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.
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:
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.
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.