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The philosopher Gottfried Wilhelm Leibniz had a dream. He hoped that progress in philosophy and mathematics would eventually yield a method to systematically figure out the truth. This video explores an approach to that dream that takes us some of the way there: Bayesianism. The basic idea of Bayesianism is to represent beliefs as probabilities and update them using the formal rules of probability theory to the best of our ability. In particular, Bayes' rule tells us how to update our degree of belief in a hypothesis after observing some evidence. Bayes' rule can inform many central tenets of scientific reasoning. One example is Cromwell's rule, which tells us with the language of probability theory that our empirical beliefs shouldn't be absolute dogmas, but always potentially put into question when new evidence comes in.
