SUO: One Stone Does Not Fit All
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Dear Ted,
This way to the egress >>>--->>>
For information on metaphysics, read books by metaphysicians.
For information on space, time, spacetime, physical objects,
physical processes, and so on, read books by mathematicians
and physicicts.
The topics in topology from Whitehead that John Sowa mentioned
are very apt, as Whitehead helped to pioneer they their use.
A middle of the last century update can be found here:
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TOP. Topology
1. Topological Spaces
1.1. Topologies and Neighborhoods
01. http://suo.ieee.org/ontology/msg03863.html
02. http://suo.ieee.org/ontology/msg03867.html
03. http://suo.ieee.org/ontology/msg03868.html
04. http://suo.ieee.org/ontology/msg03869.html
1.2. Closed Sets
05. http://suo.ieee.org/ontology/msg03870.html
1.3. Accumulation Points
06. http://suo.ieee.org/ontology/msg03871.html
07. http://suo.ieee.org/ontology/msg03872.html
1.4. Closure
08. http://suo.ieee.org/ontology/msg03874.html
09. http://suo.ieee.org/ontology/msg03880.html
1.5. Interior and Boundary
10. http://suo.ieee.org/ontology/msg03882.html
11. http://suo.ieee.org/ontology/msg03883.html
12. http://suo.ieee.org/ontology/msg03888.html
13. http://suo.ieee.org/ontology/msg03889.html
1.6. Bases and Subbases
14. http://suo.ieee.org/ontology/msg03892.html
15. http://suo.ieee.org/ontology/msg03893.html
16. http://suo.ieee.org/ontology/msg03894.html
17. http://suo.ieee.org/ontology/msg03899.html
18. http://suo.ieee.org/ontology/msg03900.html
19. http://suo.ieee.org/ontology/msg03903.html
1.7. Relativization, Separation
20. http://suo.ieee.org/ontology/msg03908.html
21. http://suo.ieee.org/ontology/msg03914.html
22. http://suo.ieee.org/ontology/msg03916.html
23. http://suo.ieee.org/ontology/msg03917.html
1.8. Connected Sets
24. http://suo.ieee.org/ontology/msg03918.html
25. http://suo.ieee.org/ontology/msg03920.html
2. Convergence [omitted]
3. Product and Quotient Spaces
26. http://suo.ieee.org/ontology/msg03921.html
3.1. Continuous Functions
27. http://suo.ieee.org/ontology/msg03922.html
28. http://suo.ieee.org/ontology/msg03923.html
29. http://suo.ieee.org/ontology/msg03924.html
30. http://suo.ieee.org/ontology/msg03925.html
3.2. Product Spaces ...
The above material is excerpted from:
| John L. Kelley, 'General Topology',
| Van Nostrand Reinhold, New York, NY, 1955.
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Dace wrote:
>
> Dear John Sowa,
>
> > Whitehead was strongly influenced by Bergson, and he developed
> > a framework that was consistent with both Bergson and the 4D
> > approach:
> >
> > >There is a way out of this impasse, and it was proposed by Henri Bergson
> in
> > >his *Introduction to Metaphysics* (1903). Bergson argued against both
> the
> > >common sense view of time, the so-called 3D model, and (later) the 4D
> model
> > >developed by Einstein.
> > >
> > >As to the 3D model, Bergson denied that time can be divided into discrete
> > >points, i.e. "moments." By contrast, space certainly can be divided into
> > >points, and an object can be said to occupy a point in space if it's at
> > >rest. But this doesn't apply to objects in motion. To claim that a
> moving
> > >object occupies a particular point in space requires that we freeze the
> > >action, so to speak, at that point. It's precisely when an object
> *stops*
> > >moving that it occupies a particular point. If an object is in motion
> from
> > >point A to point B, it cannot logically occupy any intermediate points,
> as
> > >this would imply that it has stopped at one of those points and therefore
> > >was not really in motion from point A to point B after all. Since time
> is
> > >always in motion, we cannot therefore assign it discrete points, such as
> > >"now" and "a moment ago."
> >
> > Whitehead adopted an interesting approach based on mereology
> > (which he developed independently of Lukasiewicz). In his
> > approach, space-time is made up of overlapping 4-dimensional
> > chunks. There is no such thing as a primitive point, but you
> > can define a point as an abstraction formed by a converging
> > infinite sequences of nested 4D regions.
> >
> > Tarski gave axioms for a similar 3D geometry, in which the only
> > primitive is the sphere, and points are defined as converging
> > sequences of nested spheres. In both Tarski`s and Whitehead`s
> > geometries, only finite-sized chunks of space or space-time are
> > "real", and points are abstractions defined by infinite sequences
> > of finite regions.
>
> Bergson was not interested in abstractions. He was after the big prize:
> reality (sans quotations marks), which he defined as absolute time. My
> point is that it's a lot easier to create an ontology if we have an anchor,
> that is, something we all agree is fundamental to existence. This doesn't
> necessarily make our ontology monolithic, just that whatever varieties
> emerge, they can't drift apart into irreconcilable difference.
>
> > Since Whitehead`s geometry is consistent with both Bergson and
> > other 4D approaches, there is no way that Bergson could ever
> > prove that his version implied that Einstein`s was inconsistent.
>
> Bergson explicitly denied what we now call the 4D approach. His great error
> was to believe that absolute time is incompatible with relative time. Time
> does indeed exist in relation to space, but unlike space it also exists in
> relation to itself. The "proof" of absolute time is, of course, strictly
> intuitive. Consciousness has plenty of time but no space. Time is the one
> thing we observe outside of ourselves that we also find within.
>
> I just don't see how an ontology can ever be regarded as standard without a
> core element that does not depend on abstract imagination. The trouble with
> imagination is that it's a hall of mirrors, and it's just too easy to get
> lost in there.
>
> Best,
>
> Ted Dace
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