[FOM] On "ruling out" non-standard models of first order arithmetic
neilt at mercutio.cohums.ohio-state.edu
Wed Nov 1 18:28:33 EST 2006
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?
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