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

tchow_at_lsa.umich.edu
Date: 02/02/05 

Date: 02 Feb 2005 18:05:11 GMT

In article <36cfohF4v935nU1@news.dfncis.de>,
Mitch Harris <harrisq@tcs.inf.tu-dresden.de> wrote:
>I think also I mentioned natural language as informal, and some strict
>syntax/semantics language as formal, but now I want to critique that.
>It just doesn't seem enough. Who's to say that I can't consider the
>subset of natural language that you wrote your informal example above
>to -be- the formal language (stipulate formal rules on it). How do you
>know the language of PA (or ZFC or whatever) is formal enough? Where
>(if anywhere) is the demarcation between informal and formal?
>
>And, then, what more is there if only part of the difference is precision?

See Mike Oliver's comments. Initially, I also thought that the difference
was a matter of precision, but upon further reflection, I don't think that
that is the right word. The difference, as Mike Oliver said, is the
difference between intelligibility (informal statements have meanings that
we can understand) and manipulability (formal statements have a precisely
defined syntactic structure that can be analyzed mathematically).

Drawing a clean bright line between the two is probably a misguided project.
However, we can still address your question, "How formal is formal enough?"
The proper response is, "Formal enough for what? What is your goal?" If
your goal is to prove independence results, for example, then you just need
to be formal enough to allow the appropriate mathematical analysis to be
carried out. Figuring out how formal is formal enough then becomes a
special case of the more general problem of figuring out how to formulate
problems so that they are amenable to mathematical analysis, which is a
skill that comes with practice. 

-- 
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

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