First, great blog.
Second, it would be nice to hear back from Ken. I'd like to know if the experiment suggested by Ian yielded any results (even though I think that it could be done much more rigorously than what he's suggested with little additional effort).
Third, I want to raise two points about Eliezer's post:
a) Nothing can raise the probability of something being true if this something isn't logically/mathematically possible. No matter how much evidence we find that apparently supports the claim that there's a logical contradiction in our universe, we should still believe that the claim is false and continue to look for the truth.
I'm no expert, but it seems absolutely obvious to me that a non-reducible 'entity' is a logical impossibility. I think you'll agree with me that another way to say that something is reducible is to say that the complexity of its behavior is precisely equivalent (in some mathematical sense) to the complexity of its nature, i.e. behavioral complexity must equal compositional complexity. Therefore a non-reducible entity is an entity whose behavioral complexity is greater than its compositional complexity. The supernatural, as defined by Richard Carrier, is the most extreme case of this, since the human mind is the most behaviorally complex thing that we know of.
The question I want to ask is this: Is there really a difference between behavioral complexity and compositional complexity? Aren't these two categories something that we humans have made up completely arbitrarily? Aren't compositional and behavioral complexity one and the same? Therefore, isn't the claim that something is compositionally simple but behaviorally complex exactly like the claim that that 2 = 999?
b) What is the distinction between "the discovery of information transfer between the brains in the absence of any known material connection between them" and, say, the observation made by primitive human beings thousands of years ago that striking two stones together near a piece of wood results in this weird phenomenon they decided to call "fire"? Fire has pretty complex behavior, it's practically alive according to some definitions of 'life'. And of course, there was no known reductionist explanation for fire back then. If these primitive humans had been Bayesians, would they then have been justified in favoring the supernatural explanation that a sentient flame-spirit is responsible for the existence and behavior of fire? In fact, if you're right, wouldn't the supernaturalistic explanation be preferable in every single case where there is no known naturalistic explanation for something?