Re: Terminology

[Eduardo Dubuc <edubuc@dm.uba.ar>]

I very strongly agree with J. Benabou's comments about "prone" and
"supine", and P. May's opinion that "I'd like category theory no longer to
be regarded as nonsense in this country --- it still is in many quarters,
as I could easily prove --- and such terminology is not exactly helpful to
the cause!"

I recall P. Johnstone that he himself named his book  "Elephant Book"
because every body has different version of what a topos is, reflecting
only one of the many aspects of the concept.

Names like "Prone" and "Supine" correspond (with luck) to only one of the
many aspects of the concept of cartesian and its dual (in a sense)
cocartesian.

Also, there is a clear ethical aspect involved when a stablished
terminology that has been historically introduced by particular people
suffers a move to be eliminated and reeplaced by another.

But, coming back to the question above, i am also against the habit to
name a new mathematical concept with words that have a precise meaning in
everyday language (as prone, supine, etc).

Presisely, I do not know what does it mean exactly "Cartesian" (has
something to do with Descartes ...), but I know presisely what it is a
"Cartesian arrow" (in mathematics).

Colorful terminology taken from everyday language is an strong indication
to serious mathematicians that the subject should no be taken seriously
(see for example the claims of  "Catastrofe Theory" as opposed to the
sober "Classification of singularities of C-\infty mappings", and a lot of
similar examples).

As P May points out, "  . . .  such terminology is not exactly helpful to
the cause!".

The meaning of a mathematical concept should be given by the concept
itself, and not by the connotation that its name has in everyday language.