[FOM] When is it appropriate to treat isomorphism as identity?

Jon Awbrey jawbrey at att.net
Sat Apr 25 10:18:20 EDT 2009


Some of what you say here reminds me of what Peirce said about
the "Doctrine of Individuals".  Some excerpts, commentary, and
discussion can be found in the e-neighborhood of this location:


Just by way of one salient remark:

| This distinction between the absolutely indivisible and that which
| is one in number from a particular point of view is shadowed forth
| in the two words 'individual' ('to atomon') and 'singular' ('to kath
| ekaston');  but as those who have used the word 'individual' have not
| been aware that absolute individuality is merely ideal, it has come to
| be used in a more general sense.
| C.S. Peirce, 'Collected Papers', CP 3.93

It seems to me that Peirce is relativizing identity to particular frames of
reference, much in the way that physicists found it necessary to relativize
simultaneity and other physical equivalence relations to the reference frame
of the observer.  An idea like that, pursued persistently, would have rather
interesting consequences for the theories of categories and/or sets, I think.

Jon Awbrey

CC: Arisbe, Inquiry


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