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

Martin Davis martind at
Tue Jan 26 14:14:15 EST 1999

At 02:24 PM 1/25/99 -0500, Charles Silver wrote:
>On Sun, 24 Jan 1999, Alexander Zenkin wrote:
>> can anyone to formulate explicite arguments why modern meta-mathematics
>> calls  the G.Cantor's set theory by a "naive" theory? What does that
>> "naivete" consist in? And what does the "non-naivete" of the modern
>> meta-mathematics consist in?
>	I think it was Halmos who popularized 'naive'.  (I don't know
>where it originated).

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. 

I used the book as a text for the first part of a set theory course and
found it helpful (though much better books are available today).


More information about the FOM mailing list