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

tchow_at_lsa.umich.edu
Date: 01/31/05 

Date: 31 Jan 2005 14:35:40 GMT

In article <vcbwttuhxou.fsf@beta19.sm.ltu.se>,
Torkel Franzen <torkel@sm.luth.se> wrote:
< If you mean the work in "Arithmetization of metamathematics in a general
<setting", this dealt with more pressing problems. He showed among
<other things that the incompleteness theorem holds in a general
<formulation provided we require the axioms of a theory to be defined
<by what we now call a Sigma-formula. However, a Sigma-formula which
<extensionally defines the axioms of e.g. PA can still be intensionally
<incorrect.

That sounds like the paper I was thinking of, although I don't have my copy
on me to check the title.

Perhaps I expressed myself too strongly. I didn't mean to imply that
Feferman was trying to capture exactly what "intensionally correct"
means. That project, as I understand it, is still too vague to be a
strictly mathematical investigation, and maybe it is doomed to remain
that way permanently. But it still seems to me that a background
motivation of Feferman's work was to separate off certain deviant
(i.e., intensionally incorrect) predicates from "nice" ones. Having
a clear grasp of what's going on in the transition from informal to
formal is a prerequisite for formulating such a project and carrying it
out. Now, someone of Feferman's caliber obviously doesn't need the
"thesis" I'm proposing spelled out and given a catchy name. Mere
mortals, though, might benefit.

William Elliot mentioned the term "Hilbert's thesis." Googling on this
term turns up stuff that's similar to what I'm groping for. I'll have
to think about whether it's exactly what I'm after. 

-- 
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