Dear Matthew, (01)
MW
> My experience is quite different. (02)
I'm sorry that I mentioned 4D ontologies, since that gets off
the point I was trying to make. (03)
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. (04)
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'. (05)
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) (06)
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). (07)
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. (08)
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. (09)
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. (010)
John (011)
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