Bloggingheads on the Cognitive Science of Religion

thanks for putting this up, Josh. I think the interesting stuff comes out around 35:00, when Murray starts defending Plantinga's conditional claim that if God in fact exists, then belief in God is justified. (Although Plantinga would put it in terms of warrant; given his earlier chapters in Warranted Christian Belief on the nature of justification, he would probably think the antecedent (If God exists...) is not necessary for justified belief in God, because he understands justification deontologically, and he thinks you don't need reliability (or proper function) for that.)

This is also relevant to some of the discussions last year on the Plantinga/Tooley book. I remember somebody (I forget who) pressing me on whether there is scientific information confirming that there are cognitive mechanisms in humans which are likely to produce theistic belief. Here, the participants take it for granted.

Bloom asks the interesting question about what sort of discoveries in cognitive science might provide evidence that theistic belief is not likely to be true. Murray doesn't think that there would be any other than usual reasons to disbelieve in God because of possible types of evil. I wonder if Murray's right.

I found the discussion about PvI's statue example and Murray's telescope example interesting. Murray says the question is something like "when does a naturalistic explanation undermine a supernaturalistic one?" I had a sort of knee-jerk Bayesian response that may go some way toward answering that question. This is quick and dirty.

So there are two examples:

1. The "tears" of a miraculous statue are found to be bat urine.

2. The first chapter of Genesis written in the stars is found to have a causal explanation deriving from the big bang.

We want to account for our intuition that in 1 a naturalistic explanation undermines the supernaturalistic one, but in 2 a naturalistic explanation does NOT undermine the supernaturalistic one. It seems that at least part of that intuition could be captured quantitatively.

I think it has to do with likelihoods (the conditional probability of a piece of evidence e, given an explanation or theory T - P(e|T)). Consider example 1 first. Let e be the tears from the statue. Let Tn be a naturalistic explanation, Tsn a supernaturalistic one. It is important that in neither 1 nor 2 are Tn and Tsn mutually exclusive (as Bloom points out, you could just say that God performed the miracle with bats and urine). The likelihood P(e|Tn) is fairly low, but P(e|Tsn) is, let's say, a little higher.

Now consider example 2. Here, e is first chapter of Genesis written in the stars. Tn and Tsn are the corresponding explanations. The difference here is that P(e|Tn) is incredibly low, much much lower than in example 1 (it's just not likely at all, given the big bang, etc., that stars should come to spell out the first chapter of Genesis). Again P(e|Tsn) is higher than P(e|Tn), but this time, much higher. So what does this tell us about Tn undermining Tsn in 1, but not in 2? The ratio P(e|Tsn)/P(e|Tn) is lower in 1 than in 2. My suggestion is to take that ratio as a measure of to what extent Tn undermines Tsn. The lower it is, the more undermining going on (there might be some threshold number at which the numerator explanation can be said to be undermined).

I think there is some intuitive plausibility here too. One salient feature distinguishing 2 from 1 is how incredibly unlikely it would be on a naturalistic story compared to a supernaturalistic one for e to obtain (though we're supposing that the naturalistic story is true but does not exclude - but can undermine - the supernatural story). But in example 1, that doesn't seem to be the case.

What do you think? Does that work? If so, what adjustments need to be made? Either way, interesting discussion from Murray and Bloom.

- RTS

RTS,

That's an intuitive idea. Your idea, I take it, is that the plausibility of having an undermining explanation for event e increases as the supernatural explanation for e becomes relatively improbable (relative to the naturalistic one for e). Two quick worries. Wouldn't you want a condition on the priors for e? It might be true that P(e/H') is much higher than P(e/H), where the former hypothesis is naturalistic and the latter supernaturalistic, but where both are lower than P(e/T), where T is some tautology. In this case there is presumably no undermining at all, since both hypotheses are non-starters. You'll also need conditions on what is an admissible theistic hypothesis, otherwise you'll never get any theistic explanation undermined. Suppose H' is the hypothesis, "God caused e". In that case P(e/H') = 1, since N(God causes e only if e). So no naturalistic hypothesis could be higher than the theistic one. Similarly for hypotheses like "e is part of God's divine plan", "e was providentially determined by God" and so on.

Mike:

Good points. Thanks for the feedback.
1. Your first point is that if the two theories are not exhaustive, then P(e) shouldn't be higher than P(e|Tn) or P(e|Tsn). If the theories are exhaustive, then the probability calculus already constrains P(e) to not be higher (just by expanding P(e) to P(e|T1)P(T1) + P(e|T2)P(T2)). And your constraint makes a lot of sense, at least with these examples. The P(e) where e is a candidate for a miraculous event would presumably be really low anyway (and hopefully higher on a proffered explanation).
I'm wondering whether it really would make no sense, absent the constraint on priors, to say Tn undermines Tsn (even though Tn+1 undermines Tn). There's a good chance I'm being dense this morning, but if we let the ratio from my last post measure undermining, is it a bad result that we can say one explanation undermines a second one, even though there is a third one that undermines both? I'm thinking it might be OK to say something like a Newtonian explanation of a physical event undermines an Aristotelian one, but an explanation from relativity theory undermines both. Thoughts?

2. The second point is that P(e|Tsn) shouldn't equal 1. So the constraint could be that Tsn cannot entail e. But can we can get by without it? Here's what I'm thinking. Even in cases where P(e|Tsn)=1 (since N), maybe Tn can undermine Tsn. All that's required is for the ratio P(e|Tsn)/P(e|Tn) to be low. It'll be a problem to say how low, but maybe being less than 1 is not required. If P(Tn) is much higher than P(Tsn), I'd be inclined to say Tn undermines Tsn where the P(e|Tsn)/P(e|Tn)=1 (if P(Tn) is really a lot higher than P(Tsn) maybe the ratio can be a little greater than 1). I think that explains why a naturalist can rightly think that a naturalistic explanation undermines a theistic one even when P(e|Tsn) > P(e|Tn).
It seems to me now that all I'm doing is working out the constraint you're suggesting, or offering a different one. Am I on the wrong track here?

Thanks,
RTS

Thanks for posting this. I have a question that I hope someone on here could clear up. If mutations happen randomly, why should we try to find the adaptive purpose of religion? Isn't this ascribing intentionality to the mutative process that organisms undergo? If mutations happen randomly, in what sense is it valuable to talk about the adaptive purpose of some feature of an organism? Wouldn't it be better to try to analyze how this randomly developed feature of an organism interacts, or as has interacted, with it's environment, either helping the organism in some particular way or hindering it?

I mean, it seems like when they talk about the relevance of evolutionary theory to the development of religion they both are simply stating the quest of certain thinkers to find the 'adaptive purpose' in religious belief. I could have missed the boat entirely on this one.

Thanks!

I've been thinking a little about Mike's second worry and my response. It seems if I'm going to allow for the priors of the hypotheses to figure into the measure of undermining, the measure had better show that. That is, in order to account for this last intuition/desideratum (that the priors in the explanations are relevant as to whether some explanation undermines another), our measure should have something to say about the priors of the explanations themselves. A formula that readily suggests itself in which the likelihood (if that is the most relevant factor, as it seems to be) plays a major role, as well as the prior in the explanation is, of course, Bayes’ Theorem. So maybe, as a second attempt at a measure of undermining, we'd have this:

(MU2) Pr(Tsn|e)/Pr(Tn|e), the lower the more undermining

BT includes both the likelihood and prior, but, one might worry, it also includes the expectedness. Fortunatley, the expectedness is irrelevant and does not change the ratio (MU2) at all (the likelihoods are both divided by P(e) - to see that, just write out BT for each quantity in MU2).

If anyone is still following this thread, is there some glaring obstacle in the way of letting MU2 measure undermining?
There seem to be two more plusses of a ratio analysis of undermining (in favor of either MU1 or MU2):
1. An utterly implausible (or contradictory) hypothesis (P(H)=0) is incapable of undermining any hypothesis with any plausibility at all: P(H’|e)/0 is undefined.
2. An utterly implausible (or contradictory) hypothesis will me maximally undermined by any other hypothesis with any plausibility at all: 0/P(H’)=0.

Thanks,
RTS