Theism Has A Super High Prior Probability

It's simple and elegant

I'm through accepting limits
'Cause someone says they're so

—Defying Gravity, from Wicked

(I had a thought along these lines a while ago, but it really solidified in a conversation with the excellent James Reilly—blog here).

When evaluating two theories of how the world is, one shouldn’t just look at how well they explain the data. The theory that a dragon rigged my deck of cards to give me ten royal flushes explains my getting ten royal flushes just as well as the theory that I’m cheating, but the cheating hypothesis has a much higher prior probability than the dragon theory. Thus, if we’re trying to determine whether theism is more probable than naturalism, we should look at the prior probabilities of both theories, meaning how likely they are before we look at any particular evidence.

Let me begin by addressing a common mistaken argument for why theism has a lower prior probability than naturalism. Often, people suggest that theism is, by definition, more complicated than naturalism because it posits all the stuff naturalists posit, plus some extra stuff. Because it just adds more stuff—a God and perhaps angels on top of the natural world—it is argued to be less parsimonious.

But simplicity has to do with the fundamental things that you posit, the things that aren’t explained by anything deeper. Suppose we’d already concluded that God exists. It would be foolish to say that God would create very little because the more stuff he creates the more complicated he would be. Once we think a God exists who has the power to create whatever he wants, it doesn’t add complexity to a theory to claim he made more things. If you think it did, then you should be a solipsist—you know your consciousness exists, and so anything beyond that is an extraneous posit. Similarly, on such a picture, if there are two theories and one says that a person drew a painting, and the other says the painting just exists for no reason, the theory that the person drew the painting would be worse, for it posits an extra person.

Therefore, if we want to look at the complexity of a theory, we should look only at the fundamental things it posits: the things it posits that aren’t explained by anything deeper. In the case of a theist, they will posit that the fundamental thing is God, while a naturalist will posit that the fundamental thing is some particles and laws governing the particles, or something similar—perhaps strings.

While I’m very uncertain about the nature of prior probabilities, I think there’s a powerful argument for theism having an astronomically higher prior probability than naturalism. Theism is simply, as I’ve explained here, the thesis that one of the fundamental things—either mind, goodness, perfection, power, value, or agency—exists without limit. If something is fundamental, then by definition, it’s the simplest sort of thing there is—it doesn’t reduce to anything deeper. The theory that one of the simplest things exists without limit is extremely simple—about as simple as a theory could be.

Naturalism, in contrast, is much more complex. It posits that the fundamental thing contains both particles and laws—two things of very different kinds, neither explained by something deeper, each much more complicated to describe than a being with an unlimited fundamental property.

More importantly, theism lacks arbitrary limits. Theism posits a God unlimited in power, knowledge, and goodness—a being with just a single fundamental unlimited property. Just as it’s much likelier that the universe is infinite in size than that it is exactly 4839789473928074839201789073421890473 meters across, and just as prior to empirically discovering a speed of light, we had no reason to expect there to be one, a theory that lacks inexplicable limits is better than one having inexplicable limits. Naturalism, in contrast, has inexplicable limits—particles of quite specific shapes following quite specific laws. Both the mathematical formalisms they follow and the structure of the particles are arbitrary.

For this reason, I think theism is simpler than naturalism and, more clearly, less arbitrary than naturalism. It totally dispenses with arbitrary limits. While you are left wondering, under naturalism, why the particles are, say, following the Shroedinger equation rather than some other equation, no such arbitrariness is present on theism.

I claim that this means that naturalism might have a prior probability billions of times less than theism.

To see this, first note that even slight increases in arbitrariness utterly tank the prior probability of a theory. For example, suppose we’re considering two theories. The first one holds that God is all-powerful, all-knowing, and all-good. The second theory posits that God is all-powerful, all-good, and knows everything except one fact. Even though there are infinitely more ways the second theory could be true than the first—for any of the infinite facts, on the second theory, he could not know that fact—it’s much less likely than the first. Thus, even though the theory that God knows everything except how many people got bitten by mosquitos last year only introduces one extra limit, it is infinitely less likely than the theory that there’s an omniscient God.

The general lesson of this is that even making your theory a bit more arbitrary generally makes it infinitely less probable. This isn’t the only case that bears out the principle. For example, consider the theory that somewhere in the universe, there’s a 1 foot patch where the laws of physics don’t work. That theory is much worse than the theory that there is no such patch, even though there are infinite ways there could be such a patch. Because there are infinite patch theories which together are less probable than the theory that there’s no patch, each particular patch theory—according to which at some specific location the laws of physics don’t work—is infinitely less probable than the no patch theory, even though it’s only a bit less arbitrary.

It’s not hard to think of many more similar examples. The theory of modal realism, that every possible world really, concretely exists, is much better than the theory that every possible world exists except one. The general takeaway: adding an extra arbitrary limit makes your theory infinitely less likely.

But if this is right, then theism might just be infinitely far ahead of naturalism. It has many fewer arbitrary limits—both in the laws, constants, and initial conditions. If extra arbitrary limits make a theory infinitely less likely, then the presence of many extra arbitrary limits would make naturalism have a prior infinitely lower than theism—of either zero or infinitesimal.

If this is right, then naturalism is doomed. And it seems right to me. Of course, you shouldn’t actually be certain of theism, because the argument might go wrong somewhere, and you should have different confidence levels inside and outside an argument. But still, if this is right, it’s bad news for athiesm. So…am I wrong?