Treatment and enhancement

Let's grant that my ability to use my hands is normal. Suppose a world-class violin maker loses the little finger on her non-dominant hand. This slightly impedes her ability to use her hands. But the incredible amount of gross and fine motor skills that a top violin maker needs to have exceed my own merely normal skills to such a degree that she is going to do better in any non-gerrymandered manual activity (wiggling ten fingers is gerrymandered!) than I.

But my own abilities are normal. So if her abilities exceed mine, how can hers fail to be normal? Yet it seems clear that to the extent that reattachment of the finger would be treatment rather than enhancement, even though it takes someone whose abilities are above normal, and raises her even higher above what is normal.

So we should not define the kind of abnormalcy or disability that calls for medical treatment in terms of a below-normal degree of overall function. For overall function is affected by compensation—the violin-maker's manual skills compensate for her genuine loss. Rather, we must look at something like local function, the function of a particular bodily subsystem. And here it is clear that when she lost her finger, she lost the full use of a subsystem. Disability is the loss of the full functioning of a subsystem, not necessarily of the whole.

But now here we have an interesting thing. An operation that destroys the functioning of a bodily subsystem that otherwise would have functioned properly, even if it does not adversely affect—or maybe even enhances—overall functioning of the person, nonetheless is producing a disability. Now a physician should be a healer. Sometimes to heal one must destroy a subsystem—amputating a gangrenous limb is an example. Even in those cases, the destruction is a moral reason for the physician not to do the operation, though a reason that may well be outweighed (as it is in the gangrenous limb case) by the need for healing.

But this is far more problematic when the destruction of a subsystem is not done in order to heal the system as a whole, even if in some way the person as a whole benefits. Suppose Sam has a job that consumes all his waking hours and involves no contact with people, and his normal interest in social relationships makes him less good at his job. Moreover, suppose the sad economic realities are such that he has no hope of another job. He is going to live a life of loneliness and unfulfilled sociality. Should we give him drugs that would destroy his sociality? Such drugs would improve his life, after all. Yes: but they would do so by destroying a subsystem. And their positive effect would not be a form of healing—at most a form of enhancement at adaptation to unfortunate circumstances. So there is strong—I think conclusive—moral reason why a physician should not give Sam the drugs.

And the same line of thought applies in a much more controversial, because more realistic, case: sterilization.

HHS contraception mandate

I am one of the signatories of an amicus brief by Catholic theologians and ethicists in the Gilardi case against the HHS contraception mandate. The DC Circuit Court recently ruled against the HHS in this case. The main line of thought in our brief was that a Catholic employer's providing coverage for contraception makes the employer cooperate in the employee's use of contraception. Now, Catholic moral thought not only takes (marital) contraception to be wrong, but also takes cooperation in someone else's sin to be morally problematic. Whether the cooperation is not just problematic but wrong depends on questions about the degree and kind of cooperation involved.

Reflecting on these issues makes me think there is a second really crucial thing going on, besides making employers complicit in employees' sin (and we touch on this in the brief, though I think it can be developed). One of the reasons for the HHS mandate is precisely to encourage women to use contraception (this is certainly not denied). But this means that the employer is made complicit in what the employer conscientiously takes to be the government's morally wrongful promotion of wrongdoing. And this cooperation is even closer, and thus far even more morally problematic, than cooperation with the employee's use of contraception. For the employer here acts as the government's instrument in its policy of promotion of contraception. Note that promotion does not require success: in this case, governmental promotion of contraception occurs whether or not any employees actually use the contraception.

Invariance of Popper functions under symmetries

Popper functions are primitive finitely additive conditional probabilities—i.e., P(A|B) is the fundamental quantity, and P(A) is the defined quantity. Now, in some situations we have expect our probabilities to be invariant under some group G of symmetries. For instance, if we're shooting an idealized dart at a circular target and aiming at the center, our idealized method of shooting might be rotationally invariant so that the probability of hitting some region A will be the same as the probability of hitting rA where r is some rotation about the center. (In real life, this need not be so. For instance, in archery, one might have bigger error in the vertical direction than in the horizontal direction, or vice versa, depending on one's skills.) We might also think that similarly there is invariance under reflections about lines through the center.

With unconditional probabilities, we can just formulate these invariance condition as: P(gA)=P(A) for all symmetries g in G and all (measurable) regions A. But how to formulate this for conditional probabilities?

There are two natural definitions:

• P is weakly invariant if and only if P(A|B)=P(gA|gB) for all A, B and g.
• P is strongly invariant if and only if (a) whenever A∪gA⊆B, we have P(A|B)=P(gA|B) and (b) whenever A⊆B∩gB, we have P(A|B)=P(A|gB).

Fact: Conditions (a) and (b) in the definition of strong invariance are equivalent.

Personally, I find weak invariance to be the more intuitive condition, though strong invariance has some intuitive pull. It's an interesting question how the two are related.

One interesting special case is where G is generated by symmetries of finite order. A symmetry g has finite order provided that there is a finite number n such that gⁿ is the identity—i.e., applying it n times gets you back to where you started. For instance, rotation by an angle of 360/n degrees where n is a non-zero integer has finite order—you do this |n| times and you're back where you started. And all reflections have finite order.
Fact: If every symmetry in G can be written as a combination of symmetries of finite order, then weak invariance implies strong invariance.

For instance, while most rotations in the plane don't have finite order (only ones by a rational-number angle do), any rotation in the plane can be generated by combining two reflections. Thus, in our circular target case, where we are looking at invariance under reflections and rotations, weak invariance implies strong invariance.

Armstrong in this paper claims that weak invariance implies strong invariance in general (Prop. 1.3). Unfortunately Armstrong's proof is incomplete. And well it might be. For yesterday I came up with a super-simple case showing:
Fact: Weak invariance does not imply strong invariance.

It would be interesting to characterize cases where weak invariance does imply strong invariance. Two general cases are known to me. One is where the symmetries are generated by symmetries of finite order. The second is where the conditional probabilities are defined by the ratio formula starting with a regular probability (one that assigns non-zero probability to each empty set).

Error theory

Error theorists in ethics think that claims like "Murder is wrong" are all false. But this seems to me to be a self-undermining position. For if there were no true moral claims, our moral predicates would have no meaning. They would simply be nonsense.

The irrationality of undue scepticism

One might think that sceptical tendencies are intellectually safe. It's clearly irrational for one's level of belief to exceed one's level of evidence. But it does not seem harmful to be more cautious, and hence to make one's level of belief be less than one's level of evidence.

However, if one's levels of belief are classical consistent probabilities, then when one's degree of belief in p is lower than what the evidence yields, one's degree of belief in not-p will be higher than what the evidence yields. And that is surely bad.

One might think it's not so bad as long as one's degree of belief in not-p stays well below 1/2. After all, in that case, one isn't believing not-p, and hence none of one's beliefs is irrational. Yes, but such errors are apt to add up. Suppose there are twelve independent propositions p₁,...,p₁₂ that one believes at the 0.75 level, instead of the 0.95 that the evidence supports. Then one's degree of belief in their conjunction will be (0.75)¹²=0.03, instead of the (0.95)¹²=0.54 that the evidence yields. And hence the sceptic will believe the negation of the conjunction of the 12 propositions to degree 0.97, instead of having a level of belief in the conjunction of only 0.46, as per the evidence. Excess of caution leads to excessive credulity.

That's true on classical sharp numerical probabilities. The sceptic may better off on interval-valued probabilities. But even so, depending on how one interprets the intervals, there may be a similar kind of criticism available.

The above underlines something I heard Bob Brandom say: one needs to have a reason to be a sceptic about something.

Decision theory and compatibilism

Here's a decision theoretic picture of how to make the decision between A and B. First, gain as much knowledge K as is reasonably possible about the laws and present conditions in the universe. The more information, the better our decision is likely to be (cf. Good's Theorem). Then calculate the conditional expected utility of the future given A with K, and do the same for B. Then do the action where the conditional expected utility is higher.

Let U(A,K) and U(B,K) be the two conditional expected utilities. (Note: I mean this to be neutral between causal and epistemic decision theories, but if I have to commit to one, it'll be causal.) We want to make our decision on U(A,K) and U(B,K) for the most inclusive K we can.

Now imagine that we could ask an angel for any piece of information I about the present and the laws (e.g., by asking "How many hairs do I have on my head?"), and then form a new set of information K₂ including I on which to calculate U(A,K₂) and U(B,K₂). Then we should ask for as much information as we can. But now here is a problem: if determinism holds, then once we get enough information, K_n will entail which of A and B happens. Let's say it entails A. Then U(B,K_n) is undefined. This informs one that one will do A, but makes decision-making impossible.

So how much cost-free information should we get from the angel? If we ask for so much that it entails what we're going to do, we won't be able to decide. If our choice is indeterministic, we have a simple principled answer: Ask for everything about the laws and the present. But if our choice is determined, we must stop short of full information. But where?

Perhaps we ask for full information about the laws and about everything outside our minds. But the contents of our minds are often highly relevant to our decisions. For instance, if we leave out in our decision-making the content of our minds, we won't have information on what we like and what we dislike. And in some decisions, such as when deciding whether to see a psychologist, information about our character is crucial.

Here's another interesting question. Our angel knows all about the present and the laws. It seems that he's got all the information we want to have about how we should act. So we just ask: Given all you know, does A or does B maximize utility? And he can't answer this question. For given all that he knows, only one of the two conditional utility values makes sense.

Of course, a similar problem comes up in asking an omniscient being in a case where our choices are indeterministic. We might think that we can make a better decision if that being tells about the future. ("What will AAPL close at tomorrow?") But there is a bright line that can be drawn. We cannot use in our decision any information that depends on things that depend on our decision, since then we have a vicious loop in the order of explanation. So an omniscient being metaphysically cannot give us information that essentially depends on our decisions. (In particular, if we're deciding whether to buy AAPL stock, he can't tell us what it will close at tomorrow, unless he has a commitment to make it close at that no matter what we do, since without such a commitment, what it will close at tomorrow depends—in a complex and stochastic and perhaps chaotic way—on whether we buy the stock today.)

Let me end with this curious question:

• If you have a character that determines you never to ask for help, isn't that a reason to get professional help?

I think this is an interesting question both for compatibilists and for incompatibilists.

The vagueness argument against restricted compositionality

Lewis and Sider have argued that if restricted compositionality is true—some but not all pluralities of two or more objects compose a whole—then there will be cases where it's vague how many objects there are. For instance, imagine two universes, A and B, each with the same finite set of n particles with the same intrinsic properties. But in A, the particles are neatly arranged into galaxies, trees, tables, buildings, etc. And in B there is just a blooming buzzing confusion. If restricted compositionality holds, then, assuming there are no immaterial objects, universe B has exactly n or at most n+1 objects—it's just too messy to have any cases of composition, except perhaps for the universe as a whole (that's why it might be n+1 rather than n). But A is much like our universe, and so we would expect lots of cases of composition, and hence the number of objects will be a lot more than n+1, say n+m for some large m. However, we can now imagine a continuous sequence of universes ranging from A to B, differing continuously in how the particles are arranged. As we move that continuous sequence, the number of objects will have to change from no more than n+m to n+1. But it is incredible that the object count should sharply change due to a very tiny shift in particle positions. Instead, the object count will at times be vague. But how many objects there are is a matter of which sentences using universal quantification, conjunction, negation and identity are true. But quantification, conjunction, negation and identity are not vague. So we have vagueness where we cannot have vagueness.

There may be some technical problems with the argument as I formulated it, given the assumption of no immaterial objects. Maybe we can't do without immaterial entities like God or numbers. One could reformulate the argument to restrict the counting to material entities, but "material" might actually be a vague term. Perhaps the best thing to do is to assume that these universes have no immaterial contingent entities, and then just count contingent entities. Contingency shouldn't be a vague matter, after all. The Aristotelian may balk at this. For it may well be that a necessary condition for a bunch of material entities to compose a whole that they have a form, and forms are immaterial but contingent. Maybe, though, "form" is not vague, and so we can just count the contingent non-forms.

But talking of forms suggests a more serious difficulty. If there are Aristotelian forms, then how many material objects there are may well not supervene on how material objects are spatiotemporally arranged and what intrinsic properties they have. For objects to come to compose a whole, there must come into existence a form. There is nothing absurd about there being sharp laws of nature specifying under which precise conditions a form comes into existence. There is no need for the laws of nature to be continuous (and the possibility of fundamental discreteness is empirically still open). Or perhaps God decides on a case-by-case basis whether to create a form. Then there is no vagueness as to how many material objects there are: the number of material objects equals the number of forms of material objects that in fact inform some matter (the souls of the resurrected are forms of material objects but temporarily fail to inform any matter). Of course in transitional cases we won't have much confidence whether some objects compose a whole, but that's just because we are unable to see forms except through their normal effects.

More on global nuclear war

The most surprising and important event of the second half of the 20th century was the nonoccurrence of a global nuclear war. In an earlier post, I suggested that the probability of such a war was fairly high given naturalism and fairly low given theism, and hence the nonoccurrence of such a war is evidence for theism. I want to add one more thing to that line of thought: the nonoccurrence of a global nuclear war was probably the most prayed-for event of the second half of the 20th century. All the prayers for world peace were first and foremost prayers for peace between East and West, prayers that there be no global nuclear war. And there is peace between East and West, and there was no global nuclear war.

Two legs, four legs and the Incarnation

In this picture from 30 Rock's "Brooklyn Without Limits" episode, Kenneth has only two legs and yet Kenneth has four legs. This sounds like a contradiction, but of course it is not--we can see that it's not.

How shall we resolve the contradiction? Perhaps: Kenneth has two human legs and four table legs. But that suggests that Kenneth has six legs, and that doesn't seem right to say. Maybe we can say that his human legs are also table legs, so he has only four legs: two of them doing double-duty for table legs and human legs, and two of them doing double-duty for table legs and human arms. Maybe. But even the statement "Kenneth has four legs" seems wrong or at least misleading without qualification.

Much better to qualify with a qua: Kenneth qua human has only two legs. Kenneth qua table has four legs.

This should remind us of one of the standard solutions to apparently contradictory talk of Christ incarnate. Christ is eternal. Christ is conceived in time. Christ has boundless knowledge. Christ's knowledge is bounded. And so on. The solution is to say things like: Christ qua God is eternal and has boundless knowledge. Christ qua human is conceived in time and has bounded knowledge--and has two legs.

The naturalness of qua talk in the case of Kenneth should make us less suspicious of the incarnational case.

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For the small handful of die-hard PalmOS users, I've just released all my old shareware PalmOS apps for free.

A cheap shot against Lewis on free will?

David Lewis thinks that even if determinism holds, we have the ability to act in ways other than what is entailed by the pre-human state of the universe, P, and the laws, L. Were we to have so acted, a "small miracle" would have happened. The actual world's law of nature would no longer have held. Perhaps in that world there wouldn't be enough laws for determinism or there would have been a new law with exception clauses. Here is a cheap shot:

• On this theory, billions and billions of people daily had the ability to to act such that were they to act so, the laws of nature would have been insufficient for determinism or would have had exception clauses. Why did none of them ever exercise that ability?

Is this just a cheap shot? Maybe. The best answer I see to it is:

• Look: this is all hypothetical. We don't actually live in a deterministic world. There will be deterministic worlds with neat exceptionless laws but there will be many more nearby-to-them worlds with many such exceptions. purposes, the world without exceptions. But for the purposes of considering the compatibility of free will with determinism, we posited this unlikely world.

This is a decent answer. But it does suggest that that we would never have reason to think we live in a softly deterministic world with very uniform laws. For near any such world there will be lots of worlds with less uniform laws, worlds that people had the power to actualize simply by acting differently.

Are we free to change the past?

Let P be a complete description of the ancient past and let L be the laws. Lewis agrees that our freedom includes the ability to act in a way that falsifies the conjunction P&L but denies that it includes the ability to act in such a way that were we to act so, P would be false.

But here is a plausible thesis. Fundamental particles are essentially tied to laws of nature. There would be no electrons or photons if the laws of electrodynamics were different. This is clear on the Aristotelian picture on which laws are grounded in the powers of objects, but is also plausible without that picture.

Given this plausible thesis, P entails L. And hence P&L is logically equivalent to P. Thus if we can act in a way that falsifies the conjunction P&L, we can act in a way that falsifies P. Lewis denies the thesis, but it is still plausible.

Compatibilism, trying and trying hard

Some compatibilists—e.g., Vihvelin and Fara—think that something that merely blocks the possibility of your trying to do A but doesn't block your disposition to do A when trying to do A does not take away your present power to do A. Two examples of such blocks are (a) Frankfurt cases where you'd be counterfactually prevented from doing A and (b) being determined not to do A.

But there is an interesting family of cases where you can only do something when you try hard enough. For instance, you can run distance D in time T when you try really hard, and you can only try that hard when you know a bear is chasing you. In a case like that, even though you are disposed to do A when you try hard enough, anything that blocks you from the possibility of trying hard enough also blocks you from being able to do A. Thus the absence of a bear, or even just ignorance of the presence of the bear, blocks you from being able to running D in T.

So where trying hard to do A is needed for you to do A, anything that blocks your possibility of trying hard blocks your ability to do A.

Now, anything that blocks you from the possibility of trying also blocks you from trying hard. So in cases where trying hard to do A is needed to do A, determinism and Frankfurt cases block you from being able to do A.

So in cases where success requires trying hard, blocks to trying remove the ability to succeed. But why should this only be true where success requires trying hard? So in cases where success requires trying, blocks to trying remove the ability to succeed, too.

Brains, souls and consciousness

1. (Premise) I am the only entity that has all the conscious states I presently have.
2. (Premise) I am breathing.
3. (Premise) My soul isn't breathing.
4. (Premise) My brain isn't breathing.
5. I am neither my soul nor my brain. (2-4)
6. Neither my soul nor my brain has all the conscious states I presently have. (1,5)
7. (Premise) If my soul or my brain is conscious, it has all the conscious states I presently have.
8. So, neither my soul nor my brain is conscious.

If my soul or my brain grounds my consciousness, it does not ground my consciousness by being conscious. It grounds my consciousness by having non-conscious states that ground my consciousness. These non-conscious states will then be more fundamental than my conscious states.

In particular, substance dualists should agree with naturalists that conscious states are non-fundamental. Only non-substance dualists, like hylomorphic dualists and property dualists, have a hope of saying that conscious states are fundamental. And of course a similar argument can be run for other mental states beside the conscious ones.

In practice, some substance dualists will say that I am my soul. If so, then I don't breathe (at most I cause breathing), I don't weigh anything, and so on.

Popper functions and infinite sequences of heads

Williamson gave a lovely argument that infinitesimals can't capture the probability of an infinite sequence of heads in fair independent trials: Let H_n be the event that we have heads in each of the trials n,n+1,n+2,.... Then, P(H₁)=(1/2)P(H₂). But P(H₁)=P(H₂) since they're both just the probability of getting an infinite sequence of heads. Thus, P(H₁)=(1/2)P(H₁) and so P(H₁) is zero, not infinitesimal.

It turns out that a somewhat similar result holds for Popper functions as well. For technical reasons, I need a bidirectionally infinite sequence of coin tosses, one for each integer (positive, zero or negative). Our probability space Ω of infinite sequences will then be the set of all functions from the integers Z to {H,T}. Let G be the group of transformations of Ω generated by translations defined by reflections on Z. In other words, G is generated by the transformations R_a, where a is an integer or a half-integer, and (R_as)(n)=s(2a−n) for any sequence s in Ω.

Let F be any G-invariant field in Ω that contains all the H_n. A very plausible symmetry condition on the Popper function on Ω representing the double sequence of heads then is:

1. For any g in G and any A and B in F, P(A|B)=P(gA|gB).

In other words, if we flip the sequences around, we don't change the probabilities. E.g., the probability of getting heads on tosses 2,3,4,5,... conditionally on B is the same as the probability of getting heads on tosses 1,0,-1,-2,... conditionally on R_1.5B. This symmetry condition is related to Williamson's symmetry assumption that P(H₂)=P(H₁).

A second obvious condition is that the probability of getting heads on tosses 1,2,3,... given that one has heads on 2,3,... is equal to the probability of getting heads on toss 1, i.e., is 1/2:

2. P(H₁|H₂)=1/2.

Theorem: There is no Popper function on F satisfying (1) and (2).