Introduction

Physical theories trace some aspects of the world back to laws of nature while treating others as accidental or contingent. The fact that the planets move along approximately elliptical trajectories follows from the law of gravity, for example, whereas the number and masses of planets reflect contingent facts about how our solar system formed. This distinction is essential to how physics represents the world, with the full description of any specific system arising from a complex interplay between laws and contingent facts. The rich phenomenology our theories can describe depends on how the distinction is drawn, and allowing for contingencies gives theories the flexibility to apply in a wide range of circumstances.

Recent discussions of “fine tuning” in physics and cosmology reflect a conflict between two different perspectives on this demarcation between necessity and contingency. On the one hand, various aspects of contemporary physical theories—such as values of coupling constants in particle physics and density parameters for different kinds of matter in cosmology—are determined by observations. These are contingent or accidental in the sense that they cannot be derived from first principles and apparently could have taken different values. Yet, from the second perspective, the exact values of these parameters hardly seem to be accidental: they seem instead to be essential to the universe being like it is. The existence of complex structures at a variety of scales, ranging from molecules to stars to galaxies, apparently depends sensitively on the specific values we observe. If the coupling constants in the Standard Model, or the cosmological parameters, differed from their current values, even by the slightest amount, complex structures would not emerge. Since these are plausible preconditions for the existence of life, such a universe would be utterly barren.

Features that are entirely contingent, according to current physics, are apparently necessary to account for the complexity of the observed universe and the very possibility of life. Should our theories not explain something as fundamental as the complexity of the universe, and the existence of life, in terms of the underlying laws? This question reflects assumptions, often left implicit, regarding the explanatory scope and appropriate aims of physics. The question is often posed more forcefully: the required parameter values are not just unexplained but strikingly “improbable” in some sense to be made precise. How could the values of all these parameters be just so, finely tuned to match the required values, by sheer coincidence? Even those willing to grant that some explanations bottom out with an appeal to contingent facts may balk at explanations that exhibit such sensitive dependence. This line of thought is sometimes meant to spur the development of new theories free of fine tuning; other times, it is instead to encourage the use of quite different explanatory principles from metaphysics and theology.

Those who accept (some version of) the principle of sufficient reason already demand explanations for why the universe has the properties it does. One appeal of fine-tuning arguments is that they might be effective in persuading even those who do not share such strong rationalist commitments. To make good on this appeal, advocates of fine tuning must counter a natural empiricist response, which is to dismiss fine tuning as a pseudo-problem. Fine tuning does not identify empirical anomalies or logical inconsistencies within existing theories. A finely tuned theory can successfully account for what we observe. What is the nature of the alleged deficiency in how it does so? The fine-tuning advocate insists that current theories cannot adequately account for something as essential to the universe as the presence of living things, or, less anthropocentrically, complex structures at a variety of scales. A case based on fine tuning is stronger if the nature of this deficiency can be clarified and shown to follow from criteria we routinely use in evaluating theories—criteria that even a skeptical empiricist ought to accept. One way of making the case is to argue that contemporary theories render the universe we observe to be remarkably, unbelievably, astronomically improbable. My main aim is to assess to what extent fine tuning can play this role by grounding probabilistic assessments like this in fundamental physics and cosmology.

Fine-tuning arguments (hereafter, FTAs) have played an increasingly important role in contemporary physics and cosmology, first in cosmology starting in the 1960s following the recognition that the hot Big Bang model requires a seemingly “improbable” initial state, and subsequently with discussions of “naturalness” in particle physics—giving rise to the estimates of the improbability of the universe we observe. Physicists have pursued theories that eliminate (or at least decrease) fine tuning in the past several decades, although there have been active debates regarding how this preference relates to other demands routinely placed on theories. Alongside these developments in physics, there has been a revival of interest in fine tuning in philosophy. Just as the physicists have debated what (if anything) is wrong with a finely tuned theory and how it should be remedied in a successor theory, philosophers have sought to elucidate the general structure of FTAs and assess responses to it.

Here, I explore two challenges to appealing to fine tuning in physics and cosmology in modern versions of the design argument. The first regards the nature and justification of probabilities. The basic issue regards when we can apply the mathematics of probability theory to represent uncertainty. In my view, physics theories often supply the mathematical structures needed to introduce probabilities and justify their use. Probabilities are an absolutely essential part of how physical theories are used to describe the world. We can assess the scope and reliability of the probabilistic assessments based on the success of the theory and the degree to which the probabilities follow directly from aspects of the theory we understand well. Assertions about probability in philosophical FTAs, however, often appeal to the principle of indifference applied over possible parameter values, or possible worlds, without the resources to single out a unique measure or probability distribution. Recent defenders of the design argument have attempted to bridge the gap between these cases. I argue here that these efforts fail because they elide significant conceptual contrasts between the uses of probability in the two cases.

The second challenge starts with a very different response to the role apparently contingent features, such as parameter values and initial conditions, play in explaining the universe’s complexity. From this view, given that physics provides an integrated representation of a broad array of phenomena starting from a few fundamental principles, we should expect to uncover dependencies like those emphasized and catalogued in the literature on fine tuning. By considering fragments of physical theory in isolation, we are tempted to treat various features as separable and probabilistically independent, despite the dependencies that arise when they are combined in an integrated account. The various cases of fine tuning illustrate that the explanations provided by physical theories rely on much more than just the laws—they also need to invoke facts about initial or boundary conditions, parameter values, and so on. Recognizing that these theoretical representations employ a wide variety of claims with different modal statuses does not provide a reason to reject the theories.

The article begins by returning to an influential historical case, Isaac Newton’s design argument based on the structure of the solar system, that serves a dual purpose: to both introduce the basic structure of one influential FTA and illustrate how the assessment of certain features as “improbable coincidences” can go wrong. The next two sections turn to philosophical attempts to formalize FTAs, first in terms of explanation and then in terms of assessments of the likelihood of the design hypothesis versus competitors. I review three well-known challenges to the likelihood formulation before endorsing an alternative formulation advanced by John Roberts. While the Roberts formulation avoids some of these challenges, it also undermines claims connecting the probabilities invoked in FTAs to physically respectable probabilities—as opposed to hypotheses about the nature of a Designer and their intentions. The article then turns to examining two cases in physics often thought to ground the probabilities introduced in FTAs, ultimately concluding that they fail to do so. First, I distinguish between two different ideas that (unfortunately) both fall under the label “naturalness”: autonomy of scales and statistical typicality, assessed based on a measure over theory space. In the penultimate section, I turn to the fine tuning of initial conditions in cosmology, where similar measure problems arise, before concluding the article with further reflections on the implications of this line of argument.

Design and Fine Tuning

The design argument has long played a central role in natural theology, reflecting the appeal of establishing substantive conclusions regarding the nature of the Designer on a posteriori grounds. Versions of the argument start from observations of a wide variety of striking features, ranging from the adaptations exhibited by living creatures great and small to the arrangement of the solar system. FTAs regarding physics and cosmology have dominated recent discussions, ever since evolution provided a compelling account of how design can accumulate through natural selection without a guiding intelligence. But they are not a recent innovation. Some of the earliest design arguments appealed to basic structural features of the cosmos, and it will be useful to discuss them briefly and see how they have fared in light of the evolution of physics.

Newton published an influential design argument in the General Scholium, a concluding comment added to Principia Mathematica’s second edition. René Descartes had claimed that the solar system could have emerged out of pure “chaos” merely through the action of mechanical laws. By contrast, Newton ([1687] 1999, 940) argued that “[t]his most beautiful System of the Sun, Planets, and Comets, could only proceed from the counsel and dominion of an intelligent and powerful being” due to the regularity of the motion of the planets and their satellites. The planets revolve around the sun with the same orientation and (roughly) within a plane. Newton attributed the persistence of these regular motions, despite mutual interactions among the planets, to providential design, partially implemented through the carefully orchestrated motion of comets. This only seemed plausible due to Newton’s dramatic overestimate of cometary masses as roughly on par with that of Earth. Such massive comets would have appreciable effects as they passed through the planetary orbits, and appropriate cometary motions—guided by an intelligent and powerful being—could enhance the dynamical stability of the solar system. Subsequent discussions turned to other features of the solar system thought to support a similar conclusion. William Paley ([1829] 2006, 199) devotes a chapter to astronomy, stating at the outset that, while not as compelling as arguments based on biological design, the solar system nonetheless displays “the magnificence of [the Creator’s] operations,” reflected in the central placement of the sun, which does not appear to follow from any “antecedent necessity” or from the sun’s nature (assumed to be similar to that of the planets); the choice of the laws governing the solar system, given that an inverse-square force admits stable orbits, whereas other force laws do not; and so on.

These arguments focus on features that are not only strikingly well suited for our existence but also seem unlikely to arise by chance. Several scholars took the further step of estimating the relevant probability. In response to the Academié des Sciences prize contest in 1734, Daniel Bernoulli ([1734] 1987) calculated the probability of the finely tuned initial state needed to account for the nearly co-planar orbits of the six planets known at the time. These orbits fall within 6°54′ of one another, approximately $\frac{1}{3}$ of 90° (taking orientation into account); treating them as entirely independent leads to a probability of the required initial conditions equal to $\frac{1}{13^5\hspace{0.17em}–\hspace{0.17em}1}\hspace{0.17em}=\hspace{0.17em}\frac{1}{\mathrm{371,292}}$. While admitting that this gave only a rough estimate, Bernoulli regarded it as sufficient to rule out mere chance as an explanation—and he proposed a speculative physical mechanism instead, such that this feature would be an expected, stable outcome. Paley ([1829] 2006) also argued that several apparently designed features of the solar system exhibit fine tuning in a similar sense. The specific choice of the exponent in the gravitational force law (f ∝ rⁿ), from among all possible values n, for example, falls “within narrow limits, compared with the possible laws. I much underrate the restriction, when I say, that in a scale of a mile they are confined to an inch” (Paley [1829] 2006, 207). In Paley’s case, ruling out “mere chance” left providential design (rather than a speculative physical mechanism) as the most compelling explanation of these features.

The common structure of these design arguments runs roughly as follows. We first identify several striking features of the solar system that seem to be well suited to our existence, or even necessary for it, based on a specific theory. Yet, these features are fragile, in that fact that they hold depends sensitively on features of the initial state of the system or contingent features of the laws (such as the choice of apparently unconstrained parameters). The current theory treats these features as brute facts subject to no further explanation. When we assess how likely it is that the appropriate contingent facts obtain “by mere chance,” we further discover, via arguments like Bernoulli’s, that they are incredibly improbable. This prompts the demand to seek an explanation more satisfying than an appeal to mere contingency, with two distinct responses: augmenting current theory with new physics that has the effect of replacing fragility with stability, or an appeal to the existence of a Designer.

With the recent discovery of extra-solar planets, we can now make this line of argument more concrete by comparing our solar system to the catalog of other systems (which now has several hundred entries). With respect to this catalog, the solar system does have some unusual features with regard to both the number and masses of the planets and their orbital parameters, but nothing as improbable (in the sense of frequency within this ensemble) as Bernoulli’s calculation suggests.¹ Many astronomers have advocated an anthropic response to these unusual features. Namely, they explain apparent fine tuning as the consequence of a selection effect applied to an ensemble of systems. Several features of our solar system, such as the low eccentricity of the planetary orbits and the absence of massive planets close to the sun, are plausibly essential to maintaining a planet in the so-called “Goldilocks zone” (with temperature and other conditions that are “just right” for creatures like us) for long periods of time. According to this approach, our presence explains (in some sense) the fact that the solar system has these unusual features. (Note that in this approach, what is explained is not the striking features of the solar system per se but rather the fact that creatures like us observe these unusual features.) We could not, after all, find ourselves in one of the planetary systems lacking the conditions needed to support our existence. Anthropic selection from an ensemble of systems exhibiting variation in relevant respects is the third main response to fine tuning that takes the explanatory demand as legitimate.

Philosophers have offered several refinements and formalizations of fine tuning, leading to different assessments of its validity and force and the viability of these three responses.² Before turning to these, we are already in a position to reflect on the fate of the claims of Newton and Bernoulli. The apparent contingency of several features of the solar system has proven to be a consequence of framing the research questions narrowly, and later work dissolves this illusion by providing a richer account of the formation and evolution of planetary systems. The solar system would be a puzzling configuration of bodies interacting gravitationally if the sun and planets were (somehow) assembled by chance. But this evaluation changes drastically when we regard it instead as an outcome of stellar formation in a specific environment. The evolution of a protoplanetary disk into a planetary system is expected to yield planets moving roughly in a plane with the same orientation. In contrast with Bernoulli’s speculative proposal, the modern account of stellar evolution and planet formation does far more than account for one puzzling feature of the solar system—it is the product of various lines of investigation, incorporates diverse aspects of physics and astrophysics, and generates a number of further predictions and insights. The impact on the argument from design for the solar system resembles that of evolutionary theory on biological design arguments: within this broader picture, there is a compelling and detailed account of how certain features arise. The initial evaluation that these features are strikingly improbable coincidences in need of further explanation resulted from treating the problem using a theory with narrow scope.

Surprise and Probability

In the opening scene of the film Rosencrantz & Guildenstern are Dead, Guildenstern contemplates an increasingly long run of coin tosses that come up heads. Granting that these tosses are fair and independent, his sequence of ninety-two heads has extremely low probability: ${\left(\frac{1}{2}\right)}^{92}$. Does this outcome demand an explanation? Striking real-world lottery results have often prompted similar questions. In October 2022, a lottery in the Philippines drew the following winning ticket (five numbers chosen randomly from one to fifty-five): nine, eighteen, twenty-seven, thirty-six, forty-five, fifty-four. This surprising result prompted calls for a fraud investigation and inquiries to the prominent mathematician Terence Tao.

Guildenstern considers various explanations of his run of ninety-two heads, including divine intervention. The final option is a simple denial that any explanation is needed (Stoppard 1967, 6): “[A] spectacular vindication of the principle that each individual coin spun individually is as likely to come down heads as tails and therefore should cause no surprise each individual time it does.”

Martin Smith (2017) defends this response based on what he calls the “conjunction principle”: the conjunction of two independent events, each of which is itself unsurprising, is also unsurprising. There is just as little need to explain n consecutive heads (for any n, assuming independence) as there is to explain an individual toss coming up heads. The same argument applies, of course, to any specific sequence. This seems to be the correct response to the outcome in the Philippines, although there was no investigation to determine whether criminals with a fondness for the number nine had somehow rigged the lottery.

One way of evading this conclusion is to make the case that there is something striking or distinctive about the outcome. A sequence of ninety-two heads, or the first five multiples of nine, is easier to characterize concisely than a “typical” sequence. Mathematicians maintain a catalog (The On-line Encyclopedia of Integer Sequences) of integer sequences that have previously appeared in calculations (such as the Fibonacci sequence, alongside 370,000 less famous examples). We could, for example, characterize any sequence of integers appearing in this catalog as “unusual” or “surprising.” Does a contrast along these lines justify treating an outcome as particularly salient and in need of explanation?

Any proposal for a further distinction along these lines goes beyond probability theory. The question of salience can only be answered in light of a proposed alternative hypothesis, or collection of hypotheses, regarding how the outcome has been generated—proposals that involve, in the case of Guildenstern, denying the independence of the coin tosses, the probabilities assigned to individual tosses, or both, or, in the case of a lottery, a specific way of generating an unusual sequence of integers. These examples illustrate a point that should not be controversial, even for those who doubt the conjunction principle: the probability calculus itself does not deliver verdicts regarding what requires explanation. Such judgments must draw on background knowledge, other principles, or an assessment of alternative hypotheses.

Our assessment of what calls out for explanation typically takes place against a backdrop of experience with similar cases and expectations based on them. For the reasons David Hume (1779 [1998], pt. II) emphasizes forcefully in the Dialogues Concerning Natural Religion, we should not expect these judgments to be reliable in assessing fundamental physics and cosmology, given the “limited sphere of action” of human thought: “[W]hat new and unknown principles would actuate her [Nature] in so new and unknown a situation as that of the formation of a universe, we cannot, without the utmost temerity, pretend to determine.”

I do not have the space to evaluate the extent to which Hume’s observations regarding the uniqueness of the universe, and inaccessibility of events such as its putative origin, undermine the design argument (as formulated by Cleanthes earlier in the Dialogue), but they certainly encourage skepticism about our ability to isolate explanatory targets in these domains.

There is a further reason to be skeptical of this ability, namely, recognition of the mistakes that arise from treating theoretical accounts of specific phenomena in isolation. Cory Juhl (2006) develops this line of argument and rejects the claim that fine tuning for the existence of life cries out for explanation on the grounds that we should expect dependence on constants and boundary conditions as a direct consequence of the fact that physics has succeeded in describing nature using a small number of basic components, or types of systems, and a small number of fundamental equations. Many phenomena depend on a rich web of connections among the basic ingredients employed by physics. The description of the formation and evolution of a brown dwarf star, to take one example, draws on a variety of aspects of physics. Brown dwarfs are distinct from Jovian planets in that their core reaches temperatures high enough to sustain fusion reactions—more precisely, deuterium burning. This mass threshold depends sensitively on details of nuclear physics, such as the binding energy of deuterium and the cross sections for various nuclear reactions. The success in developing an account of the structure and evolution of brown dwarfs, compatible with various observational facts, entails a number of overlapping constraints among the relevant aspects of nuclear physics and astrophysics. Rather than being surprised that the value of deuterium binding energy plays such a significant role in this account, one should expect an integrated description of the formation and evolution of these complex systems to depend sensitively on the values of various constants as well as on aspects of the environment in which the systems form (as reflected in boundary conditions).

Such sensitive dependencies do not provoke a demand for further explanation, on Juhl’s view. Rather, the existence of such dependencies should prompt recognition of the contribution constants and choices of boundary conditions make to the empirical success of physics, and the extent to which success in tying together seemingly disparate facts implies tight constraints on them (cf. Landsman 2016; Butterfield 2025). A brown dwarf is just one instance of what Juhl calls “causally ramified” phenomena, defined as phenomena that depend causally on a large number of logically independent facts. The success of physics leads us to expect causally ramified phenomena to be ubiquitous, and the existence of life is just one among many. Furthermore, any causally ramified phenomenon should be expected to exhibit sensitive dependencies on fundamental constants and boundary conditions. Note that this is not to claim that the intricate links among the relevant aspects of physics, astrophysics, chemistry, etc. and the sensitive dependencies they imply will be easy to unravel or quantify. Indeed, the literature devoted to fine tuning abounds with detailed case studies illuminating many fascinating links while also revealing the difficulties facing this kind of analysis. But given the success of natural science in accounting for causally ramified phenomena, including the existence of life, we should expect such dependencies rather than treating them as surprising and posing further explanatory demands.

These broadly Humean lines of argument raise a challenge: to vindicate intuitive judgments of surprise and the demands following from it. One response aims to avoid this challenge by reformulating FTAs in terms of probabilities. Rather than evaluating whether Guildenstern’s run of coin tosses cries out for explanation, this approach considers how such outcomes bear evidentially on competing hypotheses. The aim of the FTA is then to show that certain types of evidence, such as the structural features of the solar system noted by Paley and Newton, favor the hypothesis of a designer over other alternatives. Furthermore, the hope is that the probabilities invoked in this assessment—such as the probability that the values of coupling constants, treated as empirically determined parameters, fall within a particular interval or that the initial state has appropriate properties—can be respectably grounded in physics. But the use of probability along these lines has proven to be a double-edged sword. I first consider more formal formulations of FTAs in the following two sections before turning to two attempts to give a physical justification for probabilities.

Likelihoods

Translating the FTA into the language of formal epistemology promises to provide a clearer assessment by avoiding debates regarding explanation and instead appealing to general methodological precepts regarding how to evaluate the impact of evidence. Most philosophers of science treat questions about evidential relationships using the tools of probability theory. The probability conferred on the evidence E by a hypothesis H, called the likelihood, is taken to be given by the conditional probability P(E|H).³ One influential formulation of the FTA appeals to the likelihood principle (Sober 2003), according to which evidence E favors hypothesis H over an alternative H′ if and only if P(E|H ∧ K) > P(E|H′ ∧ K), where K indicates background knowledge.⁴

We can then reconstruct the arguments of Newton and Bernoulli as follows. Suppose the solar system could be arranged with n planets moving along nearly aribtrary trajectories. Call FT_S the claim that only an extremely small subset of allowed trajectories—those in which planets move in roughly the same plane with the same orientation—is compatible with the existence of life. (The subscript S refers to the solar system, but we can also formulate a more general claim, FT, which holds that certain parameters appearing in physical theories and boundary conditions must fall within a narrow range of the space of possibilities for life to exist.) We will take this claim, for the sake of argument, to be accepted as part of the background knowledge. Now, consider the impact of the observational claim E^*, that the planets within our own solar system fall within this narrow range of life-friendly configurations, on three alternative hypothesis: H_C =: the planetary orbits arise “by chance”; H_D =: the planetary orbits arise by providential design; and H_P =: the planetary orbits are produced by a specific physical mechanism that drives a “large” subset of initial states towards life-friendly configurations. On this reconstruction, we can see Newton as asserting that P(E^*|H_D) > P(E^*|H_C) (dropping reference to the background knowledge K, which we take to be fixed); Bernoulli, by contrast, argues that P(E^*|H_P) > P(E^*|H_C), and furthermore estimates the value of P(E^*|H_C). (Note that there are variations that consider the evidential impact of different statements of the relevant evidence, such as the fact that life exists rather than E^*. Arguably, similar challenges arise for many alternatives to E^*. The next section considers an alternative treatment of FTAs that takes FT_S to be the relevant new evidence rather than E^*.)

This pattern extends to other types of fine tuning. Physicists have uncovered a number of observed features of the universe that appear to depend sensitively on values of the parameters appearing in the Standard Model or on cosmological boundary conditions. (See John D. Barrow and Frank J. Tipler (1986) for a classic, comprehensive review, and for example, see Geraint F. Lewis and Luke A. Barnes (2016) and David Sloan et al. (2020) for recent assessments; Simon Friederich (2023) provides an overview of the philosophical literature.) Many of these reflect “complexity,” roughly characterized as the existence of stable structures of different kinds across a variety of physical scales. For example, our universe exhibits complexity in chemistry (with a wide variety of stable molecular structures, particularly those including carbon) as well as astrophysics (with stable structures ranging from stars to galaxies). Schematically, for a dimensionless parameter α, these arguments aim to show that even small variations, greater than some Δα, are not compatible with (some specific aspects of) this observed complexity. The value of the parameter appears to be fine tuned because the interval of allowed values α ± Δα is a “small” subset of the full range of values α can take. Here, we usually assume α can take a “large” range of possible values; α may be only constrained to be a real number or a positive real number, for example. It seems improbable that an “arbitrarily chosen” value of α from the full range of possible values, granting a version of H_C, would fall within this small interval. To repeat an overused intuition pump: the specific values we observe seem as improbable as hitting an exceptionally tiny bull’s-eye on a large dartboard representing the space of possible values. (Many FTAs take this form, but not all. As we will see later, naturalness problems in the Standard Model of particle physics may lead to a similar verdict—that the observed parameter values are problematic—via a different line of argument.)

The likelihood formulation of the FTA yields quite modest conclusions. The stated inequalities reflect a differential, incremental boost in the probability of specific hypotheses—but this does not imply that the favored hypothesis has high probability, or indeed probability above any stated threshold. To establish the absolute level of credence in the hypothesis requires further commitments. (Within a Bayesian approach to confirmation theory, this would take the form of an assignment of prior probabilities to the competing hypotheses, with the likelihoods then specifying how these priors change in light of the new evidence E^*.) The conclusion is also modest in a second sense. Newton’s arguments would show that H_D has higher probability than specific alternative hypotheses that account for E^* (such as H_C, and possibly H_B), but making the stronger claim that H_D has the highest probability overall would require surveying and evaluating the likelihoods of other hypotheses. This would require a global awareness of alternative hypotheses that account for the relevant evidence, such as the modern account of stellar formation. The historical case discussed earlier illustrates how difficult it is to obtain this kind of knowledge. (Note that one can take the chance hypothesis to be the denial that the action of a designer, or any other hypothetical physical mechanism, yields the relevant evidence. While this understanding of the chance hypothesis would eliminate the need to survey alternatives, it amplifies the difficulties in evaluating P(E|H_C).)

Despite its modesty, this line of argument faces (at least) three challenges regarding evaluation of the likelihoods P(E^*|H_C) and P(E^*|H_D). First, the Humean concerns regarding our ability to identify targets for further explanation prompt skepticism regarding whether the hypotheses in question yield well-defined likelihoods at all. Second, granting a successful response to the first challenge, we need a defense of the propriety of assigning probabilities in the cases of interest. It is straightforward to calculate the likelihood of Guildenstern’s outcome on the hypothesis that it is the result of ninety-two independent tosses of a fair coin, but to what extent are likelihood calculations like Bernoulli’s well grounded? Third, the fact that we exist in our solar system makes E^* more likely (independent of the truth or falsity of the relevant hypotheses), and we need to take this observational selection effect into account in assessing the evidential impact of E^*.

We confront first the challenge in trying to calculate likelihoods based on H_C, H_D. What do these hypotheses imply for specific evidential claims? Calculating P(E^*|H_D) seems to require some understanding of the goals and abilities of the postulated designer. Consider the contrasting likelihoods assigned to the expected features of a watch discovered on the heath, as in Paley’s famous example, if we knew the designer to be Jony Ive (designer of the Apple Watch), or instead Peter Henlein (credited with design of the first pendant watch in 1505). Uncertainty regarding the goals and resources of human designers pales in comparison to the uncertainty associated with a Designer. Elliott Sober (2008, sec. 2.12), echoing Hume, argues convincingly for a sharp contrast between the case of human design of artifacts and Design: in the former case, but not the latter, we have independent evidence for assumptions regarding the designer that make it possible to compute the relevant likelihoods. He also identifies the circularity in a common response to this objection: claiming the Designer preferred a solar system with the appropriate features begs the question, as it presumes H_D is true in order to specify the Designer’s aims and resources. It is also not clear how to calculate P(E^*|H_C), for the reasons discussed in the second section. At any given stage of theorizing, our best theories apparently leave various features contingent and subject to blind chance—but the line demarcating such contingencies often blurs and shifts with further work. Features of the solar system Newton regarded as left to chance are now seen as natural consequences of the process of its formation. (Other facts cited in design arguments have had a similar fate—see, e.g., Sober (2003).)

Regarding the second challenge, the phrases in scare quotes above (“small,” “large,” and “arbitrarily chosen”) prompt questions about the cogency of assigning probabilities. Making sense of the intuitive idea that an interval around the observed value is “small” compared to the range of values allowed by the theory is harder than it seems. Suppose we take it to be equally likely that α falls in any interval of the same width. This assumption cannot be maintained if α takes values on the positive real line or the full real line. There is no probability measure that assigns equal, nonzero measures to all intervals on the real numbers (or the positive real numbers). This is because the real numbers (or the positive real numbers) have infinite Lebesgue measure. If we introduce a normalized probability, any finite interval—whether intuitively “small” or “large”—is assigned zero probability (McGrew, McGrew, and Vestrup 2001; Colyvan, Garfield, and Priest 2005). Probability theory applied in this way does not capture the intuitive contrast between sensitive dependence on the value of α and relative independence from it.

The second issue regards what the “arbitrary choice” of the observed value of α means. What justifies the step from an ensemble of possible values, with the appropriate mathematical structure to introduce a measure, to the assignment of probabilities? If this is taken to be an objective probability, the “choice” of value is the outcome of some process—presumably not a literal throw at a dartboard. Assumptions about this process are needed to warrant assigning an expected value of α (see, e.g., Norton 2010). An analogous problem faces appeals to the principle of indifference. The principle enjoins us to use a uniform probability distribution. But this uniformity is defined with respect to some choice of measure, and we have to then ask how to justify the judgments implicit in the definition of a measure regarding which cases count as equal. Finally, even if the language of “choice” is merely metaphorical and the probabilities in question subjective—representing degrees of belief—there is still a further question regarding why these should be assigned in accord with a particular measure.

These complaints may seem like technical quibbles. Yet, these are exactly the questions that need to be answered to justify applying probabilities (and other tools from formal epistemology) in these cases, rather than taking claims about “unlikely” values as merely loose talk. Insofar as we treat fine tuning as involving the choice of a parameter, or initial state, from among a space of logically possible values, the source or justification of probabilities remains obscure. Physics (and much else!) comes into play in revealing the fascinating, multifaceted ways in which the complexity of the universe around us depends on parameter values. Yet, the justification of probabilities assigned to the parameter values or boundary conditions themselves is a separate question. It is not clear how to justify a unique, well-defined probability distribution based on treating parameter values as freely chosen from among the real numbers. (This is a well-known objection; see Sabine Hossenfelder (2021) for a trenchant formulation.) A proposed resolution of the normalizability problem—restricting the allowed range of α to some compact subset of the real line (Collins 2009; Barnes 2018)—makes it even less clear how to interpret and justify the relevant probabilities. We are left with deep puzzles regarding how to justify probabilities, and what low probability implies, without appropriate resources to resolve them.⁵ Later, we turn to a more detailed discussion of how probabilities can be introduced in relevant areas of physics and cosmology, which will help to clarify the contrast between these well-grounded probabilities and those appealed to in FTAs.

The third challenge concerns how to account for observational selection effects in evaluating the evidential impact of E^*. Suppose, generally speaking, that some claim E provides a useful contrast between competing hypotheses H, H', in the sense that they have very different likelihoods. An observation selection threatens to undermine the value of E, in the sense that the process of gathering evidence washes out this contrast. To reuse Arthur Eddington (1939)’s simple illustration: we cannot use a fisherman’s daily catch as evidence regarding the population of fish in a lake, for types of fish smaller than the holes in the net. Treating the fish caught in the net as if they are a random sample of the entire population neglects the selection effect due to the size of the holes. In the case at hand, our existence is intricately connected to E^*—we could not observe a solar system with radically different features than our own. (More explicitly, when we include relevant facts about our existence in K, this objection holds that we will have P(E^*|H_C ∧ K) = P(E^*|H_D ∧ K) = 1, eliminating the differential boost.) Statisticians have methods to handle selection effects, such as analyzing in detail the biases introduced by the process of observation or sampling. But within the context of FTAs, the most relevant questions regard the extent to which an appeal to selection effects serves as an adequate explanation of the initially surprising features by in effect shifting from analyzing the probability assigned to some feature to the probability assigned to our observation of that feature within a larger ensemble of possibilities. These questions have prompted an ongoing debate in philosophy, which I do not have the space to pursue further here (but see, e.g., Friederich 2023, sec. 3).

An Alternative Formulation

Roberts (2012) defends an alternative reconstruction of the FTA,⁶ relevant for my purposes because it makes particularly clear the contrast between the nature of probabilities in the FTA and those introduced in physical theories.

The leading idea is that the fine-tuning argument primarily concerns the discovery that physics requires specific parameter values and boundary conditions to be compatible with observations that are in some sense “unusual” within the space of possibilities allowed by the laws. We should consider the impact of the evidence that fine tuning is required (FT in the earlier notation) rather than the specific values required (E^*) or the existence of life, as in the previous section. Newton’s design argument in the General Scholium stems, after all, not from a sudden realization that life exists, or from measuring the specific orbital parameters characterizing different planets, but from his discovery of the apparent fragility of the solar system. The same is true for more recent discussions in physics and cosmology.

The alternative reconstruction still concerns evaluation of the likelihood of this evidence based on different hypotheses and aims to show that P(FT|H_D) > P(FT|H_C). Roberts (2012) shows that this inequality follows from two plausible assumptions that can be formulated in general terms for a case of selecting an outcome X from among a space of possibilities. Suppose there is some feature of X that obtains that “makes it intelligibly choice worthy or aim worthy” in a way that demarcates it from among other possibilities (call this proposition A, for the “aim worthiness” of X). The assumptions hold that, first, P(X ∧ H_D|A) >> P(X ∧ H_D)—a Designer is much more likely to aim for the distinguished outcome; and, second, P(X ∧ H_C|A) ≈ P(X ∧ H_C)—a “chancy” selection process ignores the features that distinguish outcome X. From these two assumptions, and Bayes’s theorem, it follows that P(A|X ∧ H_D) > P(A|X ∧ H_C)—that is, obtaining an outcome, distinguished in some way from other elements of the space of possibilities, boosts the likelihood that the value was chosen by a designer sensitive to the relevant feature.

Roberts accompanies this formal analysis with a memorable thought experiment. Suppose we first observe a dart thrown at an unmarked wall, but how and why the dart was thrown is obscure. The dart’s exact position does not help in determining whether it was thrown aimlessly (and perhaps recklessly) or by a skilled thrower aiming at a target. Next, we are given a pair of infrared goggles, leading to the discovery that the wall features a painted target, invisible to the naked eye. Suppose the dart has hit this preexisting target’s bull’s-eye. This fact then provides strong evidence that it was aimed rather than thrown at random. The crucial evidence that prompts this reevaluation is not the location of the dart itself but the fact that it is positioned in such an “aim-worthy” spot.

Roberts argues, to my mind convincingly, that this reconstruction more accurately captures current versions of cosmic fine tuning: it appropriately emphasizes, rather than the discovery that parameters have specific values, the significance of the fact that these values fall within a narrow range distinguished by being “life permitting.” He further argues that this formulation avoids some of the challenges with the likelihood formulation discussed in the previous section. Assessing the two assumptions discussed earlier does not depend on introducing a probability distribution over the space of non-aim-worthy possibilities. The technical obstacles to introducing the probabilities reviewed earlier are then, arguably, irrelevant to this formulation. The only plausible way of understanding the relevant probabilities are as credences, and the credences are plausible almost by definition (if we grant that it makes sense to treat the parameter values as determined by some kind of “choice” process): the key contrast is between a hypothesized choice by a Designer responsive to some “aim-worthy” feature and a “chance hypothesis” that ignores that same feature. Since the process by which physicists discovered that FT holds is not sufficient to guarantee its truth, concerns about selection effects do not undermine its evidential value.

Despite these advantages, this formulation renders Humean skepticism regarding our knowledge of a Desginer even more salient. What would be aim worthy for a Designer? Roberts makes the case that these assumptions hold even on a deflationary account, essentially only requiring an agent capable of drawing distinctions we recognize as intelligible. But on this formulation, the characterization of the Designer, and the Designer’s choice, comes front and center. Roberts’s goal was to provide a more accurate reconstruction of informal versions of FTAs, and in doing so he has made it clear that the relevant probabilistic claims have little to do with physics. The assessment of probabilities entirely concerns the Designer and their “choice” of parameter values or an initial state. The exchange between Roger White and Jonathan Weisberg (see fn. 6), for example, concerns whether it is more plausible for a Designer to choose “lax” laws that require supplementation by specific finely tuned parameter values or “stringent” laws that do not. I will not pursue these questions further here, but this formulation of the FTA makes it clear how little the answers to such challenges have to do with the assessments of probabilities assigned to parameter values or initial conditions within physics, to which I now turn.

Naturalness

For the last several decades, the need to fix apparent violations of “naturalness” has driven the search for extensions to the Standard Model of particle physics. In a “natural” theory, physics at low energy scales does not depend sensitively on physics at much higher energy scales—the low-energy physics decouples, in a sense that can be made precise. Naturalness is extremely appealing: insofar as it holds, ignorance of high-energy physics does not undermine efforts to describe physics at currently accessible scales, and it has played an important heuristic role in the development of the Standard Model. Major lines of research have been motivated by the need to resolve or eliminate apparent violations of naturalness, in particular the Higgs mass and the cosmological constant. Yet, the proposed remedies, such as the introduction of supersymmetry, have further consequences that have not been found experimentally. This failure has prompted active debate and reevaluation of naturalness over the past decade.

Clarifying the content and status of naturalness is a central problem in contemporary foundations of physics,⁷ but my limited purpose here is to understand how naturalness relates to fine tuning. This requires a brief overview of the relevant physics. Many fine-tuning advocates take the failures of naturalness to show that observed parameter values are incredibly improbable, leading to an extremely low likelihood P(E^*|H_C). Luke Barnes’s (2020) estimate of this likelihood as10^–136), for example, depends almost entirely on failures of naturalness.⁸ Here, I argue that this assertion elides a significant difference between distinct notions of “naturalness” (a confusion abetted by the physics literature, unfortunately).

The primary idea of naturalness can be introduced in terms of renormalization group flows on theory space. One way of formulating quantum field theory starts with the Lagrangian L, which characterizes fields, their associated mass terms, and the interactions among the fields. The fundamental equations governing the evolution of the fields, and predictions for various observable quantities, can then be derived from a specific Lagrangian. We can also consider how the dynamics and predictions depend on the values of the parameters appearing in the Lagrangian, such as the mass terms and coupling constants in the interaction terms. This leads naturally to the idea of a theory space including all possible values of these parameters. Varying, for example, the mass term for one of the fields appearing in the Lagrangian would define a trajectory through theory space: a collection of Lagrangians with the same overall form but different mass values.

The renormalization group flow identifies a particularly significant set of trajectories. Renormalization refers to mathematical techniques that play an essential role in calculating observable quantities from a Lagrangian in order to control divergences. The initial Lagrangian includes “bare” parameters that have an unclear physical interpretation because they neglect the impact of interactions: for example, the mass term in the Lagrangian describes a particle as if it were propagating through empty space (the ground state of the quantum fields), even though the presence of the particle changes the ground state due to interactions. Initial attempts to calculate the effect of including interactions led to divergent quantities, such as infinite second-order corrections to the hydrogen spectrum in quantum electrodynamics. Eliminating these divergences required including counter-terms in the Lagrangian, such as shifting from the bare mass m₀ to a renormalized mass m_r: m₀ → m_r = m₀ + δm, where δm is the counter-term. (Similar corrections have to be made to both the fields and the coupling constants.) This procedure tames the infinities that plagued calculations of observable quantities. In the best case, a finite set of transformations from bare to renormalized values eliminates all of divergences that arise at higher orders in pertubative calculations.

Crucially, counter-terms such as δm depend on a cut-off scale l introduced as part of this procedure.⁹ The cutoff scale is usually taken to be at some energy scale much higher than all of the masses and interactions relevant to the observables of interest. Renormalization group equations follow from the further assumption that the values obtained for observable quantities are independent of the choice of l. To obtain the same predictions after shifting cut-off scales, l → l', the values of the various parameters appearing in the Lagrangian have to make compensating changes. The required changes are characterized by a set of differential equations governing iterative changes in the parameters as a function of l; solutions to these equations specify trajectories through theory space. Lagrangians lying along any given trajectory describe the same low-energy physics.

The behavior of the renormalization trajectories through theory space reveals the relationship between physics at different scales. Consider, for example, a collection of theories within a large region of theory space, given a cutoff scale l, representing diverse, conflicting descriptions of high-energy physics. If they all flow towards the same point, L₀, as the cutoff l is lowered, the structure of L₀, as well as any observed quantities that can be calculated based on it, are remarkably robust to changes in high-energy physics. The theory L₀ captures the universal low-energy physics for the entire region of theory space we started with. The convergence of trajectories on a single low-energy theory makes manifest the decoupling between high- and low-energy physics.

We can also use this framework to understand failures of naturalness such as the Higgs mass. For a scalar field like the Standard Model Higgs, renormalization contributes a correction term to the mass that scales quadratically with the cutoff scale—that is, $\delta m_H^2\hspace{0.17em}\approx \hspace{0.17em}{l}^2$. (The case of the cosmological constant is even more dramatic—it scales as l ⁴!—but there are further questions regarding how to treat the coupling to gravity (see Koberinski and Smeenk 2023).) As a consequence, the low-energy theory is remarkably sensitive to detailed features of the high-energy theory. The behavior is just the opposite of the case described earlier: trajectories through points that differ by an incredibly small amount in theory space, for a specified high-energy cut-off, diverge rapidly and lead to very different low-energy theories. If we set the cutoff at the Planck scale, the counter-term $\delta m_H^2$ would need to cancel out the bare mass to roughly thirty-four orders of magnitude to yield the mass of the Higgs measured by physicists at CERN (the European Organization for Nuclear Research). Note that this is not a case of an incorrect prediction or logical inconsistency. It is possible to choose a value of the bare mass that delicately cancels the correction term to yield the observed mass. But the need to do so violates the assumption of naturalness, which holds that details of the low-energy physics should decouple from higher energies rather than exhibit such sensitive dependence on the precise parameter values and structural features at the cutoff scale.

This conception of naturalness is thus directly linked to the autonomy of physics at different energy scales. The plausibility and heuristic value of naturalness stem from this connection, which also explains why the failure to find evidence for the most plausible mechanisms to save naturalness have generated such consternation. Yet, the fragility or sensitivity of low-energy physics does not have such a direct link to fine tuning in the senses discussed earlier. The appeal to failures of naturalness by fine-tuning advocates relies on a distinct conception that has developed in the physics literature.¹⁰ This alternative treats naturalness along the same lines as other discussions of fine tuning, namely, that a model is natural if the parameters appearing in it are probable given some measure over the space of possible parameter values. This account starts with a possibility space consisting of “all viable theories of low-energy physics,” defined by varying not only the parameter values but also the symmetries and particle content of the theory. The aim is then to define a measure over this possibility space so that we can assess the probability of specific parameter values and support assertions regarding the likelihood of the observed parameter values if we imagine they are “chosen randomly.”

These two notions of naturalness are conceptually quite distinct. This is clear from the different verdicts they render on one popular extension of the Standard Model, namely, low-energy supersymmetry (Williams 2019). If it were to succeed, this proposal would exemplify restoring naturalness in the first sense. Yet, there have been active debates regarding whether it is natural in the second sense of being statistically favored in the space of low-energy theories. The reason for the contrasting verdict stems from the fact that, despite the confusing use of a single term, evaluating naturalness in the two different senses concerns distinct aspects of a theory and how it is situated in theory space. The second notion of naturalness requires “global” knowledge of the entire space of possible low-energy theories in order to first delimit the relevant possibility space and then introduce a meaningful and well-justified measure over the space. By contrast, the first notion focuses on the sensitivity of a specific theory to variation in parameters, and this sensitivity can be evaluated based on “local” knowledge restricted to the theory under consideration. Obtaining global knowledge of theory space is far more challenging, as illustrated by ongoing debates regarding swampland conjectures, which hold that apparently viable low-energy theories are not in fact compatible with theories of quantum gravity. Whether these conjectures are true or not, they reflect the difficulty of delimiting the probability space, to say nothing of justifying a measure over that space. The sensitivity of a given theory to small variations does not, by contrast, require anything like this kind of structural knowledge of the entire theory space.

Fine Tuning of the Initial State

Standard Big Bang cosmology describes the universe as having expanded and evolved over 13.8 billion years from an initial state. Although there is no “first moment” of time, we can take the physical state at the expected boundary of the domain of applicability of general relativity as the “initial state.” The initial state in the Big Bang model must have several features. It must be isotropic to remarkably high precision, to be compatible with the uniform temperature of the observed cosmic background radiation; have total energy density extremely close to the “critical” density, such that measurements of the energy density now are still close to this value; have the density fluctuations needed to provide the seeds to form galaxies and other structures through gravitational enhancement; and so on. From the standpoint of general relativity, these features all trace back to the contingent distribution of mass-energy, and gravitational degrees of freedom, at early times. The dynamical equations govern subsequent evolution but place weak constraints on allowed initial states.

The Big Bang model uses the Friedmann-Lemaître-Robertson-Walker (FLRW) expanding universe models, even in describing the very early universe. These models have maximal symmetry: they represent the universe as a sequence of spacelike surfaces of constant curvature, with one of three possible geometries, labeled by cosmic time. This dramatically simplifies the complex nonlinear dynamics of general relativity. Yet, because of this striking simplicity, they differ from what one might expect to be a “generic” or “typical” cosmological model. Roger Penrose has estimated that the probability of choosing an approximately FLRW initial state “at random” from the space of possible states allowed by general relativity is 1 part in $10^{10^{123}}$, an extraordinarily small number (Penrose 1989, and in several subsequent discussions). He often accompanies this estimate with a figure illustrating a Designer who has to carefully pinpoint a region corresponding to the observed initial state, an incredibly small volume in the phase space of allowed models. A random choice (with the chance of being realized weighted according to phase space volume) would be expected to yield an equilibrium state. The difference between the maximal entropy—based on heuristic arguments from black hole thermodynamics—and the entropy of the observed state, far from equilibrium, is used to estimate the ratio of respective volumes, leading to the dramatic probability estimate.¹¹

Does this special initial state cry out for an explanation? Physicists have considered different responses similar to those above. C. B. Collins and Stephen Hawking (1973) offered an anthropic explanation: to the question “Why is the Universe Isotropic?” (the title of the paper), they responded, “[B]ecause we are here,” following theorems regarding the growth of anisotropies in cosmological models. (In slightly more detail: if galaxies and other structures necessary for the existence of life exist only in the subset of models that tend to become increasingly isotropic, we should not be surprised to observe isotropy.) Another possibility is to introduce principles that single out a unique initial state for the universe. There is also a modern analog of Bernoulli’s approach. Alan Guth (1981) proposes that a modification of early universe dynamics, inflation, would make it possible for a “typical” early state to evolve into a state compatible with observations. This approach to explaining the observed early state of the universe has been enormously influential.

Formulating the problem this way depends on a particular understanding of the measure defined over the phase space of a dynamical theory. For a system described using classical mechanics, its possible states are represented as points in a phase space Γ. Each point in this space completely represents the system’s properties. The system’s dynamical evolution describes how its state moves through phase space over time and is given by a map D(t): Γ → Γ (for elapsed time t). The phase space has a structure that supports an intuitive notion of “similarity” among these states. The topological structure of Γ allows one to define neighborhoods of a point, which can be thought of as the collection of nearby states reached by “arbitrarily small changes” to the system’s properties. There are many distinct exact states compatible with the same value of large-scale properties. These properties can be thought of, roughly, as dividing the phase space Γ into regions.¹² Given the phase space Γ and the dynamics D, there is a preferred measure μ, known as the Liouville measure, that assigns an analog of “size” to different regions. According to this measure, subsets of the phase space stay the same size under the dynamical flow.

The measure μ enters into techniques for calculating properties of equilibrium systems in statistical mechanics. It is natural that a probability measure would play some role in such calculations to reflect our ignorance of the system’s exact state. Consider a property Q that holds if and only if the exact state of the system falls within a region of phase space Γ_Q. Roughly put, the probability this property holds, in equilibrium, is given by the fraction of the available phase space (compatible with external constraints, such as constant energy) occupied by Γ_Q.

Some textbook discussions suggest that the “principle of indifference” justifies taking phase space volume to represent the probability that a typical system will have a particular property. But there are good reasons to reject this proposal. First, as briefly noted earlier, is the well-known problem that the “indifferent” assignment of probabilities depends on how the problem is described. Second, this proposal would offer a much more sweeping justification of probabilities than actually provided by statistical mechanics. Equilibrium probabilities can be reliably used to estimate, for example, the properties of systems that have been evolving over time scales that are long compared to the time required to relax to their equilibrium state, with dynamics that effectively “erase” the imprint of earlier states. Determining when equilibrium probabilities can be used relies on models of the approach to equilibrium. The details of how this justification works are subtle and still a subject of some dispute. But my claim—that dynamics plays an essential role in this justification—does not depend on these finer points.

Turning back to the case of cosmology, can we construct an appropriate phase space measure to evaluate fine tuning of the initial state? General relativity can be formulated as a dynamical theory, similar to that described earlier. In this Hamiltonian formulation, the evolution of the gravitational field is described in terms of two variables: a spatial metric, which specifies the geometry on a three-dimensional surface, and the extrinsic curvature, which characterizes how the surface is embedded in the four-dimensional space-time. These quantities can be used to define analogs of position and momentum in the case of particle mechanics, leading to a phase space Γ.¹³ Gary W. Gibbons, Stephen Hawking, and John M. Stewart (1987) carried out this construction for a specific type of cosmological model (FLRW models with a scalar field), leading to a phase space equipped with a measure μ_GHS.

Would this measure be of any use in determining what is a “typical” initial state? Does it give the probability that the actual universe has a particular property? I argued earlier that in the case of statistical mechanics, whether the measure can be successfully applied depends on the dynamics governing the approach to equilibrium. To the extent this problem is understood for this case, the results are not encouraging. For example, the dynamical relaxation time for large-scale gravitational degrees of freedom, such as density perturbations at cosmologically relevant length scales, is estimated to be on the order of the current age of the universe. Unlike the systems that statistical mechanics is typically applied to, there is thus no reason to expect the gravitational degrees of freedom on cosmological scales will have sufficient time to equilibriate, so that μ_GHS can be applied. (A more challenging obstacle arises because the phase space has infinite measure; as a result, probabilities depend upon the choice of a regularization scheme.)

Penrose has emphasized a distinct problem with taking any such measure to provide guidance regarding the initial state (see Penrose 1989, as well as Albrecht 2004, Wald 2006, and Wallace 2023). There are a wide variety of physical processes that exhibit an arrow of time. Although evolution in either temporal direction is possible according to the underlying laws, we only observe processes unfolding in one direction. The existence of such an arrow constrains possible initial states. A “randomly chosen” initial state, such as that supposed to obtain by many early universe theorists, is expected be in equilibrium (or close to it). But, as Penrose emphasizes, it is then not obvious whether thermodynamic asymmetry could arise. He argues instead that the initial state must have extremely low entropy, and hence small phase space volume. (This is often called the “Past Hypothesis.”) He further proposes that quantum gravity may enforce this restriction on the initial state through an explicitly time-asymmetric fundamental law.

Although there is much more to be said here, this line of argument raises the following worry related to the FTA. The standard way of thinking about fine tuning the initial state may suffer from an illusion of contingency. How should we conceive of the space of “possible cosmological models” in order to pose questions about whether the observed universe is “improbable” or remarkable? If we take general relativity alone as the basis for defining the space of possible models, we will certainly overestimate how many models are possible, and hence incorrectly draw the line between contingent and necessary. We know much more about physics and cosmology than what is captured in this space of models, and the requirement that a cosmological model can incorporate other aspects of physics will presumably restrict the space of possible models further. Rather than looking for new theories free of fine tuning, we should investigate whether what we already know imposes unexpected constraints on the space of possibilities. The need to impose the Past Hypothesis as a constraint on boundary conditions is simply the most striking form of this kind of restriction. Some form of the Past Hypothesis is needed to ensure the fundamental dynamics are compatible with macroscopic thermodynamic asymmetry, but there may be other restrictions imposed on the space of possibilities for similar reasons. What strikes us at first as an arbitrary, implausible, and finely tuned “choice” about features of the initial state ends up looking instead like a condition for the applicability of various aspects of physics.

The advocate of fine tuning may continue to press her case: Does the success of physics itself not cry out for an explanation? Perhaps, but this argument would not play the role I suggested for the FTA—namely, persuading an empiricist wary of this rationalist demand.

Conclusion

We have revisited a common theme in discussions of fine tuning: What does it mean to say the value of a particular coupling constant, or the initial state of the universe, is “improbable”? While we can treat the value of the parameter, or the initial state, as part of a larger possibility space, and construct a measure over that space, I have argued here that these ways of introducing probability do not have the same status as other probabilistic claims in physics. Recognizing the contrast between the distinct uses of probability undermines the attempts to use ideas from the foundations of physics to support the design argument.

In making this case, I have developed two related lines of argument. Contemporary advocates of the design argument have claimed to make common purpose with physicists concerned about naturalness and the remarkable fine tuning of the initial state. But I have argued that, first, despite several similarities, there are significant conceptual gaps between these discussions in physics and the probabilities invoked in FTAs. The attempt to ground such probabilities in physics fails. Naturalness in the sense of scale autonomy is conceptually distinct from statistical typicality; cosmological measures do not provide a way to assess the probability of the initial state, and there exists no unique, physically motivated measure over the possibility spaces appealed to in FTAs. Roberts’s reformulation makes this disconnect explicit: the relevant probabilities concern not physics but rather claims about what a Designer can plausibly regard as aim worthy.

Second, what appears as fine tuning may be better understood as an illusion of contingency arising from incomplete theoretical understanding. The historical case of Newton and Bernoulli proves instructive: features of the solar system that seemed to require delicate fine tuning lost their status as contingencies once they were embedded in a more complete account of stellar and planetary formation. Similarly, Juhl’s insight about causally ramified phenomena suggests that sensitive parameter dependencies should be expected, not surprising, given the success of physics in providing integrated explanations across multiple domains. The dense web of constraints arising from requiring consistency across different areas of physics, from nuclear physics to chemistry to astrophysics, necessarily restricts what might initially appear as free parameters.

These arguments have further methodological implications. For physics, they suggest that unnaturalness and parameter sensitivity, while important for theory development, should not be interpreted as requiring other forms of explanation, such as design, or even necessarily pointing toward new physics that eliminates these features. The history of physics shows repeatedly that apparent fine tuning can result from taking too narrow a theoretical perspective. In addition, the failure of FTAs to justify probability assignments over parameter values does not undermine physics itself, which never required such assignments for its empirical success. More positively, the remarkable success of physics in explaining the complexity we observe should reshape our understanding of how physical theories work. In particular, we should not presume the laws bear the entire explanatory burden and regard the need to make substantive assumptions about parameters or initial conditions as revealing a failure or limitation. The intricate dependencies between fundamental parameters reflect the stringent requirements for a consistent, empirically adequate description of nature that provides an integrated account of a wide range of phenomena. The features needed to ensure this success may in fact reflect deeper structural connections that appear contingent only when viewed from the narrow perspective we have to adopt in developing our theories.

With regards to philosophy, this article began by asking whether FTAs can play a role in convincing empiricists, who do not share rationalist demands, of the need for design or some other form of explanation. FTAs fail to do so, insofar as they require prior metaphysical commitments about the nature of probability, possibility, and explanation that an empiricist need not accept. Nothing I have said settles the more fundamental question of whether the universe’s properties ultimately require explanation beyond what physics provides. The more modest conclusion is that FTAs fail to make the case that we need other explanatory resources in a way that should compel those not already committed to such a conclusion.