FOM: As to a "naivete" of G.Cantor's set theory
F. Xavier Noria
fxn at retemail.es
Tue Jan 26 16:44:39 EST 1999
At 02:24 PM 1/25/99 -0500, Charles Silver wrote:
: I think it was Halmos who popularized 'naive'. (I don't know
: where it originated).
At 26/01/99 11:14:00, Martin Davis wrote:
: I certainly knew the term before Halmos's book. His use of that title
: annoyed me, because his treatment was axiomatic amd hence not "naive" in the
: sense I had understood the word.
Perhaps the following quote from Halmos could be of interest:
I had recently learned a little about axiomatic
set theory, and I was all gun-ho about spreading
the word. I wanted to reach the student who didn't
know and the reader who didn't like the formal
manipulations of logic that frequently intervene.
The result was a book on axiomatic set theory from
the non-logical, non-formal, naive point of view.
I've been teased about my use of the word "naive",
and translators (into Dutch, French, Hungarian,
Italian, and Portuguese) have mistranslated the
title in as many different ways as the languages
they used [...] My reason for the word was innocent.
I didn't set out to find a provocative title (which
I almost always do when I give a lecture); I was
merely laboring under the misapprehension that
"naive" was a bona fide technical word in set theory,
meaning nothing more or less than the antonym of
"axiomatic". I can't remember where I got the idea,
but I think it was from one of the founding fathers
---either Cantor himself, or Russell, or a later
writer of some historical paragraphs contrasting
the points of view of Cantor and Russell on the one
hand and Zermelo and Fraenkel on the other.
Paul R. Halmos, "I Want to Be a Mathematician: An
Automathography". Springer-Verlag, 1985. Page 246.
More information about the FOM