The simplest theory does not necessarily fit the facts. When you are willing to do away with facts, you can easily have the simplest theory. We don’t have the simplest theory, so that must mean we have the most facts. When judging between religions, you should take the complexity of the doctrine of the Trinity as evidence in favor of Christianity.

The first two sentences are correct and the last two are not. Even though it’s true that the simplest theory is not always right, complexity (from a Bayesian standpoint, which is where I’m coming from) can NEVER be direct evidence for a theory in and of itself. If it could, then I could easily create a religion more complex than Christianity, and say “If we wanted to be simple we could, but we’re dealing with facts.” Lewis’ logic would demand that you raise your probability estimates of that religion being true, because complex interpretations signal factuality.

Complexity (in the formal sense) must always lower the plausibility of a theory, a priori, if only by a small amount. Since simple theories can be wrong and complex theories can be right, this means we should only use complexity as a tie-breaker when we’re judging between two theories that equally well fit the facts. Until we get to that point, we use the facts to exclude as many theories as we can. To look at complexity as a signal of facts is bad logic.

EdW: THREE types? That’s so last century? My feeling about string theory is that we are very far from knowing the real fundamental particles/entities. If we need 11 dimensions to describe them (or however many it turns out to be) it would be hard to persuade Aristotle that that’s a real improvement in simplicity.