Author’s note: Theoretical physicist Sean Carroll was recently interviewed by podcaster Alex O’Connor and asked to defend his stance that one of the most thought-provoking scientific arguments for God’s existence, the argument from cosmological fine-tuning, “is the best argument for God, but it’s still a terrible argument.” I am responding to Carroll and other critics of the fine-tuning argument in a series of posts.
Find the full series so far here.
In my last post, I established the Bayesian framework for the fine-tuning argument and identified three serious problems with the dominant subjectivist interpretation of probability: permissive priors, the old evidence problem, and the inability to account for substantive disagreement. I now expand on a better interpretation that resolves these difficulties.
The Nature of Epistemic Probabilities
The probability that something is correct does not have to be understood subjectively. There is a way of understanding probability objectively that has its origin in the work of John Maynard Keynes (1921) that has recently been further developed and extended by Nevin Climenhaga (2024). This view maintains that probabilities express objective degrees of support that are mind-independent relations among propositions.
When the probability of the truth of A is conditionalized on the truth of B, P(A|B), what is measured is the degree to which the truth of B supports that of A. This is not a psychological state as in the subjective interpretation. It is a logical and semantic relationship that captures the objective character of conditional probability. In this respect, it is analogous to entailment (if B, then A), or evidential relevance (B provides evidence for A), since these also are relations between propositions that hold independently of anyone’s subjective state of belief.
Deductive logic provides a good illustration. Consider the old chestnut “All men are mortal and Socrates is a man, therefore, Socrates is mortal.” The conclusion of this syllogism cannot be false when the premises are true. The validity of the argument has absolutely nothing to do with the psychological state of the person offering it or the one convinced by it. The argument expresses an objective logical relationship of entailment. The conclusion follows from the premises whether anyone recognizes it or not.
When I say, along with Keynes or Climenhaga, that probabilistic relations among propositions express objective degrees of support, a similar situation is in view. The truth of the proposition “Our universe bears evidence that it was intelligently designed for the purpose of supporting life” is objectively evidentially supported by the truth of the proposition that “Many of the natural constants of the universe, the values of which are determined by measurement, are fine-tuned for the existence of life.” The relationship between these propositions has nothing to do with what anyone is inclined to believe or disbelieve. When I state, as I did in my last post, that the probability of theism given fine-tuning and our background knowledge is, for all practical purposes, 1, that is, P(T|FT·B) ≈ 1, feelings of confidence are not what is in view, but rather a strong relation of objective evidential support.
Making this objective turn in our understanding of conditional probability has some very important advantages:
It Solves the Old Evidence Problem
Objective support relations among propositions are timeless, so it does not matter when we learned about them. As discussed earlier, general relativity’s precise explanation and prediction of Mercury’s precession provides support for the theory whether that support relation had been known in 1859, was shown by Einstein in 1915, or we didn’t find out about it until 2026. Genuine explanatory power does not depend on the historical order in which the relevant facts and their explanations become known.
This applies equally to the support relation between fine-tuning and theism. This evidential support is timeless and independent of our knowledge of it. The question of how strongly fine-tuning supports theism is not a matter of personal psychological predilection; it is a factual question about an objective relation. Whether we know about instances of fine-tuning before or after we recognize that they provide evidence for theism does not matter. All that matters is the objective evidential support that actual fine-tuning gives to theism.
It Makes Disagreements Substantive
The objectivity of the evidential support relation also means that when advocates of the fine-tuning argument disagree with Carroll about the support it offers to theism, we are disagreeing about a factual matter. To varying degrees of probability, one of us is right and the other is wrong. This accords well with our intuitive sense that we’re debating about something that matters, not just comparing psychological states or debating personal opinions concerning which there is no fact of the matter.
It Grounds Likelihood Assessments in Explanatory Relations
The objective degree to which one proposition supports another rests on the strength of the explanatory relation between them. When a hypothesis H would render evidence E unsurprising or expected, P(E|H) is high, whereas it is low when E would be surprising if H were true. For instance, when we claim that fine-tuning is more expected on theism than naturalism, we are saying it is an objectively better explanation for fine-tuning than naturalism. This makes a natural connection between Bayesian confirmation theory, abduction, and inference to the best explanation (IBE).
Climenhaga’s Defense
Nevin Climenhaga (2024) has provided a strong systematic defense of this understanding of evidential support.
The Argument from Explanatory Practice
Science and philosophy aim to explain aspects of the world and of our experience, and both scientists and philosophers offer judgments about what is correct or incorrect. In so doing, they are not saying “this is what I believe, but your psychology may give rational support to a different belief.” What they are saying is that certain beliefs are well supported by the evidence and others are not. When scientists say “the existence of an undirected chemical pathway to the origin of life lacks any substantial evidence to support it,” or “the cosmic microwave background and the relative abundances of the lightest elements support the Big Bang,” they are making claims about the world that are either true or false, not merely offering truthful reports on personal credences that just are whatever they are.
For this reason, Climenhaga argues that objective support relations are presupposed by rational evidential discourse. When we assess the likelihood of a hypothesis on the basis of evidence, we are not making a personal decision about how much confidence to have in the hypothesis; we are assessing the bearing the evidence has on it. The subjective interpretation of likelihood undermines explanatory practice and the grounding of explanation in reality, whereas understanding that likelihoods measure degrees of support provides a foundation for objectivity in explanation.
The Argument from Rational Criticism
Subjectivism cannot readily account for why some probability assignments are better than others, yet we criticize some probability assignments as unreasonable and not merely different. For example, if we meet a flat-earther who asserts that “evidence strongly supports the earth being flat rather than an oblate spheroid,” we don’t just say “that’s an understandable credence given your priors and your evidence.” We say that their priors are wrong, their evidence is wrong, and they are wrong. Their likelihood ratios and their posterior probability do not track the support relations that objectively obtain. The very practice of rational criticism presupposes that there are correct and incorrect probability assignments and, correspondingly, that we can be right or wrong in our probability assessments.
The Argument from Scientific Objectivity
Let me state this as starkly as possible: if Bayesian probabilities were in fact merely subjective, then scientific reasoning would collapse into autobiography. Judgments of evidential support are not merely reports of personal credences. As Climenhaga argues, the degree-of-support interpretation of Bayesian probabilities is foundational to the objectivity of scientific reasoning and concerns relations that scientists discover, not subjective credences they express.
The Connection to Inference to the Best Explanation
There is a close connection between Bayesian reasoning and inferences to the best explanation (IBE), one which is essential to the cogency of the fine-tuning argument. The essence of IBE is that we should infer the truth of the best explanation for the evidence we have. Crucial to this is the way that “best” is understood in terms of explanatory virtue. The best explanations are as simple as the phenomena allow and they cohere (are in harmony) with background knowledge; they have an explanatory scope that covers more than just the particular phenomenon in view; they have predictive fecundity; they are not ad hoc constructions; and so on.
In contrast to this, IBE and Bayesianism can seem like rivals that are in tension on the subjectivist account. IBE tells us to infer the explanation that is best whereas Bayesianism tells us to update by conditionalization, and some have argued that IBE might recommend an inference that Bayesian updating would not support. Famously, Bas van Fraassen (1989: 131-170, especially 160-170) has argued that IBE’s appeal to explanatory virtues puts it in tension with Bayesian conditionalization in ways that make it vulnerable to Dutch book arguments (a problem with subjective Bayesianism that I have discussed here). The tension arises on the subjectivist picture because explanatory virtues operate as considerations external to the probability calculus, suggesting that following them can pull an agent’s credences away from what conditionalization alone would dictate. The degree-of-support interpretation dissolves this ill-conceived tension. Explanatory virtues are constitutive of the support relations that probabilities quantify; they are not external constraints on Bayesian reasoning. So saying that H explains E well is the same thing as saying that P(E|H) is high. If H is a good explanation for E, then E would be unsurprising if H were true. The relative simplicity of H as a good explanation, for instance, ensures that P(H) is not substantially reduced by complexity penalties. The key insight is that objective explanatory considerations determine the probabilities, after which Bayesian formalism provides the calculus for reasoning with them.
This has direct implications for the fine-tuning argument. When we judge that P(FT|T) is high, we are judging that theism is a good explanation for fine-tuning. A universe fine-tuned for life is what we would expect if a necessarily existent intelligent agent exists who has purposes involving finite embodied conscious agents. When we judge that P(FT|N) is low, on the other hand, we are judging that naturalism fails to explain fine-tuning because life-permitting constants are surprising coincidences on naturalism, not expected outcomes. The likelihood ratio P(FT|T)/P(FT|N) thus measures comparative explanatory power. It quantifies how much better theism explains fine-tuning than naturalism does. In making this case, we are dealing with objective judgments about explanatory relations that are open to rational assessment and criticism, not merely expressions of personal incredulity or prior commitment.
Nonetheless, a question remains that the degree-of-support interpretation clarifies but does not, by itself, answer. We understand that P(FT|N) quantifies an objective relation, but we still need rigorous tools for evaluating it. What statistical methodology provides a disciplined rational assessment of how improbable the life-permitting values of the fundamental constants really are under the supposition that no purposive intelligence is responsible? The Bayesian framework shows that this assessment is the key to the evidential force of fine-tuning, but it does not tell us how to carry it out. For that, we need to ask whether the classical statistical tradition — Fisherian hypothesis testing, with its apparatus of null distributions, rejection regions, and significance levels — has something essential to contribute. As we shall see, it does.
Next up: “Fishers in the Bayes?”