Monday, September 03, 2007

Sets: A Physical Perspective

Maverick Philosopher, in the third of a series of related posts, avers that
the following situation is conceivable: only two physical objects exist, two iron spheres, say. Now what I said earlier implies that, given two physical objects, there exists 'automatically' the set consisting of them. By 'automatically,' I mean that the existence of the spheres is logically sufficient for the existence of the set consisting of them. There is no need for any (finite) mind to collect them into a unity. So if a is one sphere and b the other, and if the situation we are envisaging is to be possible, then a third item must also exist, namely, {a, b}.
MP may be right, philosophically, but I prefer a physical interpretation:
  • There are only two physical objects: iron spheres a and b.
  • The description of the spheres (e.g., "physical objects" and "iron") is an abstraction. (That it is an abstraction in the mind of an observer who also exists is a complication outside the scope of this analysis.)
  • The spheres, in fact, are collections of matter-energy in a specific state; there is more to than them meets the naked eye.
  • By definition, the spheres comprise all of the matter-energy in existence.
  • The universe comprises all of the matter-energy in existence.
  • Therefore, "universe" (the set {a, b} in MP's analysis) is simply an abstraction of a higher order than "iron sphere," just as "iron sphere" is an abstraction of a higher order than the particular state of matter-energy that produces an iron sphere.
What we have, then, is not three things but one thing: a universe of matter-energy that may be perceived in many ways, for example:
  • as a whole, which comprises the things that it comprises, however those things may be described
  • the coherent bits of matter-energy that are perceptible as iron spheres by the naked eye
  • more discrete forms matter-energy that are perceptible as sub-atomic particles, given the proper scientific apparatus.
Alternatively (but equivalently), we have many, many things (the various and sundry forms taken by matter-energy), which may be abstracted into such things as iron spheres and the universe.

What we don't have is three things: a, b, and the set {a, b}. Rather, a and b (and their constituent bits of matter-energy) are within {a, b}, not apart from it as separate things.

ADDENDUM (1:35 p.m. CT): An analogy can be found in the visible surface of a TV screen. That surface is the universe of the hundreds of thousands or millions of pixels it comprises. That surface also is the universe of the discernible shapes it comprises. Those discernible shapes are composed of pixels, but the pixels are not discernible without magnification. The visible surface of the TV screen, the shapes on it, and the pixels that compose the shapes are different abstractions of the same thing, not different things.