One of the blog posts I'd like to write but probably never will is an examination of the logical fallacies that are fallacies under an Aristotelian, true/false view of the world, but are valid under a Bayesian point of view.

A simple one is that absence of evidence is evidence of absence. It's a "fallacy" because absence of evidence is correctly not proof of absence, so in an Aristotelian framework where something is either true or false, it is indeed a fallacy to claim that absence of evidence proves absence. However, from a Bayesian perspective it is indeed evidence, though one must be careful in how ones works the math to determine how strong that evidence is. Sometimes it's so weak as to be irrelevant, but sometimes it can be overwhelming.