Probabilistic evidence

My own version of the fine-tuning argument will not try to show that God (or a cosmic designer) exists. Instead, I will argue for a relatively modest conclusion: the discovery of fine-tuning provides evidence that the universe was designed. To establish that conclusion, I’ll rely on a conventional conception of scientific evidence. Specifically, my argument employs the framework of Bayesian confirmation theory, the dominant philosophical account of how evidence works in science. According to this view, we gain evidence for a hypothesis whenever we learn something that increases the probability of the hypothesis.

For a fuller introduction to Bayesian confirmation theory, please refer to the chapters on Confirmation Theory and Evidence and Rationality in my online ebook Skillful Reasoning: An Introduction to Formal Logic and Other Tools for Careful Thought.

To understand how evidence works on this account, a quick primer on probability will be helpful. In mathematics, probabilities are just numbers between 0 and 1 that obey special mathematical rules. More precisely, probabilities are the numbers given by a probability function, and a mathematical function must satisfy special requirements in order to be a probability function. For more details, see this. Probabilities are used to represent many different things, including statistical frequencies, objective chances, and certain kinds of evidential symmetries. Most importantly for my argument, probabilities can also represent degrees of belief (or degrees of confidence) in a claim or hypothesis. Probabilities that represent degrees of belief are called subjective probabilities. Higher subjective probabilities represent greater confidence that a claim is true; lower probabilities represent lower confidence that it is true (and higher confidence that it is false). For example, if you are 100% certain that a claim is true, the (subjective) probability of that claim (for you) is 1. If you are only 75% sure the claim is true, its probability is ¾. If you are absolutely sure the claim is false—in other words, if you think it is 0% likely to be true—its probability is 0.

When we use probabilities to represent our own degrees of belief in this way, the mathematical rules of probability give us useful information about how our beliefs should relate to each other. For example, the mathematical rules stipulate that the probabilities we assign to mutually exclusive and exhaustive claims must sum to one. (A set of claims is mutually exclusive and exhaustive when exactly one of those claims must be true.) For example, the claim that the universe was designed and the claim that it wasn’t designed are mutually exclusive and exhaustive claims: exactly one of them must be true. So, according to the rules of probability, if your subjective probability (degree of belief) that the universe was designed is ¾, then your subjective probability for the claim that it wasn’t designed must be ¼, since those two probabilities must sum to one.

Bayes theorem

For a non-technical, visual introduction to the central mathematical principles behind Bayesian confirmation theory, see this excellent video by Grant Sanderson.

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According to Bayesian confirmation theory, there are also mathematical rules for how we should update our degrees of belief in light of new evidence. For example, suppose a new discovery or observation decisively rules out one of several mutually exclusive and exhaustive hypotheses you had been considering, reducing its probability to zero (or very near zero). Suppose, moreover, that the new discovery does not discriminate between the remaining hypotheses: it doesn’t give you a reason to favor any of the remaining hypotheses over the others. In that case, the mathematical rules imply that you should increase your degrees of belief in all of the remaining hypotheses so that their probabilities again sum to 1. (This updating process, called renormalization, preserves the ratios between the probabilities of the remaining hypotheses so long as the evidence doesn’t discriminate between them. For example, if one hypothesis was twice as likely as another, it still will be twice as likely after renormalization.)

In Bayesian confirmation theory, updating one’s beliefs in light of new evidence is called conditionalization. Renormalization is a special case of conditionalization. For further explanation of how conditionalization works in general, see this.

My fine-tuning argument

With that conceptual background in view, here’s my simple argument for the conclusion that cosmological fine-tuning provides evidence of design. The discovery of fine-tuning effectively ruled out one of the main hypotheses that scientists had previously considered plausible: namely, the hypothesis that there is just one universe which arose without being designed. Let’s call that discredited hypothesis the single-universe-chance hypothesis (SUC). Anyone who previously regarded SUC as plausible (i.e., anyone who had assigned it a non-negligible subjective probability) must now update her degree of belief in the remaining hypotheses, including the design hypothesis and the multiverse hypothesis, so that their probabilities sum to 1. Assuming for the moment that fine-tuning evidence does not discriminate between the remaining hypotheses (an assumption that I’ll challenge below), this means the probability of both the multiverse hypothesis and the design hypothesis must increase. So, fine-tuning counts as evidence for both of those hypotheses, since it raises their probabilities.

To spell out the argument a bit more carefully, let’s consider the following three mutually exclusive and exhaustive possibilities:

The fine-tuning evidence effectively eliminates possibility (3), reducing its probability to near zero.This premise of my argument can be rephrased as a normative claim: you should reduce your subjective degree of belief in the SUC hypothesis to near zero when you learn that the universe is fine-tuned for life. Here’s a simple analogy to illustrate why that is the rational thing to do. Suppose you know that your Aunt Gertrude recently won a prize in a neighborhood raffle, but you don’t know how many tickets she purchased or what proportion of the tickets were winning tickets. Initially, you think it’s likely that she purchased only one ticket, which happened to be a winner. (This single-ticket-chance hypothesis is analogous to the single-universe-chance hypothesis.) Then you learn that only a minuscule proportion of the tickets in the raffle were winners—one in a trillion, let’s say. (This new information is analogous to the discovery of cosmological fine-tuning, which revealed that only a vanishingly tiny proportion of the parameter space would yield a life-permitting universe.) Should you still think it’s likely that Aunt Gertrude bought only one ticket, which just happened to be a winner? Hardly. Either Aunt Gertrude bought a lot of raffle tickets (analogous to the multiverse hypothesis), or her selection of the winning ticket was no accident: she cheated (analogous to the design hypothesis). Your degree of belief in the single-ticket-chance hypothesis should drop to near zero. Assuming the evidence doesn’t discriminate between possibilities (1) and (2), therefore, you should regard both of them as more likely to be true than you had previously thought (prior to learning about cosmological fine-tuning). Moreover, you should increase their probabilities in proportion to the original probabilities so that the ratio between them remains the same. For example, if you had been twice as confident in the multiverse hypothesis as in the design hypothesis (or vice versa), you still should be twice as confident after renormalization—assuming, again, that the evidence doesn’t discriminate between those remaining possibilities.

But what if the evidence of fine-tuning does discriminate between the remaining hypotheses? I will argue that fine-tuning evidence does, in fact, discriminate between possibilities (1) and (2), and it discriminates in a way that favors the design hypothesis. In other words, the evidence for design becomes stronger, and evidence for the multiverse becomes weaker, when we recognize how cosmological fine-tuning bears on those two possibilities.

To see why fine-tuning favors design over the multiverse, we can subdivide each of those hypotheses into more specific possibilities. The design hypothesis (1) can be subdivided into several distinct hypotheses, for example, by distinguishing various possible designers:

Likewise, the multiverse hypothesis (2) can be subdivided into more specific (but still mutually exclusive) hypotheses. Consider four such hypotheses, specifying that the multiverse is comprised of universes with:

Of these four multiverse hypotheses, only the last one (2d) can explain why we find ourselves in a universe with finely tuned constants and initial conditions. Thus, the fine-tuning evidence eliminates the other three multiverse hypotheses (2a, 2b, and 2c) in the same way that it rules out the single-universe-chance hypothesis (SUC) mentioned above. Similarly, some of the design hypotheses may be eliminated by the fine-tuning evidence. For example, if you think the Flying Spaghetti Monster would not (even if he exists) be smart enough or powerful enough to create a finely-tuned universe, then hypothesis (1d) will be ruled out by the fine-tuning evidence.

Now, here’s the crucial difference between design hypotheses and multiverse hypotheses: none of the plausible design hypotheses are eliminated by the fine-tuning evidence; whereas, in contrast, the fine-tuning evidence rules out some of the most plausible multiverse hypotheses. After all, if our universe arose by chance through some unknown natural process, it seems reasonable to expect other universes that arise similarly to share similar features, including similar laws, constants, types of matter, and initial conditions. However, to explain the fine-tuning, we need a very special—and a priori implausible—kind of multiverse: one in which the universes vary widely in all of the parameters that appear (in our universe) to be finely tuned. A multiverse full of similar universes won’t do. For this reason, although cosmological fine-tuning may constitute evidence for both (1) and (2), the evidence weighs more heavily in favor of (1), the design hypothesis.

This conclusion is, in my judgment, a practically inescapable consequence of Bayesian confirmation theory. The only way to avoid it, without breaking the Bayesian rules, would be to assign greater probability to the existence of a very specific kind of multiverse than to the existence of (any) God, prior to learning about cosmological fine-tuning. In other words, to resist my conclusion, your degree of belief (subjective probability) in that special kind of multiverse must have been greater than your degree of belief in God already, even before you learned about the fine-tuning evidence. Such a starting position, I contend, is unreasonable. Given that there is no independent evidence (aside from the fine-tuning itself) for such a multiverse, while there is abundant evidence—of many different kinds—for God’s existence,For a careful examination of numerous kinds of evidence for Christianity, I recommend the works of Oxford philosopher Richard Swinburne. His book The Existence of God (Oxford: Oxford University Press, 2004) is a good place to start. I also recommend New Testament professor Craig Keener’s book Miracles Today: The Supernatural Work of God in the Modern World (Grand Rapids: Baker Academic, 2021), which provides a thoughtful discussion of evidence from miracles, including some medically well-documented cases of sudden healing that cannot be attributed to mere psychosomatic effects or other natural causes. believing more confidently in an untestable, wildly speculative multiverse hypothesis is not a rational starting point for scientific inquiry.