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.

Simultaneous causation and determinism

Consider the Causal Simultaneity Thesis (CST) that all causation is simultaneous. Assume that simultaneity is absolute (rather than relative). Assume there is change. Here is a consequence I will argue for: determinism is false. In fact, more strongly, there are no diachronic deterministic causal series. What is surprising is that we get this consequence without any considerations of free will or quantum mechanics.

Since there is a very plausible argument from presentism to CST (a non-simultaneous fundamental causal relation could never obtain between two existent things given presentism), we get an argument from presentism to indeterminism.

Personally, I am inclined to think of this argument as a bit of evidence against CST and hence against presentism, because it seems to me that there could be a deterministic world, even though there isn’t. But tastes differ.

Now the argument for the central thesis. The idea is simple. On CST, as soon as the deterministic causes of an effect are in place, their effect is in place. Any delay in the effect would mean a violation of the determinism. There can be nothing in the deterministic causes to explain how much delay happens, because all the causes work simultaneously. And so if determinism is true—i.e., if everything has a deterministic cause—then all the effects happen all at once, and everything is already in the final state at the first moment of time. Thus there is no change if we have determinism and CST.

The point becomes clearer when we think about how it is an adherent of CST explains diachronic causal series. We have an item A that starts existing at time t₁, persists through time t₂ (kept in existence not by its own causal power, as that would require a diachronic causal relation, but either by a conserver or a principle of existential inertia), then causes an item B, which then persists through time t₃ and then causes an item C, and so on. While any two successive items in the causal series A, B, C, ... must overlap temporally (i.e., there must be a time at which they both exist), we need not have temporal overlap between A and C, say. We can thus have things perishing and new things coming into being after them.

But if the causation is deterministic, then as soon as A exists, it will cause B, which will cause C, and so on, thereby forcing the whole series to exist at once, and destroying change.

In an earlier post, I thought this made for a serious objection to CST. I asked: “Why does A ‘wait’ until t₂ to cause B?” But once we realize that the issue above has to do with determinism, we see that an answer is available. All we need to do is to suppose there is probabilistic causation.

For simplicity (and because this is what fits best with causal finitism) suppose time is discrete. Then we may suppose that at each moment of time at which A exists it has a certain low probability p_AB of causing B if B does not already exist. Then the probability that A will cause B precisely after n units of time is (1 − p_AB)ⁿp_AB. It follows mathematically that “on average” it will cause B after p_AB/(1 − p_AB) fundamental units of time.

It follows that for any desired average time delay, a designer of the universe can design a cause that has that delay. Let’s say that we want B to come into existence on average u fundamental units of time after A has come into existence. Then the designer can give A a causal power of producing B at any given moment of time at which B does not already exist with probability p_AB = 1/(1 + u).

The resulting setup will be indeterministic, and in particular we can expect significant random variation in how long it takes to get B from A. But if the designer wants more precise timing, that can be arranged as well. Let’s say that our designer wants B to happen very close to precisely one second after A. The designer can then ensure that, say, there are a million instants of time in a second, and that A has the power to produce an event A₁ with a probability at any given instant such that the expected wait time will be 0.0001 seconds (i.e., 100 fundamental units of time), and A₁ the power to produce A₂ with the same probability, and so on, with A₁₀₀₀₀ = B. Then by the Central Limit Theorem, the average wait time between A and B can be expected to be fairly close to 10000 × 0.0001 = 1 seconds, and the designer can get arbitrarily high confidence of an arbitrarily high precision of delay by inserting more instants in each second, and more intermediate causes between A and B, with each intermediate cause having an average delay time of 100 fundamental units (say). (This uses the fact that the geometric distribution has a finite third moment and the Barry-Esseen version of the Central Limit Theorem.)

Thus, a designer of the universe can make an arbitrarily precise and reliable near-deterministic changing universe despite CST. And that really blunts the force of my anti-deterministic observation as a consideration against CST.

Plural and singular grounding

Here’s a tempting principle:

1. If x and y ground z, then the fusion of x and y grounds z.

In other words, we don’t need proper pluralities for grounding—their fusions do the job just as well.

But the principle is false. For the principle is only plausible if any two things have a fusion. But if x and y do not overlap, then x and y ground their fusion. And then (1) would say that the fusion grounds itself, which is absurd.

This makes it very plausible to think that plural objectual grounding does not reduce to singular objectual grounding.

Failures of supervenience on Lewis's system

Start with the concept of “narrowly physical” for facts about the arrangement of physical entities and first-order physical properties such as “charge” and “mass”.

Here are two observations I have not seen made:

1. On Lewis-Ramsey accounts of laws, laws of nature concerning narrowly physical facts do not supervene on narrowly physical facts.

2. On Lewis’s account of causation, causal facts about narrowly physical events do not supervene on narrowly physical facts.

This means that in a Lewisian system we have at least four things we could mean by “physical”:

3. narrowly physical

4. grounded in the laws of narrowly physical facts and/or the narrowly physical facts themselves

5. grounded in the causal facts about narrowly physical events and/or the narrowly physical facts themeselves

6. grounded in the causal facts about narrowly physical events, the laws concerning narrowly physical facts and/or the narrowly physical facts themselves.

Here’s a corollary for the philosophy of mind:

7. On a Lewisian system, we should not even expect the mental properties of purely narrowly physical beings to supervene on narrowly physical facts.

Argument for (1): The laws are the optimal systematization of particular facts. But now imagine a possible world where there is just a coin that is tossed a trillion times, and with no discernible pattern lands heads about half the time. In the best systematization, we attribute a chance of 1/2 to the coin landing heads. But now imagine a possible world with the same narrowly physical facts, but where there is an angel that thought about ℵ₃ about a million times—each time, with a good prior mental explanation of the train of thought—and each of these times was a time just before the coin landed heads. Then the best systematization of the coin tosses will no longer make them simply have a chance of 1/2 of landing heads. Rather, they will have a chance 1/2 of landing heads when the angel didn’t just think about ℵ₃.

Argument for (2): Add to the world in the above argument some cats and suppose that on any day when the fattest cat in the world eats n mice, that leads the angel to think about ℵ_n, though there are other things that can get the angel to think about ℵ_n. We can set things up so that the fattest cat’s eating three mice in a day causes the coin to land heads on the Lewisian counterfactual account of causation, but if we subtract the angel from the story, this will no longer be the case.

Functionalism implies the possibility of zombies

Endicott has observed that functionalism in the philosophy of mind contradicts the widely accepted supervenience of the mental on the physical, because you can have worlds where the functional features are realized by non-physical processes.

My own view is that a functionalist physicalist shouldn’t worry about this much. It seems to be a strength of a functionalist view that it makes it possible to have non-physical minds, and the physicalist should only hold that in the actual world all the minds are physical (call this “actual-world physicalism”).

But here is something that might worry a physicalist a little bit more.

• If functionalism and actual-world physicalism are true, there is a possible world which is physically exactly like ours but where there is no pain.

Here is why. On functionalism, pain is constituted by some functional roles. No doubt an essential part of that role is the detection of damage and the production of aversive behavior. Let’s suppose for simplicity that this role is realized in C-fiber firing in all beings capable of pain (the argument generalizes straightforwardly if there are multiple realizers). Now imagine a possible world physically just like this one, but with two modifications: there are lots of blissful non-physical angels, and all C-fiber equipped brains have an additional non-physical causal power to trigger C-fiber firing whenever an angel thinks about that brain. It is no longer true that the functional trigger for C-fiber firing is damage. Now, the functional trigger for C-fiber firing is the disjunction of damage and being thought about by an angel, and hence C-fiber firing no longer fulfills the functional role of pain. But now add that the angels never actually think about a rain while that brain is alive, though they easily could. Then the world is physically just like ours, but nobody feels any pain.

One might object that a functional role of a detector is unchanged by adding a disjunct to what is being detected. But that is mistaken. After all, imagine that we modify the hookups in a brain so that C-fiber firing is triggered by damage and lack of damage. Then clearly we’ve changed the functional role of C-fiber firing—now, the C-fibers are triggered 100% of the time, no matter what—even though we’ve just added a disjunct.

We can also set up a story where it is the aversive behavior side of the causal role that is removed. For instance, we may suppose that there is a magical non-physical aura normally present everywhere in the universe, and C-fiber firing interacts with this aura to magically move human beings in the opposite direction to the one their muscles are moving them to. The aura does nothing else. Thus, if the aura is present and you receive a painful stimulus, you now move closer to the stimulus; if the aura is absent, you move further away. It is no longer the case that C-fibers have the function of producing aversive behavior. However, we may further imagine that at times random abnormal holes appear in the aura, perhaps due to a sport played by non-physical pain-free imps, and completely coincidentally a hole has always appeared around any animal while its C-fibers were firing. Thus, the physical aspects of that world can be exactly the same as in ours, but there is no pain.

The arguments generalize to show that functionalists are committed to zombies: beings physically just like us but without any conscious states. Interestingly, these are implemented as the reverse of the zombies dualists think up. The dualist’s zombies lack non-physical properties that the dualist (rightly) thinks we have, and this lack makes them not be conscious. But my new zombies are non-conscious precisely because they have additional non-physical properties.

Note that the arguments assume the standard physicalist-based functionalism, rather than Koons-Pruss Aristotelian functionalism.

A privation theory of evil without lacks of entities

Taking the privation theory literally, evil is constituted by the non-existence of something that should exist. This leads to a lot of puzzling questions of what that “something” is in cases such as error and pain.

But I am now wondering whether one couldn’t have a privation theory of evil on which evil is a lack of something, but not of an entity. What do I mean? Well, imagine you’re a thoroughgoing nominalist, believing in neither tropes nor universals. Then you think that there is no such thing as red, but of course you can say that sometimes a red sign fades to gray. It is natural to say that the faded sign is lacking the due color red, and the nominalist should be able to say this, too.

Suppose that in addition to being a thoroughgoing nominalist, you are a classical theist. Then you will want to say this: the sign used to participate in God by being red, but now it no longer thusly participates in God (though it still otherwise participates in God). Even though you can’t be a literal privation theorist, and hold that some entity has perished from the sign, you can be a privation theorist of sorts, by saying that the sign has in one respect stopped participating in God.

A lot of what I said in the previous two paragraphs is fishy. The “thusly” seems to refer to redness, and “one respect” seems to involve a quantification over respects. But presumably nominalists say stuff like that in contexts other than God and evil. So they probably think they have a story to tell about such statements. Why not here, then?

Furthermore, imagine that instead of a nominalist we have a Platonist who does not believe in tropes (not even the trope of participating). Then the problems of the “thusly” and “one respect” and the like can be solved. But it is still the case that there is no entity missing from the sign. Yet we still recognizably have a privation theory.

This makes me wonder: could it be that a privation theory that wasn’t committed to missing entities solve some of the problems that more literal privation theories face?

An omnipotence principle from Aquinas

Aquinas believes that it follows from omnipotence that:

1. Any being that depends on creatures can be created by God without its depending on creatures.

But, plausibly:

2. If x and y are a couple z, then z depends on x and y.

3. If x and y are a couple z, then necessarily if z exists, z depends on x and y.

4. Jill and Joe Biden are a couple.

5. Jill and Joe Biden are creatures.

But this leads to a contradiction. By (4), we have a couple, call it “the Bidens”, consisting by Jill and Joe Biden, and by (2) that couple depends on Jill and Joe Biden. By (1) and (5), God can create the Bidens without either Jill or Joe Biden. But that contradicts (3).

So, Aquinas’ principle (1) implies that there are no couples. More generally, it implies that there are no beings that necessarily depend on other creatures. All our artifacts would be like that: they would depend on parts. Thus, Aquinas’ principle implies there are no artifacts.

Thomists are sometimes tempted to say that artifacts, heaps and the like are accidental beings. But the above argument shows that that won’t do. God’s power extends to all being, and whatever being creatures can bestow, God can bestow absent the creatures. If the accidental beings are beings, God can create them without their parts. But a universe with a heap and yet nothing heaped is absurd. So, I think, we need to deny the existence of accidental beings.

If we lean on (1) further, we get an argument for survivalism. Either Socrates depends on his body or not. If Socrates does not depend on his body, he can surely survive without his body after death. But if Socrates does depend on his body, then by (1) God can create Socrates disembodied, since Socrates’ body is a creature. But if God can create Socrates disembodied, surely God can sustain Socrates disembodied, and so Socrates can survive without his body. In fact, the argument does not apply merely to humans but to every embodied being: bacteria, trees and wolves can all survive death if God so pleases.

Things get even stranger once we get to the compositional structure of substances. Socrates presumably depends on his act of being. But Socrates’ act of being is itself a creature. Thus, by (1), God could create Socrates without creating Socrates’ act of being. Then Socrates would exist without having any existence.

I like the sound of (1), but the last conclusion seems disastrous. Perhaps, though, the lesson we get from this is that the esse of Socrates isn’t an entity? Or perhaps we need to reject (1)?

Valuing and behavioral tendencies

It is tempting to say that I value a wager W at x provided that I would be willing to pay any amount up to x for W and unwilling to pay an amount larger than x. But that’s not quite right. For often the fact that a wager is being offered to me would itself be relevant information that would affect how I value the wager.

Let’s say that you tossed a fair coin. Then I value a wager that pays ten dollars on heads at five dollars. But if you were to try to sell me that wager for a dollar, I wouldn’t buy it, because your offering it to me at that price would be strong evidence that you saw the coin landing tails.

Thus, if we want to define how much I value a wager at in terms of what I would be willing to pay for it, we have to talk about what I would be willing to pay for it were the fact that the wager is being offered statistically independent of the events in the wager.

But sometimes this conditional does not help. Imagine a wager W that pays $123.45 if p is true, where p is the proposition that at some point in my life I get offered a wager that pays $123.45 on some eventuality. My probability of p is quite low: it is unlikely anybody will offer me such a wager. Consequently, it is right to say that I value the wager at some small amount, maybe a few dollars.

Now consider the question of what I would be willing to pay for W were the fact that the wager is being offered statistically independent of the events in the wager, i.e., independent of p. Since my being offered W entails p, the only way we can have the statistical independence is if my being offered W has credence zero or p has credence one. It is reasonable to say that the closest possible world where one of these two scenarios holds is a world where p has credence one because some wager involving a $123.45 has already been offered to me. In that world, however, I am willing to pay up to $123.45 for W. Yet that is not what I value W at.

Maybe when we ask what we would be willing to pay for a wager, we mean: what we would be willing to pay provided that our credences stayed unchanged despite the offer. But a scenario where our credences stay unchanged despite the offer is a very weird one. Obviously, when an offer is made, your credence that the offer is made goes up, unless you’re seriously irrational. So this new counterfactual question asks us what we would decide in worlds where we are seriously irrational. And that’s not relevant to the question of how we value the wager.

Maybe instead of asking about the prices at which I would accept an offer, I should instead ask about the prices at which I would make an offer. But that doesn't help either. Go back to the fair coin case. I value a wager that pays you ten dollars on heads at negative five dollars. But I might not offer it to you for eight dollars, because it is likely that you would pay eight dollars for this wager only if you actually saw that the coin turned out heads, in which case this would be a losing proposition for me.

The upshot is, I think, that the question of what one values a wager at is not to be defined in terms of simple behavioral tendencies or even simple counterfactualized behavioral tendencies. Perhaps we can do better with a holistic best-fit analysis.

The Paradox of Charity

We might call the following three statements "the Paradox of Charity":

1. In charity, we love our neighbor primarily because of our neighbor’s relation to God.

2. In the best kind of love, we love our neighbor primarily because of our neighbor’s intrinsic properties.

3. Charity is the best kind of love.

I think this paradox discloses something very deep.

Note that the above three statements do not by themselves constitute a strictly logical contradiction. To get a strictly logical contradiction we need a premise like:

4. No intrinsic property of our neighbor is a relation to God.

Now, let’s think (2) through. I think our best reason for accepting (2) is not abstract considerations of intrinsicness, but particular cases of properties. In the best kind of love, perhaps, we love our neighbor because our neighbor is a human being, is a finite person, has a potential for human flourishing, etc. We may think that these features are intrinsic to our neighbor, but we directly see them as apt reasons for the best kind of love, without depending on their intrinsicness.

But suppose ontological investigation of such paradigm properties for which one loves one’s neighbor with the best kind of love showed that these properties are actually relational rather than intrinsic. Would that make us doubt that these properties are a fit reason for the best kind of love? Not at all! Rather, if we were to learn that, we would simply deny (2). (And notice that plenty of continentally-inclined philosophers do think that personhood is relational.)

And that is my solution. I think (1), (3) and (4) are true. I also think that the best kind of neighbor love is motivated by reasons such as that our neighbor is a human being, or a person, or has a potential for human flourishing. I conclude from (1), (3) and (4) that these properties are relations to God.

But how could these be relations to God? Well, all the reality in a finite being is a participation in God. Thus, being human, being a finite person and having a potential for human flourishing are all ways of participating in God, and hence are relations to God. Indeed, I think:

5. Every property of every creature is a relation to God.

It follows that no creature has any intrinsic property. The closest we come to having intrinsic properties are what one might call “almost intrinsic properties”—properties that are relational to God alone.

We can now come back to the original argument. Once we have seen that all creaturely properties are participations in God, we have no reason to affirm (2). But we can still affirm, if we like:

6. In the best kind of love, we love our neighbor primarily because of our neighbor’s almost intrinsic properties, i.e., our neighbor’s relations only to God.

And there is no tension with (1) any more.

First person survivalship bias?

Suppose I take a nasty fall while biking. But I remain conscious. Here is the obvious first thing for a formal epistemologist to do: increase my credence in the effectiveness of this brand of helmets. But by how much?

In an ordinary case of evidence gathering, I simply conditionalize on my evidence. But this is not an ordinary case, because if things had gone otherwise—namely, if I did not remain conscious—I wouldn’t be able to update or think in any way. It seems like I am now subject to a survivorship bias. What should I do about that? Should I simply dismiss the evidence entirely, and leave unchanged my credence in the effectiveness of helmets? No! For I cannot deny that I am still conscious—my credence for that is now forced to be one. If I leave all my other credences unchanged, my credences will become inconsistent, assuming they were consistent before, and so I have to do something to my other credences to maintain consistency.

It is tempting to think that perhaps I need to compensate for survivorship bias in some way, perhaps updating my credence in the effectiveness of the helmet to be bigger than my priors but smaller than the posteriors of a bystander who had the same priors as I did but got to observe my continued consciousness without a similar bias, since they would have been able to continue to think even were I to become unconscious.

But, no. What I should do is simply update on my consciousness (and on the impact, but if I am a perfect Bayesian agent, I have already done that as soon as it was evident that I would hit the ground), and not worry about the fact that if I weren’t conscious, I wouldn’t be around to update on it. In other words, there is no such problem as survivorship bias in the first person, or at least not in cases like this.

To see this, let’s generalize the case. We have a situation where the probability space is partitioned into outcomes E₁, ..., E_n, each with non-zero prior credence. I will call an outcome E_i normal if on that outcome you would know for sure that E_i has happened, you would have no memory loss, and would be able to maintain rationality. But some of the outcomes may be abnormal. I will have a bit more to say about the kinds of abnormality my argument can handle in a moment.

We can now approach the problem as follows: Prior to the experiment—i.e., prior to the potentially incapacitating observation—you decide rationally what kind of evidence update procedures to adopt. On the normal outcomes, you get to stick to these procedures. On the abnormal ones, you won’t be able to—you will lose rationality, and in particular your update will be statistically independent of the procedure you rationally adopted. This independence assumption is pretty restrictive, but it plausibly applies in the bike crash case. For in that case, if you become unconscious, your credences become fixed at the point of impact or become scrambled in some random way, and you have no evidence of any connection between the type of scrambling and the rational update procedure you adopted. My story can even handle cases where on some of the abnormal outcomes you don’t have any credences, say because your brain is completely wiped or you cease to exist, again assuming that this is independent of the update procedure you adopted for the normal outcomes.

It turns out to be a theorem that under conditions like this, given some additional technical assumptions, you maximize expected epistemic utility by conditionalizing when you can, i.e., whenever a normal outcome occurs. And epistemic utility arguments are formally interchangeable with pragmatic arguments (because rational decisions about wager adoption yield a proper epistemic utility), so we also get a pragmatic argument. The theorem will be given at the end of this post.

This result means we don’t have to worry in firing squad cases that you wouldn’t be there if you weren’t hit: you can just happily update your credences (say, regarding the number of empty guns, the accuracy of the shooters, etc.) on your not being hit. Similarly, you can update on your not getting Alzheimer’s (which is, e.g., evidence against your siblings getting it), on your not having fallen asleep yet (which may be evidence that a sleeping pill isn’t effective), etc., much as a third party who would have been able to observe you on both outcomes should. Whether this applies to cases where you wouldn’t have existed in the first place on one of the items in the partition—i.e., whether you can update on your existence, as in fine-tuning cases—is a more difficult question, but the result makes some progress towards a positive answer. (Of course, it woudn’t surprise me if all this were known. It’s more fun to prove things oneself than to search the literature.)

Here is the promised result.

Theorem. Assume a finite probability space. Let I be the set of i such that E_i is normal. Suppose that epistemic utility is measured by a proper accuracy scoring rule s_i when E_i happens for i ∈ I, so that the epistemic utility of a credence assignment c_i is s_i(c_i) on E_i. Suppose that epistemic utility is measured by a random variable U_i on E_i (not dependent on the choice of the c_j for j ∈ I) for i not in I. Let U(c)=∑_i∈I 1_Ei ⋅ s_i(c_i)+∑_i∉I 1_Ei ⋅ U_i. Assume you have consistent priors p that assign non-zero credence to each normal E_i, and the expectation E^p of the second sum with respect to these priors is well defined. Then the expected value of U(c) with respect to p is maximized when c_i(A)=p(A ∣ E_i) for i ∈ I. If additionally the scoring rules are strictly proper, and the p-expectation of the second sum is finite, then the expected value of U(c) is uniquely maximized by that choice of c_i.

This is one of those theorems that are shorter to prove than to state, because they are pretty obvious once fairly clearly formulated.

Normally, all the s_i will be the same. It's worth thinking if any useful generalization is gained by allowing them to be different. Perhaps there is. We could imagine situtions where depending on what happens to you, your epistemic priorities rightly change. Thus, if an accident leaves you with some medical condition, knowing more about that medical condition will be valuable, while if you don't get that medical condition, the value of knowing more about it will be low. Taking that into account with a single scoring rule is apt to make the scoring rule improper. But in the case where you are conditioning on that medical condition itself, the use of different but individually proper scoring rules when the condition eventuates and when it does not can model the situation rather nicely.

Proof of Theorem: Let c_i be the result of conditionalizing p on E_i. Then the expectation of s_i(c_i′) with respect to c_i is maximized when (and only when, if the conditions of the last sentence of the theorem hold) c_i′=c_i by propriety of s_i. But the expectation of s_i(c_i′) with respect to c_i equals 1/p(E_i) times the expectation of 1_Ei ⋅ s_i(c_i′) with respect to p. So the latter expectation is maximized when (and only when, given the additional conditions) c_i′=c_i.

Functionalism and multiple realizability

Functionalism holds that two (deterministic) minds think the same thoughts when they engage in the same computation and have the same inputs. What does it mean for them to engage in the same computation?

This is a hard question. Suppose two computers run programs that sort a series of names in alphabetical order, but they use different sorting algorithms. Given the same inputs, are the two computers engaging in the same computation?

If we say “no”, then functionalism doesn’t have the degree of multiple realizability that we thought it did. We have no guarantee that aliens who behave very much like us think very much like us, or even think at all, since the alien brains may have evolved to compute using different algorithms from us.

If we say “yes”, then it seems we are much better off with respect to multiple realizability. However, there is a tricky issue here: What counts as the inputs and outputs? We just said that the computers using different sorting algorithms engage in the same computation. But the computer using a quicksort typically returns an answer sooner than a computer using a bubble sort, and heats up less. In some cases, the time at which an output is produced itself counts as an output (think of a game where timing is everything). And heat is a kind of output, too.

In my toy sorting algorithm example, presumably we didn’t count the timing and the heat as features of the outputs because we assumed that to the human designers and/or users of the computers the timing and heat have no semantic value, but are merely matters of convenience (sooner and cooler are better). But when we don’t have a designer or user to define the outputs, as in the case where functionalism is applied to randomly evolved brains, things are much more difficult.

So, in practice, even if we answered “yes” in the toy sorting algorithm case, in a real-life case where we have evolved brains, it is far from clear what counts as an output, and hence far from clear what counts as “engaging in the same computation”. As a result, the degree to which functionalism yields multiple realizability is much less clear.

Subjective guilt and war

One of the well-known challenges in accounting for killing in a just war is the thought that even soldiers fighting on a side without justice think they have justice on their side, hence are subjectively innocent, and thus it seems wrong to kill them.

But I wonder if there isn’t an opposite problem. As is well-known, human beings have a very strong visceral opposition to killing. Even those who kill with justice on their side are apt to feel guilty, and it wouldn’t be surprising if often they not only feel guilty but judge themselves to have done wrong. Thus, it could well be that soldiers who kill on both sides of a war have a tendency to be subjectively guilty, even if one of the sides is waging a just war.

Or perhaps things work out this way: Soldiers who kill tend to be subjectively guilty unless they are waging a clearly just war. If so, then those who are on a side without justice are indeed apt to be subjectively guilty, since rarely does a side without justice appear manifestly just. And those who are on a side with justice are may very well also be subjectively guilty, unless the war is one of those where justice is manifest (as was the case for the Allies in World War II).

I doubt that things work out all that neatly.

In any case, the above considerations do show that a side with justice has very strong moral reason to make that justice as manifest as possible to the soldiers. And when that is not possible, those in charge should be persons of such evident integrity that it is easy to trust their judgment.

Intrinsic evil

Consider this argument:

1. An action is intrinsically evil if and only if it is wrong to do no matter what.

2. In doing anything wrong, one does something (at least) prima facie bad with insufficient moral reason.

3. No matter what, it is wrong to do something prima facie bad with insufficient moral reason.

4. So in doing anything wrong, one performs an intrinsically evil action.

This conclusion seems mistaken. Lightly slapping a stranger on a bus in the face is wrong, but not intrinsically wrong, because if a malefactor was going to kill everyone on the bus who wasn’t slapped by you, then you should go and slap everybody. Yet the argument would imply that in lightly slapping a stranger on a bus you do something intrinsically wrong, namely slap a stranger with insufficient moral reason. But it seems mistaken to think that in slapping a stranger lightly you perform an intrinsically evil action.

The above argument threatens to eviscerate the traditional Christian distinction between intrinsic and extrinsic evil. What should we say?

Here is a suggestion. Perhaps we should abandon (1) and instead distinguish between reasons why an action is wrong. Intrinsically evil actions are wrong for reasons that do not depend on consideration of consequences and extrinsically evil actions are wrong but not for any reasons that do not depend on consideration of consequences.

Thus, lightly slapping a stranger with insufficient moral reason is extrinsically evil because any reason that makes it wrong is a reason that depends on consideration of consequences. On the other hand, one can completely explain what makes an act of murder wrong without adverting to consequences.

But isn’t the death of the victim a crucial part of the wrongness of murder, and yet a consequence? After all, if the cause of death is murder, then the death is a consequence of the murder. Fortunately we can solve this: the act is no less wrong if the victim does not die. It is the intention of death, not the actuality of death, that is a part of the reasons for wrongness.

So, when we distinguish between acts made wrong by consequences and and wrong acts not made wrong by consequences, by “consequences” we do not mean intended consequences, but only actual or foreseen or risked consequences.

But what if Alice slaps Bob with the intention of producing an on-balance bad outcome? That act is wrong for reasons that have nothing to do with actual, foreseen or risked consequences, but only with her intention. Here I think we can bite the bullet: to slap an innocent stranger with the intention of producing an on-balance bad outcome is intrinsically wrong, just as it is intrinsically wrong to slap an innocent stranger with the intention of causing death.

Note that this would show that an intrinsically evil action need not be very evil. A light slap with the intention of producing an on-balance slightly bad outcome is wrong, but not very wrong. (Similarly, the Christian tradition holds that every lie is intrinsically evil, but some lies are only slight wrongs.)

Here is another advantage of running the distinction in this way, given the Jewish and Christian tradition. If an intrinsically evil action is one that is evil independently of consequences, it could be that such an action could still be turned into a permissible one on the basis of circumstantial factors not based in consequences. And God’s commands can be such circumstantial factors. Thus, when God commands Abraham to kill Isaac, the killing of Isaac becomes right not because of any new consequences, but because of the circumstance of God commanding the killing.

Could we maybe narrow down the scope of intrinsically evil actions even more, by saying that not just consequences, but circumstances in general, aren’t supposed to be among the reasons for wrongness? But if we do that, then most paradigm cases of intrinsically evil actions will fail: for instance, that the victim of a murder is innocent is a circumstance (it is not a part of the agent’s intention).

Trust and scepticism

To avoid scepticism, we need to trust that human epistemic practices and reality match up. This trust is clearly at least a part of a central epistemic virtue.

Now, trusting persons is a virtue, the virtue of faith. But trusting in general, apart from trusting persons, is not. Theism can thus neatly account for how the trusting that is at the heart of human epistemic practices is virtuous: it is an implicit trust in our creator.

Another way out of the metaphysical problem of evil

The metaphysical problem of evil consists in the contradiction between:

1. Everything that exists is God or is created by God.

2. God is not an evil.

3. God does not create anything that is an evil.

4. There exists an evil.

The classic Augustinian response is to deny (4) by saying that evil “is” just a lack of a due good. This has serious problems with evil positive actions, errors, pains, etc.

Here is a different way out. Say that a non-fundamental object x is an object x such that the proposition that x exists is wholly grounded in some proposition that makes no reference to x. Now we deny (3) and replace it with:

5. God does not create anything fundamental that is an evil.

How could God create something non-fundamental that is an evil? By a combination of creative acts and refrainings from creative acts whose joint outcome grounds the existence of the non-fundamental evil, while foreseeing without intending the non-fundamental evil. Of course, this requires the kind of story about intention that the Principle of Double Effect uses.

Thus, consider George Shaw’s erroneous (initial) error that there are no platypuses. God creates George Shaw. He creates Shaw’s belief. He creates platypuses. The belief isn’t an evil. The platypuses aren’t an evil. The combination of the belief and the platypuses is an error. But the combination of the two is not a fundamental entity (even if the belief and the platypuses are). God can intend the belief to exist and the platypuses to exist without intending the combination to exist.