Sometimes I think this would be a lot easier for everyone if we just hauled out Bayes' theorem and had done with it. If a hypothesis (weighted with your confide

Sometimes I think this would be a lot easier for everyone if we just hauled out Bayes' theorem and had done with it. If a hypothesis (weighted with your confidence in it) predicts that a set of observations would turn up more evidence for it than you actually find, then that is evidence against that hypothesis, and should cause you to lower your estimate of the probability that the hypothesis is correct. And vice versa. For example, suppose that I want to explain why my apples have been stolen from my apartment. I live in a hypothetical universe where there are only three possibilities, all of which have roughly the same likelihood, a priori: spontaneous combustion, alien abduction, or theft by a troupe of dastardly harlequins. If the apples combusted, I would expect to see scorch marks, or perhaps soot stains on the wall nearby. If they were abducted by aliens, I would not expect to see anything, since everyone knows that alien abduction rays leave no signs. Finally, if the vile harlequins made off with my fruit, I would expect to see some signs of their passing -- face-paint on the doorknob, perhaps a fool's cap hastily discarded in a corner. Now, I inspect my apartment. I find no scorch marks, which is evidence against spontaneous combustion. If my apples had burst into flame, it's technically possible that they could have done so without leaving marks, but unlikely. I find no evidence of alien abduction, which is exactly what I would expect to find, so it does not change my estimate of that hypothesis' likelihood. Finally, I find a scrap of ripped, brightly-colored cloth which appears to have been torn from the outfit of an interloper hastily scurrying away through my pointlessly-large ventilation ducts. My face grows grim as I raise my estimate of the likelihood of my third hypothesis. Harlequins! Foul creatures of the Commedia dell'arte! My apartment has been defiled by their acrobatics and shenanigans! And they stole my darn apples! So, in the case of spontaneous combustion, absence of evidence was evidence of absence. For alien fruit abduction, absence of evidence wasn't evidence of anything. In the third case, there was evidence above what I would expect from my prior beliefs, so that was evidence for the harlequin hypothesis.