Re: Name the thesis: "Formal sentences capture informal ones"
Helene.Boucher_at_wanadoo.fr
Date: 01/30/05
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Date: 30 Jan 2005 06:06:39 -0800
" 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.
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