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.

Lying, violence and dignity

I've argued that typically the person who is hiding Jews from Nazis and is asked by a Nazi if there are Jews in her house tells the truth, and does not lie, if she says: "No." That argument might be wrong, and even if it's right, it probably doesn't apply to all cases.

So, let's think about the case of the Nazi asking Helga if she is hiding Jews, when she is in fact hiding Jews, and when it would be a lie for her to say "No" (i.e., when there isn't the sort of disparity of languages that I argued is normally present). The Christian tradition has typically held lying to be always wrong, including thus in cases like this. I want to say some things to make it a bit more palatable that Helga does the right thing by refusing to lie.

The Nazi is a fellow human being. Language, and the trust that underwrites it (I was reading this morning that one of the most difficult questions in the origins of language is about the origination of the trust essential to language's usefulness), is central to our humanity. By refusing to betray the Nazi's trust in her through lying, Helga is affirming the dignity of all humans in the particular case of someone who needs it greatly--a human being who has been dehumanized by his own choices and the influence of an inhuman ideology. By attempting to dehumanize Jews, the Nazi dehumanized himself to a much greater extent. Refusing to lie, Helga gives her witness to a tattered child of God, a being created to know and live by the truth in a community of trust, and she he gives him a choice whether to embrace that community of trust or persevere on the road of self-destruction through alienation from what is centrally human. She does this by treating him as a trusting human rather than a machine to be manipulated. She does this in sadness, knowing that it is very likely that her gift of community will be refused, and will result in her own death and the deaths of those she is protecting. In so doing she upholds the dignity of everyone.

When I think about this in this way, I think of the sorts of things Christian pacifists say about their eschatological witness. But while I do embrace the idea that we should never lie, I do not embrace the pacifist rejection of violence. For I think that just violence can uphold the dignity of those we do violence to, in a way in which lying cannot. Just violence--even of an intentionally lethal sort--can accept the dignity of an evildoer as someone who has chosen a path that is wrong. We have failed to sway him by persuasion, but we treat him as a fellow member of the human community by violently preventing him from destroying the community that his own wellbeing is tied to, rather than by betraying with a lie the shattered remains of the trustful connection he has to that community.

I don't think the above is sufficient as an argument that lying is always wrong. But I think it gives some plausibility to that claim.

Education about sports

A lot of worthwhile texts, both fiction and nonfiction, make direct reference to particular sports or use sports analogies or metaphors. These are difficult to understand for readers who do not know the rudiments of these sports. But there is not enough education on these sports in school, except in the context of actual participation in them. But I suspect that only a minority of children in English-speaking countries participates in all of the culturally important sports that figure in English-language texts, sports such as American football, baseball, cricket, golf, hockey and soccer, understanding of which is needed for basic cultural literacy among readers of English (I have to confess to lacking that understanding in the case of most of these sports--my own school education was deficient in this respect). Thus, either there should either be broader participation--but that is unsafe in the case of American football and likely impractical in the case of golf--or there should be teaching about the rules of sports outside of contexts of participation, say in English or history class.

This post is inspired by my daughter's noting her difficulties in reading the cricket-related bits of a P. G. Wodehouse novel.

Dutch Books and infinite sequences of coin tosses

Suppose we have an infinite sequence of independent and fair coins. A betting portfolio is a finite list of subsets of the space of outcomes (heads-tails sequences) together with a payoff for each subset. Assume:

1. Permutation: If a rational agent would be happy to pay x for a betting portfolio, and A is one of the subsets in the betting portfolio, then she would also be happy to pay x for a betting portfolio that is exactly the same but with A replaced by A*, where A* is isomorphic to A under a permutation of the coins.
2. Equivalence: A rational agent who is happy to pay x for one betting scenario, will be willing to accept an equivalent betting scenario---one that is certain to give the same payoff for each outcome---for the same price.
3. Great Deal: A rational agent will be happy to pay $1.00 for a betting scenario where she wins $1.25 as long as the outcome is not all-heads or all-tails.

Leveraging the Axiom of Choice and using the methods of the Banach-Tarski Paradox, one can then find two betting portfolios that the agent would be happy to accept for $1.00 each such that it is certain that if she accepts them both, she will win at most $1.25; hence she will accept a sure loss of at least $0.75. For details of a closely related result, see Chapter 6 in Infinity, Causation and Paradox (draft temporarily here).

So what to do? I think one should accept Causal Finitism, the doctrine that causal antecedents are always finite. Given Causal Finitism, one can't have a real betting scenario based an infinite number of coin tosses. Moreover, the only known way to operationalize the use of the Axiom of Choice in the proof in a betting scenario also involves infinite causal dependencies.

Values cannot be accurately modeled by real numbers

Consider a day in a human life that is just barely worth living. Now consider the life of Beethoven. For no finite n would having n of the barely-worth-living days be better than having all of the life of Beethoven. This suggests that values in human life cannot be modeled by real numbers. For if a and b are positive numbers, then there is always a positive integer n such that nb>a. (I am assuming additiveness between the barely-liveable days. Perhaps memory wiping is needed to ensure additiveness, to avoid tedium?)

The value of victory

Is winning a game always worthwhile? Consider this solitary game: I guess a number, and if my number is different from the number of particles in the universe, then my score equals the number of particles in the universe. I can play this over and over, winning each time. If it's good for me to win at a game, I continue to rack up benefits. So for reasons of self-interest, I should play this game all the time. I could even set myself up as playing it by default: I announce that each time I breathe, the length of my inspiration in milliseconds counts as my guess. I will be racking up benefits every day, every night. But that's silly.

Another impossibility result for finitely additive probabilities and invariance

Consider a countably infinite sequence of fair and independent coin tosses. Given the Axiom of Choice, there is no finitely additive probability measure that satisfies these conditions:

1. It is defined for all sets of outcomes.
2. It agrees with the classical probabilities where these are defined.
3. It is invariant under permutations of coins.

(Sketch of proof: Index the coins with members of the free group of rank two. The members of the group then induce permutations of coins, and hence act on the space of outcomes. The set of non-trivial fixed points under that action has classical probability zero. Throwing that out, we can use a standard paradoxical decomposition of the free group of rank two to generate a paradoxical decomposition of the rest of our space of results--here Choice will be used--and that rules out the possibility of a finitely additive probability measure.)