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

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

Date: 29 Jan 2005 20:47:37 GMT

In article <vcbr7k4j7it.fsf@beta19.sm.ltu.se>,
Torkel Franzen <torkel@sm.luth.se> wrote:
>tchow@lsa.umich.edu writes:
>> Then how about, "All informal statements of ordinary mathematics are
>> expressible by formal sentences in ZFC"?
[...]
>The above is a lot more problematic to make
>precise. What is it we require of a formal sentence in ZFC if it is to
>express a given informal statement of ordinary mathematics? In
>practice, we recognize formalizations as adequate, but there are many
>different ways of formalizing informal mathematical statements, and it
>is far from clear how to characterize what counts as an adequate
>formalization.

I agree that it's far from clear how to characterize what counts as
an adequate formalization. In fact, a large part of the point of
articulating the thesis is to draw attention to this difficulty.

But by saying that it's "problematic to make precise," are you *objecting*
to my project of formulating the thesis? The very nature of my proposed
thesis prevents it from being *mathematically* precise, just as the
Church-Turing thesis isn't *mathematically* precise. That doesn't mean
that it's too imprecise to formulate as a snappy thesis. 

-- 
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

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