Lebesgue sums previsions don't always lead to Dutch Books for inconsistent credences

Suppose E is the Lebesgue-sum prevision. Namely, if W is a wager on a finite space Ω with a credence (perhaps inconsistent P) and U_W is the utility function corresponding to W, then EW = ∑_yP({ω : U_W(ω)=y}).

Suppose your decision procedure for repeated wagers is to accept a wager if and only if the wager’s value is non-negative (independently of whatever other wagers you might have accepted). Suppose, further, that Ω has exactly two points and the credence of each point is non-negative and of at least one it is positive.

Proposition: Then, no finite sequence of wagers forms a Dutch Book.

Proof: Consider the sequence of utility functions U₁, ..., U_n that corresponds to a Dutch Book sequence of wagers W₁, ..., W_n. Then U₁ + ... + U_n < 0 everywhere on Ω and yet EW_i ≥ 0 for all i. Let a and b be the two points of Ω. Reordering the wagers if necessary (the order doesn’t matter on this decision procedure), we can assume that the wagers W₁, ..., W_m are such that U_i(a)≠U_i(b) for i ≤ m, and that W_m + 1, ..., W_n are such that U_i(a)=U_i(b) for i > m. Then EW_i = U_i(a)=U_i(b) for i > m. Hence, U_i is positive everywhere on Ω for i > m. So, if W₁, ..., W_n form a Dutch Book, so do W₁, ..., W_m. Now, EW_i = αU_i(a)+βU_i(b) where α and β are the probabilities of a and b respectively. It follows that EW₁ + ... + EW_n = α(U₁(a)+...+U_m(a)) + β(U₁(b)+...+U_m(b)). Since this is a Dutch Book, it follows that the two sums on the right hand side are both negative. Since α and β are non-negative and at least one is positive, it follows that EW₁ + ... + EW_n < 0, and hence this isn’t a Dutch Book.

Divine speech acts and classical theism

Here is a question I have wondered about and have never heard or seen much discussion of:

1. What does it mean to say that God engaged in some speech act, such as commanding or asserting?

The more anthropomorphic one’s theism, the easier the question can be answered, because the closer the analogy between divine speech acts and ours. But the setting that interests me here is classical theism (both because it’s the truth theory of God and because it’s more challenging). In particular, let’s take on board divine immutability and simplicity.

Let’s think about the human case first. We’re going to have to pay close attention to such factors as intention and context. Thus, the same words in the same tone are an assertion in an ordinary conversation but not an assertion when spoken on a stage. The same handwritten sentence can be a command in one case and in another can be a handwriting exercise. Theorists will differ as to the balance between intention and context in the correct theory. But I think it is easy to argue that an important part of the distinction between assertion and play-acting or between command and handwriting exercise will be constituted by intentions. For instance, it is not simply being on a stage that makes one’s words not be assertions. The actor on stage can yell “Fire!” upon seeing the flames licking the back of the room, and that will be an assertion—even if that word happens to be exactly what the script calls for at this time. (It may be an assertion that is not taken up, though, much as an assertion might not be heard in a loud rooom.)

Very roughly speaking, to engage in a speech act of kind K, one has to form the intention to be taken by one’s audience as engaging in a speech act of kind K.

Now, there are natural rock formations that look like faces. Suppose that somewhere in the solar system there is a natural rock formation that spells out “God exists”, and one day an English speaking astronaut comes across it. Is it an assertion by God?

It is certainly something made by God. For God made everything other than himself. But did God make it with the intention that it be taken as an assertion? Or is it just a formation of rocks intended for some other purpose than to be taken as an assertion? (Presumably, it’s not a handwriting exercise, since God doesn’t need to practice being already perfect.)

On more anthropomorphic theisms, there is no special problem here about the God case. God can form the intention to make an assertion just as a human being can or, just as a human being, he can fail to form that intention. But if divine simplicity is correct, then there are no contingent intrinsic divine properties. There is just God. Any contingency is on the side of creation. In particular, there cannot be two worlds that are exactly alike except with respect to divine intentions intrinsic to God. Divine intentions must supervene on creation and on necessary truths about God. But what contingent facts about creation and necessary truths about God can make it be that the rock formation is or is not a divine assertion?

One might try to make use of divine reasons. I have argued that divine simplicity entails divine omnirationality: whenever God does something, he does it for all the good reasons there are for doing it, rather than choosing which of the good reasons to act on. Now, suppose that in fact the astronaut’s faith in God is strengthened by the rock formation. That’s a good thing. Goods provide reasons. So, God has a good reason to make the rock formation in order to strengthen the astronaut’s faith. But the astronaut’s faith is presumably strengthened by her taking the formation as a divine assertion. So, God has a reason to have the astronaut take the formation as a divine assertion. And, thus, by omnirationality, God is acting on that reason, and the rock formation is an assertion.

But take a variant case. Our astronaut lands on a planet with a rock formation that says “Kneel!” But, now, kneeling is both good and bad for the astronaut. Perhaps it is spiritually good but physically bad, because our astronaut has bad knees. The astronaut takes it as a command. That’s a good and a bad thing: she kneels, hurts her knees, and the mission is in jeopardy. But she spent a few minutes in prayer, and that was good for her. And, in fact, in a complex world there will generally be pluses and minuses of anything. Even in the case of the “God exists!” rock formation, there is some benefit to believing without such overt signs, perhaps a greater maturity of faith.

We could try to make the intention condition work something like this: God counts as intending that something assertion-like or command-like (structured symbolically in the right way) be taken as an assertion or command provided it’s good in some way that it be taken as such. But that seems overbroad. Or we could say it’s an assertion or command provided it’s good on balance that it be taken as such. But when we are dealing with incommensurable values, there may be no “on balance”. These objections aren’t fatal: but they point to a need to do serious philosophical work here.

Here is a possible different solution. We don’t need to advert to speaker intentions in every case to figure out whether something is a speech act of the right sort. When yelled from the stage, we may need to know whether “Fire!” is intended as a warning or as part of the script. But when yelled from the seats, there is no reasonable doubt. There are contexts where no reasonable person in the relevant audience would fail to take something as a certain kind of speech act. You come across the Summa Theologica in a heath. Of course, it’s a speech act, of whatever sort a theological discourse is (a series of arguments and assertions). Every reasonable person who knew the language (that’s perhaps the relevant audience component) would take it as such.

Perhaps we can now say this:

2. In contexts where every reasonable person in the relevant audience who knew the relevant context sufficiently well would take something to be a divine speech act of a certain kind, it is a primary case of a divine speech act of that kind.

For primary divine speech acts, we need some kind of reasonable luminosity: they need to be the sort of thing that one couldn’t reasonably doubt to be divine speech acts if one knew the relevant circumstances. Perhaps God builds into our nature an ability to recognize divine speech acts.

And then we have derivative cases of divine speech acts, which are when the initial audience is enlarged by means of the members of the initial audience becoming heralds of the message, and the process continues. When the herald is being faithful to the message, what the herald says counts as a speech act of the original speaker. So, the heralds pass on the word of God. And since the heralds are human, their intentions are relevant and raise no deep ontological concerns.

This story would lead to a rather restrictive view of divine speech acts. The rock formations, in a vast universe, could be reasonably doubted. So they aren’t primary divine speech acts. The primary divine speech acts may, rather, be more like cases of prophecy, where God makes it reasonably impossible for the prophet to doubt what kind of a speech act it is.

I am not very happy with any of the stories above. This is just a vague and inchoate start. I don’t really want to finish off this task. It would make a really interesting philosophical theology dissertation, though.

Partial amnesia and fission

Some cases of partial amnesia present a prima facie problem for memory theories of personal identity (the theorist will bite the bullet on total amnesia, of course). At 9 pm, Bob starts to drink. At 11 pm, he makes a fool of himself. At midnight, he passes out. At 9 am, he wakes up remembering nothing that happened after 10 pm. Obviously, at 9 am, it’s the same person as the one who made a fool of himself the night before, but there is no chain of memories from the 9 am self to the 10 pm self.

There is a simple solution: don’t talk about chains of memories, but instead talk of chains of memory-links. Memories are unidirectional (you remember later what happened earlier) but memory-links are bidirectional: when at t₂ you remember what happened at t₁, there is a memory link from t₁ to t₂ as well as from t₂ to t₁. And now we have a chain of memory links: the morning-after self is memory linked to the 9 pm night-before self, and the 9 pm night-before self is linked to the 11 pm night-before self (Bob at 11 pm remembers starting to drink at 9 pm). So the morning-after self is the same as the 11 pm night-before self, much as he might wish he weren’t.

But here is an interesting thing. If we think about this scenario, formally this is a case of fission. There are two memory branches:

1. starting at 9 pm, then going on to 10 pm, 11 pm, and up to midnight, and then fizzling out forever

2. starting at 9 pm, then going on for a little bit, then skipping until 9 am.

So, partial amnesia cases like the above are actually cases of fission. And in cases of fission, most people do not want to say that we have the same person in the two branches. The most popular solution is that fission is death, and a second option is a four-dimensionalist one on which the occurrence of fission shows that there were two people there all along. But neither option is plausible for our partial amnesia case. It is absurd to say that Bob automatically dies around between 9 and 11 pm. And it is absurd to say that there used to be two people in Bob’s body all along. Those are extreme solutions that might fit science-fictional cases, but surely are not appropriate for all-too-common cases like Bob’s.

Perhaps we can say this: real fission requires there to be two simultaneous branches. So now our theory is this:

3. when memories branch, and the two branches are simultaneous, then something metaphysically weird happens (either there were two people before the branching or the pre-branching person has died).

But (3) fails in time-travel cases. Suppose Bob owns a time-machine. At 9 pm, Bob goes into a time-machine set for midnight. He keeps on drinking in the machine for two more hours, until 2 am. Then he passes out and loses the memory of the last two hours of drinking while the time-machines auto-pilot pulls him back to midnight and dumps him in his bed. We now have two branches starting at midnight: Bob drinking in the time-machine for two hours and Bob sleeping in bed with loss of memory of two hours of drinking. But it seems wrong to say that by adding a time-machine to the original partial-amnesia story, thereby making the two branches simultaneous, we would get the weirdness of having Bob perish or having always had two persons there.

Suppose you think backwards time-travel is impossible because of the paradoxes that result. You should still think of forwards time-travel as possible. Indeed, non-instaneous forwards time-travel is possible: that’s what happens in the twin paradox from relativity theory. But there is nothing logically absurd about instantaneous forwards time-travel. But any case of simultaneous-branch fission can be transformed into a case of non-simultaneous-branch fission by forward traveling one branch right after branching to a future time after the other branch has perished. Thus, we really shouldn’t treat simultaneous and non-simultaneous branchings differently.

I think this is a serious problem for memory theories of personal identity.

An argument against time travel or for temporal parts or for internal time

Start with this plausible claim:

1. If two objects are composed of the very same particles at the same time, then they have the same shape.

But now consider a statue of a horse that is reshaped into a statue of a tree and then time-travels back to sit besides the statue of the horse. Then the statue of the horse and the statue of the tree are composed of the very same particles at the same time, and yet they do not have the same shape.

I see three ways out of this paradox.

2. Deny the possibility of time travel.

3. Subscribe to temporal parts theory and modify (1) to speak of temporal parts of particles instead of particles.

4. Distinguish external and internal time, and qualify (1) to refer to internal time.

My preference is (4).

Divine command theory and atheism

Suppose that the captain impersonates an admiral and yells: “Turn hard to starboard!” The sailors ought to turn hard to starboard and the captain had the authority to command them this. But nonetheless the captain has failed to issue a valid order. For in order to issue a valid order, the captain needs to make herself heard as the captain. The sailors’ obligation to turn to starboard is not a command-obligation but rather is an obligation of conscience to do what one believes, correctly or not, to be the commands of legitimate authority. A sailor who refused to turn would be acting badly, but would not be disobeying an order: she wouldn’t be disobeying the captain’s order, since the captain did not order anything qua captain, or the admiral’s order, since the admiral didn’t order anything.

The same thing would be true, though perhaps less clearly, if the admiral impersonated the captain and told the crew to turn to starboard. The admiral had the authority to issue the order (or so I assume), but to do that she would have to have made herself heard as the admiral.

Similarly, if the captain is a telepath and induces in the helmsman a strong moral belief that he should turn the ship to starboard, no order has been issued to the helmsman. If the helmsman refuses to turn, he is disobeying conscience but he is not disobeying the captain.

Now, consider the command version of the divine command theory: God’s commands (rather than will) define moral obligation. Now we have a prima facie problem with atheists. The atheist believes in an obligation to refrain from stealing, but is not aware of it as a divine command. Therefore, it seems that no command has been validly issued to the atheist: the case seems relevantly like that of the telepath captain. Thus it follows that on the command version of the divine command theory, the atheist has no obligations.

This was a bit too quick, however. For a promulgation condition on commands that requires actual cognitive uptake is too strong. If the captain is yelling orders as captain but the helmsman has deliberately plugged her ears so as not to hear the orders, the helmsman’s failure to hear does not impugn the validity of the orders.

But suppose instead that the helmsman is hard of hearing due to a recent explosion, and the captain whispers the order while knowing the helmsman won’t hear it. In this case, the order is invalid. It seems, roughly, that if the captain could easily make the command heard as her command but does not do so, and the failure to hear it as her command is not something the other party is antecedently at fault for, then the command is invalid.

Now, it seems that there are atheists who are not at fault for their atheism, and whose failure to hear divine commands as divine commands is not something they are at fault for. But God could easily (everything is easy to an omnipotent being) make them hear them as such. So, on the command version of divine command theory, these atheists have never been validly commanded, and hence have no obligations—which is clearly false.

Maybe I will get some pushback on the claim that there are atheists who are not at fault for atheism. Let’s consider, then, the case of Alice, a life-long atheist who is at fault for her atheism and who was never aware of any divine command as a divine command. Then, at some point t₁ of time, Alice did the first thing that made her be at fault for her atheism and/or her failure to be aware of divine commands as divine commands. Perhaps an argument for theism was being offered to her by Bob, but she refused to listen to Bob out of racism.

Now to be at fault, you have to culpably do something wrong. And, according to divine command theory, the wrong is always a violation of a (valid) divine command. So, at t₁, Alice’s action was the violation of a valid divine command. But at t₁, Alice wasn’t aware of the command as one from God, since we’ve assumed that Alice was never aware of any divine command as a divine command. And Alice’s failure to be aware of the command as one from God was not due to any antecedent fault of hers, since we have assumed that t₁ is the time of Alice’s first action that made her be at fault with respect to this failure.

Thus, it seems that the divine command theorist who takes the command part of the theory seriously has to say that those who are now atheists are atheists because they disobeyed a command from God which they were aware of as a command from God. This is deeply implausible. It is way more implausible than the already not very plausible response to the hiddenness argument that says that all atheists are morally guilty for their atheism.

But perhaps we want to distinguish epistemic from moral fault, and say that a command can still be valid if it fails to be heard due to an epistemic fault that the commander could have easily overcome, even when that epistemic fault does not correspond to a moral one. I do not think this is plausible. Being unable to parse complex sentences might be an epistemic fault. But if I issue a complex command to someone I know to be incapable of parsing such complex sentences, when I could easily have used a simpler sentence with the same content, I do not validly command.

Worshipping Apollo

Suppose Callicles worships Apollo. Callicles is doing something he shouldn’t do: he is worshipping a being that doesn’t exist. So one root of Callicles’ practical mistake is a mistake about the non-normative metaphysics of the world, which does not include Apollo.

But is that the only mistake Callicles is making? The western monotheistic tradition appears to criticize people like Callicles morally for their worship. One way to pose the question is this: Supposing Callicles were right about the existence of Apollo, would he be right to worship him?

The answer seems to me to be a clear negative. If we met an alien with Apollo’s intellectual ability, moral character and technological power, then being impressed might be called for, but clearly worship would not be.

Thus, Callicles is worshipping someone who wouldn’t be worthy of worship even if he existed. That’s a moral mistake.

Lying and normative views of assertion

I find some version of the following normative partial analysis of assertion very plausible:

1. At least a part of what makes a speech act an assertion of p is that it is the kind of speech act that should not be made if one believes p to be false.

But now:

2. If it is sometimes permissible to lie, it is sometimes obligatory to lie.

Why? Well, people’s main intuitions that it is sometimes permissible to lie are driven by cases—such as the murderer at the door—where they think it is obligatory to lie. Moreover, if an action is permissible, then typically it becomes obligatory when there is enough at stake. Thus, if it’s permissible to eat meat, it’s obligatory to eat meat when doing so is necessary to save an innocent life (e.g., an evildoer says: “Eat this burger or this innocent dies”).

Thus, to argue that lying is never permissible I just need to argue that it is never obligatory.

Now here is a flatfooted argument against lying ever being obligatory. If lying is ever obligatory, then sometimes one should assert that p when one believes p to be false. But that contradicts (1).

Of course, this is a bad argument, for two reasons. The first is that perhaps all the argument shows is that there is a real dilemma sometimes: one should lie and one shouldn’t lie. The second, and more serious, is that the norms in (1) and (2) are different: the norm in (1) is a social norm of assertion, while that in (2) is a moral norm.

However, the argument can be fixed to get around both problems. For morality is overriding in the following strong way:

3. A non-moral norm is null and void insofar as it requires what is morally forbidden.

E.g., a law requiring an immoral action is just a piece of paper with no normative force. But this means that a norm of assertion that forbids one from a speech act under circumstances in which in which that speech act is morally required is null and void under those circumstances. But a null and void norm is no norm at all and generates no “should” of the action-guiding sort. And the “should” in (1) is of the action-guiding sort. And hence the idea that sometimes lying is morally obligatory contradicts (1) precisely when we understand the “should” in (1) as expressive of an action-guiding non-moral norm.

Here’s another way to show the intuition behind the argument. The normative picture of language nicely fits with the following modified Wittgensteinian picture of language: The meaning of language comes from its normative use. But if lying is permissible, then a norm-abiding speaker of English will say “Bob is not at home” when asked by someone at the door who wants to murder Bob. Thus, the norm-abiding use of “Bob is not at home” will fail to distinguish between two candidate norms:

4. Say “Bob is not at home” only when you believe Bob is not at home.

5. Say “Bob is not at home” only when you believe that either Bob is not at home or the interlocutor wants to murder Bob.

And hence it will not be possible to read the meaning of “Bob is not at home” from its norm-abiding usage.

The argument works with minor modifications if we replace the belief norm by a truth norm, a knowledge norm or a justified belief norm.

I do, however, have a serious objection to the argument. The argument as it stands only works when the norm of assertion is of an action-guiding sort. But norms of assertion could be a different critter altogether: they could be Aristotelian teleological norms. These aren’t norms that say, at least directly, what is or is not to be done. Rather, they are norms that say what is or is not defective. Thus, a broken leg is defective, but it is, of course, a category mistake to say that a broken leg is something not to be done (and it’s a moral mistake to say that a broken leg is something not to be produced: there are times when it is obligatory to break a leg, say in the defense of the innocent). Thus, it could be that what (1) says is that a part of what makes a speech act be an assertion of p is that it is a speech act that would be defective should p turn out to be false.

I do not know how satisfactory this reading of (1) is. It seems to me that we think of the norms of assertion as something that persons are criticizable for failing to meet in a way in which no one is criticizable for having a broken leg (though one might be criticizable for breaking one’s leg).

Five views on killing the innocent

Here is a spectrum of views on killing the innocent to prevent worse evils:

1. Consequentialism: It is permissible to kill the innocent to prevent worse evils.

2. Threshold Deontology: It is permissible to kill the innocent to prevent much worse evils.

3. Standard Double Effect: It is permissible to perform an action foreseen to result in the death of an innocent to prevent worse evils when the death of the innocent is not intended.

4. Loose Carefulness: It is permissible to perform an action to prevent worse evils only when it is not likely that the action will result in the death of an innocent.

5. Strict Carefulness: It is permissible to perform an action to prevent worse evils only when there is no chance that the action will result in the death of an innocent.

In this post, my interest is in 3-4. But note that adherents of 2 may still be interested in 3-5, because they still need to have something to say about the cases which fall below the threshold of “much worse evils”.

Clearly, Strict Carefulness is too strict. On Strict Carefulness, it is wrong to drive anywhere, and in particular it is wrong to send a fire truck to rescue people from a burning building. In fact, we all the time perform actions that have a small chance of resulting in the death of the innocent.

I want to argue that if we reject Strict Carefulness, we should reject Loose Carefulness as well. The reason is that one gets a violation of Loose Carefulness by accumulating violations of Strict Carefulness. For instance, if one in a billion people vaccinated against some a deadly disease dies, then an adherent of Strict Carefulness will refuse to vaccinate anybody against that disease. That’s excessive carefulness. We should vaccinate (assuming the disease is sufficiently nasty and the vaccination is sufficiently effective, etc.). Nor does it cease to become permissible to vaccinate as the number of people vaccinated becomes sufficiently high that it it becomes likely that someone will die. Once it is granted that I may vaccinate one, clearly I may vaccinate a billion. Now, strictly speaking, that is not a counterexample to Loose Carefulness. For although those billion vaccinations are likely to result in the death of an innocent, they are not a single action that is likely to result in the death of an innocent. But that is easily fixed. Just imagine that I run a mega-clinic staffed with robotic nurses. I press a single button and a billion patients are vaccinated. Surely if it would be permissible for me to vaccinate them all one-by-one, it is permissible for me to dispatch the army of robotic nurses (assuming that they are just as effective, that they are not unduly scary to children, that all the same precautions are taken, etc.)

In other words, the adherent of Loose Carefulness who rejects (as everyone clearly should) Strict Carefulness has to make a dubious permissibility distinction between performing a single cumulative high-risk action and performing lots of separate low-risk actions.

Perhaps, though, someone could modify Loose Carefulness and replace “the death of an innocent” with “the death of a specific innocent”. In vaccinating a billion people, it seems there isn’t a specific innocent who is likely to die. I don’t think this modification is tenable. There are two different stories (and various combinations) one could tell about how the hypothetical vaccine kills one in a billion people. First, it could be that the vaccine interacts with the body of each in such a way that each individually has a one in a billion chance of death. Second, it could be that there is an undetectable condition (perhaps genetic) that occurs in one out of a billion people such that someone with that condition is nearly certain to die upon being vaccinated. I think it makes little moral difference which story is true. But on the second story, there is a specific innocent who will die when one vaccinates the billion people. Or consider Parfit’s story of releasing a lethal molecule into New York City which will kill one randomly person. That’s not significantly different from releasing a molecule into New York City that will kill one specific person.

So, neither Loose nor Strict Carefulness are right. That means that the choice we face is between Consequentialism, Threshold Deontology and Standard Double Effect, unless some other good options are found.

Broad and narrow pacifism

Narrow pacifists (about lethal violence) hold that it is wrong to intentionally kill. Depending on the correct answer to Double Effect questions, narrow pacifism may be compatible with fighting in a war in ways that one foresees to be quite lethal. On the most extreme version, defended by people like Germain Grisez, one can pretty much do any foreseeably lethal warlike activity, such as shooting enemy soldiers in the head, as long as one’s intention is to stop the enemy rather than kill, and killing is a side-effect rather than a means. On less extreme versions, one might have to put some limits on the methods of waging war, but nonetheless one will be able to wage war in ways that one foresees to be lethal. For instance, it might not be permissible to shoot the enemy in the head, but shooting them in the stomach might be acceptable, even if one foresees that a significant percentage of the time this is lethal.

Broad pacifists, on the other hand, will forbid any foreseeably lethal violence, even if the lethality is not intended. Broad pacifism better fits, I think, with what we normally mean by “pacifism”. In Woody Allen’s Love and Death, a character says: “My brother was killed in the line of duty; bayoneted to death by a Polish conscientious objector!” This is obviously funny, and it stays funny if you replace “conscientious objector” with “pacifist”. We do not expect pacifists to lethally bayonet people. Yet a narrow pacifist can do that, at least given what I think are plausible views about Double Effect.

But broad pacifism is mistaken. Here is why.

1. Either the prohibition on foreseeably lethal violence is specific to violence or not.

2. A prohibition specific to foreseeably lethal violence is ad hoc.

3. A prohibition against all foreseeably lethal action is untenable.

Let me start with premise 3. There are many counterexamples to a prohibition on all foreseeably lethal action. The most obvious cases are actions that involve a large number of people. For instance, manufacturing automobiles is foreseeably lethal. A sufficiently large construction project can be foreseen to result in someone’s death. Instituting a policy of pursuing tax frauds will lead to some suicides on the part of those on whom justice is closing. Manufacturing or requiring vaccinations, while saving many lives overall, will result in a small number of deaths due to adverse side-effects.

But perhaps the idea is that what is forbidden are actions that have a probability greater than 1/2 of resulting in the death of a specific person. This surely isn’t right. Sending an armed robot that is foreseen to kill one random enemy combatant is not morally different from sending an armed robot that is foreseen to kill one specific enemy combatant. Yet in the case of the randomly killing robot, the chance of any particular enemy combatant being killed is apt to be less than 1/2.

Let’s move on to premise 2. Suppose we prohibit foreseeably lethal violence but not other foreseeably lethal actions. For this not to be ad hoc, we would need a good moral explanation for why a foreseeably lethal action’s being an instance of violence makes it impermissible, while if it were non-violent, it would be permissible.

Here is what I think the best case is: the cases where foreseeably lethal activity are permissible are ones where consent is given or presumed on the part of those who are victimized by the activity. It is permissible to give painkillers that are expected, but not intended, to hasten the death of a terminal patient. But consent is needed. On the other hand, enemy soldiers do not consent to being killed.

Maybe, but it feels to me like something is off in grounding the impermissibility of lethal action in wartime in the lack of consent given by enemy soldiers. Whether a murderous invader consents to being repelled by lethal force or not seems morally irrelevant. And we can imagine cases of consent: for instance, an enemy might enjoy the “heroism” of fighting against lethal force. It surely makes no difference to the permissibility of lethal self-defense whether one is facing an enemy who consents to lethal resistance or one who does not.

Moreover, if we go back to the counterexampels to prohibitions on foreseeably lethal action, some of these do not involve much in the way of consent. Small children are rightly vaccinated. (It is true that we have proxy consent in that case. But proxy consent is not really consent.) Tax frauds do not consent to being pursued.

Thus, I think broad pacifism is untenable, and narrow pacifism doesn’t give the pacifist what the pacifist wants.

Double Effect and (narrow) pacifism

Suppose I see a sniper sniping at innocents, and if not stopped, she will kill a dozen innocents. Near the sniper are three enemy personnel who are standing around. I have two weapons, a precision rifle and a rocket-propelled grenade, and I can stop the sniper in one of two ways: (a) shoot her in the head or (b) fire the RPG.

Suppose that I hold this combination of views:

1. Narrow Pacifism: It is always wrong to intentionally kill.

2. The Principle of Double Effect is true.

3. Broadness of Intention: Shooting the sniper in the head would be an intentional killing.

Then I am not permitted to to use the rifle to stop the sniper. But here is a paradoxical consequence: a strong Double Effect case can be made that I am permitted to use the RPG. For in firing the RPG, I can be credibly intending to destroy the sniper’s rifle, which is a legitimate target even for a (narrow) pacifist. (I am assuming that I couldn’t destroy the sniper’s rifle with my rifle shot, perhaps because my aim isn’t good enough, or because it’s protected by a sandbag.)

So, here is an odd dilemma for the narrow pacifist who accepts Double Effect. Either the narrow pacifist accepts Broadness or rejects it.

Acceptance of Broadness, together with the above argument, leads in a number of cases to significantly more violence: the RPG will not only kill the sniper but also her comrades. Note that this is not an issue that comes up just in “small” cases involving snipers and RPGs. Narrow Pacifism plus Broadness would lead to a perverse preference to shoot a tactical nuke at the area occupied by enemy infantry—of course, just in order to destroy their weapons—over a conventional infantry attack.

Rejection of Broadness, on the other hand, means that the narrow pacifist need not actually be all that pacific: she can allow soldier to lethally shoot the enemy as long as they intend to stop the enemy rather than to kill. The narrow pacifist who rejects Broadness is a very narrow pacifist indeed.

Objection: If one accepts Broadness, one will also think that firing the RPG is an intentional killing.

Response: Thinking that firing the RPG is an intentional killing seems to me to be rejecting the central ideas behind Double Effect. The point of Double Effect is to distinguish the target of the action from side-effects. It seems perfectly reasonable to take the sniper’s rifle as one’s RPG target. Unlike in the case where one aims at the sniper’s head, there is no intention to impose any harm on the sniper, or even to physically affect the sniper’s body in any way. There is simply the intention to destroy the weapon which the sniper is using. Unfortunately, the explosion that will destroy the weapon will also kill the sniper.

Pacifism and casuistry

Pacficists who think that all lethal violence is wrong have a moral imperative to think creatively about ways in which the innocent can be protected from assault without recourse to lethal violence. These creative ways will be both preventative and reactive, and may be technological, physical (e.g., martial arts training), verbal, spiritual, self-sacrificial (e.g., hunger strikes), etc. Moreover, the pacifist needs to engage in careful philosophical discrimination to determine the boundaries of the concept of lethal violence (e.g., does it allow the use of Double Effect to engage in violent acts that are foreseen but not intended to cause death?) in order to figure out which actions of defending the innocent are permissible. The duty to engage in such thought comes from our duty to protect the vulnerable and to provide moral guidance for our neighbor.

I am not a pacifist about lethal violence. But I am, to coin a phrase, a pacifist about lying: I think lying is always wrong. Nor am I alone: pacifism about lying is the predominant Catholic position. Those of us who are pacifists about lying need to do the same thing as the pacifists about lethal violence: we need to think creatively about ways in which the innocent can be protected from assault without recourse to lying. This will involve both preventative and reactive approach, and will be of a broad variety of kinds. And we need to engage in careful philosophical discrimination. Our duty to do all this comes from our duties to the vulnerable and to our neighbor.

The tradition of casuistry about speech involving such concepts as mental reservation has been much maligned. But whatever one may think about the detailed ideas from that tradition, one has to remember that this tradition is an outgrowth of the duty to protect the vulnerable, while remaining within the confines of pacifism about lying. One should see engagement in this tradition as akin to a pacifist about lethal violence studying non-lethal martial arts.

Simultaneous actualization of potentiality

I will argue, on Aristotelian grounds, for the following thesis:

• There are cases of actualization of potentials that are simultaneous with the possession of the potentials.

In particular, it follows that Aristotelian arguments against eternalism on the grounds that eternalism makes potentials co-real with their actualities fail, because every Aristotelian has to admit that there are potentials that are co-real with their actualities.

Here is the argument for the thesis.

1. All ordinary substances have first moments of existence.

It follows from Causal Finitism that all temporal substances have a first moment of existence. By “ordinary” substances, I mean things like dogs, cats and oak trees. I am excluding weirder candidates like the wavefunction of the universe or the universe itself, as well as extraordinary substances such as angels.

Now we add this premise:

2. Every ordinary substance always actualizes a potential of itself.

For instance, ordinary substances are always emitting electromagnetic radiation, and on Aristotelian grounds such activity had better be the actualization of a potential.

Now, while time travel and backwards causation might turn out to be possible, they are extraordinary. Thus:

3. An ordinary substance never actualizes a future potential.

Moreover, transsubstantiation is also extraordinary and:

4. Every potential that an ordinary substance has is one that it has at a time at which it exists.

From 1-4, it follows that:

5. An ordinary substance in the first moment of its existence actualizes a potential that it has then.

For suppose Alice is an ordinary substance and it’s now the first moment of her existence (she has such a moment by (1)). Alice actaulizes a potential of herself by (2). That potential which she is actualizing must be had by her in the present or the future by (4), since this is the first moment of her existence. She isn’t actualizing a future potential by (3). So she must be actualizing a present one.

And (5) gives us the thesis about potentiality being sometimes simultaneous with its actuality.

Signatures, translations and lies

Suppose I am hired to be an interpreter for a diplomatic meeting. When I translate claims that I know to be lies, am I lying or deceiving?

Of course, I’m not. I am being relied on for the accuracy of the translation, not the accuracy of the claims. The point is clear if I am being paid by the side that is lied to, but whether I am lying or deceiving surely does not depend on who pays me. By the same token, the typist who takes down and posts his boss’s lying letter is not lying or deceiving.

But that one is not lying or deceiving does not mean that one is off the hook. The interpreter and typist, while neither lying nor deceiving, are cooperating in another’s lies. Whether such cooperation is morally permissible will probably depend on further details. (A fairly clear case of permissibility: One knows that the other party will see through the lies.)

But what if instead the boss asks the typist to take down a lying letter purporting to be from the competing company’s boss, which the boss plans to post on social media in order to discredit the other company? Now I think the case is different. Suppose, for simplicity, that the typist’s boss is Natalie Nixon and the other company’s boss is Cathryn Cato. When the typist signs a letter “Natalie Nixon”, he is himself purporting to the reader that the letter comes from Nixon, and if the typist signs the letter “Cathryn Cato”, he is purporting to the reader that letter is from Cato, and that’s a deceit—maybe even a lie—from the typist.

Similary, if the interpreter says “We strongly believe in freedom of speech”, she is purporting that this is what her principal said the equivalent of. If her principal said that, the interpreter is off the hook for deceit even if the claim is a lie, but if the interpreter made that up, the interpreter is deceiving.

It looks to me like the interpreter’s speech acts are equivalent to prefacing every sentence with: “X says that…”, and the typist’s speech act is equivalent to prefacing the letter with: “X claims that…”.

If this is right, then in my earlier post, Bob is actually lying. But he’s not lying in the content of the letter of recommendation, but in his secretarial claim that the letter is Alice’s.

But I am far from confident about any of this.

Two kinds of pseudonymity

Consider two examples of pseudonymity:

• Samuel Clemens writes Life on the Mississippi, signing it “Mark Twain”.

• Konrad Kujau writes The Hitler Diaries, signing them “Adolf Hitler”.

There is a crucial literary difference here: tokens of “Mark Twain” in Life on the Mississippi (say, on the title page) refer to Samuel Clemens, while any tokens of “Adolf Hitler” in The Hitler Diaries would refer to Adolf Hitler. We can correctly say that Mark Twain is Samuel Clemens and wrote Life on the Mississippi, but we cannot say that Adolf Hitler is Konrad Kujau or that Adolf Hitler wrote The Hitler Diaries. On the other hand, when Clemens’ text speaks in the first person about life on the Mississippi, the text tells us about Clemens’ life. But when Kujau’s text speaks in the first person about life in Berlin, the text tells us about Hitler’s life.

In fact, strictly speaking a pen name like “Samuel Clemens” is not pseudonymous in the etymological sense of the word—“falsely naming”—but just an additional name adopted by the author for certain purposes.

Note that the distinction is not due to the fact that Adolf Hitler is a historical person distinct from Konrad Kujau. A fake diary of a fictitious serial killer would be pseudonymous in the same sense that The Hitler Diaries are: the purported author’s name fails to refer to the real author. Of course there is this difference: in the The Hitler Diaries there is a real mass murderer to whom the text refers, while in the diary of the fictitious serial killer, the purported author’s name does not refer. (This, I think, is true even if fictional characters have existence, as a fictitious character is not a fictional character.) But in both cases the author’s name is truly false.

Real Presence and primitive locational relations

According to relationalism, space is constituted by the network of spatial relations, such as metric distance relations (e.g., being seven meters apart). If these relations are primitive, then there is a very easy way for God to ensure the Real Presence of Christ: he can simply make there be additional spatial relations between Christ and other material entities, spatial relations that are exactly like the relations that the bread and wine stood in to other material entities.

It might seem contradictory for Christ to stand in two distance relations: for instance, being one mile from me (in one church) and three miles from me (in another). But I doubt this is a contradiction. New York and London are both 5600 km and 34500 km apart, depending on which direction you go.

According to substantivalism, on the other hand, points or regions are real, and objects are in a location by standing in a relation to a point or region. If relations are primitive, again there should be no problem about God instituting additional such relations to make it be that Christ is present where the bread and wine were.

In other words, if location is constituted by a primitive relation—whether to other objects or to space—there is apt to be no difficulty in accounting for the Real Presence. The reason is that we expect, barring strong reason to the contrary, primitive relations to be arbitrarily recombinable.

If location, however, is constituted by a non-primitive relation, there might be more difficulties. For instance, as a toy theory, consider the variant of relationalism on which spatial relations are constituted by gravitational force relations (two objects have distance r if and only if they have masses m₁ and m₂ and there is a gravitational force Gm₁m₂/r² between them). In that case, for God to make Christ present in Waco would require God to make Christ stand in gravitational force relations of the sort that I stand in by virtue of being in Waco. For instance, the earth’s gravitational force on Christ would have to point from Waco to the center of the earth—but since the Eucharist is also in Rome, it would have to point from Rome to the center of the earth as well. And that might be thought impossible. But perhaps there could be two terrestrial gravitational forces on Christ: one along the Waco-geocenter vector and the other along the Rome-geocenter vector. This would require some sort of a realism about component forces, but that’s probably necessary for the gravitational toy theory. And then God would have to miraculously ensure that despite the forces, Christ is not affected in the way he would normally be by these forces. All this may be possible, but it’s less clear than if we have primitive relations.