Fair and Unfair Logic

St. Thomas discusses cases in which one should not follow the law:

As stated above (Article 4), every law is directed to the common weal of men, and derives the force and nature of law accordingly. Hence the jurist says [Pandect. Justin. lib. i, ff., tit. 3, De Leg. et Senat.]: “By no reason of law, or favor of equity, is it allowable for us to interpret harshly, and render burdensome, those useful measures which have been enacted for the welfare of man.” Now it happens often that the observance of some point of law conduces to the common weal in the majority of instances, and yet, in some cases, is very hurtful. Since then the lawgiver cannot have in view every single case, he shapes the law according to what happens most frequently, by directing his attention to the common good. Wherefore if a case arise wherein the observance of that law would be hurtful to the general welfare, it should not be observed. For instance, suppose that in a besieged city it be an established law that the gates of the city are to be kept closed, this is good for public welfare as a general rule: but, it were to happen that the enemy are in pursuit of certain citizens, who are defenders of the city, it would be a great loss to the city, if the gates were not opened to them: and so in that case the gates ought to be opened, contrary to the letter of the law, in order to maintain the common weal, which the lawgiver had in view.

He calls the attitude that leads one to set aside the law in such cases “epikeia,” or “equity,” which in this context means something like fairness or moderation:

As stated above (I-II:96:6), when we were treating of laws, since human actions, with which laws are concerned, are composed of contingent singulars and are innumerable in their diversity, it was not possible to lay down rules of law that would apply to every single case. Legislators in framing laws attend to what commonly happens: although if the law be applied to certain cases it will frustrate the equality of justice and be injurious to the common good, which the law has in view. Thus the law requires deposits to be restored, because in the majority of cases this is just. Yet it happens sometimes to be injurious—for instance, if a madman were to put his sword in deposit, and demand its delivery while in a state of madness, or if a man were to seek the return of his deposit in order to fight against his country. On these and like cases it is bad to follow the law, and it is good to set aside the letter of the law and to follow the dictates of justice and the common good. This is the object of “epikeia” which we call equity. Therefore it is evident that “epikeia” is a virtue.

“Fairness” is probably a good translation here, since someone who rigidly demands the application of the law in such a situation would often be called unfair in relation to the people involved.

Someone might object that much of the benefit of having a law directly depends on following it consistently, without making exceptions based on minute analysis of particular situations, as we saw in the last post. This is correct as far as it goes, but St. Thomas is not talking about analyzing each situation in detail and making an exception whenever there appears to be a benefit, but rather talking about situations which are extremely different from the situations considered by the law. Thus he says in the reply to the second objection:

He who follows the intention of the lawgiver, does not interpret the law simply; but in a case in which it is evident, by reason of the manifest harm, that the lawgiver intended otherwise. For if it be a matter of doubt, he must either act according to the letter of the law, or consult those in power.

To the degree that “laws of logic” can be analogously interpreted as rules for sensible thought and speech, telling one to behave in some ways and not in others, similar principles will apply. Thus, for example, an atheist confronted with the argument of Alexander Pruss for the existence of God based on the indeterminacy of language might not only be inclined to call it sophistical, but to add that it is an unfair way to argue. And indeed it is, precisely in the sense that it applies the rule “either say that A is B or say that A is not B” to situations for which it was not intended, namely situations where B is simply too vague to say. The rule is intended to make people think and speak sensibly, but Pruss is abusing the rule with the opposite result: that he does not speak and think sensibly.

Someone might agree that this is reasonable insofar as we are considering these laws as rules of behavior, but another issue comes up. Human laws are really intended to exclude some kinds of behavior that are really possible. And likewise, rules of logic are really intended to exclude some kinds of behavior that are really possible, e.g. making arguments like:

A: You always say I am wrong.

B: I said you were right about X.

A: See, you just said I was wrong again. You always say I am wrong!

I know from experience that this behavior is possible, and it does violate the laws of logic considered as rules of behavior. But someone might add that the laws of logic are also based on the nature of reality itself, and for this very reason we said that they are not conventions, but could not have been otherwise. So it seems to follow that it should be possible to expound the laws of logic in a form in which they are truly exceptionless, by expressing reality as it truly is.

There is some truth here, but there is also a problem analogous to a similar objection about human law. Consider the third objection and reply in the above article from St. Thomas:

Objection 3. Further, every wise man knows how to explain his intention by words. But those who framed the laws should be reckoned wise: for Wisdom says (Proverbs 8:15): “By Me kings reign, and lawgivers decree just things.” Therefore we should not judge of the intention of the lawgiver otherwise than by the words of the law.

Reply to Objection 3. No man is so wise as to be able to take account of every single case; wherefore he is not able sufficiently to express in words all those things that are suitable for the end he has in view. And even if a lawgiver were able to take all the cases into consideration, he ought not to mention them all, in order to avoid confusion: but should frame the law according to that which is of most common occurrence.

The objection here is similar. If there are cases where it wouldn’t be good to apply the law, the lawgiver ought to have enumerated those cases. St. Thomas replies that in reality you will not foresee every case, and that even if you could, enumerating them would simply cause confusion.

A similar thing applies if we consider the laws of logic. You can say, “If you say that A is B in an infinitely precise sense, and that B is C in an infinitely precise sense, you should also say that A is C,” and your claim might be exceptionless. The problem is that your claim has no cases: no one ever says anything in an infinitely precise sense.

And on the other hand, if you try to make your claim include some actual cases, you will not be able to avoid the possibility of exceptions, just as the human lawgiver does not foresee all cases. And as in the case of human law, if you attempt to enumerate all cases, you will simply cause confusion. Thus, for example, someone might say that the problem in the case of Queen Elizabeth is that we simply don’t have a precise enough definition for “old,” and they might then attempt to give a precise definition. But this would have several results:

1. First, the new word “old” would not have the same meaning as the original word, because the very fact that the original word is vague is part of what the word is. It is not accidental; it is not meant to have a precise cut-off.

2. Someone might attempt to remedy the above flaw by enumerating various circumstances, rather than giving a precise cut-off. “If you are less then 10 years old and you say that someone is ‘old,’ it signifies someone who is at least 15.” “If you are in your 30s and you say that someone is ‘old’, it signifies that they are at least 67.” And so on. But attempting to fix the first problem, you have simply compounded it. The new word still does not have the same meaning as the original word, because the original word was meant to be flexible; even your new rules have too much rigidity.

You could attempt to remedy the above problems by listing all the situations where people in fact use the word “old,” but that is not a definition: it is just an indefinitely long list. What St. Thomas said about human law, that it “ought not to mention them all,” is equally true about this situation. The point of defining “old” is to provide an explanation which is both general and flexible. Someone might argue that we should provide a list of all possible circumstances and what should be done in those circumstances, in order to avoid the flexibility of “epikeia,” but such an attempt would be absurd, and harmful to a good life. And it is equally absurd when we attempt to apply the same process to logic or to definitions, and harmful to sensible thought and speech.

What about reality itself? Isn’t it an exceptionless reality that a thing is what it is? Indeed. But this is neither a rule of behavior nor of speech. Nor is it a rule making something be some way; reality does not need something else to make sure that it turns out to be reality rather than something else. There is simply nothing else to be. Parmenides was right at least to this degree.

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C.S. Lewis on Punishment

C.S. Lewis discusses a certain theory of punishment:

In England we have lately had a controversy about Capital Punishment. … My subject is not Capital Punishment in particular, but that theory of punishment in general which the controversy showed to be almost universal among my fellow-countrymen. It may be called the Humanitarian theory. Those who hold it think that it is mild and merciful. In this I believe that they are seriously mistaken. I believe that the “Humanity” which it claims is a dangerous illusion and disguises the possibility of cruelty and injustice without end. I urge a return to the traditional or Retributive theory not solely, not even primarily, in the interests of society, but in the interests of the criminal.

According to the Humanitarian theory, to punish a man because he deserves it, and as much as he deserves, is mere revenge, and, therefore, barbarous and immoral. It is maintained that the only legitimate motives for punishing are the desire to deter others by example or to mend the criminal. When this theory is combined, as frequently happens, with the belief that all crime is more or less pathological, the idea of mending tails off into that of healing or curing and punishment becomes therapeutic. Thus it appears at first sight that we have passed from the harsh and self-righteous notion of giving the wicked their deserts to the charitable and enlightened one of tending the psychologically sick. What could be more amiable? One little point which is taken for granted in this theory needs, however, to be made explicit. The things done to the criminal, even if they are called cures, will be just as compulsory as they were in the old days when we called them punishments. If a tendency to steal can be cured by psychotherapy, the thief will no doubt be forced to undergo treatment. Otherwise, society cannot continue.

My contention is that this doctrine, merciful though it appears, really means that each one of us, from the moment he breaks the law, is deprived of the rights of a human being.

The reason is this. The Humanitarian theory removes from Punishment the concept of Desert. But the concept of Desert is the only connecting link between punishment and justice. It is only as deserved or undeserved that a sentence can be just or unjust. I do not here contend that the question “Is it deserved?” is the only one we can reasonably ask about a punishment. We may very properly ask whether it is likely to deter others and to reform the criminal. But neither of these two last questions is a question about justice. There is no sense in talking about a “just deterrent” or a “just cure”. We demand of a deterrent not whether it is just but whether it will deter. We demand of a cure not whether it is just but whether it succeeds. Thus when we cease to consider what the criminal deserves and consider only what will cure him or deter others, we have tacitly removed him from the sphere of justice altogether; instead of a person, a subject of rights, we now have a mere object, a patient, a “case”.

Later in the essay, he gives some examples of how the Humanitarian theory will make things worse, as in the following case:

The immediate starting point of this article was a letter I read in one of our Leftist weeklies. The author was pleading that a certain sin, now treated by our laws as a crime, should henceforward be treated as a disease. And he complained that under the present system the offender, after a term in gaol, was simply let out to return to his original environment where he would probably relapse. What he complained of was not the shutting up but the letting out. On his remedial view of punishment the offender should, of course, be detained until he was cured. And of course the official straighteners are the only people who can say when that is. The first result of the Humanitarian theory is, therefore, to substitute for a definite sentence (reflecting to some extent the community’s moral judgment on the degree of ill-desert involved) an indefinite sentence terminable only by the word of those experts–and they are not experts in moral theology nor even in the Law of Nature–who inflict it. Which of us, if he stood in the dock, would not prefer to be tried by the old system?

This post will make three points:

(1) The “Humanitarian” theory is basically correct about the purpose of punishment.

(2) C.S. Lewis is right that there are good reasons to talk about justice and about what someone deserves or does not deserve. Such considerations are, as he supposes, essential to a system of justice. Lewis is also right to suppose that many supporters of the Humanitarian theory, despite being factually correct about the purpose of punishment, are mistaken in opposing such talk as cruel and immoral.

(3) Once the Humanitarian theory is corrected in such a way as to incorporate the notion of “just deserts”, Lewis’s objections fail.

Consider the first point, the purpose of punishment. There was already some discussion of this in a previous post. In a sense, everyone already knows that Humanitarians are right about the basic purpose of punishment, including C.S. Lewis. Lewis points out the obvious fact himself: whatever you call them and however you explain them, punishments for crime are compulsory in a society because “otherwise, society cannot continue.” But why cannot society continue without punishment? What supposedly would happen if you did not have any punishments? What would actually happen if a government credibly declared that it would never again punish anything?

What would actually happen, of course, is that this amount to a declaration that the government was dissolving itself, and someone else would take over and establish new crimes and new punishments, either at that same level of generality as the original government, or at more local levels (e.g. perhaps each town would become a city-state.) In any case each of the new governments would still have punishments, so you would not have succeeded in abolishing punishment.

What happens in the imaginary situation where you do succeed, where no one else takes over? This presumably would be a Hobbesian “state of nature,” which is not a society at all. In other words, the situation simply does not count as a society at all, unless certain rules are followed pretty consistently. And those rules will not be followed consistently without punishments. So it is easy to see why punishment exists: to make sure that those rules are followed, generally speaking. Since rules are meant to make some things happen and prevent other things, punishment is simply to make sure that the rules actually function as rules. But this is exactly what the Humanitarian theory says is the purpose of punishment: to make others less likely to break the rules, and to make the one who has already broken the rules less likely to break them in the future.

Thus C.S. Lewis himself is implicitly recognizing that the Humanitarians are basically right about the purpose of punishment, in acknowledging that punishment is necessary for the very existence of society.

Let’s go on to the second point, the idea of just deserts. C.S. Lewis is right that many proponents of Humanitarian view either believe that the idea is absurd, or that if there is such a thing as deserving something, no one can deserve something bad, or that if people can deserve things, this is not really a relevant consideration for a justice system. For example, it appears that Kelsey Piper blogging at The Unit of Caring believes something along these lines; here she has a pretty reasonable post responding to some criticisms analogous to those of C.S. Lewis to the theory.

I will approach this by saying a few things about what a law is in general. St. Thomas defines law: “It is nothing else than an ordinance of reason for the common good, made by him who has care of the community, and promulgated.” But let’s drop the careful formulation and the conditions, as necessary as they may be. St. Thomas’s definition is simply a more detailed account of what everyone knows: a law is a rule that people invent for the benefit of a community.

Is there such a thing as an unjust law? In St. Thomas’s account, in a sense yes, and in a sense no. “For the common good” means that the law is beneficial. In that sense, if the law is “unjust,” it is harmful, and thus it is not for the common good. And in that sense it does not satisfy the definition of a law, and so is not a law at all. But obviously ordinary people will call it a law anyway, and in that way it is an unjust law, because it is unsuited to the purpose of a law.

Now here’s the thing. An apparent rule is not really a rule at all unless it tends to make something happen. In the case that we are talking about, namely human law, that generally means that laws require penalties for being broken in order to be laws at all. It is true that in a society with an extremely strong respect for law, it might occasionally be possible to make a law without establishing any specific penalty, and still have that law followed. The community would still need to leave itself the option of establishing a penalty; otherwise it would just be advice rather than a law.

This causes a slight problem. The purpose of a law is to make sure that certain things are done and others avoided, and the reason for penalties is to back up this purpose. But when someone breaks the law, the law has already failed. The very thing the law was meant to prevent has already happened. And what now? Should the person be punished? Why? To prevent the law from being broken? It has already been broken. So we cannot prevent it from being broken. And the thing is, punishment is something bad. So to inflict the punishment now, after the crime has already been committed, seems like just stacking one bad thing on top of another.

At this point the “Retributive” theory of justice will chime in. “We should still inflict the punishment because it is just, and the criminal deserves it.”

This is the appeal of the Humanitarian’s condemnation of the retributive theory. The Retributive theory, the Humanitarian will say, is just asserting that something bad, namely the punishment, in this situation, is something good, by bringing in the idea of “justice.” But this is a contradiction: something bad is bad by definition, and cannot be good.

The reader is perhaps beginning to understand the placement of the previous post. A law is established, with a penalty for being broken, in order to make certain things happen. This is like intending to drink the toxin. But if someone breaks the law, what is the point of inflicting the punishment? And the next morning, what is the point of drinking the toxin in the afternoon, when the money is already received or not? There is a difference of course, because in this case the dilemma only comes up because the law has been broken. We could make the cases more analogous, however, by stipulating in the case of Kavka’s toxin that the rich billionaire offers this deal: “The million will be found in your account, with a probability of 99.99%, if and only if you intend to drink the toxin only if the million is not found in your account (which will happen only in the unlucky 0.01% of cases), and you do not need to drink or intend to drink in the situation where the million is found in your account.” In this situation, the person might well reason thus:

If the morning comes and the million is not in my account, why on earth would I drink the toxin? This deal is super unfair.

Nonetheless, as in the original deal, there is one and only one way to get the million: namely, by planning to drink the toxin in that situation, and by planning not to reconsider, no matter what. As in the case of law, the probability factor that I added means that it is possible not to get the million, although you probably will. But the person who formed this intention will go through with it and drink the toxin, unless they reconsider; and they had the definite intention of not reconsidering.

The situations are now more analogous, but there is still an additional difference, one that makes it even easier to decide to follow the law than to drink the toxin. The only reason to commit to drinking the toxin was to get the million, which, in our current situation, has already failed. But in the case of the law, one purpose was to prevent the criminal from performing a certain action, and that purpose has already failed. But it also has the purpose of preventing them from doing it in the future, and preventing others from doing it. So there additional motivations for carrying out the law.

We can leave the additional difference to the side for now, however. The point would be essentially valid even if you made a law to prevent one particular act, and that act ended up being done. The retributionist would say, “Ok, so applying the punishment at this point will not prevent the thing it was meant to prevent. But it is just, and the criminal deserves it, and we should still inflict it.” And they are right: the whole idea of establishing the the rule included the idea that the punishment would actually be carried out, in this situation. There was a rule against reconsidering the rule, just as the fellow in the situation with the toxin planned not to reconsider their plan.

What is meant when it is said that a punishment is “just,” and that the criminal “deserves it,” then is simply that it is what is required by the rules we have established, and that those rules are reasonable ones.

Someone will object here. It seems that this cannot be true, because some punishments are wicked and unjust even though there were rules establishing them. And it seems that this is because people simply do not deserve those things: so there must be such a thing as “what they deserve,” in itself and independent of any rules. But this is where we must return to the point made above about just and unjust laws. One hears, for example, of cases in which people were sentenced to death for petty theft. We can agree that this is unjust in itself: but this is precisely because the rule, “someone who steals food should be killed,” is not a reasonable rule which will benefit the community. You might have something good in mind for it, namely to prevent stealing, but if you carry out the penalty on even one occasion, you have done more harm than all the stealing put together. The Humanitarians are right that the thing inflicted in a punishment is bad, and remains bad. It does not become something good in that situation. And this is precisely why it needs some real proportion to the crime.

We can analyze the situation in two ways, from the point of view of the State, considered as though a kind of person, and from the point of the view of the person who carries out the law. The State makes a kind of promise to inflict a punishment for some crimes, in such a way as to minimize the total harm of both the crimes and their punishment. Additionally, to some extent it promises not to reconsider this in situation where a crime is actually committed. “To some extent” here is of course essential: such rules are not and should not be absolutely rigid. If the crime is actually committed, the State is in a situation like our person who finds himself without the million and having committed to drink the toxin in that situation: the normal result of the situation will be that the State inflicts the punishment, and the person drinks the toxin, without any additional consideration of motivations or reasons.

From the point of view of the individual, he carries out the sentence “because it is just,” i.e. because it is required by reasonable rules which we have established for the good of the community. And that, i.e. carrying out reasonable laws, is a good thing, even though the material content includes something bad. The moral object of the executioner is the fulfillment of justice, not the killing of a person.

We have perhaps already pointed the way to the last point, namely that with the incorporation of the idea of justice, C.S. Lewis’s criticisms fail. Lewis argues that if the purpose of punishment is medicinal, then it is in principle unlimited: but this is not true even of medicine. No one would take medicine which would cause more harm than the disease, nor would it be acceptable to compel someone else to take such medicine.

More importantly, Lewis’s criticism play off the problems that are caused by believing that one needs to consider at every point, “will the consequences of this particular punishment or action be good or not?” This is not necessary because this is not the way law works, despite the fact that the general purpose is the one supposed. Law only works because to some extent it promises not to reconsider, like our fellow in the case of Kavka’s toxin. Just as you are wrong to focus on whether “drinking the toxin right now will harm me and not benefit me”, so the State would be wrong to focus too much on the particular consequences of carrying out the law right now, as opposed to the general consequences of the general law.

Thus for example Lewis supposes rulers considering the matter in an entirely utilitarian way:

But that is not the worst. If the justification of exemplary punishment is not to be based on desert but solely on its efficacy as a deterrent, it is not absolutely necessary that the man we punish should even have committed the crime. The deterrent effect demands that the public should draw the moral, “If we do such an act we shall suffer like that man.” The punishment of a man actually guilty whom the public think innocent will not have the desired effect; the punishment of a man actually innocent will, provided the public think him guilty. But every modern State has powers which make it easy to fake a trial. When a victim is urgently needed for exemplary purposes and a guilty victim cannot be found, all the purposes of deterrence will be equally served by the punishment (call it “cure” if you prefer) of an innocent victim, provided that the public can be cheated into thinking him guilty. It is no use to ask me why I assume that our rulers will be so wicked.

As said, this is not the way law works. The question will be about which laws are reasonable and beneficial in general, not about whether such and such particular actions are beneficial in particular cases. Consider a proposed law formulated with such an idea in mind:

When the ruling officials believe that it is urgently necessary to deter people from committing a crime, and no one can be found who has actually committed it, the rulers are authorized to deceive the public into believing that an innocent man has committed the crime, and to punish that innocent man.

It should not be necessary to make a long argument that as a general rule, this does not serve the good of a community, regardless of might happen in particular cases. In this way it is quite right to say that this is unjust in itself. This does not, however, establish that “what someone deserves” has any concrete content which is not established by law.

As a sort of footnote to this post, we might note that “deserts” are sometimes extended to natural consequences in much the way “law” is extended to laws of nature, mathematics, or logic. For example, Bryan Caplan distinguishes “deserving” and “undeserving” poor:

I propose to use the same standard to identify the “deserving” and “undeserving” poor.  The deserving poor are those who can’t take – and couldn’t have taken – reasonable steps to avoid poverty. The undeserving poor are those who can take – or could have taken – reasonable steps to avoid poverty.  Reasonable steps like: Work full-time, even if the best job you can get isn’t fun; spend your money on food and shelter before you get cigarettes or cable t.v.; use contraception if you can’t afford a child.  A simple test of “reasonableness”: If you wouldn’t accept an excuse from a friend, you shouldn’t accept it from anyone.

This is rather different from the sense discussed in this post, but you could view it as an extension of it. It is a rule (of mathematics, really) that “if you spend all of your money you will not have any left,” and we probably do not need to spend much effort trying to change this situation, considered in general, even if we might want to change it for an individual.

Kavka’s Toxin

Gregory Kavka discusses a thought experiment:

You are feeling extremely lucky. You have just been approached by an eccentric billionaire who has offered you the following deal. He places before you a vial of toxin that, if you drink it, will make you painfully ill for a day, but will not threaten your life or have any lasting effects. (Your spouse, a crack biochemist, confirms the properties of the toxin.) The billionaire will pay you one million dollars tomorrow morning if, at midnight tonight, you intend to drink the toxin tomorrow afternoon. He emphasizes that you need not drink the toxin to receive the money; in fact, the money will already be in your bank account hours before the time for drinking it arrives, if you succeed. (This is confirmed by your daughter, a lawyer, after she examines the legal and financial documents that the billionaire has signed.) All you have to do is sign the agreement and then intend at midnight tonight to drink the stuff tomorrow afternoon. You are perfectly free to change your mind after receiving the money and not drink the toxin. (The presence or absence of the intention is to be determined by the latest ‘mind-reading’ brain scanner and computing device designed by the great Doctor X. As a cognitive scientist, materialist, and former student of Doctor X, you have no doubt that the machine will correctly detect the presence or absence of the relevant intention.)

Confronted with this offer, you gleefully sign the contract, thinking ‘what an easy way to become a millionaire’. Not long afterwards, however, you begin to worry. You had been thinking that you could avoid drinking the toxin and just pocket the million. But you realize that if you are thinking in those terms when midnight rolls around, you will not be intending to drink the toxin tomorrow. So maybe you will actually have to drink the stuff to collect the money. It will not be pleasant, but it is sure worth a day of suffering to become a millionaire.

However, as occurs to you immediately, it cannot really be necessary to drink the toxin to pocket the money. That money will either be or not be in your bank account by 10 a.m. tomorrow, you will know then whether it is there or not, and your drinking or not drinking the toxin hours later cannot affect the completed financial transaction. So instead of planning to drink the toxin, you decide to intend today to drink it and then change your mind after midnight. But if that is your plan, then it is obvious that you do not intend to drink the toxin. (At most you intend to intend to drink it.) For having such an intention is incompatible with planning to change your mind tomorrow morning.

The discussion goes on from here for some time, but the resolution of the puzzle is easier than Kavka realizes. There is only a problem because it is implicitly assumed that the belief that you will or will not drink the toxin is something different from the intention to drink it. But in the case of voluntary actions, these are one and the same. The reason you cannot intend to drink the toxin without thinking that you will end up drinking it is simply that the intention to drink the toxin is the belief that you will end up drinking it. If the brain scanner works correctly, it registers that you intend to drink the toxin if you in fact think you will end up drinking it, and it registers that you do not intend this if you in fact think you will not drink it.

Is there a problem on the practical level? That is, is it possible for someone to get the million, or is it impossible because everyone in such a situation would expect that they would reconsider tomorrow morning, and therefore they will not believe that they will end up drinking it?

Possibly, and for some people. It is entirely possible in some situations that beliefs about what you will in fact do, apparently simply based on facts, entirely prevent certain decisions and intentions. Thus if someone has tried dozens of times in the past to give up smoking, and consistently failed, it will become more and more difficult to intend to give up smoking, and may very well become impossible.

However, Kavka gives a theoretical argument that this should be impossible in the case of his thought experiment:

Thus, we can explain your difficulty in earning a fortune: you cannot intend to act as you have no reason to act, at least when you have substantial reason not to act. And you have (or will have when the time comes) no reason to drink the toxin, and a very good reason not to, for it will make you quite sick for a day.

Again, it may well be that this reasoning would cause an individual to fail to obtain the million. But it is not necessary for this to happen. For the person does have a reason to intend to drink the toxin in the first place: namely, in order to obtain the million. And tomorrow morning their decision, i.e. their belief that they will drink the toxin, will be an efficient cause of them actually drinking the toxin, unless they reconsider. Thus if a person expects to reconsider, they may well fail to obtain the million. But someone wanting to obtain the million will also therefore plan not to reconsider. And tomorrow morning their belief that they will not reconsider will be an efficient cause of them not reconsidering, unless they reconsider their plan not to reconsider. And so on.

Thus, someone can only obtain the million if they plan to drink the toxin, they plan not to reconsider this plan, and so on. And someone with this plan can obtain the million. And maybe they will end up drinking the toxin and maybe they won’t; but the evening before, they believe that they factually will drink it. If they don’t, they fail to obtain the million. And they may well in fact drink it, simply by carrying out the original plan: going about their day without thinking about it, and simply drinking that afternoon, without any additional consideration of reasons to drink or not drink.

There is also a way to obtain the million and avoid drinking, but it cannot happen on purpose. This can happen only in one way: namely, by being lucky. You plan on every level not to reconsider, and expect this to happen, but luckily you end up being mistaken, and you do reconsider, despite expecting not to. In this case you both obtain the million, and avoid the drink.

 

Laws of Logic

In the last post, we quoted Carin Robinson’s claim:

For instance, where we use the laws of logic, let us remember that there are no known/knowable facts about logic. These laws are therefore, to the best of our knowledge, conventions not dissimilar to the rules of a game.

Law

I intend to discuss Robinson’s claim in a bit more detail shortly, but first consider the meaning of a law in its plainest sense. In the USA there is a law that you must pay your taxes for the previous year by mid April. What does this law do? Presumably the purpose of the law is to get people to pay their taxes by that time. Without the law, they would likely not pay by then, and if there were no rule that you have to pay taxes at all, people presumably would not pay taxes. So the law is meant to make something happen, namely the payment of taxes by a certain date, something that otherwise might not happen.

Rules of a game

What about the rules of a game? Consider the game of hide and seek. Wikipedia describes it in some detail:

Hide-and-seek, or hide-and-go-seek, is a popular children’s game in which any number of players (ideally at least three) conceal themselves in a set environment, to be found by one or more seekers. The game is played by one player chosen (designated as being “it”) closing their eyes and counting to a predetermined number while the other players hide. For example, count to 100 in units of 5 or count to 20, one two three and keep counting up till it reaches twenty. After reaching this number, the player who is “it” calls “Ready or not, here I come!” and then attempts to locate all concealed players.

This is partly a factual description, but it is also attempting to give the rules. It seems to be a rule that the players who are hiding have some amount of time to hide, and it would seem to be a violation of the rules if the seeker simply starts the game by announcing, “I see everyone here, so I’ve found everyone,” without there being any time to hide.

What do these rules do? Are they like the law?

Yes and no, in different respects. You can certainly imagine a player breaking the rules in the above manner. So the rules, like the law, are meant to make something happen, namely the players act in a certain manner, and they are meant to exclude what might happen without the rule, just like the law.

There is a difference, however. If a player did the above, they would not be playing the game at all. It is possible to go about your life and not pay any taxes; but it is not possible to play hide-and-seek without there being a space or time for people to hide. In this sense, the law excludes some possibilities for life, but the rule of the game does not exclude some possibilities for that game; it simply describes what the game is. It does exclude possibilities that would be rules for other games. So it excludes some possibilities; but not possibilities for the game of hide and seek.

Facts

Why does Robinson say that there are no “facts” about logic? The English word “fact” is taken from the Latin factum, which means “done” or “made.” This is not accidental to the claim here. There is nothing making things follow the rules of logic, and for this reason Robinson asserts that there are no facts, i.e. nothing made to be the case in the realm of logic. Precisely for this reason, you don’t have to go out and look at the “facts”, i.e. things that are made to be the case in the world, to determine whether or not a statement of logic or mathematics is correct or not.

Laws of Logic

Robinson argues that since the laws of logic don’t make anything be the case in the world, they must be conventional, like “rules of a game”. But in our discussion of the rules of a game, we saw that such rules do exclude certain types of possibility, while they constitute the game itself, and therefore do not exclude any possibilities for the game. How would this work if the rules of logic were rules of a game? What sorts of possibility are excluded by the rules, and what game is constituted by the rules?

As we said, it is possible to break the rules of a game, although when you do, you often stop playing the game by definition. It it similarly possible to break the laws of logic?

If we take the game to be a certain sort of speaking, yes, it is. It is possible for someone to say the words, “Blue things are not blue.” It is possible for someone to say the words, “All cats are mammals. Alvin is a cat. Therefore Alvin is not a mammal.” Someone doing this, however, is not playing the particular game in question. What is that game? I suggest we call it “speaking sensibly about reality.” Someone who breaks the laws of logic, by that very fact, fails to speak sensibly about reality, just as someone who breaks the rules of hide-and-seek fails to play the game.

The rules of hide-and-seek are conventional, in the sense that you could have other rules. But if you did have other rules, you would be playing a different game. In the same way, if you had rules other than the laws of logic for your speaking game, you would be doing something entirely different. You would not be doing what we are normally trying to do when we speak, namely speaking sensibly about reality.

Up to this point, we have actually succeeded in making a certain sort of sense out of Robinson’s claim. But does it follow, as supposed, that logic tells us nothing about reality? We pointed out in the previous post that this is not true. But why is it not, if the laws of logic are conventions about how to speak?

Do the rules of hide-and-seek tell us something about the game of hide-and-seek? Clearly they do, despite the fact that they are conventional. They tell us most of what there is to know about the game. They tell us what the game is, in fact. Likewise, the laws of logic tell us how to speak sensibly about reality. Do they also tell us about reality itself, or just about how to speak about it?

They do, in the way that considering the effect reveals the cause. Reality is what it is, and therefore certain ways of speaking are sensible and others are not. So to tell someone how to speak sensibly is to tell them something about reality. However, there is another difference between the laws of logic and the rules of a game. The rules of a game are conventional in the sense that we could have different rules and different games. And similarly, if we didn’t want to follow the “conventions” of logic, we could speak nonsensically instead of trying to speak sensibly about reality. But there is not some possible alternate reality which could be spoken of sensibly by using different “conventions.” In this sense, you can call the laws of logic rules of a game, if you wish. But they are the rules of the game of understanding, and there is only such game, not only in practice but in principle, and the rules could not have been otherwise.

Tautologies Not Trivial

In mathematics and logic, one sometimes speaks of a “trivial truth” or “trivial theorem”, referring to a tautology. Thus for example in this Quora question, Daniil Kozhemiachenko gives this example:

The fact that all groups of order 2 are isomorphic to one another and commutative entails that there are no non-Abelian groups of order 2.

This statement is a tautology because “Abelian group” here just means one that is commutative: the statement is like the customary example of asserting that “all bachelors are unmarried.”

Some extend this usage of “trivial” to refer to all statements that are true in virtue of the meaning of the terms, sometimes called “analytic.” The effect of this is to say that all statements that are logically necessary are trivial truths. An example of this usage can be seen in this paper by Carin Robinson. Robinson says at the end of the summary:

Firstly, I do not ask us to abandon any of the linguistic practises discussed; merely to adopt the correct attitude towards them. For instance, where we use the laws of logic, let us remember that there are no known/knowable facts about logic. These laws are therefore, to the best of our knowledge, conventions not dissimilar to the rules of a game. And, secondly, once we pass sentence on knowing, a priori, anything but trivial truths we shall have at our disposal the sharpest of philosophical tools. A tool which can only proffer a better brand of empiricism.

While the word “trivial” does have a corresponding Latin form that means ordinary or commonplace, the English word seems to be taken mainly from the “trivium” of grammar, rhetoric, and logic. This would seem to make some sense of calling logical necessities “trivial,” in the sense that they pertain to logic. Still, even here something is missing, since Robinson wants to include the truths of mathematics as trivial, and classically these did not pertain to the aforesaid trivium.

Nonetheless, overall Robinson’s intention, and presumably that of others who speak this way, is to suggest that such things are trivial in the English sense of “unimportant.” That is, they may be important tools, but they are not important for understanding. This is clear at least in our example: Robinson calls them trivial because “there are no known/knowable facts about logic.” Logical necessities tell us nothing about reality, and therefore they provide us with no knowledge. They are true by the meaning of the words, and therefore they cannot be true by reason of facts about reality.

Things that are logically necessary are not trivial in this sense. They are important, both in a practical way and directly for understanding the world.

Consider the failure of the Mars Climate Orbiter:

On November 10, 1999, the Mars Climate Orbiter Mishap Investigation Board released a Phase I report, detailing the suspected issues encountered with the loss of the spacecraft. Previously, on September 8, 1999, Trajectory Correction Maneuver-4 was computed and then executed on September 15, 1999. It was intended to place the spacecraft at an optimal position for an orbital insertion maneuver that would bring the spacecraft around Mars at an altitude of 226 km (140 mi) on September 23, 1999. However, during the week between TCM-4 and the orbital insertion maneuver, the navigation team indicated the altitude may be much lower than intended at 150 to 170 km (93 to 106 mi). Twenty-four hours prior to orbital insertion, calculations placed the orbiter at an altitude of 110 kilometers; 80 kilometers is the minimum altitude that Mars Climate Orbiter was thought to be capable of surviving during this maneuver. Post-failure calculations showed that the spacecraft was on a trajectory that would have taken the orbiter within 57 kilometers of the surface, where the spacecraft likely skipped violently on the uppermost atmosphere and was either destroyed in the atmosphere or re-entered heliocentric space.[1]

The primary cause of this discrepancy was that one piece of ground software supplied by Lockheed Martin produced results in a United States customary unit, contrary to its Software Interface Specification (SIS), while a second system, supplied by NASA, expected those results to be in SI units, in accordance with the SIS. Specifically, software that calculated the total impulse produced by thruster firings produced results in pound-force seconds. The trajectory calculation software then used these results – expected to be in newton seconds – to update the predicted position of the spacecraft.

It is presumably an analytic truth that the units defined in one way are unequal to the units defined in the other. But it was ignoring this analytic truth that was the primary cause of the space probe’s failure. So it is evident that analytic truths can be extremely important for practical purposes.

Such truths can also be important for understanding reality. In fact, they are typically more important for understanding than other truths. The argument against this is that if something is necessary in virtue of the meaning of the words, it cannot be telling us something about reality. But this argument is wrong for one simple reason: words and meaning themselves are both elements of reality, and so they do tell us something about reality, even when the truth is fully determinate given the meaning.

If one accepts the mistaken argument, in fact, sometimes one is led even further. Logically necessary truths cannot tell us anything important for understanding reality, since they are simply facts about the meaning of words. On the other hand, anything which is not logically necessary is in some sense accidental: it might have been otherwise. But accidental things that might have been otherwise cannot help us to understand reality in any deep way: it tells us nothing deep about reality to note that there is a tree outside my window at this moment, when this merely happens to be the case, and could easily have been otherwise. Therefore, since neither logically necessary things, nor logically contingent things, can help us to understand reality in any deep or important way, such understanding must be impossible.

It is fairly rare to make such an argument explicitly, but it is a common implication of many arguments that are actually made or suggested, or it at least influences the way people feel about arguments and understanding.  For example, consider this comment on an earlier post. Timocrates suggests that (1) if you have a first cause, it would have to be a brute fact, since it doesn’t have any other cause, and (2) describing reality can’t tell us any reasons but is “simply another description of how things are.” The suggestion behind these objections is that the very idea of understanding is incoherent. As I said there in response, it is true that every true statement is in some sense “just a description of how things are,” but that was what a true statement was meant to be in any case. It surely was not meant to be a description of how things are not.

That “analytic” or “tautologous” statements can indeed provide a non-trivial understanding of reality can also easily be seen by example. Some examples from this blog:

Good and being. The convertibility of being and goodness is “analytic,” in the sense that carefully thinking about the meaning of desire and the good reveals that a universe where existence as such was bad, or even failed to be good, is logically impossible. In particular, it would require a universe where there is no tendency to exist, and this is impossible given that it is posited that something exists.

Natural selection. One of the most important elements of Darwin’s theory of evolution is the following logically necessary statement: the things that have survived are more likely to be the things that were more likely to survive, and less likely to be the things that were less likely to survive.

Limits of discursive knowledge. Knowledge that uses distinct thoughts and concepts is necessarily limited by issues relating to self-reference. It is clear that this is both logically necessary, and tells us important things about our understanding and its limits.

Knowledge and being. Kant rightly recognized a sense in which it is logically impossible to “know things as they are in themselves,” as explained in this post. But as I said elsewhere, the logically impossible assertion that knowledge demands an identity between the mode of knowing and the mode of being is the basis for virtually every sort of philosophical error. So a grasp on the opposite “tautology” is extremely useful for understanding.

 

Perfectly Random

Suppose you have a string of random binary digits such as the following:

00111100010101001100011011001100110110010010100111

This string is 50 digits long, and was the result of a single attempt using the linked generator.

However, something seems distinctly non-random about it: there are exactly 25 zeros and exactly 25 ones. Naturally, this will not always happen, but most of the time the proportion of zeros will be fairly close to half. And evidently this is necessary, since if the proportion was usually much different from half, then the selection could not have been random in the first place.

There are other things about this string that are definitely not random. It contains only zeros and ones, and no other digits, much less items like letters from the alphabet, or items like ‘%’ and ‘$’.

Why do we have these apparently non-random characteristics? Both sorts of characteristics, the approximate and typical proportion, and the more rigid characteristics, are necessary consequences of the way we obtained or defined this number.

It is easy to see that such characteristics are inevitable. Suppose someone wants to choose something random without any non-random characteristics. Let’s suppose they want to avoid the first sort of characteristic, which is perhaps the “easier” task. They can certainly make the proportion of zeros approximately 75% or anything else that they please. But this will still be a non-random characteristic.

They try again. Suppose they succeed in preventing the series of digits from converging to any specific probability. If they do, there is one and only one way to do this. Much as in our discussion of the mathematical laws of nature, the only way to accomplish this will be to go back and forth between longer and longer strings of zeros and ones. But this is an extremely non-random characteristic. So they may have succeeded in avoiding one particular type of non-randomness, but only at the cost of adding something else very non-random.

Again, consider the second kind of characteristic. Here things are even clearer: the only way to avoid the second kind of characteristic is not to attempt any task in the first place. The only way to win is not to play. Once we have said “your task is to do such and such,” we have already specified some non-random characteristics of the second kind; to avoid such characteristics is to avoid the task completely.

“Completely random,” in fact, is an incoherent idea. No such thing can exist anywhere, in the same way that “formless matter” cannot actually exist, but all matter is formed in one way or another.

The same thing applies to David Hume’s supposed problem of induction. I ended that post with the remark that for his argument to work, he must be “absolutely certain that the future will resemble the past in no way.” But this of course is impossible in the first place; the past and the future are both defined as periods of time, and so there is some resemblance in their very definition, in the same way that any material thing must have some form in its definition, and any “random” thing must have something non-random in its definition.

 

Discount Rates

Eliezer Yudkowsky some years ago made this argument against temporal discounting:

I’ve never been a fan of the notion that we should (normatively) have a discount rate in our pure preferences – as opposed to a pseudo-discount rate arising from monetary inflation, or from opportunity costs of other investments, or from various probabilistic catastrophes that destroy resources or consumers.  The idea that it is literally, fundamentally 5% more important that a poverty-stricken family have clean water in 2008, than that a similar family have clean water in 2009, seems like pure discrimination to me – just as much as if you were to discriminate between blacks and whites.

Robin  Hanson disagreed, responding with this post:

But doesn’t discounting at market rates of return suggest we should do almost nothing to help far future folk, and isn’t that crazy?  No, it suggests:

  1. Usually the best way to help far future folk is to invest now to give them resources they can spend as they wish.
  2. Almost no one now in fact cares much about far future folk, or they would have bid up the price (i.e., market return) to much higher levels.

Very distant future times are ridiculously easy to help via investment.  A 2% annual return adds up to a googol (10^100) return over 12,000 years, even if there is only a 1/1000 chance they will exist or receive it.

So if you are not incredibly eager to invest this way to help them, how can you claim to care the tiniest bit about them?  How can you think anyone on Earth so cares?  And if no one cares the tiniest bit, how can you say it is “moral” to care about them, not just somewhat, but almost equally to people now?  Surely if you are representing a group, instead of spending your own wealth, you shouldn’t assume they care much.

Yudkowsky’s argument is idealistic, while Hanson is attempting to be realistic. I will look at this from a different point of view. Hanson is right, and Yudkowsky is wrong, for a still more idealistic reason than Yudkowsky’s reasons. In particular, a temporal discount rate is logically and mathematically necessary in order to have consistent preferences.

Suppose you have the chance to save 10 lives a year from now, or 2 years from now, or 3 years from now etc., such that your mutually exclusive options include the possibility of saving 10 lives x years from now for all x.

At first, it would seem to be consistent for you to say that all of these possibilities have equal value by some measure of utility.

The problem does not arise from this initial assignment, but it arises when we consider what happens when you act in this situation. Your revealed preferences in that situation will indicate that you prefer things nearer in time to things more distant, for the following reason.

It is impossible to choose a random integer without a bias towards low numbers, for the same reasons we argued here that it is impossible to assign probabilities to hypotheses without, in general, assigning simpler hypotheses higher probabilities. In a similar way, if “you will choose 2 years from now”, “you will choose 10 years from now,” “you will choose 100 years from now,” are all assigned probabilities, they cannot all be assigned equal probabilities, but you must be more likely to choose the options less distant in time, in general and overall. There will be some number n such that there is a 99.99% chance that you will choose some number of years less than n, and and a probability of 0.01% that you will choose n or more years, indicating that you have a very strong preference for saving lives sooner rather than later.

Someone might respond that this does not necessarily affect the specific value assignments, in the same way that in some particular case, we can consistently think that some particular complex hypothesis is more probable than some particular simple hypothesis. The problem with this is the hypotheses do not change their complexity, but time passes, making things distant in time become things nearer in time. Thus, for example, if Yudkowsky responds, “Fine. We assign equal value to saving lives for each year from 1 to 10^100, and smaller values to the times after that,” this will necessarily lead to dynamic inconsistency. The only way to avoid this inconsistency is to apply a discount rate to all periods of time, including ones in the near, medium, and long term future.