SUO: Re: 3D/4D question
On 9/9/01 10:08, "Chris Partridge" <chris_partridge@csi.com> wrote:
> Bill,
>
> You are right I think the per- (4D) view is useful (champion? Well I do not
> know)
>
> I am not sure what you mean by:
> "I have in mind David Lewis' nominalism, in which normal objects extended
> in space-time are really 5D (4D + modal counterparts) objects."
>
> I was under the impression that Lewis thought trans-world identity was
> barbarous. And that he wholeheartedly accepted mereological essentialism
> and extensionalism. Am I wrong? I hope not!
Chris, you're completely correct.
As you know (this is for the benefit of the list), Lewis does in fact reject
trans-world identity. To account for modal intuitions about trans-world
identity, he introduces the notion of a counterpart. So, when Brando says
"I could have been a contender!" (for Lewis) I mean "there is another world
W' different from this world W which has as a part another individual
Brando' (a counterpart not identical to Brando) and Brando' is a contender
in W'". Both Brando and Brando' are (for Lewis) 4D worms. This view of
course satisfies the need for merelogical essentialism and extensionalism.
So, when I said 5D, I was speaking loosely about dimensions. I suppose they
aren't strictly dimensions, since worlds aren't accessible to one another,
like points in space (or time).
> I know Achille Varsi has a paper where he makes a kind of 5D extension -
> and there is another older paper whose reference I do not have here (I am
> out of the office).
>
> However, I agree with (what I think is your underlying point) that there
> are a variety of metaphysical questions that need answering to get a
> complete(ish) position. E.g. are tenses real (I made this point in my
> original ontological architecture paper).
Yup.. There is also an expressiveness issue involved in which modal
formalism you pick, if you want to pick one. We at Ontology Works have
picked 3D + time for a reason over 4D. But the choice was made on
implementation grounds - there are efficient ways to manipulate
temporally-indexed relations and we build databases so that sewed the issue
up for us.
But, if you want modality as well, then Counterpart Theory is strictly more
expressive than modal logics with Kripke semantics. It's possible to say in
Counterpart Theory, for example, that "it is possible that there could have
been a completely different set of individuals than there in fact are". My
memory is a little fuzzy - gotta consult my notes, but I think this is an
example of something which can't be expressed in normal modal logics.
I think even Pat should be happy with CT - it's extensional and expressible
in plain-old FOPC.
.bill
--
Bill Andersen
Chief Scientist, Ontology Works
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