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

Charles Silver csilver at
Mon Jan 25 14:24:26 EST 1999

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).   For Halmos, 'naive' just meant 'informal' and
served as a contrast to 'axiomatic'.  The preface of his book (_Naive Set
Theory_) ends on a strange note: "general set theory is pretty trivial
stuff really, but if you want to be a mathematician, you need some, and
here it is; read it, absorb it, and forget it."  I've often wondered why
he'd take such a cavalier attitude about the subject, yet write an entire
(admittedly short) book on it. 


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