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Adam I. Gerard
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Dogmas About Space-Time

Continuing with the topic of major gaps in metaphysical theory, I'll turn to the topic of Space-Time (of perennial interest and even more so given the attempt to quantize Time and Space today).

Space

These may seem like trivial disputes but they've led to more than their fair-share of problems in physics (and many of the great advances in modern physics have come about by coming down on the opposite side from whence we started):

  1. Euclid or Hyperbolic?
  2. Points or Point-free geometries?

Conceptions

  1. Point-based
  2. The number-theoretic Successor Function does all the work in systems that view spatial dimensions as symmetric and as Reals or Ordinals. Function-centric approach.
  3. Mereology - rather, it's about the relationships between parts and wholes which are taken to be primitives (rather than numbers).
  4. Alternative - one can start with concentric circles or say, with concentric spheres, to define the remainder of a space.
  5. Alternative - a structuralist conception of space might view wholes and parts as requiring one another rather than as points preceding a line. (The number-theoretic view might very well be "structural" under this lens.)

Properties

  1. Relationalist (as what relations obtain between objects, secondary, Leibniz) or Absolute (as the background into which objects "inhere", primary, Newton)
  2. Textured or flat (empty or foam)?
  3. Passive or active?
  4. Continuous or discontinuous?
  5. Static and fixed or changing and growing?
  6. Having specific topological properties?
  7. Quantized or not?
  8. Mental (Kant) or Objective?

Quantized or Not

  1. Is spacetime holistic and irreducible whether it’s relational or not?
  2. Tentatively if spacetime is relational that perhaps lends support for the idea that it can be quantized (since, if it were, it would depend for its existence on the sub-entities from which it emerges).

Neo-Pythagorean

A perhaps surprising return to Pythagoras and his teachings (he was one of the first philosophers and mathematicians in the West):

  1. That geometry and especially physical geometry emerge from something non-geometric.
  2. A natural way of understanding this is by way of the set-theoretic description of a topological space whereby presumably abstract mathematical entities come to define the notion of a space.

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