Re: before Cantor

From: Torkel Franzen (torkel_at_sm.luth.se)
Date: 10/12/04 

Date: 12 Oct 2004 09:58:54 +0200

"shedar" <nobody@nonesuch.com> writes:

> The "mainstream" set-theoretical position is that questions
> about mathematical "existence" of an object are to be treated as just
> questions about which axioms of set theory are being used to show that the
> object is a "set".

  This supposed position makes no apparent sense.

> Where do all mathematical objects exist? Surely,
> they "exist" in a rational mind in the sense of being capable of being
> conceptualized there.

  This dubious piece of philosophizing is in no way an answer to the
original question.

> One of the most ingenious (some might say, expedient) axioms of ZF set
> theory is the Axiom of Extensionality (AE). It "cuts to the chaste" by
> side-stepping metaphysical and ontological issues of "existence" which are,
> perhaps, best left for philosophers and theologians when determining "set
> equality".

  Now you're going completely over the top.