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

From: Torkel Franzen (torkel_at_sm.luth.se)
Date: 01/30/05 

Date: 30 Jan 2005 09:39:24 +0100

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.

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