The Prior Probabilities of Theism and Naturalism

According to (what I think is) the right theory of intrinsic probability, there are three primary criteria which determine the prior of any given hypothesis:

1. Modesty: How little a hypothesis says about the world. 
• Example: "There is a living thing in my room" is a more modest claim than "there is a human being in my room," which in turn is more modest than "Richard Swinburne is in my room." More modest theories have more possible ways of being true: "There is a living thing in my room" could be true in any number of ways, "There is a human being in my room" in fewer ways, "Richard Swinburne is in my room" in only one way. Thus, more modest theories get a higher prior probability.
2. Coherence: How well the parts of a theory fit together, raising (or at least not lowering) one another's conditional probabilities.
• Example: "All Asian ravens are black and all non-Asian ravens are black" is a more coherent hypothesis than "All Asian ravens are black and all non-Asian ravens are white." (This is Draper's example.) Finding out that all Asian ravens are black increases the conditional probability that all of the non-Asian ravens are black, and vice versa. However, finding out that all Asian ravens are black reduces the conditional probability that all of the non-Asian ravens are white, and vice versa. So the parts of the first hypothesis raise one another's probability, while the parts of the second theory reduce one another's probability.
3. Brute limitations: Theories with arbitrary, inexplicable limitations should receive a lower prior than theories which lacks such limitations.
• Example: Consider two possible worlds, n and m. World n consists of a single particle moving at a constant finite velocity, while world m consists of a single particle moving at a constant infinite velocity. These two worlds seem to be equally modest and coherent: they both posit a single substance, behaving in a simple, uniform manner. Yet world m seems (to me at least) to be more intrinsically probable than world n. Why is this? The answer, I think, is that world n contains a brute limitation: why is the particle moving at the particular finite velocity that it is? Why not slightly faster, or slightly slower? World m, by contrast, has no such arbitrary limits. As such, it has a higher intrinsic probability.

(Note that this theory is largely a combination of Draper 2016 and Poston 2020.) It seems that if these three criteria are correct, then theism will always have an advantage over naturalism in terms of prior probability. The reason is this: the naturalist has to choose between coherence and a lack of brute limitations, whereas the theist can have both. Consider: if naturalism is true, then either every possible universe exists (i.e. there is something like a Lewisian multiverse), or else not. If not (i.e. if only one or some possible universes are realized), then the naturalist's theory will suffer from serious brute limitations. Why are these particular laws and physical structures instantiated, instead of all the other conceivable laws and physical structures which there could have been? Alternatively, if there is a Lewisian multiverse, then the naturalist's theory will avoid arbitrary limits, but only at the cost of an extreme lack of coherence (the Lewisian multiverse is just about the least uniform way that reality could conceivably be).

The upshot is that the naturalist faces an inevitable trade-off between coherence and a lack of brute limitations. The theist, however, faces no such difficulty: theism is both a highly coherent hypothesis (it posits a being with all possible perfections, which is a very uniform array of properties), and it is largely lacking in brute limitations (since God's properties are infinite). If all of this is correct, then it seems as though theism should get a relatively high prior as compared to naturalism.

Dispositionalism and Contingent Existence

[Note: Most of this post consists of fairly obvious observations about the consequences of modal dispositionalism; I just wanted to have this train of thought in writing somewhere.]

Critics of the cosmological argument will sometimes claim that while no contingent thing exists in all possible worlds, it might still be the case that all possible worlds contain at least one contingent thing. William Rowe provides the following analogy:

We know that although no horse in a given horse race necessarily will be the winner, it is, nevertheless, necessary that some horse in the race will be the winner. (1975, 164)

It turns out that dispositionalists cannot plausibly appeal to this possibility as a way of avoiding a necessary being. Here's why: either causal history is infinite, or it is not. If it is not, then the dispositionalist has very good reason to affirm the existence of a (set of) necessary being(s); see e.g. Vance (2014), Vetter (2015), and Kimpton-Nye (2021). So the dispositionalist who wishes to avoid a necessary being should assume that causal history is infinite. But, as it turns out, this strategy will not work either.

Let S be the plurality of all actually-existing contingent concrete things. (If nothing is necessary, then S will include all actually-existing concrete things.) Suppose that the cosmological arguer asks for an explanation of why the beings in S exist, and the critic gives the aforementioned reply that it is necessary for some contingent things to exist. But note that on a naturalistic dispositionalism, "every possible world contains some natural thing that actually exists... necessarily, every world contains some stretch of our actual natural past" (Leftow 2017, 326). This means that the critic's reply commits them to claiming that it is necessary for at least some of the beings in S to exist.

Is this reply at all plausible? I think not; after all, every being in S is contingent, and so fails to exist in some possible world. But it seems obvious that if x could fail to exist, and if y could fail to exist, then both x and y could jointly fail to exist; otherwise, we would have to suppose that x's nonexistence somehow forces y to exist, which seems implausible. As Vetter puts it, "the possibility, for each contingent object, that it does not exist, together with what we might call a principle of independence—that the non-existence of contingent objects can never force other contingent object into existence—yields the global possibility that none of the actual contingent objects exist" (2015, 275).

A further problem is that while the critic might claim that it is necessary for some of the beings in S to exist, there can be no particular beings in S which exist necessarily. This should be obvious merely from the fact that, as stipulated, S is the plurality of all actual contingent things; however, the point becomes more interesting when put in terms of branching causal histories. Recall that, as Leftow points out, the theory under consideration entails that "every world contains some stretch of our actual natural past" (2017, 326), which, given an infinite past-eternal universe, "would be an infinite stretch" (ibid., 326). However, this would not be the same stretch of our actual past; rather, different possible worlds would share different stretches of the actual past. To make the problem clearer: if causal history is infinite, then for any causal node n, there is an earlier node n-1. But this entails that there is no single node n which is part of the shared history of all possible worlds. Hence, the aforementioned critic of the cosmological argument must claim that it is a necessary truth that all possible worlds share a stretch of causal history with the actual world, but not any particular stretch. This does not seem like a very good explanation of the entire causal series. 

It is also worth noting that the naturalist dispositionalist is committed to claiming that "there could not have been other natural laws... [nor] could there have been a different total amount of mass-energy" (Leftow 2017, 325). Their view will also threaten modal collapse, since "If [this] theory is true and determinism is true, the actual world is the only possible world: there are no chancy causes, so there are no branches off the tree of actual history" (ibid., 326). Thus, on this view "we should take modal Spinozism precisely as seriously as we take determinism" (ibid., 326).

The upshot is that the dispositionalist must either admit that there is a (set of) necessary being(s), or else claim that it is a necessary truth that some actually-existing contingent things exist. Given that this latter claim seems extremely unlikely (if not flat-out nonsensical), entailing as it does many implausible consequences, it appears that the dispositionalist has strong reason to accept the existence of a (set of) necessary being(s).

A Convenient Way to Explain Metaphysical Modality

Consider the following question: could the laws of nature have been different?

According to physical modality, the answer is trivial: no, of course the laws of nature could not have been different. After all, physical modality just is the range of what is the modal space governed by the laws of nature.

According to logical modality, the answer is similarly trivial: yes, of course the laws of nature could have been different. After all, there is nothing logically incoherent about the idea that, say, the speed of light could have been slightly faster or slower than it in-fact is. 

Metaphysical modality, then, is that form of modality which renders non-trivial the question "could the laws of nature have been different?"