The Probabilistic Problem of Evil

Draper's argument at rung 12 was constructed to avoid a particular step, and this rung is about the step it avoided. Almost every other evidential argument from evil takes it, and almost all of the last four decades of writing on the problem has been about whether it can be taken.

The step is an inference from what we cannot find to what is not there. We look at some instance of suffering, we consider what good might justify permitting it, we come up with nothing, and we conclude that there probably is nothing. Stated that baldly it sounds either obviously reasonable or obviously fallacious, depending on temperament, and the achievement of the literature has been to show that it is neither, and that whether it works depends on a general principle about when absence of evidence is evidence of absence.

The case

William Rowe's "The Problem of Evil and Some Varieties of Atheism", published in the American Philosophical Quarterly in 1979, is the paper that set the terms.

Rowe's example is deliberately chosen to defeat the standard replies before they start. A fawn is caught in a forest fire started by lightning, is badly burned, and lies suffering for several days before dying. There is no human agent involved, so the free will defence has nothing to work on. There is no moral development in prospect, so soul-making has nothing to work on. Nobody observes it, so it teaches nobody anything. And the case is not exotic: the point of the example is that events of this kind have presumably occurred in enormous numbers throughout the history of animal life, most of them entirely unwitnessed.

Rowe later added a human counterpart, a case of a young child abused and killed, to forestall the response that suffering matters only where moral agents are involved. The two cases are usually discussed together, and the argument does not depend on either in particular. What it depends on is that there exist instances of intense suffering for which we can identify no justifying good, and that seems undeniable.

The argument

The second premise is close to a statement of what the divine attributes mean, and few theists have attacked it directly, though rung 18 will raise a complication about whether a best action is always available. The whole weight falls on the first, and the first is not observed. What is observed is that we cannot identify a justifying good, and the argument needs a bridge from that to the claim that there is none.

What justification would require

The first premise is stated in terms of a greater good, and it is worth unpacking what the theist has to supply in order to deny it, because the requirement is stricter than the casual formula suggests.

It is not enough that some good comes out of the suffering. Good comes out of a great many bad things without the bad things being justified, and the fact that a benefit followed does not show that it could not have been obtained otherwise. What is needed is a connection of necessity: the good has to be one that even an omnipotent being could not have secured without permitting the evil, or without permitting something equally bad.

That condition is severe, because omnipotence removes most of the ordinary reasons why one thing has to be paid for with another. A being who can do anything logically possible is not limited by resources, by side effects, or by the difficulty of arranging matters, so the only barriers left are logical ones. The theist therefore has to claim that permitting the evil is logically required for the good, or is required by something else that is, such as the stability of natural law or the reality of free choice.

A further condition is often added, and it does substantial work in the later rungs. Many philosophers hold that it is not sufficient for the good to be secured somewhere: it must be a good in which the sufferer shares. A being who permits a creature to be destroyed for the sake of a benefit elsewhere has used it, and using a person is exactly the sort of thing perfect goodness is supposed to exclude. This condition is the pivot of rung 16, and it is the point at which the fawn becomes hardest to handle, since a fawn that dies in a fire has no further life in which any good could accrue to it.

Notice also how little the premise asserts. It does not say that most suffering is unjustified, or that any particular case is. It says only that at least one instance of the enormous number available is one an omnipotent being could have prevented at no cost. Denying it requires holding that every single instance, across the whole history of sentient life, is connected to a good in the way described.

Running the argument backwards

Rowe himself set out the theist's most direct response, and he named it after G. E. Moore's way of handling sceptical arguments.

Moore's manoeuvre was to observe that a valid argument can be run in either direction. If the premises entail a conclusion you find less certain than the denial of one of the premises, the rational response is to reject that premise rather than to accept the conclusion. Moore used this against arguments for scepticism about the external world: he was more certain of his hands than of any premise in an argument that he could not know he had them.

Applied here, the theist grants the second premise, which is close to a definition, and denies the conclusion, on the strength of whatever grounds they have for believing in God. From those two, the denial of the first premise follows: there is no instance of suffering that an omnipotent being could have prevented at no cost, however things may look to us.

This is not a trick. It is the correct description of what happens when a valid argument meets a well-supported denial of its conclusion, and Rowe accepted that the move is available. What determines which direction the argument should be run is which the person is more confident of: the first premise, or the existence of God. That is why Rowe's atheism is friendly, and it is why the evidential argument cannot be assessed independently of everything else the person believes.

The move does have a cost, and it is worth stating. Someone who runs the argument backwards is not answering the argument but declining to be moved by it, and they thereby take on the commitment that there is a justifying good in every case, including the ones they find least tractable. That commitment is what the theodicies of the intermediate tier were attempts to discharge, and what skeptical theism proposes to hold without discharging.

Friendly atheism

Before turning to the bridge, one feature of Rowe's paper deserves notice because it is often lost when the argument is summarised.

Rowe called his own position friendly atheism. He held that the argument establishes that atheism is rational, and he explicitly allowed that a theist who has other grounds, and who is not in a position to see the force of these considerations, may be entirely rational in continuing to believe. The evidential argument, on his account, gives the atheist a good reason without convicting the theist of irrationality.

That posture follows from the argument's probabilistic form and is worth generalising. An argument that shifts a probability tells you which way to move from where you are, not where everyone must end up, and two people with different starting points and different bodies of other evidence can both respond correctly to it and still disagree. The tier's remaining arguments should all be read this way.

The bridge, and the restriction on it

The bridge premise says that our failure to find a justifying good is evidence that there is none. Stephen Wykstra's "The Humean Obstacle to Evidential Arguments from Suffering", in the International Journal for Philosophy of Religion in 1984, is the paper that questioned it, and it did so by proposing a general condition on inferences of that form.

The condition is best seen through its application. If I look in the garage and see no dog, I may reasonably conclude there is no dog there, because a dog is the sort of thing I would have seen. If I look in the garage and see no fleas, I may not conclude there are no fleas, because fleas are not the sort of thing I would have seen even if present. The failure to observe counts as evidence only when the observation had a decent chance of succeeding.

Wykstra's claim is that the goods that might justify God's permission of suffering are more like the fleas. If there is a being whose knowledge exceeds ours as much as the theistic attributes say, the goods it foresees and the connections it perceives between events would very plausibly lie beyond our detection. The parent analogy makes the point vivid: a small child has no access to the reasons behind many of a parent's decisions, and the child's inability to identify a reason is very weak evidence that there is none, given the disparity in understanding.

If that is right, Rowe's first premise is not supported by the observation offered for it. The observation is compatible with there being justifying goods, and, given theism, it is roughly what one would expect whether or not there are.

The shape of the inference

Naming the pattern did two useful things. It made clear that nothing peculiar to theology is being invoked, since noseeum inferences are everywhere in ordinary and scientific reasoning, and it located the disagreement precisely. Nobody disputes that some noseeum inferences are good. The dispute is over whether the detectability assumption holds in this case, and that is a question about our epistemic position relative to a being of the sort under discussion.

That exchange is the whole of rung 15, and the reply above is where skeptical theism's difficulties begin rather than end. What matters here is that the exchange has moved the dispute away from evil and onto epistemology, which is the main structural consequence of Wykstra's intervention.

The turn to probabilities

Rowe's response over the following years was not to defend the original inductive step but to reformulate the argument so that it does not require one. His "The Evidential Argument from Evil: A Second Look", in Daniel Howard-Snyder's collection The Evidential Argument from Evil (Indiana University Press, 1996), sets out a version in explicitly Bayesian terms.

The reformulated argument compares hypotheses rather than establishing a premise. Take the known instances of apparently pointless suffering as evidence. Ask how probable that evidence is on theism, and how probable it is on the denial of theism. Rowe's claim is that it is more probable on the denial, and that theism is therefore less probable after the evidence than before.

The advantage is that this version does not need the first premise of the 1979 argument at all. It never asserts that there is pointless suffering. It only needs a comparison of likelihoods, which is the same manoeuvre Draper made two rungs ago and for the same reason: it relocates the argument to ground where the failure to identify a justifying good does not have to be converted into a claim about what exists.

The cost is that the theist now has a new place to push back, since a likelihood comparison can be affected by anything that changes either likelihood or either prior. This is where theodicies re-enter.

This reframing changes what a theodicy has to accomplish, and it improves the theist's position in one way while worsening it in another.

It improves it because the traditional demand on theodicy was very high: to say what the actual reason is. Under the probabilistic reading, the theodicist needs only to offer an account that is not wildly improbable and that makes the observed pattern less surprising. Several partial accounts, each covering some of the evidence, can be combined.

It worsens it because the accounting is now explicit. Every addition to the hypothesis has a price in prior probability, and combining several partial theodicies multiplies the price. Nor can the theist escape by disjoining them, saying only that some theodicy or other is correct, because a disjunction that is kept vague does not confer a high probability on anything specific and therefore does not raise the likelihood much.

There is a second reason the probabilistic version has held up better, and it concerns what CORNEA can and cannot reach. Wykstra's condition constrains inferences from what one fails to observe to what does not exist. A likelihood comparison contains no such inference: it asks how probable the observations are on each hypothesis, and one can answer that question without claiming to have surveyed anything. The skeptical theist can still object, but the objection has to be that we cannot assess the likelihoods either, which is the wider claim examined at the next rung rather than the narrow condition of 1984.

The result is that both sides in this debate have migrated to comparative claims about probability, and the disagreements that remain are about the prior probability of theism and about how much a hypothesis of that generality should be expected to determine. Those are not questions the evidence of suffering can settle, which is a discouraging conclusion for anyone hoping the problem of evil would resolve the matter on its own.

Everything has to go in

The requirement is the theist's most important structural resource in this framework, and it is the reason a successful evidential argument from evil does not establish atheism.

Suppose the argument works. The evidence of apparently pointless suffering lowers the probability of theism. It does not follow that theism is improbable overall, because the evidence of suffering is not all the evidence there is. If the arguments of the intermediate tier have any force, they raise the probability, and the question is where the balance falls once everything is included.

The requirement cuts both ways, and theists invoking it should notice the second edge. The remaining rungs of this tier are a list of items that belong on the other side: hiddenness at rung 17, the no-best-world problem at rung 18, religious diversity at rung 20. A total assessment has to include those too, and the practice of invoking total evidence to blunt one argument while conducting the rest of one's case selectively is not available to either party.

There is also a subtler use of the requirement, and it bears on the previous section. When the theist adds a theodicy to raise a likelihood, the resulting hypothesis has to be assessed against the total evidence as well, and a theodicy tailored to the fawn may make other observations less probable. An account on which suffering is permitted for the sake of moral development, for instance, has to accommodate the suffering of creatures incapable of it, which is the pressure Draper's second category applied.

Where the argument stands

Three observations are fair, and none of them amounts to a verdict.

The 1979 argument, in its original inductive form, is not now regarded as decisive even by most of those sympathetic to it, and CORNEA is the main reason. Whether the noseeum assumption holds in this case is contested, but the burden of defending it has been accepted, and it was not visible before 1984.

The Bayesian reformulation is in better shape, and it has proved harder to answer, because it makes no claim about what exists. Its weak point is that both likelihoods are estimates about which reasonable people differ, and there is no procedure for settling them.

And the effect of the whole exchange has been to convert the problem of evil from an argument about God into an argument about the limits of human insight. Whether that conversion is a gain in precision or an evasion is itself disputed, and it is the question the next rung takes up.

Next

The reply that has carried the most weight in this exchange is the one that grants our inability to survey the goods God might be securing. The next rung asks what else that concession commits its holder to, and the answer given by its critics is that it spreads: to moral reasoning, to the interpretation of religious experience, and to the reliability of appearances generally. Whether it can be contained is the central question about the most popular theistic response of the last forty years.