SUO: RE: RE: First piece of 4D ontology
Matthew,
See my comment below. Edits for brevity.
-Ian
> > > ;
> > > ; #2:
> > > ;
> > > ; for all X, if there exists a Y and Y is a member of X,
> > then X is a
> > > ; member of collection.
> > > ;
> > > ; i.e. any thing that has a member is a collection.
> > > ;
> > > (forall ?x
> > > (=> (exists ?y
> > > (?x ?y)
> > > )
> > > (collection ?x)
> > > )
> > > )
> > > ; Note: This (?x ?y) is not valid SUO-KIF today, but I
> > understand it
> > > ; will be in the near future.
> >
> >
> > I'm wondering what you mean by "collection" in your axiom. I
> > thought we
> > were using this term to denote things like wolf packs,
> > football teams, etc.,
> > which are set-like, in that they have members, but, unlike
> > sets, they have a
> > spatio-temporal location. However, if this is what you
> mean, then you
> > exclude sets and classes, which have members but are not
> > collections in the
> > sense just explained.
>
> MW: In this context the string "collection" is a label that
> means precisely what the axioms say it means, not more and
> not less. So do sets and classes meet the axioms as stated?
> I.e. do they have members? If so then they are also collections.
You are right, of course. But it does create some degree of confusion, you
must admit, to axiomatize your formal notion of "collection" in such a way
that it means set or class or collection, as we appear to be using these
three terms on the SUO mailing list.