A really big choice

A messy Irenaean world which leaves much to be desired and then grows in value due to our contribution has a great value.

A perfectionistic world where everyone is already perfectly virtuous and everything is good and we just maintain that level of good also has great value.

Quite plausibly the two worlds have incommensurable value.

God could just choose between these incommensurable values. But what God does is something else: he leaves it to the first humans to choose. This seems an especially great gift: we get to choose the basic shape of the value that our world takes.

We sin, and we get the Irenaean world.

Little evils

From time to time I wonder why it is that we focus on big evils in discussing the problem of evil. After all, first consider this argument:

1. As far as we can tell, Alice’s cancer is a gratuitous evil.

2. So, probably, there is a gratuitous evil.

3. If there is a God, there is no gratuitious evil.

4. So, probably, there is no God.

And then this one:

5. As far as we can tell, Bob’s stubbed toe is a gratuitous evil.

6. So, probably, there is a gratuitous evil.

7. If there is a God, there is no gratuitious evil.

8. So, probably, there is no God.

The same kind of backing can be given to (1) and (5). We’ve thought long and hard about Alice’s cancer and its connections to the rest of the world, and can’t find a theodicy. We’ve thought long and hard about BOb’s stubbed toe and its connections to the rest of the world, and can’t find a theodicy. And the rest of the two arguments seems to flow the same way. But as far as I can tell (!), nobody’s become an atheist because of arguments like (5)-(8) while many have become atheists because of arguments like (1)-(4).

What’s going on?

Here is one answer, which at times I’ve felt some pull towards: we shouldn’t take (1)-(4) as seriously as we do.

Here is another answer: we should take (5)-(8) more seriously than we do.

But there may be a good conservative answer, one that maintains our intuition that (1)-(4) should be taken seriously while (5)-(8) shouldn’t. There is a difference in the two arguments, and it lies in the difference between the inference from (1) to (2) and the inference from (5) to (6). In the cancer case, a good that would justify God’s permission of the evil would have to be a very large good. In the stubbed toe case, a justifying good could be pretty small. But it is much easier to overlook a small good than a very large good. Thus, (5) confers much less probability on the existence of gratuitous evil than (1) does.

When I first thought of this conservative answer, I had the image of an elephant: it’s hard to overlook an elephant in the room, but a smaller thing is easier to overlook.

Is that a good image? Are bigger goods easier to see?

Sometimes. A tiny increment in pleasure may be hard to see just as it’s hard to tell the difference in color between two nearby shades of green. If the stubbed toe led to Bob having a slightly greater appreciation of his health the next day, he might not notice.

On the other hand, some really big goods are things we may take for granted, and they need to be pointed out first by some wise person for us to expressly notice them. For instance, the value of human dignity. However, goods that we take for granted are likely irrelevant here—for goods that we take for granted are unlikely to be goods that need Bob’s cancer to exist.

Furthermore, it may not be all about smaller things being harder to see. Consider Rover the dog. How likely is it that there is a cat bigger than Rover? Well, it is more likely when Rover is small than when Rover is big. Similarly, if an evil is smaller, then it is more likely that it is connected to good big enough to justfy it than if the evil is bigger.

So, I think, one can make a case that the inference from a cancer to gratuitous evil is better than the inference from a stubbed toe to a gratuitious evil. But is it much, much better? That I am not sure about. Yet we take (1)-(4) very seriously and we take (5)-(8) not seriously at all. Even if we are right to take (1)-(4) more seriously than (5)-(8), perhaps we make too big a difference between them. Perhaps we shouldn’t take (1)-(4) quite as seriously as we do, and perhaps we should take (5)-(8) more seriously, and perhaps both!

Christ's concrete human nature

One of the old puzzles of Christology is why it is that in us the soul and body together compose a person, but they do not do so in Christ.

The problem is intensified if one thinks that there is an entity composed of the soul and body of Christ, an entity one might call “Christ’s concrete human nature”. For the person of Peter just is the entity composed of the soul and body of Peter, while in Christ the quite similar (except in sin) entity composed of the body and soul is not a person, but rather is united to a person.

The standard way out of this difficulty is to say that being a person is an extrinsic feature of a concrete human nature. Thus, Peter’s concrete human nature is a person because it is not united to a person distinct from it. But Christ’s concrete human nature is not a person because it is united to a person distinct from it. A problematic consequence of this is that personhood is not an intrinsic feature of an entity.

But there is a better way to get out of the difficulty. Just deny that in Christ there is any entity composed of his soul and body, and any statements about “Christ’s human nature” we need to make about his concrete soul and body should get paraphrased as statements about two entities, Christ’s soul and Christ’s body. Since there is no such entity as Christ’s concrete human nature, there is no puzzle as to why this entity isn’t a person.

This also solves another problem. If there is such a thing as Christ’s concrete human nature, then plausibly it thinks human thoughts, just as Peter’s concrete human nature thinks human thoughts. But Christ also thinks human thoughts. So in Christ there are two human thinkers: Christ and Christ’s concrete human nature. This is implausible! Granted, we can get out of it by making human thinking extrinsic as well, but each time we do the extrinsicness move, we intensify puzzlement.

But there is still a problem: Why is it that Peter’s soul and Peter’s body compose a whole—namely, Peter’s person—while Christ’s soul and Christ’s body do not compose a whole? Here we should make an extrinsic move. Christ’s soul and Christ’s body do not compose a whole because they are personally united to something else. Peter’s soul and Peter’s body, however, are not personally united to something else (I don’t count composition as personal union).

It may seem like at this point we have made no progress: we are back to an extrinsicness move. But this extrinsicness move is plausible in non-theological cases. Suppose Fred is missing a left leg. Then Fred’s soul, head, arms, torso, and right leg compose a whole. But Peter’s soul, head, arms, torso, and right leg do not compose a whole. Why the difference? Because Peter’s soul, head, arms, torso, and right leg are personally united to something else–namely, a left leg. But Fred’s soul, head, arms, torso, and right leg are not personally united to something else.

There is another worry. Suppose we embrace survivalism and think that Peter continues to exist in a disembodied way after death and before the resurrection of the body. But now Peter’s concrete human nature is reduced to a soul, and the soul does exist. So now Peter’s soul is a person, while Christ’s soul is not, even though both exist and are intrinsically alike (apart from accidental features). However, I think there is a way out of this, too. We deny that Peter’s soul is a person. The easiest way is to go four-dimensionalist: Peter’s soul is just a part of a four-dimensional entity that includes a body, though the body doesn’t happen to exist at this time. A less easy, but still tenable, way is to say that disembodied Peter has the soul as a proper part, with no co-part, and classical mereology needs to be modified to avoid Weak Supplementation (which is the axiom that says that if an object has a proper part, then it has another non-overlapping part).

We should not make human-like AI

1. Either AI with human-like behavior is a person or is not.

2. We should not deliberately produce AI with human-like behavior when that AI is a person.

3. We should not deliberately produce AI with human-like behavior when that AI is not a person.

4. So, we should not deliberately produce AI with human-like behavior.

Obviously, the big question is whether (2) and (3) are true.

In favor of (3), a non-person with human-like behavior evokes emotional responses from us that are only apt as directed at persons. These emotional responses are of great moral importance to our life, and some of them are constitute a recognition of the object of the emotion as a being with dignity, a sacred being, and to have such emotional responses to something that lacks the relevant dignity blurs the central moral distinction between persons and non-persons.

In favor of (2), we have several arguments. Start with some Kantian ones. AI is an artifact. When we make artifacts, we make them to serve our purposes. To make a person to serve our purposes is to treat the person as a mere means to an end. And that’s wrong. This argument, I think, applies no matter what our purpose is: even if our purpose is to make the AI live its own free life. That’s still our purpose for it, and we have no right to impose a purpose on a person’s life.

Furthermore, by designing a digital person, we are designing, in its fundamentals what its basic purposes in life are and we are thus exercising a mode of control over another person that we have no right to have.

A final but least principled Kantian argument is that even if we “set free” the digital person—whatever exactly that means—it is pretty much impossible to protect digital persons from being enslaved by other humans.

There are also some non-Kantian arguments. If an AI is a person, that person will eventually be very cheap to keep in decent existence as compared to a flesh and blood human being. Since we have the duty to protect the life of a person when doing so is not an undue load on limited resources, we would have the duty to keep any person AI that we spin up running indefinitely. This is problematic as it ties the hands of future human generations, by imposing on them what one might call “an unnatural duty” to keep running all the AI persons that we make, with little benefit to the future human generations from this. The problem is the worse the greater the numbers of digital persons that we spin up. This problem is akin to the problem of frozen embryos in fertility clinics if these embryos are persons (which I think they are).

There is also a dilemma. We have the duty to protect the life of persons. But at the same time, there is something deeply unappealing about something of the level of sophistication of an ordinary human mental life extending an order of magnitude longer than the typical human life-span (rescaled as needed to take account of differences in processing speed). The most appealing religious accounts of afterlife involve a radical transformation, e.g., theosis or parinirvana. I think many of us rightly would feel that living a thousand years of the kind of life we now have isn’t appealing, though we wouldn’t mind an extra ten or twenty or maybe even hundred years. If we were ever able to indefinitely extend human life without an undue resource cost, we would find ourselves in an inextricable moral dilemma: on the one hand a duty to protect life when doing so does not carry an undue resource cost and on the other hand the monstrousness of living an order of magnitude longer than ordinary human life should be. But with digital persons, indefinite life extension would be easy, and so the dilemma would be unavoidable.

Finally, we would take a significant moral risk in designing digital persons. Training processes involve vasts amount negative feedback. We just do not know how unpleasant that might be.

Rowe's argument from evil revisited

In his 1979 classic paper, Rowe says that a necessary condition for an “omniscient, wholly good (OG) being” to fail to prevent an evil s₁ is that at least one of the following three conditions holds:

1. there is some greater good, G, such that G is obtainable by OG only if OG permits s₁, or

2. there is some greater good, G, such that G is obtainable by OG only if OG permits either s₁ or some evil equally bad or worse

3. s₁ is such that it is preventable by OG only if OG permits some evil equally bad or worse.

We might put it this way: Rowe is saying that OG will prevent all gratuitous evils, and an evil is gratuitous if none of (i)–(iii) are satisfied.

First, note that (i) can be omitted, since if we have (i), we have (ii) as well. That’s a nice simplification: we only need (ii) and (iii).

More interestingly, however, note an ambiguity in “there is some greater good”. To see the ambiguity, consider this apparent counterexample to Rowe.

Suppose both theological compatibilism and Molinism are false, and God decides to give Alice a free choice between a great moral good G₁ and a tiny moral evil s₁, in circumstances where Alice is very likely to choose G₁. Absent theological compatibilism and Molinism, God cannot, however, ensure that Alice will choose G₁. Suppose, also, that free choice is not valuable as such, but significantly freely choosing well is very valuable (where significant freedom is freedom to choose between right and wrong), and much more valuable than choosing well without significant freedom. Finally, let’s suppose Alice goes for s₁. It is reasonable to say that s₁ is non-gratuitous, for preventing s₁ would lose the opportunity for the great good of Alice significantly freely choosing G₁. But an opportunity for a good may not count as a good. Condition (iii) is not satisfied—if God didn’t give Alice the choice between G₁ and s₁, no other evil would have to be permitted. But neither is (ii). For the good G of Alice significantly freely choosing G₁ does not exist, since Alice does not in fact choose G₁.

For many years I thought that this was a counterexample to Rowe. Today it hit me that this might be uncharitable. When Rowe says “there is some greater good”, he might mean a greater possible good or a greater type of good. Thus, in my example there is a greater possible good or a greater type of good, that of Alice significantly freely choosing G₁, albeit this is a good that isn’t actually instantiated.

Thus, charitably, let’s take Rowe to be quantifying over possible goods (or, pretty much equivalently, types of goods). A weak support for this is that the “some evil” in (ii) clearly quantifies over possible evils, so it makes the conditions neater to quantify over possible goods and evils.

Here is another problem for Rowe’s account. Suppose (ii) and (iii) are not satisfied, but instead we have:

4. there is a good, G, such that G is obtainable by OG only if OG permits s₁ or something at least as bad while the only way that s₁ is preventable by OG is by permitting some lesser evil s₂ or something at least as bad as s₂, and that G plus s₁ is better than s₂.

It seems that in case like this, s₁ need not be gratuitous. But note that a case like this does not require either G to be a greater good in comparison to the evil s₁ nor does it require s₂ to be at least as bad as s₁. For intance, suppose the value of G is 10, the value of s₁ is  − 11 and the value of s₂ is  − 3. Then G plus s₁ has value  − 1, which is better than the  − 3 we get by preventing s₁ at the cost of s₂ and loss of G. In cases like this, (ii) and (iii) need not be satisfied, and yet the evil need not be gratuitous. In other words, there cases where we have a kind of mix of (ii) and (iii). (It’s hard to think of examples, but it’s also hard to think of examples of (iii). I think the examples would have to involve divine promises.)

I also worry about incommensurability. For simplicity, let’s suppose there is no incommensurability: all values and disvalues are comparable. Also, let’s suppose that there are only finitely many scenarios in play, so we don’t have to worry about infinite sequences of less and less bad options and stuff like that.

Still Rowe’s necessary condition for non-gratuity have become more complicated: (ii) or (iii) or (iv), and with the quantifiers ranging over possible goods and possible evils. And once conditions get so complicated, one starts to worry that we are missing something. It would be nice to simplify the conditions.

Here is my attempt at such a simplification:

1. There is a possible scenario where s₁ is permitted by OG which is at least as good as any possible scenario where s₁ is prevented by OG.

Before continuing, I want to worry a bit about the following. Suppose that by preventing an evil s₁ you lose a good G, where G is not a greater good, but an “equal good”, i.e., the value of G equals exactly the disvalue of s₁. In that case, it seems plausible that a morally perfect being would prevent s₁, since there is a presumption in favor of preventing evils. I will take avoid this worry simply by assuming that it’s better to have neither G nor s₁ than to have both G and s₁ in cases where the value of G equals the disvalue of s₁, i.e., that axiology has a presumption in favor of no-evil. Otherwise, we need to slightly modify (1).

Suppose (1) is true. Let G be the sum total of the goods in the scenario A that’s at least as good as any possible scenario where s₁ is prevented by OG. It follows that any way of preventing s₁ involves either the loss of G or a scenario where the totality of evil is greater than s₁. If G is a greater good compared to s₁, then we thus have (ii). If G is empty, then it seems that there are no goods in the scenario, but we must have greater evils in the s₁-prevention scenarios than in A, and so we have (iii). Finally, if G is non-empty but not greater in comparison to $s_1 then I suspect we are going to have (iv) or something very close, but it’s a bit too complicated for me to think through in detail at the moment.

Moreover, (1) is intuitive as a necessary condition on God’s permitting an evil, in a way in which the triple disjunction (ii) or (iii) or (iv) is probably too complicated to be intuitive. I take it, then, that (1) is a friendly amendment to Rowe’s atheistic argument.

But at this point there is an interesting skeptical theist move. Rowe needs to be able to be epistemically justified in pointing to some evil s₁ and denying (1). But that’s pretty hard. Claim (1) existentially quantifies over all possible scenarios where s₁ is permitted by OG. It’s not that easy to know that one of them has the property indicated in (1), given the vast range of scenarios where s₁ is permitted by OG.

Aquinas on Incarnation as a rock or animal

Aquinas thinks it would be unfitting for God to become incarnate as a non-rational creature. In Summa Theologiae III.4.1, his reasoning is that human nature had an appropriate dignity, as it “was apt to contain the Word Himself in some way through its operation, by knowing Him and loving Him”, but not so for the non-rational creatures. In Summa Contra Gentiles 4.55 we have a different and more philosophical argument:

We must also observe that the rational creature alone acts of itself, for irrational creatures are more driven by natural impetus than act of themselves [magis aguntur naturali impetu quam agant per seipsas]; thus they are to be regarded as instruments rather than principal agents. Now it was fitting that God should assume a creature capable of acting of itself as principal agent, because an instrumental agent acts through being moved to action, whereas the principal agent acts itself and of itself. Accordingly, if God were to do anything by means of an irrational creature, all that is required in accordance with that creature’s natural condition is that it be moved by God, and there is no need for it to be assumed into personal union so as to act itself, since its natural condition does not admit this, it being admitted solely by the condition of rational nature [quia hoc eius naturalis conditio non recepit, sed solum conditio rationalis naturae]. (Shapcote, with italicized phrases retranslated.)

In neither text does Thomas deny the metaphysical possibility of God being incarnate as a nonrational creature, such as a rock, plant or animal. While this is an argument from silence, I think it is a pretty strong one: if he thought it was impossible, we really would expect him to say so, rather than merely saying it was unfitting.

Both arguments seem to me to be based on the idea that if it’s fitting for God becomes incarnate as X, if there is to be much of a point to this incarnation, this X needs to be of a sort that can express the divine person in a special way. If the Logos were to become a piece of granite, the petrous behavior of the rock would not differ from that of any other piece of granite. But if the Logos becomes a human, the rational behavior of this human is able to distinctively express the Logos in a way that ordinary human persons do not. We see this in the Gospels: Jesus as a human being, in his free human choices, movingly expresses the personality of the Second Person of the Trinity. He is just as human as all of us, but all of us humans are different from one another in our operations in a way that is expressive of the person. Of course, all pieces of granite are different from another, but these differences are not due to the operations of the rock differently expressing the rock’s hypostasis (we shouldn’t say person!). Rather they are due to the differences in the matter the rock was formed from and the external forces. God can be expressed in granite.

Of course, every rock reflects God’s goodness, and some rocks especially so, say because they are formed into a beautiful statue or inscribed with a meaningful text. But the special expression of God’s goodness is just a function of the rock’s initial matter and external influences. If God wants a rock to particularly well express him, there is no advantage to God’s becoming the rock: “all that is required … is that it be moved by God”—and all rocks are ultimately moved by God. But it is different for a human, that is a self-originator of its behavior. For the self-originated agency to be fully an expression of God, the person who is human, from whom that behavior originates, needs to be a person who is God. There is thus something that the Logos can accomplish by taking on a rational nature that cannot be accomplished in any other way. We might say that all of creation is God’s self-expression by creatures, but in becoming a human, God can be self-expressed in a creature—something that could not happen if God were to become a non-rational creature. This highlights how it it is that the Incarnation is also an ultimate completion of the act of creation. God’s becoming a non-rational creature would be just God showing off, rather than God manifesting his love by living that love as a human.

TWo closing thoughts. First, I think Aquinas’ Contra Gentiles argument works best if non-rational creatures function deterministically. Given quantum mechanics, we have good reason to think they are indeterministic. But nonetheless the basic point remains: randomness is not really a self-expression, so even if the Logos were to control the quantum processes from the inside, it seems that as long as that control was fully in accordance with the nature of the non-rational creature, it wouldn’t be distinctively expressive of divinity.

Second, I am not sure that Aquinas’ Contra Gentiles argument fits well with Aquinas’ theological compatibilism, on which God can through primary causation make us freely behave a particular way. At least we can say that the argument works better if we have theological indeterminism. And thus theological indeterminism has a theological advantage: it gives us a deep reason for why the incarnation as a human is fitting.

AI and emotion

In some of my work, I use the example of a pill which gives one that warm glow that one has when one has done something sefless and morally good, but which pill one can take when one hasn’t done anything like that, just to feel good about oneself. This is wrong, because that warm glow emotion is too important morally for it to be the subject of counterfeiting. Moreover, I think it remains wrong to take the warm glow pill even if one fully knows that one hasn’t done the morally good deed that it fakes the feeling of.

Generalizing, I think we shouldn’t deliberately induce emotions in contexts where they are inapt when these emotions have a significant amount of moral importance. We shouldn’t induce them in ourselves nor in others. For instance, we shouldn’t try to make others feel like we are their friends when we are not—even if they fully know that that the feeling is misleading.

Now, there is a multitude of significantly morally important interpersonal emotions that are only apt as reactions to another person’s actions. These include feelings of being the object of good- or ill-will, feelings of gratitude or resentment, a feeling of not being alone, and of course a feeling of being a friend. Such emotions have a significant amount of moral importance. We should thus not try to induce them deliberately.

But I think a plausible case can be that current AI chatbots are tuned (both through feedback from users and the system prompt) to produce emotional reactions that are of this interpersonal sort—the communications of the chatbot are tuned to make one feel that one’s concerns are care about. And since the chatbots aren’t persons, the emotions are inapt. The tuning is thus morally wrong, even if any sensible user knows that the chatbot has no cares.

One can, sometimes, have a double-effect justification of inducing misleading emotions, when doing so is an unintended side-effect. However, given that leaked system prompts do in fact have instructions about emotional cadence, it is very implausible to think that the induction of inapt emotions is an unintended side-effect.

A couple of days ago, Anthropic offered me a decent chunk of money for doing some part-time review of the reasoning capabilities of one or more of their models. I turned it down because of moral concerns along the above lines.

I note that double-effect can, however, justify using a chatbot when one does not intend an inapt emotion that one expects in oneself (e.g., I find myself feeling grateful when I get a good AI answer), when the goods gained from the use are sufficient in comparison to the significance of the inapt emotion. But I think the risk should be taken into account.

This is all rather similar to St. Augustine’s infamous concerns about stage drama. But I think one can make a distinction between the cases. Interpersonal emotions can be categorical or hypothetical. Categorical disapproval is apt only when a person has done something morally wrong. But we also have hypothetical disapproval: we can imagine someone hypothetically acting in some situation, and then have a feeling of disapproval towards that hypothetical action. I think there is a real felt difference between these two feelings, just as there is a real felt difference between seeing a sunset and imagining a sunset. And, perhaps, the audience of a dramatic performance one only has—or at least should only have—the more hypothetical feeling.

Metaethics and emotion

Suppose that someone notes that the digits of π starting at some position n start looking like they have an odd pattern, and it occurs to someone to turn them into ASCII characters (three digits at a time, say). The result is a surprising English list:

• Murder, cruelty, torture, unjustified promise breaking, ….

The list goes on in the same vein, until after a long time comes a period.

Moral philosophers think hard, and realize that anything that is clearly wrong is on this list, that nothing on the list is such as to be clearly non-wrong, and indeed that the Prohibition Hypothesis that necessarily π at position n has a list of all and only the morally prohibited actions is quite plausible. Most moral philosophers end up accepting the Prohibition Hypothesis, and applied ethics enters a golden age where we are able to figure out whether some action is wrong simply by deciding whether it falls under some description on the list.

Obviously, the Prohibition Hypothesis still presents philosophical puzzles. Is this just random choice? Is there a God who has power even over the digits of π? Is English metaphysically special?

But now imagine that some metaethicists hypothesize that what it is for an action to be prohibited is for it to fall under one of the descriptions in the list in π starting at position n.

I think this metaethical hypothesis is something we would have good reason to reject. That growing people for organs falls under one of the descriptions on the list (say, the first one) gives us good reason to think that growing people for organs is wrong. But it’s surely not what makes growing people for organs wrong. For what makes growing people for organs wrong surely has nothing to do with what the digits of π are.

How could we back up this intuition? It is tempting to say something like this:

2. That an action falls under a description in the list at position n in π does not give me a decisive moral reason to omit the action.

But that begs the question. On the metaethical hypothesis in question, what it is for there be to a decisive moral reason for ϕing is for non-ϕing to fall under a description in the list.

Is there a way to argue against the metaethical hypothesis in a non-question-begging way? I think so.

3. There is a certain set E of emotional attitudes that is appropriately had to the fact that ϕing is prohibited.

4. The attitudes in E are not always appropriately had to the fact that ϕing falls under a description in the list in π starting at position n.

Given 3 and 4, we should not say that what it is for an action to be prohibited is for it to be on the list. We are not begging the question here. The question of what emotional attitudes are appropriate is not in general a question of what is morally obligatory. Note also that one can hold 3 and 4 while accepting the Prohibition Hypothesis. For emotional attitudes are hyperintensional. Every theist agrees that a child is smiling if and only if God knows that a child is smiling, but that a child is smiling and that God knows that a child is smiling do not appropriately give rise to the exact same emotional attitudes.

The above suggests that we have an emotional test for a metaethical theory: when the theory claims that what it is for an action to be prohibited (or required or whatever) is for it to satisfy some predicate F, we can criticize the theory if we can plausibly argue that different emotional attitudes are appropriate to the action’s being prohibited (or required or whatever) and to its satisfying F.

I suspect one can run an argument against divine command theory along these lines. The appropriate emotional attitudes (say, of disapproval) with regard to ϕing in light of ϕing being morally prohibited are different from the attitudes with regard to ϕing in light of God commanding us not to ϕ.

Mental properties and union dualism

Suppose union dualism is true (I am a composite consisting of soul and body) and I am looking at a red cube. Then I am consciously aware of a red cube in virtue of my soul having some property instance M. Now, this property instance M makes me have a perception of a red cube, but it doesn’t make my soul have a perception as a red cube, because otherwise two things have that perception, and we have the too many thinkers problem. Thus considered as a property of my soul, we shouldn’t describe M as “the property (instance) of perceiving a red cube”. Instead, it is the soul’s property (instance) of “being an x such that x’s possessor perceives a red cube”.

Is M also a property (instance) of me, or just of my soul? Indeed, can the same thing be a property (instance) of two things? Maybe. It sure seems that a watermelon is partly red because its flesh is red, and yet we shouldn’t multiply instances or tropes of red, so there is a single instance of red—which makes the part red, thereby making the whole partly red. Thus, the redness can be thought of as both a property of the flesh and of the watermelon. It is an immediate property of the flesh and a mediate property of the watermelon. As a property of the flesh, it is the property of being red. As a property of the watermelon, it is the property of being partly red. Perhaps, though, this is a merely semantic question. We might say that “property possession” is immediate property possession or that it is mediate or immediate property possession.

In any case, insofar as M is a property of my soul, there is a sense in which it is a mental property and a sense in which it is not. As a property of the soul, it is not a property of thinking, perceiving, believing or of any other of the usually named mental activities, because the soul engages in none of these, since these are activities of me, not of my soul. But at the same time, it is a property that makes me perceive, and hence can be considered mental in that sense. Perhaps we might want to say this: M is a proto-mental property, and to have a mental property is to have a soul that has the requisite proto-mental property.

In any case, I think the above considerations show that arguing for Cartesian dualism—the view that I am a soul—on the grounds that the soul has mental properties and yet there are not two thinkers is too quick (Merricks argues like that here). In one sense, the soul has mental properties, but these properties do not turn the soul, only its possessor, into a thinker. In another sense, the soul has only proto-mental properties.

Maybe it’s a bit like this. Water isn’t moist, but it makes other things moist. Water does this by having some property—a property the physical chemist will have more to say about—in virtue of which anything that has the right association with the water is moist.

Antinatalism and proxy consent

Consider the consent argument for antinatalism (the view that human reproduction is morally wrong) that we shouldn’t impose great risks on people without their consent, but by having a child one imposes great risks on them (life may turn out really badly), and one cannot get consent.

One obvious response is that we are willing to accept proxy consent in medical decision making when the patient is incapable of consent. And of course in the case of a child, normally the first people we turn to for proxy consent are the parents. So it seems reasonable to think that proxy consent from the parents should take care of any worries about the child’s not having consented to come into the world.

What kind of a response can an antinatalist give?

One response is that the whole idea of proxy consent in medical cases is itself bogus. We just should not do medical procedures on children or other non-competent persons that are of a sort that would require consent—say, procedures that are highly invasive or significantly change the course of future life in ways that are not unambiguously for the better. If it is a choice between amputating a child’s leg or letting the child die, we should just let the child die, because a choice whether to live without a leg is the kind of choice that a person should make, and if they cannot make that choice themselves, no one should make it for them.

This seems implausible. It seems pretty clear that we shouldn’t let a child with a gangrenous leg die when the parents consent to amputation. But perhaps the antinatalist can try to distinguish the cases of procreation and amputation. In the amputation case, the child already exists and will suffer a painful death if we do not amputate. Perhaps that overrides the autonomy concerns to a sufficient degree that proxy consent becomes sufficient to justify the amputation. I think that doesn’t work. We can suppose that the child is unconscious, and that in the absence of amputation death will be painless. And it still seems permissible to amputate with parental permission.

A response that I’ve seen is that the fact that standard medical proxy consent cases differ from the procreative case because one cannot even give proxy consent on behalf of someone who doesn’t exist. But this response seems to me to be rather problematic. For if one thinks one cannot give proxy consent on behalf of someone who doesn’t exist, it seems that by the same token one cannot violate the autonomy of someone who doesn’t exist.

But actually both ideas seem false. We can violate the autonomy of someone who doesn’t exist. For instance, we can manufacture a robot that is going to be dormant for 25 years, and will then activate, choose a random 20-year-old and forcibly perform cosmetic surgery on them, radically changing their appearance. By manufacturing the robot we are violating the autonomy of someone who doesn’t exist. And similarly it seems quite possible for prospective parents to provide proxy consent for emergency medical procedures prior to the existence of their children. For instance, supposing (in violation of antinatalist norms) they have several children and expect to have several more, and are afraid that they will forget to sign emergency medical consent forms for their future children, so they sign a blanket consent form for single-leg amputation in case of otherwise untreatable gangrene for all of their present and future children.

Another possible response is that while it’s acceptable for parents to give proxy consent for medical procedures for their incompetent children, the life they create in procreating will one day be the life of a competent person who never agreed. However, this just doesn’t create a disanalogy, because in a number of cases of proxy consent for medical procedures, the child’s entire future life is affected, including the future life once the child reaches competency—this is true in typical cases of amputation.

Furthermore, the idea that one cannot give proxy consent for things that can have significant negative effects on the future life of a competent person, but one can in the case of things that only affect the parts of life when the person is incompetent, leads to the following really weird consequence. A couple is ordinarily not permitted to have a child, but if they find out that they have a genetic condition which will result in the painless death at age four of any child they have (after an ordinary life, without any suffering beyond the ordinary), and if there is no afterlife, then they are permitted to have the child, because their proxy consent does not affect the future life of a competent person. That finding out about this condition would make procreation permissible, while it would be impermissible absent the condition, seems absurd.

Virtue and tasks that I don't have to do

Sometimes I have some onerous task that we seem to have a duty to perform. And then something happens—perhaps we learn something or perhaps the situation changes—and it becomes clear that I have no duty to perform the task. In this post, I am interested in morally evaluating the feeling of relief I then often have.

But start with an opposite thought that could occur to one in place of relief: “Oh, no! I had hoped to gain the merit of performing the task, to gain the intrinsic good of acting virtuously in a particularly onerous way, but now circumstances have robbed me of this.” This thought could occur to me, but in fact pretty much never does, because I am too lazy a person to look forward to doing an onerous thing. But apart from my non-virtuous reason for not having the thought, I don’t think it’s a great thought to have. I think such a thought is like treating morality like a game—“Oh, no! I was going to have this boss fight, and I accidentally found a way around it, and now I won’t get the achievement!” While it is intrinsically good to act well, I don’t think we should treat acting well as something like a win in a game. Plus, it sounds Pelagian.

Now, it can make sense to have a regret that someone else performed the task when there was a special personal reason to do the task oneself. If one’s child wants someone to explain something complex and difficult to them, and a school teacher gets to it first, one might feel a regret that one didn’t get to do it oneself.

But let’s go back to cases where one feels relief. There are different kinds of situations like this. One kind is where the goods the task was to accomplish happen without the onerous input from me. Perhaps someone else does the onerous task. In that case, it makes sense to feel gratitude to them, and this gratitude makes no sense if one isn’t on some level glad that they took the burden on themselves. So in that case, some kind of a relief is a part of the feelings of a virtuous person. Or perhaps the thing I was trying to ensure happens “on its own”. Then perhaps one doesn’t feel gratitude to any person (unless maybe one is a theist), but a gladness and relief seems as appropriate as in the case where someone else produced the goods.

A somewhat different case is where the task become moot. You promised to go with a friend to see a movie which you really didn’t want to have to sit through, and which you think your friend won’t enjoy either, but you promised and you thought that was that. But now your friend read some reviews and decided they don’t want to see it either. Again, relief is appropriate.

Of course, there are times when the reason the task became moot is itself a reason for regret. If the friend you promised to go to the boring movie with had their mother die and so is no mood for movies, any relief should be silenced or drowned out by sadness for your friend.

A third kind of case is where the goods of the task become or turn out to be unattainable. You are a surgeon and you were going to be staying up performing a life-saving operation when all your body is crying out for sleep. And then the patient dies, and it’s not your job to save their life, because it’s too late. It’s a bit like the friend’s mother’s death case. But it’s not quite the same. The virtuous person should, I think, primarily feel a regret for the loss of the goods. There is a kind of vice—a vice to which I am particularly prone—of pursuing duties because they are duties rather than for the sake of the goods achieved by the task. If one primarily feels relief because the goods turn out to be unattainable, this is a sign that one’s appreciation of these goods was insufficient, an unfortunate thing.

A fourth kind of case is where the goods of the task can still be achieved by the task, but it turns out that the task is no longer one’s duty. Perhaps after reflection I realized that the task is supererogatory. Or perhaps an authority who had required the task of me just made the task optional. A kind of “The pressure is off” relief is fitting—one is no longer obligated, and so one is in a less risky situation. One still risks losing the goods of the task, but one no longer risks wrongdoing. And that’s good. But if one instantly drops all plans for the task, and feels unalloyed gladness that one no longer has the duty, and does not care about the loss of the goods that the task would have accomplished, again it’s a sign that one’s appreciation of the goods was insufficient.

Here’s an interesting thing. A similar thing goes wrong in the case of the inappropriate “I’ve been robbed of the merit” regret and in the cases of the inappropriate relief: a self-centered failure to be sufficiently focused on and appreciative of the goods of the onerous task. This is a vice that is very common in me. I am often much more focused on "my duty" than on the first order goods to be achieved.

Corruptionism and time travel

Corruptionism is the Christian view that at death we cease to exist, and only return to existence at the resurrection of the dead. There are two kinds of corruptionism. On materialist corruptionism, the body is destroyed, and we are all gone until the resurrection. On Thomistic corruptionism, although the body is destroyed, the soul continues to exist until the resurrection, but the person cannot exist reduced to a soul, so the person ceases to exist, just as on materialist corruptionism.

Here’s an argument against corruptionism:

1. Death is a serious non-instrumental harm.

2. Forward time travel is not a non-instrumental harm.

3. If corruptionism is true, there is no significant non-instrumental value difference between death and forward time travel.

4. There is a significant non-instrumental value difference beween a serious non-instrumental harm and something that is not a non-instrumental harm.

5. So, corruptionism is not true.

Premise 3 is probably the most controversial one. The idea is this. On both corruptionism and forward time travel at some moment the person ceases to be and at a later moment the person comes back into existence. On materialist corruptionism, it is difficult, if not impossible, to find a metaphysical difference between corruptionism and forward time travel. On Thomistic corruptionism, there is a difference: the soul continues to exist in the interim between death and resurrection, but not during the skipped period of time in forward time travel. But it is not clear how the soul’s continued existence is a harm to one.

One may ask: But how does the non-corruptionist, or survivalist, Christian escape the argument? Isn’t death less bad on survivalism? Well, here I think is the difference: on survivalism during the interim period from death to resurrection, one exists in a very unfortunate state: the state of being deprived of all of one’s body. To exist without even one arm is unfortunate. But on survivalism one exists without one’s arms, legs, eyes, etc.

There is a forward time travel analogy for survivalism. While corruptionism is like standard forward time travel, survivalism is an extreme version of the following story: Due to a malfunction in the forward time machine, you got left behind, but your arms got sent to the future, so aimed that they will rejoin you when you get to the future the usual slow way. This is clearly a serious harm. Existing armlessly is a serious harm.

Finetuning the multiverse

It has occurred to me that there is a kind of fine-tuning of multiverse theories.

If there is too large a variety of universes within a multiverse, we get skeptical problems. For instance, if all possible laws of nature are realized, then induction-friendly laws like “Gravity is always attractive” are either outnumbered by or at least do not outnumber nasty laws like “Gravity is attractive until the end of March 2026 and repulsive afterwards”. Or if there are too many kinds of material arrangements, we would expect scenarios with local order, like Boltzmann brains to outnumber or at least not be outnumbered by scenarios like brains arising by evolution.

On the other hand, if there are too few universes, then the laws by which universes are generated need to be themselves fine-tuned or else there won’t be life.

So, a multiverse theory needs to be tuned as to the variety of universes it supposes. I don’t have a a great argument that this tuning is highly improbable, but it might be. My intuition says, for what it’s worth, that the on naturalism we should either expect a single universe or a very wide and varied multiverse, and the latter is likely to engender skepticism.

A new Thomistic view of the Trinity

I think the historical Aquinas’ solution to how God is one in three persons is a relative identity view that posits two kinds of identity:

1. Individual identity: the lack of a real distinction, where real distinction might come from a difference of matter (as in material substances), a difference of form (as in angels) or an opposition of real relations (as in the Trinity).

2. Sameness of essence: having the numerically same substantial form.

While this is a relative identity account, it has an advantage over more standard relative identity accounts in that it nicely explains our intuitions about absolute identity. For on Aquinas’ solution, as far as we know, except where God is involved, the two identities are co-extensive. For Aquinas (like perhaps Aristotle) believes in individual forms of creatures, so all creatures that are distinct by individual identity have numerically distinct substantial forms, and conversely there are no mere creatures with two substantial forms. Thus when we are not dealing with God, we can afford to be ambiguous between the two kinds of identity, and hence talk as if there was absolute identity. (As far as I know, Thomas never makes this point.)

The point of this post, however, is to offer an alternative version of Aquinas’ two-identities account. The alternative is thoroughly Thomistic, but it’s not what Thomas has. Here it is. We have two kinds of identity. The first is individual identity, as in the historical Aquinas’ solution. The second is:

3. Sameness of esse: having the numerically same esse or act of being.

Just as in the historical Aquinas’ solution, the alternate account has the feature that apart from theological cases, the two kinds of identity are co-extensive. Distinct individual creatures have distinct acts of being, and no creature has two acts of being.

A disadvantage of this view is that “sameness of esse” doesn’t fit quite as well as “sameness of essence” with the Nicene Creed’s “homoousion”. But some things are worth noting. The previous English translation of the Nicene Creed in the Catholic Church actually had “sameness of being”. The word ousia is the abstract form of einai, to be. And in God essence and act of being are the same by divine simplicity. So I think the disadvantage can perhaps be overcome.

An advantage, however, is that sameness of esse seems even more identity-like and unifying than sameness of form. If x and y have the very same act of being, it is hard to deny that there is a real unity between x and y. Here is one way to see the point. On Platonist metaphysics, unlike on Thomastic metaphysics, you and I have sameness of form: we each have the numerically same Form of Humanity. Granted, Platonist metaphysics may be false. But the fact that you and I count as having sameness of form on Platonist metaphysics should make a little less happy about using that as an account of the unity in the Trinity. On the other hand, once we supplement Platonist metaphysics with an act of being, it is clear that you and I will get different acts of being, since each of us can exist without the other doing so.

Moreover, this account may help cast a light on the thorny question of why Aquinas at one point posits a human esse in the incarnate Christ distinct from the divine esse (though elsewhere he denies it). For suppose that there is only one esse in Christ and we accept the sameness-of-being account. Then we would be able say that the Jesus Christ as human is God, since the one and only esse in Jesus Christ, whether as human or as God, is the divine esse, and this we shouldn’t say (and indeed Aquinas denies it). Thus if we accept the sameness of esse account, we get an argument for the two esse view of the Incarnation. Of course, we can turn this around. We might say that the two esse view is false, and hence the sameness of esse account is false.

Trinity, quaternity and naming God

One now-classic solution to some of the challenges of the doctrine of the Trinity is relative identity. On relative identity accounts of the Trinity, we do not heretically say, e.g., that the Father is absolutely identical with the Son, but instead we posit a same-essence (or same-God) relative identity relation, and say that the Father is same-essence as the Son. Now, most of the time proponents of relative identity views deny that there is any such thing as absolute identity at all. All identities are relative to a sortal. However, in their famous “Material Constitution and the Trinity”, Brower and Rea offer an account of the Trinity using relative identity within a system where there is such a thing as absolute identity, governed by the standard rules of first-order logic.

Any account of the Trinity that allows for absolute identity governed by classical logic faces an interesting problem. Suppose:

1. There is such a thing as absolute identity, denoted by “=” and governed by its standard first-order logic rules.

2. There is a name for God as such, “G”, and names for the Father, Son and Holy Spirit, respectively, “F”, “S” and “H”.

3. F ≠ S

4. S ≠ H

5. F ≠ H

6. For all x, if x = F or x = S or x = H while y = F or y = S or y = H, and if x = G, then y = G.

7. If x = x, y = y, z = z, w = w, x ≠ y, x ≠ z, y ≠ z, x ≠ w, y ≠ w and z ≠ w, then x, y, z and w are four, counting by absolute identity.

8. Then F, S, H and G are four, counting by absolute identity.

9. Heresy! In no sense is there a divine quaternity!

Premise (6) captures the idea that the persons of the Trinity have equality with respect to divinity, and hence if x and y are persons of the Trinity, then if either of x and y “is God” in some sense of “is” and “God”, then the other “is God” in the same sense.

Proof of 8 from 1–7:

1. If F = G or S = G or H = G, then F = G and S = G and H = G. By 6

2. If F = G and S = G, then F = S. By 1

3. So F ≠ G or S ≠ G. By 3 and ii

4. So F ≠ G and S ≠ G and H ≠ G. By i and iii

5. F = F, S = S, H = H. By 1

6. G = G. By 1

7. So, F, S, H and G are four, counting by absolute identity. By 3–5, iv–vi and 8

There is a way out of this, in van Inwagen’s work on the Trinity. Van Inwagen denies that there are names for the Father, Son, Spirit and God: there are just predicates, like “is divine” and “is a Father”.

This is overkill for getting out of the above. It is difficult for a Christian to completely deny the existence of divine names. After all, you become a Christian by having someone pour water over you while saying: “I baptize you in the name of the Father, and of the Son and of the Holy Spirit.”

I think the quaternity argument leaves Christians who want to uphold classical absolute identity with two options:

1. There is no name for God.

2. There are no names for the Father, Son or Holy Spirit.

Here, “name” means “proper name”, since that’s the kind of name that classical logic talks about.

Accepting both (a) and (b) is not, I think, an option. Of the two, I think (b) is the more problematic. Names are too central to human relationships with persons. Thus, I think, the Christian who wants to uphold classical absolute identity should accept (a). And there is some support in Christian tradition for denying that God has a name.

(This is not what Brower and Rea do. In footnote 7, they talk of “the name ‘God’”, albeit in the context of discussion of a heretical view, but as I read the footnote they have no reservation about “God” being a name.)

While (a) is the less problematic of the two options, I still think (a) is problematic. Grammatically, “God” and “the Trinity” and the tetragrammaton all function as proper names. While there is some precedent in the Christian tradition for denying that God has a name, that still seems a bit of a stretch.

I think that if one is going to adopt a relative-identity account of the Trinity, then one should either deny that there is such a thing as absolute identity or at least one should deny that it is governed by the rules of classical logic.

I tentatively propose the following modification to the classical theory of absolute identity as a way of getting out of the quaternity argument. Restrict the identity-introduction rule that says that for any name N we get to write down N = N to the case of what one might call hypostatic or individual names (or, perhaps, to non-essence names). Thus, we get to write “Father=Father” but not “God=God”. Now everything in the quaternity argument goes through, except we don’t get (vi) and and hence we can’t infer (vii) or (8).

A technical problem with brutal composition

Markosian once proposed brutal composition as an answer to the question of when a (proper) plurality of objects composes a whole: composition is a brute fact, where a brute fact is a fact F such that “it is not the case that F obtains in virtue of some other fact or facts.”

Here is a nitpicky objection. Obviously:

1. The xs compose a whole if and only if there is a y such that the xs compose y.

Moreover, this doesn’t just happen to be true. For:

2. The fact that the xs compose a whole is the fact that there is a y such that the xs compose y.

And:

3. If it is a fact that there is a y such that the xs compose y, then there is an object y₀ such that the fact that there is a y such that the x compose y obtains in virtue of the fact that the xs compose y₀.

This follows from the Weak Existential Grounding principle:

4. If it is a fact that ∃yF(y), then there is at least one y₀ such that the fact that F(y₀) grounds the fact that ∃yF(y).

(Strong Existential Grounding says that the fact that ∃yF(y) is grounded in every instance. There are apparent counterexamples, but Weak Existential Grounding is hard to deny.) Assuming that “obtains in virtue of” is the same as “is grounded by”, we conclude from (2)–(4) that:

5. If the xs compose a whole, then there is a y₀ such that the fact that the xs compose a whole obtains in virtue of the fact that the xs compose y₀.

What can a brutalist say about this argument? I think one move would be to deny (2).

Instead, perhaps, we have a grounding relation between the facts that the xs compose a whole and that there is a y such that the xs compose y. If this grounding relation runs right-to-left, we have an immediate contradiction to the brutal composition thesis from (2): that the xs compose a whole obtains in virtue of there being a y such that the xs compose y.

So the grounding relation would have to run left-to-right. Thus we would have to have it that the xs composing a whole grounds there being a y such that the xs compose y. But likewise the particular fact that the xs compose y₀ grounds there being such a y. Now consider the two facts:

1. that the xs compose y₀

2. that the xs compose a whole.

If neither grounds the other, then the fact that there is a y such that the xs compose y is grounding-overdetermined by (i) and (ii). This is implausible. If (i) grounds (ii), we have contradicted brutal composition. That leaves the option that (ii) grounds (i). I am dubious. For it seems implausible to think that in general the fact that the xs compose a whole grounds that the xs compose y₀. For, plausibly, we can have cases where in one world the xs compose y₀ and in another world the xs compose y₁, where y₁ ≠ y₀. (Imagine that in one world a chair is made of the xs and in another a statue is.) But if the fact that p grounds the fact that q, then p entails q by Grounding Entailment.

The Sign of the Cross and the Trinity

A principle that both Catholic and Orthodox Christians appreciate is lex orandi, lex credendi: the law of prayer is the law of faith,

Now notice that we cross ourselves with the Trinity in a specific order: “In the name of the Father, and of the Son, and of the Holy Spirit.” This is probably the most common Christian prayer in the world. And it has an order: first, the Father is mentioned, then the Son, and then the Holy Spirit. The same order is found in the baptismal formula. While Eastern Christians tend to cross themselves right-to-left and Western Christians left-to-right, the order of the words is maintained (at least in the Churches where Trinitarian words are used: more details here).

It feels badly off to pray “In the name of the Father, and of the Holy Spirit, and of the Son.” Now, we might say that the feeling of its being “off” has a deflationary psychological explanation—we are just used to a specific order. Or, somewhat better, it is off insofar as it disconnects us from the practices of the community. But the universality of the order in the most common Christian prayer together with the theological methodology of lex orandi, lex credendi and the intuition that other orders aren’t as good should impel us to see theological significance in the order.

We might, of course, see a purely missional order here. First the Father is active in the world, then the Son, and then the Holy Spirit is sent. But I think we want more than just such a temporal ordering in our explanation. After all, while the Holy Spirit is especially sent in New Testament times, it seems right to talk of the Spirit’s activity in Old Testament times. And maybe even some of the explicit mentions of Ruakh Elohim, God’s Spirit, including at the beginning of Genesis, is already an indication of the economic involvement of the Spirit. It is at least better if we can ground what feels like an important feature of a central Christian prayer in something eternal.

One solution would be a subordinationist one: the Son is subordinate to the Father, and the Holy Spirit is subordinate to the Son. But that would be a heresy.

I propose that the filioque, whether formulated in terms of the Holy Spirit proceeding from the Father and the Son or from the Father through the Son, gives an elegant eternity-based account of what makes the order in the prayer appropriate. First, the Father, from whom the Son proceeds, and then the Holy Spirit who proceeds from the Father and/through the Son. The order is not that of subordination but of procession.

The filioque

Suppose we model the Trinity as three vertices with arrows between them representing relations of procession, such that:

1. No two vertices have two arrows between them and arrows only go between distinct vertices.

2. The arrows define the vertices in the sense that there is no way to relabel the vertices while preserving which vertex has an arrow to which vertext (i.e., there is no non-trivial directed graph automorphism).

There are seven different structures possible subject to (a).

Condition (b) is a way of capturing part of the traditional Western idea that the Trinity is relational, so that the distinctions between the persons arise from the processional structure. Four of the graphs violate this condition: in (1) we can rearrange the labels in any way without changing the relational structure; in (4) and (5) we can swap A and C; in (7), we can rotate the whole graph by 120 degrees.

Aquinas captures the relationality idea by the principle that person x is distinguished from person y if and only if there is a (real) processional relation between x and y. I think this principle is too strong in one way and too weak in another way. It is too strong, because (2) would allow the persons to be distinguished, even though there is no processional relation between A and C (or B and C): A would be the unique person from whom someone proceeds; B would be the unique person that proceeds; C would be the unique person unrelated by procession. It is too weak, because in (7) we have a processional relation between each person, but it fails to distinguish the three persons. Of course, (2) and (7) have other flaws.

The following options satisfy condition (b): (2), (3) and (6).

Graph (2) is theologically unacceptable, as it has a person not related to any other. And so while the relationality in (2) would be sufficient to define the persons, because C would be unrelated to A and B, the graph does not represent a fully relational Trinity. Besides which, (2) has two persons, A and C, who do not proceed from another, and the East and West agree that only the Father does not proceed.

Graph (3) is interesting. If we adopted this model of the Trinity, we would have to take A to be the Father, since everyone agrees that the Father does not proceed for anyone. Moreover, since everyone agrees that the Son proceeds from the Father, we would hae to

In graph (3), we would have to take A to be the Father, since the Father does not proceed from any other person, as the East and West agree. Likewise, the East and West agree that the Son comes from the Father. So B would have to be the Son. That would make the Holy Spirit be C, and proceed only from the Son. Neither the East nor the West will like this. And it would violate the principle that the Son eternally has nothing beyond what the Father has, excepting what follows from the Son’s being generated by the Father, since now the Son has the Spirit proceeding from him, but the Father does not. I suppose one might try to reconcile (3) with the Western view by saying that the Spirit proceeds mediately from the Father and immediately from the Son. I don’t like this.

That leaves graph (6), the Western view of the Trinity, with A being the Father, C being the Son and B being the Holy Spirit.

This isn’t really a great argument against the Eastern view of the Trinity, because the East will deny (b), on the grounds that one can distinguish the persons not merely by the directions of the procession, but by the types of processions, with generation and spiration being different types. One can think of this Eastern move as allowing the arrows to have different colors, and then instead of (b) having the condition that there is no way to relabel the vertices while preserving which vertex has an arrow of what color to what vertex.

The point here is rather to allow us to state with some precision what principles force the western view. Namely, we have:

Theorem: Suppose:

1. There are exactly three persons in the Trinity

2. The (binary) procession relation is asymmetric: if y proceeds from x, x does not proceed from y

3. At most most one person does not proceed from another

4. There is one person from whom both of the other persons proceed

5. There is no way to relabel the persons while preserving the procession relations.

Then there is a way of respectively naming the persons “Father”, “Son” and “Holy Spirit” such that it is correct to say: “The Father does not proceed, the Son proceeds from the Father, and the Holy Spirit proceeds from the Father and the Son.”

Paley's watch and a caveman

I was teaching Paley, for the nth time, and it hit me to wonder how I would react to finding the watch if I was a caveman. There is one thing I would be sure of: the watch is not the work of a human—the difference between the watch and the most complex human technology of the time would be too vast (think of a bow and arrow—impressive as that is). Would I think it the work of a non-human designer? I am not sure. Supposing that I already thought that nature was the product of a non-human designer, it might be reasonable to think that the same designer produced the watch. The intricacy of the watch’s insides might have some resemblance to the intricacy of the internal parts of animals. But if I did not already think nature around me to be the work of design, I doubt the watch would move me. Whatever stories, if any, I told myself about nature, I would try to extend to the watch. Maybe it sprouted from the ground?

This is making me think that the objection—dismissed by Paley—that the reason we think the watch to be the product of design is that we’ve seen similar things made has more force than he grants it. It is pretty clear to me that the fact that we’ve seen things of “this sort” (understood broadly enough to included non-watches but not so broadly as to include the works of our cave-dwelling ancestors) made is an important ingredient of our inference that the watch was made.

However, I also don’t think this undercuts Paley’s argument. For it may be that seeing really complex things made opens our eyes to the possibility of an explanation that would not occur to a caveman. Indeed, here is a second thought experiment. Suppose we find something with the mechanical and functional complexity of a watch, but (a) we have never seen an artifact with this kind of function, and (b) we can determine conclusively that the item was not made by a human. How would we get (b)? Maybe the item came from space, buried in the center of a meteorite. I think I would be pretty completely confident that the item had a designer (presumably an alien). And I would surely be right.

So I think that seeing really complex things made is important to inferring design—but nonetheless the inference may be a sound one. When we find a watch on a heath, we are not just inferring that a human designed the watch, and hence the watch was designed. For even if we knew no human designed the watch, we would be confident the watch was designed. It’s just that our “explanatory imagination” has an advantage over the caveman’s.

But I am no caveman. I could be very wrong when trying to put myself in the sandals of one.

A variant of the preface paradox

Imagine being given a list generated as follows, without being told how it was generated:

1. A randomly chosen set of 2000 mutually consistent propositions that you justifiedly believe, subject to the constraint that they are consistent.

Given your fallibility, it’s highly probable that the list contains multiple falsehoods. As you look over the list, you say to yourself about each one: “Yup, that sounds right.” However, given what you know about your fallibility, you should also say: “I think some of these are false, though.” You will thus incline to disbelieve the conjunction of these propositions.

But suppose instead you were handed a list generated as follows, again without being told how it was generated:

2. A randomly chosen set of 2000 propositions that you know.

This list would look to you just like the first one. Thus, you would say about it exactly what you would have said about the first one. To each one, you would say: “Yup, that sounds right.” But then on reflection you would say: “I think some of these are false, though.” You will thus incline to disbelieve the conjunction of these propositions, just as in the first case. However, while in the first case you are correct in disbelieving, in the second you are mistaken in disbelieving.

But in any case, if you incline to disbelieve something, then you don’t know it. Hence, you do not know the conjunction of the 2000 randomly chosen propositions that you know, and so knowledge is not closed under conjunction.

A test case for explanationism

Here is a test case for explanationist stories about initial priors, on which a more explanatory theory has a higher initial prior. Consider these hypotheses:

1. The universe is not created or governed by reason, has a finite lifetime, and has low initial entropy.

2. The universe is not created or governed by reason, has a finite lifetime, and has low final entropy.

Causation goes from past to future, so absent some kind of foresight involved in the initial conditions, initial conditions are more explanatory than final conditions. Now, presumably there is a nice one-to-one correspondence between worlds where (1) and (2) hold, so absent an explanationist bias in the priors, we shouldn’t have a preference between (1) and (2).

This is just a test case, but I have to confess I don’t have any direct intuition comparing the probabilities of (1) and (2). I like explanationism, so I have a theory-laden reason to assign a higher probability to (1) than to (2).

How has Aquinas not proved the Trinity?

St Thomas holds that we cannot know by natural reason that God is a Trinity. However, he also endorses a version of St Augustine’s account of the Trinity, on which God has a mental Word or concept of himself that he generates mentally, and then there is a Love that is responsive to that Word. Why is this not a proof by natural reason?

On this point, Thomas is sadly brief in the Summa Theologiae: “Again, the similarity with our intellect does not sufficiently prove anything about God, since the intellect is not found univocally in God and in us.”

But Aquinas thinks that we can literally talk about God, even if we do so by means of analogy. He has argued, by reason, that God exists and has all perfections. One of these perfections is knowledge of everything, and thus of himself. Does this not commit Aquinas to being able to say on the basis of natural reason that God generates his self-knowledge, a self-knowledge that, by divine simplicity, must then be God himself rather than a mere creature? And does not God love himself under the description that this knowledge provides?

I think Aquinas would (with perhaps minor cavils) endorse all the claims in my previous paragraph as knowable by natural reason. How is this not a proof of the Trinity? I think the answer is this. Focus on the generation of the Son—the case of the Holy Spirit will presumably be similar. We do not know by reason whether the relation of generating self-knowledge is a real relation in God. If it is a real relation it will individuate the knower from the knowledge, thereby ensuring that there are at least two persons in God. But it needs to be a real relation in God, rather than a merely conceptual one. And here Thomas’s brief remark about univocity seems apposite. Aquinas thinks that what makes our language about God analogical rather than univocal is that the grounding of claims about God is radically different from the grounding of similar claims about creatures. Thus, when we say Socrates is wise, this is grounded by the inherence in Socrates of an accident of wisdom, while when we say God is wise, this is grounded by the identity between God and his wisdom. Because of this, even if it turns out that in us the generation of self-knowledge is a real relation (but not one between persons, since we are not simple, and hence our self-knowledge does not need to be of one essence with us), since the grounding structure of claims about God is radically different, as far as unaided human reason goes, it may not be grounded in a real relation in God—though it might be. We need God’s revelation to know if it is a real relation or not. And indeed God has revealed that it is.

Optimalism and mediocritism

We can think of the optimalist theory of ultimate explanation as the claim:

1. Necessarily, that reality is for the best explains everything.

(I won’t worry in this post about two details. First, whether “reality” in (1) includes the principle of optimality itself—Rescher has suggested that it does, since it’s for the best that everything be for the best. Second, whether “reality” is all the detail of the world, or just the “core” of the world—the aspects not set by indeterministic causation.)

Given that only truths explain, (1) entails:

2. Necessarily, reality is for the best.

Notice that one could accept (2) without accepting (1). One might, for instance, be a Leibnizian and think that there is a two-fold structure to ultimate explanation: first, God’s existence is explained by the ontological argument and, second, God creates the best contingent reality. On this account everything is for the best, but that everything is for the best is not the ultimate explanation, because it does not explain why God exists. Or one might think that reality is necessary and brute, and it brutely has to be like it is. And as a very suprising but non-explanatory matter of fact the way it is is in fact optimal.

I am emphasizing this, because I want to problematize (1). Grant (2). Why should we think that the fact that everything is for the best in fact explains everything?

Suppose that modal fatalism is true, and that it so happens that reality is exactly mid-way between the worst and the best possibility, and is in the only option mid-way between the worst and best. (I assume one can talk of options for reality even given modal fatalism. Otherwise, optimalism falls apart. The “options for reality” may be something like narrowly logically possible worlds.) Then:

3. Necessarily, reality is exactly middling.

Now suppose a “mediocritist” said: “And that reality is necessarily exactly middling explains why reality is what it is.” But why would we buy that? Or suppose that reality is necessarily the only one that is exactly 56.4% of the way up between the worst and the best (where worst would count as 0% of the way up and best as 100%)? Surely we wouldn’t conclude that its being exactly at 56.4% explains why it is the way it is. But if not, then why should its being at 50% explain it, as on mediocritism, or its being at 100% explain it, as on optimalism?

I think what the optimalist ought to say at this point is that analogously to non-Humean pushy laws of nature, there are non-Humean pushy laws of metaphysics. One of these laws is that everything is for the best. It is the pushiness of this metaphysical law that explains reality. But there is something rather odd about pushy laws prior to all beings—they seem really problematically ungrounded.

More on strong open-mindedness

For the last couple of days I have been exploring what I like to call strongly open-minded accuracy scoring rules. It’s well known that every proper scoring rule is open-minded in the sense that it never requires you to reject free information: the expected epistemic utility of updating on the free information is always at least as good as your current expected epistemic utility. It’s strictly open-minded provided that in non-trivial cases (i.e., when the information has a non-zero probability of having statistical relevance to the credences you are scoring) you are required to accept the free information.

Now there are two reasons why one might accept free information about some proposition q. First, you might be wrong about q: your credence may be high while q is false or your credence might be low while q is true. Second, even if you are right about q, the free information may boost your credence in the right direction. I say that a scoring rule is strongly open-minded provided that it licenses you to accept and update on the free information even if you disregard the first consideration. We can then tack on “strictly” if it requires you to do so in non-trivial cases. In the case of a strongly open-minded scoring rule, your acceptance of free information is not a sign of doubt in your propositions—it is not a way of hedging your bets—and thus is arguably compatible with faith in the propositions being evaluated.

A strongly open-minded scoring rule can also be characterized in the following way. There is a more ordinary kind of epistemic paternalism where I might have reason to block another from receiving free information on the grounds that this information could mislead due to the fact that the other has different likelihoods from the ones I think are right. For instance, if too many people have an unjustified mistrust of Dr. Smith such that they are likely to believe the opposite of what Dr. Smith’s experiments reveal, there is reason to give a grant to someone else, because Dr. Smith’s experiments are likely to lead people away from the truth, for no fault of Dr. Smith’s. Call this likelihood-based paternalism. But there is another kind of motivation of the refusal of free information for another, which we might call pure-risk-based paternalism. Even if someone else has the same likelihoods as you do—trusts Dr. Smith just as you do—perhaps the risk that Dr. Smith’s experiments will, by pure chance, provide evidence away from the truth is enough to justify not funding these experiments.

I’ve been collecting results about these issues. Here’s what I seem t have so far, though I have to emphasize that sometimes the proofs are just in my head and I might be wrong. I will specialize on scoring rules for a single proposition, given as a pair of functions T and F, where T(x) is the value of having credence x when the proposition is true and F(x) is the value of having credence x when the proposition is false.

1. A scoring rule sometimes calls for pure-risk-based paternalism if and only if it is not strongly open-minded.

2. A scoring rule that’s strongly open-minded is open-minded.

3. A scoring rule (T,F) is (strictly) strongly open-minded if and only if xT(x) and (1−x)F(1−x) are both (strictly) convex.

4. The logarithmic scoring rule is strictly strongly open-minded. The Brier and spherical rules are not strongly open-minded.

5. If a proper scoring rule is generated by the Schervisch-style integral representation T(x) = T(1/2) + ∫_x^1/2(1−t)b(t)dt and F(x) = F(1/2) + ∫_1/2^xtb(t)dt and b is sufficiently differentiable, then the scoring rule is strongly open-minded if and only if the derivative of log b(x) lies between (3x−2)/[x(1−x)] and (3x−1)/[x(1−x)].

6. A strongly open-minded scoring rule whose logarithm is sufficiently differentiable is unbounded.

7. [Item deleted as I discovered it to be false.]

8. For any credences p and r such that 1/2 < r and p < r, there is a strictly proper scoring rule and a situation where the scoring rule calls for the individual with credence r to have purely-risk-based epistemic paternalism for that hypothesis.

Algorithmic priors and human nature

One promising way to define priors is with algorithmic probability, such as Solomonoff priors. The idea is that we have a language L (say, one based on Turing machines), and we imagine generating random descriptions in L in a canonical way. E.g., add an end-of-string symbol to L and randomly and independently generate symbols until you hit the end-of-string symbol, and then conditionalize on the string uniquely describing a situation, and take the probability of a specific situation s to be the probability of that a random description so generated describes s.

These kinds of priors are rather appealing for science, since they appear to be induction-friendly, as they assign high probabilities to compressible—more briefly expressible—situations. Thus, if our situations are distributions of color among ravens, monochromatic distributions get much higher probability as they can be much more briefly described, like ∀x(B(x)) or ∀x(W(x)).

Philosophically, I think the big problem is with the choice of the language. It would be nice if we could let L be a language that cuts nature exactly at the joints. But we don’t know that language. And absent that language, we need something arbitrary.

Here is a particular version of the problem. Take Kuhn’s division of science into ordinary and revolutionary science. One aspect of this division is that in ordinary science, we have a scientific language, and are discovering things within it. In that case, it is reasonable to take L to be that language. However, when we are doing revolutionary science and creating new paradigms, we cannot do that. The new paradigms either cannot be described in the old language or their description is unwieldy in a way that does not do justice to the plausibility of the new paradigm. Indeed, much of the point of revolutionary science is to create a language within which the description of the world is simpler, and then argue that this language is therefore more likely to cut nature at the joints.

Another version of this problem is what language L we choose when we are generating fundamental priors. Practically speaking, we cannot use a scientific language that cuts nature at the joints, because we have not yet discovered it. If this was merely a practical concern, we could try to say that this doesn’t matter: the fundamental priors are ones that we ought to have rather than any that we actually have or could have—perhaps ought does not imply can. But the concern is not merely practical. For one of the main points of our inductive reasoning is to discover what concepts cut nature at the joints, and this is largely an empirical enterprise. If the right fundamental priors were to reflect the joints in nature, then the enterprise wouldn’t make much sense, as we would be obligated to have already completed much of the enterprise before we started it.

So, I think, we have to say L does not always cut nature at the joints, and yet this generating appropriate priors for us. But we still need a constraint on L. After all, we could imagine a language that thwarts our empirical enterprise, such as one where only fairies can be described briefly and anything else requires very long descriptions, so we have very high priors for fairies and very low priors for everything else. What will be the constraint? Practically, we pretty much have to start with some ordinary human language. I think our ideal should not be far from what is practical. Thus, I propose, if we are going to go with algorithmic priors, we should choose L to be a language that fits well with our human nature as communicators. This is an anthropocentric choice, and I think human epistemology is rightly anthropocentric.

But why think that the anthropocentric choice is apt to lead to truth? There are two stories to be told here. First, it may be that human nature requires a measure of trust in human nature. Second, that trust is vindicated if we are created by a good God who loves the truth.