According to (what I currently think is) the most plausible theory of intrinsic probability, there are three primary criteria which determine the prior of any given hypothesis:
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.
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.
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 might 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.
Great post. I'm more partial to Sobel's theory of intrinsic probability as outlined in Logic and Theism, but I think even on the theory of probability you outline here, Naturalism comes out ahead.
It's clear to me that Naturalism comes out on modesty. As Lorkowski points out in his 2013 article:
"The naturalistic position, in its simplest form, makes two claims, only one of which is unique: the natural world exists, and nothing outside of the natural world affects the natural world. The theistic position, in its simplest form, makes several claims: the shared claim that the natural world exists, and several unique claims, such as the claims that at least one supernatural entity exists, it has affected the natural world, this entity is personal, omnipotent, omniscient, morally perfect, and so forth. It, therefore, appears that the theistic position (or the relevant deistic position) must have a lower prior probability than the naturalist position due to the sheer number of assertions. The theist makes more unique claims and therefore has more ways to be incorrect. Setting aside the shared claim that the natural world exists, the only way that the naturalistic position can be incorrect is if there is at least one supernatural entity that has affected the natural world. The theistic position, on the other hand, can be incorrect in a numerous ways. Therefore, the prior probability of the theistic position is much lower than that of the naturalistic position." (Atheism, pgs. 524-525)
On Brute limitations you say Naturalism is disadvantaged in light of the fact that we can ask: "Why are these particular laws and physical structures instantiated, instead of all the other conceivable laws and physical structures which there might have been?"
But notice, this exact question arises for Theism as well. As Graham Oppy notes in his review of John Foster's "The Divine Lawmaker"
"....there are many different universes that God might have made: we are not to suppose that the existence of our universe is necessary. Furthermore, since God has libertarian freedom, there are possible worlds in which God makes those other universes. When we consider a particular regularity in our universe, the existence of that regularity is explained in terms of God's desire (or intention, or whatever) to make a universe in which that regularity is instantiated. Moreover, when we compare our actual world with a world in which God makes a universe in which some other regularity obtains, ex hypothesi, there is no explanation in either world of why God has the one set of desires (or intentions, or whatever) rather than the other. So, it seems, the naturalist is being asked to trade in (putatively) unexplained regularities in the universe for unexplainable desires (or intentions, or whatever) in God. I do not think that naturalists should accept this deal: if you really think that there must be a satisfying explanation for the holding of the regularities-one that does avoid unnecessary complexities and that minimizes residual sources of puzzlement-then you have very good reason to deny that Foster has found it. (pg. 115)
It seems that whatever considerations you raise about Naturalism in terms of brute limitations (i.e. questions about particular laws and physical structures), the same considerations can be raised in the context of God's choice of instantiating a world with those particular structures. J.L. Mackie put it best: "The particularity has not been removed, but only shelved; we should have to postulate particularities in God, to explain his choice of the particular universe he decided to create." (p. 100). And given that Naturalism comes ahead on modesty, a wash on brute limitations is ultimately going to disadvantage Theism.
On coherence, I think Naturalism has an edge as well. Almost all the properties of God (omnipotence, omniscience, necessary existence, etc) have been challenged in terms of their coherency by a wide variety of Theists and Atheists. Trying to save God's coherency, by invoking Divine Simplicity ironically makes things worse, because just ends up adding more contentious properties to your Theistic ontology (usually it's alleged that timelessness and immutability follow from ADS).
Thanks for the post! I personally do not see the need for an appeal to your third prong when assessing intrinsic probability. There are an infinite number of velocities at which the particles in worlds m and n could have been moving and each theory asserts a particular velocity and, in that sense, they are both equally modest. moreover, neither theory contains within itself more or less inductive support relations between its parts than the other so they also appear roughly equally coherent.
So here I don’t see the problem with saying they are equally probable intrinsically. Why should infinite velocity be understood as being more in need of explanation than any other particular speed? The idea seems to be that you are understanding infinite velocity as being a hard limit in the upward direction such that there is no possibility of an increase in velocity. But it’s not clear why that should matter. The difference here is only between where on the velocity continuum or range the particle sits. Theory n posits a particle with a particular velocity somewhere between the highest and lowest while theory m posits a particle with the highest. I’m having difficulty understanding what you are considering more brute, unexplained, or arbitrarily limiting about n relative to m.