SUO: Re: Proposed SUO Content Outline
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Doug, John, Pat, ...
My two cents worth inserted in the appropriate slot below.
Jon Awbrey
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Douglas McDavid wrote:
>
> Pat --
>
> I'm going to rethread this, putting my original reply to John Sowa
> at the bottom, and some responses inserted within your reply to me.
>
> > That is a good question, and your point is well taken.
> > But look where it leaves us. We will need to write
> > axioms which say that spatial coordinate systems exist,
> > without saying anything in particular about any spatial
> > coordinate system.
>
> Actually, the few statements I made were meant to imply that
> there are a lot of things we can say about coordinate systems.
> Some are very general, and would apply to all coordinate systems.
> Some are more particular, and would allow us to differentiate
> different kinds of coordinate systems.
>
> Many of those things that would be said in an upper ontology
> would have to do with point of view. This would articulate
> under what conditions a particular (type of) coordinate system
> would be appropriate.
>
> My expectation coming into this group was that an SUO would be
> used to express these kinds of issues. In general I would like
> to see us spending less time trying to convince each other of some
> particular point of view, and more time working on how to reconcile
> multiple points of view, through axioms (or whatever representation)
> that articulate what is common, what needs to be differentiated, and
> for what purpose.
>
> > How do we do that? What can be usefully said about spatial
> > coordinate systems in general, or about the general concept
> > of a spatial coordinate system? I do not mean to imply that
> > this task is impossible, but I do think it is considerably
> > harder than the task of describing one or two coordinate
> > systems and the mappings between them. At the very least,
> > such a limited exercise might be a very useful preliminary
> > study before attempting to write the mathematical masterpiece
> > of generality required for a universal theory of coordinate
> > systems in the abstract. The basic methodological point being
> > that these 'upper' theories, if they are to be nontrivial,
> > are likely to be very difficult to get right. We are trying
> > to break the sound barrier before we know how to walk.
Fortunately -- though it would be a shock to some people to think
they might have missed the Boom! -- this particular sound barrier
was pretty much conquered in the Nineteenth Century when Riemann
worked out his theory of manifolds, stealing a goodly measure of
the aweful thunder that those "manifolds of sensuous impressions"
have enjoyed since the Days of Kant, and I think that it is safe
to say that regular flights across this obstruction have been in
full operation since the Company of Category Theory, Ltd. first
began, in the late great Twentieth Century, to make it possible
for even the most workaday mathematicians to escape the tedium
of mindless calculation that they were once accustomed to call
the "pile of numbers" (PON's) approach to mathematical objects.
> Maybe I'm overly naive, but I didn't think I was proposing anything
> like a mathematical masterpiece. My view of the SUO is that it carves
> information spaces into useful areas of particularity. I see it being
> used as an organizing and indexing mechanism that acts as a framework for
> myriad particular ontologies. I believe the world is ready for a huge new
> emphasis on the *meaning* within software-based information systems. We're
> only recently in this position, with the critical mass of computing power and
> interoperation among enterprises of all types now in place. I think that
> significant progress can be made on this program of meaning reconciliation
> in a matter of months, rather than decades. I have a sinking feeling that
> this puts my out of step with the most prolific members of this group, for
> whom some issues of fundamental point of view need to be resolved before
> any progress can be made. My hope is that we can deal with many issues
> without making particularistic commitments at the uppermost level.
>
> Does this make sense?
> > > John --
> > >
> > > It seems to me that an upper-level ontology should strive to avoid
> > > most of the problems that you outline below. The kinds of things
> > > that an uppermost ontology could say, that would actually be useful
> > > to organize subtending ontologies would be things along the lines of:
> > >
> > > There are spacial coordinate systems.
> > > There can be any number of such coordinate systems.
> > > Each coordinate system exists in relationship
> > > to some specified reference point.
> > > Coordinates from one system can be mapped onto
> > > coordinates of another system.
> > > Some coordinate systems are based on fixed units of length.
> > > Some coordinate systems are based on dividing a geometrical
> > > figure into a fixed number of units.
> > > Etc.
> > >
> > > I wonder why anything in an upper ontology would ever be so
> > > particular as to require reference to any specific spacial
> > > coordinate system whatsoever?
>
> Doug McDavid
>
> Member of IBM Academy of Technology
> mcdavid@us.ibm.com -- 916-549-4600
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