[major deletion]
> If this idiosyncratic Greek connection between language and arithmetic
> were true it should be an interesting issue even to understand other
> aspects of ancient mathematics and ethnomathematics.
I suggest that there were also close connections between matters of
language and matters of geometry among the classical Greek mathematicians.
Thus one can view Euclid's *Elements* as an achievement, in part, in which
what one sees is translated into what one says. For this to be possible,
one might say that the kind of abstraction we see in connection with
"points", "lines", etc., were if not necessary for such a translation, at
least facilitated the translation, or transformation. To what extent
axiomatic arrangements in the manner of Euclid are related to grammatical
structure of languages is perhaps also interesting to consider. Formal
languages of the many sorts we have seen in the 19th and 20th centuries,
and even back to Leibniz and Wilkins (was that his name, an Englishman who
had an artificial language in the 17th century?), do seem on the face of it
to fall naturally into axiomatic formulations. If such formal languages
can be regarded as abstractions from natural languages, one might be able
to defend some sort of analogy of the form: as points, lines, circles, etc.,
in the manner of Euclid are to axiomatic foundations of geometry, so formal
languages (including computer languages?) are to axiomatic foundations of
language (e.g., relatively recently, Chomsky and others of that ilk).
Gordon Fisher gfisher@shentel.net