1. Introduction

The inductive problem of evil, as defended by Rowe and others (??ref), begins with an actual evil E, say the suffering of an animal or a rape and argues to the likely non-existence of God. There are multiple formulations of the argument; my formulation is somewhat different from Oppy’s, but this does not affect anything I say. Thus, I shall formulate the argument as follows:

(1) We cannot find any prima facie justification that God would have for allowing the evil E. (Premise)

(2) Therefore, there is no prima facie justification that God would have for allowing E.

(3) If God exists and has no prima facie justification for allowing an evil, then that evil does not occur. (Premise, following from conceptual truths about God’s goodness)

(4) E occurs. (Premise)

(5) Therefore, God does not exist.

The bulk of the discussion in the literature concerns the transition from (1) to (2), with many authors (??refs) pushing a “sceptical theism” response according to which the move from (1) to (2) is unjustified because we would expect that if God exists, the universe would be “morally deep”, with known evils often having justifications in terms of goods beyond our ken, and with a realm of value going far beyond what we know. That we cannot find any even prima facie justification for allowing E does nothing, after all, to provide evidence against the thesis that there is a good beyond our ken that justifies God in allowing E.

Oppy (??ref) has recently leveled against sceptical theism the objection that if sceptical theism is right, then we have no consequence-based reason to prevent E, because if sceptical theism is right, then we have no reason to think that preventing E results in the better state of affairs. But, barring some special duty to prevent E (say, if we are officers of the state sworn to prevent E-type evils), we only need to prevent evils when we have reason to think that preventing E results in the better state of affairs. Hence, sceptical theism should paralyze us in the face of evil. I shall argue that this conclusion cannot be drawn given a moderate sceptical theist view that allows that (1) gives an insignificant amount of evidence for (2). My argument shall, furthermore, make no controversial anti-consequentialist assumptions. Paradoxically, we shall see that it is possible to consistently hold that (1) gives an insignificant amount of evidence for (2) even while holding that we have a significant consequence-based reason to prevent E.

The structure of the paper shall be as follows. First, I will explain how Oppy succeeds in showing the falsity of what I will call a “strong sceptical theism” according to which (1) provides no evidence at all in favor of (2). Then I will discuss a simple game-theoretic case analogous to the predicament of the moderate sceptical theist deliberating whether to prevent an evil. I will then suggest that something like the sceptical theism case might be true on purely naturalistic assumptions, and nonetheless should not be seen as undercutting ethics. I will then consider a powerful objection.

2. Strong and moderate sceptical theism

The sceptical theist response comes in two varieties. On what I shall call strong sceptical theism, (1) provides no evidence at all in favor of (2). As Graham Oppy (??ref) has recently argued, strong sceptical theism is deeply implausible. On Bayesian grounds, (1) provides evidence for (2) if and only if P(we find no prima facie justification for God’s allowing E|there is a justification for God’s allowing E) < P(we find no prima facie justification for God’s allowing E|there is no justification for God’s allowing E). But the right hand side here is equal to 1, since we cannot find what does not exist. Thus, (1) provides evidence for (2) unless the conditional probability of our finding no prima facie justification given that a prima facie justification exists is equal to 1. In other words, (1) provides evidence for (2) if and only if the probability of our finding a prima facie justification given that one exists is equal to zero. But, as Oppy notes, this is deeply implausible.

In fact, it is clear that the probability of our finding a prima facie justification given that one exists is greater than zero. For sometimes we do succeed in finding prima facie justifications for evils. People may look back on their past lives and see that they have prima facie benefited from some evils. So the likelihood of finding a prima facie justification given that one exists is surely non-zero. Strong sceptical theism is simply wrong.

Oppy concludes from this that it follows that (1) provides evidence for (5) (or, more precisely, that his analogue to (1) provides evidence for his analogue to (5)). But this conclusion would require further work. For even though (2) entails (5), it is will known that evidence for an entailing proposition need not be evidence for an entailed proposition. A standard case to show this is as follows. Let’s suppose I throw two dice, a red die and a green die. Let p be the proposition that the total I throw is 12. That the red die came up 6 is evidence in favor of p, and p entails that the green die came up 6. But that the red die came up 6 is no evidence for the green die’s coming up 6.

A “moderate sceptical theist” shall be someone who says that (1) provides no significant evidence for (2). The argument in the preceding paragraph shows that one could consistently be a moderate sceptical theist and still hold that (1) provides no evidence for (5). It is, thus, not obvious that sceptical theists like ??refs who hold that (1) provides no evidence for (5) should just for that reason be classified as strong sceptical theists.

It may be that Oppy’s paralysis argument works for a strong sceptical theist. However, since Oppy gives the paralysis argument after giving what appears to be an insurmountable objection to strong sceptical theism, and given that he also wishes to refute moderate sceptical theism, the paralysis needs to refute the views of the moderate sceptical theist as well. But this, I shall show, it does not do.

On the face of it, the solution to Oppy’s problem is clear. The moderate sceptical theist when faced with a potential evil E for which she cannot see any prima facie justification will conclude that it is more likely than not that the evil would have no justification, and hence that she should fight against the evil. However, (??check if Oppy notes this) there is at least one wrinkle here. Our sceptical theist thinks the probability of non-existence of a justification would be insignificantly greater than 1/2, and an insignificant difference in probabilities is surely not sufficient to give one reason to put in much effort at all into preventing E. After all, the disvalue of the effort might be certain, whereas the likelihood of gain is small. This reasoning, however, is fallacious as we shall soon see.

3. A game

You know that George will make a thousand tosses of a pair of fair coins, a red and a green one. The R-game goes on for the thousand tosses, and whenever a red coin lands heads, you get $100 and whenever a red coin lands tails, you pay $100. On the G-game, the same is true, but with the green coin being the relevant one. You are forced to choose between the R-game and the G-game. You cannot switch between them mid-way, nor can you get out of the game before the 1000 rounds are up. However, you hold one advantage. You make your choice between the games when the coins for the first toss are already in the air, and with your superb vision and mathematical skills you can predict that the first toss will have the red coin landing heads and the green one tails. But you can make no predictions about subsequent tosses.

If you choose the R-game, you are guaranteed to win the first time, and you don’t know about the rest of the tosses. If you choose the G-game, you are guaranteed to lose the first time, and you don’t know about the rest of the tosses. It is clear that the self-interestedly rational choice is to go for the R-game. In fact, the situation you are in is just as in a choice between getting $100 for free, and then playing 999 subsequent rounds of the R-game, and paying $100, and then playing 999 subsequent rounds of the G-game. There is no reason to choose the 999 subsequent rounds of the G-game over the 999 subsequent rounds of the R-game, and so it is clear that you should just accept the free $100 and play the R-game.

But now consider the following fact. Let F be the event that over the full 1000 rounds, the red coin comes up heads more often than the green one. Your only benefit from choosing the R-game if F is going to occur. Now, P(F) is (1/2)+(1999!)/(2²⁰⁰⁰(999!)(1000!)), which is approximately 0.51. One might erroneously think that the fact that this probability is only slightly greater than 1/2 implies that one only has a slight reason to prefer the R-game, whereas in fact one has a fairly strong reason to prefer the R-game, since getting $100 for free rather than losing $100 generates a fairly strong reason.

In making a self-interested rational decision, it is the difference in expected values that matters rather than the probability that one option will have a better payoff than the other. It is very easy to set up situations where most likely one will do better by choosing one of two games but the self-interestedly rational choice is the other. For instance, suppose both games cost $1 to play; Game A offers a 2/3 probability of winning $10, while game B offers a 1/4 probability of winning a million. Most of the time, one will do better playing game A than game B, but it is clear that the self-interestedly rational game to choose is B.

Now one might object that nonetheless only a very weak reason is generated in R- and G-game case. Not only is the difference in probabilities between the R-game being better for one versus the G-game being better for one insignificant, but the gain in utility is insignificant. For what is $100 more or less when we are playing 1000 games, the stakes in each of which are $100? Most likely, we might reason, the $100 is only going to be a fairly small percentage of our winnings or losings, and as such it does not really self-interestedly matter much which game we choose. This reasoning is can be argued to be fallacious. We still are $200 ahead in expected value for choosing the R-game, and even though this may not be high as a percentage of the total gain or loss, it is still important.

But we can modify the case in such a way as to avoid the issue. Consider the high stakes variants of the R- and G-games. A dictator has a thousand innocent prisoners set to be executed tomorrow. Each time you win a round, i.e., each time the relevant coin lands heads, one of these prisoners is released. Nothing happens when you lose a round.[1] Again, you can predict how the first coins will land: the red one will land heads and the green one will land tails. At this point it becomes clear that one has a very strong reason to choose the high stakes R-game, since by doing so one increases the expected value of the total number of lives saved by one. The fact that that one life is only a relatively small percentage of the total saved or lost is irrelevant. It is still a human life. It is no less worthwhile to save the life of an innocent when that life is endangered by a natural disaster where millions die. It is still true that the likelihood of getting better consequences when playing the high stakes R-game is only 0.51. But, nonetheless, one has strong reason to play the high stakes R-game. The fact that, likely, the unknowable consequences of choosing the high stakes R-game over the high stakes G-game, namely the results of the next 999 rounds, will swamp the outcome is irrelevant.

Suppose now that Jones claims to be a perfectly good agent who can predict all coin throws in the world’s future. The choice between the high stakes R- and G-games is put to Jones. Let us suppose that we only get to observe the first round of the game, and never find out the results. What we see is the first red coin toss yielding heads, the first green coin toss yielding tails, and Jones choosing to play the G-game. Let us suppose, also, that it is clear that nothing else would be relevant to a perfectly good agent under the circumstances than the lives of the people in question.

Consider the following question: Were the two coin tosses we saw evidence against the claim that Jones made a correct choice, i.e., a choice that would save at least many lives as the other option? The answer is affirmative. What we saw was more probable on the hypothesis that Jones made an incorrect choice than on the hypothesis that Jones made a correct choice. But the two coin tosses that we saw are only insignificant evidence against the claim that Jones made a correct choice. Much of the time, which choice is the better one will not turn on the outcomes of the first tosses, since these outcomes will be swamped by subsequent ones. As we already saw, even given the initial tosses, the likelihood that the G-game is the better one to play is approximately 0.51, only insignificantly more than 1/2.

The high stakes game is parallel to the sceptical theism case. There is much we do not know about the consequences of the evil E, and how it might fit into a cosmic axiology. But likewise there is much that we do not know about the consequences of preventing E, and how the prevention might fit into a cosmic axiology. Just as goods and evils beyond our ken might result from E, so they might result from our prevention of E. This is parallel to the way we do not know the outcome of the next 99 rounds of the high stakes games. Just as the ignorance of the next 99 rounds does not take away our strong reason to opt for the game that on the first round will save a life, so too our ignorance of further long-term consequences and of cosmic values does not take away our strong reason to prevent E.

It may be that the difference in probabilities between the hypotheses that E has prima facie justification and that E does not have prima facie justification is insignificant. But the difference in expected values between preventing and not preventing E is intuitively precisely the disvalue of E, since we have no reason to suppose the aspects of the situation we do not know to favor the one case rather than the other.

4. Chaos

In a chaotic system, small changes in initial conditions lead to unpredictable large-scale changes down the road. Suppose we one day find out that humans and their environment do constitute a chaotic system. In that case, each of our actions will have unpredictable consequences down the road. It might be that if one looks 10,000 years into humanity’s future, the outcome will be very different depending on whether Mr. Jones eats a ham or turkey breast sandwich on Tuesday.

This should not be that implausible. The deviations between the outcomes on the two options might diverge more and more. Consider the potential sensitivity of some humanly important processes to changes in initial values. For instance, which of Mr. Jones’ sperm reaches Mrs. Jones’ ovum probably depends on various subtle physical details of the mating process, which details may well depend on which sandwich Mr. Jones ate. Yet the identity of the sperm that reaches an ovum will be an important causal factor in the life led by the conceived person. It will also affect the descendants of that person, both genetically and environmentally. The number of descendants Jones has in any given generation, given sufficient exogamy, will grow significantly, and may eventually include the whole human population. Now, it may be that the effects of the difference in identity of sperm reaching eventually average out in the large scale. But we really have little positive reason to believe this.

Other process that magnify small differences into large ones might include the questions of human survival after serious accidents. We often cannot predict survival likelihoods—why can’t that be because the process in fact is chaotic, so that the color of necktie worn by someone seen by the victim might in fact affect whether the person survives.

For a more metaphysically controversial case, consider indeterministic processes, be they quantum mechanical transitions or libertarian free choices. Suppose that an indeterministic experiment is performed in the maximally relevantly specific conditions C at t. Then if it is performed in the exact same conditions C at a later time t*, a different outcome may well eventuate—this is the “rollback” observation, standard in discussions of libertarian free will. But now consider a different question. Suppose the maximally relevantly specific conditions C were slightly different, say were C*. Do we have any reason to think that had the experiment been done in C* at t it would have eventuated in the same result as when it was actually done in C at t? It is at least highly plausible to answer in the negative.[2] Let us say the experiment was an indeterministic coin flip. It seems not implausible that were the relevant conditions any different, the indeterministic event would have had a probability of 1/2 of coming out differently from the way it did.

If this is right, then indeterministic processes can serve as effect multipliers. A small change in the initial conditions, and a different decision might well be made, or a different coin flip result might occur. If so, then there is very little reason to think that even very minor choices of ours make no difference in the long run. On the contrary, it seems probable that were we to make a minor choice differently, lots of indeterministic processes in the future light cone of that choice would come out differently. Now, they might in the aggregate average out against each other and the overall outcome for humanity might be the same. But we really have no reason to think this.

So, if the chaos hypothesis holds, then we all are in the position that Oppy thinks the sceptical theist is. But if so, then we all, whether we are sceptical theists, non-sceptical theists or non-theists, had better have an answer to Oppy’s problem. And it appears that the right answer is that sketched in the previous section. We need to make our decisions in light of the effects we know, and absent additional information simply act as if the unknown long-term effects were the same on both eventualities, since we have no reason to think they would be better in the one case rather than in the other. If I have a headache, I should take the aspirin without worrying about the fact that future history 10,000 years hence might be utterly different as a result, since I do not know whether it would be better or worse if I do or do not take the aspirin.

Likewise, we know the short-run effects of preventing or not preventing the evil E vis-à-vis the values that we know about. Preventing E is good and not preventing E is bad, thus far. Moreover, even if the sceptical theist is right that there are long-term effects that we know nothing about and that when we measure the outcomes by values we know nothing about the overall outcome of preventing E may be better than that of not preventing E, nonetheless preventing E is good as such and not preventing E is bad as such, just as winning the $100 on the first toss is good for us as such even if it turns out to lead to a series of losses and losing the $100 on the first toss is bad for us as such even if it turns out to lead to a series of wins. Likewise, it might be that our initial loss of $100 fits into some large-scale scheme that makes it be a constitutive part of our happiness with regard to some value we cannot now think of. But still, the loss is bad in itself for us, and for aught that we know our initial victory of $100 would also fit into some large-scale scheme that would make it be a constitutive part of our happiness.

5. An objection

In Oppy’s formulation of sceptical theism, the sceptical theist not only does not have any idea whether the occurrence of an evil might not contribute to the good from some more comprehensive point of view, but also does not have any probability assignments there—she does not, say, assign a probability of 1/2 to the claim that occurrence of E would contribute to the good, but instead assigns the full range of probabilities between 0 and 1, namely the interval [0,1]. But in the game theoretic example, probabilities can be assigned to the outcomes of the 99 subsequent rounds of the R- and G-games. Hence these examples are disanalogous to the sceptical theism case.

In response, first, note that the case of global chaos is precisely like the sceptical theism case. In fact, I do not think we are right now in the position to evaluate the global probability of the global chaos hypothesis, nor, if that hypothesis is true, are we in a position to estimate probabilities of particular outcomes 10,000 years hence. So I could simply shift to the global chaos case from the game theoretic case in my response.

As a second response, modify the game theoretic case. Now, the games are as follows. The first round of the R*-game is a toss of a red coin, with a victory if it lands heads. The first round of the G*-game is a toss of a green coin, with a victory if it lands heads. But, let us suppose, we know nothing about the subsequent rounds of both games. We do not even know how many subsequent rounds there will be, nor what they will be like. But we do know we’ll win the first round if we play the R*-game and we’ll lose the first round if we play the G*-game, and we have no choice but to play the one or the other (e.g., because one is deemed to have chosen the G*-game and its outcomes are forced on one if one does not opt for the R*-game). It still seems the more rational thing to do to opt for the R*-game. And in a high stakes variant where in the first round at least an innocent human life is at stake, it seems that opting for the R*-game is definitely the right thing to do.

Now, one’s intuitions here may be biased by the fact that if we were in fact offered such games, we might think that the people offering the games are trying to cheat us in some way, and hence we might be suspicious of the game that seems better at the start. But that thought only makes sense given background knowledge of games of chance and the kinds of characters who set them before strangers. I have assumed here that we know nothing about subsequent outcomes.

Or suppose that you find yourself living out the plot of a crazy “Choose Your Own Adventure” novel. In such novels, every couple of pages you need to make a decision, and then are given the page number to flip to depending on the decision. We could imagine such a novel—indeed, we may have read such—where there is rhyme or reason to what happens in the long-run given what we chose in the short run, and no probabilities can be assigned. But suppose we know we are living out the plot of such a novel, and we see an innocent person suffering terribly. If we know we can relieve her suffering, surely we should, even though we do not know what the crazy consequences of this there might be, at least if we have no positive reason to suppose the novel is actually perverse in such a way that doing the locally right thing tends to result in the worse results overall. We can say to ourselves: Relieving her suffering is good in itself. It may in the end be disastrous. But likewise so may a failure not to relieve her suffering. Given the complete absence of further information, I should relieve her suffering.

The above response may work even on strong sceptical theism. But given moderate sceptical theism an additional response is possible. The moderate sceptical theist will grant that the non-existence of apparent prima facie justifiers for E provides a small amount of evidence for the non-existence of prima facie justifiers for E. Thus, rather than the case being analogous to the choice between games where we know nothing about further rounds, it is more like a choice where we actually do have a small amount of evidence that the R*-game is the preferable one. If that is all the evidence we have, should we not act on it? It seems we have some evidence in favor of its being a good idea to prevent E and no evidence in favor of its being a good idea not to prevent E. So we should try to prevent E.

Now, it might be thought that when the “small amount of evidence” is tiny, the reason generated is too weak. If so, then Oppy could still show that sceptical theism generates conclusions that differ from common sense, in that they make the reasons we have for preventing evils be much smaller than otherwise. This, however, is mistaken. For the strength of a consequence-based reason to prevent an evil should be based on the difference in expected values rather than on a difference in probabilities. Now in the cases of interest to us here, we cannot estimate the overall expected utilities, because they involve cosmic considerations as well as considerations of values beyond our ken. But if so, then we need to simply act on the basis of the difference in expected values insofar as we know them, and this is the difference between the occurrence of E and the non-occurrence of E. This difference, then, should be judged precisely in the same way by the sceptical theist as by someone who is not a sceptical theist.

6. Conclusions

We need to make our practical decisions in the light of the known effects of actions when choosing between two actions that, as far as we can tell, equally may have many unknown effects. This is true even when the unknown effects might swamp the known effects. If we denied this, then we would have to admit that if we were to learn that the global chaos hypothesis is true, we would be justified in being practically paralyzed in many of our actions. But the global chaos hypothesis may well be true, and yet we are not justified in such paralysis.

[1] This is disanalogous to the initial scenario. The natural analogy would be to have the dictator capture another innocent person and line her up for execution. The problem is that if the games were like that, then on deontological grounds one might be forbidden to play either game.

[2] In ??ref, I have argued that this claim is false when irrelevancies are considered as part of the conditions.