Re: SUO: Monolithic ontologies
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.
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.
John Sowa