[FOM] ontology

Thomas Forster T.Forster at dpmms.cam.ac.uk
Fri Jan 16 05:14:07 EST 2004

My feeling is that Carlos's answer is ``obviously'' correct.  But there
is a cost to this.  It flies in the face of the idea that identity of
mathematical entities is isomorphism.  That's why i raised this example, 
as it forces us to examine this principle (that identity = isomorphims)
more closely.


Thu, 15 Jan 2004, Carlos Gonçalves wrote:

> At 18:14 14-01-2004 +0000, you wrote:
> >An essay question:
> >
> >
> >Are the finite ordinals the same mathematical objects as the finite
> >cardinals?  Give reasons...                       [\aleph_0 marks]
> Hi Thomas,
> These are different objects, the notion of ordinal, in particular, appeals 
> to a notion of order (and of well ordered set) while a cardinal is, 
> following Cantor, obtained through an operation of double abstraction, both 
> from the order in which the elements of the set are given and from the 
> nature itself of those elements.
> C. Pedro
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