"Traditional Rationality" refers to the tradition passed down by reading Richard Feynman's "Surely You're Joking", Thomas Kuhn's "The Structure of Scientific Revolutions", Martin Gardner's "Science: Good, Bad, and Bogus", Karl Popper on falsifiability, or other non-technical material on rationality. Traditional Rationality is a very large improvement over nothing at all, and very different from Hollywood rationality; people who grew up on this belief system are definitely fellow travelers, and where most of our recruits come from. But you can do even better by adding math, science, formal epistemic and instrumental rationality; experimental psychology, cognitive science, deliberate practice, in short, all the technical stuff.

There's also some popular tropes of Traditional Rationality that actually seem flawed once you start comparing them to a Bayesian standard - for example, the idea that you ought to give up an idea once definite evidence has been provided against it, but you're allowed to believe until then, if you want to. Contrast to the stricter idea of there being a certain exact probability which it is correct to assign, continually updated in the light of new evidence.

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See also