Name the thesis: "Formal sentences capture informal ones"

tchow_at_lsa.umich.edu
Date: 01/29/05 

Date: 29 Jan 2005 20:00:28 GMT

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 (*)).

At a somewhat more sophisticated level, I can testify that my own ability
to grasp intermediate-level concepts such as the proof of the reflection
theorem and Rosser-style proof predicates would have been improved if I had
already had a firm grasp of the significance of (*).

Any candidates for a catchy name for (*)? 

-- 
Tim Chow       tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth.  ---Galileo, Dialogues Concerning Two New Sciences

Relevant Pages

  • 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)
  • 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" ... ...
    (comp.theory)
  • 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)