Re: Name the thesis: "Formal sentences capture informal ones"

From: LordBeotian (pokipsy76_at_CANCELLAMIyahoo.it)
Date: 01/30/05 

Date: Sun, 30 Jan 2005 09:30:00 GMT

<Helene.Boucher@wanadoo.fr> ha scritto

> > If we take the view that the existence of n does not imply the
> > existence of 2^n, there is very much in mathematics that falls away,
> > and the question of whether Con(PA) is an adequate formalization of
> > "PA is consistent" becomes a very minor side issue.
>
> It's not a side issue to this thread, because that was what this thread
> was about.
> I'm not quite sure whether anything essential falls away, in any case.

A first problem could be that

Ex(x=n)->Ex(x=SS0*SS0*...*SS0) [SS0 multiplied n times]

is a theorem of PA for any numeral representing n.
So PA would be unsound...