Matthew, (01)
Thank you for the comments. My remarks below. (02)
> > I agree with Barry, although I may be wrong. :-) I believe
> > that there is
> > a big difference between Types and Sets.
>
> MW: I agree there is a big difference between what you understand
> as types and sets and what Pat has defined a type to be for
> COSMO. No one needs to be wrong here. (03)
CT: Yes - you are correct. My only reason for the nod to Pat is because
our raison d'etat on this list is to assist Pat (and others) with the
formulation of some axioms defining what a useful upper level ontology
might look like. Pat's paying for dinner, I thought that I should at least
save the first dance . . . (04)
> >
> > Types are suggested by the inherent categorization of the
> > ontology (whether
> > that is natural order, in the case of biological domains, or
> > based on form
> > or function in man-made domains, or whatever - it is some
> > sort of ordering
> > suggested by the domain the ontology seeks to represent).
>
> MW: A perfectly valid and ordinary sense to have for type,
> its just that what has been defined is somewhat broader.
> >
> > Sets, on the other hand, are ad hoc collections of things.
>
> MW: Not necessarily. The set of integers is highly ordered.
>
> > A formal
> > definition (suggested by set theory) might be "any collection
> > of distinct
> > things thought of as a whole". It may be based on defining
> > rules , or it
> > may be completely arbitrary. It may assist the user of the
> > an ontology,
> > but I don't see it as being part of an ontology's
> > categorization of its
> > entities.
>
> MW: The key distinction I would tend to make is that a set
> has extensionality as the basis for identity. That is, if two
> sets have the same members, then they are the same set.
>
> MW: Types on the other hand, are not necessarily expected
> to be the same if they have the same members. (05)
Yes - all good aspects that I intend to borrow for my own evolving
definitions. Thank you. (06)
I might also interject that what I call Types and what I call Classes, are
in themselves Sets. Every Type is a Set, yet not every Set is a Type -
which agrees with what Barry stated about Types being an Extension of Sets. (07)
Chuck (08)
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