Dear John, (01)
> Dear Matthew and Ed,
>
> [MW] Every so often you have to look back and see how far you
> have come, rather than worry about how far you have to go.
>
> I agree. But it's important to look at the progress on more than
> one time scale. Some people say "Look how many ontology projects
> have been started in just the past five years!" (02)
[MW] I'd rather count those that had "finished" and delivered something,
that just those that had started before thinking about progress.
>
> But I look at Aristotle as a reference point and note how far
> physics has advanced since his time. Then I compare those
> ontology projects to Aristotle, Leibniz, and Kant. On that time
> scale, the rate of progress is not impressive. For some of the
> projects, one might even say that it's negative. (03)
[MW] Well it should certainly lead one to recognise that the challenge is
not trivial.
>
> [MW] ... Especially set theory and in particular set membership
> and subset/superset.
>
> I agree that set theory is important. But I emphasize that the
> categories of an ontology are not *sets*, which are defined
> by extension. Instead, the categories are *types*, which are
> defined by intension. For example, the set of human beings
> at one point in time is very different from the set at another
> time point. But the type HumanBeing is the same.
>
[MW] I appreciate this is what many do, and they would be interested in
subtypes and supertypes and type membership, but I do not accept that one is
obliged to. (04)
So, to deal with the problem you pose above, under 4D and extensionalism the
set HumanBeing is the set of all human beings that exist in the past,
present, and future. The set that exist today are of course a subset of
those. (05)
> And you can't solve that problem by using a 4D ontology because
> you have to be able to talk about future populations under
> different economic conditions, etc. (06)
[MW] They were included anyway. It is a fundamental part of 4D that the
past, present, and future exist and are all seen as laid out on a time line. (07)
> You also have to recognize
> that two types, such as Unicorn or PerpetualMotionMachine, can
> be very different, even though their extensions are both empty. (08)
[MW] Both of which can be handled by possible worlds (or your Dunn
semantics) and quantifying over possible worlds. (09)
So there is no problem (for me). Though I am also quite content that if you
choose you can handle these issues with types if you wish. (010)
Regards (011)
Matthew West
Information Junction
Tel: +44 560 302 3685
Mobile: +44 750 3385279
matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx
http://www.matthew-west.org.uk/ (012)
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