Re: Ruling-out Nonstandard Models of 1st-Order PA

A naive question:

Why rule out non-standard models of 1st-Order PA?

What's wrong with having other models?  Why should we be making our 
model-world smaller and not larger?

Cantor's Freedom Principle, roughly, "as long as numbers a conceptually 
distinct from each other and their relations well defined, mathematics 
should be free to use them".

Why should this not be so of models of PA?

Robbie Lindauer