Monday, July 24, 2017

Death, harm and time

For the sake of this post, stipulate death to be permanent cessation of existence. Epicurus famously argues that death is not a harm to one, because the living aren’t harmed by death while the dead do not exist.

As formulated, the argument appears to require presentism—the view that only presently existing things exist. If eternalism or growing block is true, the dead would exist, albeit pastly. This would give us a nice little argument against presentism:

  1. If presentism is true, the Epicurean argument is sound. (Premise)

  2. The conclusion of the Epicurean argument—namely, that death is not a harm—is absurd. (Premise)

  3. So, presentism is false.

But things aren’t quite so simple, because one can reconstruct an Epicurean argument without presentism.

  1. One is intrinsically harmed by x iff there is a time t at which one is intrinsically harmed by x. (Premise)

  2. One is intrinsically harmed at t by x only if one exists at t. (Premise)

  3. One is not intrinsically harmed by death at any time at which one exists. (Premise)

  4. One is not intrinsically harmed by death at any time. (5 and 6)

  5. One is not intrinsically harmed by death. (4 and 7)

This argument distinguishes intrinsic from extrinsic harm. Here’s an illustration of the distinction I have in mind: if I lose a finger, that’s an intrinsic harm; if people say bad things about me behind my back, that’s an extrinsic harm—unless it causally impacts me in some negative way. Epicurus didn’t seem to think there was such a thing as extrinsic harm, so he formulated his argument in terms of harm as such. But, really, his argument was only plausible with respect to intrinsic harm, in that a no longer existent person certainly could suffer extrinsic harms, say by losing reputation or having loved ones suffer harm. And the conclusion that death is not an intrinsic harm is implausible enough. Death seems to be among the worst of the intrinsic harms. (In particular, I think my little argument against presentism remains a good one even if we weaken the conclusion of the Epicurean argument to say that death is not an intrinsic harm.)

Of course, the conclusion (8) is still false! So which premise is false?

Here is a pretty convincing argument for (5):

  1. One is intrinsically harmed at t by x only if has or lacks an intrinsic property at t because of x. (Premise)

  2. One does not have or lack any intrinsic properties at times when one doesn’t exist. (Premise)

  3. So, (5) is true.

Premise (6) is also pretty plausible.

Premise (4) is also plausible.

But there is a way out of the argument. If four-dimensionalism is true, we have a good way to reject (4). Consider first the spatial analogue of (4):

  1. One is intrinsically harmed by x if and only if there is a point z in space at which one is intrinsically harmed by x.

But (12) is implausible. Consider a spherical plant that suffers the harm of being made cylindrical. To be distorted into an unnatural shape seems to be an intrinsic harm. But it need not an intrinsic harm locatable at any point in space. At any point in space where the plant is not, surely it’s not harmed. At points where the plant is, it might be harmed—say, by the stresses induced by the unnatural shape—but it need not be. We could, in fact, suppose that the plant is nowhere stressed, etc. The harm is simply the intrinsic harm of being deformed. For another example, suppose materialism is true, and consider an animal in pain. The pain is an intrinsic harm, plausibly, but there is no harm at any single point of the brain—only at a larger chunk of the brain.

What the examples show is that spatially extended objects can be intrinsically harmed in respect of properties that cannot be localized to a single point. If four-dimensionalism is true, we are also temporally extended. We should then expect the possibility of being intrinsically harmed in respect of properties that cannot be localized to a single instant of time, and hence we should not believe (4). And death seems to be precisely such a case: one is harmed by having only a finite extent in the temporally forward direction. This could be just as much an intrinsic harm as being spatially distorted.

In fact, once we see the analogy between harm not located at a point of space and harm not located at a point of time, it is easy to find other counterexamples to (4). Consider a life of unremitting boredom. Suppose someone lives from t1 to t2 and is bored at every time. At every time t between t1 and t2 she suffers the intrinsic harm of being bored; but she has the additional temporally non-punctual intrinsic harm of being always bored. Or suppose that materialism is true. Then just as pains do not happen in respect of properties at a single spatial point, they probably do not happen in respect of properties at a single instant either: pain likely requires a sequence of neural events.

In fact, the multiplication of examples is sufficiently easy that even apart from the more abstruse question of the harms of death, someone whose theory of time or persistence forces her to endorse (4) is in trouble.

But on reflection, the moves against three-dimensionalism and maybe even presentism were too quick. Maybe even the presentist can say that we have intrinsic properties which hold in virtue of how we are over a temporally extended period of time.

Thursday, July 20, 2017

Life in the interim state and the nature of time

Assume this thesis:

  1. We go out of existence at death and return to existence at the resurrection.

Suppose, further, that:

  1. There is a last moment t1 of earthly life and a first moment t2 of resurrected life.


  1. If there are no intervening moments of time between t1 and t2, one is never dead.

  2. Whether there are any intervening moments of time between t1 and t2 depends on what happens to things other than one.

  3. So, whether one is ever dead depends on what happens to things other than one.

  4. So, whether one is ever dead is extrinsic to one.

But that’s absurd in itself, plus it implies the absurdity that death is only an extrinsic harm. So, we should reject 1. We exist between death and the resurrection.

There are two controversial assumptions in the argument: 2 and 4. Assumption 4 follows from an Aristotelian picture of time as consisting in the changes of things. Since one doesn’t exist between t1 and t2, those changes would have to be happening to things other than oneself. If one doesn’t accept the Aristotelian picture of time, it’s much harder to argue for 4.

Assumption 2 is obviously true if time is discrete. If time is continuous, it might or might not be true. For instance, it could be that one lives from time 0 to time 100, both inclusive, in which case t1 = 100, but it could also be that one lives from time 0 to time 100, non-inclusive, in which case t1 doesn’t exist. Similarly, one could be resurrected from time 3000, inclusive, to time infinity, non-inclusive, in which case t2 = 3000, but it could also be that one is resurrected from time 3000, non-inclusive, in which case t2 doesn’t exist.

However, even in the continuous case the argument has some force. For, first of all, it’s obvious that death is an intrinsic harm to us, and that obviousness does not depend on obscure details about whether the intervals of one’s life include their endpoints. Second, it is at least metaphysically possible for 1 to hold. But then in a world where 1 were to hold, our death would be merely an extrinsic harm to us, which would still be absurd.

AI and ontology

  1. Only things that exist think.

  2. Only simples and living things exist. (Cf. van Inwagen and Aristotle.)

  3. Computers are neither simple nor alive.

  4. So, computers don’t think.

Monday, July 17, 2017

Computer consciousness and dualism

Would building and running a sufficiently “smart” computer produce consciousness?

Suppose that one is impressed by the arguments for dualism, whether of the hylomorphic or Cartesian variety. Then one will think that a mere computer couldn’t be conscious. But that doesn’t settle the consciousness question. For, perhaps, if one built and ran a sufficiently “smart” computer (i.e., one with sufficient information processing capacity for consciousness), a soul would come into being. It wouldn’t be a mere computer any more.

Basically the thought here supposes that something like the following is a law of nature or a non-coincidental regularity in divine soul-creation practice:

  1. When matter comes to be arranged in a way that could engage in the kind of information processing that is involved in consciousness, a soul comes into existence.

Interestingly, though, a contemporary hylomorphist has very good reason to deny (1). The contemporary
hylomorphist thinks that the soul of an animal comes into existence at the beginning of the animal’s existence as an animal. Now consider a higher animal, say Rover. When Rover comes into existence as an animal out of a sperm and an egg, its matter is not arranged in a way capable of supporting the kind of information processing involved in consciousness. Yet that is when it acquires its soul. When finally the embryo grows a brain capable of this kind of information processing, no second soul comes into existence and hence (1) is false. (I am talking here of contemporary hylomorphists; Aristotle and Aquinas both believed in delayed ensoulement which would complicated the argument, and perhaps even undercut it.) The same argument will apply to those Cartesian dualists who are willing to admit that they were once embryos without brains.

Perhaps one could modify (1) to:

  1. When matter comes to be arranged in a way that could engage in the kind of information processing that is involved in consciousness and a soul has not already come into existence, then a soul comes into existence.

But notice now two things. First, (2) sounds ad hoc. Second, we lack inductive evidence for (2). We know of no cases where the antecedent of (2) is true. If we were to generate a computer with the right kind of information processing capabilities, we would know that the antecedent of (2) is true, but we would have no idea if the consequent is true. Third, our observations of the world so far all fit with the following generalization:

  1. Among material things, consciousness only occurs in living things.

But a “smart” computer would still not be likely to be a living thing. If it were, we would expect there to be non-“smart” computers that are alive, by analogy to how just as there are conscious living things, there are unconscious ones. But it is not plausible that there would be computers that are alive but not “smart” enough to be conscious. One might as well think that the laptop I am writing this on will be conscious.

This isn’t a definitive refutation of (2). God has the power to (speaking loosely) provide an appropriately complex computer with a soul that gives rise to consciousness. But inductive generalization from how the world is so far gives us little reason to think he would.

Sunday, July 16, 2017

Informed organs surviving the death of an individual

In my last post, I offered a puzzle, one way out of which was to accept the possibility of informed bits of an animal surviving the death of the animal. But the puzzle involved a contrived case--a snake that was annihilated.

But I can do the same story in a much more ordinary context. Jones is lying on his back in bed, legs stretched out, with healthy feet, and dies of some brain or heart problem. How does the form (=soul) leave his body? Well, there are many stories we can tell. But here's one thing that's clear: the form does not leave the toes before leaving the rest of the body. I.e., either the toes die (=are abandoned by the form) last or they die simultaneously with the rest. But in either case, then Special Relativity and the geometry of the body (the fact that one can draw a plane such that one or more toes are on one side of the plane, and the rest of the body is on the other) imply that there is a reference frame in which the form leaves one or more of the toes last. Thus, there will be a reference frame and a time at which only toes or parts of toes are informed. It is implausible to think that one is alive if all that's left alive are the toes. So organs can survive death while informed by the individual's form.

Friday, July 14, 2017

Snake annihilation and partial death

The following five principles seem to be rationally incompatible:

  1. Every part of a living organism is informed by its form.

  2. If any part of an organism is informed by its form, the organism is alive.

  3. An snake would be dead if everything but the tailmost one percent of its length were annihilated.

  4. Simultaneity is relative, as described by Special Relativity.

  5. Being informed by a form is not relative to a reference frame.

To see the incompatibility, consider this case. A snake of ordinary proportions is lying stretched out in a line and is then instantaneously completely annihilated. Notice an interesting fact about this snake:

  1. Every bit of this snake is informed by the form of the snake whenever it exists.

This follows from (1) and the setup of the situation. Note that (6) will not be true in the case of snakes that meet a more ordinary end than by complete instant annihilation: those snakes leave behind parts that are no longer informed (they may be parts only in a manner of speaking, but I think nothing in my argument hangs on this). It is to make (6) true that I supposed the snake annihilated instantaneously.

Now, by (4), the claim that the snake is must have been said with respect to some reference frame F1. But it follows from Special Relativity and the geometry of linear snakes that there will be a reference frame F2 relative to which the snake is annihilated gradually from the head to the tail rather than simultaneously. There will thus be a time t2 such that relative to F2 at t2 the snake has been annihilated except for the tailmost one percent. At t2 relative to F2, that tailmost one percent is informed by the form of the snake by (5) and (6). By (2), the snake is alive at t2 relative to F2. But by (3), it is dead at t2 relative to F2. So, the snake is both alive and dead at t2 relative to F2, which is absurd.

I am not sure what to do about this argument. I feel pushed to deny (2). Perhaps something could be dead simpliciter but still have living parts. But that’s an uncomfortble position.

Life and non-life

Assume a particle-based fundamental physics. Then the non-living things in the universe outnumber the living by many orders of magnitude. But here is a striking fact given a restricted compositionality like van Inwagen’s, Toner’s or mine on which all there are is in the universe are particles and organisms: the number of kinds of living things outnumbers the number of kinds of non-living things by several orders of magnitude. The number of kinds of particles is of the order of 100, but there are millions of biological species (they may not all correspond to metaphysical species, of course).

Counting by individuals, living things are exceptional. But counting by kinds, physical things are exceptional. Only a tiny portion of the universe is occupied by life. But on the other hand, only a tiny portion of the space of kinds of entities is occupied by non-life.

I am not sure what to make of these observations. Maybe it is gives some credence to an Aristotelian rather than Humean way of seeing the world by putting the the kinds of features as teleology that are found in living things at the center of metaphysics.

Thursday, July 13, 2017

Preponderance of evidence

I do formal epistemology, but I am no legal scholar, so this could be a complete misunderstanding. It is my understanding that in civil cases a preponderance of evidence standard is used on which the evidence needs to support the conclusion with a probability merely greater than 1/2. This seems ridiculous in cases where one is seeking compensation for damages that may or may not have occurred.

Suppose I run a business, and I treat my staff somewhat shabbily but not actionably. One day, hundreds of dollars worth of damage occurs in the server room. Review of blurry security camera footage, building security logs and other data proves beyond reasonable doubt the following facts:

  • A thin stocking was put over the camera, hence the blur.

  • There were five employees in the offices at the time, all of whom had a similar build and appearance: Alfred, Bill, Carl, David and Edgar.

  • Three of the employees went to the bathroom and returned with buckets full of water which they poured over the servers.

  • The other two employees did their best to stop the three, including calling 911 and heroically trying to block the door to the server room. As a result of the scuffle, everybody’s fingerprints are on the buckets and everybody is wet.

  • Each employee claims with equal credibility that he was one of the two trying to stop the attack. Moreover, everybody claims to be unable to identify who the “other” employee trying to stop the attack is. The video footage shows a scene of such confusion that this inability to identify is unsurprising.

So, I fire all five employees and then sue each of the five individually for damages. I argue in the case of each employee that the evidence clearly yields a 3/5 probability that he was responsible for damage, and remind the court that 3/5 > 1/2.

But surely it would be a serious miscarriage of justice for all five to be held liable for damages that two of the five sought to prevent.

I wonder if cases like this get their force solely from the fact that the probabilities involved—namely, 3/5—are low, or if there is something else going on. Suppose I had a thousand employees, and 999 were damaging company property while one was trying to stop it. Should I be able to sue all 1000, correctly claiming a probability of 999/1000 of responsibility in each case, while knowing for sure that a judgment in my favor in all 1000 cases will place a severe financial burden on exactly one innocent person?

That is an uncomfortable conclusion, but perhaps we should bite the bullet and say that this is no different from a court knowing that over the run of many cases, there will be a small minority where innocents are burdened with grave burdens—and the risk of suffering such burdens is just part of the cost of membership in the society, much as being subject to the draft is.

But it seems much more uncomfortable to say something like this in the 3/5 case—or a 51/100 case—than in a 999/1000 case.

Naive intuition: The evidence needed should scale with the burden to the defendant in the case of a finding against them. Maybe the evidence requirements do thus scale in practice. Like I said, I am no legal scholar.

Love and happiness

Could perfect happiness consist of perfect love?

Here’s a line of argument that it couldn’t. Constitutively central to love are the desire for the beloved’s good and for union with the beloved. A love is no less perfect when its constitutive desires are unfulfilled. But perfect happiness surely cannot be even partly constituted by unfulfilled desires. If perfect happiness consistent of perfect love, then one could have a perfect happiness constituted at least partly by unfulfilled desires.

When this argument first occurred to me a couple of hours ago, I thought it settled the question. But it doesn’t quite. For there is a special case where a perfect love’s constitutive desires are always fulfilled, namely when the object of the love is necessarily in a perfectly good state, so that the desire for the beloved’s good is necessarily fulfilled, and when the union proper to the love is of such a sort that it exists whenever the love does. Both of these conditions might be thought to be satisfied when the object of love is God. Certainly, a desire for God’s good is always fulfilled. Moreover, although perfect love is compatible with imperfect union in the case of finite objects of love, perfect love of God may itself be a perfect union with God. If so, then our happiness could consist in perfect love for God.

I am not sure the response to the argument works but I am also not sure it doesn’t work. But at least, I think, my initial argument does establish this thesis:

  • If perfect happiness consists of perfect love, it consists of perfect love for God.

Of course none of the above poses any difficulty for someone who thinks that perfect happiness consists of fulfilled perfect love.

Tuesday, July 11, 2017

Special Relativity and physicalism

There is, I think, an underexplored argument against physicalism on the basis of Special Relativity and the unity of apperception.

The unity of apperception seems to imply that there is always a non-relative fact of the matter whether two perceptions are co-perceived: whether I am feeling cold at the same time as I am seeing a red cube, say. (Einstein’s own definition of simultaneity presupposes this: he defines the simultaneity of two distant events in terms of the co-perception of light beams from them.) When two perceptions are co-perceived, they are simultaneous. So there must be a non-relative simultaneity in the mind. But it is very unlikely that all co-perceived perceptions are grounded in exactly the same place in the brain. And simultaneity between physical events happening at different locations is always relative. So perceptions aren’t physical events.

I don’t think this is a very strong argument, though. It’s open to the physicalist to say that perceptual time is different from physical time, and perceptual simultaneity need not correspond to physical simultaneity. The best version of physicalism is functionalism. Now imagine embedding a causally isomorphic copy of Napoleon in a universe with four spatial and one temporal dimension, but in such a way that all of the four-dimensional life of Napoleon is realized within the four spatial dimensions, at a single temporal instant. The three spatial dimensions of Napoleon would be realized within three spatial dimensions, and the temporal dimension of Napoleon would be realized within the fourth spatial dimension. All the diachronic causation in the life of our world’s Napoleon becomes simultaneous causation in the new world. All of the life of the Napoleon-copy is then lived at a single instant of physical time, but it has all of the causal richness that Napoleon’s life had, and it is causally isomorphic to Napoleon. It is plausible, then, that the functionalist will say that Napoleon-copy has the same mental life as Napoleon. But Napoleon-copy’s mental life is all at once physically. So the functionalist can say that mental time is not the same as physical time—without budging from physicalism.

Now, I think some people will find this kind of a separation between physical time and mental time to be unacceptable. If so, then they shouldn’t be physicalists. I myself am not a physicalist, but I find the separation between physical and mental time quite plausible. After all, don’t we say that sometimes time runs faster than at other times?

Monday, July 10, 2017

Permissibility of the natural

The usual way to argue that an action is permissible is to argue that the arguments against the action’s permissibility fail. But it would be really nice to be able to give a more positive argument for an action’s permissibility. Sometimes one can do so by showing that the action is obligatory, but (a) that doesn’t help with the permissibility of non-obligatory actions, and (b) often an argument for the obligatoriness of a positive action presupposes the action’s permissibility (e.g., the obligation to kill a dog that is attacking one’s child when no other means of defense is available presupposes the general permissibility of killing dogs with good reason).

Here is a place where Natural Law (NL) can provide something quite useful, namely this principle:

  1. If A is a natural action, then normally A is permissible.

This principle could, for instance, be used to generate intuitively compelling positive arguments for such controversial theses as:

  1. It is normally permissible to eat animals.

  2. It is normally permissible for us to reproduce.

  3. It is normally permissible for us to prefer those more closely related to us.

In addition to Natural Lawyers, theists in general might have reason to endorse (1), on the grounds that our nature comes from God.

Of course, there is always going to be a difficulty in determining whether the antecedent of (1) is true.

Non-theistic non-NL theories are unlikely to endorse (1) except as a rule of thumb. And it will be an interesting explanatory question on those theories why then (1) is true even as a rule of thumb.

Sunday, July 9, 2017

Infima species

There is a classic controversy in interpreting Aristotle: Is there one form per individual or one form per species?

One of the main arguments for individual forms is that the form of the human being is the soul, and it would be crazy to think that you and I have the same soul.

But what if—though this is surely not what Aristotle thought—the truth were this: There is one form per species, but humans, unlike other organisms, are each their own species (much as Aquinas thought the angels were).

This creates a discontinuity between non-human and human animals. This discontinuity is in itself a disadvantage of the view—it makes things more complicated.

However, at the same time the discontinuity would correspond nicely with some ethical intuitions. It wouldn’t be reasonable for a human to sacrifice her life for a Komodo dragon. But it could be reasonable for her to sacrifice her life for the Komodo dragon species. The view also fits with the widespread, though far from universal, intuition that it is permissible to kill non-human animals for food, but that the killing of a human being is a morally far weightier thing. Moreover, the idea that humans are infima species seems to capture important things about human individuality (I am grateful to Richard Gale for this observation), including the idea that while there is a teleological commonality between human beings, it is also the case that individual humans have individual vocations, telè that are their own only.

The main disadvantage of the view is theological. In Athanasian soteriology, it is crucial that Christ is metaphysically same species as we are. But one might hope that a Christology could be modified where being of the same genus would play the same role as being of the same species does for St Athanasius—or perhaps one where what plays the role is just the fact of a shared rational animality (which we also share with any non-human rational animals outside of the Solar System).

I don’t think the view is true, because the radical discontinuity the view posits between non-human and human animals just seems wrong. But I think there is more to be said for this view than is generally thought. And for those who think that they are not animals—for instance, people who think that they are constituted by an animal—the view seems even better.

Friday, July 7, 2017

Immaterial body parts

Here’s a difficult question: Does an artificial heart literally become a body part of the patient?

And here’s a line of thought suggestive of a negative answer.

  1. Necessarily, all our body parts are material.

  2. If one could have an artificial heart as a body part, one could have an immaterial artificial heart as a body part.

  3. So, one cannot have an artificial heart as a body part.

Why accept 2? Because presumably what makes an artificial heart suitable for being a body part is that it does the job of a heart. But we could imagine an immaterial being which does the job of a heart. For instance, an angel could move blood around the body, and do so in response to electrical activity in the brain stem. Perhaps one could say that an angel couldn't be a body part, because it is already an intelligent being. But we could then imagine something that moves blood around like the angel but doesn’t have a mind.

I am not so confident of premise 1, however. One could, I suppose, turn the argument around: An artificial heart could be a body part, so possibly some of our body parts are immaterial. And if that’s right, then given a view on which body parts are informed by the form of the person, we would have the further interesting conclusion that a form can inform something that isn’t matter.

Minds don't think

  1. Only things with minds think.

  2. Minds don’t have minds.

  3. So, minds don’t think.

Corollary: We think with minds, hence we are not minds.

There might be an exception to (2) in the case of God. By divine simplicity, God is his own mind. So God's mind has a mind, namely itself.

Wednesday, July 5, 2017

Against nihilism

Argument A:

  1. Necessarily, if there is nothing, it is impossible that anything exists.

  2. Something exists.

  3. So, by Brouwer Axiom, necessarily possibly something exists.

  4. So, the consequent of (1) is impossible.

  5. So, it is impossible that there is nothing.

The most controversial premise in this argument is (1). Premise (1) follows from a picture of modality on which possibility is prior to necessity, and the possibility of non-actual things is grounded in possibilifiers. Absent possibilifiers, nothing is possible. But suppose that instead we like a picture of modality as grounded in necessitators. Then instead we have this argument.

Argument B:

  1. Necessarily, if there is nothing, no proposition is necessary.

  2. It’s necessary that it’s necessary that 2+2=4. (Obvious, or else a consequence of S4 and the fact that it’s necessary that 2+2=4.)

  3. So the consequent of (6) is impossible.

  4. So, it is impossible that there is nothing.

And finally we have:

Argument C:

  1. Necessarily, if there is nothing, either it is impossible that anything exists or no proposition is necessary.

  2. Necessarily possibly something exists. (Premise (3))

  3. It’s neccessary that it’s necessary that 2+2=4. (Premise (7))

  4. So, the consequent of (10) is impossible.

  5. So, it is impossible that there is nothing.

Everything is beautiful

Consider something visually ugly, say one of my school painting projects. The colors are poorly chosen and the lines don’t do a good job representing what it’s meant to represent. (I am not being modest.)

But now suppose we live in an infinite universe or a multiverse, so that every possible intelligent species is realized. It is very likely that there will be some intelligent species whose electromagnetic spectral receptivities are such that the colors in the lines look gorgeous to it, and harmonize in a wonderful abstract way with the shape of the lines. This is, of course, a chance matter—I wasn’t making the painting for that mode of visual receptivity. Let’s say that the species is the xyllians. We can still say that what I made is an ugly work of art, but it is also a part of the natural world, and considered as a part of the natural world it is visuallyx (i.e., as seen with the electromagnetic reception apparatus of xyllians) beautiful while being visuallyh (i.e., as seen with human electromagnetic reception apparatus) beautiful.

Moreover, it is irrelevant whether the xyllians and humans exist. Whether they exist or not, my painting is visuallyx beautiful and visuallyh ugly. All that’s needed is that the xyllians and humans could exist. Thus, my painting really is both beautiful and ugly, even if we are the only intelligent species. And it is just as objectively beautiful as it is objectively ugly. I wasn’t supposing that the xyllians misperceive: just that they have a different pattern of spectral receptivities. We can suppose that xyllian visual perception is just as accurate in reflecting the world, including my unhappy artistic productions, as ours is.

This means that an argument from particular beauty for the existence of God must be run cautiously. Sure, sunsets and goldfish are beautiful. But so is any child’s scrawl, and quite likely any physical object is beautiful with respect to some possible sensory apparatus. Particular instances of beauty are easy to find and should not surprise us. What could surprise us, however, is:

  1. That the particular sensorily beautiful things around us—such as sunsets and goldfish—are in fact beautiful with respect to the sensory apparatus of the intelligent species that dwells near them.

We might also attempt to mount arguments from beauty to God on the basis of these remarkable facts:

  1. That there is such a property as (objective) beauty at all.

  2. That we are able to perceive beauty.

  3. That we enjoy beauty.

  4. That we are able to make correct judgments of beauty.

And bracketing the question of arguing for the existence of God on the basis of beauty, the realization that all material things are beautiful should lead us to glorify God. For while I said that it’s chance that my poor attempts at painting are visuallyx beautiful, that’s only so loosely speaking. God is omnirational, and that the paintings are visuallyx beautiful is a redeeming quality that surely God did not fail to intend.

Friday, June 30, 2017

A curious bug

Here's a bug I haven't had before: my code broke because something else was improved. I had some Arduino code that needed to display text on a two-line LCD. Everything worked a couple of months ago. Today I made some changes irrelevant to the screen display code, and the screen display started omitting characters. I got worried it was a hardware issue of some sort, but my best guess what happened was this: The Arduino IDE was reinstalled, and the new version must have optimized something. As a result, the code ran faster than before, and the LCD couldn't keep up with it. To fix, I had to add about five microseconds extra delay per byte being sent to the LCD.

If this wasn't microcontroller code, one would use a timer rather than a hardcoded delay, and the problem wouldn't occur. But using a timer would likely be less efficient, and I wanted maximum efficiency in this part of the code. I'm not used to dealing with hardware at this low level, and so I'm not used to "too fast" being a problem (except with user interaction).

The variety of beauty

A crucial part of Diotima’s ladder is the progress from sensible beauty to the non-sensible beauty of mind, law and mathematics. From time to time I’m struck by how very strange it is that such very different things as paintings, faces, poems, minds and theorems have beauty in common.

If one has a view of beauty as that which gives a certain “aesthetic pleasure”, it’s easy to explain this: it is not that surprising that different inputs could give rise to the same kind of pleasure. But that view of beauty is false. (We would not make my preschool scribbles more beautiful than Monet’s mature paintings by brainwashing people into taking more aesthetic pleasure in the former than in the latter.)

Plato’s famous explanation is that all these different things participate in the same form. But that leaves mysterious why it is that a painting that exhibits a certain harmonious play of colors and a theorem that is illuminating and unifying in a certain way both end up necessarily participating in the form of beauty. There needs to be a connection between the configurations that give rise to beauty and the participation in the form of beauty. The historical Plato seems to have thought that there was a common mathematical structure in all these configurations, but this seems quite implausible given the great variability of them.

Perhaps a theistic explanation can make some progress. All beauty is a participation in God. But God is infinitely beyond all else, so this participation is from an infinite distance, and it is not so surprising that the infinite richness of God can be participated in in infinitely many different ways.

The difficulty with this explanation is that beauty is not the only property that’s a participation in God. Every positive property is a participation in God. And some positive properties—say, knowledge—are much more unified than beauty. Perhaps it helps, though, to have the medieval view that beauty, goodness and being are all in some sense interchangeable. So perhaps every participation in God constitutes beauty, and so the great variety of participations in God gives rise to the great variety of types of beauty.

Wednesday, June 28, 2017

Intention and credence

In a paper on Double Effect, I offer this kind of an example. Jim has sneaked into a zoo on a mission to kill the first mammal he sees at the zoo, because a very rich eccentric has informed him that he’d give a very large sum of money to famine relief if Jim did that. Jim sees the zookeeper and kills him, reasoning that zookeepers are mammals, and hence the kill will satisfy the eccentric’s condition. In the paper, I argued that Jim need not be intending to kill a human being even if he knows the zookeeper is a human being. His intention need simply be to kill that mammal. Of course, this is still a murder, and hence I argue that the Principle of Double Effect should not be formulated in the classical way in terms of intentions.

I think a lot of people are incredulous of my claim that Jim can know that the mammal he is shooting is a human being and yet not intend to be killing a human being. It’s just occurred to me that there may be a way to help overcome that incredulity by making the story more gradual. Jim first sees a shadowy figure in the dark in the primate enclosure very far away. He assumes it’s an ape, and aims his rifle. However, he doesn’t want to miss, so he comes a couple of steps closer. As he gradually approaches, he has a very vague impression that there is something a little human-like about the movements of that primate. He thinks to himself, however, that apes are close relatives to humans, so it’s almost certainly still an ape. But as he approaches, his evidence that what is before him is a human rather than an ape increases. Finally, by the time he’s close enough to shoot, the evidence is conclusive: he knows it’s a human. But he doesn’t care a whit—the only thing that matters to this callous individual is that it’s a mammal. So he shoots and murders.

Let’s suppose that Jim’s credence that the mammal is human goes from 0.0001 to 0.9999 as he walks forward. At the 0.0001 point, it’s clearly not Jim’s intention to kill a human being. Nor at the 0.5000 point. Nor even at the 0.5001 point. Could it be that Jim’s intention becomes one to kill a human being once his credence gets high enough for him to count as believing, or maybe even knowing, that this is a human being? But it is implausible that a merely numerical increase in the credence suddenly forces a change in Jim’s intention. Intention just does not seem to be degreed in a way that lines up with the degreed nature of Jim’s credence.

So, what should we say? I think it is this: Whether Jim’s credence was 0.0001 or 0.9999 at the time of the shot, as long as he was acting callously and not caring about whether the victim is ape or human, he accomplished the death of a human being. This accomplishment (or something close to it) makes him a murderer. Of course, at the 0.0001 credence point, it would be hard to prove in a court of law that he accomplished the death, that he shot without caring whether the victim is ape or human, caring only that the victim was a mammal.

Tuesday, June 27, 2017

Set size and paradox

Some people want to be able to compare the sizes of sets in a way that respects the principle:

  1. If A is a proper subset of B, then A ≤ B but not B ≤ A.

They do this in order to escape what they think are paradoxical consequences of the Cantorian way of comparing sizes. But from one paradox they fall into another. For the following can be proved without the Axiom of Choice:

  1. If there is a transitive and reflexive relation ≤ between sets of reals (or just countable sets of reals) that satisfies (1), then the Banach-Tarski Paradox holds.
And the Banach-Tarski Paradox is arguably more paradoxical than the paradoxes of infinity that (1) is supposed to avoid.

Anthropomorphism and theism

Sometimes theists are accused of anthropomorphism in their concept of God. But it is important to note that theists hold that God is the entity least like humans. Rocks are closer to us in intellectual capacity than God is. Amoebae are more like us in love than God is. Wet noodles resembles us in power more than God does. All creatures are more like one another than they are like God.

Of course, even if God is the entity least like humans, humans could be the entities most like God. But typical religious theists think even that is false: the angels are more like God than humans are.

None of this denies that there are particular (and controversial) theological views that may suffer from an undue anthropomorphism. I suspect certain motivations for taking God to be mutable to be like that.

Monday, June 26, 2017

Command ethics

I think one of the most powerful objections to divine command theory is MacIntyre’s question as to which divine attributes make it be the case that the obligatory is what God commands. It’s not God’s creating us: for imagine a naturalistic universe where a crazy scientist creates people—surely the crazy scientist’s commands do not constitute obligations. It’s not God’s being omnipotent—that just seems irrelevant. Omniscience also doesn’t seem to help. Etc.

Here’s a theory that just occurred to me which avoids this problem:

  • the obligatory is what is validly commanded by someone.

This is a command theory instead of a divine command theory. The difficulty with this theory is giving an account of a valid command that does not proceed by saying that a valid command is one that it is obligatory to obey. Perhaps, though, one could suppose that there is a fundamental property of non-derivative authority (actually, a relational property: non-derivative authority over x with respect to R) that some persons have. For instance, God has this property in a very broad and non-derivative way, but God might not be the only one (maybe parents have it with respect to children, and governments with respect to people). This theory solves the MacIntyre problem with divine command theory. And while there is a cost to having a primitive account of non-derivative authority, there is some reason to think that even if we grounded obligations in something other than commands, we might still have to take non-derivative authority to be primitive.

Of course, without God the command theory is just implausible: clearly there are ordinary obligations we have that do not come from the commands of other ordinary persons.

I certainly don’t endorse the theory. But it’s worth thinking about, and in particular it’s worth thinking whether it’s not superior to divine command theory.

Friday, June 23, 2017

The unknown mechanism of action of the IUD

A fellow philosopher just sent me this very interesting quote from an article in a reputable medical journal:
[I]f it was conclusively shown that the sole or principal mode of action [of the IUD] was to prevent the embryo from implanting, then this method, as in the case with emergency contraception, would be considered by the Roman Catholic church as causing an early abortion. As a result many agencies involved in the research, development or delivery of contraception prefer to leave the mechanism of action issue unresolved, which may explain why research into the contraceptive mechanisms of IUDs has been sparse in the last 20 years.

The quote’s invocation of politics fits with vague suspicions I had.

But in any case, I wonder whether leaving the “the mechanism of action issue unresolved” helps all that much morally. Suppose that prevention of implantation is morally on par with paradigmatic cases of killing an adult human. Now consider this story. You are a doctor on board a spaceship marooned on an alien planet. All your drugs have been destroyed but one of your patients is suffering severe pain. The aliens have a callous attitude to human life, but in exchange for a piece of fine art they offer you a drug. The aliens always tell the truth and they guarantee that the drug “terminates the pain.” But when you ask them about the mechanism by which it does so, they say: “Trade secret. It terminates the pain.” You try asking more general questions like: “Does it suppress pain signals in the brain?” They just say: “That would terminate the pain. It terminates the pain. Why ask more?” Then someone else in your crew asks: “Does it terminate the patient?” And the aliens say: “That would terminate the pain. It terminates the pain. Why ask more?”

The end result is that you have no idea whether the drug terminates the pain by suppressing the pain as such or by killing the patient. It is clear that in that case we should not use the drug, except as a last-ditch hope for a patient who is already dying. (I am not saying it is acceptable to kill someone who is already dying. But if someone is already dying, then one can tolerate a greater risk of unintended death.)

I am not saying, of course, that we need to find evidence against every crazy hypothesis. There is, after all, the hypothesis that ibuprofen works by annihilating the patient and calling in aliens that replace the patient with a pain-free simulacrum. The tiny but non-zero probability of that hypothesis should not keep us from using ibuprofen. But when we do not know how some drug or procedure works, and one of the serious hypotheses is that it works by killing someone, then that’s a problem.

Given the callousness of the aliens, the hypothesis that they are offering a euthanasia drug is a serious hypothesis. Likewise, the hypothesis that the IUD works primarily by preventing implantation is a serious hypothesis (see the suggestive evidence in the above-quoted paper). In both cases, then, unless we can find significant evidence against this serious hypothesis, the use of the drug or method is wrong (except perhaps in exceptional cases).

We rightly have a guilty-until-proved-innocent approach to medical interventions. Apart perhaps from exceptional cases (e.g., terminal ones), a medical intervention must be tested for its effects on the directly affected parties. The manufacturer's failure to gather data on the effects of the IUD on some of the directly affected parties, namely the embryos, means that the IUD has not been tested up to the morally required standards of testing medical interventions, and hence cannot be licitly used (apart perhaps from some exceptional cases), even absent the data that we have that is suggestive of fatal effects on those parties.

Abortifacient effects of contraception and the Principle of Double Effect

Suppose that a contraceptive has the following properties:

  • Fewer than 1% of users have a pregnancy annually.

  • At least 5% of users annually experience a cycle where the contraceptive fails to prevent fertilization but does prevent implantation.

I think there is good empirical reason to think there are such contraceptives on the market. But that’s a matter for another post. Here I want to look at just the ethics question. So let’s suppose that the above stipulated properties obtain, and in fact that they are known to obtain.

The cases where the contraceptive prevents implantation are cases where the contraceptive kills an early embryo: in short, they are cases where the contraceptive is being abortifacient. The question I want to address in this post is this: Could someone who thinks early embryos have whatever property (personhood, membership in the human race, the imago dei, the possession of the soul, etc.) that makes it paradigmatically wrong to kill adult human beings nonetheless defend the contraceptive on the grounds that the deaths due to implantation-prevention are just an unintended and unfortunate side-effect?

Basically, the defense being envisioned would invoke some version of the Principle of Double Effect, which allows for some actions that have a bad side-effect that isn’t intended as a means or as an end. Of course, Double Effect requires that there not be other reasons why the action is wrong. But let’s bracket the question—which I address at length in my One Body book—whether there are other reasons the contraceptive could be wrong to use, and just focus on the abortifacient effect.

We can ask the question from two points of view:

  1. Can the manufacturer justify the production of the contraceptive on the grounds that failures of implantation are just an unfortunate side-effect?

  2. Can the user justify the use on those grounds?

Regarding 1, here’s a thought. For the contraceptive to be competitive, it has to be highly effective. If one does not count the 5% of annual cases where fertilization occurs but implantation is prevented as part of the contraceptive’s effectiveness, then one can at most claim 95% effectiveness for the contraceptive. And that effectiveness would put the contraceptive significantly behind the most effective formulations of the pill. In fact, it will put it somewhat behind the results that can be achieved by Natural Family Planning by a well-prepared and well-motivated couple. So for commercial purposes, the manufacturer will have to be advertising 99% effectiveness. But one cannot with moral consistency claim 99% effectiveness while holding that 5% of that is an unfortunate side-effect. By claiming 99% effectiveness, one is putting oneself behind the mechanisms that one knows are being used to achieve that effectiveness.

Suppose that a manufacturer advertises an analgesic that is guaranteed to be 99% effective at pain relief. But suppose that 5% of the time, the analgesic kills the patient and 94% of the time it relieves pain non-fatally. Then indeed the analgesic relieves pain 99% of the time, since killing the patient stops the pain. But by holding out 99% effectiveness, the manufacturer is showing that that it is really intending this to be a pain-relief-cum-euthanasia drug rather than a mere pain-relief drug.

What about 2? As we saw from the case of the manufacturer, the user cannot intend 99% effectiveness while saying that the deaths of early embryos are unfortunate side-effects. But the user, unlike the manufacturer, can say: “From my point of view, this is about 94% effective, with a 5% likelihood of a fatal side-effect, which side-effect I don’t intend.”

There are two points I want to make here. First, Double Effect requires there to be no reasonable alternatives to the course of action. But there are methods of fertility control that do not cause implantation-failure, for instance Natural Family Planning, and some of these methods are not less effective when compared against the 94% figure. And one cannot with moral consistency compare these method against the 99% effectivness figure while holding out that 5% of that is an unfortunate side-effect one would like to avoid.

Finally, imagine a hypothetical male contraceptive pill that works by releasing genetically engineered sperm-eating viruses that has the following annual properties:

  • Fewer than 1% of female partners get pregnant.

  • But 5% of female partners get a fatal viral infection from it.

  • No men die.

Clearly, nobody would tolerate such a product. Both the manufacturer and the men using it would be accused of murder. Technically, it might not be murder if the deaths of the women were not intended, but the act would be closely akin to vehicular homicide through criminal negligence. Any Double Effect justification would have no hope of succeeding, because Double Effect requires that the unintended bads not be disproportionate to the intended goods. But a 5% annual chance of death is just not worth the contraceptive effect, especially when there are alternatives present. Indeed, even if the only alternative to using this nasty contraceptive were abstinence, which isn’t the case, surely total abstinence would typically be preferable to inducing a 5% annual chance of death (unless perhaps the woman were already suffering from a terminal disease).

Of course, my arguments are predicated on the assumption that killing an early embryo is morally on par with killing an adult. That's another argument.

Friday, June 16, 2017

Optimalism about necessity

There are many set-theoretic claims that are undecidable from the basic axioms of set theory. Plausibly, the truths of set theory hold of necessity. But it seems to be arbitrary which undecidable set-theoretic claims are true. And if we say that the claims are contingent, then it will be arbitrary which claims are contingent. We don’t want there to be any of the “arbitrary” in the realm of necessity. Or so I say. But can we find a working theory of necessity that eliminates the arbitrary?

Here are two that have a hope. The first is a variant on Leslie-Rescher optimalism. While Leslie and Rescher think that the best (narrowly logically) scenario must obtain, and hence endorse an optimalism about truth, we could instead affirm an optimalism about necessity:

  1. Among the collections of propositions, that collection of propositions that would make for the best collection of all the necessary truths is in fact the collection of all the necessary truths.

And just as it arguably follows from Leslie-Rescher optimalism that there is a God, since it is best that there be one, it arguably follows from this optimalism about necessity that there necessarily is a God, since it is best that there necessarily be a God. (By the way, when I once talked with Rescher about free will, he speculatively offered me something that might be close to optimalism about necessity.)

Would that solve the problem? Maybe: maybe the best possible—both practically and aesthetically—set theory is the one that holds of necessary truth.

I am not proposing this theory as a theory of what necessity is, but only of what is in fact necessary. Though, I suppose, one could take the theory to be a theory of what necessity is, too.

Alternately, we could have an optimalist theory about necessity that is theistic from the beginning:

  1. A maximally great being is the ground of all necessity.

And among the great-making properties of a maximally great being there are properties like “grounding a beautiful set theory”.

I suspect that (1) and (2) are equivalent.

Brute necessities and supervenience

There is something very unappealing about unexplained, i.e., brute, metaphysical necessities that are “arbitrary”. For instance, suppose that someone said that some constant in a law of nature had the precise value it does by metaphysical necessity. If that contant were 1 or π or something like that, we could maybe buy that. But if the constant couldn’t be put in any neat way, could not be derived from deeper metaphysical necessities, but just happened necessarily to be exactly 1.847192019... (in a natural unit system) for some infinite string of digits? Nah! It would be much more satisfactory to posit a theory on which that constant has that value contingently. “Arbitrariness” of this sort is evidence of contingency, though it is a hard question exactly why.

Here is an application of this epistemic principle. It seems very likely that any view on which mental properties supervene of metaphysical necessity on physical ones will involve brute metaphysical necessities that are “arbitrary”.

For instance, consider a continuum of physical arrangements, starting with a paradigmatic healthy adult human and ending with a rock of the same mass. The adult human has conscious mental properties. The rock does not. Given metaphysically necessary supervenience, there must be a necessary truth as to where on the continuum the transition from consciousness to lack of consciousness occurs or, if there is vagueness in the transition, then there must be a necessary truth as to how the physical continuum maps to a vagueness profile. But it is very likely that any such transition point will be “arbitrary” rather than “natural”.

Or consider this. The best naturalist views make mental properties depend on computational function. But now consider how to define the computational function of something, say of a device that has two numerical inputs and one numerical output. We might say that if 99.999% of the time when given two numbers the device produces the sum of the numbers, and there is no simple formula that gives a higher degree of fit, then the computational function of the device is addition. But just how often does the device need to produce the sum of the numbers to count as an adder? Will 99.99% suffice? What about 99.9%? The reliability cut-off in defining computational function seems entirely arbitrary.

It may be that there is some supervenience theory that doesn’t involve arbitrary maps, arbitrary cut-offs, etc. But I suspect we have no idea how such a theory would go. It’s just pie in the sky.

If supervenience theories appear to require “arbitrary” stuff, then it is reasonable to infer that any supervenience is metaphysically contingent—perhaps it is only nomic supervenience.

This line of argument is plausible, but to make it strong one would need to say more about the notion of the “arbitrary” that it involves.

Tuesday, June 13, 2017

Death, dignity and eternal life

One way to look at the difference between the deaths of humans and brute animals is to say that the death of a human typically deprives the human of goods of rational life that the brute animal is not deprived of. While it is indeed an important part of the evil of typical cases of death in humans that they are deprived of such goods, however, focusing on this leads to a difficulty seeing what is distinctively bad about the death of humans who are not deprived of such goods by death, say elderly humans who have already lost the distinctive goods of rational life.

Sure, one can say that the death of a human is the death of a being that normally has the goods of rational life. But it is unclear why the death of a being that normally has the goods of rational life but actually lacks them is worse than the death of a being that actually and normally lacks the goods of rational life.

(Of course, not everybody shares the normative view that there is something distinctively bad about the death of a human being even when the goods of rational life have already been lost. A significant number of people think that euthanasia in such cases is morally licit. But even among those who think that euthanasia in such cases is morally licit, I think many will still think that there is something particularly morally bad about killing such human beings against their clear prior wishes, and those may find something plausible about what I say below.)

How, then, do we explain the distinctive bad in the death of human beings, even ones that lack the distinctive goods of rational life? In the end, I think I would like to invoke human dignity here, but to a significant degree that’s just giving a name to the problem. Instead of invoking and trying to explain human dignity, I want to explore a different option, one that I think in the end will not succeed, but perhaps there is something in the vicinity that can.

Here is a hypothesis:

  • It is the nature of human beings to live forever and never die, but the nature of brute animals is to have a finite life.

If this is true, then death always constitutes a mutilation of the human being. It is what directly deprives the human being of the normative diachronic shape of its life. And killing a human mutilates the human being.

Objection 1: If a murderer didn’t kill her victim, the victim would still have died at some later point.

Response: The murderer is still the proximate cause of the victim’s not living forever. And such proximate causation matters. Suppose that my brother murdered Sally’s brother, and to avenge her brother, in true Hammurabic fashion, Sally seeks to kill me. When she finally comes upon me, I am already falling off a cliff. A moment before I would have hit the ground, Sally shoots and kills me. Sally has murdered me, a grave evil. She is the proximate cause of my death. And that matters, even though it would make little difference to my life if Sally hadn’t killed me.

Objection 2: Even if it is the nature of brute animals to have a finite life, it is not the nature of brute animals to die young. But it is not wrong to kill a brute animal when it is young, even though doing so mutilates the brute animal in much the same way that killing a human mutilates the human by causing her life to be finite if the hypothesis is true.

Response: Agreed: it does mutilate the brute animal to kill it when it is young. But to foreshorten the life of a human being from infinity to a finite amount is much worse—in a sense, infinitely worse—than to foreshorten the life of a brute animal from a longer finite length to a shorter finite length.

Objection 3: Christian faith holds that humans will be resurrected. Thus, killing a human being does not succeed in causing the human being to lose infinite life.

Response: Yes, but according to the hypothesis it is not only the nature of human beings to have an infinite future life but it is also the nature of human beings to have a death-free infinite future life.

Objection 4: Imagine an otherwise unremarkable shrub which has a very special nature: it is supposed to live forever, undying. Destroying this shrub would feel distinctively bad as compared to destroying an ordinary shrub, but still not bad in the same way that killing a human being is. Hence, reference to the normativeness of an infinite future life is not enough to explain the distinctive badness of killing humans.

Response: I think that this objection is decisive. Mere invocation of the normativeness of an infinite deathless life is not enough to solve the problem of the distinctive badness of human death. One still needs something like a story about the special dignity of human beings. But it might be that the hypothesis still helps: it multiplies the synchronic dignity of the human being by something like infinity. So less needs to be accomplished by the dignity part of the account.

Questions that interest me on norm institution and grounding

For any norm Nk that we institute, there is a prior norm Nk − 1 that specifies that when the acts of institution of Nk are performed, then Nk has such-and-such force.

On pain of a regress incompatible with the empirical facts of humanity’s finite past, any instituted norm must be grounded in an uninstituted norm. What are these uninstituted norms like?

Are they specific to our human nature or do they apply to all rational beings or are some of one sort and some of the other? Thinking about some issues in ethics, language, epistemology and decision theory has made me think that it is likely that at least some of the uninstituted norms are specific to human nature rather than to all rational beings.

Also, what types of norms are the uninstituted norms, and how do they relate to the types of norms that they ground? For instance, are instituted linguistic norms grounded in uninstituted linguistic norms or in some other kinds of norms, say moral ones?

For those of us who love theoretical simplicity, it would be a great joy if it turned out that all the uninstituted norms were of one type. If so, that type would be the moral. For, plausibly, no norm can ground an instituted norm that has greater force than itself, and moral norms have greater force than any others. In any case, either there are multiple types of uninstituted norms, or they are all moral. In the latter case all norms are moral or derive by institution from moral ones.

Note that the uninstituted norms need not be fundamental. There could be grounding relations between uninstituted norms. For instance, neither the moral norm not to torture the innocent nor the moral norm not to torture innocent blue-eyed people is instituted, but the latter (assuming it really counts as a norm, rather than an application or something like that) is clearly grounded in the former. If it turns out that, as I think, some uninstituted norms are specific to our human nature, it could still be the case that all the uninstituted norms that are specific to our human nature are grounded in a norm not specific to human nature—say, the universal norm to act in accordance with one’s nature.

Furthermore, there are norms that govern rational behavior as such and norms that do not govern rational behavior as such, such as the norm that two legs is good for humans and four legs is good for pigs. What grounding relationships are there between these? Are all the uninstituted norms of one sort or the other, or are they of both sorts?

There is material for interesting dissertations exploring questions like this. Of course, such questions have been explored in multiple contexts, but perhaps not quite in the above structure.

Monday, June 12, 2017

National self-defense

I think many of us have the intuition that it is permissible, indeed often morally required, for a decent country to defend itself against invaders when there is a reasonable hope of victory. The “decent” condition needs to be there: it was not permissible for Nazi Germany to defend itself against the Allies—they had the duty of surrendering. The “reasonable hope” condition needs to be there as well: if the consequence of fighting is nuclear attacks on all one’s cities, one should probably surrender.

If the Ruritanians invade Elbonia, a decent country, with the goal of killing all Elbonians, then at least if there is a reasonable chance of repelling the invaders, it is permissible for the Elbonians to defend themselves with lethal force. Only slightly less clearly, if the Ruritanians intend to cause no physical harm to Elbonians if the Elbonians surrender, but will wipe out Elbonian culture—they will forbid the use of the Elbonian language, ban the national pastime of painting intricate landscapes on pigeon feathers, and so on—then lethal self-defense is still likely to be permissible.

But what if the Ruritanians invade Elbonia simply in order to take away Elbonia’s sovereignty, so that if the Elbonians surrender, they lose sovereignty but nothing else? The Ruritanians won’t kill anyone, won’t disposs any individuals or corporations of their property, won’t interfere with any aspects of Elbonian culture, won’t conscript Elbonians into their military (the Ruritanians have an all-vounteer army), will not harm the Elbonian economical, educational and healthcare systems, etc. But they will take over national sovereignty. Moreover, the Elbonians are confident of this because the Ruritanians have a centuries-long record of expanding their empire on such terms, and many neighboring countries have lost their sovereignty but had no other losses. Furthermore, it is the Elbonians alone that are at issue. For geographic reasons, the Ruritanians are unable to expand any further, and so Elbonians in defending themselves cannot say that they doing so to protect other countries. And there are no other countries in the world capable of imperialism.

It is only permissible to wage war for the sake of a good that is proportionate to the great evils of war, after all. The question here is this: Is maintenance of national sovereignty worth the deaths—both Elbonian and Ruritanian—and manifold other harms of war?

I don’t know. A state is a valuable form of human community. The destruction of a state is prima facie a bad thing. But if the goods of culture and ordinary life are maintained, it does not seem to be a great bad. Suppose that there was no invasion, but the Elbonians voluntarily voted to join the Ruritanian Empire. Then while there would be some bad in the loss of the Elbonian state, it need not be a tragedy, and on balance it could even be for the good. It is, of course, gravely wrong for the Ruritanians to bludgeon the Elbonians into joining their Empire. But the good of sovereignty just might not be great enough for the Ruritanians to have a moral justification to resist to the death.

If this is right, then sometimes the mere fact that a war is one of just national self-defense is not enough to justify fighting. Do such perfectly clean cases occur? I doubt it: imperialist countries aren’t likely to be as nice as my hypothetical Ruritanians. However, one might have cases that are slightly less clean, where the expected damage to local culture is likely to be small relative to the expected harms of a protracted war, even if that war can be won by the defenders. Moreover, in real-life cases one needs to consider the value of policies that discourage future such attacks by this and other imperialist countries. If all small countries surrendered as soon as there was a Ruritanian-style invasion, then we could expect Ruritanians and others to mount a lot more invasions, which could indeed be harmful.

So our initial intuition about the permissibility of national self-defense is, I think, roughly right, though only roughly.

Thursday, June 1, 2017


Some properties that a thing has partially or wholly explain other properties the thing has or doesn’t have. For instance, my having a body partially explains my being in Waco and wholly explains my having a body or horns. Some properties that a thing has do not explain, even partially, what other properties the thing has or doesn’t have. Call such properties “explanatorily fundamental”.

So, here’s a theory. The primary essential properties of a thing are the explanatorily fundamental properties of the thing. The primary essential properties are both essential in the medieval explanatory sense and the contemporary modal sense (properties a thing cannot exist without).

What about the case of Christ, who is essentially divine and essentially human, and yet prior (in the order of explanation) to the incarnation was not human? Here’s what we could say: Divinity is the one and only primary essential property of Christ. But humanity is a secondary essential property. A secondary essential property of a thing is the sort of property that (a) is not a primary essential property of that thing, but (b) normally is the primary essential property of its possessor. In the case of Christ, his divinity is explanatorily prior to his humanity, but normally a thing’s humanity does not have any property of that thing explanatorily prior to it.

Tuesday, May 30, 2017

Drawers for small electronic components

With various ongoing projects, I've acquired a lot of small electronic components in little baggies. To store them, I designed a set of customizable plastic drawers that I could run off on my 3D printer. I am stingy, so I tried to reduce the amount of plastic that goes into them by making dividers thin and a grid-like pattern for the walls.

Location, causation and transsubstantiation

Here’s a fun thought experiment. By a miracle (say) I am sitting in my armchair in Waco but my causal interaction with my environment at the boundaries of my body would be as if I were in Paris. There is a region of space in Paris shaped like my body. When a photon hits the boundary of that region, it causally interacts with me as if I were in Paris: I have the causal power to act at a distance to reflect Parisian photons as if I were in that region in Paris. Alternately, that photon might be absorbed by me: I have the causal power to absorb Parisian photons. As a result, it looks to Parisians like I am in Paris, and as I look around, it looks to me like Paris is all around me. The same is true for other interactions. When my vocal cords vibrate, instead of causing pressure changes in Texan air, they cause pressure changes in chilly France. As I walk, the region of space shaped like my body in Paris that is the locus of my interaction with Parisians moves in the usual way that bodies move.

Furthermore, my body does not interact with the environment in Waco at all. Wacoan photons aimed at my body go right through it and so I am invisible. In fact, not just photons do that: you could walk right through my body in Waco without noticing. My body is unaffected by Texan gravity. It is simply suspended over my sofa. As I wave my hand, my hand does in fact wave in Texas, but does not cause any movement of the air in Texas—but in Paris, the region of space in which I interact with the Parisians changes through the wave, and the air moves as a result. When I eat, it is by means of Parisian food particles that come to be incorporated into my Wacoan body.

To me, to Wacoans and to Parisians it looks in all respects like I am in Paris. But I am in Waco.

Or am I? There is a view on which the causal facts that I’ve described imply that I am in Paris, namely the view that spatial relationships reduce to causal relationships. It is an attractive view to those like me who like reductions.

But this attractive view threatens to be heretical. Christ’s body is here on earth in the Eucharist, as well as in heaven in the more normal way for a body to be. But while the body is surely visible in heaven and interacts with Mary and any other embodied persons in heaven, it does not interact physically with anything on earth. Granted, there is spiritual interaction: Christ’s presence in the Eucharist is a means of grace to recipients. But that probably isn’t the sort of interaction that would ground spatial location.

There is, however, a way to modify the causal reduction of location that handles the case of the Eucharist. Actual causal interactions do not seem to be enough to ground location. The reduction very likely needs needs dispositional causal interactions that typically ground causal counterfactuals like:

  1. If Parisians were to shine a flashlight into that dark alley, they’d see me.

However, dispositions can be masked. For instance, sugar is still soluble even if God has promised to miraculously keep it from dissolving when it is placed in water. In such a case, the sugar still has the disposition to dissolve in water, but fails to ground the counterfactual:

  1. The lump would be dissolved were it placed in water.

We might, thus, suppose that when the Mass is being celebrated in Waco, Christ comes to have the dispositional causal properties that would ordinarily be contitutive of his being present in Waco, such as the disposition to reflect Texan photons, and so on. But by miracle, all these dispositions are masked and do not result in actual causal interaction. The unmasked dispositions are those corresponding to spiritual interaction.

Here’s an interesting lesson. The kind of causal-reductive view of location that I’ve just considered seems to be one of the least transsubstantiation-congenial views of location. But, nonetheless, the transsubstantiation can still be made sense of on that view when the view is refined. This gives us evidence that transsubstantiation makes sense.

And we can now go back to the story of my being in Waco while interacting in Paris. The story was underspecified. I didn’t say whether I have the dispositions that go with being in Waco. If I do, these dispositions are being miraculously masked. But they may be enough to make me count as being in Waco. So on the story as I’ve told it, I might actually be both in Waco and in Paris.

Final question: Can external temporal location be similarly causally grounded? (Cf. this interesting paper.)

Thursday, May 25, 2017

Can destruction be good for something?

It is good for a mouse to occupy a limited region of space: if a mouse were cat-sized, it would be incapable of excellent engagement in many of its characteristic behaviors (scurrying around in narrow passages). If time is relevantly like space, we would expect that there be things for which it is good that they occupy a limited interval of time--i.e., it is good for them to die, or at least good for them to die in a particular way. (It is good for a mouse to be spatially bounded--but only certain kinds of spatial bounds, those delimited by healthy skin and fur, are good for the mouse.)

One category of things whose destruction is a part of their flourishing is things whose purpose is to give rise to something else. For instance, sperm and egg are destroyed in giving rise to a zygote, and that it is their flourishing to be destroyed in this manner. But that's not the only category. It may be a part of the flourishing of a skin cell that it perish in order to make way for a newer skin cell. Both of these categories are subsumed in the category of things directed at the good of something other than themselves.

But I think human beings are not like that.

Tuesday, May 23, 2017

Natural Law decision theory

One of the things I’ve learned from the St Petersburg Paradox and Pascal’s Wager is that we are rationally required to have attitudes to risk that significantly discount tiny chances of benefits, rather than to maximize expected utility. This requirement is rational because failure to have such attitudes to risk makes one subject to two-person diachronic Dutch Books. But it is also clearly irrational to significantly discount large chances of benefits.

But where are the lines to be drawn? Maybe it’s not worth enduring an hour of sitting on an uncomfortable chair for a 1/101000 chance of any finite length of bliss, but enduring an hour of sitting in such a chair for a 45% chance of 1000 years of bliss is worthwhile. As long as we thought the decisions were to be made on the basis of expected utility, we could have said that the lines are to be non-arbitrarily drawn by multiplying probabilities and utilities. But that fails.

It is possible, I suppose, that there is a metaphysically necessary principle of rationality that says where the line of the negligibility of chances is to be drawn. Perhaps an hour in the uncomfortable chair for a 1/101000 chance of a finite benefit cannot possibly be worthwhile, but for a 1/106 chance of a large enough finite benefit it is worth it, and there is a cut-off precisely at π ⋅ 10−9. But the existence of any such a metaphysically necessary cut-off is just as implausible as it is to think that the constants in the laws of nature are metaphysically necessary.

(Vagueness is of no help. For even if the cut-off is vague, the shape—vague or exact—of the vagueness profile of the cut-off will still look metaphysically contingent.)

One could leave it to the individual. Perhaps rationality requires each individual to have a cut-off but where the cut-off lies is up to the individual. But rationality also places constraints on that cut-off: the person who is unwilling to sit in an uncomfortable chair for an hour for a 45% chance of 1000 years of bliss is irrational. (I deliberately made it 45%. The cut-off isn’t at 1/2, which would be satisfyingly non-arbitrary.) And where the constraints on the cut-off lie is itself something to be explained, and again it is implausible that it is metaphysically necessary.

In morals, we also have similar cut-off phenomena. It is morally wrong to put someone in prison for life for stealing an ordinary book, while a week of community service is morally permissible. Whence the cut-off? The problem in both cases comes from two features of the situation:

  1. We have a parameter that seems to have a normative force independent of our minds.

  2. That parameter appears to be contingent.

Utilitarianism provides an elegant answer, but no analog of that answer seems to apply in the rationality/risk case. Kantianism is out of luck. Divine command theory provides an answer, but one whose analogue in the case of rationality is quite implausible: it is irrational to be unwilling to sit in the uncomfortable chair for the 45% chance of the great benefit, rather than forbidden by God.

Natural Law, on the other hand, provides a framework for both the moral and the rational cases by saying that the parameter necessarily comes from our nature. Our nature is independent of our minds, and hence we do justice to (1). But while it is presumably not a contingent fact that we have the nature we do, it is a contingent fact that the persons that inhabit the world have the natures they do. Humans couldn’t have these normative risk or moral parameters other than they do, but there could easily have existed non-humans somewhat similar to us who did. The explanation is parallel to the Kripkean explanation of the seeming arbitrariness of water having two hydrogen atoms. Water couldn’t have had a different number of hydrogen atoms, but something similar to water could have had.

More and more, I think something like Natural Law is a powerful framework in normative areas outside of what is normally construe to be moral theory: in decision theory and epistemology. (I hedge with the “normally construe”, because I happen to think that both decision theory and epistemology are branches of moral theory.)

Wednesday, May 17, 2017

Could God be divinity?

Here's a plausible thesis:

  1. If it is of x's essence to be F, then Fness is prior to x.
This thesis yields a fairly standard argument against the version of divine simplicity which identifies God with the property of divinity. For if God is divinity, then divinity is prior to divinity by (1), which is absurd.

But (1) is false. For, surely:

  1. It is of a property's essence to be a property.
But propertyhood is a property, so it is of propertyhood's essence to be a property, and so propertyhood is prior to propertyhood if (1) is true, which is absurd. So, given (2), we need to reject (1), and this argument against the God=divinity version of divine simplicity fails.

What else might properties do?

Suppose that we think of properties as the things that fulfill some functional roles: they are had in common by things that are alike, they correspond to fundamental predicates, etc. Then there is no reason to think that these functional roles are the only things properties do. It is prima facie compatible with fulfilling such functional roles that a property do many other things: it might occupy space, sparkle, eat or think.

Can we produce arguments that the things that fulfill the functional roles that properties are defined by cannot occupy space, sparkle, eat or think? It is difficult to do so. What is it about properties that rules out such activity?

Here's one candidate: necessity. The functional roles properties satisfy require properties to exist necessarily. But all things that occupy space are contingent. And all things that sparkle or eat also occupy space. So no property occupies space, sparkles or eats. (Yes, this has nothing to say about thinking.) Yeah, but first of all it's controversial that all properties are necessary. Many trope theorists think that typical tropes are both contingent and properties. Moreover, it may be that my thisness is a property and yet as contingent as I am. Second, it is unclear that everything that occupies space has to be contingent. One might argue as follows: surely, for any possible entity x, it could be that all space is vacant of x. But it does not follow that everything that occupies space has to be contingent. For we still have the epistemic possibility of a necessary being contingently occupying a region space. Christians, for instance, believe that the Second Person of the Trinity contingently occupied some space in the Holy Land in the first century--admittedly, did not occupy it qua God, but qua human, yet nonetheless did occupy it--and yet the standard view is that God is a necessary being. (Also, God is said to be omnipresent; but we can say that omnipresence isn't "occupation" of space, or that all-space isn't a region of space.)

So the modal argument isn't satisfactory. We still haven't ruled out a property's occupying space, sparkling or eating, much less thinking. In general, I think it's going to be really hard to find an argument to rule that out.

Here's another candidate: abstractness. Properties are abstract, and abstracta can't occupy space, sparkle, eat or think. But the difficulty is giving an account of abstracta that lets us be confident both that properties are abstract and that abstract things can't engage in such activities. That's hard. We could, for instance, define abstract things as those that do not stand in spatiotemporal relations. That would rule out occupying space, sparkling or eating--but the question whether all properties are abstracta would now be as difficult as the question whether a property can occupy space. Likewise, we could define abstract things as those that do not stand in causal relations, which would rule out sparkling, eating and thinking, but of course anybody who is open to the possibility that properties can do these activities will be open to properties standing in causal relations. Or we could define abstractness by ostension: abstract things are things like properties, propositions, numbers, etc. Now it's clear that properties are abstracta, but we are no further ahead on the occupying space, sparkling, eating or thinking front--unless perhaps we can make some kind of an inductive argument that the other kinds of abstracta can't do these things, so neither can properties. But whether propositions or numbers can do these things is, I think, just as problematic a question as whether properties can.

All in all, here's what I think: If we think of the Xs (properties, propositions, numbers, etc.) as things that fulfill some functional roles, it's going to be super-hard to rule out the possibility that some or all Xs do things other than fulfilling these functional roles.

For more related discussion, see this old contest.

Tuesday, May 16, 2017

Pascal's Wager and the bird-in-the-hand principle

My thinking about the St Petersburg Paradox has forced me to reject this Archimedean axiom (not the one in the famous representation theorem):

  1. For any finite utility U and non-zero probability ϵ > 0, there is a finite utility V such that a gamble that offers a probability ϵ of getting V is always better than a certainty of U.
Roughly speaking, one must reject (1) on pain of being subject to a two-player Dutch Book. But rejecting (1) is equivalent to affirming:
  1. There is a finite utility U and a non-zero probability ϵ > 0, such that no gamble that offers a probability ϵ of getting some finite benefit is better than certainty of U.
With some plausible additional assumptions (namely, transitivity, and that the same non-zero probability of a greater good is better than a non-zero probability of a lesser one), we get this bird-in-the-hand principle:
  1. There is a finite utility U and a non-zero probability ϵ > 0, such that for all finite utilities V, the certainty of U is better than a probability ϵ of V.
Now, Pascal's Wager, as it is frequently presented, says that:
  1. Any finite price is worth paying for any non-zero probability of any infinite payoff.
By itself, this doesn't directly violate the bird-in-the-hand principle, since in (3), I said that V was finite. But (4) is implausible given (3). Consider, for instance, this argument. By (3), there is a finite utility U and a non-zero probability ϵ > 0 such that U is better than an ϵ chance at N days of bliss for every finite N. A plausible limiting case argument suggests that then U is at least as good as an ϵ chance at an infinite number of days of bliss, contrary to (4)--moreover, then U+1 will be better than an ϵ chance at an infinite number of days of bliss. Furthermore, in light of the fact that standard representation theorem approaches to maximizing expected utility don't apply to infinite payoffs, the natural way to argue for (4) is to work with large finite payoffs and apply domination (Pascal hints at that: he gives the example of a gamble where you can gain "three lifetimes" and says that eternal life is better)--but along the way one will violate the bird-in-the-hand principle.

This doesn't, however, destroy Pascal's Wager. But it does render the situation more messy. If the probability ϵ of the truth of Christianity is too small relative to the utility U lost by becoming a Christian, then the bird-in-the-hand principle will prohibit the Pascalian gamble. But maybe one can argue that little if anything is lost by becoming a Christian even if Christianity is false--the Christian life has great internal rewards--and the evidence for Christianity makes the probability of the truth of Christianity not be so small that the bird-in-the-hand principle would apply. However, people's judgments as to what ϵ and U satisfy (2) will differ.

Pleasantly, too, the bird-in-the-hand principle gives an out from Pascal's Mugger.

Friday, May 12, 2017

More on St Petersburg

I’ve been thinking about what assumptions generate the St Petersburg paradox. As stated, the paradox depends on the assumption that we should maximize expected utility, an assumption that will be rejected by those who think risk aversion is rational.

But one can run the St Petersburg paradox without expected utility maximization, and in a context compatible with risk aversion. Suppose finite utilities can be represented by finite real numbers. Assume also:

  1. Domination: If a betting portfolio B is guaranteed to produce at least as good an outcome as A no matter what, then B is at least as good as A.

  2. Archimedeanism: For any finite utility U and non-zero probability ϵ > 0, there is a finite utility V such that a gamble that offers a probability ϵ of getting V is always better than a certainty of U.

  3. Transitivity: If C is better than B and B is at least as good as A, then C is better than A.

(Note: For theistic reasons, one might worry about Construction when the Vi are very negative, but we can restrict Construction to positive finite utilities if we add the assumption in Archimedeanism that V can always be taken to be positive.)

For, given these assumptions, one can generate a gambling scenario that has only finite utilities but that is better than the certainty of any finite utility. Proceed as follows. For each positive integer n, let Vn be any finite utility such that probability 1/2n of Vn is better than certainty of n units of utility (this uses Archimedeanism; the apparent use of the Axiom of Choice can be eliminated by using the other axioms, I think) and Vn ≥ Vn − 1 if n > 1. Toss a fair coin until you get heads. Let your payoff be Vn if it took n tosses to get to heads.

Fix any finite utility U. Let n be a positive integer such that U < n. Then the gambling scenario offers a probability of 1/2n of getting at least Vn, so by Domination, Transitivity and the choice of Vn, it is better than U.

And the paradoxes in this post apply in this case, too.

If we have expected utility maximization, we can take Vn = 2n and get the classic St Petersburg paradox.

Given the plausibility of Domination and Transitivity, and the paradoxes here, it looks like the thing to reject is Archimedeanism. And that rejection requires holding that there is a probability ϵ so small and finite utility U so large that no finite benefit with that probability can outweigh U.

Wednesday, May 10, 2017

Teleology and the direction of time

It would be depressing to think that one will never swim as fast as one is swimming today. But it would uplifting to think that that one has never swum as fast as one is swimming today.

I used to think the direction of time was defined by the predominant direction of causation. That may be the case, but if one takes humanistic cases like the above as central, one might think that perhaps the predominant direction of teleology is a better way to define the direction of time. Of course, telê are there to be achieved, and so the direction of teleology needs to fit well with the direction of causation, at least in the case of things that concern us. Moreover, there is some reason to think that teleology is behind all causation—causation aims at an effect.

Certamen machine

My kids are involved in a Classics oriented quiz game called Certamen at school. These involve teams and buttons and a machine that determines the order in which buttons were pressed. Surprisingly, these machines seem to cost a ridiculous $500 and up, despite seeming to be quite a simple thing: 12 buttons, display which order the buttons are pressed in, lock out fellow team members once one member of a team has pressed it.

So I offered my kids' school to design and build one for them as a fun summer project for me and an opportunity for my kids to learn to solder. I ordered about $60 of parts, mostly from Aliexpress, centered on an Arduino Mega (I haven't done any Arduino-based programming, but I've used the Arduino toolchain with an ESP8266 before). The parts have started to come in, including the Mega, so I've started writing some code and prototyping. According to my oscilloscope, the quick and dirty polling code I have gets a worst-case detection speed of 0.1 milliseconds, which should be good enough for a quiz game. (I continue to be grateful to the Austin guy who gave had an oscilloscope for sale for $50 on Craigslist, but when I wanted to buy it, gave it to me for free because he liked the sorts of things I was going to use it for.)

I am a bit nervous about signal problems over the three five-meter CAT6 cables (the most expensive single parts of the project) from the control box to the buttons, but I ordered some capacitors for noise suppression, and once my RJ45 jacks come in, I can do some testing.