3.1. Statement of the view

The first nontheistic alternative is the simulation hypothesis: our universe is a computer simulation, and our physics is fine-tuned for life because the programmer(s) designed the simulation to be that way. Chalmers (Reference Chalmers2022) makes the point that such a simulator is a “god that even a naturalist can believe in” (p. 135). Is this hypothesis—simulation, for short—more plausible than RT? Mizrahi (Reference Mizrahi2017) argues that several criteria for comparing theories suggest that simulation is superior: testability, coherence, and simplicity.Footnote ⁷ The criteria at issue implicate not the likelihood of fine-tuning given either hypothesis, but their prior probabilities. With the odds form of Bayes’ Theorem in mind, one can see that if the likelihoods are equal, but the ratio of the priors favors simulation, then it will follow that the posteriors favor simulation:

(4) $$ \mathrm{P}\left(\mathrm{RT}|\mathrm{F}\right)<\mathrm{P}\left(\mathrm{simulation}|\mathrm{F}\right). $$

3.2. Assessment

Fortunately, we need not go through each of Mizrahi’s criteria because the simulationist faces a dilemma: either (i) embrace a hypothesis that may have a non-negligible prior probability but cannot explain fine-tuning, or (ii) shift to a hypothesis that can explain fine-tuning, but that has both a low prior and a low likelihood. Chalmers (Reference Chalmers2022) is correct that while “[t]oday’s VR and [augmented reality] systems are primitive….[t]hese temporary limitations will pass” (p. xiii). Imagine plugging yourself into something akin to the Matrix and entering a world indistinguishable from your prior experience. It does seem that upon reentering the “real” world, you might begin to wonder whether this world, too, was a simulation. Thus, our technological capacity, even if not yet fully realized, motivates a non-negligible prior for simulation. But then, consider two versions of that hypothesis:

1. 1. Our universe is a simulation within a world that instantiates fine-tuned physics.

2. 2. Our universe is a simulation within a world that instantiates non-fine-tuned physics.

Which one does the simulationist propose? Hypothesis (1) will not help. If the unsimulated world has our physics, then that world will be fine-tuned for life. So, while simulation on this interpretation could in a sense explain local fine-tuning (of our simulation), it could not explain global fine-tuning and is therefore beside the point.

But suppose the simulationist advances (2). The problem is then twofold. The first issue is that the likelihood of F given (2) is low. How might we go about arguing that agents in a universe of alien physics would likely produce simulations that give rise to observers such as ourselves? Any inductive inference from our preferences to theirs is extremely thin. For all we know, such simulators did not evolve via Darwinian means. On what basis could we then extrapolate from us to them, from our preferences to theirs? Consider Chalmers’s (Reference Chalmers2022) claim that “people who run simulated universes will often be more interested in universes that contain life than in universes that don’t” (pp. 131–132). That contention is plausible if by “people” one means Homo sapiens. But that substitution will not work in this context. Even supposing we can get sufficient grip on the psychology of our simulators to claim that they would want a life-permitting simulation, a different problem arises. It is likely that they would design a simulation mirroring the mathematical framework of their own physics. Why? Because copying a framework of physics known to work at generating and housing observers at a high level of granularity seems far easier than creating a new physics from scratch. So, either the likelihood of F given (2) is low, or (1) becomes far more plausible than (2).

The simulationist might reply by making their hypothesis more specific: our universe is a simulation within a nonfine-tuned world, generated by agents with a preference for life-permitting simulations and novel physics. But that revision leads directly to the second problem: a prohibitively low prior probability. The fact that we will (probably) reach the point of technological development where we can run simulations raises the prior on (1) far more than it does (2). Those capacities support the proposition that worlds with our physics produce simulations. But worlds with our physics are fine-tuned. For our future simulation capacities to increase the plausibility of (2), we would have to encounter very specific simulations: those (a) in which the physics differs from our own, (b) that allow for observers, and (c) that are not discernibly simulations. That third condition is crucial: video games often feature different physics, but at a level of detail that quickly breaks down upon closer inspection. At present, we have no reason to think that these conditions will obtain. Moreover, it is far from clear that there are any other law structures aside from our own that allow for complexity and life. Barnes (Reference Barnes2019, p. 1231) writes that we have “zero examples” of laws that do not require fine-tuning to permit life. Collins (Reference Collins, Craig and Moreland2009) details several ways in which the “laws and principles of nature themselves have just the right form to allow for [life]” (p. 211). All our forays into the space of alternative mathematical structures have found laws that either do not permit complex life, or do allow it but at the expense of fine-tuning.

In short, the simulation hypothesis, to function as an explanation for fine-tuning as such, must tack on increasingly ad hoc claims. By contrast, as will become clear below in my discussion of cosmopsychism, RT is a simple hypothesis, consistent with the existence, or lack thereof, of life-permitting physics beyond our own. All other things being equal, we ought to prefer RT to simulation.Footnote ⁸

4.1. Statement of the view

Continuing our tour, Goff (Reference Goff2019) contends that the universe designed itself and that this hypothesis is superior to RT. Here Goff advances teleological cosmopsychism, the view that “the universe can be deemed an intelligent, rational agent with its own first-person perspective” (Cawdron, Reference Cawdron2024, p. 152). The universe can see that some courses of action are more objectively valuable than others, and it pursues the maximal amount of value that it can. Note that cosmopsychism is a form of panpsychism, the view that consciousness is ubiquitous in the universe.Footnote ⁹ Physical laws are fine-tuned for life because the universe recognized that it would be good for life to arise, and it chose values for the constants that allowed that possibility to unfold. Call this hypothesis universe. Applying Eq. (1), Goff seeks to establish that

(5) $$ \mathrm{P}\left(\mathrm{RT}|\mathrm{F}\right)<\mathrm{P}\left(\mathbf{universe}|\mathrm{F}\right). $$

Inequality 5 follows, not because the likelihoods favor universe over RT, but because facts beyond fine-tuning show that the prior probability of universe is higher than RT: the problem of evil, and considerations of simplicity.

4.2. Evil and suffering

Goff contends that universe explains evil and suffering better than RT. In particular, Goff (Reference Goff2023) argues for the cosmic sin intuition, the claim that “it would be immoral for an all-powerful being to deliberately create a universe like ours” (p. 91). He offers a few thought experiments to bolster that intuition, but consider just one: the utilitarian doctor who kills one patient so that they can harvest their organs and thereby save five more. It seems clear that such a doctor would be immoral. He would be violating the rights of the first patient. Similarly, even if a world with evil and suffering is better overall than one without, God would be violating our rights by subjecting us to that suffering.

This contention faces two substantial objections.

Evil is evidence against cosmopsychism. Even granting that evil is evidence against RT and therefore the prior probability of RT is low, evil is also evidence against universe. Goff recognizes the problem: if the universe seeks to realize value, why is there so much disvalue? His answer is that the laws of physics place “quite severe constraints as to what [the universe] is able to do” (Goff, Reference Goff2023, p. 131). The universe is not omnipotent but can only work within the mathematical framework that physical laws provide. But this qualified hypothesis does not avoid the problem. A cosmic agent could have reduced the total quantity of suffering in our universe without contravening the laws of physics. A world where the Holocaust did not happen, for example, is consistent with physics.Footnote ¹⁰ Goff may reply by further restricting the universe: perhaps the cosmos can only control its constants, not its initial conditions, the state of the universe at $ t=0 $ .Footnote ¹¹ If we accept determinism, then once the constant values are in place, the universe can do nothing to alter subsequent events. But Goff himself rejects determinism.Footnote ¹² Indeed, Goff’s account just is the claim that the universe freely chooses life-permitting values for its constants. Goff would therefore have to contend that the universe is free prior to the Planck time, but determined thereafter, an implausible and unmotivated bifurcation.

But even setting that point aside, these stipulations are ad hoc. Borrowing an illustration from Hildebrand (Reference Hildebrand2023), if I flip a coin 10 times, I will come up with a specific sequence S of heads and tails. S had a very small probability of coming up randomly: roughly 0.1%. Given that sheer improbability, is S evidence, say, that demons meddled with the coin toss? No. A demon seems equally likely to prefer any string of heads and tails. The likelihood of S given the demon hypothesis is identical to that likelihood given chance: 0.1%. But of course, we could make the hypothesis more specific: a demon, who prefers sequences like S, meddled with the coin toss. S is now more likely under the demon hypothesis than an appeal to chance. However, in moving from the general to the specific demon hypothesis, we have merely shifted the improbability of S given “general demons” to the prior probability of “S-preferring demons” itself. For every possible sequence of heads and tails, there is a specific demon hypothesis that predicts that sequence. Therefore, P(S-specific demons) = P(S | general demons). A similar shifting of improbability goes for universe and the added stipulations required to make it cohere with evil and suffering.

Moreover, exempting initial conditions from the cosmos’ influence is self-defeating because several such conditions are themselves fine-tuned. We need not delve into the physics, but many claim that both entropy—the amount of disorder in the universe—and Q-uniformity—the fluctuations in the mass/energy density of the early universe—are fine-tuned for life. Barnes (Reference Barnes2012) writes that “the fact that the entropy of the universe is not at its theoretical maximum, coupled with the fact that entropy cannot decrease, means that the universe must have started in a very special, low entropy state” (p. 538), reporting later that Q-uniformity’s “value is… $ 2\cdot {10}^{-5} $ , meaning that in the early universe the density at any point was typically within 1 part in 100,000 of the mean density” (p. 543). Were the magnitude of these fluctuations slightly smaller or larger, either no galaxies would have formed, or else supermassive structures would have coalesced and collapsed into black holes. Either way, no life. But in this case, universe can no longer explain fine-tuning.

Of course, Goff is free to amend universe, perhaps postulating that the cosmos is past-eternal and that the initial conditions vary from epoch to epoch. In that case, “the patient cosmic mind waits until the state of the universe is such that it can bring about life by tweaking the values of certain cosmic constants.”Footnote ¹³ But this reply just reinforces universe’s ad hoc nature. If the cosmic agent can alter physical constants but not conditions within the universe, a task that seems inherently easier, why is that? This strikes me as a contrived, “just so” response developed to save universe from a corresponding problem of evil. Goff’s hypothesis increasingly resembles “specific demon” hypotheses.

Goff’s case for a cosmic sin intuition is not decisive. Although I suspect many share Goff’s intuition that an all-powerful being would be immoral for creating our universe, we have to be careful not to move directly from a human sin intuition to the divine case. It would be wrong for any human being to create a universe like ours. A simulator would have to answer for their dereliction in allowing our suffering, for instance. But what about an all-powerful, all-knowing, perfectly good being? Though one might think the latter even worse for creating our cosmos—they know exactly what will follow from their choices, and they have the ability to do otherwise—things are not so clear. Durston (Reference Durston2000) contends that any historical event “can lead to an exponentially increasing number of consequences, affecting an increasing number of causal chains” (p. 65). For any occurrence x, we do not know what alternative timeline would have resulted were x not to have transpired, a limitation that hinders our ability to assess for any x that it is pointless or gratuitous. Of course, Durston’s argument faces objections.Footnote ¹⁴ In general, the debate surrounding the problem of evil is complex, nuanced, multifaceted. For that reason, I doubt that a one-off appeal to intuition could settle it. Indeed, the utilitarian doctor thought-experiment supports my point. Chan and Chan (Reference Chan and Chan2024) point out that it is easy to come up with scenarios where subjecting someone to suffering, or even death, for the benefit of others is morally permissible. For instance, imagine that “killing an innocent baby is necessary to saving the human lives of [New York],” or even when doing so “is necessary to [save] the whole human species from perishing” (p. 215). In both cases, someone would not be acting immorally by killing the baby. On this count alone, Goff’s argument for the cosmic sin intuition fails.

4.3. Simplicity

Goff (Reference Goff2019, p. 106) also suggests that RT (i) is more qualitatively complex than universe, postulating a nonphysical God in addition to the physical universe and (ii) breaks up the world into natural and supernatural categories, leading to a less unified view of reality than what cosmopsychism affords us. Thus, RT has a lower prior probability than universe.

Like Goff’s first contention, the simplicity argument for universe has two flaws. First, there are several respects in which universe is a complex hypothesis. Chan and Chan (Reference Chan and Chan2024) emphasize that cosmopsychism “postulates more distinct and independent brute facts than theism” (p. 207), each of which lowers the prior probability of universe relative to RT by multiplying improbabilities: the existence of physical laws, the existence of the universe, and limitations on the universe’s power. Our analysis above adds several items to their list: a capacity to affect constants but not initial conditions nor future states of the universe, and a truncated kind of free will consistent with the prior stipulation. Indeed, there are at least two more stipulations that universe requires.

i. Objective value. Goff’s account is committed to value realism. The universes chooses life-permitting values because life is valuable. But universe has to postulate the existence of the cosmos and objective value separately, thereby increasing its complexity. It is true that the theist is also committed to value realism, but they need not posit fine-tuning and value separately. According to one way of relating God and value, God is goodness itself. Baggett and Walls (Reference Baggett and Walls2011) contend that God is morality’s “exemplar, perfect standard, ultimate paradigm, and final source” (p. 94), and they go on to defend the plausibility of this analysis from several objections. As for why a theist might accept this metaethical view, Craig (Reference Craig2008, p. 182) contends that if we understand God as the greatest conceivable being, then a being which is the standard of goodness is greater than one that conforms to an external standard. Theism thus has the theoretical resources to explain both the existence of value and the universe, thereby unifying phenomena in a way that cosmopsychism does not.

ii. The non-uniform physics of the early universe. When did the universe fine-tune its laws? Goff has to stipulate that the constants do not retain their values all the way back to t = 0 but took on their precise form during the Planck era, the first $ 1\times {10}^{-43} $ split second of the universe’s history. But consider Carroll’s (Reference Carroll, Dardashti, Dawid and Thebault2019) example of (i) general relativity and (ii) general relativity with the added stipulation that “Newton’s constant will suddenly change sign in the year 2100” (p. 307). While acknowledging that both theories have identical empirical consequences, the “second theory would be considered extremely unlikely, as it is unnecessarily complicated without gaining any increase in consistency, scope, or fruitfulness” (p. 307).Footnote ¹⁵ Goff’s required modification is just as ad hoc, and hence improbable, as supposing that the gravitational constant, G, will change its value in the year 2100. Swapping in 13.7 billion years ago for 2100 C.E. does not change the underlying logic. Theism, by contrast, allows for the uniformity of physics all the way back to $ t=0 $ .

Second, RT offers a less ad hoc, more unified account of reality than cosmopsychism. We have already seen how RT unifies physical and moral reality. Moreover, limitlessness is simple in a way that limitations are not. Swinburne (Reference Swinburne2010) points out that RT attributes unlimited power, knowledge, and goodness to God, and unlimited properties are simple. Compare the stipulation that the laws of physics apply everywhere versus the claim that they apply everywhere except for the Andromeda galaxy. The latter is more complex, and therefore less likely, than the former. Carroll’s point above is an application of precisely this insight. Finally, RT may inherit the simplicity we ascribe to universal generalizations in science, as Miller (Reference Miller2016) contends. Consider the claim that all electrons have mass 9.1 × $ {10}^{-28} $ g, a quantity denoted by $ {m}_e $ . The negation of that claim is not an equally simple rival but is instead a massive disjunction of alternatives: all electrons except for one have the same mass, all electrons save for two, save for three, and so on. Our evidence, that every electron ever observed has mass $ {m}_e $ , would be (almost) equally likely on many of these exception-riddled alternatives. If only one electron had a deviant mass, the chance that we would have detected that rogue electron is incredibly small. The fact that we nevertheless conclude that the universal generalization is more likely than the entire disjunction of alternatives—that is, we think the generalization is more likely than not—suggests that universal generalizations have a much higher prior probability than their ad hoc rivals. But then theism, the hypothesis that God has all powers, all knowledge, and the maximal degree of goodness, will be more intrinsically probable than the disjunction of hypotheses that stipulate limitations on a designer’s power, knowledge, or goodness.

One could, of course, deny the connection between simplicity and probability. But that reply is both implausible and a double-edged sword. It is implausible because, following Draper (Reference Draper2025), we can isolate two factors affecting a hypothesis’s intrinsic probability: modesty and coherence. The former concerns a hypothesis’s specificity—how much it says about the world—while the latter denotes how well the various components of a hypothesis inductively support one another. The lower the modesty and coherence—factors that typically correlate with intuitive notions of simplicity—the lower the probability. RT is far more coherent than universe. Draper’s analysis is prima facie plausible, and a flat denial of the relevance of coherence and modesty to probability is unmotivated.Footnote ¹⁶ But more importantly: the sword will cut both ways. If greater simplicity is no indication of greater likelihood, then even if universe were simpler than RT, that would not make it more likely to be true.

In short, Goff’s arguments for universe’s higher prior fail. While I agree that RT splits reality into natural and supernatural categories, it also unifies the moral and physical domains in a way that universe does not. Insofar as unification factors into prior probability, cosmopsychism has no clear advantage. Moreover, while it is true that RT is the more qualitatively complex of the two, that factor is only one of several that determine the simplicity of a theory. Given that Goff’s hypothesis so outstrips RT in terms of the ad hoc stipulations it requires to get off the ground, RT is plausibly simpler, all things considered.

4.4. Comparing theories

Even if we grant, then, that

(6) $$ \mathrm{P}\left(\mathrm{F}|\mathrm{RT}\wedge \mathrm{k}\right)=\mathrm{P}\left(\mathrm{F}|\ \mathrm{universe}\wedge \mathrm{k}\right). $$

Goff has not shown that evil and considerations of simplicity establish

(7) $$ \mathrm{P}\left(\mathrm{RT}\right)<\mathrm{P}\left(\mathrm{universe}\right). $$

I have in fact suggested a few reasons to think that the opposite is true: RT is simpler, and therefore more probable, than universe, even when we take account of evil. Thus, we may instead affirm

(8) $$ \mathrm{P}\left(\mathrm{RT}\right)>\mathrm{P}\left(\mathrm{universe}\right). $$

Indeed, Goff’s move to restrict a cosmic agent’s abilities to affecting the physical constants suggests that the ratio of the likelihoods will favor RT as well: RT can account for fine-tuning in initial conditions, thereby making the conjunction of all fine-tuning instances more likely than universe. In that case, Eq. (6) will change:

(9) $$ \mathrm{P}\left(\mathrm{F}|\mathrm{RT}\right)>\mathrm{P}\left(\mathrm{F}|\mathrm{universe}\right). $$

But then, if both the ratio of the priors and the likelihoods favor RT, we may combine those results with the odds form of Bayes’ Theorem set out in Section 2 and infer

(10) $$ \mathrm{P}\left(\mathrm{RT}|\mathrm{F}\right)>\mathrm{P}\left(\mathrm{universe}|\mathrm{F}\right). $$

Of course, Goff is free to amend his hypothesis to the stipulation that the cosmic agent is able to determine initial conditions as well as constants, but nevertheless cannot affect states of affairs later on in cosmic history. That hypothesis, universe+, would equalize the likelihood ratio and account for evil and suffering—but at the cost of even more added complexity. RT, I submit, looks quite parsimonious by comparison.Footnote ¹⁷

5.1. Statement of the view

Several philosophers defend axiarchism, the view that a fact or state of affairs x obtains because it is good that x should obtain. They often apply this framework to existence itself: there is something rather than nothing because it is good that there should be something.Footnote ¹⁸ In the present context, axiarchism thus defined proposes that the universe is fine-tuned for life because such an outcome is good—and that is all there is to it. Leslie (Reference Leslie2003) writes that “[a]n absence of all existents would be in a way tragic because there might have been a good situation instead. And a situation sufficiently good…could perhaps have an existence required not just ethically, but with creative effect” (pp. 160–161). The ethical requirement that good things exist is itself creatively effective. So long as we are willing to entertain objective value, we have all we need to account for fine-tuning, and even the existence of the universe itself.

5.2. Assessment

I contend that axiarchism is not so much wrong as it is incomplete. Compare the situation to RT: God crafted a life-permitting universe because life is good, and a perfectly good being would therefore not be unlikely to do such a thing. Whether one deems it a good explanation, one can at least see the explanatory mechanism at work. Similarly with respect to teleological cosmopsychism: the universe is fine-tuned for life because it chose to take on values that allow for valuable phenomena. Again, this hypothesis is at least minimally illuminating and complete. But suppose we delete the underlying mechanisms that “breathe fire” into the axiological considerations and just assert that the bare value of the universe alone explains why it exists. What does this mean? What explanatory material is left?

We can press this objection more precisely in the form of a dilemma: either axiarchism posits a causal relationship between abstract and concrete objects, or it does not. In either case, I will contend, axiarchism so construed has a very low prior probability, even if it matches RT in the likelihood it attributes to fine-tuning. These two options correspond to what Mulgan (Reference Mulgan2017) calls “substantive” and “formal” axiarchism.

Substantive axiarchism. Consider the first alternative: on this view, the abstract object goodness, or perhaps ethical requiredness, causes the universe to exist.Footnote ¹⁹ In some of his latest comments, Leslie expresses his view partly as the idea of “God conceived as a creative force” (Lougheed, Reference Lougheed2025, p. 5), suggesting a robust causal relationship. The problem is then that abstract objects are just not the right sort of thing to cause anything, much less bring the universe into being. Indeed, causal impotence is one way philosophers draw the distinction between abstract and concrete objects, a point that Falguera et al. (Reference Falguera, Martinez-Vidal and Rosen2022, Section 3.5.3) make well. Leslie (Reference Leslie2003) protests that “the fact of being square (an abstraction of a sort) can prevent a peg from fitting into a round hole” (p. 176). But this example fails to distinguish between properties and property-instances. The abstract property being square does not enter into a causal relationship with edges of the round hole; rather, the concrete property instance, the particular shape and dimensions of a particular square object, causally affect the world. At every point, one has a concrete–concrete causal interaction.

One might think moral knowledge poses a problem for the contention that abstracta cannot cause anything. Benacerraf (Reference Benacerraf1973) gave particular attention to the problem that “for X to know that S is true requires some causal relation to obtain between X and the referents of the names, predicates, and quantifiers of S” (p. 671). Now, if we think that there are objective moral facts and we, at least some of the time, know these facts, then we seem forced to conclude that moral facts can stand in causal relations to our moral beliefs.Footnote ²⁰

That implication, however, does not follow. We are presented with three jointly incompatible claims:

1. 1. We have knowledge of moral facts.

2. 2. In order for a person S to have knowledge of x, there must be some causal relation between x and S.

3. 3. There can be no causal relation between us and moral facts.

The objector affirms (1) and (2) and therefore denies (3), but we could instead affirm (1) and (3) and deny (2): the causal constraint on knowledge is false. Indeed, Huemer (Reference Huemer2005) writes that it “is easy enough to respond by rejecting the accounts of knowledge assumed in the [Benacerraf objection]. There are serious objections to [them]—not least of which is the very fact that they cannot accommodate a priori knowledge—and there are several alternative analyses of knowledge available” (p. 123), a point that Enoch (Reference Enoch2011, p. 157) makes as well. The question here is one of comparative plausibility, and it seems to me that (1) and (3) are more plausible than the stipulation that all possible knowledge must be mediated by a causal connection, particularly in the case of a priori knowledge. All this is to say: moral knowledge does not increase the plausibility of the substantive axiarchic picture.

Formal axiarchism. So, suppose that the axiarchist is not positing causal interaction between the abstract and the concrete. Instead, they contend that “this universe is actual because it is good that it be actual” and, moreover, “nothing causes this to happen” (Mulgan, Reference Mulgan2017, p. 5). But then, what are formal axiarchists proposing? Consider again the assertion that the universe exists because it is good that it should. We have seen that theists affirm that claim as well. But they add a causal mechanism (God’s will) that connects axiological value to existence. The former is the reason motivating God’s choice. But now, delete that causal story. Delete God. Delete any agent or object that acts on value-based reasons. It is unclear what kind of explanation remains. Another way of making the point: RT and cosmopsychism provide a link between value considerations and concrete existence; formal axiarchism does not, threatening to render it vacuous. Consider for comparison the assertion that the universe exists because it is logically possible that it exists. What would that mean? If someone combined this claim with Lewisian modal realism, according to which every logically possible world exists as a concrete spacetime, we might have something amounting to an explanation. But now delete modal realism. It is not clear what one is even asserting, much less that it is plausible. Indeed, Leslie (Reference Leslie2009) makes the point that “[l]ogical necessities look too ‘IFfy-THENny’. If there are bachelors who are cannibals then there are wifeless non-vegetarians but this cannot itself explain why such individuals exist” (p. 175). I agree, but then it seems that precisely the same point holds for ethical necessity or requiredness. If a loving family of five exists, then such a family is necessarily good. But the ethical necessity attaching to that state of affairs seems no more capable of explaining why the family exists than does the fact that it is logically necessary that the set of three kids added to the set of two parents must yield five people. So, while Leslie claims that creatively effective ethical requiredness “is not immediately absurd, logically absurd, like a creative power attaching to Three fives must make fifteen” (p. 177), the opposite is true: they appear equally problematic.

Mulgan (Reference Mulgan2017) cites the laws of logic as an analogy for axiarchic-type explanation. Imagine an impossible world $ \alpha $ where various contradictions are true or a world $ \beta $ where $ 2+2=5 $ . What prevents $ \alpha $ and $ \beta $ from being actual? A “natural reply is that there are logical requirements that constrain reality,” but of course, “[n]o thing causes [ $ \alpha $ and $ \beta $ ] not to be actual. Logical requirements play a different restrictive role” (p. 2). Similarly, perhaps axiological restrictions or “laws” delimit the space of possible worlds to those that are valuable, though not in any causal way. But the laws of logic will not help the axiarchist. Logical consistency is only a necessary condition for existence. The laws of logic do not determine that something exists, but only that if something exists, then it will be logically consistent. A creatively effective ethical principle, by contrast, would not merely delimit the range of possible worlds. Instead, the axiarchist is proposing that this law, by ruling out the empty world wherein nothing exists, is sufficient for existence. It is that implication that is so difficult to get one’s head around. It is true that both logical and axiarchic principles are constraints that rule out worlds—but the latter, by “ruling out” the empty world, goes far beyond the conditional constraints supplied by the former.Footnote ²¹

Leslie (Reference Leslie2003, pp. 174–175) counters that asking for deeper explanations here is akin to asking why pain is qualitatively worse than pleasure. There is no deeper reason beyond: it just is. But Leslie has at most provided an analogy for the axiarchist position rather than an argument for its plausibility. I grant that it is a mistake to ask for a mechanism that explains, for instance, why a certain felt quality is worse than another. But that point does nothing to show that it is a mistake to ask for that mechanism in unrelated contexts. In the case of qualitative experience, it is relatively clear that there cannot be a causal explanation for the relation involved. In the case of axiarchism, we do not have this intuition. So, while Leslie (Reference Leslie2009) claims that “there is absolutely no valid question of what could make the ethical requiredness creatively effective” (p. 181), I counter: it certainly looks like a valid question if anything does, in contrast to pain versus pleasure. That gives us grounds for rejecting axiarchism as the final explanation of existence.Footnote ²²

5.3. Comparing theories

I have suggested a sense in which theism provides a more satisfying explanation of fine-tuning than axiarchism. Goff (Reference Goff2023) cashes this insight out in terms of explanatory depth: RT is deeper than axiarchism. But how do we model “depth” in a Bayesian context? Taking a look at Eq. (1) and plugging everything in

(11) $$ \frac{\mathrm{P}\left(\mathrm{RT}|\mathrm{F}\right)}{\mathrm{P}\left(\mathrm{axiarchism}|\mathrm{F}\right)}=\frac{\mathrm{P}\left(\mathrm{RT}\right)}{\mathrm{P}\left(\mathrm{axiarchism}\right)}\cdot \frac{\mathrm{P}\left(\mathrm{F}|\mathrm{RT}\right)}{\mathrm{P}\left(\mathrm{F}|\mathrm{axiarchism}\right)}. $$

I now ask: where does “depth” factor in? I propose the following analysis: with respect to a body of evidence e, a hypothesis x is explanatorily deeper than a hypothesis y iff

(12) $$ \frac{\mathrm{P}\left(e|x\right)}{\mathrm{P}\left(e|y\right)}>\frac{\mathrm{P}(y)}{\mathrm{P}(x)}. $$

That is, the gain in likelihood must outweigh the cost in terms of priors. White (Reference White2005) explains that “[a]ll explanations must end somewhere, but some stopping points are more satisfying than others” (p. 6). We reject the trickster evil demon hypothesis precisely because this condition is not met; the gain in likelihood does not outweigh the prior improbability of demons with very specific preferences for sequences of heads and tails. The implication is that “depth” as such yields no new information that a proper application of Bayes’ Theorem does not already provide. Given that the likelihood ratio between axiarchism and RT is equal, the critical issue then comes into view: is it more likely that there are these creatively effective axiological requirements, or that God exists? Here, the axiarchist might contend that the prior odds will not favor RT. Both Leslie (Reference Leslie2003, p. 175) and Mulgan (Reference Mulgan2017, p. 5) contend that positing an immaterial God who brings the universe into being through sheer will is just as mysterious as appealing to axiological requiredness.

But the respective mysteries postulated by RT and axiarchism are not symmetrical. Formal axiarchism proposes a sui generis explanation, whereas RT’s explanatory appeal is familiar. Axiarchism offers no explanation for the link between value and existence; instead, it makes an opaque appeal to creatively efficacious metaphysical principles for which there is no deeper explanation. We know of nothing else like creatively effective axiology. Indeed, the claim that something exists because it is good that it should is difficult to comprehend. RT proposes that God designed the universe for life because doing so would be a good thing to do. God acts on the basis of reasons that we can specify, thereby illuminating the connection between value and existence through a familiar mode of explanation. We trade in personal explanations all the time. Why are my clothes folded? Because my partner tidied up. Why is the barista calling out my name in the café? Because I ordered a cup of coffee. Whatever implausibility we ascribe to God’s creating the universe out of nothing, moreover, will only worsen under axiarchism. In the latter case, we are to imagine the universe coming into being without even an efficient cause.Footnote ²³ Moreover, as I have contended throughout, RT is theoretically virtuous, simple in its postulate of a God limitless in power, knowledge, and goodness. I do not see a parallel argument for axiarchism.Footnote ²⁴

Given these considerations, I conclude that there are plausible grounds for preferring RT to axiarchism when confronted with cosmic fine-tuning.

6.1. Assessment

When Nagel speaks of teleological laws, what metaphysics does he intend? Clearly, divine voluntarism will not help the non-theist in this context, so we can distinguish three interpretations of laws: Humean, primitive, and dispositional.

Humean teleology. The view here would be that, as a matter of fact, processes in the universe evolve toward life and mind, and that’s it. I have sympathy for the intuition that a purely descriptive claim such as this explains precious little. But regardless of that general complaint with Humeanism as such, it is not clear that a Humean approach can make sense of teleology in the first place. Consider two claims: (1) the universe is fine-tuned for life, and (2) the universe tends toward life-permitting ends. Per Humeanism, what is the difference between (1) and (2)? It is difficult to see—in which case, the Humean spin on laws is not teleological at all but instead merely redescribes the thing to be explained: fine-tuning.

Primitive teleology. Perhaps instead we should think that laws, teleological or otherwise, do govern and constrain, but that we cannot further analyze them. They are instead primitive features of our ontology. Hildebrand (Reference Hildebrand2023) articulates the “axiom for primitive laws” as the claim that “[t]he locution ‘it is a law that’ functions as a modal operator axiomatized as follows: necessarily, for all statements p, $ \ulcorner $ it is a law that p $ \urcorner $ entails p. A primitive law, then, is just a primitive entity that makes the statement of law true” (p. 32). Chen (Reference Chen2024, p. 22) defends a “minimal primitivist” view according to which laws of nature (i) are primitive entities in our ontology, and (ii) govern by constraining the physical possibilities. Maudlin (Reference Maudlin2007), espousing a similar view, explains that by (i), one means that “[n]othing further, neither relations among universals nor role in a theory, promotes a regularity into a law” (p. 17). To illuminate (ii), Chen points to the laws of logic and axioms of mathematics to flesh out the governing relation between laws and the world. Truths like these constrain the world to conform to what is logically and mathematically possible; similarly, physical laws constrain the world to what is physically possible. In particular, perhaps there are laws that direct the universe toward various ends, like life and consciousness.

Primitive teleology, however, faces a specification problem. Goff (Reference Goff2023) writes that “[p]resumably the teleological laws could have pointed to anything” (p. 116). Let us distinguish two versions of laws:

1. 1. There are primitive teleological laws.

2. 2. There are primitive life-oriented teleological laws.

Recall from Section 2 that one estimate for the likelihood of fine-tuning (F) given chance is 1 part in $ {10}^{136} $ . If we grant that figure, Goff’s remarks suggest that the likelihood of F given (1) is also 1 part in $ {10}^{136} $ . That is, F is terribly unlikely given (1) because that hypothesis does not inform us about that toward which the laws are aiming. We made the same point when considering the “general” trickster-demon hypothesis and the S coin toss sequence.

But suppose we build into the hypothesis life-specific ends, as in (2). In that case, the likelihood of F given (2) is very high. The problem, however, is that, just like with the “specific” trickster demons, we have merely transferred the improbability of F given (1) to the prior probability of (2) itself. That is to say, now we will ask: against a background where we do not know if F obtains, what is the epistemic probability that there are teleological laws oriented toward life? It would seem that that probability is no different from the likelihood of F given (1): 1 part in $ {10}^{136} $ . From that epistemic vantage point, there could be a law directed toward any set of constant values. All this is to say: we gain nothing by building the evidence into the hypothesis, whether it be demons or teleology.Footnote ²⁸ Now, if a proponent of (2) adopts axiarchism, they can evade this problem.Footnote ²⁹ On this view, (2) obtains because it is good that it should, and there are metaphysical principles that guarantee good outcomes. The prior on (2) will therefore be non-negligible. But of course, now laws loses all motivation: if ethical requiredness can bring natural laws into existence, then we can dispense with the middle man and affirm the simpler axiarchic explanation for fine-tuning. The universe is fine-tuned for life because it is good that it should be. Laws reduces to axiarchism and thereby inherits all the problems explored above.Footnote ³⁰

Dispositional teleology. Dispositional teleology is the view that natural processes have in-built tendencies or capacities to unfold toward various ends. An acorn, we might say, has an in-built capacity to develop into an oak tree. Similarly, perhaps the universe has a capacity to develop toward good ends like life, consciousness, and reason. But here the point about explanatory depth manifests itself: what is dispositional teleology asserting? Notice that cosmopsychism also contends that the universe has a capacity to develop toward life. But it undergirds that point by explaining what that capacity consists in: the choices of the conscious universe itself. In the case of an acorn, we can analyze it under the microscope and see the complex molecular and chemical mechanisms that carry out the instructions encoded in its DNA for developing into an oak tree. But suppose we sever off that explanatory layer. Appeal to capacities within the universe then reminds me of Molière’s satire The Imaginary Invalid, wherein a medical student, when asked how opium causes sleep, replies that “opium has a dormitive virtue, whose nature it is to make the senses drowsy.” There may be something to this explanation, but it leaves much to be desired. A general appeal to tendencies within the universe strikes me in much the same way. Moreover, dispositional teleology does no better than primitive versions thereof in solving the specification problem: it seems that the universe could have had a capacity to evolve toward any particular end, life being only one of a vast range of alternatives.

6.2. Comparing theories

Under any interpretation of laws, it struggles to make fine-tuning more expected than appeal to sheer chance. The question will then be whether the same specification problem afflicts RT. Consider two versions of the design hypothesis:

1. 1. An agent designed our universe.

2. 2. A perfectly good, all-powerful agent designed our universe.

The problem with opting for (1) in our design inference is that it seems to have zero predictive power. Goff (Reference Goff2023) explains that “[h]owever the universe turns out, we could just say it was created by a designer who wanted to make a universe like that. This kind of very broad design hypothesis fits equally well with any evidence, and hence explains nothing” (p. 111). The likelihood of fine-tuning given (1) is the same as that likelihood given chance. But then, if we build more into our hypothesis to increase the likelihood of fine-tuning, we end up with a more predictive hypothesis—option (2). The issue then is that (2), RT, appears to have a very low prior probability. Wynn (Reference Wynn1993, p. 332) points out that there is only one way to be an infinite being, but there are many ways to be a finite being. Consider the many ways a designer might have limited power, for instance—able to create apples but not oranges, build a computer but not climb a mountain, “create bears but not badgers or butterflies” (Leslie, Reference Leslie2009, p. 175), and so on. But there is only one way to have unlimited power.Footnote ³¹

There are several things one might say in reply, but one will suffice: we have already seen that it is wrong to treat a limitless attribution as one value along with all limited or finite ascriptions in a probability distribution. In general, if uniformity is a priori more likely than variety, then RT, given its uniform and unlimited attribution of power, knowledge, and goodness to God, will be simpler, and therefore more likely, than any other specification of (1).Footnote ³²