- 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 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.
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