Very rough draft of Infinity, Causation and Paradox

A very rough draft of Infinity, Causation and Paradox is now on github. Chapter 7 is the weakest, I think. I welcome comments about everything, by email or, preferable, with the issue tracker on github.

Utilities and deontology

You are a police officer, and it is looking to you like Glossop is about to kill Fink-Nottle with a shotgun. You hear Glossop say to Fink-Nottle: "This will pay you back for stealing Madeline's affections." Your justified credence that Glossop is about to murder Fink-Nottle is, say, 0.9999. Though there is some small chance that, say, Glossop and Fink-Nottle are practicing a fight scene for an amateur theatrical. The only thing you can see that you can do to save Fink-Nottle is to shoot Glossop dead (you can't yell at them, as you're too far away for them to hear you--you only know what Glossop is saying because you can read his lips). This seems to be the right thing to do, even though you risk a probability of 0.0001 that you are killing an innocent man.

On the other hand, it is not permissible to kill someone you know for sure to be innocent in order to save 9999 others.

There is an apparent tension between these two judgments. Standard decision-theoretic considerations suggest that if it is worth taking a 0.0001 probability risk of an adverse outcome (the killing of an innocent person, in this case) in order to secure a 0.9999 chance of some benefit (saving an innocent's life) then the disvalue of the adverse outcome must be less than 9999 times greater than the value of the benefit. Thus, it would follow from the first judgment that the disvalue of killing an innocent person is less than 9999 times the value of saving the life of an innocent person. But if so, then it seems it would be worthwhile to kill one innocent to save 9999 others.

Risk aversion is relevant to such judgments. But risk aversion tends to reduce the choiceworthiness (or at least apparent choiceworthiness) of actions involving uncertainty, so it's going to make it harder to justify killing Glossop, and that only strengthens the argument that if it's permissible to kill Glossop, it's permissible to kill one innocent to save 9999.

The deontologist might use the above line of argument to challenge the applicability of standard decision-theoretic considerations to moral questions. The person committed to such a decision theory might, instead, use the line of argument to undermine deontology.

But the whole above line of thought is, however, fallacious. For in killing Glossop, you accept a risk of 0.0001 of

1. killing an innocent who looks guilty to you.

But in killing the person you know for sure to be innocent, you accept a certainty of

2. killing an innocent who is known by you to be for sure innocent.

These are different actions, and hence it is unsurprising that they have different disvalues. Indeed, suppose you have amnesia and you know that you did (1) or (2) yesterday. You then clearly have reason to hope that what you did was (1). So the above argument for a tension between decision-theory and deontology fails. I suspect others succeed, but that's for other occasions.

RaspberryJamMod for Forge/Minecraft 1.8.8

I just updated RaspberryJamMod, which allows one to run python code in Minecraft (using a variant of the Raspberry PI Minecraft API), to work with Minecraft 1.8.8 (with the latest beta of Forge). Merry Christmas!

Here's a rebel fighter from Space Janitors (using a mesh in their Janitor's Closet) generated with the render.py script.

Trusting leaders in contexts of war

Two nights ago I had a dream. I was in the military, and we were being deployed, and I suddenly got worried about something like this line of thought (I am filling in some details--it was more inchoate in the dream). I wasn't in a position to figure out on my own whether the particular actions I was going to be commanded to do are morally permissible. And these actions would include killing, and to kill permissibly one needs to be pretty confident that the killing is permissible. Moreover, only the leaders had in their possession sufficient information to make the judgment, so I would have to rely on their judgment. But I didn't actually trust the moral judgment of the leaders, particularly the president. My main reason in the dream for not trusting them was that the president is pro-choice, and someone whose moral judgment is so badly mistaken as to think that killing the unborn is permissible is not to be trusted in moral judgments relating to life and death. As a result, I refused to participate, accepting whatever penalties the military would impose. (I didn't get to find out what these were, as I woke up.)

Upon waking up and thinking this through, I wasn't so impressed by the particular reason for not trusting the leadership. A mistake about the morality of abortion may not be due to a mistake about the ethics of killing, but due to a mistake about the metaphysics of early human development, a mistake that shouldn't affect one's judgments about typical cases of wartime killing.

But the issue generalizes beyond abortion. In a pluralistic society, a random pair of people is likely to differ on many moral issues. The probability of disagreement will be lower when one of the persons is a member of a population that elected the other, but the probability of disagreement is still non-negligible. One worries that a significant percentage of soldiers have moral views that differ from those of the leadership to such a degree that if the soldiers had the same information as the leaders do, the soldiers would come to a different moral evaluation of whether the war and particular lethal acts in it are permissible. So any particular soldier who is legitimately confident of her moral views has reason to worry that she is being commanded things that are impermissible, unless she has good reason to think that her moral views align well with the leaders'. This seems to me to be a quite serious structural problem for military service in a pluralistic society, as well as a serious existential problem.

The particular problem here is not the more familiar one where the individual soldier actually evaluates the situation differently from her leaders. Rather, it arises from a particular way of solving the more familiar problem. Either the soldier has sufficient information by her lights to evaluate the situation or she does not. If she does, and she judges that the war or a lethal action is morally wrong, then of course conscience requires her to refuse, accepting any consequences for herself. Absent sufficient information, she needs to rely on her leaders. But here we have the problem above.

How to solve the problem? I don't know. One possibility is that even though there are wide disparities between moral systems, the particular judgments of these moral systems tend to agree on typical acts. Even though utilitarianism is wrong and Catholic ethics is right, the utilitarian and the Catholic moralist tend to agree about most particular cases that come up. Thus, for a typical action, a Catholic who hears the testimony of a well-informed utilitarian that an action is permissible can infer that the action is probably permissible. But war brings out differences between moral systems in a particularly vivid way. If bombing civilians in Hiroshima and Nagasaki is likely to get the emperor to surrender and save many lives, then the utilitarian is likely to say that the action is permissible while the Catholic will say it's mass murder.

It could, however, be that there are some heuristics that could be used by the soldier. If a war is against a clear aggressor, then perhaps the soldier should just trust the leadership to ensure that the other conditions (besides the justness of the cause) in the ius ad bellum conditions are met. If a lethal action does not result in disproportionate civilian deaths, then there is a good chance that the judgments of various moral systems will agree.

But what about cases where the heuristics don't apply? For instance, suppose that a Christian is ordered to drop a bomb on an area that appears to be primarily civilian, and no information is given. It could be that the leaders have discovered an important military installation in the area that needs to be destroyed, and that this is intelligence that cannot be disclosed to those who will carry out the bombing. But it could also be that the leaders want to terrorize the population into surrender or engage in retribution for enemy acts aimed at civilians. Given that there is a significant probability, even if it does not exceed 1/2, that the action is a case of mass murder rather than an act of just war, is it permissible to engage in the action? I don't know.

Perhaps knowledge of prevailing military ethical and legal doctrine can help in such cases. The Christian may know, for instance, that aiming at civilians is forbidden by that doctrine. In that case, as long as she has enough reason to think that the leadership actually obeys the doctrine, she might be justified in trusting in their judgment. This is, I suppose, an argument for militaries to make clear their ethical doctrines and the integrity of their officers. For if they don't, then there may be cases where too much disobedience of orders is called for.

I also don't know what probability of permissibility is needed for someone to permissibly engage in a killing.

I don't work in military ethics. So I really know very little about the above. It's just an ethical reflection occasioned by a dream...

Sharp OZ/ZQ 7xx organizer code

Back when I was a grad student, my dad gave me a Sharp OZ 730 organizer. It had a Z80 processor, and could (slowly) run BASIC programs. Some folks figured out how to run assembly code on it, and then I figured out how to target it with C code, and I wrote most of a library, designed a file system that hid in hidden recesses of the device, prepared an SDK and wrote or co-wrote a bunch of apps: games, a serial terminal emulator, a function grapher (it's really nice and polished, as I just discovered on trying it out after many years), an ebook reader, a Greek New Testament, some utilities. I got a couple more Sharp organizers, as a guy from Sharp UK liked what I was doing. (I think he liked that one could hook up the device to a modem and use the terminal emulator to check email.) Eventually, the unit got discontinued.

Recently, I've been digging out my code archives. They're mostly now on github, though perhaps not always the latest version. The code is a messy mix of Z80 assembly and C. The SDK worked by launching a CP/M emulator, running the Hi-Tech C compiler in the emulator, and then running a peephole optimizer. With limited memory and CPU power, one had to do a lot of optimization. I remember looking carefully at the code-cycle charts for the assembly, and then doing nasty little things like storing variables inside self-modifying code (instead of allocating two bytes for a global variable and then accessing it with, say, ld bc,(address), the first time the variable is accessed, I can do ld bc,value and store the variable right inside the immediate value), and implementing some of these in the peephole optimizer.

My big kids have one organizer unit each, so a couple of weeks I ordered a $2 USB-serial adapter from banggood. It came today and I can once again transfer the apps to the device (the hard drive on the computer I used to use for development of this stuff failed, and my laptops don't have a serial port). Sharp still has the downloader software here (I run it on Win 8 x64 in Win98+Admin compatibility mode). I even put a ZMachine emulator (not written by me) on my son's so he can play Zork (purchased from GOG).

Critical discussion of One Body

The latest issue of Annals of Philosophy has critiques by Murphy, Taliaferro and Perez, Trakakis, Hamilton, Archard, Griffiths, Wielenberg, Kąkol, Hershenov and Watt of my One Body book on sexual ethics. The critiques are powerful and interesting. There is also a retrospective account by me of what I am doing in One Body as well as a response to each critic (but not to each criticism--I typically picked one point per critic).

Causation and collapse

If determinism were true, then since each state could be project from the initial state, we could simply suppose that the whole four-dimensional shebang came into existence causally "all at once", so that there would be no causal relations within the four-dimensional universe. The only relevant causation could that of God's causing the universe as a whole--and an atheist might just think the four-dimensional universe to be uncaused.

I think that this acausal picture could be adapted to give an attractive picture of the role of causation in a collapse interpretation of quantum mechanics (whether the collapse is of the GRW-type or of the consciousness-caused type). On a collapse picture, we have an alternation between a deterministic evolution governed by the Schroedinger equation and an indeterministic collapse. Why not suppose, then, that there is no causation within the deterministic evolution? We could instead suppose that the state of the universe at collapse causes the whole of the four-dimensional block between that collapse and the next. As long as collapse isn't too frequent, this could allow occasions of causation to be discrete, with only a finite number of such occasions within any interval of time. And this would let us reconcile quantum physics with causal finitism even with a continuous time. (Relativity would require more work.)

Retributive punishment and Christian forgiveness

Start with this argument:

1. Christians ought to forgive all wrongdoing.
2. Forgiving includes foregoing retribution.
3. All ought to forego retribution in the absence of wrongdoing.
4. Therefore, Christians ought in all cases to forego retribution.

And, yet the following also seem true:

5. Retributive justice is central to the concept of punishment.

and:

6. Punishment is often needed for the public good.

What is the Christian to do? Well, one thought is that we should weaken (1). Thomas Aquinas in his sermons on the Lord's Prayer says that we are only required to forgive those who ask us for forgiveness. (After all, Christ tells us to expect God to forgive us as we forgive others; but we do ask God for forgiveness.) Forgiving the unrepentant is supererogatory, he says. That weakens the conflict between the displayed claims. Nonetheless, there are times when the criminal justice system needs to punish someone who we have good reason to think is repentant, because the risks to society of letting her go free may be unacceptably high. Furthermore, Aquinas's modification of (1) doesn't help all that much because the supererogatory is by definition always right. So even with Aquinas's modification of (1), we still seem to get a conflict between forgiveness and the needs of the public good.

Another move, and it may be the most promising, is to distinguish between the individual and the community. Forgiveness is the individual Christian's duty (or at least supererogation--but for brevity I won't consider that option any more), but there are wrongs that, on account of the public good, the community should not forgive. I think this is a quite promising option, but I am not completely convinced. One reason I am not convinced is that Catholic social teaching allows for the possibility of a Christian state, with Vatican City being an example. And there is some plausibility in thinking that the Christian state should behave rather like the Christian individual, but a Christian state has need of punishment for safeguarding the public good. Now maybe forgiveness and punishment are one of the things that varies between the Christian individual and the Christian state, so that the individual should forgive while the state sometimes is not permitted to do so. But it would be good to have another approach.

Think about sports and victory. The very concept of a fencing match cannot be understood apart from seeing it as a practice whose internal end is getting to a score of five before the opponent does. Nonetheless, it is possible to have a friendly and honorable match where no one is intentionally pursuing victory. Rather, the players are exercising their skills in excellent ways that tend to promote victory without actually seeking victory. (The clearest case may be a parent fencing with a child and hoping that the child's skills are so good that the parent will be defeated; but one can have cases where each wants the other to win.)

Similarly, perhaps, just as sports cannot be understood apart from victory, punishment cannot be understood apart from retribution. But just as there are reasons besides victory to play, there are reasons apart from retribution to punish. In those cases, punishment is not intended by the agent. (Another example: I have argued that sex cannot be understood apart from its reproductive end; however, agents can permissibly refrain from pursuing reproduction in particular cases of sex.) This suggests that perhaps we should weaken premise (2) of the initial argument to:

7. Forgiving includes refraining from pursuit of retribution.

The weakened argument only yields the conclusion that Christians ought to refrain from pursuing retribution. But refraining from pursuit of retribution may well be compatible with punishment. And the public goods that render punishment necessary need not include retribution--retribution can be left to the God who says: "Vengeance is mine".

This may be a part of why John Paul II says in Evangelium Vitae that for the death penalty to be justified in some particular (and presumably very rare) case it must be justified on grounds of protection of society. In other words, it is the protection of society, rather than retribution, that is to be sought.

Thinking big numbers

If physicalism is true, then the nature of human beings is probably essentially tied to the nature of our brains, which in turn is essentially tied to the laws of nature. So a human being couldn't have a radically transformed brain. But there are limits on the information storage of our brains. This makes plausible the first premise of the following valid argument:

1. If physicalism is true, there are only finitely many integers that it is metaphysically possible for humans to think about (without externalist crutches).
2. It is metaphysically possible for humans to think about any integer (without externalist crutches).
3. So, physicalism is not true.

Of course, the controversial premise is (2), and I wouldn't worry too much about the argument if I were a physicalist. But, still, there is some plausibility to (2), so the argument has some little force.

God is truth

The statement that God is truth is deeply mysterious. Now the statement that God is love is also mysterious, but it is easier to get a start at what is being said:

1. God isn't identical with our loving, but rather God is identical with his own loving, and our loving is but a participation in God's loving.

By analogy, we would expect to say:

2. God isn't identical with our truthing, but rather God is identical with his own truthing, and our truthing is but a participating in God's truthing.

Except that English has no verb "to truth" (there is a verb "to true", which may be relevant, but I will pass on that line of exploration). However, the above sets us on what may be a promising course. We are looking for an action underlying truth.

I see two options: one reactive and one active. The reactive action is one that finds reality and unveils it (Heidegger suggests unveiling as at the heart of the etymology of the Greek aletheia--I have no idea if he's right as a matter of philology). The active one makes truths them true. If we're looking for something in God, the active one is more promising.

Here is a suggestion. God makes all truths true, though not always in the sense of "truthmaking". Propositions are divine ideas. Their ground is identical with God by divine simplicity. True propositions divide into the necessary and the contingent. Necessary propositions are made true by God himself: God is their ultimate truthmaker, and he makes them true by his being. So in the case of necessary truths, truthing is God's activity of making necessary propositions be true in virtue of himself. In the case of contingent truths, truthing is God's activity of making contingent propositions be true by creating the reality that grounds them.

Our truthing, on the other hand, is both active and reactive. Some truths we make true in the active way by being or creating the reality that grounds them. Others we merely react to. In both cases, our truthing is derivative from God's: our creative abilities are mere participations in God's, and require God's constant cooperation, and our reactions are ultimately reactions to God.

I do not have a great amount of confidence in this speculative analysis.

Marriage in heaven

Question 1: Are there marriages in heaven?

Answer: No. Jesus explicitly says that there is no marrying or giving in marriage in heaven (Luke 20:27-38). So no new marriages are entered into in heaven. That might seem to leave open the question whether existing marriages might not continue. But the context of the discussion is of a woman who was married to a sequence of brothers and the paradoxical consequences of that if these marriages continue in the afterlife. Jesus' answer only solves the paradox if we accept the implicature that there is no marriage in heaven. Moreover, it would be an odd view if existing marriages persisted in heaven but new ones couldn't be entered into. If marriage in heaven would be a good thing for us, this kind of a setup just wouldn't be fair to a loving couple who was murdered minutes before their wedding was to take place.

Question 2: Why are there no marriage in heaven?

Answer: It's good that way. Well, that's true, but not informative: it applies to everything about heavenly life. But we can think a bit about why it's good for it to be so.

One thought is that only marriage for eternity would be fitting for heavenly life. Divorce just doesn't seem the sort of thing that is fitting for heavenly life. But I think it would be problematic for humans to bind themselves to one another for an eternal heavenly life. Heavenly life is unimaginable to us now, radically transcending our current knowledge. Because of this, it would not be appropriate for us to commit ourselves now to be bound to another person for an infinite length of time in that utterly different life. Now one might think that once in heaven the problem disappears. But I suspect it does not. I suspect that the heavenly life is a life of eternal and non-asymptotic growth (hence my recent swollen head argument against Christian physicalism). I don't know if the beatific vision itself increases eternally, but I suspect that at least the finite goods of heavenly life do. So some of the reasons why it would not be fitting for us to bind ourselves now to one another for eternity would apply in heaven: in year ten of heavenly life, perhaps, one cannot imagine what year one billion will be like; in year one billion, one cannot imagine what year 10¹⁰⁰ will be like; and so on. Eternity is long.

A second thought is that there is something about the exclusivity of marriage that is not fitted for heavenly life. The advocates of free love had something right: there is something limiting about exclusivity. This limitation is entirely fitting given the nature of marriage and its innate links to reproduction and sexual union as one body. But nonetheless it seems plausible to me that an innately exclusive form of love is not fitted to heaven.

A third and most speculative thought: There is a link--worth exploring in much greater depth than I am going to do here--between the exclusivity of marriage and the appropriateness of according privacy to sexual activity. But I suspect that there is a great transparency in heavenly life. What is hidden is revealed. It is a life of truth rather than of withholding of information. In regard to the emotional life, those in heaven will have highly developed faculties of empathy. After all, my model is one of continued growth. People can grow immensely in empathy in this life--how much more will they likely grow in heaven! These faculties of empathy would enable people to have great empathetic insight into the sexual lives of others, to a point where that insight could make them empathetic participants in that life, in a way incompatible with the exclusivity of marriage and the privacy of sexuality.

Physicalism, swollen heads, heaven and recurrence

Assuming physicalism, for any fixed volume V, there are only finitely many internalistically-distinct mental states that a human brain of volume less than or equal to V can exhibit. (There may be infinitely many brain states, space and time perhaps being continuous, but brain states that are close enough together will not yield mentally relevant differences. There may also be infinitely many externalistically-distinct states given semantic externalism.) Therefore, given physicalism and a robust supervenience of the mental on the physical, in heaven either the volume of the human head will swell beyond all bounds, or else eventually we will only have reruns of the internalistically-same mental states. Neither option is acceptable. So, Christians should reject physicalism.

Coin guessing using past data, once again

In my previous post, I showed that given a backwards infinite sequence of coin tosses, there is a simple strategy leveraging data about infinitely many past coin flips that guarantees that you guessed correctly infinitely often. I then suggested that this supports the idea that one can't leverage an infinite amount of past data, and that in turn supports causal finitism--the denial of the possibility of infinite causal histories. But there is a gap in that argument: Maybe there is some strategy that guarantees infinitely many correct guesses that doesn't require the guesser to make use of data about infinitely many past coin flips. If so, then the paradox doesn't have much to do with infinite amounts of data.

Fortunately for me, that gap can be filled (modulo the Axiom of Choice). Given the Axiom of Choice, it's a theorem that there is no strategy leveraging merely a finite amount of past data at each step that guarantees getting any guesses right. In other words, for every strategy that leverages a finite amount of past data, there is a sequence of coin flips such that that sequence would result in the guesser getting every guess wrong. The proof uses the Compactness Theorem for First-Order Logic.

Coin guessing without the Axiom of Choice

You've existed for an infinite amount of time, and each day until the year 2100 a coin is tossed. You always know the results of the past tosses, and before each toss you are asked to guess the next toss. Given the Axiom of Choice, there is a mathematical strategy that guarantees you make only a finite number of mistakes.

Here's a simpler fact, no doubt well-known, but not dependent on the Axiom of Choice. There is a mathematical strategy that guarantees that you guess correctly infinitely often. This is surprising. Granted, it's not surprising that you guess correctly infinitely often--that is what you would expect. But what is surprising is that there is a guarantee of it! Here's the simple strategy:

• If among the past tosses, there were infinitely many heads, guess "heads"
• Otherwise, guess "tails".

The way this works is that by just looking at past tosses, you can tell whether the whole sequence contains infinitely many heads or not, since whenever you look at past tosses, you are missing information only about finitely many future tosses. The first rule guarantees that if infinitely many heads come up in the whole game (as has probability one if the coins are independent and fair), you are right each time heads comes up. The second rule guarantees that if only finitely many heads come up, you are right each time tails comes up.

I take the paradoxical existence of this mathematical strategy to be evidence for causal finitism: causal finitism rules out the possibility of your having observational information from infinitely many past tosses. Thus the strategy remains purely mathematical: it cannot be implemented in practice.

The unreality of time

McTaggart argued that time is unreal. Hence, time is real.

Heaven and materialism: The swollen head problem

Suppose, as Christian materialists believe, that materialism is true and yet some people have eternal life in heaven. Good experiences happen daily in heaven, and bad things never do. It is a bad thing to fail to remember a good experience. So in heaven people will have more and more good experiences that they remember. But it is plausible that there is a maximum information density in our brains, and given materialism, all the information in memory is stored in the brain. Thus, it follows that those who will be in heaven will have their heads swell without bound. Humans will eventually have heads that are millions of light-years in diameter, just to hold all the good experiences that have happened to them. But a life with such big heads just doesn't seem to be the life of human fulfillment.

Objection 1: Perhaps there are patterns to the good experiences in heaven such that the total information content in the infinite future of good experiences is finite.

Response: If the total information content is finite, then it seems likely that one will eventually get bored. Moreover, plausibly, human flourishing involves continual growth in knowledge, and it would not be fitting for heaven if this growth were to slow down eventually in order to ensure an upper bound on the total information content.

Objection 2: The laws of nature will be different in heaven, and while there is maximum information density in our current brains, heavenly brains will be made of a different kind of matter, a matter that either has infinitely many particles in any finite volume or that is infinitely subdivisible. After all, the Christian tradition does hold that we will function differently--there is speculation that we may be able to go through solid walls as Jesus apparently did after the resurrection, move really fast, see really far, etc.

Response: This seems to me to be the best materialist response. But given that on materialism the brain is central to the kinds of beings we are, there is a worry that such a radical reworking of its structure into a different kind of matter would create beings that aren't human. The dualist can allow for a more radical change in the physical aspects of the body while allowing that we still have the same kind of being, since the kind of being could be defined by the soul (this is clearest in the hylomorphic theory).

Objection 3: The dualists face the same problem given that we have good reason to think that memories are stored in the brain.

Response: Maybe memories are not entirely stored in the brain. And see the response to Objection 2: the finer-matter response is more defensible in the case of the dualist.