Wolterstorff on worship and intention

In Acting Liturgically, Wolterstorff offers a necessary and sufficient condition for when someone “is performing acts of worship or just saying the words and making the gestures”:

if a participant performs some prescribed verbal or gestural action with the intention of not thereby performing whatever be the act of worship prescribed to be performed thereby, then he has not performed that act of worship; otherwise he has

In other words:

1. One worships with the action as the community does if and only if one does not intend to dissent from the community’s understanding of the action.

But both directions of the biconditional are false.

Case 1: Alice visits a foreign country where she does not know the language and enters an ornate religious building. She believes the building to be a pagan temple and, seeing people kneeling, she thinks them to be thereby worshiping some pagan deity. She feels an urge to pray to God, and she kneels with the dual intention of thereby worshiping God and of not doing what the local community is doing. Her worship is heartfelt and sincere. But unbeknownst to her, the building is a church and the people are worshiping God by kneeling.

Alice is worshiping God by kneeling. An intention to worship God by kneeling while acting in a heartfelt and sincere way is sufficient for the kneeling to constitute worship of God. But by Wolterstorff principle, because she also intends—perhaps in Wolterstorff’s own words (she might be a reader of his)—to “not thereby perform[…] whatever be the act of worship prescribed to be performed” by the kneeling, she is not performing “that act of worship”. But that act of worship—the one the community has prescribed the kneeling to constitute—is worship of God. So if Wolterstorff’s no-intended-dissent condition is necessary for worship, Alice doesn’t worship God. But she does. So the no-intended-dissent condition is not necessary.

Objection: Alice is not worshiping communally but individually. The community is worshiping communally. So, Alice does not perform what the community understands the action to be, namely communal worship.

Response: Add to the story that this particular church has a special meaning for “kneeling”: it’s not just worship, but individual worship.

Case 2: Bob visits a foreign country where he does not know the language and enters an ornate religious building. He believes the building to be a Christian church and, seeing people kneeling, he thinks them to be worshiping God. He intends to worship God, kneels and prays in a heartfelt and sincere way. The thought that there might be some pagans in this country does not even occur to him, since the country is known for being very Christian. He kneels with the intention of worshiping God. But unbeknownst to him, the building is a pagan temple and the people are worshiping a pagan deity by kneeling.

Since it doesn’t occur to Bob that the community’s kneeling might be worship of a pagan deity, he does not form any intention to dissent from the community’s understanding. Granted, his own explicit intention to worship God disagrees with the community’s understanding of what they are doing. But to have an intention that in fact disagrees with the community’s understanding of what they are doing is not the same as intending to do otherwise than the community understands. Compare: If an expert uses complicated verbage to deny the existence of life on Mars, and I misunderstand him to be saying there is life on Mars, and I say “Indeed, there is life on Mars”, I am not intending to say otherwise than the expert did—even though what I am intending to say is, as a matter of fact, otherwise than what the expert said.

It is tempting to say that explicit intentions about the meaning of the action trump implicit ones, and so both Alice and Bob are worshiping God, and neither is worshiping a pagan deity. But that’s not quite right. A religious person may intend for the community’s understanding of an action to trump at least certain aspects of their own understanding. For instance, when a Christian prays the Nicene Creed, they may have their own understanding of “consubstantial with the Father”, but they would do well to defer to the Church for what it really means. Thus, their explicit intention to worship the Son as X (where X is their understanding of consubstantiality with the Father) is overridden by their faithful intention to worship the Son under whatever description the Church means by these words.

So, probably, what we want to say is that the individual worshiper can have a complex of set of intentions with priorities between them. For instance, the faithful Christian who prays the Nicene Creed may have intentions where their understanding of “consubstantial” is subordinated to the community’s understanding, but only within some limits. If it were to turn out that what the community means by “consubstantial with the Father” is that the Father and the Son are finite deities with beards of equal bushiness, then the faithful Christian’s intention to worship an immaterial and infinite God trumps their intention to go with the community’s understanding. I suspect there is no good way to encapsulate the complex ways that the prioritization between intentions can go in a simple definition like Wolterstorff’s.

Could there be a grain of truth in Wolterstorff’s condition? I think one could say that one defaults to worshiping as the community does in the absence of overriding intentions. I am not sure I would agree with that, but it might be true.

I am grateful to Tyler Sharp and Juliana Kazemi for pointing me to Wolterstorff’s very interesting ideas on this, and for conversations on this. In a recent conference presentation, they gave an example that has a lot of similarity with Case 2.

Random causation across temporal gaps

Suppose that causation across temporal gaps is possible: that an object x can have a direct effect in a future time, with no intermediate causes. Given that a cause clearly can have a random effect—say, you press a button and you get a green light or a red light at random—then it should also be possible for a cause to have an effect at a random future time.

Now imagine a button that, when pressed, causes a flash of light at a random time in the future, from tomorrow onward, with the probability that the flash happens in n days being 1/2ⁿ.

This is not very different from a button that, when pressed, triggers a sequence of fair coin tosses, one per day, with a beep that goes off as soon as heads comes up. The probability that there will be a beep in n days is 1/2ⁿ.

But there is still an important difference between the flash and the beep, even though they are probabilistically isomorphic. The flash is guaranteed but the beep is not (it is possible to get tails everyday). On open-future views, it is true that the flash will happen but not true that the beep will.

One could imagine the flash method being used by God in connection with indefinite-time future promises like “One day I’m going to make a flash of light.” God can just create the button that causes the flash to happen on a random future day and then trigger the button.

Appearances of atemporality

Here’s a way to think about presentism. We have a three-dimensional reality and temporal modal operators, such as Prior’s P, F, H and G (pastly, futurely, always-pastly and always-futurely), with appropriate logical rules.

But now imagine this scenario: Reality consists of an eternally frozen time slice from a complex two-way-deterministic Newtonian world resembling our world—“frozen Newtonian world” for short. There are particles at various positions with various momenta (I assume that q = mdx/dt is a law of nature rather than a definition of momentum, and momentum is fundamental), but they are ever still, unchanging in their Newtonian properties. Now if Q is one of the operators P, F, H and G, define the operator Q′ as follows:

• Q′p if and only if either (a) reality consists of an eternally frozen Newtonian world and in an unfrozen Newtonian world that agrees with reality on its present slice we would have Qp or (b) we have Qp and reality does not consist of an eternally frozen Newtonian world and we have Qp.

Then the primed operators behave logically just like the unprimed ones. But according to the primed operators, “there is change and motion”. For instance, for a typical particle z eternally frozen at location x, it will be the case that P′(z is not at x) and F′(z is not at x), since in an unfrozen Newtonian world whose present slice is just like our world’s, there will be past and future times at which z is not at x.

So what? Well, the presentist’s big intuition is that on a B-theory of time there is no change: there is just a four-dimensional block, where one dimension just happens to be called “time” and things are different at different locations along that dimension, but simply calling a dimension “time” doesn’t make it any different from the spatial ones.

But the B-theorist can respond in kind. On presentism there is no change: there is just a three-dimensional world related to other three-dimensional worlds via certain modal operators that are called “pastly”, etc., but simply calling a modal operator P “pastly” doesn’t make it any different from deviant operators like P′.

The presentist will, presumably, say that it’s not just a matter of calling the operator P “pastly”, but rather the operator is the primitive pastly operator, so that if something pastly is different from how it’s now, it has changed. But now the B-theorist can just respond in the same way. It’s not just a matter of calling one of the four dimensions “time”, but rather the dimension is the primitive time dimension, so that if something is different at a different time from how it is now, it has changed or will change.

(Granted, a B-theorist does not need to think that the distinction between space and time is primitive. I am inclined not to, and hence I cannot make the above response.)

Presumably, even after this dialogue, the B-theorist’s alleged reality will look static to the presentist. But I think the presentist’s alleged reality can look atemporal to the B-theorist—it’s just a three-dimensional world with no time dimension and some modal operators relating it to other three-dimensional worlds.

Always-false open-futurism and the end of time

On always-false open-futurism, reports of future contingents are always false.

Now, imagine that it is contingent whether the time continues past t₁. Perhaps God sustains the world in existence, and has promised to sustain it until t₁ inclusive, but is free to stop sustaining it right then.

Suppose it is now t₁. Thus, now is potentially the last moment of time, but potentially not. What does the previous sentence mean? It seems to mean the conjunction of these two claims:

1. How things are now is compatible with its not being the case that there will be time.

2. How things are now is compatible with its being the case that there will be time.

But on always-false open-futurism, when the very existence of future time is contingent in light of how things are now, all will-claims have to be false. Thus, how things are now necessitates that its not the case that there will be time. In other words, we don’t have (2).

If this is correct, then on always-false open-futurism there cannot be a moment which is both potentially the last moment of time and potentially not the last moment of time. Each moment of time either is necessarily not last or necessarily last. This is a bit of a burden for the theory.

On trivalent open-futurism on which will-claims about future contingents are neither true nor false, the problem disappears. That now is potentially the last moment of time but potentially not can be taken to be equivalent to:

3. It is neither true nor false that there will be time.

A Thomistic argument for the Principle of Proportional Causality

The Principle of Proportionate Causality (PPC) defended by Aquinas and other scholastics says that a perfection P can only be caused by something that has P either formally or eminently. To have P formally is to have P. Roughly, to have P eminently is to have a perfection greater than P.

(Some add: “has P virtually” to the list of options. But to have P virtually is just to have the power to produce P, and as our student Colin Causey has noted, this trivializes PPC.)

There are obvious apparent counterexamples to PPC:

• Two parents who are bad at mathematics can have a mathematical genius as a child.

• Ugly monkeys typing at random can produce a beautiful poem.

• A robot putting together parts at random can make a stronger and smarter robot.

It’s tempting to throw PPC out. But there are also cases where one feels a pull towards PPC:

• How can things that represent come from non-representing stuff?

• How can the conscious come from the non-conscious?

• How can something with dignity come from something without any?

• How can the active come from the inactive?

• How can an “ought” come from a mere “is”, i.e., something with normativity from something without any?

Many contemporary philosophers think there is no impossibility even in these cases, but I think most will agree that there is something puzzling about these kinds of causation—that we have some sort of an intuition towards PPC in these cases, of a sort we do not have in the cases of the “obvious apparent counterexamples”. What is the difference between the cases?

Well, in the counterexamples, the differences between the cause and the effect are, arguably, a matter of degree. The two parents have a much lower degree of mathematical ability. The monkeys have a certain beauty to them—being productive of beauty is a kind of beauty—albeit perhaps a lesser one than their lucky output. The robot’s output is just a more sophisticated bunch of moving parts than the robot itself.

But in the examples where one feels pulled to PPC, the differences appear to be differences in kind. Indeed, I think we can all agree that the most plausible way to resist the implied claim in the “How can…?” questions that the thing is impossible is to show how to reduce the seemingly more perfect thing to something of the same sort as the alleged cause.

But “differences in kind” doesn’t seem quite sharp enough. After all, pretty much everyone (even, I assume, young earth creationists) will agree that dogs can come from wolves.

I’ve been puzzled by how one might understand and argue for PPC for a long time, without much progress. This morning I had an inspiration from Nicholas Rescher’s article on Aquinas’ “Principle of Epistemic Disparity”, that lesser minds cannot comprehend the ways of greater ones.

Suppose we order the types of good by a comprehensibility relation ≤ where G ≤ H means that it is possible to understand G by understanding H. Then ≤ is a partial preorder, i.e., a reflexive and transitive relation. It generates a strict partial preorder < where G < H provided that G ≤ H but not H ≤ G.

Next, say that good types G₁ and G₂ are cases of the same perfection provided that G₁ ≤ G₂ and G₂ ≤ G₁, i.e., that each can be understood by the other. Basically, we are taking perfections to be equivalence classes of types of good, under the relation ∼ such that G₁ ∼ G₂ if and only if G₁ ≤ G₂ and G₂ ≤ G₁. The relation ≤ extends in a natural way to the perfections: P ≤ Q if and only if whenever G is a case of P and H is a case of Q then G ≤ H. Note that ≤ is a partial order on the perfections. In particular, it is antisymmetric: if we have P ≤ Q and Q ≤ P, then we have P ≠ Q. Write P < Q provided that P ≤ Q and P ≠ Q.

Now on to a Thomistic argument for the PPC.

Being, truth and goodness are transcendentals. The cognitively more impressive perfection Q is thus also axiologically more impressive. Thus:

Axiological Thesis: If P < Q for perfections P and Q, then Q is a better kind of perfection than P.

The following is plausible on the kind of Aristotelian intrinsic notion of causation that Thomas works with:

Causal Thesis: By understanding the cause one understands the effect.

Thomistic ideas about transcendentals also yield:

Understandability Lemma: To understand a thing one only needs to understand the goods instantiated by the thing.

Finally, let’s add this technical assumption:

Conjunction Lemma: The conjunction of co-instantiable goods is a good.

And now on to the PPC. Suppose x causes y to have a good G and y has a type of good G that is a case of a perfection P. By the Causal Thesis, we understand G by understanding x. By the Conjunction Lemma, let H be the conjunction of all the good of x. By the Understandability Lemma, we understand x by understanding H. Thus, G ≤ H. Let Q be the perfection that H is a case of. Then P ≤ Q and x has Q. Then either P = Q or P < Q. In the former case, the cause has P formally. In the latter case, by the Axiological Thesis, the cause has P eminently.

Of course, the Axiological and Causal Theses, together with the Understandability Lemma, all depend on large and controversial parts of Aquinas’ system. But I think we are making some progress.

I am also toying with an interesting concept. Say that a perfection Q is irreducible provided that it cannot be understood by understanding any conjunction of perfections P such that P < Q. It’s not obvious that there are irreducible perfections, but I think it is plausible that there are. If so, one might have a weaker PPC restricted to irreducible perfections. I have yet to think through the pluses and minuses here.

Divine willing

A correspondent asked me how a simple God can choose. I've thought much about this, never quite happy with what I have to say. I am still not happy (nor is it surprising if "how God functions" is beyond us!) but the following helps me a little.

Suppose I am choosing between making a brownie or a smoothie, and end up making a smoothie. Then there are four stages with each stage causing the next:

1. Deliberation between brownie and smoothie (and any other options).

2. An internal intention for a smoothie.

3. Physical movements.

4. Output: smoothie!

At Stage 1, I am still open between brownie and smoothie. Starting with Stage 2, I am internally set on the smoothie, and at that point I become morally responsible for setting myself on the smoothie.

Now one great thing about God’s power is that God doesn’t need means: he can produce effects directly.

In particular, God will omit stage 3: he doesn’t need moving limbs (nor anything else beyond himself) to produce the smoothie in the way that I need them.

Now suppose we apply perfect being theology to God. It’s a perfection of power not to need means. But stage 3 is not the only means in the above story: stage 2 is also a means. If God really doesn’t need means, then stage 2 will also be omitted in God, and we will have the two (non-temporal) stage production:

1. Deliberation between brownie and smoothie (and infinitely many other options).

2. Output: smoothie!

In particular, nowhere in this account is there an internal intention. It’s not needed: God acts directly on the external world.

We might ask: How does God know that he intends to create a smoothie? I think it’s by direct observation of the output, stage B in the divine case. (And God’s knowledge of contingencies is extrinsically grounded in the contingencies.)

If that sounds wrong, let’s ask how we know what we intend. Sometimes we know what we intend by introspection: by observing the internal intention of stage 2. But not always. Sometimes stage 2 is not conscious—we deliberate, we presumably form an internal intention but we are not directly aware of it, and then we act. When we deliberate whether to do something minor like whether to lift the left or the right hand, sometimes the first thing we are aware of is not an internal intention or specific act of will, but the movement of the hand itself. Thus, even in us, knowledge of our intentions is sometimes read off from stage 3.

Moreover, in some cases, for us, stage 3 is not distinct from stage 4. For we have bodies that we move, and sometimes—as in the hand-lift case—the output is the same as the physical movements. In some such cases, then direct knowledge of the merges stages 3 and 4 is how we know our own intention. There may even be rare cases where stage 3 and stage 4 are distinct, but in our consciousness, the knowledge of stage 4 comes first. Suppose I am deliberating whether to press the space-bar or the enter key in response to the computer saying “Press any key”. I choose to press the space-bar. It may well be that in the order of consciousness, I first feel the impact of my finger on the keyboard, then I discern the subtler kinesthetic sensation of my finger having moved through the air, and then only then do I realize what key I intended to press. I don’t know if this is how it happens—it’s too fast to be confident of phenomenology—but it seems like an intelligible possibility.

In any case, there is nothing absurd about knowing an intention by direct observation of the output.

While writing the above, it occurred to me that perhaps we shouldn’t be all that confident that we always have a stage 2. In the cases where our knowledge of what we intend comes from knowledge of stage 3 or 4, and we do not have direct conscious access to an internal act of intention, the internal act of intention is a mere theoretical posit. Perhaps that theoretical posit is correct, but perhaps it is not. If it is not, then one can intend a specific output without having an internal specified act of intention.

Why do we like being confident?

We like being more confident. We enjoy having credences closer to 0 or 1. Even if the proposition we are confident in is one that is such that it is a bad thing that it is true, the confidence itself, abstracted from the badness of the state of affairs reported by the proposition, is something we enjoy.

Here is a potential justification of this attitude in many cases. We can think of the epistemic utility of one’s credence r in a proposition p as measured by an accuracy scoring rule given by two functions T(r) and F(r), where T(r) gives the value of having credence r in p when p is actually true and F(r) gives the value when p is actually false. Most people thinking about scoring rules think they should satisfy the technical condition of being strictly proper. But strict propriety implies that the function V(r) = rT(r) + (1−r)F(r) is strictly convex. Now suppose the scoring rule is also symmetric, so that T(r) = F(1−r). Then V(r) is a strictly convex function that is symmetric about r = 1/2. Such a function has its minimum at r = 1/2, and is strictly decreasing on [0,1/2] and strictly increasing on [1/2,1]. But the function V(r) measures your expectation of your epistemic utility. How happy you are about your credence, perhaps, corresponds to your expectation of your epistemic utility. So you are most unhappy at credence 1/2, and you get happier that closer you are to 0 or 1.

OK, it’s surely not that?!

Observations and risk of confirmation/disconfirmation

It seems that a rational agent cannot guarantee their credence in a hypothesis H to go up by choosing what observation to perform. For if no matter what I observe, my credence in H goes up given my observation, then my credence should already have gone up prior to the observation—I should boost my credence from the armchair.

But this reasoning is false in general. For in performing the observation, I not only learn which of the possible observable results is in place, but I also learn that I have performed the observation. In cases where the truth of H has a correlation with whether I actually perform the observation, this can have a predictable direction of effect on my credence in H.

Suppose that the hypothesis H is the conjunction that I am going to look in the closet and there is life on Mars. By looking to check if there is a mouse in my closet, I ensure that the first conjunct of H is true, and hence I increase my credence in H—no matter what I find out about mice.

This is a very trivial fact. But it does mean that we need to qualify the statement that any observation that can confirm a hypothesis can also disconfirm it. We need to specify that the confirmation and disconfirmation happen after one has already updated on the fact that one has performed the observation.

Epistemic utilities and decision theories

Warning: I worry there may be something wrong in the reasoning below.

Causal Decision Theory (CDT) and Epistemic Decision Theory (EDT) tend to disagree when the payoff of an option statistically depends on your propensity to go for that option. The most example of this phenomenon is Newcomb’s Problem (where money is literally put into a box or not depending on what your propensities are), and there is a large literature of other clever and mind-twisting examples. From the literature, one might get a feeling that these cases are all somehow weird, and normally there is no such dependence.

But here is a family of cases that happens literally almost all the time to us. Pretty much whenever we act we gain information relevant to facts about ourselves, and specifically to facts about our propensities to act. For instance, when you choose chocolate over vanilla ice cream you raise your credence for the hypothesis that you have a greater propensity to choose chocolate ice cream than to choose vanilla ice cream. But truth about oneself is valuable and falsehood about oneself is disvaluable. If in fact you have a greater propensity to choose chocolate ice cream, then by eating chocolate ice cream you gain credence in a truth, which is a good thing. If in fact your propensity for vanilla ice cream is at least as great as for chocolate ice cream, then by eating chocolate ice cream, you gain credence in a falsehood. The payoffs of your decision as to flavor of ice cream thus statistically depend on what your propensities actually are, and so this is exactly the kind of case where we would expect CDT and EDT to disagree.

Let’s be more precise. You have a choice between eating chocolate ice cream (C), eating vanilla ice cream (V) or not eating ice cream at all (N). Let H be the hypothesis that you have a greater propensity for eating chocolate ice cream than for eating vanilla ice cream. Then if you choose C, you will gain evidence for H. If you choose V, you will gain evidence for not-H. And if you choose N, you will (plausibly) gain no evidence for or against H. Your epistemic utility with respect to H is, let us suppose, measured by a single-proposition accuracy scoring rule, which we can think of as a pair of functions T_H and F_H, where T_H(p) is the value of having credence p in H if in fact H is true and F_H(p) is the value of having credence p in H if in fact H is false.

The expected evidential utilities of your three options are:

• E_e(C) = P(H|C)T_H(P(H|C)) + (1−P(H|C))F_H(P(H|C))

• E_e(V) = P(H|V)T_H(P(H|V)) + (1−P(H|V))F_H(P(H|V))

• E_e(N) = P(H|N)T_H(P(H|N)) + (1−P(H|N))F_H(P(H|N)) = P(H)T_H(P(H)) + (1−P(H))F_H(P(H)).

The expected causal utilities are:

• E_c(C) = P(H)T_H(P(H|C)) + (1−P(H))F_H(P(H|C))

• E_c(V) = P(H)T_H(P(H|V)) + (1−P(H))F_H(P(H|V))

• E_c(N) = P(H)T_H(P(H|N)) + (1−P(H))F_H(P(H|N)) = P(H)T_H(P(H)) + (1−P(H))F_H(P(H)).

We can make some quick observations in the case where the scoring rule is strictly proper, given that P(H|V) < P(H) < P(H|C):

1. E_c(C) < E_c(N)

2. E_c(V) < E_c(N)

3. At least one of E_e(C) > E_e(N) and E_e(V) > E_e(N) is true.

Observations 1 and 2 follow immediately from strict propriety and the formulas for E_c. Observation 3 follows from the fact that the expected accuracy score after Bayesian update on evidence is better (in non-trivial cases where the scoring rule is strictly proper) than before update, and the expected accuracy score after update on what you’ve chosen is:

• P(C)E_e(C) + P(V)E_e(V) + P(N)E_e(N)

while the expected accuracy score before update is equal to E_e(N). Since P(C) + P(V) + P(N) = 1, it follows from the superiority of the post-update expectation that at least one of E_e(C) and E_e(V) must be bigger than E_e(N).

The above results seem to be a black eye for CDT, which recommends that if what you care about is your epistemic utility with regard to your propensities regarding chocolate and vanilla ice cream, then you should always avoid eating ice cream!

(What about ratifiability? Some CDTers say that only ratifiable options should count. Is N ratifiable? Given that you’ve learned nothing about H from choosing N, I think N should be ratifiable. But I may be missing something. I find the epistemic utility case confusing.)

It also seems to me (I haven’t checked details) that on EDT there are cases where eating either flavor is good for you epistemically, but there are also cases where only one specific flavor is good for you.

"Swapping memories"

In Shoemaker’s Lockean memory theory of personal identity, in the absence of fission and fusion personal identity is secured by a chain of first-personal episodic quasimemories. All memories are quasimemories, but in defining a quasimemory the condition that the remembered episode happened to the same person is dropped to avoid circularity. It is important that quasimemories must be transmitted causally by the same kind of mechanism by which memories are transmitted. If I acquire vivid apparent memories of events in Napoleon’s life by reading his diaries, these apparent memories are neither memories nor quasimemories, because diaries are not the right kind of mechanism for memory transmission, and so Shoemaker can avoid the absurd conclusion that we can resurrect Napoleon by means of his diaries. If you wrote down an event in a diary, and then forgot the event, and then learned of the event from the diary, you should not automatically say “I now remember” (of course, the diary might have jogged your memory—but that’s a different phenomenon from your learning of the event from the diary).

It seems to me that discussion of memory theory after Shoemaker have often lost sight of this point, by engaging in science-fictional examples where memories are swapped between brains without much discussion of whether moving a memory from one brain to another is the right kind of mechanism for memory transmission. Indeed, it is not clear to me that there is a principled difference between reading Napoleon’s memory off from a vivid description in his diary and scanning it from his brain. With our current brain scanning technology, the diary method is more accurate. With future brain scanning technology, the diary method may be less accurate. But the differences here seem to be ones of degree rather than principle.

If I am right, then either the memory theorist should allow the possibility of resurrecting someone by inducing apparent memories in a blank brain that match vivid descriptions in their diary (assuming for the sake of argument that there is no afterlife otherwise) or should deny that brain-scan style “memory swapping” is really a quasimemory swap and leads to a body-swap between the persons. (A memory swap that physically moves chunks of brain matter is a different matter—the memories continue to be maintained and transmitted using the usual neural processes.)

An instability in Newcomb one-boxing

Consider Newcomb’s Paradox, and assume the predictor has a high accuracy but is nonetheless fallible. Suppose you have the character of a one-boxer and you know it. Then you also know that the predictor has predicted your choosing one box and hence you know that there is money in both boxes. It is now quite obvious that you should go for two boxes! Of course, like the predictor, you predict that you won’t do it. But there is nothing unusual about a situation where you predict you won’t do the rational thing: weakness of the will is a sadly common phenomenon. Similarly, if you have the character of a two-boxer and you know it, the rational thing to do is to go for two boxes. For in this case you know the predictor put money only in the clear box, and it would be stupid to just go for the opaque box and get nothing.

None of what I said above should be controversial. If you know what the predictor did, you should take both boxes. It’s like Drescher’s Transparent Newcomb Problem where the boxes are clear and it seems obvious you should take both. (That said, some do endorse one-boxing in Transparent Newcomb!) Though you should be sad that you are the sort of person who takes both.

This means that principles that lead to one-boxing suffer from an interesting instability: if you find out you are firmly committed to acting in accordance with these principles, it is irrational for you to act in accordance with them. Not so for the principles that lead to two-boxing. Even when you find out you are firmly committed to them, it’s rational to act in accordance with them.

This instability is a kind of flip of the usual observation that if one expects to be faced with Newcomb situations, and one has two-boxing principles, then it becomes rational to regret having one-boxing principles. That, too, is an odd kind of inconsistency. But this inconsistency does not seem particularly telling. Take any correct rational principle R. There are situations where it becomes rational to regret having R, e.g., if a madman is going around torturing all the people who have R. (This is similar to the example that Xenophon attributes to Socrates that being wise can harm you because it can lead to your being kidnapped by a tyrant to serve as his advisor.)

Virtue and value

Suppose you have a choice between a course of action that greatly increases your level of physical courage and a course of action that mildly increases your level of loyalty to friends. But there is a catch: you have moral certainty that in the rest of your life you won’t have any occasion to exercise physical courage but you will have occasions to exercise loyalty to friends.

It seems to be a poor use of limited resources to gain heroic physical courage instead of improving your loyalty a bit when you won’t exercise the heroic physical courage.

If this is right, then the exercise of virtue counts for a lot more than the mere possession of it, as Aristotle already noted with his lifelong coma argument.

But now modify the case. You have a choice between a course of action that greatly increases your level of physical courage and feeding one hungry person for a day. Suppose that you don’t have the virtue of generosity, and that feeding the hungry person won’t help you gain it, because you have a brain defect that prevents you from gaining the virtue of generosity, though it allows you to act generously. And as before suppose you will never have an occasion to exercise physical courage. It still seems clear that you should feed the hungry person. Thus not only does the exercise of virtue count for a lot more than mere possession of virtue, acting in accordance with virtue, even in the absence of the virtue, counts for more than mere possession of virtue.

Next, consider a third case. You have a choice between two actions, neither of which will affect your level of virtue, because shortly after the actions your mind will be wiped. Action A has an 85% chance of saving a life, and if you perform action A, it will certainly be an exercise of generosity. Action B has a 90% chance of saving a life, and the action will be done in accordance with physical courage but will not be an exercise of virtue. Which should you do? It seems that you should do B. Thus, that an action is an exercise of a virtue does not seem to count for a lot in deliberation.

Nuclear deterrence, part II: False threats

In my previous post, I considered the argument against nuclear deterrence that says it’s wrong to gain a disposition to do something wrong, and a disposition to engage in nuclear retaliation is a disposition to dosmething wrong. I concluded that the argument is weaker than it seems.

Here I want to think about another argument againt nuclear deterrence under somewhat different assumptions. In the previous post, the assumption was that the leader is disposed to retaliate, but expects not to have to (because the deterrence is expected to work). But what about a case where the leader is not disposed to retaliate, but credibly threatens retaliation, while planning not to carry through the threat should the enemy attack?

It would be wrong, I take it, for the leader to promise to retaliate in such a case—that would be making a false promise. But threatening is not promising. Suppose that a clearly unarmed thief has grabbed your phone is about to run. (Their bathing suit makes it clear they are unarmed.) You pick up a realistic fake pistol, point it at the them, and yell: “Drop the phone!” This does not seem clearly morally wrong. And it doesn’t seem to necessarily become morally wrong (absent positive law against it) when the pistol is real as long as you have no intention or risk of firing (it is, of course, morally wrong to use lethal force merely to recover your property—though it apparently can be legal in Texas). The threat is a deception but not a lie. For, first, note, that you’re not even trying to get the thief to believe you will shoot them—just to scare them (fear requires a lot less than belief). Second, if the thief keeps on running and you don’t fire, the thief would not be right to feel betrayed by your words.

So, perhaps, it is permissible to threaten to do something that you don’t intend to do.

Still, there is a problem. For it seems that in threatening to something wrong, you are intentionally gaining a bad reputation, by making it appear like you are a wicked person who would shoot an unarmed thief or a wicked leader who would retaliate with an all-out nuclear strike. And maybe you have a duty not to intentionally gain a bad reputation.

Maybe you do have such a duty. But it is not clear to me that the leader who threatens nuclear retaliation or the person who pulls the fake or real pistol on the unarmed thief is intentionally gaining a bad reputation. For the action to work, it just has to create sufficient fear that one will carry out the threat, and that fear does not require one to think that the threatener would carry out the threat—a moderate epistemic probability might suffice.

Nuclear deterrence, part I: Dispositions to do something wrong

I take it for granted that all-out nuclear retaliation is morally wrong. Is it wrong (for a leader, say) to gain a disposition to engage in all-out nuclear retaliation conditionally on the enemy performing a first strike if it is morally certain that having that disposition will lead the enemy not to perform a first strike, and hence the disposition will not be actualized?

I used to think the answer was “Yes”, because we shouldn’t come to be disposed to do something wrong in some circumstance.

But I now think it’s a bit more complicated. Suppose you are stuck in a maze full of lethal dangers, with all sorts of things that require split-second decisions. You have headphones that connect you to someone you are morally certain is a benevolent expert. If you blindly follow the expert’s directions—“Now, quickly, fire your gun to the left, and then grab the rope and swing over the precipice”—you will survive. But if you think about the directions, chances are you won’t move fast enough. You can instill in yourself a disposition to blindly do whatever the expert says, and then escape. And this seems the right thing to do, even a duty if you owe it to your family to escape.

Notice, however, that such a disposition is a disposition to do something wrong in some circumstance. Once you are in blind-following mode, if the expert says “Shoot the innocent person to the right”, you will do so. But you are morally certain the expert is benevolent and hence won’t tell you anything like that. Thus it can be morally permissible to gain a disposition which disposes you to do things that are wrong under circumstances that you are morally certain will not come up.

Perhaps, though, there seems to be a difference between this and my nuclear deterrence case. In the nuclear deterrence case, the leader specifically acquires a disposition to do something that is wrong, namely to all-out retaliate, and this disposition is always wrong to actualize. In the maze case, you gain a general disposition to obey the expert, and normally that disposition is not wrong to actualize.

But this overstates what is true of the nuclear deterrence case. There are some conditions under which all-out retaliation is permissible, such as when 99.9% of one’s nuclear arsenal has been destroyed and the remainder is only aimed at legitimate military targets, or maybe when all the enemy civilians are in highly effective nuclear shelters and retaliation is the only way to prevent a follow-up strike from the enemy. Moreover, it may understate what is permissible in the expert case. You may need to instill in yourself the specific willingness to do what at the moment seems wrong, because sometimes the expert may tell you things that will seem wrong—e.g., to swing your sword at what looks like a small child (but in fact is a killer robot). I am not completely sure it is permissible to have an attitude of trust in the expert that goes that far, but I could be convinced of it.

I was assuming, contrary to fact in typical cases, that there is moral certainty that the nuclear deterrence will be effective and there will be no enemy first strike. Absent that assumption, the question is rather less clear. Suppose there is a 10% chance the expert is not so benevolent. Is it permissible to instill a disposition to blindly follow their orders? I am not sure.

Memory theories of personal identity and faster-than-light dependence

Consider this sequence of events:

• Tuesday: Alice’s memory is scanned and saved to a hard drive.
• Wednesday: Alice’s head is completely crushed in a car crash.
• Thursday: Alice’s scanned memories are put into a fresh brain.

It seems that on a memory theory of personal identity, we would say that fresh brain on Thursday is Alice.

But now suppose that on Thursday, Alice’s scanned memories are put into two fresh brains.

If one of the operations is in the absolute past—the backwards light-cone—of the other, it is easy to say that what happens is that Alice goes to the brain that gets the memories first.

Fine. But what if which brain got the memories first depends on the reference frame, i.e., the two operations are space-like separated? It’s plausible that this is a case of symmetric fission, and in symmetric fission Alice doesn’t survive.

But now here is an odd thing. Suppose the two operations are simultaneous in some frame, but one happens on earth and the other on a spaceship by alpha-Centauri. Then whether Alice comes into existence in a lab on earth depends on what happens in a spaceship that’s four light-years away, and it depends on it in a faster-than-light way. That seems problematic.

Killing coiled and straight snakes

Suppose a woman crushes the head of a very long serpent. If the snake all dies instantly when its head is crushed, then in some reference frame the tail of the snake dies before the woman crushes the head, which seems wrong. So it seems we should not say the snake dies instantly.

I am not talking about the fact that the tail can still wiggle a significant amount of time after the head is crushed, or so I assume. That’s not life. What makes a snake be alive is having a snake substantial form. Death is the departure of the form. If the tail of the headless snake wiggles, that’s just a chunk of matter wiggling without a snake form.

What’s going on? Presumably it’s that metaphysical death—the separation of form from body—propagates from the crushed head to the rest of the snake, and it propagates at most at the speed of light. After all, the separation is a genuine causal process, and we are supposed to think that genuine causal processes happen at the speed of light or less.

So we get a constraint: a part of the snake cannot be dead before light emitted from the head-crushing event could reach the part. But it is also plausible that as soon as the light can reach the part, the part is dead. For a headless snake is dead, and as soon as the light from the head-crushing event can reach a part, the head-crushing event is in the absolute past of the part, and so the part is a part of a headless snake in every reference frame. Thus the part is dead.

So death propagates to the snake exactly at the speed of light from the head-crushing, it seems. Moreover, it does this not along the snake but in the shortest distance—that’s what the argument of the previous paragraph suggests. That means that a snake that’s tightly coiled into a ball dies faster than one that is stretched out when the head is crushed. Moreover, if you have a snake that is rolled into the shape of the letter C, and the head is crushed, the tail dies before the middle of the snake dies. That’s counterintuitive, but we shouldn’t expect reality to always be intuitive.

Proportionate causality

Let’s assume for the sake of argument:

Aquinas’ Principle of Proportionate Causality: Anything that causes something to have a perfection F must either have F or some more perfect perfection G.

And let’s think about what follows.

The Compatibility Thesis: If F is a perfection, then F is compatible with every perfection.

Argument: If F is incompatible with a perfection G, then having F rules out having perfection G. And that’s limitive rather than perfect. Perhaps the case where G = F needs to be argued separately. But we can do that. If F is incompatible with F, then F rules out all other perfections as well, and as long as there is more than one perfection (as is plausible) that violates the first part of the argument.

The Entailment Thesis: If F and G are perfections, and G is more perfect than F, then G entails F.

Argument: If F and G are perfections, and it is both possible to have F without having G and to have F while having G, it is better to have both F and G than to have just G. But if it is better to have both F and G than to have just G, then F contributes something good that G does not, and hence we cannot say that G is more perfect than F—rather, in one respect F is more perfect and in another G is more perfect.

From the Entailment Thesis and Aquinas’ Principle of Proportionate Causality, we get:

The Strong Principle of Proportionate Causality: Anything that causes something to have a perfection F must have F.

Interesting.

More on velocity

From time to time I’ve been playing with the question whether velocity just is rate of change of position over time in a philosophical elaboration of classical mechanics.

Here’s a thought. It seems that how much kinetic energy an object x has at time t (relative to a frame F, if we like) is a feature of the object at time t. But if velocity is rate of change of position over time, and velocity (together with mass) grounds kinetic energy as per E = m|v|²/2, then kinetic energy at t is a feature of how the object is at time and at nearby times.

This argument suggests that we should take velocity as a primitive property of an object, and then take it that by a law of nature velocity causes a rate of change of position: dx/dt = v.

Alternately, though, we might say that momentum and mass ground kinetic energy as per E = |p|²/2m, and momentum is not grounded in velocity. Instead, on classical mechanics, perhaps we have an additional law of nature according to which momentum causes a rate of change of position over time, which rate of change is velocity: v = dx/dt = p/m.

But in any case, it seems we probably shouldn’t both say that momentum is grounded in velocity and that velocity is nothing but rate of change of position over time.

Experiencing something as happening to you

In some video games, it feels like I am doing the in-game character’s actions and in others it feels like I am playing a character that does the actions. The distinction does not map onto the distinction between first-person-view and third-person-view. In a first-person view game, even a virtual reality one (I’ve been playing Asgard Wrath 2 on my Quest 2 headset), it can still feel like a character is doing the action, even if visually I see things from the character’s point of view. On the other hand, one can have a cartoonish third-person-view game where it feels like I am doing the character’s actions—for instance, Wii Sports tennis. (And, of course, there are games which have no in-game character responsible for the actions, such as chess or various puzzle games like Vexed. But my focus is on games where there is something like an in-game character.)

For those who don’t play video games, note that one can watch a first-person-view movie like Lady in the Lake without significantly identifying with the character whose point of view is presented by the camera. And sometimes there is a similar distinction in dreams, between events happening to one and events happening to an in-dream character from whose point of view one looks at things. (And, reversely, in real life some people suffer from a depersonalization where feels like the events of life are happening to a different person.)

Is there anything philosophically interesting that we can say about the felt distinction between seeing something from someone else’s point of view—even in a highly immersive and first-person way as in virtual reality—and seeing it as happening to oneself? I am not sure. I find myself feeling like things are happening to me more in games with a significant component of physical exertion (Wii Sports tennis, VR Thrill of the Fight boxing) and where the player character doesn’t have much character to them, so it is easier to embody them, and less so in games with a significant narrative where the player character has character of their own—even when it is pretty compelling, as in Deus Ex. Maybe both the physical aspect and the character aspect are bound up in a single feature—control. In games with a significant physical component, there is more physical control. And in games where there is a well-developed player character, presumably to a large extent this is because the character’s character is the character’s own and only slightly under one’s control (e.g., maybe one can control fairly coarse-grained features, roughly corresponding to alignment in D&D).

If this is right, then a goodly chunk of the “it’s happening to me” feeling comes not from the quality of the sensory inputs—one can still have that feeling when the inputs are less realistic and lack it when they are more realistic—but from control. This is not very surprising. But if it is true, it might have some philosophical implications outside of games and fiction. It might suggest that self-consciousness is more closely tied to agency than is immediately obvious—that self-consciousness is not just a matter of a sequence of qualia. (Though, I suppose, someone could suggest that the feeling of self-conscious is just yet another quale, albeit one that typically causally depends on agency.)

More decision theory stuff

Suppose there are two opaque boxes, A and B, of which I can choose one. A nearly perfect predictor of my actions put $100 in the box that they thought I would choose. Suppose I find myself with evidence that it’s 75% likely that I will choose box A (maybe in 75% of cases like this, people like me choose A). I then reason: “So, probably, the money is in box A”, and I take box A.

This reasoning is supported by causal decision theory. There are two causal hypotheses: that there is money in box A and that there is money in box B. Evidence that it’s 75% likely that I will choose box A provides me with evidence that it’s close to 75% likely that the predictor put the money in box A. The causal expected value of my choosing box A is thus around $75 and the causal expected value of my choosing box B is around $25.

On evidential decision theory, it’s a near toss-up what to do: the expected news value of my choosing A is close to $100 and so is that of my choosing B.

Thus, on causal decision theory, if I have to pay a $10 fee for choosing box A, while choosing box B is free, I should still go for box A. But on evidential decision theory, since it’s nearly certain that I’ll get a prize no matter what I do, it’s pointless to pay any fee. And that seems to be the right answer to me here. But evidential decision theory gives the clearly wrong answer in some other cases, such as that infamous counterfactual case where an undetected cancer would make you likely to smoke, with no causation in the other direction, and so on evidential decision theory you refrain from smoking to make sure you didn’t get the cancer.

In recent posts, I’ve been groping towards an alternative to both theories. The alternative depends on the idea of imagining looking at the options from the standpoint of causal decision theory after updating on the hypothesis that one has made a specific choice. In current my predictor cases, if you were to learn that you chose A, you would think: Very likely the money is in box A, so choosing box A was a good choice, while if you chose B, you would think: Very likely the money is in box B, so choosing box B was a good choice. As a result, it’s tempting to say that both choices are fine—they both ratify themselves, or something like that. But that misses out the plausible claim that if there is a $10 fee for choosing A, you should choose B. I don’t know how best to get that claim. Evidential decision theory gets it, but evidential decision theory has other problems.

Here’s something gerrymandered that might work for some binary choices. For options X and Y, which may or may not be the same, let e_X(Y) be the causal expected value of Y with respect to the credences for the causal hypotheses updated with respect to your having chosen X. Now, say that the differential restrospective causal expectation d(X) of option X equals e_X(X) − e_X(Y). This measures how much you would think you gained, from the standpoint of causal decision theory, in choosing X rather than Y by the lights of having updated on choosing X. Then you should the option that provides a bigger d(X).

In the case where there is a $10 fee for choosing box A, d(B) is approximately $100 while d(A) is approximately $90, so you should go for box B, as per my intuition. So you end up agreeing with evidential decision theory here.

You avoid the conclusion you should smoke to make sure you don’t have cancer in the hypothetical case where cancer causes smoking but not conversely, because the differential retrospective causal expectation of smoking is positive while the differential retrospective causal expectation of not smoking is negative, assuming smoking is fun (is it?). So here you agree with causal decision theory.

What about Newcomb’s paradox? If the clear box has a thousand dollars and the opaque box has a million or nothing (depending on whether you are predicted to take just the opaque box or to take both), then the differential retrospective causal expectation of two-boxing is a thousand dollars (when you learned you two-box, you learn that the opaque box was likely empty) and the differential retrospective causal expectation of one-boxing is minus a thousand dollars.

So the differential retrospective causal expectation theory agrees with causal decision theory in the clear case (cancer-causes-smoking), the difficult case (Newcomb), but agrees with evidential decision theory in the $10 fee variant of my two-box scenario, and the last seems plausible.

But (a) it’s gerrymandered and (b) I don’t know how to generalize it to cases with more than two options. I feel lost.

Maybe I should stop worrying about this stuff, because maybe there just is no good general way of making rational decisions in cases where there is probabilistic information available to you about how you will make your choice.

Position: Assistant Professor of Bioethics, Tenure Track, Department of Philosophy, Baylor University

We're hiring again. Here's the full ad.

My AI policy

I’ve been wondering what to allow and what to disallow in terms of AI. I decided to treat AI as basically persons and I put this in my Metaphysics syllabus:

Even though (I believe) AI is not a person and its products are not “thoughts”, treat AI much like you would a person in writing your papers. I encourage you to have conversations with AIs about the topics of the class. If you get ideas from these conversations, put in a footnote saying you got the idea from an AI, and specifically cite which AI. If you use the AI’s words, put them in quotation marks. (If your whole paper is in quotation marks, it’s not cheating, but you haven’t done the writing yourself and so it’s like a paper not turned in, a zero.) Just as you can ask a friend to help you understand the reading, you can ask an AI to help you understand the reading, and in both cases you should have a footnote acknowledging the help you got. Just as you can ask a friend, or the Writing Center or Microsoft Word to find mistakes in your grammar and spelling, you can ask an AI to do that, and as long as the contribution of the AI is to fix errors in grammar and spelling, you don’t need to cite. But don’t ask an AI to rewrite your paper for you—now you’re cheating as the wording and/or organization is no longer yours, and one of the things I want you to learn in this class is how to write. Besides all this, last time I checked, current AI isn’t good at producing the kind of sharply focused numbered valid arguments I want you to make in the papers—AI produces things that look like valid arguments, but may not be. And they have a distinctive sound to them, so there is a decent chance of getting caught. When in doubt, put in a footnote at the end what help you got, whether from humans or AI, and if the help might be so much that the paper isn’t really yours, pre-clear it with me.

An immediate regret principle

Here’s a plausible immediate regret principle:

1. It is irrational to make a decision such that learning that you’ve made this decision immediately makes it rational to regret that you didn’t make a different decision.

The regret principle gives an argument for two-boxing in Newcomb’s Paradox, since if you go for one box, as soon as you have made your decision to do that, you will regret you didn’t make the two-box decision—there is that clear box with money staring at you, but if you go for two boxes, you will have no regrets.

Interestingly, though, one can come up with predictor stories where one has regrets no matter what one chooses. Suppose there are two opaque boxes, A and B, and you can take either box but not both. A predictor put a thousand dollars in the box that they predicted you won’t take. Their prediction need not be very good—all we need for the story is that there is a better than even probability of their having predicted you choosing A conditionally on your choosing A and a better than even probability of their having predicted you choosing B conditionally on your choosing B. But now as soon as you’ve made your decision, and before you opened the chosen box, you will think the other box is more likely to have the money, and so your knowledge of your decision will make it rational to regret that decision. Note that while the original Newcomb problem is science-fictional, there is nothing particularly science-fictional about my story. It would not be surprising, for instance, if someone were able to guess with better than even chance of correctness about what their friends would choose.

Is this a counterexample to the immediate regret principle (1), or is this an argument that there are real rational dilemmas, cases where all options are irrational?

I am not sure, but I am inclined to think that it’s a counterexample to the regret principle.

Can we modify the immediate regret principle to save it? Maybe. How about this?

2. No decision is such that learning that you’ve rationally made this decision immediately makes it rationally required to regret that you didn’t make a different decision.

On this regret principle, regret is compatible with non-irrational decision making but not with (known) rational decision making.

In my box story, it is neither rational nor irrational to choose A, and it is neither rational nor irrational to choose B. Then there is no contradiction to (2), since (2) only applies to decisions that are rationally made. And applying (2) to Newcomb’s Paradox no longer yields an argument for two-boxing, but only an argument that it is not rational to one-box. (For if it were rational to one-box, one could rationally decide to one-box, and one would then regret that.)

The “rationally” in (2) can be understood in a weaker way or a stronger way (the stronger way reads it as “out of rational requirement”). On either reading, (2) has some plausibility.

An odd decision theory

Suppose I am choosing between options A and B. Evidential decision theory tells me to calculate the expected utility E(U|A) given the news that I did A and the expected utility E(U|B) given the news that I did B, and go for the bigger of the two. This is well-known to lead to the following absurd result. Suppose there is a gene G that both causes one day to die a horrible death and makes one very likely to choose A, while absence of the gene makes one very likely to choose B. Then if A and B are different flavors of ice cream, I should always choose B, because E(U|A) ≪ E(U|B), since the horrible death from G trumps any advantage of flavor that A might have over B. This is silly, of course, because one’s choice does not affect whether one has G.

Causal decision theorists proceed as follows. We have a set of “causal hypotheses” about what the relevant parts of the world at the time of the decision are like. For each causal hypothesis H we calculate E(U|H∧A) and E(U|H∧B), and then we take the weighted average over our probabilities, and then decide accordingly. In other words, we have a causal expected utility of D

• E_c(U|D) = ∑_HE(U|H∧D)P(H)

and are to choose A over B provided that E_c(U|A) = E_c(U|B). In the gene case, the “bad news” of the horrible death on G is a constant addition to E_c(U|A) and to E_c(U|B), and so it can be ignored—as is right, since it’s not in our control.

But here is a variant case that worries me. Suppose that you are choosing between flavors A and B of ice cream, and you will only ever ever get to taste one of them, and only once. You can’t figure out which one will taste better for you (maybe one is oyster ice cream and the other is sea urchin ice cream). However, data shows that not only does G make one likely to choose A and its absence makes one likely to choose B, but everyone who has G derives pleasure from A and displeasure from B and everyone who lacks G has the opposite result, and all the pleasures and displeasures are of the same magnitude.

Now, background information says that you have a 3/4 chance of having G. On causal decision theory, this means that you should choose A, because likely you have G, and those who have G all enjoy A. Evidential decision theory, however, tells you that you should choose B, since if you choose B then likely you don’t have the terrible gene G.

In this case, I feel causal decision theory isn’t quite right. Suppose I choose A. Then after I have made my choice, but before I have consumed the ice cream, I will be glad that I chose A: my choice of A will make me think I have G, and hence that A is tastier. But similarly, if I choose B, then after I have made my choice, and again before consumption, I will be glad that I chose B, since my choice B will make me think I don’t have G and hence that B was a good choice. Whatever I choose, I will be glad I chose it. This suggests to me that my there is nothing wrong with either choice!

Here is the beginning of a third decision theory, then—one that is neither causal nor evidential. An option A is permissible provided that causal decision theory with the causal hypothesis credences conditioned on one’s choosing A permits one to do A. An option A is required provided that no alternative is permissible. (There are cases where no option is permissible. That’s weird, I admit.)

In the initial case, where the pleasure of each flavor does not depend on G, this third decision theory gives the same answer as causal decision theory—it says to go for the tastier flavor. In the second case, however, where the pleasure/displeasure depends on G, it permits one to go for either flavor. In a probabilistic-predictor Newcomb’s Paradox, it says to two-box.

Gaze dualism and omnisubjectivity

I have toyed with a pair of theories.

The first is what I call gaze-dualism. On gaze-dualism, our sensory conscious experiences are constituted by a non-physical object—the soul—“gazing” at certain brain states. When the sensory data changes—say, when a sound goes from middle A to middle C—the subjective experience changes. But this change need not involve an intrinsic change in the soul. The change in experience is grounded in a change in the gazed-at brain state, a brain state that reflects the sensory data, rather than by a change in the gazing soul. (This is perhaps very close to Aquinas’ view of sensory consciousness, except that for Aquinas the gazed-at states are states of sense organs rather than of the brain.)

The second is an application of this to God’s knowledge of contingent reality. God knows contingent reality by gazing at it the way that our soul gazes at the brain states that reflect sensory data. God does not intrinsically change when contingent reality changes—the change is all on the side of the gazed-at contingent reality.

I just realized that this story makes a bit of progress on what Linda Zagzebski calls “omnisubjectivity”—God’s knowledge of all subjective states. My experience of hearing a middle C comes from my gazing at a brain state B_C of my auditory center produced by nerve impulses caused by my tympanic membrane vibrating at 256 Hz. My gaze is limited to certain aspects of my auditory center—my gaze tracks whatever features of my auditory center are relevant to the sound, features denoted by B_C, but does not track features of my auditory center that are not relevant to the sound (e.g., the temperature of my neurons). God’s gaze is not so limited—God gazes at every aspect of my auditory center. But in doing so, he also gazes at B_C. This does not mean that God has the same experience as I do. My experience is partly constituted by my soul’s gaze at B_C. God’s experience is partly constituted by God’s gaze at B_C. Since my soul is very different from God, it is not surprising that the experiences are different. However, God has full knowledge of the constituents of my experience: myself, my gaze, and B_C, and God’s knowledge of these is basically experiential—it is constituted by God’s gazing at me, my gaze, and B_C. And God also gazes at their totality. This is, I think, all we need to be able to say that God knows my sensory consciousness states.

My non-sensory experiences may also be constituted by my soul’s gazing at a state of my brain, but they may also be constituted by the soul’s gazing at a state of the soul. And God gazes at the constituents and whole again.

Diversity of inner lives

There is a vast and rather radical diversity in the inner conscious lives of human beings. Start with the differences in dreams: some people know immediately whether they are dreaming and others do not; some are in control of their dreams and others are not; some dream in color and others do not. Now move on to the differences in thought. Some think in pictures, some in words with sounds, some in a combination of words with sounds and written words, and some without any visual or aural imagery. Some people are completely unable to imagine things in pictures, others can do so only in a shadowy and unstable way, and yet others can do so in detail. Even in the case of close friends, we often have no idea about how they differ in these respects, and to many people the diversity in inner conscious lives comes as a surprise, as they assume that almost everyone is like them.

But in their outer behavior, including linguistic behavior, people seem much more homogeneous. They say “I think that tomorrow is a good day for our bike trip” regardless of whether they thought it out in pictures, in sounds, or in some other way. They give arguments as a sequence of logically connected sentences. Their desires, while differing from person to person, are largely comprehensible and not very surprising. People are more homogeneous outside than inside.

This contrast between inner heterogeneity and outward homogeneity is something I realized yesterday while participating in a workshop on Linda Zagzebski’s manuscript on dreams. I am not quite sure what to make of this contrast philosophically, but it seems really interesting. We flatten our inner lives to present them to people in our behavior, but we also don’t feel like much is lost in this flattening. It doesn’t really matter much whether our thoughts come along with sights or sounds. It would not be surprising if there were differences in skill levels that correlated with the characteristics of inner life—it would not be surprising if people who thought more in pictures were better at low-dimensional topology—but these differences are not radical.

Many of us as children have wondered whether other people’s conscious experiences are the same as ours—does red look the same (bracketing colorblindness) and does a middle C sinewave sound the same (bracketing hearing deficiencies)? I have for a while thought it not unlikely that the answer is negative, because I am attracted to the idea that central to how things look to us are the relationships between different experiences, and different people have sets of experiences. (Compare the visual field reversal experiments, where people who wear visual field reversal glasses initially see things upside-down but then it turns right-side-up, which suggests to me that the directionality of the visual field is constituted by relationships between different experiences rather than being something intrinsic.) I think the vast diversity in conscious but non-sensory inner lives gives us some reason to think that sensory consciousness also differs quite a bit between people—and gets flattened and homogenized into words, much as thoughts are.

Extrinsic well-being and the open future

Klaus: Sometimes how well or badly off you are at time t₁ depends on what happens at a later time t₂. A particularly compelling case of this is when at t₁ you performedan onerous action with the goal of producing some effect E at t₂. How well off you were in performing the action depends on whether the action succeeded—which depends on whether E eventuates at t₂. But now suppose the future is open. Then in a world with as much indeterminacy as ours, in many cases at t₁ it will be contingent whether the event at t₂ on which your well-being at t₁ depends eventuates. And on open future views, at t₁ there will then be no fact of the matter about your well-being. Hence, the future is not open.

Opie: In such cases, your well-being should be located at t₂ rather than at t₁. If you jump the crevasse, it is only when you land that you have the well-being of success.

Klaus: This does not work as well in cases where you are dead at t₂. And yet our well-being does sometimes depend on what happens after we are dead. The action at t₁ might be a heroic sacrifice of one’s life to save one’s friends—but whether one is a successful hero or a tragic hero depends on whether the friends will be saved, which may depend on what happens after one is already dead.

Opie: Thanks! You just gave me an argument for an afterlife. In cases like this, you are obviously better off if you manage to save your friends, but you aren’t better off in this life, so there must be life after death.

Klaus: But we also have the intuition that even if there were no afterlife, it would be better to be the successful hero than the tragic hero, and that posthumous fame is better than posthumous infamy.

Opie: There is an afterlife. You’ve convinced me. And moral intuitions about how things would be if our existence had a radically different shape from the one it in fact has are suspect. And, given that there is an afterlife, a scenario without an afterlife is a scenario where our existence has a radically different shape. Thus the intuition you cite is unreliable.

Klaus: That’s a good response. Let me try a different case. Suppose you perform an onerous action with a goal within this life, but then you change your mind about the goal and work to prevent that goal. This works best if both goals are morally acceptable, and switching goals is acceptable. For instance you initially worked to help the Niners train to win their baseball game against the Logicians, but then your allegiance shifted to the Logicians in a way that isn't morally questionable. And then suppose the Niners won. Your actions in favor of the Niners are successful, and you have well-being. But it is incorrect to locate that well-being at the time of the actual victory, since at that time you are working for the Logicians, not the Niners. So the well-being must be located at the time of your activity, and at that time it depends on future contingents.

Opie: Perhaps I should say that at the time Niners beat the Logicians, you are both well-off and badly-off, since one of your past goals is successful and the other is unsuccessful. But I agree that this doesn’t quite seem right. After all, if you are loyal to your current employer, you’re bummed out about the Logicians’ loss and you’re bummed out that you weren’t working for them from the beginning. So intuitively you're just badly off at this time, not both badly and well off. So, I admit, this is a little bit of evidence against open future views.

Consciousness and the open future

Plausibly:

1. There is a “minimal humanly observable duration” (mhod) such that a human cannot have a conscious state—say, a pain—shorter than an mhod, but can have a conscious state that’s an mhod long.

The “cannot” here is nomic possibility rather than metaphysical possibility.

Let δ denote an mhod. Now, suppose that you feel a pain precisely from t₀ to t₂. Then t₂ ≥ t₀ + δ. Now, let t₁ = t₀ + δ/2. Then you feel a pain at t₁. But at t₁, you only felt a pain for half an mhod. Thus:

2. At t₁, that you feel pain depends on substantive facts about your mental state at times after t₁.

For if your head were suddenly zapped by a giant laser a quarter of an mhod after t₁, then you would not have felt a pain at t₁, because you would have been in a position to feel pain only from t₀ to t₀ + (3/4)δ.

But in a universe full of quantum indeterminacy:

3. These substantive facts are contingent.

After all, your brain could just fail a quarter of an mhod after t₁ due to a random quantum event.

But:

4. Given an open future, at t₁ there are no substantive contingent facts about the future.

Thus:

5. Given an open future, at t₁ there is no fact that you are conscious.

Which is absurd!

Discrete time and Aristotle's argument for an infinite past

Aristotle had a famous argument that time had no beginning or end. In the case of beginnings, this argument caused immense philosophical suffering in the middle ages, since combined with the idea that time requires change it implies that the universe was eternal, contrary to the Jewish, Muslim and Christian that God created the universe a finite amount of time ago.

The argument is a reductio ad absurdum and can be put for instance like this:

1. Suppose t₀ is the beginning of time.

2. Before t₀ there is no time.

3. It is a contradiction to talk of what happened before the the beginning of time.

4. But if (1) is true, then (2) talks of what is before the beginning of time.

5. Contradiction!

It’s pretty easy to see what’s wrong with the argument. Claim (2) should be charitably read as:

• Not (before t₀ there is time).

Seen that way, (2) doesn’t talk about what happened before t₀, but is just a denial that there was any such thing as time-before-t₀.

It just struck me that a similar argument could be used to establish something that Aristotle himself rejects. Aristotle famously believed that time was discrete. But now argue:

6. Suppose t₀ and t₁ are two successive instants of time.

7. After t₀ and before t₁ there is no time.

8. It is a contradiction of what happened when there is no time.

9. But if (7) is true, then (7) talks of what is when there is no time.

10. Contradiction!

Again, the problem is the same. We should take (7) to deny that there is any such thing as time-after-t₀-and-before-t₁.

So Aristotle needed to choose between his preference for the discreteness of time and his argument for an infinite past.

What if there is no tomorrow?

There are two parts of Aristotle’s theory that are hard to fit together.

First, we have Aristotle’s view of future contingents, on which

1. It is neither true nor false that tomorrow there will be a sea battle

but, of course:

2. It is true that tomorrow there will be a sea battle or no sea battle.

Of course, nothing rides on “tomorrow” in (1) and (2): any future metric interval of times will do. Thus:

3. It is true that in 86,400,000 milliseconds there will be a sea battle or not.

(Here I adopt the convention that “in x units” denotes the interval of time corresponding to the displayed number of significant digits in x. Thus, “in 86,400,000 ms” means “at a time between 86,399,999.5 (inclusive) and 86,400,000.5 (exclusive) ms from now.”)

Second, we have Aristotle’s view of time, on which time is infinitely divisible but not infinitely divided. Times correspond to what one might call happenings, the beginnings and ends of processes of change. Now which happenings there will be, and when they will fall with respect to metric time (say, 3.74 seconds after some other happening), is presumably something that is, or can be, contingent.

In particular, in a world full of contingency and with slow-moving processes of change, it is contingent whether there will be a time in 86,400,000 ms. But (3) entails that there will be such a time, since if there is no such time, then it is not true that anything will be the case in 86,400,000 ms, since there will be no such time.

Thus, Aristotle cannot uphold (3) in a world full of contingency and slow processes. Hence, (3) cannot be a matter of temporal logic, and thus neither can (2) be, since logic doesn’t care about the difference between days and milliseconds.

If we want to make the point in our world, we would need units smaller than milliseconds. Maybe Planck times will work.

Objection: Suppose that no moment of time will occur in exactly x₁ seconds, because x₁ falls between all the endpoints of processes of change. But perhaps we can still say what is happening in x₁ seconds. Thus, if there are x₀ < x₁ < x₂ such that x₀ seconds from now and x₂ seconds from now (imagine all this paragraph being said in one moment!) are both real moments of time, we can say things about what will happen in x₁ seconds. If I will be sitting in both x₀ and x₂ seconds, maybe I can say that I will be sitting in x₁ seconds. Similarly, if Themistocles is leading a sea battle in 86,399,999 ms and is leading a sea battle in 86,400,001 ms, then we can say that he is leading a sea battle in 86,400,000 ms, even though there is no moment of time then. And if he won’t lead a sea battle in either 86,399,999 ms or in 86,400,000 ms, neither will he lead one in 86,400,000 ms.

Response: Yes, but (3) is supposed to be true as a matter of logic. And it’s logically possible that Themistocles leads a sea battle in 86,399,999 ms but not in 86,400,001 ms, in which case if there will be no moment in 86,400,000 ms, we cannot meaningfully say if he will be leading a sea battle then or not. So we cannot save (3) as a matter of logic.

A possible solution: Perhaps Aristotle should just replace (2) with:

4. It is true that will be: no tomorrow or tomorrow a sea battle or tomorrow no sea battle.

I am a bit worried about the "will" attached to a “no tomorrow”. Maybe more on that later.

An attempt to define possible futures for open futurism

On all-false open future (AFOF), future contingent claims are all false. The standard way to define “Will p” is to say that p is true in all possible futures. But defining a possible future is difficult. Patrick Todd does it in terms of possible worlds apparantly of the classical sort—ones that have well-defined facts about how things are at all times. But such worlds are not in general possible given open future views—it is not possible to simultaneously have a fact about how contingent events go on all future days (assuming the future is infinite).

Here is an approach that maybe has some hope of working better for open future views. Take as primitive not classical possible worlds, but possible moments, ways that things could be purely at a time. Possible moments do not include facts about the past and future.

Now put a temporal ordering on the possible moments, where we say that m₁ is earlier than m₂ provided that it is possible to have had m₁ obtaining before m₂.

For a possible moment m, define:

• open m-world: a maximal set of possible moments including m such that (a) all moments in the set other than m are earlier or later than m and (b) the subset of moments earlier than m is totally ordered

• possible history: a maximal totally ordered set of possible moments

• possible future: a possible history that contains m.

Exactly one possible moment is currently actual. Then:

• possible future: a possible future of the currently actual moment.

Now consider the problem of entailment on AFOF. The problem is this. Intutiively, that I will freely mow my lawn entails that I will mow my lawn, but does not entail that I will eat my lawn. However, since on AFOF “I will freely mow my lawn” is necessarily false—it is false at every possible moment, since “will” claims concerning future contingent claims are always false—both entailments have necessarily false antecedents and hence are trivially true.

Given a set S of moments and a moment m ∈ S, any sentence of Prior’s (or Brand’s) temporal logic can be evaluated for truth at (S,m). We can now define two modalities:

• p is OW-necessary: p is true at (W,m) for every open m-world W

• p is PH-necessary: p is true at (H,m) for every possible history H that contains m.

And now we have two entailments: p OW/PH-entails q if and only if the material conditional p → q is OW/PH-necessary.

Then that I will freely mow my lawn is OW-impossible, but PH-possible, and that I will freely mow my lawn OW-entails that I will eat my lawn, but does not PH-entail it. The open futurist can now say that our intuitive concept of entailment, in temporal contexts, corresponds to PH-entailment rather than OW-entailment.

I think this is helpful to the open futurist, but still has a serious problem. Consider the sentence “I will mow or I will not-mow.” On AFOF, this is false. But it is true at every possible history. Hence, it is PH-necessary. Thus, PH-necessity does not satisfy the T-axiom. Thus PH-entailment is such that a truth can PH-entail a falsehood. For instance, since “I will mow or I will not-mow” is PH-necessary, it is PH-entailed by every tautology.

On trivalent logics, if "I will mow or I will not-mow" is neither true nor false, we have a similar problem: a truth PH-entails a non-truth.

There are is a more technical problem on some metaphysical views. Suppose that it is contingent whether time continues past a certain moment. For instance, suppose there is no God and empty time is impossible, and there is a particle which can indeterministically cease to exist, and the world contains just that particle, so at any time it is possible that time is the last—the particle can pop out of existence. Oddly, because of the maximality condition on possible histories, there is no possible future where the particle pops out of existence.

I wonder if there is a better way to define entailment and possible futures that works with open future views.