This one probably requires a little explanation. I’ve approached quantum theory and a few other deep questions in sonnets, but the dismissal of the supernatural as such is a little trickier.
The first question is: what do you mean by “the supernatural”? And, “What do you want ‘the supernatural’ to DO?”
Most people answer the first question as: “Stuff that is fundamentally incapable of explanation, that is mysterious, unknowable.” And they answer the second question as: “Explain stuff!”
These two answers are contradictory.
Bayes’ Theorem says that anything that can explain anything can itself be known via the thing explained.
Formally, the theorem says that the posterior probability of a proposition being true (the probability after some piece of evidence is known) is proportional to the prior probability (the probability before that piece of evidence is known) times the probability of the evidence occurring given the proposition is true, divided by the overall probability of the evidence occurring all else being equal.
Mathematically this is just simple arithmetic:
P(prop given evidence) = P(evidence given prop)*P(prop)/P(evidence)
The example I like to use to illustrate this is naked people.
Consider the probability of the proposition, “There is a naturist conference being held nearby.” The prior probability is not that high: naturist conferences are pretty rare.
Now suppose that you see a naked person wandering by. That’s evidence! The odds of a naked person wandering by IF there is a naturist conference around are pretty good. But the probability of a naked person wandering by, all else being equal, is pretty low.
So the probability of “there is a naturist convention nearby” takes a big jump when you see a naked person wandering by (something which has happened to me rarely, although on the occasions it has, it has always involved hippies, not naturists.)
The thing is, Bayes’ Theorem is invertible–it is just simple arithmetic, after all. You can screw with the math so as to allow inference about the cause from the effect as well as the effect from the cause. That means that “supernatural explanation” is just incoherent, to a Bayesian: insofar as something is capable of being an explanation it is ordinary, knowable, plain. Insofar as it is unknowable and mysterious, it is incapable of being an explanation in the Bayesian sense.
And here’s the kicker: Jaynes’ “How Does the Brain Do Plausible Reasoning” or his equivalent argument (based ultimately on Cox) in the book “Probability Theory: the logic of science” shows that Bayes’ Theorem is a necessary consequence of the only formalism for reasoning that produces self-consistent results.
Ergo, insofar as you value self-consistency, you necessarily deny the supernatural. Every time anyone invokes a “supernatural explanation” they are simply contradicting themselves, which is a fact that needs to be more widely appreciated.