T = theism
N = naturalism
E = there is some evil
I = there is inscrutable evil
I have little direct intuition about P(I|T). I have to actually calculate. Start with:
P(I|T) = P(I|E&T)P(E|T).
Now, what is P(E|T)? The kind of evil we have the best reason to expect a priori is bad free choices by significantly free persons (SFPs), understood in the libertarian sense.
P(God creates SFPs | T) = P(God creates SFPs | T & SFPs are creatable)
P(SFPs are creatable | SFPs are possible & T) P(SFPs are possible |
Now, given that God isn’t a SFP (in the libertarian sense), and given that God if he exists, exists necessarily, I suppose P(SFPs are creatable | SFPs are possible & T) = 1. After all, given theism, a being other than God is possible iff it is creatable. And P(God creates SFPs | T & SFPs are creatable) is moderately high. Not too high, because there is a not too low probability that God would create nothing, since the only-God world is very valuable–it exhibits the values of simplicity, unity, beauty and lack of local flaws to an extraordinary degree. But given that God creates something, that God creates SFPs is fairly likely. Maybe the probability that God creates something given that SFPs are creatable is about 1/2 to 3/4, maybe closer to 1/2. Let’s say it’s half way: 0.625. And the probability that God creates SFPs given that he creates something is very high, maybe 0.9. So:
P(God creates SFPs | T) = 0.5625.
Now, P(E | God creates SFPs) is slightly more than P(an SFP sins | God creates SFPs). Why only slightly? Because it’s plausible that evils in a world where nobody sins would be unjust or that God would be the author of them in an objectionable way. Maybe: P(E | God creates SFPs) = 1.2 P(an SFP sins | God creates SFPs). So, approximately:
P(E | T) = P(someone sins | God creates SFPs) P(God creates SFPs | T) / 1.2 = 0.46875 P(someone sins | God creates SFPs).
Now, what is P(someone sins | God creates SFPs)? Given that probably God would create several SFPs if he created at least one, it’s not too unlikely. But God might create SFPs that are very unlikely to sin. I think such SFPs would probably count as less free, and their free choices would likely be less valuable, but it’s a possibility not to be dismissed. So, maybe P(someone sins | God creates SFPs) = 0.75. So, approximately:
P(E | T) = 0.35
P(I | T) = 0.35 P(I | E & T).
Now my intuition is that it is moderately likely that if E, all the evils are either sins or punishments for sin or results of sin needed for freedom, and all of these are scrutable. So P(I | E & T) is not too high. So, P(I | E & T) is about 0.3. So:
P(I | T) = 0.11.
Trent in an earlier post said P(I | T) is not too low, and I guess this is support for that.
Now, let N = naturalism.
P(I | N) = P(I | E & N) P(E | N).
Plausibly: P(I | E & N) is very high, I’d say 0.999 or higher. (Unless I is taken to entail that there are beings that can discern.) So, approximately:
P(I | N) = P(E | N).
Now, P(E | N) is approximately equal to P(E | conscious beings & N) P(conscious beings | N).
P(E | conscious beings & N) = P(pain or SFPs | conscious beings & N &
values) P(values | conscious beings & N),
where values is the claim that there really are values (which is entailed by E). Now, P(values | conscious beings & N) is approximately P(values | N), we may suppose. While P(values | T)=1, since God is by definition good, I think that P(values | N) is no more than 0.5 (think of the plausibility of non-realist accounts of value given N). So:
P(E | conscious beings & N) = 0.5 P(pain or SFPs | conscious beings & N & values).
If there are values, it’s very likely that damage to the body is bad. And there are clear benefits to being aware of damage to the body qua bad, etc. So pain seems likely if damage to the body is possible. However, the concept of damage to the body depends on the concept of proper function. Now P(proper function | N & values & conscious beings) is bigger than P(proper function | N), but it’s still not that high. (Maybe the only values are elegance of laws.) The naturalistic accounts of proper function all fail, I think (and I have arguments for it). On the other hand, proper function is very likely needed for consciousness–consciousness needs content, and indicator theories of content need proper function (this is a substantive claim, but I can defend it). So:
P(proper function | conscious beings & N) = 0.8.
So, we might approximate:
P(proper function | conscious beings & values & N) = 0.9.
And P(pain | proper function & conscious beings & values & N) is close to 1.
P(E | conscious beings & N) = 0.45.
Now, what is P(conscious beings | N)? Well, the best stories about consciousness and content (let’s suppose consciousness is contentful–unless pain is indicative to damage, it’s unlikely to be bad) require proper function. So maybe:
P(conscious beings | N) = 1.25 P(conscious beings | proper function & N) P(proper function | N).
Now, P(conscious beings | proper function & N) is moderately high, but not too high. From indicators to consciousness is still a leap: we might think we could imagine beings with content and no consciousness, and it’s not clear that proper function and indicators are enough for consciousness. Moreover, we still need an evolutionary process leading to representational states complex enough for content, though a multiverse might take care of that (we also need organisms, but P(organisms | proper function & N) is close to 1–see argument later). So, maybe, we can let P(conscious beings | proper function & N) =
0.7, or more likely less. So:
P(conscious beings | N) = 0.875 P(proper function | N).
Now, plausibly, if there is proper function, there are organisms that exhibit it. It’s hard to imagine, given N, any place for proper function that in organisms or in artifacts made by organisms.
Now, there are two plausible stories about proper function: the Aristotelian story and the evolutionary. I shall suppose the two are mutually exclusive. If the Aristotelian story is true, we’re very unlikely to get proper function in organisms given N. We would need proper function transmitting laws, or something weird like that.
P(proper function | Aristotelian account & organisms & N) = 0.05
What about the evolutionary account? I think:
P(proper function | evolutionary account & organisms & N) = 0.95.
This is less than 1, because if there is a multiverse, there might be non-evolved organisms, and there might be problems with making sense of the probabilities that evolution requires given a multiverse.
And maybe there is some other account? Accounts in terms of agency aren’t going to work given N, since agency presupposes content and hence proper function given N. Let’s give a probability 0.1 to “some other account”.
Now, the evolutionary accounts of proper function have really, really serious objections. So, at most:
P(evolutionary account | organisms & N) = 0.25.
P(proper function | organisms & N) = (0.05)(0.65) + (0.95)(0.25) + 0.10 = 0.37.
Now, P(organisms | N) is high if there is a multiverse and low otherwise (fine-tuning intuitions). How likely is there to be a multiverse? Maybe fairly high, maybe not. One reason to think it’s fairly high is that if N is true, then PSR is false, and if PSR is false, we expect to see all sorts of weird stuff coming into existence ex nihilo. On the other hand, maybe there has to be an all-encompassing spacetime, and maybe it’s of limited size? But perhaps the naturalist can’t grant that if N is true, we expect to see all sorts of weird stuff coming into existence ex nihilo, as that would undercut science. Moreover, there
is a pretty good chance there’d be nothing if N. So:
P(organisms | N) = 0.05 P(~multiverse | N) + 0.99 P(multiverse | N).
P(multiverse | N) = 0.6.
(Probably less as P(nothing | N) seems high.)
P(organisms | N) = 0.614.
So at most:
P(proper function | N) = P(proper function | organisms & N)
P(organisms | N) = (0.37)(0.614) = 0.28.
P(conscious beings | N) = 0.245.
P(E | N) = (0.45)(0.245) = 0.11.
P(I | N) = 0.11.
And that’s what we said about P(I | T). So, inscrutable evil doesn’t provide a significant reason to believe theism over naturalism.
Honestly, I didn’t rig it. That’s just how the numbers came out. (But I could kind of see that my intuitions were leading that way.) 🙂
Actually, if one does the calculations to three decimal places, one gets a slight difference (about 0.005) between P(I | N) and P(I | T), in favor of P(I | N), but I can’t claim enough precision in my intuitions above to make that difference count as significant.
On reflection, I’d change at least two estimates. I’d raise the probability of values given N, and I’d lower the probability of evolutionary accounts of proper function.