William Lane Craig on the Prior Probability of Theism and the Fine-Tuning Argument

One objection to fine-tuning arguments for God’s existence goes like this: simply showing that so-called ‘fine-tuning’ is more probable on theism than on atheism isn’t enough to show that God exists. One must also take into account the prior probability of theism.

William Lane Craig responds to this objection in a recent Q&A on his website. He begins:

Your professor’s objection will be more comprehensible if we put it into the context of the probability calculus. Let’s compare the probability of theism vs. atheism relative to the fine-tuning of the universe. Let G stand for the hypothesis that God exists and ¬G for the hypothesis that God does not exist. Let FT stand for the fine-tuning of the universe. The comparative probabilities will be computed as follows:


Now what you argued in your paper was that the third ratio favored theism. The fine-tuning of the universe is considerably more probable given God’s existence than given God’s non-existence. The evidence is therefore strongly confirmatory of theism. So far so good!

What your professor wants to say is that your argument still does not prove that God’s existence is more probable than His non-existence relative to the fine-tuning of the universe. That is the first ratio on the left-hand side of the equation. In order to show that this ratio favors theism, you also need to show that the prior probability of God’s existence is not greatly lower than the prior probability of God’s non-existence. That’s the middle ratio above. The idea here is that the greater explanatory power of a hypothesis can be offset by the enormous improbability of the hypothesis itself.

So far, so good. Craig now turns to his responses.

There are two responses you might make to this objection. First, you might deny that you were trying to prove that the first ratio favors theism. You might simply rest content with showing that the evidence we have is hugely confirmatory of theism.

Yes, a proponent of a ‘fine-tuning’ argument for God’s existence could respond that way. But then they would just be admitting that the objection is correct. That’s about as ineffective a response as possible.

Collins, for example, points out that in science we often do not have any way of estimating the prior probability of a hypothesis, and so we simply rest with arguments showing a hypothesis’ greater explanatory power. It may be that the prior probability of the hypothesis is just inscrutable.

While that may be true of some unspecified, generic hypothesis, this isn’t true of theism, atheism, or naturalism. Craig evinces no awareness of Purdue University philosopher Paul Draper’s work on intrinsic probability, which functions as a kind of prior probability and is particularly useful for ‘ultimate’ metaphysical hypotheses like theism and naturalism.

You might even point out that in order to resist your confirmatory argument on behalf of theism, it’s the atheist who has the burden of proof of showing that theism is considerably more improbable than atheism.

Again, Craig’s unawareness of Draper’s work on intrinsic probability comes back to haunt him. This challenge can be easily met. Craig needs to interact with Draper’s argument that metaphysical naturalism, which entails atheism, has an objective intrinsic probability which is greater than that of theism.

Second, you could argue that theism is not intrinsically much more improbable than atheism. For the prior probabilities Pr (G) and Pr (¬G) are not, despite appearances, computed in a vacuum. Rather these probabilities are computed relative to our background information about the world. You subtract the information about the fine-tuning of the universe from what we know about the world, and whatever is left is our background information. That information will include the evidence featured in all the other theistic arguments, such as the contingency of the universe, the beginning of the universe, the objectivity of moral values and duties, the applicability of mathematics to the physical universe, intentionality, the facts concerning the resurrection of Jesus, and so forth. I think that we should be prepared to argue that the prior probability of theism is much greater than that of atheism relative to our background information. In that way we successfully argue that theism is much more probable than atheism given the fine-tuning of the universe.

First, this reply just pushes the problem back a step. I fully support the idea of cumulative cases, but what Craig seems to forget is that all cumulative cases have to start somewhere. Whatever he wants to use as his first piece of evidence must confront the fact that theism has a lower intrinsic probability than naturalism. For example, if he wants to make the contingency of the universe his first argument, he has to confront it there.

Second, many of Craig’s arguments, including his fine-tuning argument, are textbook examples of arguments which commit the fallacy of understated evidence.

Third, Craig also ignores the fact that there are other lines of evidence, independent of those related to his understated evidence, which favor naturalism over theism.