Punishment and amnesia

There is an interesting philosophical literature on whether it is appropriate to punish someone who has amnesia with respect to the wrong they have done.

It has just occurred to me (and it would be surprising if it’s not somewhere in that literature) that it is obvious that rewarding someone who has amnesia with respect to the good they have done is appropriate. To make the intuition clear, imagine the extreme case where the amnesia is due to the heroic action that otherwise would cry out for reward.

If amnesia does not automatically wipe out positive desert, it also does not automatically wipe out negative desert.

Fine-tuning of both physical and bridge laws

A correspondent pointed me to a cool paper by Neil Sinhababu arguing that the theist can’t consistently run a fine-tuning argument on which it is claimed that it is unlikely that the constants in the laws of physics permit intelligent life, because if God exists, then for any constants in the physical laws God can make psychophysical bridge laws that make sure that there is intelligent life. By choosing the right bridge laws, God can make a single electron be conscious, after all. Thus any set of constants in laws of physics is compatible with intelligent life.

A quick response is that in the context of the fine-tuning argument, by “intelligent life” we should probably mean “intelligent biological life”. For instance, angels and conscious electrons don’t count, as they aren’t biological. And in fact, I think, in practice the fine-tuning argument is more about biological life than intelligent life as such. This suggests, however, that proponents of the fine-tuning argument should be clearer here. In particular, we (I am one of the proponents) should emphasize that there is a great value in the existence of biological life, and especially intelligent biological life, and this value is not found in intelligent non-biological life. This value is why a perfect being is not unlikely (or at least not extremely unlikely) to fine-tune the universe to for such life.

Second, I think Sinhababu’s argument points to a more subtle way to formulate the fine-tuning thesis. What’s fine-tuned is not the laws of physics alone, but the combination of the laws of physics and the bridge laws, and they are fine-tuned together in such a way as to ensure that there is neither too little nor too much intelligent life. For instance, a set of psychophysical laws where any computation isomorphic to the kinds of computations our brains results in mental functioning like ours would result not just in panpsychism but omnisapientism—everything around us is sapient. For with some cleverness we can find an isomorphism between the states of a single particle and the states of the brain that preserves causation. But omnisapientism isn’t very good: it damages the significance of morality if everything we do creates and destroys vast numbers of sapient beings.

Per se and per accidens multiplication of causes

Can there be an infinite sequence of efficient causes? Famously, Aquinas says both “No” and “Yes”, and makes a distinction between a per se ordering (“No”) and an accidental ordering (“Yes”). But it is difficult to reconstruct how the distinction goes, and whether there is good reason to maintain given modern physics.

Here is the central passage from Summa Theologiae I.46.2 reply 7, in Freddoso’s translation:

It is impossible to proceed to infinity per se among efficient causes, i.e., it is impossible for causes that are required per se for a given effect to be multiplied to infinity—as, for instance, if a rock were being moved with a stick, and the stick were being moved by a hand, and so on ad infinitum.

By contrast, it is not impossible to proceed to infinity per accidens among agent causes, i.e., it is not impossible if all the causes that are multiplied to infinity belong to a single order (ordinem) of causes and if their multiplication is incidental (per accidens)—as, for instance, if a craftsman were to use many hammers incidentally, because one after another kept breaking. In such a case, it is incidental to any given hammer that it acts after the action of a given one of the other hammers. In the same way, it is incidental to this man, insofar as he generates, that he himself was generated by another. For he generates insofar as he is a man and not insofar as he is the son of some other man, since all the men who generate belong to the same order (gradum) of efficient causality, viz., the order of a particular generating cause. In this sense, it is not impossible for man to be generated by man ad infinitum.

However, it would indeed be impossible for the generation of this man to depend upon that man, and upon an elemental body [a corpore elementari], and upon the sun, and so on ad infinitum.

What’s going on here? Re-reading the text (and double-checking against the Latin) I notice that per se and per accidens are introduced not as modifying the causal relations, but the infinite multiplication of causes. No indication is given initially that the causation functions differently in the two cases. Further, it is striking that both of the examples of per accidens multiplication of causes involve causes of the same type: hammers and humans (Freddoso’s “man” translates homo throughout the text).

To a first approximation, it seems then that what is forbidden is a regress of infinitely many types of causes, whereas a regress of infinitely many tokens is permitted. But that is too simple. After all, if an infinite causal sequence of humans generating humans were possible, it would surely also be possible for each of these humans to be qualitatively different from the others—say, in exact shade of eye color—and hence for there to be infinitely many types among them. In other words, not just any type will do.

Let’s focus in on two other ingredients in the text, the observation that the humans all “belong to the same order of efficient causality”, and the sun–elementary body–human example. Both of these rang a bell to me, because I had recently been writing on the Principle of Proportionate Causality. At Summa Theologiae I.4.2, St Thomas makes a different distinction that distinguishes between the human–human and the sun–body–human cases:

whatever perfection exists in an effect must be found in the effective cause: either in the same formality, if it is a univocal agent—as when man reproduces man; or in a more eminent degree [eminentiori modo], if it is an equivocal agent—thus in the sun is the likeness of whatever is generated by the sun’s power.

Here is a suggestion. In distinguishing per se and per accidens infinite multiplication of causes, Aquinas is indeed distinguishing counting types and tokens. But the types he is counting are what one might call “causal types” or “perfections”. The idea is that we have the same causal type when we have univocal agency, “as when man reproduces man”, and different causal type when we have equivocal agency, as when the sun generates something, since on Aquinas’ astronomical theory the sun is sui generis and hence when the sun generates, the sun is quite different from what it generates. In other words, I am tentatively suggesting that we identify the gradus of efficient causality of I.46.2 with the modus of perfection of I.4.2.

The picture of efficient causation that arises from I.4.2 is that in a finite or infinite causal regress we have two types of moves between effect and cause: a lateral move to a cause with the same perfection as the effect and an ascending vertical move to a cause that has the perfection more eminently.

The lateral moves only accidentally multiply the explanations, because the lateral moves do not really explain the perfection. If I got my humanity from another human, there is a sense in which this is not really an explanation of where my humanity comes from. The human I got my humanity from was just passing that humanity on. I need to move upwards, attributing my humanity to a higher cause. On this reading, Aquinas is claiming that there can only be finitely many upwards moves in a causal regress. Why? Maybe because infinite passing-on of more to less eminent perfections is just as unexplanatory as finite passing on of the same perfection. We need an ultimate origin of the perfections, a highest cause.

I like this approach, but it fits better with the sun–elemenatary body–human example than the hand–stick–rock example. It seems, after all, that in the hand–stick–rock example we have the same relevant perfection in all three items—locomotion, which is passed from hand to stick and then from stick to rock. This would thus seem like a per accidens multiplication rather than a per se one. If so, then it is tempting to say that Aquinas’ hand–stick–rock example is inapt. But perhaps we can say this. Hand-motion is probably meant to be a voluntary human activity. Plausibly, this is different in causal type from stick-motion: going from stick to hand is indeed an explanatory ascent. But it’s harder to see the progression from rock to stick as an explanatory ascent. After all, a rock can move a stick just as much as a stick can move a rock. But perhaps we can still think we have an ascent from rock-moving to stick-moved-by-hand, since a stick-moved-by-hand maybe has more of the perfection of the voluntary hand motion to it? That sounds iffy, but it’s the best I can do.

I wish Aquinas discussed a case of stick–stick–stick, where each stick moves the next? Would he make this be a per se multiplication of causes like the hand–stick–rock case? If so, that’s a count against my reading. Or would he say that it’s an accidental multiplication? If so, then my tentative reading might be right.

It’s also possible that Aquinas’ examples of hand–stick–rock and sun–elementary body–human are in fact more unlike than he noticed, and that it is the latter that is a better example of per se multiplication of causes.

Per se and per accidens ordered series

I’ve never been quite clear on Aquinas’ famous distinction between per se and per accidens ordered series, though I really like the clarity of Ed Feser’s explanation. Abridging greatly:

An instrumental cause is one that derives whatever causal power it has from something else. … [A]ll the causes in [a per se] series other than the first are instrumental [and thus] are said to be ordered per se or “essentially,” for their being causes at all depends essentially on the activity of that which uses them as instruments. By contrast, causes ordered per accidens or “accidentally” do not essentially depend for their efficacy on the activity of earlier causes in the series. To use Aquinas’s example, a father possesses the power to generate sons independently of the activity of his own father … .

The problem here is that it’s really hard to think of any examples of purely instrumental causes in this sense. Take Aquinas’s example of a per se series where the hand moves a stick which moves the stone. That may work in his physics, but not in ours. Every stick is basically a stiff spring—there are no rigid bodies. So, for ease of visualization, let’s imagine a hand that pushes one end of a spring, and the other end of the spring pushes the stone. When you push your end of the spring, the spring compresses a little. A compression wave travels down the spring and the tension in the spring equalizes. The spring is now “charged” with elastic potential energy. And it then pushes on both the hand and the stone by means of the elastic potential energy. There is an unavoidable delay between your pushing your end of the spring and the other end pushing the stone (unavoidable, because physical causation doesn’t exceed the speed of light).

Now, once the spring is compressed, its pushing on the stone is its own causal activity. We can see this as follows. Suppose God annihilated your hand. For a very short while, the other end of the spring wouldn’t notice. It would still be pushing against the stone, and the stone would still be moving. Then the spring would decompress in the direction where the hand used to be, and the stone’s movement would stop. But a very short while is still something—it’s enough to show that the spring is acting on its own. The point isn’t that the stone would gradually slow down. The point, rather, is that it takes a while for the stone’s movement to be at all affected, because otherwise we could have faster-than-light communication between the hand and the spring.

What goes for springs goes for sticks. And I don’t know any better examples. Take Feser’s example in his Five Ways book of a cup held up by a desk which is held up by a floor. Feser says the desk “has no power on its own to hold the cup there. The desk too would fall to the earth unless the floor held it aloft”. Yes, it would—but not instantly. If the floor were to disappear, the tension in the desk’s legs—which, again, are just stiff springs—would continue to press upward on the desktop, which would press upward on the cup, counteracting gravity. But then because the bottoms of the legs are unsupported, the tension in the legs would relax, the legs would imperceptibly lengthen, and the whole thing would start to fall. Still, for a short while the top of the desk would have been utterly unaffected by the disappearance of the floor. It would only start accelerating downward once the tension in the legs dissipatated. It takes a time of at least L/c, where L is the length of the legs and c is the speed of light, for that to happen. Again, the legs of the table are charged-up springs whose internal tension is holding up the desktop.

If this is right, then we don’t have any clear examples of the kind of purely instrumental causality that Feser—and, fairly likely, Aquinas—is talking about. Now, it may be that the deep metaphysics of causation is indeed such that indeed all creaturely causation is indeed of this instrumental sort, being the instrument of the first cause. But since Aquinas is using the idea of per se causal series to establish the existence of the first cause, we need an argument here that does not depend on the existence of the first cause.

On Rasmussen and Bailey's "How to build a thought"

[Revised 11/21/2025 to fix a few issues.]

Rasmussen and Bailey prove that under certain assumptions it follows that there are possible thoughts that are not grounded in anything physical.

I want to offer a version of the argument that is slightly improved in a few ways.

Start with the idea that an abstract object x is a “base” for types of thoughts. The bases might be physical properties, types of physical facts, etc. I assume that in all possible worlds exactly the same bases abstractly exist, but of course what bases obtain in a possible world can vary between worlds. I also assume that for objects, like bases, that are invariant between worlds, their pluralities are also invariant between worlds.

Consider these claims:

1. Independence: For any plurality xx of bases, there is a possible world where it is thought that exactly one of the xx exists and there is no distinct plurality yy of bases such that it is thought that exactly one of the yy obtains.

2. Comprehension: For any formula ϕ(x) with one free variable x that is satisfied by at least one base, there is a plurality yy of all the bases that satisfy ϕ(x).

3. Plurality: There are at least two bases.

4. Basing: Necessarily, if there is a plurality xx of bases and it is thought that exactly one of the xx obtains, then there obtains a base z such that necessarily if z obtains, it is thought that exactly one of the xx obtains.

By the awkward locution “it is thought that p”, I mean that something or some plurality of things thinks that p, or there is a thinkerless thought that p. The reason for all these options is that I want to be friendly to early-Unger style materialists who think that there no thinkers. :-)

Theorem: If Independence, Comprehension, Plurality and S5 are true, Basing is false.

Here is how this slightly improves on Rasmussen and Bailey:

• RB’s proofs use the Axiom of Choice twice. I avoid this. (They could avoid it, too, I expect.)

• I don’t need a separate category of thoughts to run the argument, just a “it is thought that exactly one of the xx exists” predicate. In particular, I don’t need types of thoughts, just abstract bases.

• RB use the concept of a thought that at least one of the xx exists. This makes their Independence axiom a little bit less plausible, because one might think that, say, someone who thinks that at least one of the male dogs exists automatically also thinks that at least one of the dogs exists. One might also reasonably deny this, but it is nice to skirt the issue.

• I replace grounding with mere entailment in Basing.

• I think RB either forgot to assume Plurality or are working with a notion of plurality where empty collections are possible.

Some notes:

• RB don’t explicitly assume Comprehension, but I don’t see how to prove their Cantorian Lemma 2 without it.

• Independence doesn’t fit with the necessary existence of an omniscient being. But we can make the argument fit with theism by replacing “it is thought” with “it is non-divinely thought”.

• I think the materialist could just hold that there are pluralities xx of bases such that no one could think about them.

Proofs

Write G(z,xx) to mean that z is a base, the xx are a plurality of bases, and necessarily if z obtains it is thought that exactly one of the xx obtains.

The Theorem follows from the following lemmas.

Lemma 1: Given Independence, Basing and S5, for every plurality of bases xx there is a z such that G(z,xx) and for every other plurality of bases yy it is not the case that G(z,yy).

Proof: Let w be a possible world like in Independence. By Basing, at w there obtains a base z such that G(z,xx). By S5 and the bases and pluralities thereof being the same at all worlds, we have G(z,xx) at the actual world, too. Suppose now that we actually have G(z,yy) with yy other than xx. Then at w, it is thought that exactly one of yy exists. But that contradicts the choice of w. Thus, actually, we have G(z,xx) but not G(z,yy).

Lemma 2: Assume Comprehension and Plurality. Then there is no formula ϕ(z,xx) open only in z and xx such that for every plurality of bases xx there is a z such that ϕ(z,xx) while for every other plurality of bases yy it is not the case that ϕ(z,yy).

Proof: Suppose we have such a ϕ(z,xx). Say that z is an admissible base provided that there is a unique plurality of bases xx such that ϕ(z,xx). I claim that there is an admissible base z such that z is not among any xx such that ϕ(z,xx). For suppose not. Then for all admissible bases z, z is among all xx such that ϕ(z,xx). Let a and b be distinct bases. Let ff, gg and hh be the pluralities consisting of a, of b, and of both a and b respectively. Then the above assumptions show that we must have ϕ(a,ff), ϕ(b,gg) and either ϕ(a,hh) or ϕ(b,hh), and either of these options violates our assumptions on ϕ. By Comprehension, then, let yy be the plurality of all admissible bases z such that z is not among any xx such that ϕ(z,xx). Let z be an admissible base such that ϕ(z,yy). Is z among the yy? If it is, then it’s not. If it is not, then it is. Contradiction!

Omniscience, timelessness, and A-theory

I’ve been thinking a lot this semester, in connection with my Philosophy of Time seminar, about whether the A-theory of time—the view that there is an objective present—can be made consistent with classical theism. I am now thinking there are two main problems here.

1. God’s vision of reality is a meticulous conscious vision, and hence if reality is different at different times, God’s consciousness is different at different times, contrary to a correct understanding of immutability.

2. One can only know p when p is true; one can only know p when one exists; thus, if p is true only at a time, one can only know p if one is in time. On an A-theory of time, there are propositions that are only true in time (such as that presently I am sitting), and hence an omniscient God has to be in time. Briefly: if all times are the same to God, God can’t know time-variable truths.

I stand by the first argument.

However, there may be a way out of (2).

Start with this. God exists at the actual world. Some classical theists will balk at this, saying that this denies divine transcendence. But there is an argument somewhat parallel to (2) here. If all worlds are the same to God, God can’t know world-variable truths, i.e., contingent truths.

Moreover, we can add something positive about what it is for God to exist at world w: God exists at w just in case God actualizes w. There is clearly nothing contrary to divine transcendence in God’s existing at a world in the sense of actualizing it. And of course it is only the actual world that God actualizes (though it is true at a non-actual world w′ that God actualizes w′; but all sorts of false things are true at non-actual worlds).

But given the A-theory, reality itself includes changing truths, including the truth about what it is now. If worlds are ways that all reality is, then on A-theory worlds are “tensed worlds”. Given a time t, say that a t-world is a world where t is present. Argument (2) requires God to exist at a t-world in order for God to know something that is true only at a t-world (say, to know that t is present).

Now suppose we have an A-theory that isn’t presentism, i.e., we have growing block or moving spotlight. Then one does not need to exist at t in order to exist at a t-world: on both growing block and moving spotlight our 2025-world has dinosaurs existing at it, but not in 2025, of course. But if one does not need to exist at t in order to exist at a t-world, it is not clear that one needs to exist in time at all in order to exist at a t-world. The t-world can have a “locus” (not a place, not a time) that is atemporal, and a being that exists at that atemporal locus can still know that t is present and all the other A-propositions true at that t-world.

Next suppose presentism, perhaps the most popular A-theory. Then everything that exists at a t-world exists at t. But that God exists at the t-world still only consists in God’s actualizing the t-world. This does not seem to threaten divine transcendence, aseity, simplicity, immutability, or anything else the classical theist should care about. It does make God exist at t, and hence makes God in time, but since God’s existing in time consists in God’s actualizing a t-world, this kind of existence in time does not make God dependent on time.

I still have some worries about these models. And we still have (1), which I think is decisive.

A bit of finetuning

Here’s a bit of finetuning in the world’s laws that I just noticed. All the four fundamental forces of nature are conveniently local, in the sense that they drop off to nearly zero with distance. If any one of them weren’t local, the world would not be likely to be predictable to limited knowers like us.

Towards a solution to the "God as author of evil" problem for the Thomistic model of meticulous providence

On the Thomistic primary/secondary causation model of meticulous divine providence, when we act wrongly, God fully determines the positive aspects of the action with primary causation, and we in parallel cause the action with secondary causation.

Like many people, I worry that this makes God the author of sin in an objectionable way.

Alice and Bob are studying together for a calculus exam that will be graded on a curve. In order that she may do terribly on the exam, and thus that he might do better, and hence be more likely to get into his dream PhD program in ethics, Bob lies to Alice, who has missed three weeks of class, that the derivative of the logarithm is the exponential.

What does God cause in Bob’s action on the Thomistic model? It seems that all of the following are positive aspects:

1. The physical movements in Bob’s mouth, throat, and lungs.

2. The sounds in the air.

So far we don’t have a serious theological problem. For (1) and (2) are not intrinsically bad, since Bob could virtuously utter the same sounds while playacting on stage. But let’s add some more aspects:

3. Bob’s intention that the speech constitute an assertion of the proposition that the derivative of the logarithm is the exponential.

4. Bob’s intention that the asserted proposition be a falsehood that Alice comes to believe and that leads to her doing terribly on the exam.

Perhaps one can argue that falsity a negative thing—a lack of conformity with reality. However, intending falsity seems to be a positive thing, a positive (but wicked) act of the will. Thus it seems that (3) and (4) are positive things. But once we put together all of (1)–(4), or even just (3) and (4), then it’s hard to deny that what we have is something wicked, and so if God is intending all of (1)–(4), it’s hard to avoid the idea that this makes God responsible for the sin in a highly problematic way.

There may be a way out, however. In both written and spoken language, meaning is normally not constituted just by the positive aspects of reality but also by negative ones. In spoken language, we can think of the positive aspects as the peaks of the soundwaves (considered as pressure waves in the air). But if you remove the troughs from the soundwaves, you lose the communication. In print, on the other hand, the meaning depends not just on the ink that’s there, but on the ink that’s not there. A page wholly covered with ink means nothing. We only have meaningful letters because the inked regions are surrounded by non-inked regions.

It could well turn out that the language of the mind in discursively thinking beings like us is like that as well, so that a thought or intention is constituted not only by ontologically positive but also by ontologically negative aspects. Now you could be responsible for the ink within the print inscription

5. The derivative of the logarithm is the exponential

without being responsible for the inscription. For instance, you and a friend might have had a plan to draw a black rectangle and you divided up the labor as follows: you inked the region of rectangle covered by the letters of “The derivative of the logarithm is the exponential” and then your friend would ink the rest of the containing rectangle—i.e., everything outside the letters. But your friend didn’t do the job. Similarly, then, if intentions are constituted by both positive and negative features, God could intend the positive features of an intention without being responsible for the intention as such.

This does place constraints on the language of the mind, i.e., on the actual mental accidents that constitutes our thoughts, and specifically our intentions. Note, though, that we don’t need that all intentions have a negative constituent. Only intentions to produce negative things, like falsehood, need to have a negative constituent for us to avert the problem of God willing intentional sin. We could imagine a written language where positive phrases are written in two colors of ink, one for the letters and the other for the surrounding rectangle, and their negations are written by omitting the ink for the letters. In such a language, statements involving positive phrases are purely positive, while those involving negative phrases are partly negative.

I am not very happy with this solution. I still worry that being responsible for the ink in (5) makes one responsible for (5) when one chooses not to have the rest of the rectangle filled in.

Perfect vision

One of the major themes in modern philosophy was concerns about the way that our contact with the world is mediated by our “ideas”. Thus, you are looking at a tree. But are you really seeing the tree, or are you just seeing your sense-impression, which doesn’t have much in common with the tree? Even direct realists like Reid who say you are seeing the cat still think that your conscious experience involves qualia that aren’t like a tree.

Thinking about this gives us the impression that an epistemically better way to relate to the tree would be if the tree itself took the place of our sense-impressions or qualia. Berkeley did that, but at the cost of demoting the tree to a mere figment of our perception. But if we could do that without demoting the tree, then we would be better kinds of perceivers.

However, that on some theory we would be better kinds of perceivers is not a strong reason to think that theory is true! After all, we would be better perceivers if we could see far infrared, but we can’t. It’s not my point to question the orthodoxy about our perceptions of trees.

But now think about beatitude, where the blessed see God. If seeing God is like seeing a tree in the sense that there is something like a mediating supersense-impression in us, then something desirable is lacking in the blessed. And that’s not right. Such a mediated vision of God is not as intimate as we could wish for. Would it not be so much more intimate if it were a direct vision of God in the fullest sense, where God himself takes the place of our qualia? We shouldn’t argue from “it would be better that way” to “it is that way” in our earthly lives, but in beatitude it does not seem such a terrible argument.

But where this kind of argument really comes into its own is when we think of what the epistemic life of a perfect being would be like. The above considerations suggest that when God sees the tree (and it is traditional to compare God’s knowledge of creation to vision), the vision is fully direct and intimate, and the tree itself plays the role of sense-impressions in us. We would expect a perfect being’s vision to be like that.

Now notice, however, that this is an account of God’s vision of the world on which God’s vision is partly extrinsically constituted: the tree partly constitutes God’s conscious experience of the tree. This is the extrinsic constitution model of how a simple God can know. We have thus started with us and with considerations of perfection, and have come to something like this model without any considerations of divine simplicity. Thus the model is not an ad hoc defense of divine simplicity. It is, rather, a model of the perfect way to epistemically relate to the world.

An argument against the Thomistic primary/secondary causation account of strong providence

Most people agree that one cannot have circularity in the order of explanation when one keeps the type of explanation fixed. Some like me think one cannot have circularity in the order of explanation at all. I argued for this thesis in my previous post today. Now I want to draw an interesting application.

On one influential (and I think exegetically correct, pace Eleonore Stump) reading of Aquinas, God decides what our free choices will be. Our free choices cannot be determined by created causes, but they are determined by God. This is because God’s causation is primary causation which is of a different sort from the secondary causation which is creaturely causation. God can primarily cause you to freely secondarily cause something, and this is how providence and free will interact. Often the analogy between an author and a character is given: the author decides what the character will freely do and this does not infringe on the character’s freedom.

But now observe this (which was brought home to me by a paper of one of our grad students). On this picture, God will presumably sometimes providentially make earlier actions happen because of later ones. Thus, God may want you to perform some heroic self-sacrifice in ten years. So, right now God prepares you for this by having you freely engage in small self-sacrifices now. In the “because” corresponding to the explanatory order of providence and primary causation, we thus have:

1. You engage in small self-sacrifices because you will engage in a great self-sacrifice.

However, divine primary causation does not undercut secondary causation, and we have the standard Aristotelian story of habituation at the level of secondary causation in light of which we have:

2. You will engage in a great self-sacrifice because you are engaging in small self-sacrifices.

These explanations form a heterotypic explanatory loop (i.e., we have explanations of two different sorts in opposite directions). But if I am right that no explanatory loop is possible, the above story is not possible. However, there is nothing to rule out the above story if the above Thomistic account of primary and secondary causation’s role in providence is correct. Hence, I think we should reject that account.

If no homotypic circles of explanation, no heterotypic ones either

Most people agree that one cannot have circularity in the order of explanation when one keeps the type of explanation fixed, i.e., there are no homotypic circles of explanation. Some like me think one cannot have circularity in the order of explanation at all. Why? One intuition might be that explanations of all types are still explanations, and so the circularity is still an explanatory circularity. :-) (Yes, that begs the question.) More seriously, heterotypic explanations (namely, explanations of different types) can be combined, sometimes chainwise (A explains B and B explains C, and thereby A explains C) and sometimes in parallel (A explains B and C explains D so A-and-C explains B-and-D). This means that the types of explanation are not quite as separate as they might seem.

Here is an argument building on the second intuition. We need two concepts. First, we can talk of two sets of explanatory relations as independent, namely without any interaction between the explanatory relations in the two sets. Second, given two type of explanation₁ and explanation₂, I will say that explanation_1|2 is a type of explanation where explanation₁ and explanation₂ are combined in parallel.

1. If circularity in explanation is possible, it is possible to have a two-item heterotypic explanatory loop.

2. If it is possible to have a two-item heterotypic explanatory loop, it is possible to have two independent two-item heterotypic explanatory loops where each loop involves the same pair of explanation types as the other loop.

3. Necessarily, if A explains₁ B and C explains₂ D, and the two explanatory relations here are independent, then A-and-C explains_1|2 B-and-D.

4. Necessarily, the relations explains_1|2 and explains_2|1 are the same.

5. It is not possible to have a circle of explanations of the same type.

6. Suppose circularity in explanation is possible. (Assume for reductio)

7. There is a possible world w, such that at w: there are A, B, C and D such that A explains₁ B, B explains₂ A, D explains₁ C and C explains₂ D, and the above explanatory relations between A and B are independent of the above explanatory relations between C and D. (6,1,2)

8. At w: A-and-C explains_1|2 B-and-D. (3,7)

9. At w: B-and-D explains_2|1 A-and-C. (3,7)

10. At w: B-and-D explains_1|2 A-and-C. (4,9)

11. At w: there is a circle of explanations of type 1|2. (8,10)

12. Contradiction! (5,11)

13. So, circularity in explanation is impossible.

I think the most problematic premise in this argument is (4). However, if (4) is not true, we have a vast multiplication in types of explanation.

Symmetric relations and logic

Suppose Alice and Bob are friends, and that friendship is a fundamental relation. Consider the facts expressed by these two sentences:

1. Alice and Bob are friends.

2. Bob and Alice are friends.

It is implausible that these are different facts. For if they were different facts, they would both be fundamental facts (otherwise, which of them would be the fundamental one?), and we would be multiplying fundamental facts beyond necessity—only one of the two is needed in the totality of fundamental facts.

Furthermore, I think that the propositions expressed by (1) and (2) are the same. Here’s one reason to think this. Imagine a three-dimensional written language where plural symmetric predicates like “are friends” are written (say, laser-inscribed inside a piece of glass) with “and are friends” on one horizontal layer, with “Alice” on a layer below the “and” and “Bob” on a layer above it. If (1) and (2) express different propositions, we would have to ask which of them is a better translation of the three-dimensional language. But surely there is no fact about that.

If this is right, then First Order Logic (FOL) fails to accurately represent propositions about fundamental relations, by having two atomic sentences, F(a,b) and F(b,a), where there is only one fundamental fact. Moreover, FOL will end up having non-trivial proofs whose conclusion expresses the same proposition as the premise, since we will presumably have an axiom like ∀x∀y(F(x,y)→F(y,x)) that lets us prove F(b,a) from F(a,b). This is not the only example of this phenomenon. Take the proof that ∀xF(x) follows from ∀yF(y), even though surely the two express the same proposition, namely that everything is F.

In particular, the logic of sentences appears to differ from the logic of propositions, since the proposition that Bob and Alice are friends follows by reiteration from the proposition that Alice and Bob are friends if they are the same proposition, but sentence (2) does not follow from sentence (1) by reiteration (nor is this true for the FOL versions).

If we think there is a One True Logic, it presumably will be a logic of propositions rather than sentences, then. But what it will be like is a difficult question, to answer which we will have to a worked out theory of when we have the same proposition and when we have different ones.

An argument for dualism from Special Relativity and unity of consciousness

Here’s a valid argument:

1. There is always an absolute fact about whether two conscious states are hosted simultaneously.

2. If the mind is physical, there is not always an absolute fact about whether two conscious states are hosted simultaneously.

3. So, the mind is not physical.

Why believe (2)? Well, if the mind is physical, it is a brain—that’s by far and away our best physical theory of the mind. The brain is spatially extended, and it is very plausible that different brain regions are involved in different conscious states. But now we can imagine that one conscious state ends almost when another begins, so that the overlap time between the two conscious states is very, very small—say, a picosecond. If the brain brain regions involved in the two conscious states are sufficiently different (more precisely, if their convex hulls differ sufficiently in comparison to the distance light travels during the overlap time), then there will also be some reference frame in which the two conscious states do not temporally overlap. Hence, it depends on reference frame whether the two conscious states overlap, and there is no fact of the matter about simultaneity of the conscious states.

If I were a physicalist, I think I would attack (1).

Three fixity principles

In debates about free will and foreknowledge as well as about compatibility and incompatibilism, fixity-of-history theses come up. Here is such a thesis:

1. If a decision is causally or logically necessitated by the history behind the decision, then one could not have decided otherwise.

But now we have a crucial question as to what is meant by “the history behind the decision”. There are at least two takes on this. On the temporal version, the history behind the decision is the sum total of what happened temporally prior to the decision. On the causal version, the history is the sum total of what happend causally prior to the decision.

This is not just a nitpicking question. Linda Zagzebski for instance nicely shows that if we go for the causal-history version of (1), then the main argument for the incompatibility of free will and foreknowledge does not get off the ground assuming God’s forebelief is not causally prior to the action. On the other hand, if we go the temporal-history version, then we have a prima facie argument for such incompatibility (though I think it’s blockable).

I am pretty confident that we should go for the causal-history version, and this has to do with the fact that the temporal-history version is not strong enough to capture our fixity intuitions. Suppose that we live in a world with simultaneous causation—say, a Newtonian world with rigid objects such that if you push object A and A pushes B, then B begins to move at exactly the same time as you start pushing (rather than with a delay caused by then need for a compression wave traveling through nonrigid materials at less than the speed of light). Then we could imagine cases where someone’s decision is causally necessitated by something outside the agent that is simultaneous with the decision. Such causal necessitation would just much make it true that one could not have decided otherwise as would causal necessitation by something in the past.

Furthermore, if backwards causation is possible, then a neurosurgeon in the future who used a backwards-causing machine to determine your decision would clearly prevent you from deciding otherwise, even though the neurosurgeon’s action was not in the temporal history. We may not believe backwards causation is possible, but it is clear that if it were possible, then deterministic backwards causation would be just as threatening for free decisions as deterministic forwards causation. This shows that causal determination is indeed a threat.

Of course, my above argument only shows that if we need to choose between the causal and temporal history versions of (1), we should definitely go for the causal one. But perhaps we don’t need to choose. We could accept both versions. But if we think we accept both versions, I think what we really should accept is an even stronger principle, where “history” is causal-cum-temporal (cct). On that stronger principle, event A counts as in the cct history of event E provided that it is either temporally or causally prior to E. The resulting fixity principle is pretty strong principle, but also a bit gerrymandered. And I think accepting this principle not that plausible, because the much simpler causal version captures our intuitions about all the ordinary cases (not involving God, or backwards or simultaneous causation), since in all ordinary cases causal and temporal history coincide, and we should not go for a more complex principle without pretty good reason.

God's forebeliefs are soft facts

The most commonly discussed argument against the compatibility of foreknowledge and free will is based on the “fixity of the past”—that nothing you can do can affect how things were, and hence nothing you can do can affect what God had believed.

However, everyone except the logical fatalist agrees that the “fixity of the past” does not apply to so-called “soft facts”. An example of a soft fact (an expansion of an example of Richard Gale) is to suppose that Alice drank a cup of poison, but hasn’t died yet. Alice would survive if Bob calls 911, but he’s not going to. Then it’s a fact that Alice drank a fatal cup, but this is a soft fact, and there is no difficulty in saying that Bob can make this fact not to have obtained. It is only the hard facts about the past that are supposed to be fixed.

Thus, much of the discussion has focused on the question of whether God’s past forebeliefs could be soft facts. In this post, I want to note that classical theists have very good reason to think that God’s past forebeliefs are soft facts.

Start with the following plausible principle:

1. If a fact F expressed by a past-tense statement is partly grounded in a fact G about the present or future, then F is a soft fact.

Of course, defining a fact “about the present or future” is just as difficult as defining a soft fact, but I am not trying to give a definition of a soft fact, just giving a sufficient condition for being one.

Now, on classical theism, God is simple and hence has no intrinsic accidental features. God’s beliefs about contingent realities then have to be partly constituted by those contingent realities (this is the extrinsic constitution model, and it is unavoidable). Such partial extrinsic constitution is a type of grounding. Thus, God’s belief in a fact is partly grounded in that fact.

Hence, God’s having believed in a fact about the present or future is partly grounded in that fact, and thus by (1) is a soft fact. And everyone except the logical fatalist agrees that soft facts are not subject to the fixity of the past, and hence soft facts about God’s forebeliefs do not threaten free will.

Causal histories and freedom

Linda Zagzebski proposes the plausible principle that one is able to ϕ only if ϕing is compatible with one’s causal history relevant to ϕing.

Suppose Alice is considering whether to rob a bank. While she is doing so, God loudly announces to her nearby friend Bob that Alice will not rob the bank. God’s announcement is in Swahili, which Bob knows and Alice used to know in childhood but completely forgot. But the sound of the language her loving parents spoke to her as a child leads to Alice putting more emphasis on virtue in her deliberation, and she freely decides not to rob the bank.

Since God cannot lie, and since God’s announcement is a part of Alice’s causal history in her deliberation, Alice’s robbing the bank is incompatible with causal history and by Zagzebski’s principle, Alice cannot rob the bank. Yet it is unclear how God’s announcement removes her freedom to rob. After all, had God announced in Swahili that Alice will have breakfast, that would have influenced her deliberation in the same way, and yet obviously she would still have been free to rob the bank. But since Alice doesn’t know Swahili, the content seems causally irrelevant.

I think there are two ways out of this. First, we might cut events very finely. There is (a) God’s saying something or other in Swahili and there is (b) God’s saying in Swahili that Alice will not rob the bank. To determine the causal history, we pare away from the events all that’s causally irrelevant, and so we include (a) but not (b) in the causal history.

Alternately, we might say this. Whether or not Alice knows Swahili, her decision is affected by the detailed facts about the sounds in God’s announcement. Indeed, by essentiality of origins, her deliberation is a numerically different process because of the difference of sounds. And now we can say that God cannot make the announcement, because doing so would result in a circularity in the explanatory order: God would be making the announcement because Alice is not going to rob and Alice is not going to rob because God is making the announcement because she is not going to rob. So it is not so much that the announcement takes away God’s freedom, but that God cannot produce explanatory circularities.

It’s worth noting that Molinism does not seem to help. Sure, the subjunctive conditional of free will

1. Were God to announce in Swahili that Alice won’t rob, Alice wouldn’t rob

is true. But it is necessarily true independently of Molinism!

Two decreases in tension between faith and science

Over the past two hundred years or so, one new tension point arose for the relationship between Christianity and science due to scientific progress—namely, evolution. At the same time, several tension points disappeared due two other instances of scientific progress.

The first instance of this scientific progress was the general abandonment of the Aristotelian eternal world model of the universe with Big Bang cosmology. In the middle ages, Jewish, Islamic and Christian thinkers struggled with the tension between the science/philosophy of the day strongly tending towards a universe that always existed and the theological commitment to a creation a finite amount of time ago. That problem is gone.

The second instance is our scientific understanding of the continuity of organic development from zygote to embryo to infant to adult, which has made quite implausible the old view of discontinuous transition in utero from vegetable to animal to human. This old view was the dominant scientific view of human origins until fairly recently, and it had serious tensions with Christian theology.

The first of these embryological tensions was with Christian moral views about abortion. While traditionally Christians opposed both contraception and abortion, abortion was morally seen as a form of homicide. But on the discontinuous transition view, abortion prior to human ensoulment would only be contraception.

The second embryological tension was a technical problem in Christology. Suppose that in the Incarnation we have the vegetable, mere animal and rational animal sequence. Then Aquinas observes there are two possibilities, neither of which is theologically appealing.

First, it could be that God becomes incarnate as a vegetable or a mere animal. But this seems, as Aquinas says, “unbecoming”. And he seem to be right. The Incarnation reveals to us the person of the Logos, and it would be unbecoming that the Logos become a non-personal being.

Second, it could be that the Incarnation happens only at the beginning of the third stage of development, namely once everything is ready for a rational animal. But then Aquinas says “the whole conception could not be attributed to the Son of God”. Indeed, don’t we even have a tension with the Apostles’ Creed line that Christ “was conceived by the Holy Spirit”? For on this option, Christ was not conceived at all. What was conceived was a vegetable, not Christ. (Indeed, none of us were conceived on this view.) Moreover, one might worry that then there would be a sense in which the flesh of Christ would pre-exist the Incarnation. And that makes it difficult to say that the Word became flesh—for the flesh that Scripture says he “became” would already in a sense have been there, and one can’t become this flesh, since this flesh already has its own identity. (Granted, there may well be some Aristotelian metaphysics one can do to lessen this last worry.)

Aquinas solves the problem by supposing that Christ is conceived fully formed in Mary’s womb, and hence has the rational soul from the first moment of his existence. But this solution is itself problematic. Absent gradual development from a zygote, is this conception at all? If God were to create an adult human either ex nihilo or out of some pre-existing matter, we would not consider that a conception. But neither should we then consider it a conception if God creates a fully-formed fetus, even if he does that out of the pre-existing matter of Mary. So we still have a problem with the Apostles’ creed’s “was conceived by the Holy Spirit”. Moreover, it seems that this deprives Mary of a significant chunk of her motherhood.

But the problem entirely disappears once we think that the human beings begin their existence at conception. Christ is conceived by the Holy Spirit, presumably in that Mary’s ovum is transformed into a zygote by the infinite power of the Holy Spirit, which zygote is the Christ who then grows in utero like we all do.

(Catholics also note that the new scientific understanding of human embryonic development also helps with the doctrine of Mary’s immaculate conception—for only a rational being can be immaculately conceived, since original sin or freedom from it can only apply to a rational being.)

Divine attributes

In previous posts I’ve noted piecemeal that standard definitions of omniscience and omnipotence are incomplete. God’s omnipotence isn’t just that God knows everything—it has to be that he knows it certainly and consciously. We might even say: with maximal certainty and vividness. God’s omnipotence isn’t just that God can do everything—he does it all effortlessly.

It has now occurred to me that both devotionally and philosophically it is fruitful to think about divine attributes by asking what is left out by the rather thin and colorless analytic accounts of them.

Take a flat account of God’s moral perfection as saying that God always does the morally right thing. Well, first, we have to add: and for the right reasons (indeed all the right reasons). Second, we should add that God does this with the perfect attitude—with the appropriate alacrity, without inappropriate regrets, etc.

Or consider the account of God’s being a creator on which God creates everything other than himself. We probably should minimally add that he does this with perfect freedom.

At the moment, this is all I have in the way of clear examples. But I think it’s a worthwhile avenue for exploration and devotion.

Beyond metaphysical immutability

For years I was convinced that the extrinsic constitution model of divine knowledge, which theists who accept divine simplicity must accept, solves the problem of divine immutability in an A-theoretic world where truth changes. The idea was that God’s knowledge of contingent facts is constituted by God’s unchanging essential features (which given simplicity are God himself) together with the changing contingent realities that God knows, that God’s gaze extends to. (This idea is not original to me. Aquinas already had it and probably many contemporary people have independently found it.)

But I now think that this was too quick. For let’s take the idea seriously. The point of the idea is that an unchanging God can have changing knowledge. But now notice that God’s knowledge is conscious. The language of “God’s gaze” that I used above (and which Boethius also uses in his famous discussion of divine knowledge of free actions) itself suggests this—God sees the changing reality. At one time God sees Adam sinless. At another time God sees Adam sinful. This is a difference in conscious state. Granted, this difference in conscious state is entirely metaphysically constituted by the changing reality. But it still means that God’s conscious state changes. It changes in virtue of its extrinsic constituent, but it is still true that God at t₁ is conscious of one thing and God at t₂ is conscious of something else instead. And I submit that that is incompatible with divine immutability.

I think there are two responses the classical theist who believes in changing truths can give. The first is to deny that God is conscious of the changes. I think this is unacceptable. The more vivid and the more vision-like knowledge is, the more perfect it is. The idea that God has merely unconscious knowledge of contingents does not do justice to the perfection of omniscience.

The second response is to bite the bullet and say that God’s conscious state changes but this is compatible with immutability as long as this does not involve an intrinsic change in God. I think this is untenable. That God’s conscious state does not change is, I think, a central part of the content of immutability, regardless of whether this conscious state is intrinsically or extrinsically constituted. For a non-physical being, change of conscious mental state is a paradigmatically central kind of change—regardless of the metaphysics of how that change of conscious state comes about. When God says in Malachi 3:6 that he does not change, it seems very implausible to think that the listener is supposed to say: “Sure, but sometimes God has one conscious state and sometimes another, and because this change is grounded extrinsically, that’s OK.” Malachi isn’t doing heavy-duty scholastic/analytic metaphysics. Similarly, when the early Church Fathers say that God is unchanging I doubt they would tolerate the idea that God’s conscious state changes. The extrinsic constitution story is an explanation of what makes God’s conscious state change, and I expect the Church Fathers wouldn’t have cared what the explanation would be—they would just deny the change.

Jumping from the Church Fathers to the modern period, Calvin says that God “cannot be touched with repentance, and his heart cannot undergo changes. To imagine such a thing would be impiety.” But if God’s conscious states are extrinsically constituted and can change, there would be nothing to prevent the idea of God’s “heart” undergoing changes: when people behave well, God feels pleased; when people behave badly and deserve vengeance, God feels vengeful. The differences in God’s feeling would be, one could imagine, constituted by the differences in human behavior and divine response to it. But it would be implausible to think that Calvin would say “Well, as long as the change is extrinsically constituted, it’s OK.” We then wouldn’t need Calvin’s famous story—itself going back to the Church Fathers—of the accommodation of divine speech to our needs. When Calvin insists that God’s heart cannot undergo changes, he isn’t just concerned about divine metaphysics. He is rightly concerned about a picture of a God with a changing mental life. And here at least, Calvin is with the mainstream of the Christian tradition.

If I am right in the above, there is a disanalogy between how God’s mental state behaves across possible worlds and across times. We have to say that in different possible worlds God has different (extrinsically constituted according to divine simplicity) conscious states. But we cannot say that God has different conscious states at different times.

Some thinkers, especially open theists, want the doctrine of divine immutability not to be about metaphysics but about the constancy of God’s character, purposes and promises. I think they are wrong: the doctrine of immutability really does include what we might call metaphysical immutability, that God has no intrinsic change. But metaphysical immutability is not enough. A mental and especially conscious immutability is also central to how we understand divine immutability.

And this is not compatible with the A-theory of time, given omniscience. Which is too bad. While I myself am a B-theorist, the reasoning in yesterday’s post was giving me the hope that we could detach the A- and B-theoretic debate from theism, so that the theist wouldn’t need to take a stand on it. But, alas, I think a stand needs to be taken.

Could a being in time be eternal in Boethius' sense?

Famously, Boethius says that an eternal being, unlike a merely temporally everlasting being, embraces all of its infinite life at once, “possess[ing] the whole fulness of unending life at once”. What’s that mean?

Our life is strung out across time. Sitting right now I as I am I do not embrace the past and future portions of my life where I am lying down or standing up. If I fully and vividly knew my past and my future, I would be a little closer to being eternal, but it would still not be true that I possess the fullness of that life at once. For it would still be true that I now only possess the property of being seated and not the property of lying down or of standing up. So I think epistemic things are not enough for eternity. And this seems intuitively right—eternity is not an epistemic matter. (Could you have an eternal being that isn’t minded? I don’t see why not.) A necessary condition for being eternal is being unchanging.

But being unchanging is not sufficient. Suppose I were everlastingly frozen sitting in front of my laptop. It would still be true that in addition to the present part of my life there is the future part and the past part, and further subdivisions of these, even if they happen to be boringly all alike. The life of an eternal being does not have temporal divisions, even boring ones. It is all at once.

Here is a weird thought experiment. Imagine you are an everlasting point-sized being with a rich and changing mental life. Suppose all your life is spent at the one spatial location (x₀,y₀,z₀). But now imagine that you get infinitely multilocated across all time, in such a way that your numerically same life occurs at every x-coordinate. Thus, you live your everlasting and rich mental life (x,y₀,z₀) for every possible value of x, and it’s the very same life. Your life isn’t spatially divided. The life at x-coordinate  − 7.0 is not merely qualitatively but numerically the same life as the one at x-coordinate  + 99.4.

Now, one more step. Your life is within a four-dimensional spacetime. Assume that spacetime is Galilean or Minkowskian. Now imagine rotating your life in the four-dimensional spacetime in such a way that what was previously along the x-axis is along the t-axis and vice versa. So now your rich and temporally varied mental life becomes temporally unchanging, but all the variation is now strung out spatially along the x-axis. Furthermore, whereas previously due to multilocation you had your life wholly at every x-coordinate, now you have your life wholly—and the numerically same life—at every t-coordinate. Thus, you have an infinite life all at once at every time for everlasting time. Your life isn’t temporally divided: tomorrow’s life is not simply just like today’s, but it is the numerically same as today’s, because your life is fully multilocated at all the different times.

Here is an interesting thing to note about this. This “sideways life”, varying along the x-axis, satisfies the Boethian definition of eternity even though the life is found in time—indeed at every time. If this is right, then having an eternal life in the Boethian sense is compatible with being in time!

Of course, God is not like you are in my weird story. In my story, your life includes different instances of consciousness strung out along the x-axis, though not along the t-axis. Still this kind of inner division is contrary to the undividedness of the divine mind. An eternal God would not have such divisions either. Nor would he be spatial. Perhaps an argument can be made that if God possesses Boethian eternity, then he has to be timeless. But I think that’s not going to be an easy argument to make.

If this is right, then I have overcome an obstacle to combining classical theism with the A-theory of time. I am convinced that an omniscient being has to be in time if the A-theory is true. But if a being can be in time and yet eternal in the Boethian sense, then a classical theist may be able to accept the A-theory of time. After all, Boethius is paradigmatically a classical theist.

That said, my own view is that the above argument just shows that Boethius has not given us a fully satisfactory characterization of eternity. And I have other reasons to reject the A-theory besides theistic ones.

Towards quantifying the good of success

Yesterday, I argued that the good of success contributes to one’s well-being at the time of one’s striving for success rather than at the time of the success itself.

It seems, then, that the longer you are striving, the longer the amount of time that you are having the good of success. Is that right?

We do think that way. You work on a book for five years. Success is sweeter than if you work on a book for one year.

But only other things being equal. It’s not really the length of time by itself. It’s something like your total personal investment in the project, to which time is only one contribution. Gently churning butter for an hour while multitasking other things (using a pedal-powered churn, for instance) does not get you more good of success than churning butter with maximum effort for fifteen minutes, if the outputs are the same.

We might imagine—I am not sure this is right—that the good of success is variably spread out over the time of striving in proportion to the degree of striving at any given time.

What else goes into the value of success besides total personal investment? Another ingredient is the actual value of the product. If you’ve decided to count the hairs on your toes, success is worth very little. Furthermore, the actual value of the product needs to be reduced in proportion to the degree to which you contributed.

Thus, if Alice and Bob both churned butter and produced n pounds, the value of the output is something like bn, where b is the value of butter per pound. If the investments put in by Alice and Bob are I_A and I_B, then Alice’s share of the value is bnI_A/(I_A+I_B). But since the value of success is proportional also to the absolute investment, I think that the considerations given thus far yield a formula for the value of success for Alice proportional to:

• bnI_A²/(I_A+I_B).

Next note that one way to think about the degree to which you contributed is to think as above—what fraction of the total investment is yours. However, even if you are the only person working on the project, the degree of your contribution may be low. Let’s say that you have moved into a house with a mint bush. Mint bushes are aggressive. They grow well with little care (or so we’ve found). But you do water it. The mint bush added half a pound to its weight at the end of the season. You don’t, however, get credit for all of that pound, since even if you hadn’t watered it, it would likely have grown, just not as much. So you only get credit for the portion of the output that is “yours”. Moreover, sometimes things work probabilistically. If the success is mostly a matter of chance given your investment, I think you only get good-of-success credit in proportion to the chance of success—but I am not completely sure of this.

But here is something that makes me a little uncertain of the above reasoning. Suppose that you have some process where the output is linearly dependent on the investment of effort. You invest I, and you get something of value cI for some proportionality constant c. By the above account, to get the value of success, you should multiply this by I again, since the value of success is proportional to both the value of the output and the effort put in. Thus, you get cI². But is it really the case that when you double the effort you quadruple the value of the success? Maybe. That would be interesting! Or are we double-counting I?

Another question. When we talk about the value of the output, is that the objective value, or the value you put on it, or some combination of the two? Counting the hairs on your toes has little objective value, but what if you think it has significant value? Doesn’t success then have significant value? I suspect not.

But what about activities where the value comes only from your pursuit, such as when you try to win at solitaire or run a mile as fast as you can? In those cases it’s harder to separate the value of the output from the value you put on it. My guess is that in those cases there is still an objective value of the output, but this objective value is imposed by your exercise of normative power—by pursuing certain kinds of goals we can make the goal have value.

Let’s come back to counting hairs on toes. If you’re doing it solely for the sake of the value of knowledge, this has (in typical circumstances) little objective value. But if your hobby is counting difficult to count things, then maybe there is additional value, beyond that of trivial knowledge, in the result.

I suspect there are further complications. Human normativity is messy.

And don’t ask me how this applies to God. On the one hand, it takes no effort for God to produce any effect. On the other hand, by divine simplicity God is perfectly invested in everything he does. But since my metaethics is kind-relative, I am happy with the idea that this will go very differently for God than for us.

From three or four problems of omniscience down to one

The three most influential problems of omniscience are:

1. Boethius’ problem of foreknowledge: What is known is necessarily so, and thus if God knows what you will do, you will necessarily do it.

2. Pike’s problem of foreknowledge: If you can act otherwise, you can thereby make it be that either God didn’t exist or that God wasn’t omniscient or that God had believed otherwise than God actually did, and you just can’t do that.

3. The simplicity and knowledge of contingents problem: If the world had been different, God’s beliefs would have been different, which implies that God’s beliefs are accidents of God, contrary to divine simplicity.

Of these, (1) is fully solved by Boethius/Aquinas by distinguishing between necessity of consequence and necessity of consequent. The problem in (1) is just a simple matter of a fallacy of modal scope ambiguity. It’s a non-problem.

I now want to argue that the most widely accepted solution to (3) also solves (2).

This solution, likely already known to Aquinas, is that God’s belief in contingent facts is partly extrinsically constituted by creatures, and all the contingency is on the created side. For instance, God’s belief that there are zebras is grounded in essential facts about God that do not vary between possible worlds and the actual existence of zebras, which only obtains in some possible worlds.

Suppose we apply this solution to (3). Then God’s belief that you will ϕ at t is partly grounded in your ϕing at t and partly in essential facts about God. At this point it is obvious that:

4. If you were not to ϕ at t, God wouldn’t have believed you would ϕ at t.

For the contingent part of the grounds of God’s believing that you would ϕ at t is your actually ϕing at t, so when you take that away, God’s belief goes away. And if instead you ψ at t, your action thereby constitutes the contingent part of the grounds of God’s believing that you would ψ at t, and so:

5. If you were to ψ at t, God would have believe you would ψ at t.

If God’s past belief is partly constituted by our actions, it is no surprise that there is counterfactual dependence between our actions and God’s past belief. In other words, the classical theist who accepts divine simplicity has a way out of Pike’s argument that is motivated completely independently of considerations of time and freedom, namely by embracing counterfactuals like (4) and (5) that Pike considers absurd.

Of course the extrinsic constitution of divine beliefs is somewhat hard to swallow, notwithstanding excellent work by people like W. Matthews Grant to make it more plausible (I myself have swallowed it). But once we do that, problem (2) is gone, and problem (1) was never there as it was based on a fallacy.

There is a fourth problem, a more recondite one, which is about the incompatibility between God’s knowledge of what time is objectively present (assuming the A-theory of time) and divine immutability. Probably the most extensive pressing of this problem is in Richard Gale’s On the Nature and Existence of God. But Aquinas (according to the very plausible interpretation by Miriam Pritschet in an excellent paper I heard yesterday at the ACPA) responds to the fourth problem precisely by using the extrinsic constitution of God’s knowledge of continent facts (indeed this is why I said that the solution to the simplicity problem was likely known to Aquinas). So even that fourth problem reduces to the third—or just doesn’t get off the ground if the B-theory of time is true.

Aquinas on God's knowledge of propositions

Does God know that the sky is blue?

That seems like a silly question. It’s not like we’re asking whether God knows future contingents, or counterfactuals of freedom. That the sky is blue is something that it is utterly unproblematic for God to know.

Except that it is tempting to say that God has no propositional knowledge, and knowing that the sky is blue is knowing a proposition.

It seems that Aquinas answers the question in Summa Theologiae I.14.14: “God knows all the propositions that can be formulated” (that’s in Freddoso’s translation; the older Dominican translation talks of “enunciable things”, but I think that doesn’t affect what I am going to say). It seems that God does have propositional knowledge, albeit not in the divided or successive way that we do.

But what he is up to in I.14.14 is not what it initially sounds like to the analytic philosopher’s ear.

For consider Thomas’s argument in I.14.14 that God knows all formulable propositions:

Since (a) to formulate propositions lies within the power of our intellect, and since (b), as was explained above (a. 9), God knows whatever lies within either His own power or the power of a creature, it must be the case that God knows all the propositions that can be formulated.

But now notice an ambiguity in “God knows the proposition that the sky is blue.” In one sense, which I will call “alethic”, this just means God knows that the sky is blue. In another sense, the “objectual”, it means that God knows a certain abstract object, the proposition that the sky is blue. In the objectual sense, God also knows the proposition that the sky is green—God fully knows that proposition, just as he knows other objects, like the person Socrates. But God does not, of course, have the alethic knowledge here—God does not know that the sky is green, because the sky is not green.

If it was the alethic sense that Thomas was after, his argument would be invalid. For in article 9, the discussion clearly concerns objectual knowledge. Exactly the same argument establishes that God knows the proposition that the sky is green as that he knows the proposition that the sky is blue. Furthermore, the Biblical quote Thomas gives in support of his view is “The Lord knows the thoughts of men” (Psalm 93:11). But the Lord doesn’t know all of them to be true, doesn’t know all of them alethically, because not all of the thoughts of humans are true.

Furthermore, if it was alethic knowledge that Aquinas was after, it would be inaccurate to say God knows all propositions. For only “half” of the propositions can be known alethically—the true ones!

All that said, I think we can still bootstrap from the objectual to the alethic knowledge. God’s knowledge of objects is perfect (Aquinas relies on this perfection multiple times in Question 14) and hence complete. If God knows something, God also knows all of its properties, intrinsic and relational. Thus, if God knows a proposition objectually, and that proposition has a truth value, God knows that truth value. In particular, if that proposition is true, God knows that it is true. And that seems to suffice for counting as knowing the proposition alethically.

So, it looks like Aquinas is committed to God objectually knowing both the propositions that the sky is green and that the sky is blue, and also knowing that the former is false and the latter is true—which seems to be enough for God to count as knowing that the sky is blue. (Though I could see this last point getting questioned.)

Freedom: a problem for presentism and growing block

A number of people have told me that they have the intuition that a four-dimensional picture of reality like that in the B-theory undercuts free will.

I want to suggest that there is one way in which it is a presentist picture of temporal reality that undercuts free will. (A similar argument applies to growing block, but curiously enough not to shrinking block.)

Assume that open future views are false: there are always determinate facts about contingent future events. (If your reason for thinking that four-dimensional theories undercut free will is because you are an open futurist, then you won’t be impressed by what I say.) Suppose it is a fact that tomorrow morning I will have oatmeal for breakfast. On presentism, this fact can only be grounded in what is present, since on presentism, what is present is all there is. Maybe it’s grounded in the present existence of a future-tensed fact or maybe it’s grounded in my having a future-tensed property of being such that I will eat oatmeal in nine hours. But in any case, things right now are already such as to ground and guarantee that I will have oatmeal for breakfast. Moreover, this was already true five minutes ago—five minutes ago, things were also already such as to ground and guarantee that I will have oatmeal for breakfast tomorrow. This sure feels like it should undercut free will! It seems pretty intuitive that freedom isn’t compatible with there existing grounds that guarantee the action prior to the choice.

On the other hand, on a four-dimensional view while it is a fact that I will eat oatmeal for breakfast tomorrow, the grounds of this fact are not located in the present—and were never located in the past. Rather, the grounds of this fact are where they should be—at tomorrow morning. How things are on the present slice of reality, or on past slices, does not determine (assuming indeterminism) what I will have for breakfast tomorrow. That’s left for tomorrow.

The neatest way out for the presentist is to deny with Merricks that contingent truths about the future and past have any grounds. But that’s also costly.

After writing the above, I came across this related paper by Hunt. No time to revise right now to see what similarities or differences there are.

The good of success is not at the time of success

It’s good for one to succeed, at least if the thing one succeeds in is good. And the good of succeeding at a good task is something over and beyond the good of the task’s good end, since the good end might be good for someone other than the agent, while the good of success is good for the agent.

Here’s a question I’ve wondered about, and now I think I’ve come to a fairly settled view. When does success contribute to one’s well-being? The obvious answer is: when the success happens! But the obvious answer is wrong for multiple reasons, and so we should embrace what seems the main alternative, namely that success is good for us when we are striving for the end.

Before getting to the positive arguments for why the good of success doesn’t apply to us at the time of success, let me say something about one consideration in favor of that view. Obviously, we often celebrate when success happens. However, notice that we also often celebrate when success becomes inevitable. Let’s now move to the positive arguments.

First, success at good tasks would still be good for one even if there were no afterlife. But some important projects have posthumous success—and such success is clearly a part of one’s well-being. And it seems implausible to respond that posthumous success only contributes to our well-being because as a matter of fact we do have an afterlife. Note, too, that in order to locate the good of success at the time of success, we would not just need an afterlife, but an afterlife that begins right at death. For instance, views on which we cease to exist at death and then come back into existence later at the resurrection of the dead (as corruptionist Christians hold) won’t solve the problem, because the success may happen during the gap time. I believe in an afterlife that begins right at death, but it doesn’t seem like I should have to in order to account for the good of success. Furthermore, note that to use the afterlife to save posthumous success, we need a correlation between the timeline the dead are in and the timeline the living are in, and even for those of us who believe in an afterlife right at death, this is unclear.

Second, suppose your project is ensure that some disease does not return before the year 2200. When is your success? Only in 2200. But suppose your project is even more grandiose: the future is infinite and you strive to ensure that the disease never returns. When is your success? Well, “after all of time”. But there is no time after all of time. So although it may be true that you are successful, that success does not happen at any given time. At any given time, there is infinite project-time to go. So if you get the good of success at the time of success, you never get the good of success here. Even an afterlife won’t help here.

Third, consider Special Relativity. You work in mission control on earth to make sure that astronauts on Mars accomplish some task. You are part of the team, but the last part of the team’s work is theirs. But since light can take up to 22 minutes (depending on orbital positions) to travel between Earth and Mars, the question of at what exact you-time the astronauts accomplished their task depends on the reference frame, with a range of variation in the possible answers of up to 22 minutes. But whether you are happy at some moment should not depend on the reference frame. (You might say that it depends on what your reference frame is. But there is no unambiguous such thing as “your” reference frame in general, say if you are shaking your head so your brain is moving in one direction and the rest of your body in another.)

Here is an interesting corollary of the view: the future is not open (by open, I mean the thesis that there are no facts about how future contingents will go). For if the future is open, often it is only at the time of success that there will be a fact about success, so there won’t be a fact of your having been better off for the success when you were striving earlier for the success. That said, the open-futurist cannot accept the third argument, and is likely to be somewhat dubious of the second.

More on A-theory and divine timelessness

Argument One:

1. If from x’s point of view there is an objective fact about what time it presently is, then x is in time.

2. If x knows an objective fact about something, then from x’s point of view there is an objective fact about it.

3. If the A-theory of time is true, then there is an objective fact about what time it presently is.

4. God knows all objective facts.

5. So, if the A-theory of time is true, then God knows an objective fact about what time it presently is. (3 and 4)

6. So, if the A-theory of time is true, from God’s point of view there is an objective fact about time it presently is. (2 and 5)

7. So, if the A-theory of time is true, God is in time. (1 and 6)

Note that no claim is made that if the A-theory of time is true, God changes.

Argument Two:

1. God is actual.

2. Everything actual is in the actual world.

3. If the A-theory of time is true, the actual world is a temporally-centered world (one where there is a fact as to what time is present).

4. Anything that is in a temporally-centered world is in time.

5. So, if the A-theory of time is true, God is in time.

Many will dispute 3, but if we think of worlds as ways for everything to be, then I think it is hard to dispute 3.

I wonder if a classical theist who is an A-theorist might be able to respond that, yes, God is in time but God is not a temporal being. Compare that by doctrine of omnipresence, God is in space, but God is not a spatial being. Still, I think there is a difference. For as the above arguments show, the claim that God is in time is more limiting than the claim that God is spatially omnipresent—it is a claim that God is at the one objectively present point of time (he was and will be at others, of course).

Quantifying saving infinitely many lives

Suppose there is an infinite set of people, all of them worth saving, and you can save some subset of them from drowning. Can you assign a utility U(A) to each subset A of the people that represents the utility of saving the people in A subject to the following pair of reasonable conditions:

1. If A is a proper subset of B, then U(A) < U(B)

2. If A is a subset of the people, and x is one of the people not in A while I is an infinite set of people not in A, then U(A∪{x}) ≤ U(A∪I)?

The first condition says that it’s always better to add extra people to the set of people you save. The second condition says it’s always at least as good to add infinitely many people to the set of people you save as to add just one. (It would make sense to say: it’s always better to add infinitely many, but I don’t need that stronger condition.)

Theorem. For any infinite set of people, there is no real-valued utility function satisfying conditions (1) and (2), but there is a hyperreal-valued one.

It’s obvious we can’t do this with real numbers if we think of the value of saving n lives as proportional to n, since then the value of infinitely many lives will be ∞ which is not a real number. What’s mildly interesting in the result is that there is no way to scale the values of lives saved in some unequal way that preserves (1) and (2).

Proof: The hyperreal case follows from Theorem 2 here, where we let Ω = Ω′ be the set of people, G be the group of permutations of the set of people that shuffle around only finitely many people, and let U be the hyperreal probability (!) generated by the theorem. For this group is clearly locally finite, and any utility satisfying condition (1) and invariant under G will satisfy (2) (apply invariance to a permutation π be that swaps x and a member of I and does nothing else to conclude that U(A∪{x}) = U(A∪{πx}) which must be less than U(A∪I) by (1)).

The real case took me a fair amount of thought. Suppose we have a real U satisfying (1) and (2). Without loss of generality, the set of people is countably infinite, and hence can be represented by rational numbers Q. For a real number x, let D(x) be the Dedekind cut {q ∈ Q : q < x}. Fix a real number x. Choose any rational q bigger than x. Then for any real y > x we will have D(y) ∖ D(x) infinite, and by (1) and (2) we will have:

3. U(D(x)) < U(D(x)∪{q}) ≤ U(D(y)).

Let b = inf_y > xU(D(y)). It follows that U(D(x)) < b ≤ U(D(y)) for all y > x. Let f(x) be the open interval (D(x),b). Then f(x) and f(y) are disjoint and non-empty for x < y. But the collection of disjoint non-empty open intervals of the reals is always countable. (The quick argument is that we can choose a different rational in each such interval.) So f is a one-to-one function on the reals with countable range, a contradiction.

Notes: The positive part of the Theorem uses the Axiom of Choice (I think in the form of the Boolean Prime Ideal Theorem). The negative part doesn’t need the Axiom of Choice if the set of people is countable (the final parenthetical argument about intervals and rationals ostensibly uses Choice but doesn’t need it as the rationals are well-ordered); in general, the argument of the negative part uses the weak version of the Countable Axiom of Choice that says that every infinite set has a countably infinite subset.