Can there be evidence for God? Can there be evidence for a Halting Oracle? For the Hidden Variables Interpretation?

The volley between Jerry and PZ over whether there could even in principle be evidence of a "god" continues apace, with other bloggers weighing in as well. Okay, my turn!

First of all, I think Jerry and PZ are both failing to define their terms clearly enough. Both of them seem to recognize this problem, but then just go on ignoring it, like everybody "knows what they mean." PZ has made a whole lot of noise, some of it surprisingly sloppy (am I mistaken, or in one post did he argue that "I haven't ever seen any of this evidence" implies that "no such evidence could even in principle exist"?!), but if I may, I think I can boil his argument down to two assumptions, the first of which I definitely agree with, the other which I think is controversial:

1) Anything "supernatural" by definition does not exist, because if something we previously though were supernatural were shown to exist in the physical world, then it would be, by definition, "natural."

2) A necessary feature of a prospective god is that it must be supernatural.

Fair enough, but it seems to me to be begging the question.

Jerry, on the other hand, seems to reject the first premise! He seems to think there is a definition of "supernatural" that would allow a thing with that trait to exist -- even though it wouldn't exist as part of the "natural" world? I don't understand that, and I would need a pretty specific definition of "supernatural" before I would accept it. A number of commenters at WEIT have mounted attempts, but I remain unconvinced by all of them.

So my opinion had been somewhere in between... I reject the possibility of the supernatural (by definition!), but I don't think that possessing supernatural traits is a prerequisite to godhood. Therefore, I thought that, while the evidence would have to be pretty staggering, we might imagine sufficient evidence to convince me of the existence of a being worthy of the appellation "god".

An exchange with Ben Goren has altered my thinking with this somewhat. I still think it's a question of definition, but he has convinced me that there is a particular aspect that is rather fundamental to most useful definitions of "god(s)", and that if I accept that as part of the definition, I must state that I cannot imagine any evidence that would convince me of the existence of god(s). I will stop just short of saying there can never be such evidence, but a case for this type of god(s) would have to first address some important theoretical objections before the evidential case could even begin.

First, the critical aspect of the definition. Let me try and state it as specifically and formally as I can:

Any being which is referred to as a "god" must either a) have created sui generis everything that exists, or b) be part of a pantheon that is either collectively responsible for creating or contains one or more members who created sui generis everything that exists.

If we further assume that said "god" has any type of volition, which seems reasonable given the apparent features of all major religions (oh noes, apophatic theology FTW!), then Ben Goren argues -- and I agree -- that such a god cannot by definition exist. If it exists, and it created everything that exists, then it must have created itself sui generis, and there is not even in principle a way by which a being with volition could create itself sui generis. It just doesn't make sense. It would have to have had volition first, and volition is something, therefore it's not sui generis!

Of course, this is a logical proof, and apparently sound logical proofs have turned out to be wrong before based on hidden assumptions that were not apparent until some new leap forward in understanding was achieved. So I don't reject the possibility that it could be wrong. And FWIW, I stand by that, despite the fact that I am about to constrain it even more.

Ben Goren responds that this may be so, but that the soundness of this proof is comparable to the soundness of the proof of the Halting Problem. Of course, I have not formalized it (probably someone somewhere has?) but in general I agree with Ben. So could there be evidence that would convince me that a Halting Oracle could be implemented in a Turing machine? Well, maybe, but I can't imagine it.

I'd prefer to talk about the Hidden Variables Interpretation of Quantum Mechanics, mostly because it's fresher in my mind than the Halting Problem. Bell's Theorem proves that, unless QM is just plain wrong, there can be no hidden variables. (And we're not talking wrong like "Newtonian mechanics is wrong because it over-generalizes a special case of general relativity", we're talking wrong like "Aristotelean physics is wrong") It does so by making predictions on the behavior of entangled particles, known as Bell's Inequalities.

In a nutshell: If there were some hidden variable, then the sum of the probabilities of a certain set of outcomes should be greater than or equal to the probability of another outcome -- because if that latter outcome were true due to some hidden variable, it would entail that all of the other outcomes would also necessarily have been true, if that's what we had been measuring for.

Turns out Bell's Inequalities are violated all the frakkin' time in quantum mechanics, and we can confirm this with observation. And confirm it we have -- again, and again, and again, and again. Bell's Inequalities just plain aren't obeyed. This is a fact of reality.

So any consistent theory of physics which attempted to predict the outcome of quantum interactions based on a heretofore unknown variable -- some trait or state of the particle that we didn't yet know about -- would have to begin by explaining how Bell's Inequalities were violated. If it couldn't do that, then regardless of whatever kinds of copious evidence is amassed in its favor, we would be justified in discounting its accuracy.

(That said, if somebody was able to, say, consistently predict a priori where an individual electron would hit the screen in the double-slit experiment, and this experiment were easily replicated... then we'd be wise to listen up to her theoretical explanation, even if that explanation failed to address Bell's Theorem. Unless and until that were addressed, though, I think we would still provisionally assume that there was some other phenomenon facilitating the prediction, rather than a heretofore hidden variable.)

So it is with a Creator god. I cannot imagine what evidence would convince me of the existence of a Creator god, and any such case would have to begin by mounting a satisfying explanation of the apparent existential contradiction discussed above. Unless and until that contradiction were satisfactorily addressed, we would have to provisionally assume that said god(s) came into existence via some natural process, rather than the other way around -- regardless of any other evidence. That includes your 900 foot Jesus scenarios. Heal as many amputees as you want, turn the Pacific Ocean into 2001 vintage California Cabernet Savignon, prove to me the existence of an afterlife, maybe even show me that you are powerful and benevolent enough to be worthy of worship -- I still ain't buying the Creator thing until you explain that part of it to me.

Now, maybe the Creator aspect is not entirely necessary. It depends on your definitions, of course. I think that's part of where Jerry's going with it (though I think he fails in refusing to nail down what he means by "supernatural" in a meaningful way) and I think that's okay. It leaves you vulnerable to challenges like "are the programmers of the Matrix gods?" or "Is Q from Star Trek a god?", but I don't necessarily think those challenges are insurmountable. (If the programmers of the Matrix made me sing crappy songs, asked for ten percent of my income, and played mean tricks like "Stab your son -- psyche!", then yeah, that pretty much sounds like Yahweh to me...)

So there's my final answer: If you mean the Creator god, then no, I cannot imagine any evidence that would convince me -- although there is an important caveat that my inability to imagine such evidence does not necessarily rule out its existence, though it puts some pretty strict conditions on what form the evidence would have to take. If your definition of god is more expansive, of course, then all bets are off.