FOM: As to a "naivete" of G.Cantor's set theory

F. Xavier Noria fxn at
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.


-- Xavier

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