A little more on miracles

Scott Alexander and Flying Lion With a Book continue to diss David Hume’s argument on miracles. I get where they're coming from, and I haven't read Hume's argument closely in a while so I don't want to exactly defend Hume. But, again, I want to stick up for something in the neighbourhood.

Let me start with a case where I think the Humean position feels pretty natural: the faster than light neutrinos that were observed a few years ago.

We had a natural law (relativity) that gave us a very low prior on observing things traveling FTL, and measurements that seemed to indicate that actually, something had traveled faster than light. Scientists had to decide: did they have more confidence in the measurement, or the theory? In this case, less confidence in the measurement. But, suppose the measurement had stood up. The obvious thing scientists would have done is... abandon the law! They would have said, "this phenomenon is good evidence that relativity isn't the whole story and whatever theory replaces it will probably allow for things going FTL, at least in certain specific circumstances".

Notably, no one would even consider the theory, "relativity is actually right, and nothing can go faster than light, but just this once the laws of nature were suspended"--even most theists would presumably reject this as a miracle, or as evidence of God... But why? The observation of FTL neutrinos would be something with a ~0% chance of happening under our best physical laws, so why not say, this is evidence against physicalism, not just evidence against our best physical theory?

Examples like this convince me that theists do actually get the pull of Hume's position, so I think it's worth drilling down into what's supposed to be different about miracles: in terms of which events we consider as candidates for non-Humean reasoning, and also what exactly the non-Humeanness is meant to actually consist of.

I'll take the latter point first: what exactly is non-naturalistic about a miracle? One question to ask is: do miracles operate through naturalistic means? Must the operation of a miracle be consistent with the laws of physics? Is mass/energy conserved? Is the miracle state of the world obtained by a unitary transform of the pre-miracle state? I think saying “yes” to these questions makes it difficult to say that the miracle wasn't predicted under naturalism: if the miracle happened in a way that didn't violate any laws of physics... then, why isn't that a naturalistic explanation of the miracle?

The only responses I can think of here all have a sort of "fine tuning" character: the miracle occurs according to the operation of the usual laws of physics, but it requires a measure-zero set of initial conditions to get such a miracle, so the ICs must have been fine-tuned to achieve this result.

I think this is reasonable but: strictly speaking, you're not performing a Bayesian update on p(event|naturalism), so that framing is wrong, and more importantly, this leads us into pretty murky waters about what we think about what the measure of the set of ICs that lead to "events like this" are.

But I think this is a viable option.

I also think you could imagine that the actual laws of physics are such that sometimes they don't actually have a unique continuation of a given solution up to some time, and so miracles are when God chooses solutions that are naturalistically available, but not naturalistically inevitable. I think though this ends up looking a lot like the previous case: it's still not correct to say the miracle was unlikely under naturalism, or at least, not without having a sense of what the other possible continuations looked like, and how likely they were each to occur without God intervening.

But on this way of thinking, Hume is still basically right: the miracle didn't violate the laws of nature; what's surprising is that the laws of nature produced this particular result, but that's an issue of fine-tuning, not really a miracle.

But anyway, given the way people talk about events being “hard to explain under naturalism” or the like, I don't think the above is what most miracle-proponents have in mind. The idea is that, in fact, the miracle-state is not just the unitarily evolved version of the previous world-state. The laws of nature were really broken. So, go back to the neutrino example: how come we don't just do what Planck does on seeing the violation of the Rayleigh-Jeans "law" of blackbody radiation, or Einstein on seeing the violation of the "law" of ether waves, and formulate a new law?

I think the answer is: miracle-proponents do want to propose a new law, they just don't want it be a law of nature. Unlike Einstein and Planck, they don't want to replace Naturalistic Theory A with Naturalistic Theory B, they want to replace Theories Should Be Naturalistic with A Non-Naturalistic Theory. Before turning to the question of when we should be willing to consider making this move (again, why weren't the FTL neutrinos a miracle?), I want to ask: what is a non-naturalistic theory of how the world works?

Theists like FLWAB give the analogy of computer simulation: suppose the simulation runs on a set of laws, but there are "backdoors" that the programmers have put in that can override the usual simulation laws. I think the Humean point of view is that upon seeing a violation of the simulation laws, the simulation-dwellers ought to decide that the simulation laws aren't actually the real laws of nature that govern them--and they're right to do so! The actual physical laws that govern them are our laws of nature, which determine how we build and operate computers, and determine how and when we intervene in the simulation. That is: there is a naturalistic explanation for the “miracles” that occur in a simulation, but they are formulated in the language of the base level.

I'm not sure what sort of constraints there are on stimulated beings learning about the base level; maybe it's impractical to ever learn the base level natural laws, and the best you can do is model it as “simulation-level natural laws, plus random interventions”, but the Humeans in simulation-world are actually right! The laws being violated aren't the real laws; the apparent miracles do conform with a deeper natural law--it's just too hard to find.

Again, I think this is basically fine, but I don't think that's what theists want from miracles. The point isn't that God is just a powerful simulator who is Himself bound by natural laws, it's that He stands outside natural law in some sense.

I'm not sure I understand what that sense is, but given how strongly theists want to contrast it with naturalism, I think they have to bite the bullets that come with this as a true alternative to naturalism, and not just a different flavour of naturalistic theory, as Hume would have it. It means that there is an arbitrariness at the heart of how the world works: the patterns we see aren't the real thing going on, they're just how God chooses to interact with us most of the time. The law of conservation of energy is false, unitary evolution of the state vector is false, and not in the “Newtonian gravity gives way to Einsteinian gravity” sort of way; the true theory is “energy is conserved when God wants it to be, and isn’t when He doesn't”.

Now, once again, I think this is something you can believe about the world but, to me this is bordering on radical skepticism: everything about how the world operates is actually rooted in God's will, which can override any pattern you foolishly think of as a law. To the extent we want to believe that any of the patterns we observe will continue to hold, we can only believe so on the basis of our theory of God himself: physics just becomes Divine Psychology.

I think this is a sort-of-tenable view of the world, but it's pretty extreme: I think it's no accident that people like BB have to have a metaphysics where the primary things are vague, poorly-understood concepts like “mind” in order to live in this space: it's deeply at odds with the scientific worldview, and requires a lot of, IMO, wishful thinking regarding the guarantees we can have about God and how much He's willing to deceive us to get anything off the ground at all, but if you're willing to root your entire understanding of the world in hazy metaphysical stuff, it's a live option.

But there's yet one more problem: BB and FLWAB and others still want physics to be possible. Yes, the laws of physics are fake laws that can be overridden at whim, but nevertheless we can rely on them for all practical purposes, perhaps because God is generous enough to override them only rarely. But this requires you to know when the laws of physics are being overridden or not! If your worldview is, “you can build an understanding of the world that obeys natural law that works for all events except those in the set S”, you have to know what is in S to avoid trying to learn about the world from the exceptions!

And I think this is the point where, even if you are a theist, you almost certainly want to remain a Humean for practical purposes. What do I mean? Suppose someone heals from a disease from which no one has healed before. A team of researchers arrives on the scene, ready to take blood samples, assemble a case history, and try and figure out how this person survived to see if there's anything that can be learned for other patients. But, then an anti-Humean shows up and says, “no, no, no... The odds of this healing happening under naturalism were basically 0; this is strong evidence that God intervened in a non-naturalistic way, and so whatever happened here isn't going to be something you can understand naturalistically. So you're wasting your time with your blood tests and cheek swabs; what happened here isn't replicable by the tools of science”. Should the doctors listen? I think the answer is a very obvious, “of course not!”. The doctors should say, “look, even if I buy the argument, and accept that maybe events can happen that don't accord with the implicate natural order of things--even then, unless those events come clearly labeled, I have no choice but to act as if any given event was indeed naturalistic”.

We're finally back at point 1: when should we be willing to entertain non-naturalistic explanations? Why couldn't Einstein have saved everyone a lot of trouble by saying, “my theory is that there is a luminiferous ether, but whenever you try measure it with an interferometer, God does a miracle to hide its effects”? My answer is: you should never assume non-naturalistic explanations when trying to understand the natural world. But the problem is, events don't come neatly labeled by whether or not we should try use them to understand the natural world. Every miracle healing is a potential opportunity to understand how to defeat a disease; every case of levitation is an opportunity to understand the physics of flight.

I think miracle proponents want to say that, the cases where they advocate for miracles are cases where there isn't any important information about natural law to be learned, but by the very nature of being events where something hard to square with naturalism happens, that can't be the case. Accepting a miracle means writing off your ability to ever explain certain phenomena naturalistically. Even if you think there are phenomena that can't be explained naturalistically, I hope it's clear that it's a huge cost to do that in specific cases: it's a license to ignore evidence.

So where do I come down on all of this, in the end? Well, I think my position is clear: the only alternative to Humeanism is a radical idealism that is very hard to keep from bleeding into radical skepticism, and even if you hold that view, you should be a Humean in any case where you're trying to learn about the natural world. Since, by hypothesis miracles are extremely rare, you should have a strong bias towards being a Humean in any given situation. A compromise position I can offer is that, while I think you should be Humean in any particular instance, I can imagine a view where you're Humean in particular but not in general: where for any given situation you only consider alternate naturalistic explanations, but where you're allowed to nevertheless have a credence that non-naturalism is true in general... Just not for any specific event. I'm not sure how you really think about the evidence for miracles if you're methodologically not considering individual events to be miracles; I don't think this is really something that fits neatly in a Bayesian framework, but it's the best compromise I can think of between recognizing that methodological naturalism is necessary to make sense of the world at all, and recognizing that methodological naturalism isn't really different from a trapped prior on naturalism.