Dear John, (01)
> As we've discussed before, I agree that sets are involved --
> as they are in the model theory for any logic.
> > MW: Also 4D ontologies that use possible worlds can define
> > classes as sets, as has been discussed on this list in the past.
> Yes. But when you talk about sets in possible worlds or sets
> in 4D regions that are inaccessible because they are outside
> the time cone of observability, you can't get any information
> from them -- except for whatever assumptions you put into
> the definitions of those worlds. (02)
MW: You can also postulate facts that will be true in a particular possible
world. I would consider it disingenuous to construe those as definitions of
the world. This principle is central to the way that possible worlds are
used in practice for e.g. planning.
> > MW: A problem with defining classes as sets for ontologies with other
> > foundations is that you cannot talk about imaginary things like
> > because they all equate to the null set, and other definitions might
> > accidentally give identical sets, even though they are not necessarily
> > identical.
> I agree.
> But I would add that you can have possible worlds with non-null sets
> of unicorns. (03)
MW: Of course. That is why the use of possible worlds permits you a system
that does not depend on types. (04)
> However, any data you get about unicorns in those worlds
> are just implications of your starting assumptions about them. (05)
MW: No they are not. They can also be facts that you stipulate to be the
case in that particular possible world. Facts are not assumptions. (06)
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