Dear Rob, (01)
> I'm trying to narrow things down to the main points.
> I think you make two main points.
> 1) If you had a FO it would in principle be easy to move between
> particular theories, and so multiple theories would not matter.
> 2) Generating theories will give the same result as having an infinite
> number of theories.
> On 1) I agree. I just don't think it is possible to find a theory
> which will map between all other theories (see my post to Pat C asking
> him to find a FO for mathematics.) (02)
MW: It is the search for such a theory that has lead me to 4D,
extensionalism of individuals and classes, and possible worlds, as used in
ISO 15926. I am quite happy to issue the challenge to identify some other
viewpoint that cannot be mapped into or out of it (I can only learn
something from the result). On the other hand I would agree that it is hard
to be certain you have one when in principle there are an infinite number of
viewpoints. So you are looking for a good-enough solution that is able to
map credible and widely used ontologies.
> On 2) I agree. I like this part of John's thinking. Though I can't
> imagine how to model an infinity of theories, let alone move between
> them, unless it is by generating them. (03)
MW: You are not interested in all of them so it does not matter. That there
is "space" in the lattice for an infinite set of theories is the important
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> On Tue, Feb 2, 2010 at 9:52 PM, Matthew West
> <dr.matthew.west@xxxxxxxxx> wrote:
> > Dear Rob,
> >> On Tue, Feb 2, 2010 at 10:00 AM, Patrick Cassidy <pat@xxxxxxxxx>
> >> >
> >> > ...
> >> > If you think that *every* application that wants to communicate
> >> > accurately with *any* other application could do so by a different
> >> tactic
> >> > with that degree of ease, I would certainly be interested in
> >> how.
> >> John can answer for himself, but my answer is that the real reason
> >> not backing a FO is not the cost or the need. The real reason is
> >> a comprehensive FO is impossible.
> > MW: It depends what you mean by comprehensive, and it depends what
> you want
> > to be able to do.
> >> The evidence is that there will always be more than one way of
> >> at the world, and generally these ways will be contradictory.
> > MW: Yes. But for interoperability (Pat's interest) that is not a
> > You only need to pick one. You then only need to be able to map other
> > into and out of it. Alternatively, if you want to capture many
> > viewpoints, you can adopt John's Lattice of Theories.
> >> This is
> >> an insurmountable problem for a "foundation ontology". Unless you
> >> it to contradict itself.
> >> What is needed is a way to tease apart when
> >> these different ways of looking at the world apply
> > MW: To be properly a foundation ontology you should be able to deal
> > life-the-universe-and-everything. So you can choose. Pragmatically,
> there is
> > no problem specifying that different theories for the same thing (say
> > gravity) apply in different conditions. The conditions just become
> part of
> > the theory.
> >> (and a way to
> >> generate them, because the number is probably infinite.)
> > MW: That is the lattice of theories again.
> > Regards
> > Matthew West
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