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

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

Date: Sun, 30 Jan 2005 14:25:24 GMT

<Helene.Boucher@wanadoo.fr> ha scritto

> " so we have to change the axioms of PA"
>
> Since I would suggest changing the axioms of PA - specifically
> eliminating the successor axiom - you do not need to draw this
> conclusion. I grant it.
>
> "an enormous part of mathematics (which is all connected with
> arithmetic)"
>
> In such a system you cannot prove
> (x)(y)(x + y = y + x).
> On the other hand, one can prove
> (x)(y)(z)(x + y = z => y + x = z)
> I would suggest there is not an essential loss.

By successor axiom do you mean the axiom (Sx=Sy)->(x=y) ?