Bayes' Theorem tells us that the quest for certain knowledge, which drove a great deal of science and philosophy in the pre-Bayesian era (before about 1990, when Bayesian methods started to gain real traction in the scientific community) is much like the alchemist's quest for the secret of transmutation: it is simply the wrong goal to have, even though it generated a lot of interesting and useful results.<p>One of the most important consequences of this is noted by the article: "Confirmation and falsification are not fundamentally different, as Popper argued, but both just special cases of Bayes’ Theorem." There is no certainty, even in the case of falsification, because there are always alternatives. For example, superluminal neutrinos didn't prove special relativity false, although they did provide some evidence. But the alternative hypothesis that the researchers had made a mistake turned out to be much more plausible.<p>Bayesian reasoning--which is plausibly the only way of reasoning that will keep our beliefs consistent with the evidence--cannot produce certainty. A certain belief is one that has a plausibility of exactly 1 or 0, and those are only asymptotically approachable applying Bayes' rule. Such beliefs would be immune from any further evidence for or against them, no matter how certain it was, essentially because Bayesian updating is multiplicative and anything times zero is still zero.<p>There is a name for beliefs of this kind, which to a Bayesian are the most fundamental kind of error: faith.