean is, suppose I asked 
you to formalize the argument in your previous posting.  Would it 
correspond to one of the standard proofs of the consistency of PA?  Which 
one?  Presumably it would not be a ZF-proof, since ZF explicitly assumes 
the set of natural numbers as a complete infinity, and you're claiming 
that your proof employs no such assumption.

Tim