Tuesday, August 27, 2013

Explaining the simplicity of theories

The following is a basic presupposition of science:

  1. If two scientific theories equally well fit our observations, and one of them is by far simpler than the other, then the simpler theory is more likely to be true.
Granted, we don't have a good account of "far simpler" or even of "equally well fit", but nonetheless something like (1) is surely true. And that is an amazing fact about the world. What explains that fact?

Note that we cannot really explain (1) simply by citing the fundamental physical laws of nature. For (1) is true in reality as discovered across the disciplines, not just in fundamental physics. It is surely true of biological, geological, astronomical and sociological theories.

Fact (1) suggests that the laws and other structure of our world are generated in a way that tends towards simplicity given the same empirical outcomes. Why? Well, I see three stories.

Theism: Simplicity is good, either intrinsically for aesthetic reasons or instrumentally because it helps agents like us get the good of empirical knowledge, and so a perfect being will prefer simpler structures when they can produce the same empirical outcomes.

Axiarchism: Simplicity is good, as above, and there is a fundamental law of metaphysics that all must be for the best.

Logocentrism: The world is generated by something like a random process that randomly generates a complete coherent descriptive sentence, in a non-gerrymandered language, with longer sentences having lower probability.

I find Logocentrism incredible: Why should the length of a linguistic expression matter except where there is a mind?

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