Promises and permissibility

Here is an initially plausible idea:

• A promise can take an action that absent the promise is merely permissible and turn it into an action that is obligatory, but it cannot take an action that absent the promise is impermissible and turn it into an action that is obligatory.

I wanted to use this idea in an argument. But I have since come to a fairly definitive refutation. Suppose last year I promised you that today I would drive to Waco airport and sit for one minute on a bench and come back home. (Maybe we were playing some game, and this was the agreed-upon penalty for losing.) Plausibly, I am obligated to do so. But absent the promise, it would be impermissible for me to do it, because it would be pointless, and it is wrong to drive pointlessly, since each time one drives one (a) endangers human life and (b) contributes to environmental degradation.

Of course, a promise can’t take an action that is intrinsically wrong and make it obligatory.

Withholding and withdrawing treatment, once again

Consider one more pair of cases to challenge the standard view that there is no significant moral difference between withholding and withdrawing treatment.

A patient’s knee became inflexible with age. The only treatment available is an artificial replacement. The patient is competent, informed, free, but eccentric. Consider two cases:

1. The patient doesn’t agree to an artificial replacement, because the patient thinks that if their leg is flexible, they will be expected to do half of the chores in their two-person household, whereas right now they are getting away with doing only a quarter on account of their bad knee.

2. The patient has already received an artificial replacement, but is dismayed by the fact that they are now expected to do half of the chores, so they demand that a physician inject epoxy into the artificial knee to restore the inflexibility they enjoyed prior to the replacement.

In case 1, it is clear that it is a violation of the patient’s bodily integrity and autonomy to force the knee replacement on them, even if one thinks that the patient’s reason for refusal is terrible.

But in case 2, it would be reasonable for a physician to refuse to inject the epoxy, as this would violate the do-no-harm principle which forbids performing medical procedures, even ones requested by the patient, that on balance harm the patient.

Refraining from implanting an artificial knee is an instance of withholding medical treatment. Refraining from injecting epoxy into the artificial knee is an instance of withdrawing medical treatment by disabling a medical device. It’s a different way of disabling than just by throwing a switch, but it is the least damaging way to disable the artificial knee (removing the artificial knee would be tantamount to amputating the leg above the knee).

The judgment that in case 1, acceding to the patient’s refusal is clearly right, while in case 2, refusing the patient’s request for discontinuation of the artificial knee treatment for joint inflexibility at the very least can be right. Hence withholding and withdrawing are not morally equivalent.

Withholding, withdrawing, and the magic of medicine

Consider two cases where a patient ended up with an implanted device D that benefits the patient by ameliorating an otherwise fatal medical condition.

1. Alice got in a fight with Carl the hospital janitor. The janitor grabbed the first weapon at hand—an injector for device D—and stabbed Alice with it, thereby ensuring that Alice now has D implanted in her.

2. Alice’s twin sister Brenda got D duly implanted by Carl’s sister Dr. Diana, a physician at the hospital.

Now suppose that Alice and Brenda both demand a physician to remove D.

It seems that Alice’s demand is completely on par with the demand to remove a bullet or a kidney stone. But normally a physician needs to make a judgment that a procedure requested by a patient is likely to on-balance benefit the patient, and ought to refuse otherwise. If a physician is asked to remove a bullet or a kidney stone, but professionally judges that the patient will die without the bullet or kidney stone, they must refuse the request. It thus appears that the physician ought to refuse to remove D from Alice, unless there are significant burdens from D to Alice (maybe D is not a burden at all, but Alice just wants to die).

But in the case of Brenda, removing D is not just “a procedure”, but it constitutes the withdrawing of a medical treatment. On a standard view, just as one must withhold a medical treatment when a patient competently demands withholding it, even if the treatment would save the patient’s life, a demand for withdrawing is exactly on par, and hence must be honored, even if D does not impose any significant burden on Brenda.

Suppose the standard view is right. Then the above shows you can have two patients who are in exactly the same physical state, and are making exactly the same demand, but the demands are treated differently by standard medical ethics. The reason they are being treated differently is that in Alice’s case, D’s presence does not constitute a medical treatment because D was injected by the janitor in the course of a fight, while in Brenda’s case, D;’s presence does constitute a medical treatment because D was duly injected by a physician.

I find this troubling. It seems to be taking medicine as something magical, as if the status of D inside Alice’s and Bob’s became different when D came to be present “medically”.

Maybe one way to avoid the “magical” thinking is to think that consensual medical implantations come with an explicit or implicit agreement between the patient and the provider (the medical professional or maybe the medical institution) to withdraw the item should one so demand it? Then the magic is not due to medicine but due to promising. (I don’t think this completely resolves the questions, because not all promises need to be kept.)

A problem for Van Inwagen's life condition for composition

Van Inwagen thinks that a plurality of xs composes something if and only if either there is only one thing among the xs or the xs have a life together.

He also agrees that the fundamental particles making up a cell in a multicellural organism have a life together, and so there are cells.

Here is a problem. The following seem true:

1. It is possible to have two overlapping cells in a multicellular organism neither of which is a part of the other.

2. The cells of a multicellular organism together with any intercellular fundamental particles have a life together.

Why think (1)? Because, first, conjoint twins show that multicellular organisms can have “proper overlap”: i.e., they have a part in common but neither is a part of the other, and it seems hard to deny that cells, too, could in principle be like that. Second, it seems plausible that mid-way through a process of mitosis we have two cells that properly overlap.

It seems hard to deny (2), assuming there are cells.

But now consider a multicellular organism which happens to have two overlapping cells. Its cells, together with any intercellular fundamental particles, have a life together. Hence, by van Inwagen’s famous account of composition, the cells and the intercellular fundamental particles compose something. But van Inwagen’s definition of composition includes a no-overlap condition: if the xs compose y, no two xs overlap. And yet in our case we have life and overlap.

What should van Inwagen do? One move would be to weaken the Special Composition Question. Instead of asking when the xs compose something, he could ask when non-overlapping xs compose something. But that makes his view rather less informative than we might think, if overlap between cells is fairly common. Presumably in a body of my size, at any given time, mitosis is occuring in a number of cells (I haven’t done the math, but it seems likely).

Withholding and withdrawing treatment

I have heard that there is a consensus on the equivalence of the actions of withholding medical treatment and withdrawing it, even when the withdrawal requires a positive action from the medical professional (e.g., disconnecting a machine).

Here is a reason to doubt this consensus.

Consider first this pair of cases. In both, the following facts hold. A patient will die within hours without a ventilator, and competently requests that they be on a ventilator. However, an enemy of the patient has very credibly threatened the doctor with death if the patient is on a ventilator tomorrow. The only way the enemy can get at the patient is through the doctor, and there is no way to protect the doctor from the enemy. The difference between the two cases, however, is that in one case, the patient is already on a ventilator and in the other the patient is not yet on it.

If the patient is already on the ventilator, the doctor should refuse to disconnect the patient because of the enemy’s threat. Disconnecting the patient would be a wrongful cooperation in murder, and one should die rather than do that. Disconnecting the patient would be tantamount to murder. On the other hand, if the patient is not yet on the ventilator, then it would be supererogatory for the doctor to ventilate the patient at the expense of the doctor’s life. The doctor does not have the duty to save the patient’s life at the nearly certain expense of their own life. And even if one thinks it is a duty, failure in this duty is far below the wickedness of murder.

But disconnecting is withdrawal and failure to connect is withholding. Thus the two are not equivalent actions, because they can differ in moral evaluation even when done for the same reason (avoidance of the threat).

One might think the two become equivalent when the patient refuses to consent to the treatment (whether its continuation or initiation). It seems odd to think that the patient’s refusal somehow turns both actions equivalent.

But anyway, consider a reversal of the threat case. A “friend” of the refusing patient informs the doctor that they will cut off the doctor’s thumbs unless the patient is on a ventilator tomorrow, and suppose that the ventilation in question is invasive. It seems pretty plausible that in the case where the patient is not yet on the ventilator, the doctor should refuse to invasively ventilate them. For to invasively ventilate the patient would be an assault on the patient’s bodily integrity, and one should suffer a greater loss to one’s own bodily integrity rather than impose a lesser loss on another.

But in the case where the patient is already on the ventilator, it seems that the doctor has no obligation to suffer a greater loss themselves in order to respect the patient’s wish to be disconnected from the ventilator.

Thus, even in the case where the patient refuses consent, withholding and withdrawing are not equivalent.

Length and the memory theory of personal identity

1. That there is an entity that is 25 inches long in 1973 and 72 inches long in 1993 is not even partly grounded in facts about anybody’s memory.

2. If the memory theory of personal identity is true, the existence of such an entity is at least partly grounded in facts about my memory.

3. So, the memory theory of personal identity is false.

Premise (1) is a raw appeal to intuition.

Premise (2) follows from the following:

1. Normally an existentially quantified fact is grounded in each of its instances.

2. I was 25 inches long in 1973 and 72 inches long in 1993.

3. I was a person.

4. The case at hand is a relevantly normal case.

I suppose the memory theorist just needs to deny (1).

Van Inwagen is right: We should not expect an answer to the General Composition Question

Van Inwagen’s General Constitution Question (GCQ) is to provide necessary and sufficient conditions for the xs to compose y in non-mereological terms. Van Inwagen is skeptical of whether the GCQ has any non-trivial answer. Here is a reason to think he’s right to be skeptical.

It might well be true that atomism is necessarily true, namely that every object has a simple part. But given atomism, the following is true:

1. Necessarily, z is a part of y if and only if there are xs that include z and that compose y.

(Proof: The right to left part is trivial: if the xs compose y, they are parts of y. Conversely, suppose z is a part of y. Let the xs consist of z and all the atomic parts of y that aren’t parts of z. It is easy to see that the xs compose y.)

Thus, if atomism is true, an answer to GCQ will provide a non-mereological account of all of mereology. That seems to be too much to expect.

Even if atomism is true, an answer to GCQ will provide a non-mereological account of the parthood of all wholly non-gunky objects (where an object is partly gunky provided that it has some part that has no simple parts). That is also more than we should expect.

Why does God create those he knows will reject him?

Question: Suppose Alice goes to hell, having conclusively rejected God’s grace. Given that God knew that Alice will reject his grace, why did this knowledge not lead him to refrain from creating Alice?

Answer: It is impossible that the following two claims are true:

1. God refrains from creating Alice.

2. God knows that Alice will reject his grace.

For 1 entails:

3. Alice won’t exist

while 2 entails:

4. Alice will reject God’s grace

which in turn entails:

5. Alice will exist.

(Of course, if Molinism is true, one can ask a very similar question to the one I started with. But Molinism is false.)

Animalism without biologism

Animalism holds that we are animals. This is a pretty common-sense view. We are clearly mammals, and mammals are animals.

However, there is a common objection: cerebrum transplants. As the objection goes, if your cerebrum is transplanted from your skull to a different skull (or to a supportive vat), you follow the cerebrum, while the animal stays with the lower brain and the rest of the body. So you are not the animal.

Let me say something that will sound silly: This objection is guilty of biologism about animals. The biologism here consists in the claim that we should take how biologists think about the continuity of animal life to be normative for how we should think about the identity of animals. You might think it’s obvious that we should engage in biologism about animals. But biologists are not metaphysicians, and the question of the metaphysical identity over time of animals does not really enter into the empirical investigations biologists engage in.

On what I think is the correct metaphysics of animals, the identity of an organism over time is grounded in the persistence of the animal’s soul or form, a metaphysical feature of the animal which is largely beyond the interest of contemporary biologists. Moreover, the animal’s form is responsible for its teleological structure, which defines what the animal’s flourishing is, and what is and is not central to that flourishing. It is plausible—though not necessary—to think that the form tends to remain with those components of the animal that are more central to its flourishing as the kind of thing it is.

In the case of homo sapiens, central to its flourishing is the exercise of the excellences of intellect and will. And the cerebrum is more directly involved in these exercises than any other part of the body, so it is plausible to think that the human animal goes with the cerebrum in a transplant.

Biologistically speaking, it is tempting to think of the intellect and will as subserving the animal functions of homeostatic maintenance, growth and reproduction. But that is a mistake. In a human, the functioning of the intellect and will is more central to flourishing than the animal functions.

This may seem discontinuous from other animals. Some will be happy with the discontinuity and some will think it’s a reductio ad absurdum of the view. But I think there is less discontinuity than seems to be the case. Think of dogs. It seems that their social life, with one another and with humans, constitutes more of their flourishing than their performance of the functions that define biological life. The social life presumably evolved because it promoted nutrition, growth and reproduction, but the social life appears more valuable. Given the likely ties between this social life and the cerebrum, it would not surprise me if dogs went with their cerebra in a cerebrum transplant.

The questions here are ones of value, and we should avoid biologism about value, even in non-human animals.

Classical theists should take externalism in philosophy of mind more seriously

After Kripke, pretty much everyone nowadays accepts moderate mental externalism: the content of our thoughts depends on the extra-mental world. On earth where the predominant colorless liquid with such-and-such properties, the word “water” refers to water (i.e., H₂O), while on twin-earth where it is XYZ that has these properties, the word “water” refers to XYZ, and the thoughts that are expressed with sentences using “water” have a content involving water and XYZ, respectively, even if they are grounded in the same internal states of the brain and/or soul.

But there are stronger forms of mental externalism. First, we could have much more radical mental content externalism. Perhaps in one world the very same internal state means that there is water in the lake and in another world it means that the lake is dry but full of elephants. Second, we could have externalism about the subjective experience—the qualia—of mental activity. Thus, perhaps, depending on how extra-mental reality is, in one world one has the experience of seeing a red cube and in other that of smelling a daisy, despite having the same internal state in both worlds.

These stronger forms of mental externalism are rather counterintuitive and strange.

The point of this post, however, is that those of us who accept classical theism should take them much more seriously than we have tended to do. For on classical theism, God is simple and yet knows contingent extra-mental reality. This means that in different worlds God has different knowledge, while yet by simplicity remaining exactly internally the same. Hence we have an extremely strong mental content externism in the case of God: the very same state could mean that the universe consists of a lake with water and that it consists of a mountain covered by elephants. Moreover, if we add—as surely we should—that God’s knowledge is a conscious “vision” of reality, we also have to admit that externalism about subjective exerience is true of God.

Now, we cannot simply go from these externalisms being true of God to their being true of us. But I think we should take the externalisms in our case to be a very serious possibility.

A first attempt at exploring this kind of externalism in the case of subjective experience is here.

Subjective time and self-locating probability

Suppose I am sluggish mentally in the morning and function fast mentally in the afternoons. I find myself in a dark room with no information about what time it is. Consider the two hypotheses MORN, that it is between 7am and 8am and AFT, that it is between 1pm and 2pm. Which is more likely, or are they equally likely?

It seems obvious that if I function mentally the same way in the morning and afternoon, MORN and AFT should be equally likely.

But now suppose I live in a world where every morning all processes in the solar system slow down by a factor of two, returning to the normal speed in the afternoon. Then, surely, for all practical purposes, the period from 7am to 8am is half an hour long! And so it seems right to say P(MORN) = (1/2)P(AFT). But the case of my own mental sluggishness seems to be just a more localized version of the solar system slowing down. Thus, in my original story we should say that likewise P(MORN) < P(AFT).

Here is one way to imagine mental functioning slowing down: my thinking is divided into discrete moments (like a computer’s internal clock, where basic operations take a clock cycle), and in the morning there are fewer of these discrete moments of thinking. If so, then it seems reasonable to say that the probability that the current time is between x and y is proportional to the number of discrete moments of thought between x and y, and hence P(MORN) < P(AFT), there being fewer moments of thought in the morning.

But I have a hard time getting good intuitions about the continuous case.

Preference and choice disposition

Here is an initially plausible thesis about deliberation that I've long felt is right:

1. Normally, when choosing between options, you are more likely to choose an option X than an option Y if and only if you prefer X to Y.

Now consider a normal case where you must choose between four options:

1. Cookies and Earl Gray
2. Cookies and chamomile
3. Crackers and Earl Gray
4. Crackers and chamomile.

Suppose that you mildly prefer cookies to crackers and Earl Gray to chamomile, so that you have a 60% chance of choosing cookies over crackers and 60% chance of choosing Earl Gray over chamomile. Further, suppose you have no preferences about the combination as such. Then the chances of your four options are:

• P(A) = 36%

• P(B) = 24%

• P(C) = 24%

• P(D) = 16%.

Clearly, you can choose A. But notice an odd thing. You can organize your deliberation to start as follows: First choose between A and the disjunction B or C or D. (Maybe then if you chose B or C or D, you decide between B and C or D. And finally if you chose C or D, you decide between C and D.) However, here is another plausible principle of rationality:

2. Normally, if you prefer A to every disjunct of a disjunction, you prefer A to the disjunction.

Organizing your deliberation as above is not abnormal. So, (2) should still apply. You prefer A to B, and you prefer A to C, and you prefer A to D. So you should prefer A to the disjunction B or C or D, and hence you prefer A over the disjunction B or C or D. Thus, by (1) you are more likely to choose A than the disjunction B or C or D. In particular, the chance of your choosing A isn’t 36%, but must be more than 50%.

Hence, (1) predicts that the probabilities of our choices greatly depend on how one coarse-grains the options in one’s deliberation. This shouldn’t be. I thus reject (1). Which makes me sad, as it was a very neat thesis.

Explanatory infinitism

I wish one could formulate and defend a version of explanatory finitism, roughly saying that nothing has infinitely many explanations or an infinite chain of explanations, even if these explanations are not causal (causal finitism of course rules out the causal case). But it seems hard to do so. There do seem to be counterexamples to explanatory finitism. Here some I’m thinking about right now:

1. Why are there infinitely many primes? Because there are infinitely many primes bigger than two. Why are there infinitely many primes bigger than two? Because there are infinitely many primes bigger than three. And so on.

2. Alice has just gone to heaven. Why is she going to experience a day of bliss? Because she will have a day of bliss tomorrow. And also because she will have a day of bliss the day after tomorrow. And also because she will have a day of bliss the day after that. And so on.

3. Alice has just gone to heaven. Why is she going to experience bliss on every future day? Partly because she will have bliss tomorrow. And partly because she will have bliss the day after tomorrow. And so on.

Determining camera pose from three landmarks and accelerometer: initial notes

Suppose we have three landmarks at known locations in three dimensional space, not all on one line, and a camera that is not located at any landmark but sees all three landmarks, with known optical parameters such as focal length. The problem of determining the camera pose—the camera position and angles—from the positions of the landmarks in the camera image is known as the P3P problem. It is known that in general there will be at most four solutions for camera pose. And indeed sometimes there will be four solutions.

What if we have some additional information, namely we know how the camera is oriented with respect to gravity (e.g., because the camera is held horizontally or it’s equipped with an accelerometer)? Call the problem of reconstructing the camera image from n landmarks and gravity data PnPA. I recently showed that with just two landmarks, i.e., P2PA, there will be either one, two or infinitely many solutions, and geometrically characterized exactly which case occurs when.

Question: What can we say about the number of solutions to P3PA?

In this post I will make some slight progress on this question.

First we characterize when there are more than two solutions. Note that once we know the camera position, we can calculate the direction it’s pointing from the camera image (Lemma 4 in my paper). So we only need to look at the number of solutions for camera position.

Fact 1: There are at most two solutions for P3PA, except in the case where the three landmarks and camera all lie on one horizontal circle, in which case there are infinitely many solutions.

Proof: For P2PA, we have more than two solutions in precisely the following cases: (a) the two landmarks are on a single vertical line; (b) the two landmarks are in the same horizontal plane and so is the camera; and (c) the two landmarks and the camera are all on one line. To have more that two solutions for P3PA, each pair of landmarks must satisfy at least one of (a)–(c). Suppose this is so.

Suppose first that two landmarks, say m₁ and m₂, satisfy (a). Next suppose that no two landmarks lie on the same horizontal plane, so (b) is satisfied for no pair of landmarks. Then the third landmark m₃ does not lie on the same line as both m₁ and m₂, and hence neither the pair m₁ and m₃ nor th epair m₂ and m₃ satisfies (a), and at least one of these pairs fails to satisfy (c). Hence we have a pair that fails to satisfy any of (a)–(c), and we have at most two solutions by my P2PA result.

Now, continuing to suppose m₁ and m₂ satisfy (a), suppose that some pair of landmarks lies on the same horizontal plane. It can’t be m₁ and m₂ (as then they will be at the same point, and hence all three landmarks will be on one line). Without loss of generality, suppose m₁ and m₃ lie on the same horizontal plane H. The pair m₁ and m₃ cannot satisfy (a) (or else m₃ is at the same point as m₁). If it satisfies either (b) or (c), the camera is on the plane P, and hence in any case we have (b).

Furthermore, if no two landmarks satisfy (a), then since it can’t be that every pair of landmarks satisfies (c) as that would put all the landmarks on one line, at least one pair of landmarks must satisfy (b).

We thus have reduced to the case where a pair of landmarks satisfies (b): they are on the same horizontal plane H as the camera C. Let’s say that these landmarks are m₁ and m₂. Let m′₃ be the projection of m₃ to this plane. From the camera’s optical parameters and the camera image, we can calculate the angles m₁Cm₂, m₁Cm′₃ and m₂Cm′₃. It is known that the locus of points in a plane that subtend the same angle to two fixed points is an arc through these points. Thus, if we are to have more than two solutions, the arcs respectively through m₁Cm₂, m₁Cm′₃ and m₂Cm′₃ must intersect in at least three points. This would require m₁, m₂, m′₃ and C to all lie on the same circle T.

Now, suppose m₃ lies off the plane H. Then given the camera image and the gravity vector, we can measure the angle between m₃, the camera and the plane H, and given the position of m₃ we can compute the distance from m′₃ to the camera. This constrains the camera to lie on the circle T as well as on a second circle T′ around m′₃. Since m′₃ lies on T, these two circles intersect in at most two points. Thus, we have at most two solutions.

On the other hand, when m₃ is in the same plane, so m₁, m₂, m₃ and the camera lie on the same horizontal circle, we will have infinitely many solutions. For if A and B are two fixed points on a circle, and C is a third point on the same side as A and B, the angle ACB will be constant regardless of the choice of C. The landmarks m₁, m₂ and m₃ split T into three arcs, and the camera could be anywhere in the arc it’s in as far as the image goes.

Fact 2: There are cases where there are exactly two solutions.

Proof by picture: Suppose m₁ and m₂ lie on the same plane and m₃ lies off the plane. Suppose the camera is horizontally oriented, and pointed at m₁. Wherever the camera is on the blue arc, it sees m₁ and m₂ the same way (because the angle indicated by the dotted lines does not change, as discussed above). The image of m₃ in the camera is always directly above or below the image of m₁, and as long as the distance from camera to m₁ is the same, the image of m₃ does not move. Thus, the image of m₃ does not change as the camera moves on the red circle. Hence, at the two points where the red and blue circles intersect, the camera sees the same thing, and hence we have two solutions.

Against Arianism

1. The Christian’s deepest desire is for direct union with God.

2. Our union with the Father must always be mediated by the Son.

3. So, if only the Father is God, then the Christian’s deepest desire cannot be fulfilled.

4. The Christian’s deepest desire can be fulfilled.

5. So, it is false that only the Father is God.