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

From: William Elliot (marsh_at_privacy.net)
Date: 01/30/05 

Date: Sat, 29 Jan 2005 21:02:09 -0800

On Sat, 29 Jan 2005, r.e.s. wrote:

> <tchow@lsa.umich.edu> wrote ...
>>
>> (*) Formal sentences (in PA or ZFC for example) adequately express
>> their informal counterparts.
>
> That reminds me of what Davis & Hersh say about
> Hilbert's "formalist premise" ...
>
It's the converse of Hilbert's thesis, that every informal mathematical
statement can be formalized.

> "Hilbert's program rested on two unexamined premises;
> first, the Kantian premise that _something_ in mathematics -- at least
> the purely "finitary part" -- is a solid foundation,
> is indubitable; and second, the formalist premise, that a
> solidly founded theory about formal sentences could validate
> the mathematical activity of real life [...]"
>
> --r.e.s.
>