Re: Name the thesis: "Formal sentences capture informal ones"
From: Mitch Harris (harrisq_at_tcs.inf.tu-dresden.de)
Date: 02/02/05
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Date: 2 Feb 2005 22:32:15 GMT
tchow@lsa.umich.edu wrote:
>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).
hmmm... but what does intelligible mean? is correctness involved with
that?
Wouldn't you say that some informal statements are imprecise, and so
must not be intelligible? That is, to the extent we can understand a
statement correctly, that must be formal enough (rather than informal).
(I'm not trying to be contrary for arguments sake; I'm trying to get a
reasonable understanding of what informal to mean for the purposes of your
proposed "thesis")
>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.
but this sense seems to be captured fully by "precision" or "removal of
doubt"
Mitch
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