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

tchow_at_lsa.umich.edu
Date: 02/04/05 

Date: 04 Feb 2005 14:56:36 GMT

In article <36d2nfF4uqm0mU1@news.dfncis.de>,
Mitch Harris <harrisq@tcs.inf.tu-dresden.de> wrote:
>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).

Sticking to the view that informality has something to do with
intelligibility while formality has something to do with manipulability,
I would say that some informal statements are imprecise, while others are
quite precise, as far as meaning goes. In mathematics we're usually
interested in the ones that are precise---or at least, we can't do much
in the way of mathematical analysis until we have precise statements to
work with.

Having a precise *meaning* doesn't mean that the syntactic *form* of the
sentences is precisely specified enough to allow mathematical manipulations
of that formal structure.

>(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")

Informal statements are the ones we understand the meanings of. Formal ones
are the ones we can manipulate syntactically.

[Re: how formal is formal enough]
>but this sense seems to be captured fully by "precision" or "removal of
>doubt"

For independence results, the syntactic form does indeed need to be
precisely specified enough. But my point is that the term "precision"
can be applied either to *meaning* or to *syntactic form*. Either of
these can be precise or imprecise. My "thesis" is that when you make
the transition from something whose meaning we already understand to
something with a syntactic form that can be manipulated, nothing of
consequence is lost. 

-- 
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