Dennis E. Hamilton
dennis.hamilton at acm.org
Fri Jan 16 16:19:25 EST 2004
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?
From: Thomas Forster, January 16, 2004 02:08 (pst)
The reason for my asking this question is that - if you are
platonist - you must have an answer to it. [...] I would have a very strong
inclination to say that [finite ordinals and finite cardinals] are clearly different things
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