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Can one learn to be rational? How would this be done?

One can certainly learn what rationality is: You can take courses in logic, in probability and statistical reasoning, etc. And you can study the limits on rationality: Much work has been done by cognitive scientists on "bounded rationality" (the work of Nobel-prize winner Herbert Simon on methods for making rational decisions in the presence of incomplete, inconsistent, or "noisy" information and within strict time limits), on errors in probability judgments (e.g., the work of another Nobel-prize winner, Daniel Kahneman, and his late colleague Amos Tversky), and on reasoning errors based on incorrect "mental models" (P.N. Johnson-Laird). Whether any of this can teach you to be rational will largely depend on how much of it you take to heart and practice in your daily life.