[FOM] On "ruling out" non-standard models of first order arithmetic

[Neil Tennant]

On Wed, 1 Nov 2006, Aatu Koskensilta wrote:

> ... if we
> consider some array of structures, it is by means of some set of 
> concepts, some set of mathematical ideas and ways of describing 
> structures. And then we can unproblematically say that the standard ones 
> are those for which induction holds - in the form of the informal 
> principle - and in particular that if induction fails for some structure 
> living in the mathematical world envisioned in terms of those concepts 
> and ideas, it is non-standard. 

Isn't part of the problem that mathematical induction holds (for all
first-order instances) in the non-standard models?

Neil Tennant