Well, I would say Bayes Theorem itself is purely logical, but realizing how it applies to updating your belief network and scoring your hypothesis, and then using it that way, especially the part of devising tests that could falsify your hypothesis, is rationality. I knew Bayes Theorem before discovering Less Wrong, I even knew a bit about Bayesian networks in computer science, but I never realized how deep Bayes Theorem was (and how it was a more powerful, more technical version of the scientific method) before reading the "intuitive explanation" and the Sequences.

But of course, the two are far from totally isolated. Words are fuzzy boundaries, not precise definitions.