Re: SUO: Re: 3D/4D question
On Sun, Sep 09, 2001 at 01:10:31PM -0500, Bill Andersen wrote:
>
> 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
^^^^^^^^^^^^^^^^^^^^^^^^
Hi Bill, I don't recall this as being Lewis's view. For us, a more
interesting point is probably: does it follow from Lewis's view? As far as
I understand, counterpart theory certainly doesn't commit you to the
'individuals are 4D worms' model.
Generally, individuals in CT are not composites (mereological or
otherwise) of their counterparts across possible worlds: there isn't a
single wormy Brando-ish thing that is both a contender and a
non-contender. Thus, even considering different times as different worlds
(which, at least as I understand it, is also not Lewis's view: history is
actual), the 4D model would not be a direct or 'natural' extension of
counterpart theory.
> 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.
You mean 'saying' or 'satisfying'? The 'saying' part is most likely
independent of the counterpart vs TW identity issue. The satisfying part
might be. But here, I am not so sure how this sentence should be
interpreted: it sounds more like a sentence about the models than a
sentence in a modal language (if so, it would be rather a sentence in
ZFC). If so, it doesn't seem correct that Kripke semantics allows only
models in which the set of individuals is the same at all possible worlds.
>
> I think even Pat should be happy with CT - it's extensional and expressible
Isn't Kripke semantics? It'd better be expressible in first order ZFC
(which of course is extensional and expressible in FOPC).
Regards,
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