Trouble in Paradise: Evil, Evidence, and the Problem of Paradise

In the previous post, I considered arguments for the conclusion that evil is evidence for the existence of God. In this post, I want to consider an argument for the conclusion that evil is evidence against the existence of God. The argument is defended by appeal to what is known in the academic literature as the problem of paradise, which Matthew A. Benton, John Hawthorne, and Yoaav Isaacs introduce as follows:

Problem of Paradise: Consider a world of pleasures with no pain, of goods with no evil— an Eden. If the world were like that, then we think that would constitute a fairly overwhelming argument for the existence of God. In such an Edenic world, atheists would face the problem of paradise. But if the probability of God is higher given the complete absence of evil (in an Edenic world), then the presence of evil (as in our world) must reduce the probability of God. Put otherwise: if the absence of evil is evidence for God, then the presence of evil is evidence against the existence of God ("Evil and Evidence," pg. 5-6).

The idea that if the world we live were an Edenic world, then this would be strong evidence for the existence of God is intuitively compelling. If this is so, the argument goes, then what this shows is that the non-existence of evil is evidence for the existence of God. Consequently, the existence of evil is evidence against the existence of God. Benton and company argue for this by appealing to a standard Bayesian account of evidence along with the following theorem of probability theory (where H is a hypothesis and E is a piece of evidence—see the previous post for a very brief introduction to Bayesian evidence and probability theory):

Theorem: Pr(H | ¬E) > Pr(H) ↔ Pr(¬H | E) > Pr(¬H).

If we let theism (the thesis that there exists an omnipotent, omniscient, and perfectly good Creator of the universe, i.e., God) stand in for H and evil stand in for E, then what the theorem says is that the probability of theism given the non-existence of evil is greater than the prior probability of theism if and only if the probability of atheism (the negation of theism) given the existence of evil is greater than the prior probability of atheism.

Now, what the scenario proposed by the problem of paradise is supposed to show is that the probability of theism given the non-existence of evil is greater than the prior probability of theism. By the foregoing theorem, it then follows that the probability of atheism given the existence of evil is greater than the prior probability of atheism. This brings us to the following standard Bayesian definition of evidence (where H is a hypothesis and E is a piece of evidence):

Bayesian Evidence: E is evidence for H means that Pr(H | E) > Pr(H).

Since, therefore, we have reached the conclusion that the probability of atheism given the existence of evil is greater than the prior probability of atheism, it follows by definition that the existence of evil is evidence for atheism and hence against theism. The entire argument may be semi-formalized as follows:

1. Pr(Theism | ¬Evil) > Pr(Theism) (Problem of Paradise).
2. Pr(Theism | ¬Evil) > Pr(Theism) ↔ Pr(¬Theism | Evil) > Pr(¬Theism) (Theorem).
3. So, Pr(¬Theism | Evil) > Pr(¬Theism) (from 1 & 2).
4. Pr(¬Theism | Evil) > Pr(¬Theism) → the existence of evil is evidence against theism (Bayesian Evidence).
5. Therefore, the existence of evil is evidence against theism (from 3 & 4).

The soundness of this argument implies that any approach to the evidential problem of evil that holds that evil is not evidence against theism cannot succeed. This includes both skeptical theism (which often claims that evil is not evidence against theism) and reversing the problem of evil (which claims that evil is evidence for theism). If we assume standard Bayesian epistemology and probability theory, then premises (2) and (4) are entirely unimpeachable. Hence, the soundness of the argument crucially turns on (1).

On behalf of approaches to the evidential problem of evil which reject (5), it seems to me that (1) is challengeable. At the very least, the support that the problem of paradise is supposed to provide to (1) is dubious. Consider again the envisaged scenario: the world contains many goods with no evils. It is surely not just the absence of evil that is important here but also the presence of good. It is the conjunction of both of these elements that is driving our intuition that such a state of affairs would be compelling evidence for theism. For consider a world that has no evil but also no good. It is highly plausible that such a world would not be evidence for theism. In fact, it would seem to be evidence against theism.

If all of this is right, then it is no longer clear that the problem of paradise establishes (1). Rather, what it seems to establish is (1*): the probability of theism given both the non-existence of evil and the existence of good is greater than the prior probability of theism. Symbolically, Pr(Theism | ¬Evil & Good) > Pr(Theism). Now, the following entailment does not in general hold (where H is a hypothesis and ¬E1 and E2 are pieces of evidence):

Pr(H | ¬E1 & E2) > Pr(H) → Pr(H | ¬E1) > Pr(H).

Here is a counterexample: Suppose that we roll fair, six-sided die. Let H = "the die lands on an even number." Let ¬E1 = "the die does not land on a number greater than 6" and E2 = "the die lands on a number greater than 3." In this case, Pr(H) = 1/2 and Pr(H | ¬E1 & E2) = 2/3. So, it is true that Pr(H | ¬E1 & E2) > Pr(H). However, Pr(H | ¬E1) = Pr(H). Hence, it is false that Pr(H | ¬E1) > Pr(H). This suffices for the counterexample.

Consequently, there isn't anything that would guarantee the truth of the following implication:

Pr(Theism | ¬Evil & Good) > Pr(Theism) → Pr(Theism | ¬Evil) > Pr(Theism).

Since, therefore, the problem of paradise at best establishes merely the antecedent of this implication, it cannot, by itself, establish the truth of (1). Barring a further argument, then, it seems that the problem of paradise does not after all provide us with compelling evidence for (1). Instead, it provides us with compelling evidence for (1*).

From (1*), it follows—in conjunction with (2) and (4)—that Pr(¬Theism | ¬(¬Evil & Good)) > Pr(¬Theism) and that therefore ¬(¬Evil & Good) is evidence against theism. Now, by De Morgan's laws, ¬(¬Evil & Good) is logically equivalent to Evil or ¬Good. This disjunction being evidence against theism is compatible with the existence of evil not being evidence against theism; for it could be that the non-existence of good is responsible for all of the evidential impact of this disjunctive evidence.

What is more is that it is even compatible with the existence of evil being evidence for theism! In other words, it can be the case that Pr(Theism | Evil) > Pr(Theism) and Pr(Theism | ¬Evil & Good) > Pr(Theism). This can be seen by the fact that, in general, it is possible for it to be the case that Pr(H | E1) > Pr(H) and Pr(H | ¬E1 & E2) > Pr(H). Here is an example: Suppose that we roll a fair, six-sided die. Let H = "the die lands on a number divisible by 3." Let ¬E1 = "the die does not land on 3" and E2 = "the die lands on a number greater than 4." Then, Pr(H) = 1 / 3, Pr(H | E1) = 1, and Pr(H | ¬E1 & E2) = 1 / 2. Hence, Pr(H | E1) > Pr(H) and Pr(H | ¬E1 & E2) > Pr(H).

The problem of paradise, therefore, does not constitute a successful argument against the viability of either skeptical theism or reversing the problem of evil.