# [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.

Thomas

On
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
>
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom
>

```