SUO: One Stone Makes a Beach
Dear Jon,
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>
> Dear Ted,
>
> This way to the egress >>>--->>>
>
> For information on metaphysics, read books by metaphysicians.
Naturally.
> For information on space, time, spacetime, physical objects,
> physical processes, and so on, read books by mathematicians
> and physicicts.
"Spacetime," yes. "Space" and "time," no. Taken separately these are not
physical concepts.
Einstein did us all a big favor by positing physics on strictly relativistic
terms. Even the so-called "absolute" of acceleration (which is correlated
with gravity under General Relativity) exists only in relation to the object
being accelerated. As to the "absolute" speed of light in Special
Relativity, this applies only to a perfect vacuum, and, of course, no such
thing exists. While physics works a lot better when we don't try to define
anything as intrinsically real, in the absence of a thing that exists
in-and-of itself, science reduces to nihilism, a castle in the sky. It's
impossible to nail down a definitive ontology because ultimately it's all up
in the air.
Hence the need for a metaphysical anchor. RealTime serves as a natural
ground for all subsequent ontological categories. Topology and set theory,
etc., add nothing to our direct intuition of time itself. The point is not
to add further to our already unwieldy calculations but to provide an
overall framework in which to make sense of them.
Ted
> 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:
>
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>
> 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.
>
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>
> 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
>
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>