Dear John, (01)
We've been through how sets across possible worlds are essentially
equivalent to types at least once before and probably twice. So let's not
rehearse the arguments again. (02)
Regards (03)
Matthew West
Information Junction
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> -----Original Message-----
> From: ontology-summit-bounces@xxxxxxxxxxxxxxxx [mailto:ontology-summit-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
> Sent: 06 February 2012 22:52
> To: ontology-summit@xxxxxxxxxxxxxxxx
> Subject: Re: [ontology-summit] Roles, Fillers, and Role Relations
>
> Dear Matthew,
>
> MW
> > My experience is quite different.
>
> I'm sorry that I mentioned 4D ontologies, since that gets off
> the point I was trying to make.
>
> MW
> > I would talk about states rather than time worms, but that is just
> > terminology. In practice I find statements become more precise a
regular.
> > The vast majority of statements end up being spatio-temporal
mereological
> > statements, i.e. whole-part, especially temporal whole-part, and
connection.
> > Much of the rest of what you need to say is around classifying the
states,
> > which is again also well understood.
>
> I have no quarrel with any of those topics. But the point I was trying
> to make is that we need to use the basic concepts of logic in order
> to define the notion of 'role'.
>
> MW
> > In fact all the relations I have used for the system/system component
> > example have been one of:
> > - whole-part (or a subtype of whole part like temporal whole-part)
> > - classification (set membership)
> > - specialisation (subset/superset)
>
> That's fine. But one concept is missing from that list: the
> distinction between a type (as defined by a monadic predicate or
> relation) and the set that happens to be the denotation of that
> type in a particular domain (or space-time region).
>
> Predicates are much more fine-grained than sets because the same
> set can be the denotation of many different monadic predicates.
> And the same type can specify different sets in different
> regions of space-time or different possible worlds.
>
> For example, Plato observed that the set of rational animals
> happened to be identical to the featherless bipeds. But that is
> a coincidence that was falsified when people managed to breed
> featherless chickens.
>
> Basic principle: if you use the distinction between intensions and
> extensions, the definition of 'role' is clear and simple. But
> if you don't make that distinction, it's extremely difficult
> to state the issues clearly and precisely.
>
> John
>
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