Paul Draper’s Argument from Evil (part 1)

by Luke Muehlhauser on May 25, 2010 in Guest Post,Problem of Evil

Now that looks painful.

Now that looks painful.

Guest blogger John D of Philosophical Disquisitions summarizes contemporary articles in philosophy of religion in plain talk so that you can be up to speed on the God debate as it ensues at the highest levels of thought. Visit John’s blog for more helpful summaries of contemporary philosophical works.


Among so many conveniences in nature they had to find many inconveniences; storms, earthquakes, diseases, etc. These, they maintain, happen because the Gods are angry on account of wrongs done to them by men, or on account of sins committed in their worship. And though their daily experience contradicted this, and though infinitely many examples showed that conveniences and inconveniences happen indiscriminately to the pious and impious alike, they did not on that account give up their long-standing prejudice.1

Those words were written some 350 years ago by Amsterdam’s finest lens-grinder, and part-time philosopher, Baruch Spinoza. He was not much impressed with the reactions of religious believers to our evidence concerning human suffering. For despite the indiscriminate nature of suffering, the religious clung to their “long-standing prejudice”.

Paul Draper is similarly unimpressed. In his article “Pain and Pleasure: An Evidential Problem for Theists” he offers a highly sophisticated argument, utilizing the tools of modern probability theory, suggesting that our knowledge of the biological utility of pain and pleasure is deeply troubling for theism.

In this series, I hope to offer a detailed summary of Draper’s article. In this first part, I will pull together the various conceptual tools we need in order to understand Draper’s argument.

Before getting started, I should note that Draper’s article is over 20 years old. There have, of course, been responses and modifications made to it. This series will only cover the original. Hopefully, this will give you the firm foundation needed to explore the subsequent literature.

Explaining Stuff

We are all thrust, somewhat unprepared, into the booming buzzing confusion of the world. To make any headway in the face of this confusion, we need to choreograph our experience and render it intelligible. In other words, we need to offer explanations for why things are as they appear to be or, alternatively, explanations for why appearances can so often be deceptive.

When taking up this explanatory task, there are basically two options open to us.

The first is to use the method of inference to best explanation (IBE). Here, we take an observation, develop an explanatory hypothesis that would entail that observation, and then test that hypothesis against other candidate explanations. This testing procedure will usually involve seeing how well the hypotheses measure up against a list of explanatory virtues, such as testability, informativeness, scope, ontological economy and so on.

The second method is that of confirmation theory. This involves the use of probability theory to test the relative strengths of competing hypotheses. It is not necessarily in opposition to IBE, but it does add a nice mathematical sheen to our assessment of explanations.

Draper’s argument uses confirmation theory. So before we consider its structure, let’s consider some fundamental concepts in probability theory.

Probability Theory: Some Basic Concepts

Fortunately, Draper’s argument is not too heavily weighed-down with the formal trappings of the probability calculus. To understand its structure we initially only need to deal with four concepts: (i) antecedent probability; (ii) objective/physical probability; (iii) epistemic/subjective probability; and (iv) conditional probability.

An example will help to illustrate each of these. Suppose Paul and Benedict are taking turns betting that one of them will draw an ace from the top of a fairly-shuffled deck of cards. In deciding how much to bet, they need to work out the probabilities across a range of scenarios.

In the first scenario, neither Paul nor Benedict knows anything about how a deck of cards works. Sure, they know that there are 52 cards in a deck and 4 aces, but beyond that they know nothing, not even how to interpret the importance of the deck being “fairly shuffled.”

In such a scenario, there is some controversy as to whether Paul and Benedict are entitled to say anything about the probability of drawing an ace. However, one option is to use the principle of indifference and say that all cards are equally likely. Therefore, the probability of drawing an ace is a 4/52 or 1/13. We would call this the antecedent probability because it is prior to experience or observation.

In the second scenario, Paul and Benedict are well-versed in the workings of fairly-shuffled decks of cards. They have performed thousands of trial drawings on such decks and have carefully recorded the frequency with which each card occurs.

For simplicity’s sake, we’ll assume that the thousands of trials have revealed that each card is in fact equally likely to be drawn from a fairly-shuffled deck. Thus, we end up with 1/13 again. This is the objective probability because it is based on some well-understood principles governing the operation of a physical system.

To spice things up, in the third scenario one card is taken from the top of the deck and shown to both Paul and Benedict. It is removed, and they are then asked to assess the probability that the next card is an ace.

This is when the conditional probability is relevant. The conditional probability is the probability of one event or hypothesis (A) given that another event or hypothesis (B) is true.

Suppose that when the top card is shown it is revealed to be an ace. Given this bit of information, what is the probability that the next card will also be an ace? The answer is, of course, 3/51 or 1/17.

For those who would like to know, the formula for deriving conditional probabilities is as follows:

Pr(A|B)=\frac{Pr(A and B)}{Pr(B)}

Note: Pr (A|B) reads “the probability of A given B”.

In the final scenario, we deal with epistemic or subjective probabilities. These are conditional probabilities where the relevant condition is the individual current subjective knowledge. The important point about these probabilities is that they vary from person to person.

To illustrate, suppose that before Benedict enters the room, Paul is shown the top card in the deck. The card is then returned to the deck and when Benedict enters he is asked to assess the probability of the top card being an ace.

Paul and Benedict are now in completely different epistemic situations. Paul knows with absolute certainty whether or not the top card is an ace (Pr = 1 or 0). Benedict does not. For him, the probability that the top card is an ace remains 1/13.

(click for full size to read text)

(click for full size to read text)

The Structure of Draper’s Argument

Now that we understand those concepts, we are in a position to understand the broad outline of Draper’s argument. Put simply, he wants to compare the probabilities of two hypotheses:

(T) the hypothesis of theism

(HI) the hypothesis of indifference

According to T, the universe was created and is sustained by an omnipotent, omniscient and morally perfect personal being. According to HI, neither nature nor the condition of sentient beings here on earth is the result of benevolent or malevolent actions on the part of personal beings.

HI is happy with metaphysical naturalism, but it is also consistent with the existence of supernatural personal beings. It just assumes that such beings are not concerned with our welfare.

Draper thinks that there are certain observations (O) we have made concerning the nature of human and animal pain and suffering that are less probable on T than they are on HI. That is:

Pr(O|T) < Pr(O|HI)

To paraphrase: “The probability we would observe what we do about suffering given theism is less than the probability we would make such observations given the hypothesis of indifference.”

This is based on antecedent and subjective calculations of the relevant conditional probabilities. In other words, prior to considering the evidence we would be much more surprised to see that O was true if we were theists than if we accepted the hypothesis of indifference.

Draper’s argument comes in three stages. First, he argues that Pr (O|T) – “the probability of our observations about suffering given theism” – is indeed much lower than the Pr (O|HI) – “the probability of our observations about suffering given the hypothesis of indifference.” Second, he argues that theodicies – rationales for God allowing pain – do not raise the probability of T enough (if at all) to warrant favouring it over HI. Third, he discusses the implications of his argument for other theistic arguments.

In the next part, we will consider the first of those stages.

  1. Spinoza, Ethics, Appendix to Part I. []

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{ 10 comments… read them below or add one }

Atheist.pig May 25, 2010 at 6:29 am

Nice to see Spinoza mentioned, one of my favourite thinkers.


Hermes May 25, 2010 at 8:57 am

On the issue of evil, I think it is only a problem for theists who consider that their set of deities are scrupulously benevolent.

Yet, there’s a part where that falls down; I don’t know of a single deity that is — when all the religious texts that are said to describe them are examined — claimed to be continuously and scrupulously benevolent let alone omnibenevolent. Occasionally or frequently generous? Sure. Favors are granted, usually for a bribe of some sort or subservient flattery. Yet, often enough the gods often described are dismissive or jealous, vengeful or absent. That is the case even before reality in general is examined.

Occasionally, some theists admit that their deities aren’t benevolent. Their deity doesn’t need to meet any standard and those who are impacted by anything approaching evil should just accept their condition. After all, who are we to complain? We live, thrive, and suffer at the discretion of the gods; they brought us into this world and can on a whim take us out, and if they did not have a hand in our existence they still have the power over it. In some religions, there is an attitude of justification for treating people as if they were chattel or as ignorant children as vessels worthy of only abuse.

* * *

Yes, it is true that Christians are famous for either generally considering their deity triumvirate to be intrinsically omnibenevolent. Specific texts are also offered as support that their deity is the exception.

Yet, no matter how it is stacked up I find that stunningly unconvincing; the other parts of the Christian religious texts have not been excised.

As pointed out by the most vocal and strident of Christian leaders — both fringe and mainline — various punishments are attributed to the wrath of their deity. Cancer to AIDS, and earthquakes with tsunamis to floods from hurricanes are brought on by the direct action of some variant of the deity to punish whole regions because of a human lack of modest dress or sexual practice let alone not providing the required level of dreadful toadying [longer version].

When those examples and more subtle ones are examined, these attempts at seeing flat edges on curved circles seems to me to end with the theist asking everyone to join them in making a penitent plea for mercy and submission to an unknown hypothetical. They tie themselves into knots in attempts to square that circle, and end that task by frequently redefining what a square is before declaring victory with a knotted bow as a flourish on top as if anything outside of sectarian presuppositions and un-scriptural abstractions have actually been addressed.


Martin May 25, 2010 at 11:34 am

I think the Old Testament God’s behavior is definitely a problem for the traditional mono-theistic conception of an omnibenevolent God. This is one area where people like WLC, who are normally chock full of good answers, seem to be much less convincing than normal.


TaiChi May 25, 2010 at 5:36 pm

Excellent. I’m looking forward to this, having been writing on the problem of evil myself.

“On the issue of evil, I think it is only a problem for theists who consider that their set of deities are scrupulously benevolent.” ~ Hermes

And why think that? Because any God worth the name should be worthy of worship. As the concept of God as a real force in the world wanes, the concept of God as morally superior becomes ever stronger (and the converse is true, too). That relationship is explained by the need for God to be worship-worthy.


Morgan-LynnGriggs Lamberth May 25, 2010 at 6:06 pm

We owe no being worship, and no rational being would want worship.


James Onen May 26, 2010 at 1:57 am


Great comments!


Hermes May 26, 2010 at 5:34 am

[ bows ]


Hermes May 27, 2010 at 3:28 am

TaiChi, don’t let any of my comments impact your plans even in the slightest. I am often informed by and rarely disagree with your comments, and even those disagreements are mostly on minor points of emphasis.

I sincerely would appreciate any corrections or comments, no matter how blunt; if I’m an idiot, or simply mistaken, I’d like to correct that problem if I am able to.

For now, I will suppose the comments you express are based on a difference of perspective, and within that perspective I will assume that you are correct. With that in mind, I offer my own take on the issue.

* * *

Let’s examine a generic deity. It is immortal or very long lived, powerful enough to bend and make reality by some vague power not available to humans (‘supernatural’) and, broadly, it has no rivals in those reality bending abilities except in the case of other deities (if any). This is not a perfect description, but I hope it is close enough for a basic discussion.

For now let’s assume one of the following is true;

I. One or more deities actually exists and is independent of humans. (Opinion: unlikely.)

II. #I is incorrect, and any deities that exist, exist only as abstractions derived from human thought and perceptions (correct and incorrect), and innate biology. (Opinion: likely.)

Even though I don’t believe it, let’s continue as if #I is true even if there is some value to #II.

With the above as a given, humans are in an entirely different category from any deity. Regardless of that, there is no intrinsic reason that anything would be worth worshiping by a human just for having the characteristics of a deity.

That said, a specific deity may have additional characteristics that change things and may justify or even compel (with or without force) worship.

So, when I wrote;

On the issue of evil, I think it is only a problem for theists who consider that their set of deities are scrupulously benevolent.

I was considering the generic deity category but I was not considering feedback of any kind to the deity from humans as a part of that equation. Why would a human consider a special activity of worship for a non-human entity?

Of course, there could be reasons for cross-entity communication and even the toadying I only somewhat sarcastically referenced before. The reasons could range from threats from the deity to bribing the deity for favors as well as more esoteric ones with specialized language and insistence (agape …). Yet, none of these are tied to the generic deity ideas.

[ I'd write less and better, but I'm in a hurry before going on a trip and I don't have time to condense things. When things let up, I'll be back. ]


TaiChi May 27, 2010 at 10:02 pm

I wasn’t disagreeing with you. When I began “And why think that?”, it was short for “And why should theists consider their set of deities scrupulously benevolent?”, my answer being that, if the idea of God as intervening in the world has become implausible, then the retaining of belief in God means finding some other conception of God which is worship-worthy in another way, and God as morally perfect is an obvious alternative.

I had in mind something I read in Sobel’s Logic and Theism:
“John Findlay is right to “pin God down . . . as the ‘adequate object of religious attitudes’” (Findlay 1955[1948], p. 48[176]). Findlay speaks in this regard of reverence, adoration, abasement, awe, wonder, extreme gratitude, and, above and before all others not included in it, of worship. God, it seems agreed by all, would need to be an appropriate object for at least some attitudes or emotions and behavior, including this one. That much is fixed by the meaning of ‘the true god’. It would be very odd to say that God exists or that some being is the one and only true god, and to say this with indifference or while countenancing indifference. It is a plausible linguistic conjecture that at least part of the meaning of ‘god’ is that, even though psychologically possible, such indifference would be inappropriate on the part of those who believingly speak God’s name and in a way impossible for those who speak with understanding of The One of whom they would speak. God, it seems, just must, at least in the end and on full reflection and appreciation, matter to, and be worshiped at least in their hearts by, those who believe that God exists. Those who believe that God exists just must, at least in the end, believe in God, where this includes, in addition to the belief that, a worshipful attitude. In Plato’s opinion The Good, an impersonal Idea or Form, must matter and be loved by all who know it. He considered its indifferent apprehension to be quite impossible. God would, according to ordinary religious thought and talk, be like that. God would be in an objectively normative manner a proper object for religious attitudes. This is a fixed point of agreement in our use of the name ‘God’ in religious discourse.”

If that’s so, then the waxing and waning of these two conceptions of God makes perfect sense – one or the other of them is necessary for belief in God.
Well, that was my thought. As for yours, I’m quite in agreement with you about the unbiblical conception of God as morally perfect. I agree with you that being a deity does not entail worship-worthiness, though I agree with Sobel that we should take it to be part of what Westerners understand by “God”. In short, I quite agree that we mostly agree, and where we don’t agree, well, perhaps we agree after all. ;)


Ex Hypothesi May 29, 2010 at 6:02 pm

You should have John D. exposit Plantinga’s response to Draper in “On Being Evidentially Challenged” in Howard-Snyder’s “The Evidential Problem of Evil”.


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