Theistic Humeanism?

Here’s an option that is underexplored: theistic Humeanism. There are two paths to it.

The path from orthodoxy: Start with a standard theistic concurrentism: whenever we have a creaturely cause C with effect E, E only eventuates because God concurs, i.e., God cooperates with the creaturely causal relation. Now add to this a story about what creaturely causation is. This will be a Humean story—the best I know is the David Lewis one that reduces causation to laws and laws to arrangements of stuff. Keep all the deep theistic metaphysics of divine causation.

The path from heterodoxy: Start with the metaphysics of occasionalism. Don’t change any of the metaphysics. But now add a Humean analysis of creaturely causation in terms of regularities. Since the metaphysics of occasionalism affirms regularities in the world, we haven’t changed the metaphysics of occasionalism, but have redescribed it as actually involving creaturely causation.

The two paths meet in a single view, a theistic Humeanism with the metaphysics of occasionalism and the language of concurrentism, and with creaturely causation described in a Humean way.

This theistic Humeanism is more complex than standard non-theistic Humeanism, but overcomes the central problem with non-theistic Humeanism: the difficulty of finding explanation in nature. If the fact that heat causes boiling is just a statement of regularity, it does not seem that heat explains boiling. But on theistic Humeanism, we have a genuine explanatory link: God makes the water boil because God is aware of the heat.

There is one special objection to theistic Humeanism. It has two causal relations, a divine one and a creaturely one. But the two are very different—they don’t both seem to be kinds of causation. However, on some orthodox concurrentisms, such as Aquinas’s, there isn’t a single kind of thing that divine and creaturely causation are species of. Instead, the two stand in an analogical relationship. Couldn’t the theistic Humean say the same thing? Maybe, though one might also object that Humean creaturely causation is too different from divine causation for the two to count as analogous.

I suppose the main objection to theistic Humeanism is that it feels like a cheat. The creaturely causation seems fake. The metaphysics is that of occasionalism, and there is no creaturely causation there. But if theistic Humeanism is a cheat, then standard non-theistic Humeanism is as well, since they share the same metaphysics of creaturely causation. If non-theistic Humeanism really does have causation, then our theistic Humeanism really does have creaturely causation. If one has fake causation, so does the other. I think both have fake causation. :-)

Simultaneous causation and occasionalism

In an earlier post, I said that an account that insists that all fundamental causation is simultaneous but secures the diachronic aspects of causal series by means of divine conservation is “a close cousin to occasionalism”. For a diachronic causal series on this theory has two kinds of links: creaturely causal links that function instantaneously and divine conservation links that preserve objects “in between” the instants at which creaturely causation acts. This sounds like occasionalism, in that the temporal extension of the series is entirely due to God working alone, without any contribution from creatures.

I now think there is an interesting way to blunt the force of this objection by giving another role to creatures using a probabilistic trick that I used in my previous post. This trick allows created reality to control how long diachronic causal series take, even though all creaturely causation is simultaneous. And if created reality were to control how long diachronic causal series take, a significant aspect of the diachronicity of diachronic causal series would involve creatures, and hence the whole thing would look rather less occasionalist.

Let me explain the trick again. Suppose time is discrete, being divided into lots of equally-spaced moments. Now imagine an event A₁ that has a probability 1/2 of producing an event A₂ during any instant that A₁ exists in, as long as A₁ hasn’t already produced A₂. Suppose A₁ is conserved for as long as it takes to produce A₂. Then the probability that it will take n units of time for A₂ to be produced is (1/2)^n + 1. Consequently, the expected wait time for A₂ to happen is:

• (1/2)⋅0 + (1/4)⋅1 + (1/8)⋅2 + (1/16)⋅3 + ... = 1.

We can then similarly set things up so that A₂ causes A₃ on average in one unit of time, and A₃ on causes A₄ on average in one unit of time, and so on. If n is large enough, then by the Central Limit Theorem, it is likely that the lag time between A₁ and A_n will be approximately n units of time (plus or minus an error on the order of n^1/2 units), and if the units of time are short enough, we can get arbitrarily good precision in the lag time with arbitrarily high precision.

If the probability of each event triggering the next at an instant is made smaller than 1/2, then the expected lag time from A₁ to A_n will be less than n, and if the probaility is bigger than 1/2, the expected lag time will be bigger than n. Thus the creaturely trigger probability parameter, which we can think of as measuring the “strength” of the causal power, controls how long it takes to get to A_n through the “magic” of probabilistic causation and the Central Limit Theorem. Thus, the diachronic time scale is controlled precisely by creaturely causation—even though divine conservation is responsible for A_i persisting until it can cause A_i + 1. This is a more significant creaturely input than I thought before, and hence it is one that makes for rather less in the way of occasionalism.

This looks like a pretty cool theory to me. I don’t believe it to be true, because I don’t buy the idea of all causation being simultaneous, but I think it gives a really nice.

Why did Alice make this lectern?

Converse essentiality of qualitative origins holds that if possible objects x and y have the same qualitative causal history—i.e., their initial state is qualitatively the same and the causes of that are qualitatively the same, etc.—then x = y. Kripke’s lectern argument basically makes it plausible to think that if converse essentiality of qualitative origins holds, so does essentiality of origins—the thesis that an object couldn’t have had a different qualitative causal history than it did.

If we reject converse essentiality of origins, then we have a thorny explanatory problem: When Alice took piece of wood W and shaped it into a lectern with shape S, what explains why lectern L₁ rather than, say, lectern L₂ resulted?

One way out of this explanatory problem is a partial occasionalism: Whenever an object comes into existence, while creatures may decide what the qualities of the object are, God causes the specific haecceity.

Another way out is to replace converse essentiality of qualitative origins with a converse essentiality of full origins thesis: if possible objects have the qualitatively and numerically (apart possibly from their own identity) causal history, then they are the same. Then when Alice takes W and shapes it into a lectern with shape S, only L₁ (say) can result. But if Alice’s identical twin Barbara did it, it would have been (say) L₂.

We thus seem to have three options as to the explanation of why Alice produced L₁ rather than L₂.

1. converse essentiality of qualitative origins

2. converse essentiality of full origins

3. partially occasionalistic haecceitism.

Maybe there are other good ones.

Two kinds of occasionalism

Suppose a burner is turned on, a pot is heated, and the water in the pot is boiled. On occasionalism, the heating of the pot is caused only by God, and the same is true for the boiling of the water.

But there are two ways of understanding this:

1. God causes the water to boil because the pot is being heated. God causes the pot to be heated because the burner is on. God causes the burner to be on because….

2. God causes the water to boil just because God causes the pot to be heated. God causes the pot to be heated just because God causes the burner to be turned on. God causes the burner to be on just because God causes…

On type 1 occasionalism, God reacts to events in the world, and one has real but non-causal explanatory connections in the world: the water boils because the burner is on. On type 2 occasionalism, there are no real explanatory connections between events in the world: they are all just the effects of God’s plan. Leibniz has type 2 occasionalism in intermonadic causation. And that’s a problem.

I am not saying that type 1 occasionalism has no problems. But at least it makes for real explanatory connections between events in the world, even if these are not causal.

Parameters in ethics

In physical laws, there are a number of numerical parameters. Some of these parameters are famously part of the fine-tuning problem, but all of them are puzzling. It would be really cool if we could derive the parameters from elegant laws that lack arbitrary-seeming parameters, but as far as I can tell most physicists doubt this will happen. The parameters look deeply contingent: other values for them seem very much possible. Thus people try to come up either with plenitude-based explanations where all values of parameters are exemplified in some universe or other, or with causal explanations, say in terms of universes budding off other universes or a God who causes universes.

Ethics also has parameters. To further spell out an example from Aquinas' discussion of the order of charity, fix a set of specific circumstances involving yourself, your father and a stranger, where both your father and the stranger are in average financial circumstances, but are in danger of a financial loss, and you can save one, but not both, of them from the loss. If it's a choice between saving your father from a ten dollar loss or the stranger from an eleven dollar loss, you should save your father from the loss. But if it's a choice between saving your father from a ten dollar loss or the stranger from a ten thousand dollar loss, you should save the stranger from the larger loss. As the loss to the stranger increases, at some point the wise and virtuous agent will switch from benefiting the father to benefiting the stranger. The location of the switch-over is a parameter.

Or consider questions of imposition of risk. To save one stranger's life, it is permissible to impose a small risk of death on another stranger, say a risk of one in a million. For instance, an ambulance driver can drive fast to save someone's life, even though this endangers other people along the way. But to save a stranger's life, it is not permissible to impose a 99% risk of death on another stranger. Somewhere there is a switch-over.

There are epistemic problems with such switch-overs. Aquinas says that there is no rule we can give for when we benefit our father and when we benefit a stranger, but we must judge as the prudent person would. However I am not interested right now in the epistemic problem, but in the explanatory problem. Why do the parameters have the values they do? Now, granted, the particular switchover points in my examples are probably not fundamental parameters. The amount of money that a stranger needs to face in order that you should help the stranger rather than saving your father from a loss of $10 is surely not a fundamental parameter, especially since it depends on many of the background conditions (just how well off is your father and the stranger; what exactly is your relationship with your father; etc.) Likewise, the saving-risking switchover may well not be fundamental. But just as physicists doubt that one can derive the value of, say, the fine-structure constant (which measures the strength of electromagnetic interactions between charged particles) from laws of nature that contain no parameters other than elegant ones like 2 and π, even though it is surely a very serious possibility that the fine-structure constant isn't truly fundamental, so too it is doubtful that the switchover points in these examples can be derived from fundamental laws of ethics that contain no parameters other than elegant ones. If utilitarianism were correct, it would be an example of a parameter-free theory providing such a derivation. But utilitarianism predicts the incorrect values for the parameters. For instance, it incorrectly predicts that that the risk value at which you need to stop risking a stranger's life to certainly save another stranger is 1, so that you should put one stranger in a position of 99.9999% chance of death if that has a certainty of saving another stranger.

So we have good reason to think that the fundamental laws of ethics contain parameters that suffer from the same sort of apparent contingency that the physical ones do. These parameters, thus, appear to call for an explanation, just as the physical ones do.

But let's pause for a second in regard to the contingency. For there is one prominent proposal on which the laws of physics end up being necessary: the Aristotelian account of laws as grounded in the essences of things. On such an account, for instance, the value of the fine-structure constant may be grounded in the natures of charged particles, or maybe in the nature of charge tropes. However, such an account really does not remove contingency. For on this theory, while it is not contingent that electromagnetic interactions between, say, electrons have the magnitude they do, it is contingent that the universe contains electrons rather than shmelectrons, which are just like electrons, but they engaged in shmelectromagnetic interactions that are just like electromagnetic interactions but with a different quantity playing the role analogous to the fine-structure constant. In a case like this, while technically the laws of physics are necessary, there is still a contingency in the constants, in that it is contingent that we have particles which behave according to this value rather than other particles that would behave differently. Similarly, one might say that it is a necessary truth that such-and-such preferences are to be had between a father and a stranger, and that this necessary truth is grounded in the essence of humanity or in the nature of a paternity trope. But there is still a contingency that our world contains humans and fathers rather than something functionally very similar to humans and fathers but with different normative parameters.

So in any case we have a contingency. We need a meta-ethics with a serious dose of contingency, contingency not just derivable from the sorts of functional behavior the agents exhibit, but contingency at the normative level--for instance, contingency as to appropriate endangering-saving risk tradeoffs. This contingency undercuts the intuitions behind the thesis that the moral supervenes on the non-moral. Here, both Natural Law and Divine Command rise to the challenge. Just as the natures of contingently existing charged objects can ground the fine-structure constants governing their behavior, the natures of contingently existing agents can ground the saving-risking switchover values governing their behavior. And just as occasionalism can have God's causation ground the arbitrary-seeming parameters in the laws of physics, so God's commands can ground the arbitrary-seeming parameters in ethics (the illuminating analogy between occasionalism and Divine Command is due to Mark Murphy). Can other theories rise to the challenge? Maybe. But in any case, it is a genuine challenge.

It would be particularly interesting if there were an analogue to the fine-tuning argument in this case. The fine-tuning argument arises because in some sense "most" of the possible combinations of values of parameters in the laws of physics do not allow for life, or at least for robust, long-lasting and interesting life. I wonder if there isn't a similar argument on the ethics side, say that for "most" of the possible combinations of parameters, we aren't going to have the good moral communities (the good could be prior to the moral, so there may be no circularity in the evaluation)? I don't know. But this would be an interesting research project for a graduate student to think about.

Objection: The switchover points are vague.

Response: I didn't say they weren't. The puzzle is present either way. Vagueness doesn't remove arbitrariness. With a sharp switchover point, just the value of it is arbitrary. But with a vague switchover point, we have a vagueness profile: here something is definitely vaguely obligatory, here it is definitely vaguely vaguely obligatory, here it is vaguely vaguely vaguely obligatory, etc. In fact, vagueness may even multiply arbitrariness, in that there are a lot more degrees of freedom in a vagueness profile than in a single sharp value.

An account of laws

According to the Lewisian best system analysis of laws, a proposition p is a fundamental law if and only if it is an axiom in the best system. There is room for variation in the concept of a best system, but a standard version in deterministic settings is that the best system comprises only truths and optimizes the brevity of its axioms and the informativeness of its theorems about the world. The biggest problem for me with the best system account is that the fact that something is an axiom in the best system simply does not make it be explanatory.

I think this is a better account. A proposition p is a fundamental law of nature provided that:

1. p is an axiom in the best system, and
2. God wills p, as such.

(I am not sure if the will in (2) should be taken to be antecedent or consequent. If miracles are counterinstances to laws, it must be antecedent. But a lot of people think that's a bad account of miracles, and that allows it to be consequent.)

The "as such" in (2) rules out a case where God instead of willing p, wills something that entails p.

This account solves the explanatory problem with Lewis's account by making the fundamental laws be explanatory. They are not explanatory directly because they are axioms in the best system, but rather because God wills them.

Interestingly, I think (1) may imply (2) in the actual world, by divine omnirationality. For that p has the kind of simplicity and fecundity that axioms in the best system are going to have gives God a reason to will p. And since p in fact holds, presumably God willed p. The only exception is going to be if p reports the sort of thing that God has reason to distance himself from. Suppose, for instance, that everyone who is tempted a certain way sins. Then that universal generalization might be a best system axiom, but God has reason not to will it. But in fact it does not seem that any axioms in our world's best system are going to be like that—such regularities don't seem to be far-reaching enough. All the candidates we hear about from physics are propositions that God does not seem to have reason to distance his will from.

If this is right, then in the actual world, all the axioms in the best system are fundamental laws, and Lewis is contingently right. Moreover, this line of thought shows that the fact that p is an axiom in the best system makes it likely that God wills it. Consequently, as long as we know that God exists, we get to keep the epistemological benefits of Lewis's system.