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

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

Date: Sun, 30 Jan 2005 11:13:08 GMT

<Helene.Boucher@wanadoo.fr> ha scritto

> First, as a concrete example use instead the much simpler
>
> (x)(Nx => Ex Sxy) .
>
> Then this a theorem of PA, since it is an axiom of PA. It would not,
> however, be provable in the systems of which I speak.

What is the relevance of its being unprovable in that particular system?
What is special about that system?

> Anyway, I'm not quite sure what essential falls away if PA proves
> propositions which are not true.

Uhm... if it is not true that Ex(x=n)->Ex(x=SS0*SS0*...*SS0) we should add
its negation to PA, but this lead to inconsistency, so we have to change the
axioms of PA and so an enormous part of mathematics (which is all connected
with arithmetic) should be changed.

Relevant Pages