After studying inductive logic for so long, I’ve decided it is finally time to reread Richard Swinburne’s The Existence of God (second ed., New York: Oxford University Press, 2004) and reconsider his inductive case for God’s existence. In doing so, I think I may have discovered a new objection to his cosmological argument. This is very rough and any comments would be appreciated.

Swinburne’s Terminology

The first thing we need to do is to get clear on Swinburne’s terminology and abbreviations.

Abbreviations:

E: A complex physical universe exists (over a period of time).

k: mere tautological evidence

h: the hypothesis of theism

P(h | k): the prior probability of theism. (Note: in the case of his cosmological argument, where he is abstracting away all contingent facts, the prior probability of theism reduces to the intrinsic probability of theism. More on that below.)

P(e | h & k): the probability that there be a physical universe caused by God

P(e|~h & k) : the probability that there be a physical universe without anything else having brought it about.

Definitions:

“C-inductive argument”: an argument in which the premisses ‘confirm’  or add to the probability of the conclusion, i.e., P(e | h & k) > P(e | h).

“P-inductive argument”: an argument in which the premisses make the conclusion more probable than not, i.e., P(e | h & k) > 1/2.

The Central Claim of Swinburne’s Cosmological Argument

Swinburne claims that his cosmological argument is a good C-inductive argument. In other words, if we start with just the intrinsic probability of theism and then add the evidence of the existence of a complex physical universe–and only that evidence–the output is a probability higher than what we started with. Let’s call that Swinburne’s “central claim.”

Swinburne’s Primary Reason for His Central Claim

As I read him, Swinburne’s primary reason for the central claim of his cosmological argument can be summed up in one word: simplicity.

According to Swinburne, the prior probability of any hypothesis is determined by three factors: (1) the internal simplicity of h; (2) the narrowness of scope of h; and (3) how well h fits in with our general background knowledge of the world contained in k. In the case of his cosmological argument, I interpret Swinburne as arguing that (2) and (3) do not apply; instead, his cosmological argument invites us to compare P(e | h & k) to the intrinsic probability of theism, P(h | k). When we do, Swinburne tells us, we will see that considerations of simplicity support his central claim.

And what does Swinburne mean by “simplicity”? His answer:

The simplicity of a theory, in my view, is a matter of it postulating few (logically independent) entities, few properties of entities, few kinds of entities, few kinds of properties, properties more readily observable, few separate laws with few terms relating few variables, the simplest formulation of each law being mathematically simple. … A theory is simpler and so has greater prior probability to the extent to which these criteria are satisfied. But, of course, it is often the case that only a theory that is less than perfectly simple can satisfy the other criteria (for example, explanatory power) for probable truth. The best theory may be less than perfectly simple; but, other things being equal, the simpler, the more probably true. (p. 53)

Some Objections to Swinburne’s Cosmological Argument

1. Even if Swinburne’s central claim is correct, a critic might argue, it is evidentially insignificant. Not only is Swinburne’s concept of a good C-inductive argument compatible with h being probably false, it is also compatible with there being a good C-inductive argument for a rival hypothesis, such as metaphysical naturalism. (In fairness to Swinburne, it should be noted that he admits this.) But the problem is even worse. His concept of a good C-inductive argument is compatible with there being a good C-inductive argument for a rival hypothesis and the latter argument being a stronger, or even much stronger, than the former argument. As I shall argue next, Swinburne’s cosmological argument suffers from precisely this problem.

2. Let N represent “metaphysical naturalism,” the hypothesis that the universe is a closed system, which means that nothing that is not part of the natural world affects it. Notice that, so defined, N entails that the universe exists, i.e., P(universe | N) = 1. In contrast, theism does not entail the existence of a universe; God could have decided not to create anything. Swinburne himself argues that God has both good reasons to create and not to create humanly free agents; Swinburne regards both possibilities as equally likely. Although Swinburne doesn’t explicitly state this, his comments seem to entail that the probability of the universe, on the assumption that theism is true, is somewhere between 1/2 and 1, i.e.,

1/2 < P(e | h & k) < 1.

Even if that is correct, however, it would still be the case that:

P(universe | h & k) < P(universe | N & k).

Careful readers will note that I have just switched from ‘e’ to ‘universe.’ Why? It seems to me that the existence of a universe simpliciter is a more “fundamental” item of evidence than the existence of universe that is complex, and so the more appropriate starting point for an inductive cosmological argument. (This, of course, leaves Swinburne with the option of making the following reply: given that a universe exists, the fact that it is complex favors theism over naturalism. This raises an important question: how do we measure “complexity”? I’m going to leave that question and this possible reply to the side, for possible consideration in a future post.)

So, to sum up, given a very common definition of metaphysical naturalism, the evidence of the universe favors naturalism over theism for the simple reason that naturalism entails a universe whereas theism does not. 

This conclusion invites another reply: “Okay, smarty pants. Sure, if you build the existence of the universe into the definition of naturalism, then of course you’re going to be able to argue that naturalism entails the universe. But why should we build the definition of the universe into the definition of naturalism? Isn’t that just ad hoc?” As I shall argue next, the answer to that question is, “No.” To see why, let’s turn to my third objection to Swinburne’s cosmological argument.

3. My third objection to Swinburne’s argument is that his approach to prior probability (and intrinsic probability) is wrong because simplicity doesn’t play the role he thinks it does. Simplicity qua simplicity does not help to determine prior probability (and intrinsic probability). Rather, simplicity is, at best, correlated with prior probability.

As Paul Draper has argued, there are two and only two things which determine the prior probability of a hypothesis: modesty and coherence. Here is Draper on modesty.

The degree of modesty of a hypothesis depends inversely on how much it asserts (that we do not know by rational intuition to be true). Other things being equal, hypotheses that are narrower in scope or less specific assert less and so are more modest than hypotheses that are broader in scope or more specific.[1]

The degree of coherence of a hypothesis depends on how well its parts (i.e. its logical implications) fit together. To the extent that the various claims entailed by a hypothesis support each other (relative only to what we know by rational intuition), the hypothesis is more coherent. To the extent that they count against each other, the hypothesis is less coherent. Hypotheses that postulate objective uniformity are, other things being equal, more coherent than hypotheses that postulate variety, either at a time or over time.[2]

Although I won’t defend the claim here, it appears that all of Swinburne’s examples (to support his claim that simplicity partially determines prior probability) involve examples where modesty, coherence, or both come into play. He does not seem to provide any examples supporting his criterion of simplicity which do not also involve modesty, coherence, or both. So let’s suppose Draper is right about intrinsic probability generally. What, then, can we say about Swinburne’s cosmological argument?

One of Swinburne’s supporting reasons is the notion that the existence of the universe is less simple than the existence of God, and so less to be expected a priori than the existence of God, i.e., P(h | k) > P(e | k). In his words:

There might have been a physical universe governed by quite different laws, or there might have been no universe at all. But it is always simpler to postulate nothing rather than something; and so, in the absence of observable data made probable by the hypothesis that quite different non-fundamental laws were operating in the past, the hypothesis that the universe came into existence a finite time ago will remain the more probable hypothesis.” (p. 140, italics are mine)

If intrinsic probability is determined solely by modesty and coherence, however, then this argument is just flat out wrong. To be charitable, let’s take coherence off the table and assume that theism is perfectly coherent. That leaves us with modesty. It’s far from obvious that h is more modest than e.

Besides, if we compare theism and naturalism as rival explanatory hypotheses and limit ourselves to just the evidence of the universe, the comparison does not go well for theism. Both supernaturalism and naturalism are equally modest and equally coherent, so both theories have equal intrinsic probabilities. Notice, however, that theism is a variant of supernaturalism in the sense that theism entails supernaturalism but is not entailed by it. In other words, theism could be false even if supernaturalism is true. This is because theism says everything that supernaturalism says, but then adds on several additional claims. That is why theism is less modest than both supernaturalism and naturalism. That is also why theism has a lower prior probability than naturalism.

An Inductive Cosmological Argument against Theism

These insights enable us to formulate an inductive cosmological argument against theism. Let B be our background information; E be the existence of the universe; T be theism; and N be naturalism. Here is the explanatory argument.

1. E is known to be true, i.e., Pr(E) is close to 1.

2. T is not intrinsically much more probable than N, i.e., Pr(T | B) is not much more probable

than Pr(N | B).

3. Pr(E | N) =1 > Pr(E | T).

4. Other evidence held equal, T is probably false, i.e., Pr(T | B & E) < 1/2.