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

From: r.e.s. (r.s_at_ZZmindspring.com)
Date: 01/29/05 

Date: Sat, 29 Jan 2005 20:40:37 GMT

<tchow@lsa.umich.edu> wrote ...
> The Church-Turing thesis is familiar to many people, largely because it
> has been widely discussed both in textbooks and in popular science
> writing.
> Having a name helps, too.
>
> There is an analogous thesis that is relevant to logic and the foundations
> of mathematics:
>
> (*) Formal sentences (in PA or ZFC for example) adequately express
> their informal counterparts.
>
> Years of discussion, on USENET and elsewhere, has convinced me that the
> average level of understanding of foundational issues would be enormously
> improved if (*) were, like the Church-Turing thesis, given a name and
> widely discussed.
>
> As matters stand today, a lot of people don't seem to even acknowledge the
> existence of informal mathematical discourse, despite the fact that all
> but
> a tiny fraction of mathematical discourse they've ever seen is informal
> (in
> the sense of (*)).

That reminds me of what Davis & Hersh say about
Hilbert's "formalist premise" ...

   "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.

Relevant Pages

  • Re: Name the thesis: "Formal sentences capture informal ones"
    ... > The Church-Turing thesis is familiar to many people, ... > There is an analogous thesis that is relevant to logic and the foundations ... > existence of informal mathematical discourse, ... Hilbert's "formalist premise" ... ...
    (sci.logic)
  • Name the thesis: "Formal sentences capture informal ones"
    ... The Church-Turing thesis is familiar to many people, ... has been widely discussed both in textbooks and in popular science writing. ... a tiny fraction of mathematical discourse they've ever seen is informal (in ... theorem and Rosser-style proof predicates would have been improved if I had ...
    (comp.theory)
  • Name the thesis: "Formal sentences capture informal ones"
    ... The Church-Turing thesis is familiar to many people, ... has been widely discussed both in textbooks and in popular science writing. ... a tiny fraction of mathematical discourse they've ever seen is informal (in ... theorem and Rosser-style proof predicates would have been improved if I had ...
    (sci.logic)