Should the prior probability for gratuitous evil be high?


The discussion of the problem of evil has developed from a logical disproof, to an inductive argument, to a abductive inference. Here an even more modest approach to using evil is suggested: that evil shows that the prior probability of Theism must be very low, prior to any further investigation. This approach sidesteps the standard defences to the problem of evil, and thus indeed permits Atheist to adopt a more defensive strategy. All they need to do is show that the balance of arguments that may be offered do not shift this prior assignment. Here the field is briefly surveyed, the new approach is defended from two more obvious lines of attack.


The discussions surrounding the problem of evil has developed quickly in the last sixty or so years. It used to be thought that evil could deductively show that God (per classical theism) could not exist. Since Plantinga’s work on this topic, the discussion soon moved to using evil as an inductive argument, that although God couldn’t be logically dismissed, evil provided strong evidence against him. A similar complaint has been pressed in abductive form, that our observed balance of evils is expected more on Atheism than on Theism.

The discussion of this evidential problem of evil has been to try and show that the evidence isn’t that good. There are two main approaches. The first is to show that on reflection there is a plausible defence for the evils we observe, for soul-making, free will, uniformity of nature, and so on. This closely follows the historical practise of theodicy, although modern philosophers take theodicy to mean the actual reasons why God permits evils, and they restrict themselves to providing a defence – that is, to give a plausible story as to why God may have to permit the evils that appear to us, even if they aren’t God’s actual reasons for so doing. The second approach is to perform an epistemic decapitation: to show that we simply can’t trust our appearances to say whether there are God justifying reasons for the evils present in the world.

Both approaches are subject to lively discussion. However, both are trying to accomplish a fairly evidentially modest goal – to show that the appearances of evil we see aren’t too surprising given Theism, that we shouldn’t assign P(E|T) as particularly low. This mightn’t be enough to screen off the argument from evil – for if the appearances of evil are pretty much exactly what we’d expect on Atheism, that P(E|¬T) is very high, then evil still provides (modest) evidence for atheism. But this sort of mild confirmation is not particularly interesting – many other factors might provide mild evidence of this sort, so in which case the problem of evil is far from a decisive consideration.

Yet perhaps this gives Theism too much slack. Theism entails a very particular, and very unusual distribution of goods and evils – one which we should take to be very unlikely by it’s own lights. Given this, a cursory inspection of evil means that the prior probability of Theism is low: that Theism is (borrowing Carnap) statically disconfirmed by the peculiarity of the moral distribution it demands. The fact that further inspection might not provide any further dynamic disconfirmation, that it may say little either way just means we keep our low prior of Theism. The evidential burden on Theist is now heavier – he not only needs to reach the bar of showing the appearance of evil isn’t that unlikely given theism, he now must show the likelihood ratio is high enough to elevate our priors of a ‘Theist-friendly’ distribution to be not that unlikely.

Moral metaphysics

Theists tend to agree that evils exist. They assert, however, that God has good reasons for permitting these evils. Exactly what this entails isn’t entirely agreed upon. Most would accept something like this:

For an evil E, E is not gratuitous if there is no way E can be prevented without either incurring a greater evil or denying an outweighing good.

Now consider a moral modal space of all possible worlds with at least one evil. In this space, consider one such world, Wi, and one evil within it, Ei. Clearly, without making any assumptions about this space, that Ei will be probably gratuitous. Although it could just be that Ei is linked up to other evils and goods such that it cannot be removed without removing greater goods or incurring greater evils, this seems very unlikely to all the other ways Ei can be linked up to other goods and evils (e.g. that preventing Ei would incur extra goods and prevent greater evils). Indifference over possibilities should lead us to therefore believe that any given evil is more likely than not (perhaps much more likely than not) gratuitous. Now consider Wi, a given world with at least one evil. Because of this, it is more likely than not (perhaps much more likely than not) it is gratuitous. Further, the more evils we believe Wi contains, the greater the likelihood Wi is a world containing gratuitous evil.

Now consider our world. Most of us agree there are a large number (probably a vast number) of evils within it. Yet if we consider a modal space comprising all worlds with a vast number of evils, we can be almost certain that any given world in this space will have gratuitous evil, because it’d be unlikely that any given evil in any given world would be non-gratuitous, and especially unlikely that all the evils any given world would be non-gratuitous. It follows that (without any reason to favour any subset over another) that our actual world is almost certainly in the subset of worlds that contain gratuitous evil, rather than in the one that does not.

This assessment leads one to say that as the prior probability of our world having gratuitous evil is very high, the prior probability of Theism (which entails there being no gratuitous evil) is very low. This means the odds are stacked against Theism from the outset when considering evil – any attempts by Atheist to show a particular evil or set of evils to be gratuitous are evidential ‘icing on the cake’. In effect, they attempt to give further reasons to believe our world is one of the majority that has gratuitous evil by showing examples of the same.

Criticism and defence

Is the case for giving Theism barren priors right? There are several lines of reply one could make.

One could disagree with the moral calculus made to arrive at the poor likelihoods. One may think it is much more likely than it is made out for evils and goods to ‘just happen’ to fall into relationships that render evils non-gratuitous. Thus worlds without gratuitous evils aren’t as rare as the above suggests. The only reply here seems to be trusting to common intuition: that surely it isn’t more likely than not that evils fall into what amounts to God-justifying patterns, so much so that vast numbers of them will really ‘fall together’ in this way in a typical world. (This would also suggest that God could pick a world ‘out of a hat’ and find that actualizing it is consistent with his nature, which seems slightly counter-intuitive). Doubtless sensible people will disagree, but one can be confident most, Theists included, will hold the intuitions to accept this case. (A related objection would be to deny our world has any, or a great number of, evils: the reply is the same.)

Perhaps another approach is to suggest the approach taken above is a subtle way of begging the question of Theism. After all, God is a necessary being, and thus the modal space we imagine will be truncated if God exists – for if God exists, any world that exists will not have impermissible evils. Yet if we aren’t sure about God existing, we also shouldn’t be sure whether we are in this truncated modal space or not, and thus it is ‘cheating’ to construct this modal space presuming God doesn’t exist to show it is improbable.

This approach is misguided, but in a very interesting way. The moral space intimated above must surely be an epistemic space – it merely points to all the ways evils and goods could fall out. The right question to ask is not what someone with a middling degree of belief in Theism should think, but rather what should someone think with their degree of belief about Theism subtracted or ignored. When we ignore the issue of God, and just stare at the possibilities of how goods and evils can link up, we end up seeing that ‘Theism-friendly’ distributions of evil are very rare, and so our priors for Theism should be low. Importing our prior degree of belief in to change these priors isn’t on.

Two examples to make this clearer. First, consider fine tuning. Accept arguendo that the modal space in question is such that life permitting universes are rare. It surely wouldn’t be a licit move for Atheist to reply, “Despite life permitting universes being rare in the modal space, I’m pretty confident of Atheism. I therefore reject indifference and slant the likelihoods such that it just is much more likely to land in a region of modal space that has life permitting universes.” This is surely an exercise in question begging.

Use ‘gratuitous evil’ instead of Theism to make the point clearer here. For Theist to say, “Yet I am pretty confident of Theism, therefore the likelihood must be slanted so that one is more likely than not to end up in a world without gratuitous evil,” is again question begging. In both cases, one is screening off an unpalatable case by asserting the matter under discussion. Of course, in neither case are these concerns decisive – however, what we need is reasons. So Theist could say “in fact the modal space for evil is such-and-such for I have good arguments for Theism”. Yet this needs to be made. In short, we must start from our indifferent modal space and argue our way from there. We may think that argument may lead us from our ‘tabula rasa’ priors far elsewhere, but that doesn’t mean we can deny what those priors should be in the first place.

Evidential irony

‘Burden of proof’ tends to be surrounded with canards, principally surrounding how Atheists aren’t ‘making a positive statement’, or that onus is on Theist to ‘support their claim’. These are misunderstandings: barring question begging assumptions that Atheism is more probable, both sides have to ‘make their case’, and neither is obliged to account for themselves before another to demonstrate their rationality. Yet if the foregoing is true, then Theist really does bear the burden of proof. He is saddled with defending an assertion about the actual world that seems by inspection of moral metaphysics very unlikely indeed – that it contains no gratuitous evil. Even if Atheist can’t come up with a convincing way to show this assertion to be false, this assertion remains very unlikely indeed by simple modal inspection. Theist needs to do the philosophical heavy labour of making this assertion plausible.

What moves should Theist make? In some sense, the same ones as before. As Theism entails that the world contains no gratuitous evil, arguments for Theism are arguments for this assertion. The problem is that the very low prior for this assertion entails a very low prior for Theism, and thus arguments for Theism have an evidential mountain to climb – once you get close to P(T)=0, you need very high ratios of P(X|T)/P(X|¬T) to move you very far towards 1.

Given this, Theist may want to fight at least some of his campaign on evil, to show a more informed inspection suggests we should slant our likelihood of the possibilities to Theism’s favour. Yet the task is now difficult: showing that our observation of evil is unsurprising if there were in fact no gratuitous evil is not enough – that makes matters an evidential wash and we return to our (inhospitable) priors. Rather, it must now be shown that our observations of evil confirm the no-gratuitous-evil hypothesis over the world having some gratuitous evil. Not only is this task far beyond the ambitions of current work on the problem of evil, such a case would need to be made against the teeth of Atheists who can gleefully ransack the argumentative resources Theists have developed and turn these against them.

Theist can’t rely on any controversial philosophical theses (like free will and incompatibilism) like before without providing convincing reasons in favour – as these theses could be false, and thus the case in theism’s favour is restricted by the (probably middling) likelihood of the thesis in question. In a delicious irony, however, it would be sceptical theism that could prove the most lethal weapon against Theist. For now it is Theist who needs to use appearances to build his case, and the careful work done to argue these appearances can’t be trusted undermine any case he hopes to make. Atheist can now happily endorse these arguments, safe in the knowledge that if putative God-justifying reasons would lie beyond their epistemic ken, Theist simply lacks epistemic access to provide an argument to change the inhospitable priors – even if he can produce a convincing argument from our appearances, it should not be trusted. Skepticism is a double-edged sword, and it’s now Atheist’s turn to have a swing.


There has been a progressive retreat on the part of philosophical Atheism to find more and more defensible redoubts to deploy the argument from evil. The prior development represents what must be the very last line Atheist can take. It seems pretty impregnable: it now indirectly shows, via pretty resilient moral and modal intuitions, that Theism is wedded to an a priori highly improbable assertion about the actual world. It throws down the gauntlet to Theist to make this assertion plausible, which requires him to go far further in the work of justifying evil than he’d ever though he’d need to. Further, in doing so, Atheist doesn’t forfeit all the moves he could make in the ‘standard’ evidential argument from evil – and now they only need be persuasive enough to make counter-offers to Theists case, rather than decisive.

Of course, reasonable people may have good reasons for believing Theism likely, and these may be first-person experiences that aren’t easily inter-subjective. Yet if the above is right, the deck is now strongly stacked against Theism. Barring powerful personal experience, or a ‘silver bullet’ from natural theology, one can be confident in one’s Atheism.

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