The Fine-Tuning Argument and the Anthropic Principle Objection

Not ten years ago, physicist Paul Davies claimed, “There is now broad agreement among physicists and cosmologists that the universe is in several respects ‘fine-tuned’ for life.”[1] If the universe were just slightly different in one of many respects – if, for instance, the mass of the neutron were increased by 1/700 its actual mass – then life would almost certainly not exist.[2] Consequently, that the universe is capable of supporting life has led some to believe that the universe was “fine-tuned”: specifically designed or created for the purpose of supporting life, in particular human life. According to proponents of this line of thinking, the odds that the universe just happened to be capable of supporting life – the odds that the universe would be capable of supporting life without having been fine-tuned to do so – are so minuscule that we ought to believe that the universe was fine-tuned by God, and thus that God exists. In Alvin Plantinga’s words,

It’s as if there are a large number of dials that have to be tuned to within extremely narrow limits for life to be possible in our universe. It is extremely unlikely that this should happen by chance, but much more likely that this should happen if there is such a person as God.[3]

Following Robin Collins, we can formulate this fine-tuning argument for the existence of God more explicitly as follows:

1.     The existence of apparent fine-tuning is not improbable under theism. (Premise)

2.     The existence of apparent fine-tuning is very improbable under atheism. (Premise)

3.     The existence of apparent fine-tuning provides strong evidence in favor of theism over atheism. (1, 2, prime principle of confirmation)[4]

 (3) follows from (1), (2), and the prime principle of confirmation, which states that an observation counts as evidence in favor of one hypothesis over another if it has a higher probability under that hypothesis.[5]

Like any philosophical argument, the fine-tuning argument has its detractors. In this essay, I will consider the merits of a key objection raised by opponents of the fine-tuning argument – what Collins calls the anthropic principle objection – and argue that this objection does not mitigate against the argument.[6]

Before we address the anthropic principle objection directly, it is helpful to reflect on what exactly the fine-tuning argument is designed (as it were) to achieve. As Collins notes, the argument itself does not purport to prove theism; it only purports to provide strong evidence in favor of theism, all else being equal. Just how strong that evidence is can be determined by using Bayes’ Theorem, which allows us to calculate how the epistemic probability of a hypothesis (in this case, the theistic hypothesis) is affected by specific evidence (in this case, apparent fine-tuning). Let us, then, “plug in” the fine-tuning argument to Bayes’ Theorem.

Suppose that P(T), the prior probability of theism (i.e., the probability of theism without taking apparent fine-tuning into consideration), is 0.5. (As a result, of course, P(~T), the prior probability of atheism, is also 0.5.) Suppose further that P(F|T), the probability of apparent fine-tuning under theism (i.e., the probability that the universe is apparently fine-tuned if God exists), is 0.5, and that P(F|~T), the probability of apparent fine-tuning under atheism (i.e., the probability that the universe is apparently fine-tuned if God does not exist), is 0.1. Then, according to Bayes’ Theorem, P(T|F), the posterior probability of theism (i.e., the probability of theism after apparent fine-tuning has been taken into consideration), is [P(T) x P(F|T)]/[P(T) x P(F|T) + P(~T) x P(F|~T)] = [(0.5)(0.5)]/(0.5 x 0.5 + 0.5 x 0.1) = 0.25/0.3 ≈ 0.83, or 83%. Therefore, if our values for P(T), P(F|T), and P(F|~T) are correct, then the existence of apparent fine-tuning increases the probability of theism substantially, by approximately 33%.

This claim, in essence, is the claim of the fine-tuning argument. In Bayesian terms, the fine-tuning argument states that the values of P(F|T) and P(F|~T) are such that P(T|F) is significantly higher than P(T): If P(F|T) is much higher than P(F|~T), then P(T|F) will be markedly higher than P(T), and apparent fine-tuning will serve as strong evidence for theism.

Recasting the fine-tuning argument in these Bayesian terms is useful because it makes clear how one ought to go about responding to the fine-tuning argument: namely, by ascertaining the relative values of P(F|T) and P(F|~T). If one can demonstrate that P(F|~T) is not appreciably lower than P(F|T), then the fine-tuning argument loses its force. (Presumably, one could also respond to the argument by questioning the applicability of Bayes’ Theorem to the argument, but the use of that theorem in this case has not been a main point of contention.) In addition, the Bayesian formulation of the argument makes clear how one ought not to go about responding to the argument. In particular, any response to the fine-tuning argument that does not consider the relative values of P(F|T) and P(F|~T) misses the point.

Unfortunately, some responses to the fine-tuning argument either do not focus on these values or confuse them with other values. Most notable of these inadequate responses is the aforementioned anthropic principle objection:

According to the weak version of [the] so-called anthropic principle, if the laws of nature were not fine-tuned, we would not be here to comment on the fact. Some have argued, therefore, that the fine-tuning is not really improbable or surprising at all under atheism, but simply follows from the fact that we exist.[7]

The objection’s underlying intuition is simple: If the universe were not apparently fine-tuned, then life would not exist, and we would not be able to observe any apparent fine-tuning. But we are able to observe apparent fine-tuning; our ability to do so follows from our existence as living things. Why, then, should we be surprised at the existence of apparent fine-tuning in our universe?

This intuition can be restated in terms of the relationship between two values: P(L), the probability that life exists in the universe, and P(F), the probability that the universe is apparently fine-tuned. Roughly speaking, the intuition seems to be that P(L) = P(F). If P(L) were 0 – that is, if life did not exist in the universe – then P(F) would also be 0. (After all, if life did not exist in the universe, then we would have no evidence to support the claim that the universe was apparently fine-tuned for life!) On the other hand, if P(L) is 1 – if life does exist in the universe – then P(F) is also 1, because apparent fine-tuning is necessary for life to exist.

The problem, of course, is that neither P(L) nor P(F) factors into the Bayesian formulation of the fine-tuning argument. That P(L) and P(F) both equal 1 says nothing in and of itself about the values of P(F|T) and P(F|~T). As far as I can tell, then, those who employ the anthropic principle objection have erred simply by confusing P(F) with P(F|~T): They have attempted to refute the fine-tuning argument by demonstrating that P(F) is very high (which, though true, does nothing to undermine the argument) instead of demonstrating that P(F|~T) is very high (which would undermine the argument). The important thing to realize, though, is that P(F) is largely irrelevant to the fine-tuning argument. Even if P(F) equals 1, P(F|~T) can still be very low – and if P(F|~T) is very low (and lower than P(F|T)), then the fine-tuning argument retains its thrust.

To understand how P(F|~T) can be very low even if P(F) is 1, and to understand the confusion behind the anthropic principle objection, Collins provides a firing squad analogy.[8] Suppose that I am a prisoner scheduled to be executed by a firing squad of fifty expert marksmen; when the time comes for me to be executed, however, all fifty marksmen miss me. What should I conclude from the fact that all fifty marksmen missed me? As Collins notes, it would be extremely odd for me to say, “Of course I survived! If I hadn’t survived, I wouldn’t be alive to observe my survival!” On the contrary, I would probably react to my survival by concluding that the marksmen were (for whatever reason) trying to miss me.

Why is the latter reaction by far the more natural and reasonable reaction? We can answer that question by analyzing my thought process in terms of specific probabilities. Assume that I believed before my failed execution that there was a 10% chance that the marksmen would intentionally try miss me. If the marksmen were in fact trying to miss me, then there was a 99.9% chance that they would miss me – but if the marksmen were not trying to miss me, then there was only a 0.1% chance that they would miss me. Thus, P(I), the probability that they would intentionally try to miss me, is 0.1; P(M|I), the probability that they would miss me if they intentionally tried to miss me, is 0.999; and P(M|~I), the probability that they would miss me if they did not intentionally try to miss me, is 0.001. From these three pieces of information, we can again use Bayes’ Theorem to conclude that P(I|M), the probability that the marksmen intentionally tried to miss me in light of the fact that they did actually miss me, is  [P(I) x P(M|I)]/[P(I) x P(M|I) + P(~I) x P(M|~I)], or approximately 99.1%.

Notoriously absent from these considerations is P(M), the probability that the marksmen actually missed me. Obviously, P(M) = 1: They did, in fact, miss me. Nonetheless, the fact that they missed me does not entail that they had to miss me – remember, the men in question are marksmen – nor does it entail that they were not intentionally trying to miss me. Consequently, to determine whether or not they were intentionally trying to miss me, we must consider P(I), P(M|I), and P(M|~I) – not P(M).

What is the point of this analogy? Just as P(M|~I) can be quite low even if P(M) = 1, P(F|~T) can be quite low even if P(F) = 1. Just as the fact that the marksmen missed me does not entail that they had to miss me or that they were not intentionally trying to miss me, the fact that life exists in the universe does not entail that life had to exist in the universe or that God did not fine-tune the universe. Just as P(I|M) does not at all depend on P(M), P(T|F) does not at all depend on P(F). Returning to the original objection therefore, the proponent of the fine-tuning argument can say the following:

I do not dispute the weak version of the anthropic principle: If the universe were not apparently fine-tuned, then we would not exist to discuss fine-tuning. But we should still be surprised by the fact that there is apparent fine-tuning in the universe, because we should still be surprised by the fact that we exist. Granted, we couldn’t possibly observe any possible universe in which there was no apparent fine-tuning and in which life did not exist. However, those other universes, unobservable though they would be, still could have existed – and since they all could have existed, our existence and the apparent fine-tuning of our universe are still both much more improbable under atheism than under theism.

If that thinking is correct, then the anthropic principle objection poses no threat to the fine-tuning argument.

Obviously, in spite of the shortcomings of the anthropic principle objection, other objections to the fine-tuning argument remain. Although Collins lists four kinds of fine-tuning that suggest that P(F|~T) is quite low – the fine-tuning of the laws of physics, the fine-tuning of the constants of physics, the fine-tuning of the initial conditions of the universe, and the fine-tuning of certain higher-level features of the universe – other physicists, such as Victor Stenger, have challenged the low value assigned to P(F|~T) by proponents of the fine-tuning argument.[9]^,[10] Of course, as a non-scientist, I am not well equipped to adjudicate disputes over the precise value of P(F|~T). (That being said, I do find it telling that even Stephen Hawking, a committed skeptic, agrees that “the values of [the dimensionless fundamental physical constants] seem to have been very finely adjusted to make possible the development of life,” implying that life would not exist in the vast majority of possible universes.)[11] Nevertheless, the anthropic principle objection itself, insofar as it fails to take P(F|~T) into direct consideration, does not mitigate against the fine-tuning argument.

---

[1] P. Davies, “How bio-friendly is the universe?”

[2] J. Leslie, Universes

[3] A. Plantinga, “The Dawkins Confusion; Naturalism ad absurdum”

[4] R. Collins, “God, Design, and Fine-Tuning.” For the sake of simplicity, Collins’ original argument has been modified slightly.

[5] Ibid.

[6] Ibid.

[7] Ibid.

[8] Ibid.

[9] Ibid.

[10] V. Stenger, “The Anthropic Principle”

[11] S. Hawking, A Brief History of Time