T.Forster at dpmms.cam.ac.uk
Sat Jan 17 04:47:17 EST 2004
No! This question is *absolutely* nothing to do with abstract set
On Fri, 16 Jan 2004, Dennis E. Hamilton wrote:
> I was wondering if maybe there is also some muddling of intensional and extensional invited by the question. I don't know how to come to grips with this. It is a suspicion I harbor.
> Then I wonder whether the tacit confinement of this question to abstract set theory (if that is indeed the case) confuses matters even further. What I have in mind is the (finite) von Neumann ordinals happening to have, as sets, the (finite) cardinality that we associate with the same natural numbers (including 0). It's a very tidy construction. What is unclear to me is anything necessary about arranging to apply "the same" mathematical objects for those purposes. I also don't see how it unconceals any commitment to Platonism in having done so. Perhaps in the identification of these mathematical objects with the natural numbers?
> -- Dennis
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