Defining Order

Earlier I discussed Aristotle’s senses of before and after. Using yesterday’s discussion of one and many, we can now find a more exact definition of the same terms.

We can define “second” as the formal part of something two, namely the part by which the two is two.

Thus “first” is the part of something two which is not the second. This way of defining first and second may seem backwards, but it is analogous with how we defined the unity of a thing by negating division.

Something first, as such, implies the existence of something second, and likewise something second implies the existence of something first. However, the existence of two implies the existence of one (as a part), while the existence of one does not imply the existence of two. This corresponds to the difference in the definitions of first and second given above. The second is the part by which two is two, while the first is a part, but not the part by which two is two. If first and second are considered only with respect to what is formal in them, then, as “not that by which two is two”, and “by which two is two”, then according to this consideration the first does not imply a second, but the second implies a first.

From this we can see that being before by nature, or as Aristotle says, “what does not reciprocate according to consequence of being,” if not the first thing to which the words before and after are applied, is nonetheless first in the nature of things to possess the before and after.

We can also see that this sense of before and after must be found in some way in all other senses, for every case of before and after will involve something first and something second.

This can be illustrated with the order of time, the first thing to which the words before and after are actually applied. At first it might seem that such a before and after are completely separate from the idea of reciprocation according to consequence of being, since one day can exist without another, nor is it evident that the existence of one day implies that another day existed or that another will exist.

If we consider our actual experience of the past and present (since we have no experience of the future), however, we find something different. Our experience of the present includes our memory of the past, and in this respect implies the past existence of the past. But our experience of the past, namely not the present experience of remembering the past, but the remembered experience of the past that was once present, does not include anything of the present. In this way the present implies the past, but the past does not imply the present, and thus according to these considerations the past is before the present even according to consequence of being.

This is not to deny that according to other considerations the present might be before the past. Rather, these considerations show why the past is considered to be before the present, namely because the present seems to build on the past, as though the past were one block of wood, with the present being a second block of wood stacked on top of the first block. We will find that something similar is the case in every way in which we can say that one thing is before or after another thing.

One and Many

“Many” has two meanings:

  1. That which is divided, namely something and something else such that the something is not the something else. Taken in this way, the idea of many comes before the idea of one, because many in this sense is simply defined by distinction.
  2. A whole composed of ones as parts. In this sense many comes after one.

Using the second definition, we can define numbers according to what sort of parts they have. Thus for example two is something many in the second way, such that it does not have any part which is itself many. Similarly, three is something many such that it has a part which is two, but does not have any part which has a part which is two. One can define other numbers in a similar way. Of course such definitions will quickly become nearly unintelligible as one increases the value of the number. This is not so much a problem with this kind of definition, as a sign of the fact that numbers are not very intelligible to us in themselves, and that we grasp them in practice mainly by the use of the imagination.

The Evidence Still Does Not Change Sides

Our Mormon protagonist, still shaken by his discovery about the book of Abraham, now discovers another fact:

(A) Although Joseph Smith claimed to translate the Book of Mormon from ancient golden plates, there are many passages that evidently borrow from the King James Bible in particular.

Our protagonist considers this for a while and then thinks, (B) “God is just more tolerant of this sort of thing than I realized…”

On my earlier post, Michael Bolin commented:

While this is technically correct, it is worth noting that something akin to the evidence changing sides does happen, due to the practical difficulty with assigning probabilities. Namely, realizing that some fact is true, which in itself lowers the probability of the original hypothesis, may cause one to assign different values to the probability of a bunch of other facts given the hypothesis, such that the net effect after taking those other facts into account is to make the hypothesis more likely than it would have been if one had taken those other facts into account without the original observation.

I responded at the time:

It’s not clear to me what you are saying in practice, and seems to me that such a thing cannot happen without a violation of the laws of probability (this does not necessarily mean it cannot be reasonable, if the meaning is that you realize that your prior probability distribution was simply mistaken in the first place).

This is in fact what is happening when our protagonist concludes that God is more tolerant than he supposed. Fact (A) is evidence against the truth of Mormonism. But when this fact is considered together with the original fact about the book of Abraham, our protagonist concludes that “God is tolerant about false claims about the origin of his revealed texts” is more probable given the truth of Mormonism than he originally supposed. This is a change in his prior probability distribution, and it weakens the evidence against Mormonism found in the two claims about the Book of Abraham and about the Book of Mormon.

If someone in fact adjusted his probability of the truth of Mormonism based on the fact about the Book of Abraham, then discovered (A) and adjusted his probability of (B) by changing his prior, then the probability of Mormonism being true might indeed become somewhat higher than it was simply after the discovery about the book of Abraham.

However, several things should be noted concerning this:

(1) In practice, people have a very hard time admitting that there is any evidence at all against their position. Now if someone believes that the Book of Abraham was in fact translated from an ancient Egyptian manuscript, he would probably realize (if he thought about it), that if this turns out to be false, it would be evidence against Mormonism. Consequently, if he thinks that Mormonism is true, he likely sets a prior where it is nearly impossible for Smith’s claim about the book of Abraham to be false. In other words, he more or less thinks that if the Book of Abraham was not translated from the Egyptian manuscript, Mormonism would be false. But when he realizes that the Book of Abraham was not translated from the manuscript, he does not conclude that Mormonism is false, but rather tries to make the evidence change sides. So in effect he already adjusts his prior, and in fact in an inappropriate way, because even if his original prior was excessively against the possibility of the fact about the Book of Abraham, that fact is objectively evidence against Mormonism, not in favor of it. And when he discovers fact (A), this too is evidence against Mormonism, and he should adjust his probability in this direction, and not in the opposite direction.

(2) If someone actually adjusted his probabilities in the appropriate way after the discovery of the first fact about the Book of Abraham, the discovery of (A) and the conclusion (B) could somewhat increase the probability of the truth of Mormonism over what he supposed it was after the original discovery about the Book of Abraham. However, according to the new prior, both the fact about the Book of Abraham and the fact (A) would still constitute evidence against the truth of Mormonism, and thus the probability of Mormonism would remain less than it would be with the new prior but without the facts concerning the origin of the texts.

(3) Similarly, there is little reason to suppose that the final probability of Mormonism would be greater than the original probability before the change in the prior. Rather, you would have something like this:

  1. Original probability of Mormonism: 95%.
  2. Probability after adjusting for discovery about the book of Abraham: 25%.
  3. Probability after adjusting for fact (A): 10%
  4. Probability after adjusting the prior with conclusion (B): 75%.

Of course these are randomly invented numbers, and in practice a real person does not adjust this much, and his original probability is likely even higher than 95%. Nonetheless it is an illustration of what is likely to happen in terms of the evidence. Even after adjusting the prior, the facts about the origins of the texts simply remain evidence against Mormonism, not evidence for it, and consequently the final probability remains less than the original probability.

The evidence still does not change sides.

Whole and Part

To have a whole made of parts requires at least three things: the whole, one part, and another part.

The whole must be distinct from each of the parts, i.e. it must not be one of the parts, since if the whole were the part, the part would not be a part, but the whole. Likewise each of the parts must be distinct from one another.

On other other hand, if there was no other relationship between the parts and the whole, we would simply be talking about three unrelated things. In order for the parts to be parts, they must be something of the whole. The part thus expresses something of the existence of the whole, a mode of its existence, but not its existence overall. Thus for example body and soul are aspects of a man, but neither is the man overall.

In order to be a whole, therefore, a thing must exist in three ways: as itself, as something which it is not, and as something else which it is not. Each of these three must be distinct from the other two.

The whole is greater than the part insofar as the whole exists not only as that part (which of itself would cause equality), but also as itself and as the other part.

Being and Unity

The unity of a being is simply a certain negation of distinction or division. As was said in the last post, distinction consists in the fact that this thing is not that thing. To say that a thing is one is to say that it is “this thing” rather than “this thing which is not that thing, and that thing which is not this thing”. Thus saying that the thing is one does not deny all distinction, since “this thing” remains “not that thing.” But it denies the distinction within “this thing and that thing,” since this is not one thing.

Or with a concrete example, if I am talking about an apple and an orange, the apple is not the orange, and the orange is not the apple. By reason of this mutual distinction, “the apple and the orange” does not constitute something one. But the apple is one precisely because it is not something like this; “apple” does not name a distinct something and something else. Likewise the orange is one, for the same reason, despite the fact that the apple is not the orange.

St. Thomas explains that it follows that one and being are in some way the same:

“One” does not add any reality to “being”; but is only a negation of division; for “one” means undivided “being.” This is the very reason why “one” is the same as “being.” Now every being is either simple or compound. But what is simple is undivided, both actually and potentially. Whereas what is compound, has not being whilst its parts are divided, but after they make up and compose it. Hence it is manifest that the being of anything consists in undivision; and hence it is that everything guards its unity as it guards its being.

In other words, if you cut the apple into two halves, there is no longer an apple, but one half and another half. And just as you no longer have an apple, you no longer have the being that you had, since that being was an apple. The apple is always one apple; and one apple is always an apple. In this way being and unity are convertible.

On the other hand, just as there are many ways of being, there are many ways to be one. Thus although the two halves are not an apple, and consequently not one apple, they are a pair of apple halves. And being a pair of something is being something at least in some way; and consequently they are also one pair.

Real Distinction

To say that two things are really distinct simply means that one thing is not the other. Thus a chair and a desk are really distinct simply because the chair is not the desk.

This argues against the formal distinction of Duns Scotus, because if we take two things which are said to be formally distinct in his sense, either the first is not the second, or the first is the second. If the first is not the second, they are really distinct, and there is no need for his formal distinction. If the first is the second, then they are really the same, and it is enough to speak of a distinction in concept.

However, it should be noted that in another sense, no distinction is real. The distinction consists in the fact that one thing is not another, and “not being another” is not a being, but a lack of being. Thus distinction is always something generated by the mind when understanding reality, rather than something that exists in itself.

Nonetheless, “this concept differs from that one” differs from “this is not that,” and consequently we distinguish between conceptual distinctions and real distinctions in this way, even though in themselves all distinctions are conceptual.

When First We Practise to Deceive

Mark Shea potentially provides an example of the sort of reasoning from moral considerations that we discussed yesterday:

The woman in the video says (and I see no particular reason to doubt her) that this is the nickname her recently deceased grandmother called her when she was a little girl and that her four year did not and could not have known that.

Hmmmmmmmm…..  Could be fake.  Could be demonic (evil spirits can reveal to humans things they cannot know naturally).  Could be a divine gift of knowledge.  Thing is, without context and connection to the rest of her story it’s very hard to know what’s going on.

When he says, “could be fake,” he may mean that the woman could be lying, which is certainly possible, but which seems to go against “I see no particular reason to doubt her”.

In any case, “I see no particular reason to doubt her,” appears to be an example of reasoning from moral considerations. We don’t have a special reason to think the woman is wicked or a liar, so we would be treating her better by trusting her.

In fact, even without additional investigation, there is at least one particular reason to doubt her, namely the very existence of the video, as opposed to an after-the-fact narration. The existence of the video suggests that the woman knew what was going to happen, which suggests deceit.

But for the sake of discussion we can assume there is no particular reason to doubt her, as Mark says. The fact that the woman makes a claim is evidence for that claim, but one can still ask which of these statements is true:

(1) For the most part, when someone claims to communicate with a dead person or to witness such communication, the events in question have natural causes such as lying or being mistaken.

(2) For the most part, when someone claims to communicate with a dead person or to witness such communication, the events in question have supernatural or preternatural causes such as divine revelation, demonic deception, or actual communication from a departed soul.

If (2) happens to be the case, there is no problem with trusting the woman, and no problem with going on to consider possible supernatural or preternatural causes.

But if (1) happens to be the case, there may be a problem. I may have “no particular reason to doubt her”, but this is a moral consideration which does not affect the probability of the facts in question, and according to (1), even after her claim, it remains more probable than not that either she is lying, or she is deceived (e.g. she previously used the nickname in the girl’s presence but does not remember this.)

The basic problem here is that it is very difficult, although not impossible, to think that something is true while accepting that it probably isn’t. So if I actually trust the woman, in most cases I will end up thinking that she is probably telling the truth, which according to (1), would be mistaken. Nor can it be said that this is a case where the mistake does not pertain “to the evil of the intellect,” as St. Thomas says about cases where we mistakenly suppose that someone is a good person. Instead, making a mistake of this sort can lead us into very serious intellectual errors. For if we immediately suppose that the woman is probably telling the truth, and if we do the same thing in numerous other cases, we are quite likely to conclude that (2) is the case, when by hypothesis it is not. But a world where (2) is the case might very well be a quite different world from one in which (1) is the case, and thus the error might very well lead us astray about the very nature of reality. This might be somewhat less clear to someone who supposes that (2) is in fact true, or at least isn’t very unlikely to be true, but one could consider similar cases where someone claims to have experienced facts verifying the truth of Scientology or some similar insanity. Believing a person simply because there is “no particular reason to doubt them” can indeed lead to errors of enormous magnitude.

A personal anecdote may illustrate the same thing in a different way. On one occasion, waiting at a bus stop in Vienna, I was approached by an old man who asked, “May I speak with you?”

I replied, “Well, I have to get on the bus when it arrives, but until then it is fine.”

He told his story. “About two weeks ago, I met a poor man on the street who said he had no money and no place to stay. I invited him to stay in my apartment for a while. He did, and everything was fine for a while. But he disappeared yesterday, and he took with him €2,000 in cash and my credit card. Now I always thought that if you did good to others, good would come back to you…”

At the moment the bus arrived, so I simply said, “There could be a lot to say about that, but I need to go…” and got on the bus.

It may be charitable not to judge a poor man by assuming he is the kind of guy who would steal from you. And it may be charitable not to judge someone by assuming he is the kind of person who would lie to you. But charitable or not, if you don’t want to lose €2,000, then you have to consider the actual probability that the person may steal from you. And likewise, if you don’t want to be led into serious errors, you have to consider the actual probability that someone would lie or be mistaken.

What a Tangled Web We Weave

Suppose that someone accepts that life is meaningful for the reasons given in the last post.

Suppose he then says, “Since there’s no point in considering the possibility that life is meaningless, I might as well consider the fact that life is meaningful to be absolutely certain.”

Suppose he then forgets how he came to this point, and only notices that there is something he is absolutely certain about. He therefore says that this claim has a probability of 100%. And in order to be consistent, he adds that he is absolutely certain about having his absolute certainty.

He may well then proceed to develop a philosophy of human nature based on the position that he has the ability to possess absolute subjective certainty. And he may assign an extremely high probability to this philosophy, or even say that it is itself completely certain.

There is something very odd about this whole procedure. The starting point, that life is meaningful, is true. But the endpoint, a philosophy built on the possibility of absolute subjective certainty, is likely false, for reasons given previously. Where did we go astray? The problem appears in the second step above, when we go from excluding the possibility that life is meaningless, to saying that “life is meaningful” is absolutely certain.

It was pointed out in the last post that truth is only one of the possible motives for believing something, and there are other possible motives as well. This implies that “reasons for believing” something can be said to two ways. In one way, it signifies reasons why the thing would be true, or would be likely to be true. In another way, it signifies reasons why it would be good for someone to believe it. The fact that something is true is also a reason why it would be beneficial to believe it, and this could lead us to confuse the two meanings. Likewise, believing something involves claiming that it is true, and for this reason we might suppose that any reasons that make it good to believe something, should mean it’s likely to be true.

But in reality these kinds of reasons can be completely distinct. Thus it may be beneficial for a Muslim in an Islamic country to maintain his faith, in order to avoid being killed as an apostate. But this motive does not increase the probability of Islam in any way; it is not a reason which makes the thing true or likely to be true. The problem with the reasoning process described at the beginning of this post is that we collapsed these two types of reason: we had a moral reason to adopt the view that life is meaningful without reservation, but that moral reason does not increase the probability that life is meaningful. That life is meaningful should be considered to be extremely probable in itself, since it is simply common sense. But when we exclude potential reservations for moral reasons, we should not then suppose that we are suddenly absolutely certain.

St. Thomas gives another example of a moral reason for holding a certain opinion:

From the very fact that a man thinks ill of another without sufficient cause, he injures and despises him. Now no man ought to despise or in any way injure another man without urgent cause: and, consequently, unless we have evident indications of a person’s wickedness, we ought to deem him good, by interpreting for the best whatever is doubtful about him.

He admits that following this process may lead one into error, but says that the error is relatively minor compared to the danger of doing harm by thinking badly of a good man:

He who interprets doubtful matters for the best, may happen to be deceived more often than not; yet it is better to err frequently through thinking well of a wicked man, than to err less frequently through having an evil opinion of a good man, because in the latter case an injury is inflicted, but not in the former.

Again, as in the other cases, our moral reason is a real reason for thinking something, but it does not suddenly make that thing more probable than it otherwise was. And if we understand this in the latter way, we may fall into serious errors indeed. For example, a juror might think it is extremely certain that an alleged criminal is guilty. But then he might say to himself, “It would be more charitable to suppose that there is only a 90% chance he is guilty,” followed by, “It would be still more charitable to suppose that there is only an 80% chance he is guilty,” and so on, with the conclusion that the man is certainly innocent.

This is related to St. Thomas’s claim that when we judge well of another in this way, even when we are mistaken, this does not pertain “to the evil of the intellect, even as neither does it pertain to the intellect’s perfection to know the truth of contingent singulars in themselves.” This may be true insofar as it goes, meaning that the error in question is not a serious evil. But if we understand this to mean that our interpretation changes the probability of certain facts, this may indeed lead to serious evils, in a practical sense as in the case of the juror, or even in a speculative sense as in our original example. Since a moral reason does not in fact make the thing more probable, someone who asserts that the thing is more probable is asserting something false, even if the thing in question happens to be true in fact, and if he attempts to justify this false assertion of greater probability, he will be able to do so only by continuing to assert other falsehoods. And thus one begins to weave a tangled web indeed.

None of this implies that one should not believe things for moral reasons. It simply means that one should make sure to distinguish between the reasons that make something probably true, and reasons that make it good to think it is true, and not to confuse the two by supposing that one’s moral reasons make something likely to be true.

Things it is Better to Believe

Since belief is voluntary, it follows that truth is only one of the possible motives for belief, and people can believe things for the sake of other ends as well. Consequently there may be some things that it is always better to believe, even without making a special effort to determine whether they are true or not.

Consider the claim that “Life is meaningful,” understood to mean that there are purposes in life, and therefore good and evil.

If this is true, it is good to believe it, because it is true, and because we need to be aware of our ends in order to seek them.

If it is not true, then it does no harm to believe it, because good and evil do not exist in that situation. And likewise, it cannot be better not to believe it in this situation, since better and worse do not exist.

Thus the strategy of believing that life is meaningful weakly dominates the strategy of believing that life is not meaningful, although it does not “strictly” dominate, since the payoffs of the two strategies are equal if life is not in fact meaningful. Consequently the better thing is to choose to believe that life is meaningful, even without a particular investigation of the facts.

As another particular example of this kind of reasoning, we can consider this discussion from chapter 9 of Eric Reitan’s book Is God a Delusion? A Reply to Religion’s Cultured Despisers:

In his Letter to a Christian Nation (2006), Sam Harris notes that, statistically speaking, somewhere in the world right now a little girl is being abducted, raped, and killed. And the same statistics suggest that her parents believe that “an all-powerful and all-loving God is watching over them and their family.” Harris asks, “Are they right to believe this? Is it good that they believe this?” His answer? “No.” According to Harris, this answer contains “the entirety of atheism” and is simply “an admission of the obvious.” He encourages his readers to “admit the obvious”: that when devout Hurricane Katrina victims drowned in their attics while praying to God for deliverance, they “died talking to an imaginary friend” (pp. 50-2). With righteous indignation, Harris condemns the “boundless narcissism” of those who survive a disaster only to “believe themselves spared by a loving God, while this same God drowned infants in their cribs” (p. 54).

After some discussion of this, Eric Reitan’s strategy is not to try to make things look any better, but to make them look even worse:

A mother, running late for a morning meeting, rushes out the door with both her children. The older son is to be dropped off at preschool, the baby girl at a nearby daycare. When the preschool lets out, the daycare’s minivan will bring the son to the daycare, where he will wait with his baby sister until their mother gets off work.

The mother gets to work, leaving the car in a sunny lot. It’s a hot day. She makes it to her meeting and has a productive day. At five o’clock she gets in her car and drives to the daycare. Her son runs to her. She picks him up and kisses his head, then looks around for her baby girl. Not seeing her, she asks one of the daycare workers. “I’m sorry, ma’am. You didn’t drop her off this morning.” The reply, tentative and apologetic, doesn’t have the tone of something that should tear a life apart. But it does. The mother’s hands go numb. Her son falls from her grasp. It feels as if all the darkness in the world is pressing outward from inside her. No. Impossible. But she has no memory of unstrapping that precious little girl, of carrying her into the daycare. No memory, in the rush of the morning, the urgency to get to her meeting on time. Driving to the daycare after work, looking forward to seeing her children, she never looked at what was in the back seat. And now her knees give out and the sobs escape even before she makes it to the car, even before she sees what’s there. Someone is soothing the son, who stands at the daycare door. The mother is beating at the car windows with her fists. In her imagination the baby girl is screaming for mommy, for comfort, as the car grows hotter and hotter, while all the while the mother is in her stupid meeting, talking about stupid contracts, feeling relieved that she’d made it to work on time. And the son, distressed beyond understanding by his mother’s behavior, breaks free of the daycare worker and runs towards her – into the path of an oncoming car.

This story is loosely based on real events. And there are life stories bleaker than this. Horror is real. According to the 2007 Global Monitoring Report put out by the World Bank, there are at present more than one billion people on earth living in “extreme” poverty (that is, on less than $1 per day). Such poverty is not only dire in itself but renders the poor terribly vulnerable to exploitation, disease, and natural disasters. I could fill a book with harrowing stories of human lives crushed by a combination of poverty, brutal abuse, and the grim indifference of nature. But that isn’t needed, I think, in order to convince most readers that there are horrors in the world so devastating that those who undergo them feel as if their entire lives are stripped of positive value, as if they’d be better off dead – while those who are implicated in them, once they come to appreciate the full measure of their complicity, are torn apart by self-loathing. If there is a God, His reasons for permitting such evils are hidden from us. And, as Marilyn Adams has pointed out, even if traditional theodicies give some general sense of why God might create a world in which evils exist, these theodicies bring no comfort to the mother as she turns away from her infant’s corpse just in time to see her son crushed under the wheels of a screeching car. It won’t give meaning to her life. It won’t eliminate the horror. Her existence has, in a few heartbeats, become worse than a void. It’s become come a space of affliction compared to which the void would be preferable. This woman needs salvation.

In order to survive such a situation, Reitan says, it is necessary to believe in the redemption of evil, namely that in some way a greater good is brought out of such horrors:

For most horror victims, the sense that their lives have positive meaning may depend on the conviction that a transcendent good is at work redeeming evil. Is the evidential case against the existence of such a good really so convincing that it warrants saying to these horror victims, “Give up hope”? Should we call them irrational when they cling to that hope or when those among the privileged live in that hope for the sake of the afflicted? What does moral decency imply about the legitimacy of insisting, as the new atheists do, that any view of life which embraces the ethico-religious hope should be expunged from the world?

He concludes the chapter with this response to Sam Harris:

Somewhere, even as I write this, a girl is being raped and murdered. Her parents believe in a transcendent God of love who will redeem even the most shocking horrors.

Are they right to believe this? Is it good that they believe this?

In the darkness of affliction, Harris’s answer rings hollow.

This example differs in some ways from my original example of the claim that life is meaningful. The original claim was understood to be the assertion that good and evil exist in life, and thus the denial would be that there is no good and evil in life. But in Reitan’s discussion, the claim is stronger, namely something like “God exists and will always bring good out of evil.” Harris’s denial of this claim does not in itself imply the non-existence of good and evil, at least not without additional consideration. In fact, his position is that very great evils exist and that we should not try to explain them away with this claim about God, so he is not, on the face of it, denying that good and evil exist. Consequently one cannot immediately deduce that believing the claim about God is a dominant strategy.

Nonetheless, if Reitan’s and Harris’s views are compared here with respect to the good of the people concerned, a fair comparison, since Harris was the one who the claimed that it was bad for people to believe such things, it does seem that Reitan has a much stronger case. The woman does seem much better off believing the claim about God and the redemption of evil.

But this is not the whole story.

The Unexpected Hanging

Wikipedia tells the tale of the unexpected hanging:

A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day.

Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that the “surprise hanging” can’t be on Friday, as if he hasn’t been hanged by Thursday, there is only one day left – and so it won’t be a surprise if he’s hanged on Friday. Since the judge’s sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday.

He then reasons that the surprise hanging cannot be on Thursday either, because Friday has already been eliminated and if he hasn’t been hanged by Wednesday night, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all.

The next week, the executioner knocks on the prisoner’s door at noon on Wednesday — which, despite all the above, was an utter surprise to him. Everything the judge said came true.

Doubtless there are various ways to explain what is going on here. But the moral of the story is simply that no matter how solid your reasoning seems to you, no matter how absolutely conclusive, reality does not have to care. You can be wrong anyway.