FOM: What is the standard model for PA?

[Vaughan Pratt]

>Our understanding of the natural numbers isn't based on any formal
>definitions - rather, we rely on that understanding in proposing formal
>definitions.

Since our understanding of the natural numbers seems to include
finiteness---every number has only finitely many numbers between it
and 0---any indeterminacy in the notion of finiteness would seem to be
inherited by our understanding of natural numbers.

Are you contradicting this, or claiming that our understanding of
finiteness is determinate?

Vaughan Pratt