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.

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.

 

Spooky Action at a Distance

Albert Einstein objected to the usual interpretations of quantum mechanics because they seemed to him to imply “spooky action at a distance,” a phrase taken from a letter from Einstein to Max Born in 1947 (page 155 in this book):

I cannot make a case for my attitude in physics which you would consider at all reasonable. I admit, of course, that there is a considerable amount of validity in the statistical approach which you were the first to recognize clearly as necessary given the framework of the existing formalism. I cannot seriously believe in it because the theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance. I am, however, not yet firmly convinced that it can really be achieved with a continuous field theory, although I have discovered a possible way of doing this which so far seems quite reasonable. The calculation difficulties are so great that I will be biting the dust long before I myself can be fully convinced of it. But I am quite convinced that someone will eventually come up with a theory whose objects, connected by laws, are not probabilities but considered facts, as used to be taken for granted until quite recently. I cannot, however, base this conviction on logical reasons, but can only produce my little finger as witness, that is, I offer no authority which would be able to command any kind of respect outside of my own hand.

Einstein has two objections: the theory seems to be indeterministic, and it also seems to imply action at a distance. He finds both of these implausible. He thinks physics should be deterministic, “as used to be taken for granted until quite recently,” and that all interactions should be local: things directly affect only things which are close by, and affect distant things only indirectly.

In many ways, things do not appear to have gone well for Einstein’s intuitions. John Bell constructed a mathematical argument, now known as Bell’s Theorem, that the predictions of quantum mechanics cannot be reproduced by the kind of theory desired by Einstein. Bell summarizes his point:

The paradox of Einstein, Podolsky and Rosen was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore to the theory causality and locality. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics. It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty. There have been attempts to show that even without such a separability or locality requirement no “hidden variable” interpretation of quantum mechanics is possible. These attempts have been examined elsewhere and found wanting. Moreover, a hidden variable interpretation of elementary quantum theory has been explicitly constructed. That particular interpretation has indeed a grossly non-local structure. This is characteristic, according to the result to be proved here, of any such theory which reproduces exactly the quantum mechanical predictions.

“Causality and locality” in this description are exactly the two points where Einstein objected in the quoted letter: causality, as understood here, implies determinism, and locality implies no spooky action at a distance. Given this result, Einstein might have hoped that the predictions of quantum mechanics would turn out to fail, so that he could still have his desired physics. This did not happen. On the contrary, these predictions (precisely those inconsistent with such theories) have been verified time and time again.

Rather than putting the reader through Bell’s math and physics, we will explain his result with an analogy by Mark Alford. Alford makes this comparison:

Imagine that someone has told us that twins have special powers, including the ability to communicate with each other using telepathic influences that are “superluminal” (faster than light). We decide to test this by collecting many pairs of twins, separating each pair, and asking each twin one question to see if their answers agree.

To make things simple we will only have three possible questions, and they will be Yes/No questions. We will tell the twins in advance what the questions are.

The procedure is as follows.

  1. A new pair of twins is brought in and told what the three possible questions are.
  2. The twins travel far apart in space to separate questioning locations.
  3. At each location there is a questioner who selects one of the three questions at random, and poses that question to the twin in front of her.
  4. Spacelike separation. When the question is chosen and asked at one location, there is not enough time for any influence traveling at the speed of light to get from there to the other location in time to affect either what question is chosen there, or the answer given.

He now supposes the twins give the same responses when they are asked the same question, and discusses this situation:

Now, suppose we perform this experiment and we find same-question agreement: whenever a pair of spacelike-separated twins both happen to get asked the same question, their answers always agree. How could they do this? There are two possible explanations,

1. Each pair of twins uses superluminal telepathic communication to make sure both twins give the same answer.

2. Each pair of twins follows a plan. Before they were separated they agreed in advance what their answers to the three questions would be.

The same-question agreement that we observe does not prove that twins can communicate telepathically faster than light. If we believe that strong locality is a valid principle, then we can resort to the other explanation, that each pair of twins is following a plan. The crucial point is that this requires determinism. If there were any indeterministic evolution while the twins were spacelike separated, strong locality requires that the random component of one twin’s evolution would have to be uncorrelated with the other twin’s evolution. Such uncorrelated indeterminism would cause their recollections of the plan to diverge, and they would not always show same-question agreement.

The results are understandable if the twins agree on the answers Yes-Yes-Yes, or Yes-No-Yes, or any other determinate combination. But they are not understandable if they decide to flip coins if they are asked the second question, for example. If they did this, they would have to disagree 50% of the time on that question, unless one of the coin flips affected the other.

Alford goes on to discuss what happens when the twins are asked different questions:

In the thought experiment as described up to this point we only looked at the recorded answers in cases where each twin in a given pair was asked the same question. There are also recorded data on what happens when the two questioners happen to choose different questions. Bell noticed that this data can be used as a cross-check on our strong-locality-saving idea that the twins are following a pre-agreed plan that determines that their answers will always agree. The cross-check takes the form of an inequality:

Bell inequality for twins:

If a pair of twins is following a plan then, when each twin is asked a different randomly chosen question, their answers will be the same, on average, at least 1/3 of the time.

He derives this value:

For each pair of twins, there are four general types of pre-agreed plan they could adopt when they are arranging how they will both give the same answer to each of the three possible questions.

(a) a plan in which all three answers are Yes;

(b) a plan in which there are two Yes and one No;

(c) a plan in which there are two No and one Yes;

(d) a plan in which all three answers are No.

If, as strong locality and same-question agreement imply, both twins in a given pair follow a shared predefined plan, then when the random questioning leads to each of them being asked a different question from the set of three possible questions, how often will their answers happen to be the same (both Yes or both No)? If the plan is of type (a) or (d), both answers will always be the same. If the plan is of type (b) or (c), both answers will be the same 1/3 of the time. We conclude that no matter what type of plan each pair of twins may follow, the mere fact that they are following a plan implies that, when each of them is asked a different randomly chosen question, they will both give the same answer (which might be Yes or No) at least 1/3 of the time. It is important to appreciate that one needs data from many pairs of twins to see this effect, and that the inequality holds even if each pair of twins freely chooses any plan they like.

The “Bell inequality” is violated if we do the experimental test and the twins end up agreeing, when they are asked different questions, less than 1/3 of the time, despite consistently agreeing when they are asked the same question. If one saw such results in reality, one might be forgiven for concluding that the twins do have superluminal telepathic abilities. Unfortunately for Einstein, this is what we do get, consistently, when we test the analogous quantum mechanical version of the experiment.

Miracles and Anomalies: Or, Your Religion is False

In 2011 there was an apparent observation of neutrinos traveling faster than light. Wikipedia says of this, “Even before the mistake was discovered, the result was considered anomalous because speeds higher than that of light in a vacuum are generally thought to violate special relativity, a cornerstone of the modern understanding of physics for over a century.” In other words, most scientists did not take the result very seriously, even before any specific explanation was found. As I stated here, it is possible to push unreasonably far in this direction, in such a way that one will be reluctant to ever modify one’s current theories. But there is also something reasonable about this attitude.

Alexander Pruss explains why scientists tend to be skeptical of such anomalous results in this post on Bayesianism and anomaly:

One part of the problem of anomaly is this. If a well-established scientific theory seems to predict something contrary to what we observe, we tend to stick to the theory, with barely a change in credence, while being dubious of the auxiliary hypotheses. What, if anything, justifies this procedure?

Here’s my setup. We have a well-established scientific theory T and (conjoined) auxiliary hypotheses A, and T together with A uncontroversially entails the denial of some piece of observational evidence E which we uncontroversially have (“the anomaly”). The auxiliary hypotheses will typically include claims about the experimental setup, the calibration of equipment, the lack of further causal influences, mathematical claims about the derivation of not-E from T and the above, and maybe some final catch-all thesis like the material conditional that if T and all the other auxiliary hypotheses obtain, then E does not obtain.

For simplicity I will suppose that A and T are independent, though of course that simplifying assumption is rarely true.

Here’s a quick and intuitive thought. There is a region of probability space where the conjunction of T and A is false. That area is divided into three sub-regions:

  1. T is true and A is false
  2. T is false and A is true
  3. both are false.

The initial probabilities of the three regions are, respectively, 0.0999, 0.0009999 and 0.0001. We know we are in one of these three regions, and that’s all we now know. Most likely we are in the first one, and the probability that we are in that one given that we are in one of the three is around 0.99. So our credence in T has gone down from three nines (0.999) to two nines (0.99), but it’s still high, so we get to hold on to T.

Still, this answer isn’t optimistic. A move from 0.999 to 0.99 is actually an enormous decrease in confidence.

“This answer isn’t optimistic,” because in the case of the neutrinos, this analysis would imply that scientists should have instantly become ten times more willing to consider the possibility that the theory of special relativity is false. This is surely not what happened.

Pruss therefore presents an alternative calculation:

But there is a much more optimistic thought. Note that the above wasn’t a real Bayesian calculation, just a rough informal intuition. The tip-off is that I said nothing about the conditional probabilities of E on the relevant hypotheses, i.e., the “likelihoods”.

Now setup ensures:

  1. P(E|A ∧ T)=0.

What can we say about the other relevant likelihoods? Well, if some auxiliary hypothesis is false, then E is up for grabs. So, conservatively:

  1. P(E|∼A ∧ T)=0.5
  2. P(E|∼A ∧ ∼T)=0.5

But here is something that I think is really, really interesting. I think that in typical cases where T is a well-established scientific theory and A ∧ T entails the negation of E, the probability P(E|A ∧ ∼T) is still low.

The reason is that all the evidence that we have gathered for T even better confirms the hypothesis that T holds to a high degree of approximation in most cases. Thus, even if T is false, the typical predictions of T, assuming they have conservative error bounds, are likely to still be true. Newtonian physics is false, but even conditionally on its being false we take individual predictions of Newtonian physics to have a high probability. Thus, conservatively:

  1. P(E|A ∧ ∼T)=0.1

Very well, let’s put all our assumptions together, including the ones about A and T being independent and the values of P(A) and P(T). Here’s what we get:

  1. P(E|T)=P(E|A ∧ T)P(A|T)+P(E|∼A ∧ T)P(∼A|T)=0.05
  2. P(E|∼T)=P(E|A ∧ ∼T)P(A|∼T)+P(E|∼A ∧ ∼T)P(∼A|∼T) = 0.14.

Plugging this into Bayes’ theorem, we get P(T|E)=0.997. So our credence has crept down, but only a little: from 0.999 to 0.997. This is much more optimistic (and conservative) than the big move from 0.999 to 0.99 that the intuitive calculation predicted.

So, if I am right, at least one of the reasons why anomalies don’t do much damage to scientific theories is that when the scientific theory T is well-confirmed, the anomaly is not only surprising on the theory, but it is surprising on the denial of the theory—because the background includes the data that makes T “well-confirmed” and would make E surprising even if we knew that T was false.

To make the point without the mathematics (which in any case is only used to illustrate the point, since Pruss is choosing the specific values himself), if you have a theory which would make the anomaly probable, that theory would be strongly supported by the anomaly. But we already know that theories like that are false, because otherwise the anomaly would not be an anomaly. It would be normal and common. Thus all of the actually plausible theories still make the anomaly an improbable observation, and therefore these theories are only weakly supported by the observation of the anomaly. The result is that the new observation makes at most a minor difference to your previous opinion.

We can apply this analysis to the discussion of miracles. David Hume, in his discussion of miracles, seems to desire a conclusive proof against them which is unobtainable, and in this respect he is mistaken. But near the end of his discussion, he brings up the specific topic of religion and says that his argument applies to it in a special way:

Upon the whole, then, it appears, that no testimony for any kind of miracle has ever amounted to a probability, much less to a proof; and that, even supposing it amounted to a proof, it would be opposed by another proof; derived from the very nature of the fact, which it would endeavour to establish. It is experience only, which gives authority to human testimony; and it is the same experience, which assures us of the laws of nature. When, therefore, these two kinds of experience are contrary, we have nothing to do but subtract the one from the other, and embrace an opinion, either on one side or the other, with that assurance which arises from the remainder. But according to the principle here explained, this subtraction, with regard to all popular religions, amounts to an entire annihilation; and therefore we may establish it as a maxim, that no human testimony can have such force as to prove a miracle, and make it a just foundation for any such system of religion.

The idea seems to be something like this: contrary systems of religion put forth miracles in their support, so the supporting evidence for one religion is more or less balanced by the supporting evidence for the other. Likewise, the evidence is weakened even in itself by people’s propensity to lies and delusion in such matters (some of this discussion was quoted in the earlier post on Hume and miracles). But in addition to the fairly balanced evidence we have experience basically supporting the general idea that the miracles do not happen. This is not outweighed by anything in particular, and so it is the only thing that remains after the other evidence balances itself out of the equation. Hume goes on:

I beg the limitations here made may be remarked, when I say, that a miracle can never be proved, so as to be the foundation of a system of religion. For I own, that otherwise, there may possibly be miracles, or violations of the usual course of nature, of such a kind as to admit of proof from human testimony; though, perhaps, it will be impossible to find any such in all the records of history. Thus, suppose, all authors, in all languages, agree, that, from the first of January, 1600, there was a total darkness over the whole earth for eight days: suppose that the tradition of this extraordinary event is still strong and lively among the people: that all travellers, who return from foreign countries, bring us accounts of the same tradition, without the least variation or contradiction: it is evident, that our present philosophers, instead of doubting the fact, ought to receive it as certain, and ought to search for the causes whence it might be derived. The decay, corruption, and dissolution of nature, is an event rendered probable by so many analogies, that any phenomenon, which seems to have a tendency towards that catastrophe, comes within the reach of human testimony, if that testimony be very extensive and uniform.

But suppose, that all the historians who treat of England, should agree, that, on the first of January, 1600, Queen Elizabeth died; that both before and after her death she was seen by her physicians and the whole court, as is usual with persons of her rank; that her successor was acknowledged and proclaimed by the parliament; and that, after being interred a month, she again appeared, resumed the throne, and governed England for three years: I must confess that I should be surprised at the concurrence of so many odd circumstances, but should not have the least inclination to believe so miraculous an event. I should not doubt of her pretended death, and of those other public circumstances that followed it: I should only assert it to have been pretended, and that it neither was, nor possibly could be real. You would in vain object to me the difficulty, and almost impossibility of deceiving the world in an affair of such consequence; the wisdom and solid judgment of that renowned queen; with the little or no advantage which she could reap from so poor an artifice: all this might astonish me; but I would still reply, that the knavery and folly of men are such common phenomena, that I should rather believe the most extraordinary events to arise from their concurrence, than admit of so signal a violation of the laws of nature.

But should this miracle be ascribed to any new system of religion; men, in all ages, have been so much imposed on by ridiculous stories of that kind, that this very circumstance would be a full proof of a cheat, and sufficient, with all men of sense, not only to make them reject the fact, but even reject it without farther examination. Though the Being to whom the miracle is ascribed, be, in this case, Almighty, it does not, upon that account, become a whit more probable; since it is impossible for us to know the attributes or actions of such a Being, otherwise than from the experience which we have of his productions, in the usual course of nature. This still reduces us to past observation, and obliges us to compare the instances of the violation of truth in the testimony of men, with those of the violation of the laws of nature by miracles, in order to judge which of them is most likely and probable. As the violations of truth are more common in the testimony concerning religious miracles, than in that concerning any other matter of fact; this must diminish very much the authority of the former testimony, and make us form a general resolution, never to lend any attention to it, with whatever specious pretence it may be covered.

Notice how “unfair” this seems to religion, so to speak. What is the difference between the eight days of darkness, which Hume would accept, under those conditions, and the resurrection of the queen of England, which he would not? Hume’s reaction to the two situations is more consistent than first appears. Hume would accept the historical accounts about England in the same way that he would accept the accounts about the eight days of darkness. The difference is in how he would explain the accounts. He says of the darkness, “It is evident, that our present philosophers, instead of doubting the fact, ought to receive it as certain, and ought to search for the causes whence it might be derived.” Likewise, he would accept the historical accounts as certain insofar as they say the a burial ceremony took place, the queen was absent from public life, and so on. But he would not accept that the queen was dead and came back to life. Why? The “search for the causes” seems to explain this. It is plausible to Hume that causes of eight days of darkness might be found, but not plausible to him that causes of a resurrection might be found. He hints at this in the words, “The decay, corruption, and dissolution of nature, is an event rendered probable by so many analogies,” while in contrast a resurrection would be “so signal a violation of the laws of nature.”

It is clear that Hume excludes certain miracles, such as resurrection, from the possibility of being established by the evidence of testimony. But he makes the additional point that even if he did not exclude them, he would not find it reasonable to establish a “system of religion” on such testimony, given that “violations of truth are more common in the testimony concerning religious miracles, than in that concerning any other matter of fact.”

It is hard to argue with the claim that “violations of truth” are especially common in testimony about miracles. But does any of this justify Hume’s negative attitude to miracles as establishing “systems of religion,” or is this all just prejudice?  There might well be a good deal of prejudice involved here in his opinions. Nonetheless, Alexander Pruss’s discussion of anomaly allows one to formalize Hume’s idea here as actual insight as well.

One way to look at truth in religion is to look at it as a way of life or as membership in a community. And in this way, asking whether miracles can establish a system of religion is just asking whether a person can be moved to a way of life or to join a community through such things. And clearly this is possible, and often happens. But another way to consider truth in religion is to look at a doctrinal system as a set of claims about how the world is. Looked at in this way, we should look at a doctrinal system as presenting a proposed larger context of our place in the world, one that we would be unaware of without the religion. This implies that one should have a prior probability (namely prior to consideration of arguments in its favor) strongly against the system considered as such, for reasons very much like the reasons we should have a prior probability strongly against Ron Conte’s predictions.

We can thus apply Alexander Pruss’s framework. Let us take Mormonism as the “system of religion” in question. Then taken as a set of claims about the world, our initial probability would be that it is very unlikely that the world is set up this way. Then let us take a purported miracle establishing this system: Joseph Smith finds his golden plates. In principle, if this cashed out in a certain way, it could actually establish his system. But it doesn’t cash out that way. We know very little about the plates, the circumstances of their discovery (if there was any), and their actual content. Instead, what we are left with is an anomaly: something unusual happened, and it might be able to be described as “finding golden plates,” but that’s pretty much all we know.

Then we have the theory, T, which has a high prior probability: Mormonism is almost certainly false. We have the observation : Joseph Smith discovered his golden plates (in one sense or another.) And we have the auxiliary hypotheses which imply that he could not have discovered the plates if Mormonism is false. The Bayesian updates in Pruss’s scheme imply that our conclusion is this: Mormonism is almost certainly false, and there is almost certainly an error in the auxiliary hypotheses that imply he could not have discovered them if it were false.

Thus Hume’s attitude is roughly justified: he should not change his opinion about religious systems in any significant way based on testimony about miracles.

To make you feel better, this does not prove that your religion is false. It just nearly proves that. In particular, this does not take into an account an update based on the fact that “many people accept this set of claims.” This is a different fact, and it is not an anomaly. If you update on this fact and end up with a non-trivial probability that your set of claims is true, testimony about miracles might well strengthen this into conviction.

I will respond to one particular objection, however. Some will take this argument to be stubborn and wicked, because it seems to imply that people shouldn’t be “convinced even if someone rises from the dead.” And this does in fact follow, more or less. An anomalous occurrence in most cases will have a perfectly ordinary explanation in terms of things that are already a part of our ordinary understanding of the world, without having to add some larger context. For example, suppose you heard your fan (as a piece of furniture, not as a person) talking to you. You might suppose that you were hallucinating. But suppose it turns out that you are definitely not hallucinating. Should you conclude that there is some special source from outside the normal world that is communicating with you? No: the fan scenario can happen, and it turns out to have a perfectly everyday explanation. We might agree with Hume that it would be much more implausible that a resurrection would have an everyday explanation. Nonetheless, even if we end up concluding to the existence of some larger context, and that the miracle has no such everyday explanation, there is no good reason for it to be such and such a specific system of doctrine. Consider again Ron Conte’s predictions for the future. Most likely the things that happen between now and 2040, and even the things that happen in the 2400s, are likely to be perfectly ordinary (although the things in the 2400s might differ from current events in fairly radical ways). But even if they are not, and even if apocalyptic, miraculous occurrences are common in those days, this does not raise the probability of Conte’s specific predictions above any trivial level. In the same way, the anomalous occurrences involved in the accounts of miracles will not lend any significant probability to a religious system.

The objection here is that this seems unfair to God, so to speak. What if God wanted to reveal something to the world? What could he do, besides work miracles? I won’t propose a specific answer to this, because I am not God. But I will illustrate the situation with a little story to show that there is nothing unfair to God about it.

Suppose human beings created an artificial intelligence and raised it in a simulated environment. Wanting things to work themselves out “naturally,” so to speak, because it would be less work, and because it would probably be necessary to the learning process, they institute “natural laws” in the simulated world which are followed in an exceptionless way. Once the AI is “grown up”, so to speak, they decide to start communicating with it. In the AI’s world, this will surely show up as some kind of miracle: something will happen that was utterly unpredictable to it, and which is completely inconsistent with the natural laws as it knew them.

Will the AI be forced by the reasoning of this post to ignore the communication? Well, that depends on what exactly occurs and how. At the end of his post, Pruss discusses situations where anomalous occurrences should change your mind:

Note that this argument works less well if the anomalous case is significantly different from the cases that went into the confirmation of T. In such a case, there might be much less reason to think E won’t occur if T is false. And that means that anomalies are more powerful as evidence against a theory the more distant they are from the situations we explored before when we were confirming T. This, I think, matches our intuitions: We would put almost no weight in someone finding an anomaly in the course of an undergraduate physics lab—not just because an undergraduate student is likely doing it (it could be the professor testing the equipment, though), but because this is ground well-gone over, where we expect the theory’s predictions to hold even if the theory is false. But if new observations of the center of our galaxy don’t fit our theory, that is much more compelling—in a regime so different from many of our previous observations, we might well expect that things would be different if our theory were false.

And this helps with the second half of the problem of anomaly: How do we keep from holding on to T too long in the light of contrary evidence, how do we allow anomalies to have a rightful place in undermining theories? The answer is: To undermine a theory effectively, we need anomalies that occur in situations significantly different from those that have already been explored.

If the AI finds itself in an entirely new situation, e.g. rather than hearing an obscure voice from a fan, it is consistently able to talk to the newly discovered occupant of the world on a regular basis, it will have no trouble realizing that its situation has changed, and no difficulty concluding that it is receiving communication from its author. This does, sort of, give one particular method that could be used to communicate a revelation. But there might well be many others.

Our objector will continue. This is still not fair. Now you are saying that God could give a revelation but that if he did, the world would be very different from the actual world. But what if he wanted to give a revelation in the actual world, without it being any different from the way it is? How could he convince you in that case?

Let me respond with an analogy. What if the sky were actually red like the sky of Mars, but looked blue like it is? What would convince you that it was red? The fact that there is no way to convince you that it is red in our actual situation means you are unfairly prejudiced against the redness of the sky.

In other words, indeed, I am unwilling to be convinced that the sky is red except in situations where it is actually red, and those situations are quite different from our actual situation. And indeed, I am unwilling to be convinced of a revelation except in situations where there is actually a revelation, and those are quite different from our actual situation.

Explaining Causality

A reader asks about a previous post:

a) Per Hume and his defenders, we can’t really observe causation. All we can see is event A in spacetime, then event B in spacetime. We have no reason to posit that event A and event B are, say, chairs or dogs; we can stick with a sea of observed events, and claim that the world is “nothing more” but a huge set of random 4D events. While I can see that giving such an account restores formal causation, it doesn’t salvage efficient causation, and doesn’t even help final causation. How could you move there from our “normal” view?

b) You mention that the opinion “laws are observed patterns” is not a dominant view; though, even though I’d like to sit with the majority, I can’t go further than a). I can’t build an argument for this, and fail to see how Aristotle put his four causes correctly. I always end up gnawing on an objection, like “causation is only in the mind” or similar. Help?

It is not my view that the world is a huge set of random 4D events. This is perhaps the view of Atheism and the City, but it is a mistaken one. The blogger is not mistaken in thinking that there are problems with presentism, but they cannot be solved by adopting an eternalist view. Rather, these two positions constitute a Kantian dichotomy, and as usual, both positions are false. For now, however, I will leave this to the consideration of the reader. It is not necessary to establish this to respond to the questions above.

Consider the idea that “we can’t really observe causation.” As I noted here, it does not make sense to say that we cannot observe causation unless we already understand what causation is. If the word were meaningless to us, we would have no argument that we don’t observe it; it is only because we do understand the idea of causation that we can even suggest that it might be difficult to observe. And if we do have the idea, we got the idea from somewhere, and that could only have been… from observation, of course, since we don’t have anything else to get ideas from.

Let us untie the knot. I explained causality in general in this way:

“Cause” and “effect” simply signify that the cause is the origin of the effect, and that the effect is from the cause, together with the idea that when we understand the cause, we understand the explanation for the effect. Thus “cause” adds to “origin” a certain relationship with the understanding; this is why Aristotle says that we do not think we understand a thing until we know its cause, or “why” it is. We do not understand a thing until we know its explanation.

Note that there is something “in the mind” about causality. Saying to oneself, “Aha! So that’s why that happened!” is a mental event. And we can also see how it is possible to observe causality: we can observe that one thing is from another, i.e. that a ball breaks a window, and we can also observe that knowing this provides us a somewhat satisfactory answer to the question, “Why is the window broken?”, namely, “Because it was hit by a ball.”

Someone (e.g. Atheism and the City) might object that we also cannot observe one thing coming from another. We just observe the two things, and they are, as Hume says, “loose and separate.” Once again, however, we would have no idea of “from” unless we got it from observing things. In the same early post quoted above, I explained the idea of origin, i.e. that one thing is from another:

Something first is said to be the beginning, principle, or origin of the second, and the second is said to be from the first. This simply signifies the relationship already described in the last post, together with an emphasis on the fact that the first comes before the second by “consequence of being”, in the way described.

“The relationship already described in the last post” is that of before and after. In other words, wherever we have any kind of order at all, we have one thing from another. And we observe order, even when we simply see one thing after another, and thus we also observe things coming from other things.

What about efficient causality? If we adopt the explanation above, asserting the existence of efficient causality is nothing more or less than asserting that things sometimes make other things happen, like balls breaking windows, and that knowing about this is a way for us to understand the effects (e.g. broken windows.)

Similarly, denying the existence of efficient causality means either denying that anything ever makes anything else happen, or denying that knowing about this makes us understand anything, even in a minor way. Atheism and the City seems to want to deny that anything ever makes anything else happen:

Most importantly, my view technically is not that causality doesn’t exist, it’s that causality doesn’t exist in the way we typically think it does. That is, my view of causality is completely different from the general every day notion of causality most people have. The naive assumption one often gets when hearing my view is that I’m saying cause and effect relationships don’t exist at all, such that if you threw a brick at glass window it wouldn’t shatter, or if you jumped in front of a speeding train you wouldn’t get smashed to death by it. That’s not what my view says at all.

On my view of causality, if you threw a brick at a glass window it would shatter, if you jumped in front of a speeding train you’d be smashed to death by it. The difference between my view of causality vs the typical view is that on my view causes do not bring their effects into existence in the sense of true ontological becoming.

I am going to leave aside the discussion of “true ontological becoming,” because it is a distraction from the real issue. Does Atheism and the City deny that things ever make other things happen? It appears so, but consider that “things sometimes make other things happen” is just a more general description of the very same situations as descriptions like, “Balls sometimes break windows.” So if you want to deny that things make other things happen, you should also deny that balls break windows. Now our blogger perhaps wants to say, “I don’t deny that balls break windows in the everyday sense, but they don’t break them in a true ontological sense.” Again, I will simply point in the right direction here. Asserting the existence of efficient causes does not describe a supposedly “truly true” ontology; it is simply a more general description of a situation where balls sometimes break windows.

We can make a useful comparison here between understanding causality, and understanding desire and the good. The knowledge of desire begins with a fairly direct experience, that of feeling the desire, often even as physical sensation. In the same way, we have a direct experience of “understanding something,” namely the feeling of going, “Ah, got it! That’s why this is, this is how it is.” And just as we explain the fact of our desire by saying that the good is responsible for it, we explain the fact of our understanding by saying that the apprehension of causes is responsible. And just as being and good are convertible, so that goodness is not some extra “ontological” thing, so also cause and origin are convertible. But something has to have a certain relationship with us to be good for us; eating food is good for us while eating rocks is not. In a similar way, origins need to have a specific relationship with us in order to provide an understanding of causality, as I said in the post where these questions came up.

Does this mean that “causation is only in the mind”? Not really, any more than the analogous account implies that goodness is only in the mind. An aspect of goodness is in the mind, namely insofar as we distinguish it from being in general, but the thing itself is real, namely the very being of things. And likewise an aspect of causality is in the mind, namely the fact that it explains something to us, but the thing itself is real, namely the relationships of origin in things.

Statistical Laws of Choice

I noted in an earlier post the necessity of statistical laws of nature. This will necessarily apply to human actions as a particular case, as I implied there in mentioning the amount of food humans eat in a year.

Someone might object. It was said in the earlier post that this will happen unless there is a deliberate attempt to evade this result. But since we are speaking of human beings, there might well be such an attempt. So for example if we ask someone to choose to raise their right hand or their left hand, this might converge to an average, such as 50% each, or perhaps the right hand 60% of the time, or something of this kind. But presumably someone who starts out with the deliberate intention of avoiding such an average will be able to do so.

Unfortunately, such an attempt may succeed in the short run, but will necessarily fail in the long run, because although it is possible in principle, it would require an infinite knowing power, which humans do not have. As I pointed out in the earlier discussion, attempting to prevent convergence requires longer and longer strings on one side or the other. But if you need to raise your right hand a few trillion times before switching again to your left, you will surely lose track of your situation. Nor can you remedy this by writing things down, or by other technical aids: you may succeed in doing things trillions of times with this method, but if you do it forever, the numbers will also become too large to write down. Naturally, at this point we are only making a theoretical point, but it is nonetheless an important one, as we shall see later.

In any case, in practice people do not tend even to make such attempts, and consequently it is far easier to predict their actions in a roughly statistical manner. Thus for example it would not be hard to discover the frequency with which an individual chooses chocolate ice cream over vanilla.

Mixing Water and Wine

St. Thomas discusses what happens if you mix consecrated wine with another liquid:

I answer that, The truth of this question is evident from what has been said already. For it was said above (3; 5, ad 2) that the species remaining in this sacrament, as they acquire the manner of being of substance in virtue of the consecration, so likewise do they obtain the mode of acting and of being acted upon, so that they can do or receive whatever their substance could do or receive, were it there present. But it is evident that if the substance of wine were there present, then some other liquid could be mingled with it.

Nevertheless there would be a different effect of such mixing both according to the form and according to the quantity of the liquid. For if sufficient liquid were mixed so as to spread itself all through the wine, then the whole would be a mixed substance. Now what is made up of things mixed is neither of them, but each passes into a third resulting from both: hence it would result that the former wine would remain no longer. But if the liquid added were of another species, for instance, if water were mixed, the species of the wine would be dissolved, and there would be a liquid of another species. But if liquid of the same species were added, of instance, wine with wine, the same species would remain, but the wine would not be the same numerically, as the diversity of the accidents shows: for instance, if one wine were white and the other red.

But if the liquid added were of such minute quantity that it could not permeate the whole, the entire wine would not be mixed, but only part of it, which would not remain the same numerically owing to the blending of extraneous matter: still it would remain the same specifically, not only if a little liquid of the same species were mixed with it, but even if it were of another species, since a drop of water blended with much wine passes into the species of wine (De Gener. i).

Now it is evident that the body and blood of Christ abide in this sacrament so long as the species remain numerically the same, as stated above (4; 76, 6, ad 3); because it is this bread and this wine which is consecrated. Hence, if the liquid of any kind whatsoever added be so much in quantity as to permeate the whole of the consecrated wine, and be mixed with it throughout, the result would be something numerically distinct, and the blood of Christ will remain there no longer. But if the quantity of the liquid added be so slight as not to permeate throughout, but to reach only a part of the species, Christ’s blood will cease to be under that part of the consecrated wine, yet will remain under the rest.

Given the doctrine of transubstantiation, at least as St. Thomas understands it, so that it implies the existence of accidents without a subject, it is very difficult to understand how such a mixing would be possible at all. But his general position here is that a process analogous to substantial change necessarily happens if you mix anything into the consecrated wine, either according to a part of the wine, or according to the whole. He explains this kind of change in article five of the same question:

I answer that, Since “the corruption of one thing is the generation of another” (De Gener. i), something must be generated necessarily from the sacramental species if they be corrupted, as stated above (Article 4); for they are not corrupted in such a way that they disappear altogether, as if reduced to nothing; on the contrary, something sensible manifestly succeeds to them.

Nevertheless, it is difficult to see how anything can be generated from them. For it is quite evident that nothing is generated out of the body and blood of Christ which are truly there, because these are incorruptible. But if the substance, or even the matter, of the bread and wine were to remain in this sacrament, then, as some have maintained, it would be easy to account for this sensible object which succeeds to them. But that supposition is false, as was stated above (75, 2,4,8).

Hence it is that others have said that the things generated have not sprung from the sacramental species, but from the surrounding atmosphere. But this can be shown in many ways to be impossible. In the first place, because when a thing is generated from another, the latter at first appears changed and corrupted; whereas no alteration or corruption appeared previously in the adjacent atmosphere; hence the worms or ashes are not generated therefrom. Secondly, because the nature of the atmosphere is not such as to permit of such things being generated by such alterations. Thirdly, because it is possible for many consecrated hosts to be burned or putrefied; nor would it be possible for an earthen body, large enough to be generated from the atmosphere, unless a great and, in fact, exceedingly sensible condensation of the atmosphere took place. Fourthly, because the same thing can happen to the solid bodies surrounding them, such as iron or stone, which remain entire after the generation of the aforesaid things. Hence this opinion cannot stand, because it is opposed to what is manifest to our senses.

And therefore others have said that the substance of the bread and wine returns during the corruption of the species, and so from the returning substance of the bread and wine, ashes or worms or something of the kind are generated. But this explanation seems an impossible one. First of all, because if the substance of the bread and wine be converted into the body and blood of Christ, as was shown above (75, 2,4), the substance of the bread and wine cannot return, except the body and blood of Christ be again changed back into the substance of bread and wine, which is impossible: thus if air be turned into fire, the air cannot return without the fire being again changed into air. But if the substance of bread or wine be annihilated, it cannot return again, because what lapses into nothing does not return numerically the same. Unless perchance it be said that the said substance returns, because God creates anew another new substance to replace the first. Secondly, this seems to be impossible, because no time can be assigned when the substance of the bread returns. For, from what was said above (4; 76, 6, ad 3), it is evident that while the species of the bread and wine remain, there remain also the body and blood of Christ, which are not present together with the substance of the bread and wine in this sacrament, according to what was stated above (Question 75, Article 2). Hence the substance of the bread and wine cannot return while the sacramental species remain; nor, again, when these species pass away; because then the substance of the bread and wine would be without their proper accidents, which is impossible. Unless perchance it be said that in the last instant of the corruption of the species there returns (not, indeed, the substance of bread and wine, because it is in that very instant that they have the being of the substance generated from the species, but) the matter of the bread and wine; which, matter, properly speaking, would be more correctly described as created anew, than as returning. And in this sense the aforesaid position might be held.

However, since it does not seem reasonable to say that anything takes place miraculously in this sacrament, except in virtue of the consecration itself, which does not imply either creation or return of matter, it seems better to say that in the actual consecration it is miraculously bestowed on the dimensive quantity of the bread and wine to be the subject of subsequent forms. Now this is proper to matter; and therefore as a consequence everything which goes with matter is bestowed on dimensive quantity; and therefore everything which could be generated from the matter of bread or wine, if it were present, can be generated from the aforesaid dimensive quantity of the bread or wine, not, indeed, by a new miracle, but by virtue of the miracle which has already taken place.

This is rather strange, because he seems to be saying that the subsequent substantial forms inhere in quantity as in a subject, and that there is no matter there. But if this is possible in any way, and in particular if things remain in this state permanently, as he seems to suggest, then there seems to be little reason not to adopt Descartes’s view of material substance in general, and say that quantity is always the subject of substantial forms, rather than saying that some parts of the world have matter as a subject, and other parts quantity. The account might be more reasonable if he were to accept that when a new substance is generated, matter again comes to be, not by being “created anew,” but because the being of matter in general is from substantial form.

As we can see, this discussion is especially complex on account of the doctrine of transubstantiation and St. Thomas’s account of that doctrine. But if we simply consider the mixing of two liquids in general, various difficulties will remain. Suppose we have a glass of water and a glass of wine, and mix the two together. What exactly will happen?

It is manifest to the senses that when we do this, there is a period of time when parts of the resulting liquid are water, just as it was, and parts are wine, just as it was, without any mixture. But what about the surface where the two are in contact? What is happening there?

According to St. Thomas, there will be a quantitative part which shares in the qualities of each. And this is pretty reasonable. Just as we can see that part is wine and part is water, at a certain point we can see that part is watery wine. But how exactly did that watery part get that way? If it is a certain size, was there a sudden transition of a part which was water into the watery wine? Or the like with the wine becoming watery? Or was there a continuous process with an expanding mixed region? The last possibility seems most consistent with what we see, but it might be difficult to analyze this in terms of substantial change, as St. Thomas does, because such a continuous process would have no first moment when the mixed substance came to be. For if it did, it would come to be with a definite size, and thus the process would not be continuous, but would imply that some part suddenly went from not being watery wine to being watery wine.

Of course, it is one thing to say there are difficulties. It is quite another to say that they mean that the thing cannot happen. So none of this proves that the mixing of liquids is not a substantial change. Nonetheless, many of the ancient naturalists were moved by such considerations to adopt some form of atomic theory. If water and wine are each composed of atoms, the mixing process is easily understood — it is simply the movement in place of these atoms. Each part of the water remains as it was even qualitatively, and likewise each part of the wine, but the resulting mixture has different sensible qualities because one cannot distinguish the diverse qualities of each, just as mixing two very fine sands of different color may appear to result in a third color, even though the grains of sand are not changing qualitatively.

Modern atomic theory, of course, has far stronger arguments for it, but they are in principle, or at least were in the 18th and 19th centuries, of a very similar kind: atomic theory simply does a good job of explaining many of the things that we see happen in the world.

This is closely related to the discussion in the last post. When we construct a bicycle out of parts, it is manifest to the senses that the parts look just like they did before they were parts. And this is necessary, if it is true that those parts are governed by the same natural laws after they become parts that they were before they became parts. For however the parts “look,” they look this way because of how they act on the senses. So if their action does not change, the “way they look” will not change. Similarly, when we mix liquids, if the water parts and the wine parts do not change how they behave, the account one gives of the mixture must be an atomic theory or something very like it. That is, there must remain very small parts that act like water, and very small parts that act like wine. Or, given that wine and water are not in fact elements, at least the basic elemental parts must continue to act like those elemental parts.