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

Helene.Boucher_at_wanadoo.fr
Date: 01/30/05 

Date: 30 Jan 2005 00:51:10 -0800

Torkel Franzen wrote:
> Helene.Boucher@wanadoo.fr writes:
>
> > Look at it this way. Proof(x,y) - the first-order wff in PA that x
is
> > a Godel number of a proof P of the theorem T represented by the
Godel
> > number of y - asserts more than that P is a proof of T. One can
> > imagine the situation where there is a proof P of T, but not that
there
> > is the extremely large number x which is used to represent the
proof
> > P.
>
> 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.

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