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.