Department of Philosophy
Carnegie Mellon University
Ockham's Razor, Descriptive Set Theory, and Some Funny Numbers
"Ockham's razor" says "when in doubt about the truth, choose the simplest empirical theory compatible with experience". But how could simplicity lead us to the truth when the truth might be complex? I will propose an unfamiliar answer based on some easy ideas from descriptive set theory. The idea is that following Ockham's razor may result in disaster, but any violation of Ockham's razor opens you up to even worse disasters (in terms of the number of errors or retractions of prior theories before one converges to the right answer). Part of the story involves subtracting finite quantities from the tails of ordinals and extending ordinal arithmetic to the results of so doing.