I’ve recently completed my PhD and I thought I’d create this blog post to explain it as simply as possible.
There are three main sections to the work and one minor section.
Section 1. Bayes’ Theorem and Swinburne.
This section describes and explains Bayes’ Theorem, which is P(h|e) = P(e|h)P(h) / P(e), or, the probability our theory is right, given evidence, is, the probability we’d see that evidence, given the theory, times the prior probability of the theory (without looking at evidence), divided by the probability of the evidence itself. There are lots of nuances and things around the theorem, e.g. whether P(e) is theory-independent, but let’s leave it at that.
1. Swinburne argues that God likely exists because God is simple, because (a) he is a person, and (b) a _simple_ person, with (c) simple properties. He then argues that in terms of Bayes’, P(e), the prior of the (e)vidence, is low, because our universe is rare and special. He also argues that P(h) is high, because God is simple, and we prefer simpler hypotheses (h = hypothesis). Lastly, he argues that theism (h) explains the universe (e), that is, P(e|h) is high, or in English, this universe is just the sort God would make. If we do the calculation, however, we see he is wrong. If you put a very small value into Bayes’ Theorem for P(e) in the denominator, you have to also have a very small value for either P(h) or P(e|h) in the numerator. So Swinburne has a choice; either P(h) is low - God is not simple - or, P(e|h) is low - God doesn’t explain our universe. That’s the first, and most damaging problem.
2. The second problem is we can’t objectively get values for P(e) and P(h) anyway, because we just don’t know how likely theism is, without begging the question - that is, assuming that it is true. Moreover, we only know how our own universe is, and have no frequency measure for it, so we can’t give a solid value to P(e). Swinburne tries ⅓ at one stage, but that’s way too high.
3. If God’s omnipotent, he can make any universe at all, and there are at least N possible universes which are equally very good, that he could choose from. So even in a scenario like that, P(e) must be 1/N, very small. It’s worth noting that the atheists usually accept this point even with the Anthropic Principle in place. I’ll critique that principle some other time. However, if P(e) is very small, even given theism, it means that P(e|h) is small. Which means P(h) has to be very large indeed, because both P(e) and P(e|h) are very small. Yet we’ve already argued that P(h) can’t be large. So either P(e|h) is very small, or P(h) is very small - meaning that either theism is vanishingly implausible, or theism just doesn’t explain our universe. Necessarily, from the mathematics.
There’s also a question about whether God is simple, and whether P(h) is high for simple things. I dispute both of those. Consider pantheism and omnipresence. If God is everywhere, pervading everything, ie omnipresent, and he knows everything, ie., omniscient, it suggests that he’s more complex than the universe, since he’s everywhere, contains it, and thinks about it at all times (creatio continuans). If so, then P(h) would be very very low. Which would be fine, if we wanted to counterbalance the very low P(e) in the divisor, mentioned earlier. But it doesn’t match Swinburne’s claim that P(h) is very high.
Section 2. Atheistic evidence
Atheists like to argue that the Multiple Universe Theory (MUT) - that there are many universes, probably millions - combined with the Anthropic Principle (that we find ourselves in life-hospitable conditions, because that’s the only place we _could_ find ourselves), shows that our universe is likely. In other words, the atheist argues that our universe is probable, or P(e) is in fact high. There are many troubles with this approach.
1. MUT has some problems, e.g. no solid evidence for it. Also, the competing model, PUT (Pulsating Universe Theory), strikes me as plausible. (Many universes in a row, rather than existing simultaneously).
2. Anthropic Principle, which I don’t discuss at length, is a mere truism and doesn’t seem to prove anything. A theist could agree with it and still maintain that we exist in a universe which is life-capable, or could only find ourselves in such a universe, because God made it so. So it’s useless to the atheist.
3. P(e) being high means P(h) has to be high, or P(e|h) has to be high, either of which would actually support Swinburne who claims P(h) is high and P(e|h) is high.
4. The Gambler’s Fallacy (and Hacking’s Inverse Gambler’s Fallacy) affects all atheistic models. That is, just because we now find ourselves in a life-capable universe, does not mean there are many more (either parallel, or preceding ours).
So the atheistic replies to theistic cosmology are weak too.
This means there’s a stalemate.
Section 3. The problem of evil.
Theists claim that God is all-good, all-knowing, and all-powerful, meaning he deplores evil, knows about absolutely all of it, and could do anything to stop any of it. Yet clearly evil exists. Theists offer many explanations for this, the most famous three being
1. Free-will theodicy/defence: That we have free-will, and therefore choose to do evil (evil is our fault),
2. Soul-making Theodicies: God allows evil so that we can be better persons, have free-will, be heroic, learn, etc., and,
3. Skeptical theism: We are finite beings who can’t understand God’s good plans for the future, and existing current evils are necessary for that good future which we can’t see.
Atheists however can respond.
1. Free-will theodicy/defence: We might well not have free-will. For more on this, see for example Derk Pereboom’s work. Furthermore, even if we had free-will, we can still have limited choices. God could limit us to choose between tea and coffee, rather than, say, genocide and working in a soup kitchen. Free will doesn’t have to be made available through extreme choices. God could give us partial free-will, or compatibilist free will (you get what you want because you wanted it). For more on compatibilism, see Frankfurt and Watson. It also doesn’t help against natural evils, where animals suffer, yet animals don’t have free-will.
2. Soul-Making Theodicies, that is, that God allows evil for a reason (e.g. to teach us endurance, persistence, heroism), is however a morally obnoxious position when one compares the virtues gained (heroism, etc), to the level of evil (Hitler, etc.). They’re disproportionate, and an omniscient being should have foreseen that. We only need courage, etc., because evil exists. If evil never existed, we’d not need courage etc.
3. Skeptical theism: Naturally, we could not know all the things an omniscient deity would know. However, if we can’t know God’s reasons for evil, we should not be claiming to know his reasons for good. Why would he hide the former and reveal the latter? It’s question-begging to suppose that there are reasons other than arbitrariness. In a formula: if we know why God created the universe (with evil), then we know why God created the universe with evil. Since we deny knowing the latter, necessarily, of logical necessity, we must deny the former, since they’re logically equivalent.
This means that either we can’t defend theism with cosmology, as argued in Section 1, or, God is neutral (not all-good), or, theism is false. Personally, I think the theist should go with “not all good”, since it seems to me quite clear that nature is neither good nor evil, and so should its Creator be. And indeed, it’s only Western and post-medieval philosophers and theologians who insist on the all-good thing. Hindus, Buddhists, Taoists, Jews, Muslims, Wiccans, etc., all allow that God can be malevolent, punitive or violent (as we understand these terms).
Section 4. Faith
I then conclude with a brief point on faith. We generally take it as true, when a Geography teacher tells us that Madrid is in Spain. We take it on faith from an authority. We know Madrid is in Spain, even if we’ve not been there (we have no evidence). And most people take God on faith. Hence, if we can know things through faith, we might still know God exists. More work in this regard is needed.