The paradox of the Jolly Givers

Consider the Grim Reaper (GR) paradox. Fred’s alive at midnight. Only a GR can kill him. Each GR has an alarm with a wakeup time. When the alarm goes off, the GR looks to see if Fred’s alive, and if he is, the GR kills him. Otherwise, the GR does nothing. Suppose the alarm times of the GR’s are 12:30 am, 12:15 am, 12:07.5 am, …. Then Fred’s got to be dead, but no GR could have killed him. If, say, the 12:15 GR killed him, that means Fred was alive at 12:07.5, which means the 12:07.5 GR would have killed him.

A Hawthorne answer to the GR paradox is that the GRs together killed Fred, though no one of them did.

Here’s a simple variant that shows this can’t be true. You hang up a stocking at midnight. There is an infinite sequence of Jolly Givers, each with a different name, and each of which has exactly one orange. There are no other oranges in the world, nor anything that would make an orange. When a JG’s alarm goes off, it checks if there is anything in the stocking. If there is, it does nothing. If there is nothing in the stocking, it puts its orange in the stocking. The alarm times are the same as in the previous story.

The analogous Hawthorne answer would have to be that the JGs together put an orange in the stocking. But then one of the JGs would need to be missing his orange. But no one of the JGs is missing his orange, since no one of them took it out of his pocket. So, the orange would have had to come out of nowhere.

And, to paraphrase a very clever recent comment, if it came out of nowhere, why would it be an orange, rather than, say, a pear?

I think the JG paradox also suggests an interesting link between the principle that nothing comes from nothing and the rejection of supertasks.

Explanation and understanding

In the 1960s, it dawned on philosophers of science that:

1. Other things being equal, low-probability explanation confers equally good understanding as high-probability explanation.

If I have a quantum coin that has a probability 0.4 of heads and 0.6 of tails, and it yields heads, I understand why it yielded heads no less well than I would have had it yielded tails—the number is simply different.

On the other hand, the following thesis (which for years I’ve conceded to opponents to low-probability explanations):

2. Other things being equal, low-probability explanations are less good than high-probability ones.

Finally, add this plausible comparative thesis:

3. What makes an explanation good is how much understanding it confers (or at least would confer were it true)

which plausibly fits with the maxim that I’ve often been happy to concede that the job of an explanation is to provide understanding.

But (1)–(3) cannot all be true. Something must go. If (2) goes, then Inference to Best Explanation goes as well (I learned this from Yunus Prasetya’s very recent work on IBE and scientific explanation). I don’t want that (unlike Prasetya). And (1) seems right to me, and it also seems important to defending the Principle of Sufficient Reason in stochastic contexts.

Reluctantly, I conclude that (3) needs to go. And this means that I’ve overestimated the connection between explanation and understanding.

A simpler formulation of the paradox of short pains

On reflection, my paradox of short pains can be simplified. Start with:

1. Whether I have had a pain does not depend on the future.

2. It is impossible for me to have a pain that lasts less than a picosecond.

3. I once started to be in pain for the first time in my life.

Now imagine that the first pain in my life just started half a picosecond ago. Then anybody who has the power to annihilate me in the next quarter (say) picosecond has the power to make it be the case that I had not yet had a pain, since if they so annihilate me, then I won’t have had a pain by (2). But whether someone will annihilate me in the next quarter second is a fact about the future, so whether I have had a pain depends on the future.

To put this in Ockhamist terminology, if we accept (2), then we have to accept that facts about whether one has had a pain can be soft facts.

I like the idea of denying (1), though I think this may make presentists (and others) uncomfortable.

I also like the idea of saying that the argument equivocates between phenomenal and physical time. The duration of pain is a phenomenal duration that does not correspond in a precise way to a physical duration.

Preprint: Conditional, Regular Hyperreal and Regular Qualitative Probabilities Invariant Under Symmetries

Abstract: Classical countably additive real-valued probabilities come at a philosophical cost: in many infinite situations, they assign the same probability value---namely, zero---to cases that are impossible as well as to cases that are possible. There are three non-classical approaches to probability that can avoid this drawback: full conditional probabilities, qualitative probabilities and hyperreal probabilities. These approaches have been criticized for failing to preserve intuitive symmetries that can easily be preserved by the classical probability framework, but there has not been a systematic study of the conditions under which these symmetries can and cannot be preserved. This paper fills that gap by giving complete characterizations under which symmetries understood in a certain "strong" way can be preserved by these non-classical probabilities, as well as by offering some results to make it plausible that the strong notion of symmetry here may be the right one. Philosophical implications are briefly discussed, but the main purpose of the paper is to offer technical results to inform more sophisticated further philosophical discussion.

Preprint here.

More on the problem of short pains

Consider these two very plausible theses:

1. Whether I have pain at time t does not depend on any future facts.

2. There is a length of time δt such that you cannot have a pain lasting no more than δt, but you can have a pain lasting 4δt.

Now imagine that I feel a pain that lasts from t₀ to t₂ = t₀ + 4δt. Let t₁ = t₀ + (1/2)δt. Suppose it is now t₁. Then I am in pain. But now I claim that this counterfactual is true:

3. Were it to be the case that I was to be annihilated at t₀ + (3/4)δt, I wouldn’t have felt any pain now.

Why? For if I were so annihilated, my pain could only have lasted (3/4)δt, which is too short for a pain by (2).

But by (3), whether I feel pain now depends on whether I will shortly be annihilated, contrary to (1).

Hence, we need to reject one of (1) and (2).

It is hard to reject (2). After all, imagine the sequence of times: a second, a quarter second, a sixteenth of a second, …, 2⁻⁴⁰ seconds. Clearly I can feel a pain that lasts a second. The last of these is less than a picosecond, and clearly I can’t feel a pain that short. So somewhere in that sequence I must reach a δt which is too short for a pain, but where 4δt isn’t too short for a pain.

I think denying (1) isn’t as bad as it may seem.

But perhaps a less counterintuitive move is to deny that phenomenal times and physical times are as closely correlated as they intuitively seem. Here is a possible story. Phenomenal times are discrete points while physical times are continuous (or discrete on a much finer timescale). You can feel a pain that is located at exactly one phenomenal time. The spacing between the phenomenal times corresponds to a fairly large (and non-uniform) spacing between physical times, say of the order of magnitude of a millisecond. So, you can feel a pain that is there one millisecond and gone the next, but you may feel it at exactly one point of phenomenal time.

As far as I can tell, it is not possible to run the annihilation argument while keeping careful track of the continuous physical and discrete phenomenal timelines. I guess this is a way of rejecting (2) by making it not make sense.

Here is a third way out of the argument. Imagine that what it is to have a pain at t is to have had some constitutive physical or spiritual process P have lasted some threshold period of time δt. On this view, before P lasted over a period of δt, there was no pain: pain only starts once P has lasted δt. We might now suppose that δt is something like a millisecond. Then it is possible to have a pain that lasts only a picosecond: for that, all we need is the underlying process P to have lasted δt plus a picosecond—and only the last picosecond of that process would have constituted a pain. But we no longer need to make the implausible claim that we can be aware of picosecond-scale stuff. For in paining, our awareness is the awareness of the underlying process P, and that process always needs to have taken something in the millisecond range for it to constitute a paining.

This way out of the argument also has the consequence that it is not possible to have a pain before completing the first δt of one’s existence. Pain is not a momentary property.

The third way out will not appeal to dualists who think phenomenal states are fundamental.

Promising to try

Here’s a natural thing to say. The sentence

1. “I promise to try to ϕ”

should be analyzed as straightforwardly an instance of the schema:

2. “I promise to ψ”

for an action ψ, in the special case where ψing is the action of trying to ϕ.

I am now fairly convinced that this is wrong: that (1) is not a mere special case of (2).

Here are two cases to make one more friendly to this.

• I promised you to try to call you tomorrow. Come tomorrow, I called you accidentally, i.e., without trying to. If the content of my promise was literally to try to call you, then I haven’t fulfilled that, and I have reason to call you, this time intentionally. But that’s silly.

• I promised to try to email you a paper tonight. Come tonight, I try, but my email software puts up the dialog: “Your email did not go through due to a temporary problem. The problemm is now resolved. Should I send it? Yes/No.” I press “No” on the grounds that my promise has been fulfilled: I already tried. That’s vicious, surely.

There are easy ways out of the two cases that are compatible with the straightforward analysis of promising-to-try. But the cases are nonetheless suggestive of the fact that “I promise to try to ϕ” should not be read too literally.

My promise to you to ψ typically accomplishes three things:

• It creates a reason for me to ψ

• It tells you that I will ψ

• It creates an obligation of apology or compensation if I do not ψ (regardless of whether I am culpable).

In particular, because it tells you that I will ψ, it normally creates an expectation in you that I will ψ, which is apt to lead to your organizing your life around my ψing.

I suggest that a promise to try to ϕ instead accomplishes these three things:

• It creates a reason for me to ϕ

• It tells you that I will make a reasonable effort to ϕ

• It creates an obligation of apology or compensation if I do not make a reasonable effort to ϕ.

In other words, I think that my promising to try to ϕ gives rise to exactly the same reason in me as promising to ϕ would. However, it holds back the assurance that I will ϕ, replacing it with an assurance that I will try. Now whether you expect me to ϕ will depend on your judgment of how likely my attempts are to succeed. And by using the weaker wording, I am typically implicating to you an uncertainty about success which should give you some evidence of my unreliability. Finally, my promising to try to ϕ weakens the duties of apology or compensation to only apply when I didn’t make a reasonable effort.

In other words, to promise and to promise-to-try are two different kinds of speech acts, and it is obviously useful to have both.

Synchronization and the unity of consciousness

The problem of the unity of consciousness for materialists is what makes activity in different areas of the physical mind come together into a single phenomenally unified state rather than multiple disconnected phenomenal states. If my auditory center active in the perception of a middle C and my visual center is active in the perception of red, what makes it be the case that there is a single entity that both hears a middle C and sees red?

We can imagine a solution to this problem in a computer. Let’s say that one part of the computer has and representation of red in one part (of the right sort for consciousness) and a representation of middle C in another part. We could unify the two by means of a periodic synchronizing clock signal sent to all the parts of the computer. And we could then say that what it is for the computer to perceive red and middle C at the same time is for an electrical signal originating in the same tick of the clock to reach a part that is representing red (in the way needed for consciousness) and to reach a part that is representing middle C.

On this view, there is no separate consciousness of red (say), because the conscious state is constituted not just by the representation of red (say) in the computer’s “visual system”, but by everything that is reached by the signals emanating from the clock tick. And that includes the representation of middle C in the “auditory system”.

The unification of consciousness, then, would be the product of the synchronization system, which of course could be more complex than just a clock signal.

This line of thought shows that in principle the problem of the unity of consciousness is soluble for materialists if the problem of consciousness is (which I doubt). This will, of course, only be a Pyrrhic victory if it turns out that no similar pervasive synchronization system is found in the brain. The neuroscience literature talks of synchronization in the brain. Whether that synchronization is sufficient for solving the unity problem may be an empirical question.

The above line of thought also strongly suggests that if materialism is true, then our internal phenomenal timeline is not the same as objective physical time, but rather is constructed out of the synchronization processes. It need not be the case for this that the representation of red and the representation of middle C happen at the same physical time. A part further from the clock will receive the synchronizing signal later than a part closer to the clock, and so the synchronization process may make two events that are not simultaneous in physical time be simultaneous in computer time. I suspect that a similar divide between mental time and physical time is true even if dualism is (as I think) true, but for other reasons.

Bennett's positive and negative instrumentality

Bennett offers this account of positive vs. negative instrumentality. If the volume of the space of possible bodily movements occupied by doing A is greater than that occupied by doing not-A, then doing A is a negative instrumentality; if it is less, then it is positive. Thus, raising one’s hand is positive: one can, for instance, raise, lower or keep one’s hand level, and raising occupies less volume of movement space than not-raising.

Here’s a curious consequence. Let M be the maximum speed at which I can move. Let A be moving at a velocity of magnitude greater than half of M. Then A occupies more of the space of possible bodily movements than not-A and hence counts as negative by Bennett’s criteria.

Why? Well, velocity is a vector: it has a magnitude and a dimension. The relevant action space (assuming the movement is two-dimensional—we can’t fly) is a disc of radius M. The subset occupied by not-A is the a (closed) disc of radius M/2. The area (the two-dimensional analogue of volume) occupied by not-A is (1/4)πM². The area of the whole movement space is πM². The area occupied by A is thus πM² − (1/4)πM² = (3/4)πM². Thus, A occupies three times the area occupied by not-A. Hence, not-A is a positive action and A is a negative action.

This seems quite wrong.

Postdoc at Baylor

“Baylor University seeks application for a postdoctoral fellowship for up to three years from those working in virtue ethics, moral psychology, or social philosophy. Suitable candidates will have a background in psychology or neuroscience that equips them to participate in data collection, qualitative analysis, study design and intervention development with our team of philosophers, psychologists, and practitioners.”

Details here.

Microphysics and philosophy of mind

Much (but not all) contemporary philosophy of mind is written as if microphysics were fundamental physics. But as far as I know, only on those interpretations of quantum mechanics that disallow indeterminacy as to the number of particles can microphysics be fundamental physics. The most prominent such interpretation is Bohmianism. On most other interpretations, the most we can say about the number of particles is that we are in a superposition between states with different numbers of particles. But reality has to have determinate numbers of fundamental entities. The picture of reality we get from both relativity theory and mainstream interpretations of quantum mechanics other than Bohmianism and its close cousins is that fundamental physical reality consists of global entities such as the spacetime manifold or the wavefunction of the universe rather than microscopic entities like particles. (I am attracted to a non-mainstream interpretation on which the fundamental physical entities may include mid-sized things like dogs and trees.)

Sometimes, pretending microphysics is fundamental physics is excusable. For certain discussions, it doesn’t matter what the fundamental physics is—the arguments work equally well for global and local fundamental entities. In other cases, all that matters is relative fundamentality. Thus, facts about chemistry might be held to be more fundamental relative to biology, and facts about microphysics might be fundamental relative to chemistry, even if the microphysics facts themselves are not fundamental simpliciter, being reducible, say, to facts about global fields.

But even when the arguments do not formally rely on fundamental physics being microphysics, it is risky in a field so reliant on intuition to let one’s intuitions be guided by acting as if fundamental physics were microphysics. And doing this is likely to mis-focus one’s critical attention, say focusing one more on the puzzle of why the functioning of various neurons produces a unified consciousness than on the puzzle of how the functioning of a handful of global entities results in the existence of billions of minded persons.

Bostock v. Clayton County

In Bostock, the Supreme Court ruled that hiring discrimination against a gay person is discrimination on the basis of sex, and hence forbidden, because one wouldn’t refuse to, say, hire a woman who is attracted to men, and hence to refuse to hire a man who has the same “trait”, namely being attracted to men, is discrimination on the grounds of his sex.

Here is a clear counterexample to this line of reasoning. Consider an employer who refuses to hire a man who claims in a job application to be a woman on the grounds that this man is a liar. (Suppose this is a man in every socially accepted sense of the word: he is biologically male, he socially identifies as a man in every context other than this interview, etc.) Such an employer would not refuse to hire a woman with the same “trait”, namely claiming to be a woman. Hence by the Bostock reasoning, the employer discriminates on the basis of sex. But this is absurd: the basis for the discrimination is not the sex of the prospective employee, but lying about one’s sex. Similarly, discrimination against a white person who claims to be African American on the grounds of a mismatch between their claims and reality is not discrimination against white people.

In other words, the basis for the discrimination is not the sex of the candidate but the relationships between the candidate’s actual sex and the candidate’s claimed sex.

And logically speaking, this is all very much like the gay case, where the basis for the discrimination is not the sex of the candidate but the relationship between the candidate’s sex and the sex of the persons the candidate is attracted to.

I am not claiming that it is morally wrong to be attracted to persons of the same sex in the way in which it is wrong to lie (or in any any other way, for that matter). Nor am I claiming that it is reasonable or legal for an employer to discriminate on the basis of such attraction. All I am claiming is that such discrimination is not discrimination on the basis of the candidate’s sex.

Objection: There is an important difference between the trait of being attracted to men and the trait of claiming to be a man. Being attracted to men is essentially the same trait whether it is found in a man or a woman, while claiming to be a man is radically different when it is found in a man and in a woman, since it is truth-telling in the one case and lying in the other.

Response: This response would require the court to settle the question whether indeed the trait of being attracted to men is basically the same trait when found in men and when found in women, in a way in which the trait of claiming to be a man is not the same trait when found in men and when found in women. That is perhaps the real philosophical question here, and it is presumably precisely what the employer in question would dispute. The court cites the example of how discriminating on the grounds of interracial marriage is racial discrimination. Now, here I would say that the trait of marrying a person of race R is the same trait whether found in a person of race R or not. But clarifying exactly what it means to be basically the same trait is very difficult.

Disclaimer: I am no lawyer or legal scholar, just a philosopher with an eye for counterexamples.

Weak invariance of full conditional probabilities

In two papers (here and here), I explored two different concepts of symmetry for conditional probabilities. The concept of strong invariance says that P(gA|B)=P(A|B) for a symmetry g as long as A and gA are subsets of B. The concept of weak invariance says that P(gA|gB)=P(A|B) for a symmetry g. In some special cases, the weak concept implies the strong concept.

Anyway, here’s an interesting thing: the weak concept does not capture our symmetry intuitions. Take perhaps the simplest case, a lottery on the set of integers Z, and say that the symmetries are shifts. It turns out that there is a weakly shift-invariant full conditional probability P such that:

1. P({m}|{m, n}) = P({n}|{m, n}) (singleton fairness)

2. P(A|A ∪ B)=0 and P(B|A ∪ B)=1 whenever B has infinitely many positive integers and A has finitely many positive integers.

Condition (2) implies that it is more likely that the winning ticket is a power of two than that that is a negative integer. So weak shift invariance is very far from strong invariance.

(And in fact one can have strong invariance for the lottery on Z if one wants. One can even have have strong invariance under shifts and reflections if one wants.)

The proof is a modification of West's proof of a result for qualitative probabilities.

Temporary intrinsics and internal time

The main problem the literature presents for eternalist theories is the problem of temporary intrinsics: how an object can have an intrinsic property at one time and lack it at another.

The most common solution is perdurantism: four-dimensional objects have ordinary properties derivatively from their instantaneous temporal parts or slices having them, and since the slices only exist at one time, the properties can be as intrinsic as one likes.

Another solution that has found some purchase is a view on which the properties that we previously thought were intrinsic, such as shape and charge, are in fact fundamentally relational, defined by a relation to a time. Thus, to be square is to be square at some time or other. This results in a more commonsense ontology than perdurantism, but it has the problem of just denying that there are temporary intrinsic properties.

This morning it’s occurred to me that if we say that substances carry with them an internal time sequence that is intrinsic to them, then relationalism can admit temporary intrinsic properties. A property of a substance, after all, can be intrinsic even if the property is relational, as long as the relations that the possession of the property is grounded in are intrinsic to the object, say by being relations between parts or other metaphysical components of that object. After all, shape is seen as the paradigmatic case of an intrinsic property, and yet it is often seen as grounded in the relations between the particles making up an object. But on a view on which substances carry an internal time sequence, the internal times can be taken to be intrinsic aspects of the substance, and then ordinary properties can be seen as relational to the these internal times. Thus, to be square is more fundamentally to be square at some internal time or other.

What kinds of intrinsic aspects of the substance are the internal times? Here, there are multiple options. They could be sui generis aspects of the substance. They could be tropes—for instance, if substances all have beginnings, one could identify a time with the trope of having survived for a temporal duration D.

Internal times could even be time slices of the substance. This last option may seem to take us back to perdurantism, but it does not. For it is one thing to say that I am in pain because my temporal part ARP_t is in pain—it sure seems implausible to say that I am in pain derivatively from something else being in pain—and another to say that my being in pain is constituted by a relation to ARP_t, which part is in no pain at all. (That pain is constituted by a relation between the aspects of a substance is not at all strange and unfamiliar as a view: a materialist may well say that pain is constituted by relations between neuronal activities.)

Note, too, a view on which intrinsics are relational to internal times also solves another problem with views on which ordinary properties are relational to times: if those times are external, then time travel to a time at which one “already” exists is ruled out.

My own preferred view is that a nested trope ontology. I have a trope of being human. That trope then has an infinite number of temporal existence tropes, corresponding to all the different internal times at which I exist. These temporal existence tropes—or maybe even temporal human existence tropes—are then the internal times. And I can even say what the relation that makes a temporary intrinsic obtain at a temporal existence tropes t is: that temporary intrinsic obtains at t provided that it is a trope of t.

Should we see Christian division as a scandal?

[I am now thinking that the main point of this post may be mistaken for the reasons I state my in 11:58 AM October 5, 2020 comment. Nonetheless, I think the Bayesian stuff at the bottom of the post may be correct, and so perhaps the disunity between Christians should not as such count as evidence against the truth of Christianity.]

It is often said that the fact that Christianity is divided into multiple denominations is a scandal and a tragedy. Now, in one sense the question of scandal is empirical: are people led away from the truth by this division? I don’t know the answer to the empirical question. On the one hand, it seems likely that some are. On the other hand, if all Christians had exactly the same doctrine, I suspect many would be suspicious of whether this unity is produced by the strength of the evidence or by social control.

But in any case, the question I want to address is not empirical, but rather whether it makes sense to be intellectually scandalized by the division of Christianity into multiple denominations and whether we should see it as a tragedy. And here there is a point that I have never seen address: when we discuss Christian division, we need to get clear on what we are comparing it to.

For the sake of argument (but not contrary to fact!) let’s suppose that if there is a true version of Christianity, it is the Catholic one. My argument will if anything be more compeling if a smaller denomination is singled out as the best candidate for the truth. Then, rounding to the nearest billion, we live in this world:

• w₁: 8 billion people, of whom 2 billion are Christians, of whom 1 billion are Catholic and the other billion are divided among multiple
  denominations.

But now compare to this world:

• w₂: 8 billion people, of whom 1 billion are Christians, all of whom are Catholic.

This is a world with no religious division. But from the Christian point of view is there reason to think this is a better world? Assuming the true version of Christianity is Catholicism, in w₁ and w₂ we have an equal number of people who identify with the true version of Christianity. But in w₁ there is another billion people who identify with other versions of Christianity. If Catholicism is the true version of Christianity, still these other versions are closer to the truth that not being a Christian is. (And a Christian who thinks Catholicism is not the true version of Christianity will presumably think that w₁ is much better than w₂.)

If the the relevant contrast to our denominationally divided world w₁ is w₂, then there is no tragedy and no one should be scandalized by the denominational division.

I suppose that when one thinks of the denominational division as a tragedy and a scandal, one is comparing w₁ to something like:

• w₃: 8 billion people, of whom 2 billion are Christians, all of whom are Catholic.

And, indeed, if Christianity is correct and the right version of Christianity is Catholicism, then as far as these numbers go, w₃ is better than w₁.

So, it all depends on what we are comparing the denominational division scenario to: are we comparing it to a scenario where the actual world’s non-Catholics (still assuming arguendo that the normative form of Christianity is Catholicism) aren’t Christian or to a scenario where they are Catholic?

Moreover, it is clear that even if a Catholic says that it is a tragedy that a billion Christians aren’t Catholic, it is a much greater tragedy that 7 billion humans aren’t Catholic, and 6 billion of them aren’t even Christian.

What if we don’t care about numbers, and just care about the fact of division? Suppose, abstractly, that there is a theistic religion R. Should we see significant division between adherents of R as evidence for R, against R or neutral? From a Bayesian point of view, one question to pose seems to be:

1. Given that R is the true religion, would we expect to see significant division or unity among the adherents of R?

Here is an argument for the unity answer. If God exists, he wants people to know the truth, so we would expect that everyone or nearly everyone should subscribe to the correct form of R, call that form R₁, and if that’s true, then of course nearly all adherents of R will be adherents of R₁.

But thinking about it this way mixes up two different arguments against Christianity: the argument from disunity and the argument from the fact that most people aren’t Christian. It’s the argument from disunity that we want to evaluate. To that end, instead of asking (1), I think we should ask:

2. Given that R is the true religion and yet the majority of human beings does not subscribe to R, would we expect to see significant division or unity among the adherents of R?

But now I don’t think we have much reason to say that we should expect unity. Let’s say that abstractly we have versions R₁, ..., R_n of religion R, that R₁ is in fact the correct one, and that all the versions agree on some fundamental claims F definitive of R as such. So, should we expect that all those who accept F should accept R₁ as well?

I see one main reason to think this: God wants us to know the truth. But it is already a part of the background assumptions in (2) that God’s desire that we know the truth does not result in the majority of humans subscribing to R, much less R₁. Given this part of the background, why should we expect the majority of those humans who subscribe to F to accept R₁?

Now, it may be that some religions are obviously logically interwoven, such that if one accepts the fundamental claims, the rest follows with sufficient obviousness that we would expect the vast majority of people who accept the fundamental claims to accept the less fundamental ones. But it seems to me that there is little reason a priori to think that the true religion should have such obvious logical interweaving.

So, I don’t think that given both that R is the true religion and that the majority of people do not accept R, I do not think we have reason to expect unity among the adherents of R. Indeed, we might reasonably expect that if there is a true version R₁ of R, there will be a significant core of people who accept R₁ and then a penumbra of people who accept some parts of R₁ but reject others, thereby landing themselves in some other version R_i of R.

In light of this, it seems to me that once we have evidentially taken into account the fact that the majority of people are not Christians, the further fact that the Christians are denominationally divided does not seem to be significant evidence against Christianity.

Inquiring as to intentions

Thomson and other opponents of the idea that intention deeply affects moral permissibility like to point to the idea that it is silly to think that when having someone perform some task, we need to figure out what intentions they would have, when the intentions don’t affect how they will act. To use Thomson’s example, it seems silly to think that when you ask a doctor to administer a dose of morphine to a terminally ill patient where you foresee that any dose sufficient to remove the pain is also sufficient to cause death, you need to find out whether the doctor intends death by the dose or intends to play by Double Effect rules and only pursue pain-relief. As long as in both cases the doctor will give the same dose and in the same way, it doesn’t matter what they are intending when we ask them to act.

If this line of argument shows that intentions don’t affect permissibility, it proves too much. For suppose that you need a nurse to give a patient an injection of a small amount of morphine after an operation. You know there are only two nurses around. One of them is a murderer who swapped the vial of morphine in the dispensary for cyanide. Fortunately, you caught the swap, and reversed it. Unfortunately, you don’t yet know which of the two nurses is which. Suppose you know for sure that both nurses will inject the morphine equally well, but one of them will be committing attempted murder with it, thinking that it’s cyanide. It seems to me that if one is impressed by Thomson’s argument in the foreseeably lethal dose of morphine case, one should also think that in this case it doesn’t matter which nurse one chooses (as long as you know that both will do the same task the same way, and that the murderous nurse won’t swap the vial again). But in this case it is clear that it matters: one nurse would be committing attempted murder and the other wouldn’t. And we should avoid bringing it about that someone will commit attempted murder.

What about a more extreme case? Alice deeds an injection to live. Only Bob is qualified to do it. Bob, however, wants Alice dead. But Bob is mistakenly convinced that the vial of life-saving medicine is a vial of cyanide. Is it permissible to ask Bob to perform the injection?

That’s tough. Still, even if we say it’s permissible, I think it’s very plausible that it should be a last resort: if there were another to administer the injection, we should go for the other.

I am inclined to think it’s not permissible. For one’s action plan depends on Bob's attempting murder (that’s why we don’t correct his error about the vial!), and it’s wrong to intend that someone attempt murder.

Acting on a desire

Suppose I have a desire for A, and I act on this desire to get A. There are at least three different stories about my motivations that are compatible with this:

1. I pursued A non-instrumentally.

2. I pursued A instrumentally in order to satisfy my desire.

3. I pursued A instrumentally in order to rid myself of my desire.

The distinction between (2) and (3) should be somewhat familiar to many: when one struggles with temptation, the temptation whispers to one that if one gives in, the struggle will be over. (This is, of course, a deception: for if one gives in, the temptation is likely to return strengthened later.) The distinction between (1) and (2) is subtler. In case (1), the desire reveals to us something desirable and we pursue it. The pursuit satisfies our desire, but we don’t do it to satisfy the desire, but simply because the thing is desirable.

Intentions and reasons

An interesting question is whether one’s intentions in an action supervene on facts about one’s reasons and desires in the action. I don’t know the answer, but I also don’t know of a good way to account for intentions in terms of reasons and desires.

Judith Jarvis Thomson suggests this:

• for a person to X, intending an event E, is for him to X because he thinks his doing so will cause E, and he wants E.

This is false. The standard (at least for me) method of generating counterexamples to conjunctive principles is to find cases where the conjuncts are coincidentally satisfied in ways other than what one had in mind in formulating the principles.

So, here is the counterexample. I am alone in an eccentric friend’s house, and I want to take an ibuprofen. I look in the medicine cabinet, and I see a jar full of pills of different sizes, colors and shapes all jumbled together. I call up my friend asking where the ibuprofen is. My friend says: “Ah, ibuprofen. That’s the pill that will hurt your throat when you swallow them.” I look in the jar, and indeed there is exactly one pill that is large enough to hurt the throat upon swallowing. I swallow the pill because I think doing this will hurt my throat. But I don’t intend my throat to get hurt. So far I don’t have a counterexample: I have failed to satisfy the “he wants E” conjunct. But now just throw that conjunct into the story in a motivationally irrelevant way. Perhaps I want my throat to be hurt, due to my being a masochist. But I promised my accountability partner that I would refrain from intentionally hurting myself, and I’ve gotten pretty good at keeping this promise, so I don’t intend to get hurt.

One could add to Thomson’s conditions:

• and his wanting E is a cause of his action.

But we can just multiply the the coincidental satisfaction of conditions. For instance, perhaps my psychiatrist informed me that my masochistic desires are caused by headaches, and so if I get rid of my headache, my masochistic desires will disappear. Thus, my desire to hurt my throat is a cause of my relieving my headache. But I don’t relieve my headache in order to hurt my throat.

All this makes me think that it’s not unlikely that having a particular intention in an action is a primitive datum about the action: perhaps actions are teleological entities, and the intentions are their telê.