Pat, (01)
I agree with your comments, but I'll add a quibble. (02)
It is certainly true that the identity criterion for sets
(namely, having the same members) is simple. (03)
But the identity criterion for types is also easy to state:
logically equivalent definitions. But the proof of
equivalence might be nontrivial. (04)
For mathematical sets, the "simple" criterion usually
involves a proof of equivalence: for anything other than
small finite sets, it is necessary to prove that the two
specifications determine exactly the same elements. (05)
So there is not much difference for mathematical sets
and types. For real world entities, both sets and types
have to address the same kinds of messy details. (06)
John (07)
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