[FOM] Ontology

Thomas Forster 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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