Occam's Razor

28 Sep 2020 10:19

... is not, in any of its commonly-used modern senses, a principle enunciated by William of Occam (or Ockham). (Though how far his rule "Plurality [of entities] is not to multiplied beyond necessity" is from our ideas about preferring simpler theories, or models, or explanations [not the same things, except on accounts in which they are] is a nice question in diachronic semantics.) That we --- i.e., just about anyone reading this page --- have such a preference is very plainly true, but what's less plainly true is that our shared preference has anything to recommend it. Any hope that the truth is simple, or even that simpler theories are (in some incomprehensible sense) more likely to be true, seems flat-out contradicted by experience.

Instead, I am very partial to the idea of Kevin Kelly (disclaimer: a friend) that the Razor is valuable not as a description of the universe, but as a guide to inquiry. That is, by sticking to the simplest theory compatible with the evidence, we converge on the truth faster than if we made up un-necessary complexities. This is nearly the only work on justifying the Razor I know of which doesn't either beg the question, change the subject, or make massive assumptions about the nature of the world, Divine Providence, etc. Unfortunately this correspondence between Occam and efficient convergence on the truth isn't obviously correct, and when Kevin and his collaborators try to prove theorems, there are (so far) some less-than-compelling to features to the way they've had to define key terms like "complexity" and "faster". These feel like solvable complications, however, rather than fundamental difficulties.

See also: Learning, Inference, Induction; The Minimum Description Length Principle; Model Selection; "Occam"-style Bounds for Long Programs; Scientific Method and Philosophy of Science;