I don't wish to steal Chris' thunder, however I have a few comments below .
. . (01)
ontac-dev-bounces@xxxxxxxxxxxxxx wrote on 02/03/2006 04:55:39 AM: (02)
> Dear Chris,
>
>
> > > > An instance of a Type is not the same as a member of a
> > mathematical
> > > > set.
> >
> > More exactly, I think: the instance_of relation between
> > things and types
> > is a different relation from the membership relation between
> > things and
> > sets.
> >
> I asked this question before and didn't get an answer. Could
> you explain please what the difference is between the instance_of
> relation and the membership relation? (03)
This only works if we see the relation between Types and Instances as
being the "instance_of" - i.e. the traditional view of a Type within a
formal language (all instances inherit the properties and concepts of their
parent type, yet are distinct from each other in some way, etc). (04)
A set, however, if we are thinking of a set from set theory, is not bound
by any such rules. It MAY have such rules in place (all members of the Set
"fruit" share the concept of fruitiness). Or it may be something
completely different (the set {apple, sock, Memorization, Brazil} has no
real clear domain-inspired (natural order, etc) type that all the sets
members are instances of. (05)
Chuck (06)
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