Age of Em

This is Robin Hanson’s first book. Hanson gradually introduces his topic:

You, dear reader, are special. Most humans were born before 1700. And of those born after, you are probably richer and better educated than most. Thus you and most everyone you know are special, elite members of the industrial era.

Like most of your kind, you probably feel superior to your ancestors. Oh, you don’t blame them for learning what they were taught. But you’d shudder to hear of many of your distant farmer ancestors’ habits and attitudes on sanitation, sex, marriage, gender, religion, slavery, war, bosses, inequality, nature, conformity, and family obligations. And you’d also shudder to hear of many habits and attitudes of your even more ancient forager ancestors. Yes, you admit that lacking your wealth your ancestors couldn’t copy some of your habits. Even so, you tend to think that humanity has learned that your ways are better. That is, you believe in social and moral progress.

The problem is, the future will probably hold new kinds of people. Your descendants’ habits and attitudes are likely to differ from yours by as much as yours differ from your ancestors. If you understood just how different your ancestors were, you’d realize that you should expect your descendants to seem quite strange. Historical fiction misleads you, showing your ancestors as more modern than they were. Science fiction similarly misleads you about your descendants.

As an example of the kind of past difference that Robin is discussing, even in the fairly recent past, consider this account by William Ewald of a trial from the sixteenth century:

In 1522 some rats were placed on trial before the ecclesiastical court in Autun. They were charged with a felony: specifically, the crime of having eaten and wantonly destroyed some barley crops in the jurisdiction. A formal complaint against “some rats of the diocese” was presented to the bishop’s vicar, who thereupon cited the culprits to appear on a day certain, and who appointed a local jurist, Barthelemy Chassenée (whose name is sometimes spelled Chassanée, or Chasseneux, or Chasseneuz), to defend them. Chassenée, then forty-two, was known for his learning, but not yet famous; the trial of the rats of Autun was to establish his reputation, and launch a distinguished career in the law.

When his clients failed to appear in court, Chassenée resorted to procedural arguments. His first tactic was to invoke the notion of fair process, and specifically to challenge the original writ for having failed to give the rats due notice. The defendants, he pointed out, were dispersed over a large tract of countryside, and lived in many villages; a single summons was inadequate to notify them all. Moreover, the summons was addressed only to some of the rats of the diocese; but technically it should have been addressed to them all.

Chassenée was successful in his argument, and the court ordered a second summons to be read from the pulpit of every local parish church; this second summons now correctly addressed all the local rats, without exception.

But on the appointed day the rats again failed to appear. Chassenée now made a second argument. His clients, he reminded the court, were widely dispersed; they needed to make preparations for a great migration, and those preparations would take time. The court once again conceded the reasonableness of the argument, and granted a further delay in the proceedings. When the rats a third time failed to appear, Chassenée was ready with a third argument. The first two arguments had relied on the idea of procedural fairness; the third treated the rats as a class of persons who were entitled to equal treatment under the law. He addressed the court at length, and successfully demonstrated that, if a person is cited to appear at a place to which he cannot come in safety, he may lawfully refuse to obey the writ. And a journey to court would entail serious perils for his clients. They were notoriously unpopular in the region; and furthermore they were rightly afraid of their natural enemies, the cats. Moreover (he pointed out to the court) the cats could hardly be regarded as neutral in this dispute; for they belonged to the plaintiffs. He accordingly demanded that the plaintiffs be enjoined by the court, under the threat of severe penalties, to restrain their cats, and prevent them from frightening his clients. The court again found this argument compelling; but now the plaintiffs seem to have come to the end of their patience. They demurred to the motion; the court, unable to settle on the correct period within which the rats must appear, adjourned on the question sine die, and judgment for the rats was granted by default.

Most of us would assume at once that this is all nothing but an elaborate joke; but Ewald strongly argues that it was all quite serious. This would actually be worthy of its own post, but I will leave it aside for now. In any case it illustrates the existence of extremely different attitudes even a few centuries ago.

In any event, Robin continues:

New habits and attitudes result less than you think from moral progress, and more from people adapting to new situations. So many of your descendants’ strange habits and attitudes are likely to violate your concepts of moral progress; what they do may often seem wrong. Also, you likely won’t be able to easily categorize many future ways as either good or evil; they will instead just seem weird. After all, your world hardly fits the morality tales your distant ancestors told; to them you’d just seem weird. Complex realities frustrate simple summaries, and don’t fit simple morality tales.

Many people of a more conservative temperament, such as myself, might wish to swap out “moral progress” here with “moral regress,” but the point stands in any case. This is related to our discussions of the effects of technology and truth on culture, and of the idea of irreversible changes.

Robin finally gets to the point of his book:

This book presents a concrete and plausible yet troubling view of a future full of strange behaviors and attitudes. You may have seen concrete troubling future scenarios before in science fiction. But few of those scenarios are in fact plausible; their details usually make little sense to those with expert understanding. They were designed for entertainment, not realism.

Perhaps you were told that fictional scenarios are the best we can do. If so, I aim to show that you were told wrong. My method is simple. I will start with a particular very disruptive technology often foreseen in futurism and science fiction: brain emulations, in which brains are recorded, copied, and used to make artificial “robot” minds. I will then use standard theories from many physical, human, and social sciences to describe in detail what a world with that future technology would look like.

I may be wrong about some consequences of brain emulations, and I may misapply some science. Even so, the view I offer will still show just how troublingly strange the future can be.

I greatly enjoyed Robin’s book, but unfortunately I have to admit that relatively few people will in general. It is easy enough to see the reason for this from Robin’s introduction. Who would expect to be interested? Possibly those who enjoy the “futurism and science fiction” concerning brain emulations; but if Robin does what he set out to do, those persons will find themselves strangely uninterested. As he says, science fiction is “designed for entertainment, not realism,” while he is attempting to answer the question, “What would this actually be like?” This intention is very remote from the intention of the science fiction, and consequently it will likely appeal to different people.

Whether or not Robin gets the answer to this question right, he definitely succeeds in making his approach and appeal differ from those of science fiction.

One might illustrate this with almost any random passage from the book. Here are portions of his discussion of the climate of em cities:

As we will discuss in Chapter 18, Cities section, em cities are likely to be big, dense, highly cost-effective concentrations of computer and communication hardware. How might such cities interact with their surroundings?

Today, computer and communication hardware is known for being especially temperamental about its environment. Rooms and buildings designed to house such hardware tend to be climate-controlled to ensure stable and low values of temperature, humidity, vibration, dust, and electromagnetic field intensity. Such equipment housing protects it especially well from fire, flood, and security breaches.

The simple assumption is that, compared with our cities today, em cities will also be more climate-controlled to ensure stable and low values of temperature, humidity, vibrations, dust, and electromagnetic signals. These controls may in fact become city level utilities. Large sections of cities, and perhaps entire cities, may be covered, perhaps even domed, to control humidity, dust, and vibration, with city utilities working to absorb remaining pollutants. Emissions within cities may also be strictly controlled.

However, an em city may contain temperatures, pressures, vibrations, and chemical concentrations that are toxic to ordinary humans. If so, ordinary humans are excluded from most places in em cities for safety reasons. In addition, we will see in Chapter 18, Transport section, that many em city transport facilities are unlikely to be well matched to the needs of ordinary humans.

Cities today are the roughest known kind of terrain, in the sense that cities slow down the wind the most compared with other terrain types. Cities also tend to be hotter than neighboring areas. For example, Las Vegas is 7 ° Fahrenheit hotter in the summer than are surrounding areas. This hotter city effect makes ozone pollution worse and this effect is stronger for bigger cities, in the summer, at night, with fewer clouds, and with slower wind (Arnfield 2003).

This is a mild reason to expect em cities to be hotter than other areas, especially at night and in the summer. However, as em cities are packed full of computing hardware, we shall now see that em cities will  actually be much hotter.

While the book considers a wide variety of topics, e.g. the social relationships among ems, which look quite different from the above passage, the general mode of treatment is the same. As Robin put it, he uses “standard theories” to describe the em world, much as he employs standard theories about cities, about temperature and climate, and about computing hardware in the above passage.

One might object that basically Robin is positing a particular technological change (brain emulations), but then assuming that everything else is the same, and working from there. And there is some validity to this objection. But in the end there is actually no better way to try to predict the future; despite David Hume’s opinion, generally the best way to estimate the future is to say, “Things will be pretty much the same.”

At the end of the book, Robin describes various criticisms. First are those who simply said they weren’t interested: “If we include those who declined to read my draft, the most common complaint is probably ‘who cares?'” And indeed, that is what I would expect, since as Robin remarked himself, people are interested in an entertaining account of the future, not an attempt at a detailed description of what is likely.

Others, he says, “doubt that one can ever estimate the social consequences of technologies decades in advance.” This is basically the objection I mentioned above.

He lists one objection that I am partly in agreement with:

Many doubt that brain emulations will be our next huge technology change, and aren’t interested in analyses of the consequences of any big change except the one they personally consider most likely or interesting. Many of these people expect traditional artificial intelligence, that is, hand-coded software, to achieve broad human level abilities before brain emulations appear. I think that past rates of progress in coding smart software suggest that at previous rates it will take two to four centuries to achieve broad human level abilities via this route. These critics often point to exciting recent developments, such as advances in “deep learning,” that they think make prior trends irrelevant.

I don’t think Robin is necessarily mistaken in regard to his expectations about “traditional artificial intelligence,” although he may be, and I don’t find myself uninterested by default in things that I don’t think the most likely. But I do think that traditional artificial intelligence is more likely than his scenario of brain emulations; more on this below.

There are two other likely objections that Robin does not include in this list, although he does touch on them elsewhere. First, people are likely to say that the creation of ems would be immoral, even if it is possible, and similarly that the kinds of habits and lives that he describes would themselves be immoral. On the one hand, this should not be a criticism at all, since Robin can respond that he is simply describing what he thinks is likely, not saying whether it should happen or not; on the other hand, it is in fact obvious that Robin does not have much disapproval, if any, of his scenario. The book ends in fact by calling attention to this objection:

The analysis in this book suggests that lives in the next great era may be as different from our lives as our lives are from farmers’ lives, or farmers’ lives are from foragers’ lives. Many readers of this book, living industrial era lives and sharing industrial era values, may be disturbed to see a forecast of em era descendants with choices and life styles that appear to reject many of the values that they hold dear. Such readers may be tempted to fight to prevent the em future, perhaps preferring a continuation of the industrial era. Such readers may be correct that rejecting the em future holds them true to their core values.

But I advise such readers to first try hard to see this new era in some detail from the point of view of its typical residents. See what they enjoy and what fills them with pride, and listen to their criticisms of your era and values. This book has been designed in part to assist you in such a soul-searching examination. If after reading this book, you still feel compelled to disown your em descendants, I cannot say you are wrong. My job, first and foremost, has been to help you see your descendants clearly, warts and all.

Our own discussions of the flexibility of human morality are relevant. The creatures Robin is describing are in many ways quite different from humans, and it is in fact very appropriate for their morality to differ from human morality.

A second likely objection is that Robin’s ems are simply impossible, on account of the nature of the human mind. I think that this objection is mistaken, but I will leave the details of this explanation for another time. Robin appears to agree with Sean Carroll about the nature of the mind, as can be seen for example in this post. Robin is mistaken about this, for the reasons suggested in my discussion of Carroll’s position. Part of the problem is that Robin does not seem to understand the alternative. Here is a passage from the linked post on Overcoming Bias:

Now what I’ve said so far is usually accepted as uncontroversial, at least when applied to the usual parts of our world, such as rivers, cars, mountains laptops, or ants. But as soon as one claims that all this applies to human minds, suddenly it gets more controversial. People often state things like this:

“I am sure that I’m not just a collection of physical parts interacting, because I’m aware that I feel. I know that physical parts interacting just aren’t the kinds of things that can feel by themselves. So even though I have a physical body made of parts, and there are close correlations between my feelings and the states of my body parts, there must be something more than that to me (and others like me). So there’s a deep mystery: what is this extra stuff, where does it arise, how does it change, and so on. We humans care mainly about feelings, not physical parts interacting; we want to know what out there feels so we can know what to care about.”

But consider a key question: Does this other feeling stuff interact with the familiar parts of our world strongly and reliably enough to usually be the actual cause of humans making statements of feeling like this?

If yes, this is a remarkably strong interaction, making it quite surprising that physicists have missed it so far. So surprising in fact as to be frankly unbelievable. If this type of interaction were remotely as simple as all the interactions we know, then it should be quite measurable with existing equipment. Any interaction not so measurable would have be vastly more complex and context dependent than any we’ve ever seen or considered. Thus I’d bet heavily and confidently that no one will measure such an interaction.

But if no, if this interaction isn’t strong enough to explain human claims of feeling, then we have a remarkable coincidence to explain. Somehow this extra feeling stuff exists, and humans also have a tendency to say that it exists, but these happen for entirely independent reasons. The fact that feeling stuff exists isn’t causing people to claim it exists, nor vice versa. Instead humans have some sort of weird psychological quirk that causes them to make such statements, and they would make such claims even if feeling stuff didn’t exist. But if we have a good alternate explanation for why people tend to make such statements, what need do we have of the hypothesis that feeling stuff actually exists? Such a coincidence seems too remarkable to be believed.

There is a false dichotomy here, and it is the same one that C.S. Lewis falls into when he says, “Either we can know nothing or thought has reasons only, and no causes.” And in general it is like the error of the pre-Socratics, that if a thing has some principles which seem sufficient, it can have no other principles, failing to see that there are several kinds of cause, and each can be complete in its own way. And perhaps I am getting ahead of myself here, since I said this discussion would be for later, but the objection that Robin’s scenario is impossible is mistaken in exactly the same way, and for the same reason: people believe that if a “materialistic” explanation could be given of human behavior in the way that Robin describes, then people do not truly reason, make choices, and so on. But this is simply to adopt the other side of the false dichotomy, much like C.S. Lewis rejects the possibility of causes for our beliefs.

One final point. I mentioned above that I see Robin’s scenario as less plausible than traditional artificial intelligence. I agree with Tyler Cowen in this post. This present post is already long enough, so again I will leave a detailed explanation for another time, but I will remark that Robin and I have a bet on the question.

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Is and Ought

In Book III of his Treatise of Human Nature, David Hume argues that reason and morality are completely independent:

Reason is the discovery of truth or falsehood. Truth or falsehood consists in an agreement or disagreement either with the real relations of ideas, or with real existence and matter of fact. So anything that isn’t capable of this agreement or disagreement isn’t capable of being true or false, and can never be an object of our reason. Now, our passions, volitions, and actions are basic facts and realities; they are complete in themselves and aren’t in any way about other passions, volitions, and actions; so they aren’t capable of either of those sorts of agreement or disagreement; so they can’t be sorted into ‘true’ and ‘false’, and can’t be either in conflict with reason or in accord with it.

It is true that an action is not true or false, nor can it be the conclusion of an argument. And in that sense there is some separation between action and reason, as Hume says here. Nonetheless, Hume intends to imply something more, namely that reason cannot tell us what we should do. If reason can tell us what we should do, then doing something else instead is an action in conflict with reason, even though it is not a false statement.

Later, Hume clarifies his position:

I can’t forbear adding an observation that may be found of some importance. In every system of morality I have met with I have noticed that the author proceeds for some time reasoning in the ordinary way to establish the existence of a God, or making points about human affairs, and then he suddenly surprises me by moving from propositions with the usual copula ‘is’ (or ‘is not’) to ones that are connected by ‘ought’ (or ‘ought not’). This seems like a very small change, but it is highly important. For as this ‘ought’ (or ‘ought not’) expresses some new relation or affirmation, it needs to be pointed out and explained; and a reason should be given for how this new relation can be—inconceivably!—a deduction from others that are entirely different from it. Authors don’t ordinarily take the trouble to do this, so I recommend it to you; and I’m convinced that paying attention to this one small matter will subvert all the vulgar systems of morality and let us see that the distinction between vice and virtue is not based merely on the relations of objects, and is not perceived by reason.

Hume suggests that it is “inconceivable” that a statement involving the word “ought” would derive from statements without that word. This can be taken as a mere point of logic: the conclusion of a syllogism will not contain a term which is not contained in the premises. But if we understand it in this way, his point is true but rather unimportant, at least in relation to his argument about morality. For the same thing is true of all terms. In the statement, “Trees have leaves and branches,” the word “trees” cannot possibly be logically derived from statements that do not mention trees. It does not follow that statements about trees are somehow cut off from all the rest of reality. It does not even follow that people cannot explain what they mean by a “tree.” Someone can explain this by referring to various fairly common experiences that people have.

So as a logical point, this proves nothing in particular about morality, although it is a partial explanation for the difficulty of philosophy. I pointed out in the discussion of Spinoza’s Ethics that the fact that philosophy wishes to speak about reality in general implies that it must use a practically unlimited number of terms, and consequently that it cannot be built up as a formal system like geometry.

In his Nicomachean Ethics, Aristotle discusses ethics as a kind of art which aims at an end:

Every art and every inquiry, and similarly every action and pursuit, is thought to aim at some good; and for this reason the good has rightly been declared to be that at which all things aim. But a certain difference is found among ends; some are activities, others are products apart from the activities that produce them. Where there are ends apart from the actions, it is the nature of the products to be better than the activities. Now, as there are many actions, arts, and sciences, their ends also are many; the end of the medical art is health, that of shipbuilding a vessel, that of strategy victory, that of economics wealth. But where such arts fall under a single capacity- as bridle-making and the other arts concerned with the equipment of horses fall under the art of riding, and this and every military action under strategy, in the same way other arts fall under yet others- in all of these the ends of the master arts are to be preferred to all the subordinate ends; for it is for the sake of the former that the latter are pursued. It makes no difference whether the activities themselves are the ends of the actions, or something else apart from the activities, as in the case of the sciences just mentioned.

If, then, there is some end of the things we do, which we desire for its own sake (everything else being desired for the sake of this), and if we do not choose everything for the sake of something else (for at that rate the process would go on to infinity, so that our desire would be empty and vain), clearly this must be the good and the chief good. Will not the knowledge of it, then, have a great influence on life? Shall we not, like archers who have a mark to aim at, be more likely to hit upon what is right? If so, we must try, in outline at least, to determine what it is, and of which of the sciences or capacities it is the object. It would seem to belong to the most authoritative art and that which is most truly the master art. And politics appears to be of this nature; for it is this that ordains which of the sciences should be studied in a state, and which each class of citizens should learn and up to what point they should learn them; and we see even the most highly esteemed of capacities to fall under this, e.g. strategy, economics, rhetoric; now, since politics uses the rest of the sciences, and since, again, it legislates as to what we are to do and what we are to abstain from, the end of this science must include those of the others, so that this end must be the good for man. For even if the end is the same for a single man and for a state, that of the state seems at all events something greater and more complete whether to attain or to preserve; though it is worth while to attain the end merely for one man, it is finer and more godlike to attain it for a nation or for city-states. These, then, are the ends at which our inquiry aims, since it is political science, in one sense of that term.

If we understand ethics in this way, this explains what is meant by saying that something “ought” to be done, because we know what is meant when we say, for example, “If you want to attach those boards with a nail, you ought to use a hammer.” This implies that a hammer is useful, or perhaps even necessary, in relation to the goal in question. In fact, “ought” is sometimes replaced with “must,” which is a word directly expressing necessity.

Of course, “you must use a hammer” does not imply that there is a physical necessity that you use a hammer, so that you cannot avoid using one. The necessity is a hypothetical one: given that you are going to obtain the end, you must use a hammer. If you do not use a hammer, you will not obtain the end.

This explains, in a certain way, why Hume has difficulty with the point. A repeated concern in his work is that he cannot see a way to understand the idea of necessity. He says for example that he has a hard time understanding any “necessary connection” between cause and effect:

Having thus explained how we reason beyond our immediate impressions, and conclude that such and such causes must have such and such effects, we must now retrace our steps and pick up again the question that first occurred to us, and that we dropped along the way (near the end of section 2). The question is: What is our idea of necessity, when we say that two objects are necessarily connected? As I have often said already, if we claim to have such an idea we must find some impression that gives rise to it, because we have no idea that isn’t derived from an impression. So I ask myself: In what objects is necessity commonly supposed to lie? And finding that it is always ascribed to causes and effects, I turn my attention to two objects that are supposed to be related as cause and effect, and examine them in all the situations in which they can occur. I see at once that they are contiguous in time and place, and that the one we call ‘cause’ precedes the one we call ‘effect’. In no instance can I go any further: I can’t find any third relation between these objects.

He does go on to say that there is something else, but in turns out to be something like the vividness with which the mind expects the effect, or in other words, a property of the mind, not of the causes and effects. Similar concerns lead him to deny the possibility of probable knowledge about the future, and here to effectively deny the possibility of the knowledge of morals. If moral knowledge consists in knowing that something must be done, even for the sake of an end, then according to Hume, it is not possible to know this. If we cannot even know that the sun will rise tomorrow, we also cannot know that we need to use a hammer in order to attach two boards.

Aristotle’s account of ethics is, I think, the correct account. But people find it troubling, mostly because they suspect that it has unlikely or unpleasant implications. If saying that you “ought” to do something only means that you must do it in order to obtain a certain end, what if you do not care about that end? There will no longer be a need to do that thing. Likewise, if you do want certain ends, then perhaps you ought to do certain things which we really think you ought not do. For example, if you want to inherit money, perhaps you ought to murder your elderly relatives. But this consequence is absurd: of course you ought not to murder your relatives.

In order to be sure e.g. that you ought not to murder your relatives, regardless of what ends you have in mind, people prefer something like Immanuel Kant’s categorical imperatives. I will not discuss Kant’s moral philosophy in detail at the moment, nor am I necessarily asserting that the usual understanding of his philosophy is correct. But the usual idea is that the rule is absolute: “you must not kill” is not relative to an end, but stands in itself.

This seems to me to be a mistake, and one where Hume’s criticism would be valid. There is obviously no physical necessity that you abstain from killing. It is quite possible to kill people, and it is sometimes done. So if you say that you “must” not kill, and you do not refer to hypothetical necessity, to what do you refer? There does not seem to be anything left here. And this is probably the motivation behind error theory. The obvious interpretation of the theory is that it is saying, “I do not believe in right and wrong.” In reality, however, it seems to be based on the mistaken assumption that right and wrong refer to something like categorical imperatives, and then it proceeds to rightly deny the existence of these things. For no one except an actual follower of Hume would deny the existence of hypothetical necessity, namely that if you want to obtain certain ends, you must use certain means. In this sense, error theory is mistaken, but it is mistaken much in the way that Richard Dawkins is mistaken to suppose that theists intend to speak of something complex when they speak of God.

The objection to Aristotelian ethics, then, is that it is too flexible, and may ultimately imply that people may do whatever they want. I would respond to this by making two claims, although I will not establish their truth in this post.

First, the truth about ethics is in fact more flexible than people suppose. If you take extremely complex situations, the moral truth about those situations will be complicated, not simple.

Second, the truth about ethics is less flexible than people tend to suppose would follow from an Aristotelian account. It does not follow in any meaningful way, for example, that it is sometimes fine to murder your relatives in order to obtain an inheritance.

 

Settled Issues

In chapter 5 of his book Probability Theory: The Logic of Science, E. T. Jaynes discusses ESP:

I. J. Good (1950) has shown how we can use probability theory backwards to measure our own strengths of belief about propositions. For example, how strongly do you believe in extrasensory perception?

What probability would you assign to the hypothesis that Mr Smith has perfect extrasensory perception? More specifically, that he can guess right every time which number you have written down. To say zero is too dogmatic. According to our theory, this means that we are never going to allow the robot’s mind to be changed by any amount of evidence, and we don’t really want that. But where is our strength of belief in a proposition like this?

Our brains work pretty much the way this robot works, but we have an intuitive feeling for plausibility only when it’s not too far from 0 db. We get fairly definite feelings that something is more than likely to be so or less than likely to be so. So the trick is to imagine an experiment. How much evidence would it take to bring your state of belief up to the place where you felt very perplexed and unsure about it? Not to the place where you believed it – that would overshoot the mark, and again we’d lose our resolving power. How much evidence would it take to bring you just up to the point where you were beginning to consider the possibility seriously?

So, we consider Mr Smith, who says he has extrasensory perception (ESP), and we will write down some numbers from one to ten on a piece of paper and ask him to guess which numbers we’ve written down. We’ll take the usual precautions to make sure against other ways of finding out. If he guesses the first number correctly, of course we will all say ‘you’re a very lucky person, but I don’t believe you have ESP’. And if he guesses two numbers correctly, we’ll still say ‘you’re a very lucky person, but I still don’t believe you have ESP’. By the time he’s guessed four numbers correctly – well, I still wouldn’t believe it. So my state of belief is certainly lower than −40 db.

How many numbers would he have to guess correctly before you would really seriously consider the hypothesis that he has extrasensory perception? In my own case, I think somewhere around ten. My personal state of belief is, therefore, about −100 db. You could talk me into a ±10 db change, and perhaps as much as ±30 db, but not much more than that.

The idea is that after Mr. Smith guesses 7 to 13 numbers correctly (when by chance he should have a probability of 10% of guessing each one correctly), Jaynes will begin to think it reasonably likely that he has ESP. He notes that this is his subjective opinion, saying, “In my own case,” and “My personal state of belief.”

However, Jaynes follows this up by stating that if this happened in real life, he would not be convinced:

After further thought, we see that, although this result is correct, it is far from the whole story. In fact, if he guessed 1000 numbers correctly, I still would not believe that he has ESP, for an extension of the same reason that we noted in Chapter 4 when we first encountered the phenomenon of resurrection of dead hypotheses. An hypothesis A that starts out down at −100 db can hardly ever come to be believed, whatever the data, because there are almost sure to be alternative hypotheses (B1, B2,…) above it, perhaps down at −60 db. Then, when we obtain astonishing data that might have resurrected A, the alternatives will be resurrected instead.

In other words, Jaynes is saying, “This happened by chance,” and “Mr. Smith has ESP” are not the only possibilities. For example, it is possible that Mr. Smith has invented a remote MRI device, which he has trained to distinguish people’s thoughts about numbers, and he is receiving data on the numbers picked by means of an earbud. If the prior probability of this is higher than the prior probability that Mr. Smith has ESP, then Jaynes will begin to think this is a reasonable hypothesis, rather than coming to accept ESP.

This does not imply that Jaynes is infinitely confident that Mr. Smith does not have ESP, and in fact it does not invalidate his original estimate:

Now let us return to that original device of I. J. Good, which started this train of thought. After all this analysis, why do we still hold that naive first answer of −100 db for my prior probability for ESP, as recorded above, to be correct? Because Jack Good’s imaginary device can be applied to whatever state of knowledge we choose to imagine; it need not be the real one. If I knew that true ESP and pure chance were the only possibilities, then the device would apply and my assignment of −100 db would hold. But, knowing that there are other possibilities in the real world does not change my state of belief about ESP; so the figure of −100 db still holds.

He would begin to be convinced after about 10 numbers if he knew for a fact that chance and ESP were the only possibilities, and thus this is a good representation of how certain he is subjectively.

The fact of other possibilities also does not mean that it is impossible for Jaynes to be convinced, even in the real world, that some individual has ESP. But it does mean that this can happen only with great difficulty: essentially, he must be convinced that the other possibilities are even less likely than ESP. As Jaynes says,

Indeed, the very evidence which the ESP’ers throw at us to convince us, has the opposite effect on our state of belief; issuing reports of sensational data defeats its own purpose. For if the prior probability for deception is greater than that of ESP, then the more improbable the alleged data are on the null hypothesis of no deception and no ESP, the more strongly we are led to believe, not in ESP, but in deception. For this reason, the advocates of ESP (or any other marvel) will never succeed in persuading scientists that their phenomenon is real, until they learn how to eliminate the possibility of deception in the mind of the reader. As (5.15) shows, the reader’s total prior probability for deception by all mechanisms must be pushed down below that of ESP.

This is related to the grain of truth in Hume’s account of miracles. Hume’s basic point, that an account of a miracle could never be credible, is mistaken. But he is correct to say that the account would not be credible unless “these witnesses are mistaken or lying” has a lower prior probability than the prior probability of the miracle actually happening. His mistake is to suppose that this cannot happen in principle.

Something like this also happens with ordinary things that we are extremely sure about. For example, take your belief that the American War of Independence happened before the Civil War. You can imagine coming upon evidence that the Civil War happened first. Thus for example suppose you found a book by a historian arguing for this thesis. This would be evidence that the Civil War came first. But it would be very unpersuasive, and would change your mind little if at all, because the prior probability of “this is a work of fiction,” or indeed of “this a silly book arguing a silly thesis for personal reasons” is higher.

We could call this a “settled issue,” at least from your point of view (and in this case from the point of view of pretty much everyone). Not only do you believe that the War of Independence came first; it would be very difficult to persuade you otherwise, even if there were real evidence against your position, and this is not because you are being unreasonable. In fact, it would be unreasonable to be moved significantly by the evidence of that book arguing the priority of the Civil War.

Is it possible in principle to persuade you to change your mind? Yes. In principle this could happen bit by bit, by an accumulation of small pieces of evidence. You might read that book, and then learn that the author is a famous historian, and that he is completely serious (presumably he became famous before writing the book; otherwise he would instead be infamous.) And then you might find other items in favor of this theory, and find refutations of the apparently more likely explanations.

But in practice such a process is extremely unlikely. The most likely way you could change your mind about this would be by way of one large change. For example, you might wake up in a hospital tomorrow and be told that you had been suffering from a rare form of amnesia which does not remove a person’s past memories, but changes them into something different. You ask about the Civil War, and are told that everyone agrees that it happened before the War of Independence. People can easily give you dozens of books on the topic; you search online on the matter, and everything on the internet takes for granted that the Civil War came first. Likewise, everyone you talk to simply takes this for granted.

The reason that the “one big change” process is more likely than the “accumulation of small evidences” process is this: if we want to know what should persuade you that the Civil War came first, we are basically asking what the world would have to be like in order for it to be actually true that the Civil War came first. In such a world, your current belief is false. And in such a world it is simply much more likely that you have made one big mistake which resulted in your false belief about the Civil War, than that you have made lots of little mistakes which led to it.

 

Neither Will They Believe if Someone Rises From the Dead

Jesus tells the parable of the rich man and Lazarus:

“There was a rich man who was dressed in purple and fine linen and who feasted sumptuously every day. And at his gate lay a poor man named Lazarus, covered with sores, who longed to satisfy his hunger with what fell from the rich man’s table; even the dogs would come and lick his sores. The poor man died and was carried away by the angels to be with Abraham. The rich man also died and was buried. In Hades, where he was being tormented, he looked up and saw Abraham far away with Lazarus by his side. He called out, ‘Father Abraham, have mercy on me, and send Lazarus to dip the tip of his finger in water and cool my tongue; for I am in agony in these flames.’ But Abraham said, ‘Child, remember that during your lifetime you received your good things, and Lazarus in like manner evil things; but now he is comforted here, and you are in agony. Besides all this, between you and us a great chasm has been fixed, so that those who might want to pass from here to you cannot do so, and no one can cross from there to us.’ He said, ‘Then, father, I beg you to send him to my father’s house—for I have five brothers—that he may warn them, so that they will not also come into this place of torment.’ Abraham replied, ‘They have Moses and the prophets; they should listen to them.’ He said, ‘No, father Abraham; but if someone goes to them from the dead, they will repent.’ He said to him, ‘If they do not listen to Moses and the prophets, neither will they be convinced even if someone rises from the dead.’”

It is ordinarily understood that Abraham is blaming the men for refusing to believe Moses and the prophets, and indeed, for refusing no matter how strong the reasons given for believing them.

While one should refrain from judging people subjectively, it seems reasonable to think that such an absolute refusal is morally blameworthy. In this sense, Hume’s refusal to accept the fact of a miracle on any testimony whatsoever is morally blameworthy. But this is not limited to people’s rejection of religious beliefs or testimony in favor of them. In a similar way, without remarking on his subjective situation, Kurt Wise’s refusal to accept the fact of evolution, no matter how much it is supported by evidence, may be morally blameworthy.

But Abraham’s statement in the parable may be true in a more general way, one which is not relevant to praise or blame. It can be understood as a general statement about the relationship between testimony and external support such as miracles. If someone is a credible witness, a miracle may support his testimony. But if someone is not a credible witness, he will not suddenly become credible because a miracle happens.

In May 1990, Bishop Pavao Zanic published a statement, “The Truth about Medjugorje” (text here, pp. 45-63). This text contains the following:

16. The “seer” Ivan Dragicevic. Regarding the “great sign”, Vicka mentions this 13 times in the diaries, it is mentioned 14 times in the Parish chronicle, 52 times on the cassettes, and on numerous occasions in talks with the bishop. In the spring of 1982, I asked the “seers” to write everything they knew about the sign without making the “secret” public. The way I suggested they do it was to write down information on paper in duplicate. Then this would be sealed in an envelope and one copy would remain with them, and one with the bishop. Then, when the “sign” occurs, we would open the envelopes and see whether or not the “sign” was predicted. Father Tomislav Vlasic, pastor of Medjugorje at the time, told the “seers” to say that Our Lady had told them not to write anything down for anybody, and so they did not. Ivan Dragicevic was in the Franciscan minor seminary at Visoko, Bosnia at that time and he wasn’t informed of this on time. Two members of the first commission, Dr. M. Zovkic and Dr. Z. Puljic (now bishop of Dubrovnik), went to visit Ivan in Visoko. They gave him a sheet of paper which was somewhat greenish in colour with questions typed out on it. Ivan wrote down the content of the “sign”, dated the document and signed it in their presence without a word or any sign of fear. A few years later, Father Laurentin wrote that Ivan told him personally that he wrote absolutely nothing down on that sheet of paper and that he tricked the two members of the commission. On 7 March 1985, three members of the commission went to ask Ivan if what Laurentin writes is true. Ivan said it was true, and that they could freely go ahead and open the envelope in the chancery office because in it they will only find a white sheet of paper. They came back to Mostar where the commission was having a meeting and before all the members, they opened the envelope. In the envelope on a greenish sheet of paper they found written the content of the sign:

Our Lady said that she would leave a sign. The content of this sign I reveal to your trust. The sign is that there will be a great shrine in Medjugorje in honour of my apparitions, a shrine to my image. When will this occur? The sign will occur in June. Dated: 9 May 1982. Seer: Ivan Dragicevic.

“There will be a great shrine” is intended to mean that one will be miraculously created, without being built by human beings. And although in principle it is possible to take “the sign will occur in June” ambiguously, namely that it will occur in June of an unknown year, it is plain enough that Ivan was writing about June 1982.

Needless to say, this did not happen. And the consequence is that Ivan Dragicevic is not a trustworthy witness to the truth. He is not trustworthy because of the false claim that there would be such a sign, and he is not trustworthy because of the false claim that he wrote nothing on the paper.

And the fact that he is not trustworthy will not be changed simply by external support. His testimony is not credible. And it remains that way even if rosaries turn to gold, and would remain that way even if someone were to rise from the dead.

 

Miracles and Multiple Witnesses

A fairly frequent claim, often in connection with the alleged Marian apparitions at Medjugorje, although not only in that connection, is the claim that rosary chains have changed to gold, or become golden plated. Thus for example Fr. Francis Marsden makes this claim in a letter published in the Tablet on May 26, 1990:

Leaving for Medjugorje after Easter 1989, I decided I would take my own ordination pair of rosary beads (received from the Vatican in 1984). I had seldom used them but kept them as a memento. As I put them in a little cloth bag in my trouser pocket, I checked that they were silver. “If it does happen, I’d like it to happen to this pair”, I thought.

They remained in my pocket untouched down to Heathrow, and out to Zagreb, Split and Medjugorje, from Saturday night through to Monday lunchtime. Five of us priests were on top of Krizevac, the Hill of the Cross. I took out the rosary to say the Glorious Mysteries. To my shock and near-disbelief, the links by the medal glittered gold in the sunshine. Inspecting further, I found that all the links touching either a bead or the crucifix were now golden. “My God, it’s happened”, I thought, much moved.

The extra links separating the decades remained silver. The message for me was, “It is prayer which changes things”.

Later I checked the inside of the little cloth bag. The lining was clean. There were no signs of any metal having rubbed off. I also asked a priest friend with an identical Vatican silver rosary to try rubbing off the silver. He told me that after a long time scraping with a coin, he began to get a very slight dull bronze tinge to the silver. That degree of abrasion was impossible in my pocket.

Fr. Francis is here giving reasons for supposing that the change was not natural. Continuing in the same vein, he says:

So Mr. Falkiner’s theory fails to explain all the observed facts. Undoubtedly he is correct in some cases in suggesting that prolonged, sweaty use will cause tarnishing. But in my case and many others there has been no “hard use”. Nor has the trans-coloration been over all the links, but selectively and with a beautiful subtlety. I have seen several other patterns to the transformation.

Does air travel at 30,000 ft produce the change? Do some Medjugorje locals steal pilgrims’ rosaries from their pockets at night and spray them? Is it psychological wish-fulfilment? If so, please instruct me how to harness this power and, like Midas, I will try it out on some of our silver chalices and patens.

One Jesuit priest told me how he actually saw his rosary change colour. He and a friend were walking up Krizevac, joking about the phenomenon. taking 10p and 20p coins out of their pockets: “Has this one changed yet, Bernard?” “No, let’s have a look at this one . . .”. And as he was holding his rosary in his hand, he saw the golden colour come over it.

He has given some reasons for supposing that the change was not natural, but one could object that there is no external proof of the change. But in various cases people say that they experienced such a change, and confirmed it later by external testing. For example, William Simon says in his autobiography, A Time for Reflection,

After our first Mass at Medjugorje, I remember telling my son Billy, “That is the closest I’ve ever felt to heaven on earth.” I then pulled out the old, inexpensive rosary beads that I had bought about ten years earlier, and noticed that the chain was glittering in the sun. That was strange. The chain was just some cheap, dull alloy, yet it suddenly appeared radiant and golden and vibrant and remained so. I wasn’t quite sure what to make of it, and upon my return brought the rosary to a jeweler for an appraisal. He confirmed that the chain, inexplicably, had turned to solid gold. I can’t explain the transformation, either of the rosary  or of my own life, except as a sign of divine intervention, and accept it as such.

The total number of people who have claimed to have observed such cases is probably at least many hundreds, or more likely many thousands. I have seen one such rosary myself and can confirm that it appeared a golden color when I saw it. And while most people do not appear to have had any specific tests done, a number did do this, like William Simon in the above quotation.

Like reports of meteorites in the 18th century, these reports should be taken seriously. However, note that although we have multiple witnesses, the witnesses are not all to the same event, but to different events, and this can make a significant difference.

Suppose we took one such rosary, and passed it from person to person, each of them taking it and having it tested, and each confirmed that the metal of the chain had actually changed. If several dozen people confirmed this without exception, without bias in the selection of persons, including persons that had no interest in such a miracle, such as Jews and atheists, there would be no reason to doubt that the rosary chain was now gold or golden plated. It would be quite wrong to follow Hume’s advice and to dismiss this as risible rather than a matter of argument.

However, the argument in reality is much weaker because in fact these witnesses are testifying to separate events. If we have the situation described above, where dozens of witnesses confirm the same event, without a bias in the selection of witnesses, then if they are all wrong, something very unlikely has taken place: either they are all lying, their tests were all mistaken, or some combination of these things. This would be very unlikely indeed, in the situation described, and could easily be made more unlikely to whatever degree one desired, by renewed testing.

But suppose that in the actual case of multiple witnesses attesting to multiple events, no rosary chain has actually undergone such a change. This still implies that all of our witnesses are mistaken or lying. But it does not imply anything extremely improbable: there may have been people who tested their rosaries, and confirmed that nothing had changed, but there was no reason for them to publish the matter. Instead, only those published who were willing to lie, were mistaken, or who received mistaken results from their jewelers or chemists.

Thus it is very possible that the latter situation is the actual truth, and it would be a mistake to reject this possibility simply on the grounds that it is distrustful of human testimony.

But it is also possible that some of these chains have in fact changed to gold or become gold plated.

Miracles and Meteorites

Stanley Jaki, in his book God and the Sun at Fatima, comments on the scientific history of meteorites:

Once the Académie des Sciences in Paris decided that eyewitness accounts about fiery streaks dashing toward the earth should not be trusted, meteorites were discarded from the collection of other scientific academies as well. No less a scientist than Lavoisier changed the written statement of an eyewitness because it countered his disbelief in meteors. Laplace shouted, “We have had enough such myths,” when his fellow academician Marc-Auguste Pictet urged, in the full hearing of the Académie des Sciences, that attention be given to the report about a huge meteor shower that fell at L’Aigle, near Paris, on April 26, 1803.

This is not untypical. Historically, the scientific community showed a similar reluctance to accept the reality of earthquake lights, rogue waves, and other phenomena.

Laplace’s concern, of course, was probably not that the idea of stones coming from the sky seemed to him absurd in itself, but that it did not seem possible to explain it by natural principles known to him. The idea of continental drift was long rejected for this reason, namely the apparent lack of a mechanism that might bring it about.

This concern is not entirely unreasonable. If scientists were to accept all eyewitness accounts as they stand, they might be forced to constantly add new principles in order to explain the most recent stories. On the other hand, it would be reasonable for them to give somewhat more attention to accounts which come up repeatedly, as happened with the accounts of the above phenomena.

Accounts of miracles can in fact be treated much like such accounts. A miracle does not mean something which has never been seen in any age or country, as Hume defines it, but something which does not have natural principles. Thus, for example, if a man rises from the dead we do not (generally speaking) believe that this could have resulted from natural principles. This does not prove that it cannot happen at all, as Hume supposes, but only that if it does happen, it results from some additional principle, above and beyond the principles of nature.

 

Hume’s Error on Miracles

After his comparison with the idea of the Real Presence, Hume continues by saying that we should proportion our beliefs to the evidence for them:

Though experience be our only guide in reasoning concerning matters of fact; it must be acknowledged, that this guide is not altogether infallible, but in some cases is apt to lead us into errors. One, who in our climate, should expect better weather in any week of June than in one of December, would reason justly, and conformably to experience; but it is certain, that he may happen, in the event, to find himself mistaken. However, we may observe, that, in such a case, he would have no cause to complain of experience; because it commonly informs us beforehand of the uncertainty, by that contrariety of events, which we may learn from a diligent observation. All effects follow not with like certainty from their supposed causes. Some events are found, in all countries and all ages, to have been constantly conjoined together: Others are found to have been more variable, and sometimes to disappoint our expectations; so that, in our reasonings concerning matter of fact, there are all imaginable degrees of assurance, from the highest certainty to the lowest species of moral evidence.
A wise man, therefore, proportions his belief to the evidence. In such conclusions as are founded on an infallible experience, he expects the event with the last degree of assurance, and regards his past experience as a full proof of the future existence of that event. In other cases, he proceeds with more caution: he weighs the opposite experiments: he considers which side is supported by the greater number of experiments: to that side he inclines, with doubt and hesitation; and when at last he fixes his judgement, the evidence exceeds not what we properly call probability. All probability, then, supposes an opposition of experiments and observations, where the one side is found to overbalance the other, and to produce a degree of evidence, proportioned to the superiority. A hundred instances or experiments on one side, and fifty on another, afford a doubtful expectation of any event; though a hundred uniform experiments, with only one that is contradictory, reasonably beget a pretty strong degree of assurance. In all cases, we must balance the opposite experiments, where they are opposite, and deduct the smaller number from the greater, in order to know the exact force of the superior evidence.

While Hume is right to say that convictions should in some way be proportionate to the evidence for them, we can already see here the cause of a serious error. As I have pointed out elsewhere, Hume does not have a developed mathematical theory of probability. Hence his talk of how one should “deduct the smaller number from the greater, in order to know the exact force of the superior evidence.” If one takes this literally, this would suggest that something with no experiments supporting it has a force of 0; something with 35 experiments supporting it and nothing against has a force of 35; something with 40 experiments supporting it and 5 against has the same force; and so on. All of this, of course, is evidently absurd.

He then brings up the example of the testimony of witnesses:

To apply these principles to a particular instance; we may observe, that there is no species of reasoning more common, more useful, and even necessary to human life, than that which is derived from the testimony of men, and the reports of eye-witnesses and spectators. This species of reasoning, perhaps, one may deny to be founded on the relation of cause and effect. I shall not dispute about a word. It will be sufficient to observe that our assurance in any argument of this kind is derived from no other principle than our observation of the veracity of human testimony, and of the usual conformity of facts to the reports of witnesses. It being a general maxim, that no objects have any discoverable connexion together, and that all the inferences, which we can draw from one to another, are founded merely on our experience of their constant and regular conjunction; it is evident, that we ought not to make an exception to this maxim in favour of human testimony, whose connexion with any event seems, in itself, as little necessary as any other. Were not the memory tenacious to a certain degree; had not men commonly an inclination to truth and a principle of probity; were they not sensible to shame, when detected in a falsehood: were not these, I say, discovered by experience to be qualities, inherent in human nature, we should never repose the least confidence in human testimony. A man delirious, or noted for falsehood and villainy, has no manner of authority with us.
And as the evidence, derived from witnesses and human testimony, is founded on past experience, so it varies with the experience, and is regarded either as a proof or a probability, according as the conjunction between any particular kind of report and any kind of object has been found to be constant or variable. There are a number of circumstances to be taken into consideration in all judgements of this kind; and the ultimate standard, by which we determine all disputes, that may arise concerning them, is always derived from experience and observation. Where this experience is not entirely uniform on any side, it is attended with an unavoidable contrariety in our judgements, and with the same opposition and mutual destruction of argument as in every other kind of evidence. We frequently hesitate concerning the reports of others. We balance the opposite circumstances, which cause any doubt or uncertainty; and when we discover a superiority on any side, we incline to it; but still with a diminution of assurance, in proportion to the force of its antagonist.
This contrariety of evidence, in the present case, may be derived from several different causes; from the opposition of contrary testimony; from the character or number of the witnesses; from the manner of their delivering their testimony; or from the union of all these circumstances. We entertain a suspicion concerning any matter of fact, when the witnesses contradict each other; when they are but few, or of a doubtful character; when they have an interest in what they affirm; when they deliver their testimony with hesitation, or on the contrary, with too violent asseverations. There are many other particulars of the same kind, which may diminish or destroy the force of any argument, derived from human testimony.
Suppose, for instance, that the fact, which the testimony endeavours to establish, partakes of the extraordinary and the marvellous; in that case, the evidence, resulting from the testimony, admits of a diminution, greater or less, in proportion as the fact is more or less unusual. The reason why we place any credit in witnesses and historians, is not derived from any connexion, which we perceive à priori, between testimony and reality, but because we are accustomed to find a conformity between them. But when the fact attested is such a one as has seldom fallen under our observation, here is a contest of two opposite experiences; of which the one destroys the other, as far as its force goes, and the superior can only operate on the mind by the force, which remains. The very same principle of experience, which gives us a certain degree of assurance in the testimony of witnesses, gives us also, in this case, another degree of assurance against the fact, which they endeavour to establish; from which contradiction there necessarily arises a counterpoize, and mutual destruction of belief and authority.
I should not believe such a story were it told me by Cato, was a proverbial saying in Rome, even during the lifetime of that philosophical patriot. The incredibility of a fact, it was allowed, might invalidate so great an authority.
The Indian prince, who refused to believe the first relations concerning the effects of frost, reasoned justly; and it naturally required very strong testimony to engage his assent to facts, that arose from a state of nature, with which he was unacquainted, and which bore so little analogy to those events, of which he had had constant and uniform experience. Though they were not contrary to his experience, they were not conformable to it.

While we might disagree that someone would be reasonable in refusing to accept testimony concerning the effects of frost, Hume’s general points here are fairly reasonable.

But when he attempts to apply to this miracles, he basically attempts to reason from the invalid mathematical points in the previous text:

But in order to increase the probability against the testimony of witnesses, let us suppose, that the fact, which they affirm, instead of being only marvellous, is really miraculous; and suppose also, that the testimony considered apart and in itself, amounts to an entire proof; in that case, there is proof against proof, of which the strongest must prevail, but still with a diminution of its force, in proportion to that of its antagonist.
A miracle is a violation of the laws of nature; and as a firm and unalterable experience has established these laws, the proof against a miracle, from the very nature of the fact, is as entire as any argument from experience can possibly be imagined. Why is it more than probable, that all men must die; that lead cannot, of itself, remain suspended in the air; that fire consumes wood, and is extinguished by water; unless it be, that these events are found agreeable to the laws of nature, and there is required a violation of these laws, or in other words, a miracle to prevent them? Nothing is esteemed a miracle, if it ever happen in the common course of nature. It is no miracle that a man, seemingly in good health, should die on a sudden: because such a kind of death, though more unusual than any other, has yet been frequently observed to happen. But it is a miracle, that a dead man should come to life; because that has never been observed in any age or country. There must, therefore, be a uniform experience against every miraculous event, otherwise the event would not merit that appellation. And as a uniform experience amounts to a proof, there is here a direct and full proof, from the nature of the fact, against the existence of any miracle; nor can such a proof be destroyed, or the miracle rendered credible, but by an opposite proof, which is superior.
The plain consequence is (and it is a general maxim worthy of our attention), ‘that no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavors to establish; and even in that case there is a mutual destruction of arguments, and the superior only gives us an assurance suitable to that degree of force, which remains, after deducting the inferior.’ When anyone tells me, that he saw a dead man restored to life, I immediately consider with myself, whether it be more probable, that this person should either deceive or be deceived, or that the fact, which he relates, should really have happened. I weigh the one miracle against the other; and according to the superiority, which I discover, I pronounce my decision, and always reject the greater miracle. If the falsehood of his testimony would be more miraculous, than the event which he relates; then, and not till then, can he pretend to command my belief or opinion.

There are various ways to read this, but each way leads to problems. Hume has told himself that he believes that he has found a conclusive proof that accounts of miracles should never be accepted; and this implies that he must be saying that his condition, that the testimony should “be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavors to establish,” can never be satisfied.

But there is no reasonable understanding where this condition can never be satisfied. Hume seems to be equating “more miraculous” with “less probable,” but there is no degree of probability that could not be established by witnesses in principle. Even if each witness has only a small chance of telling the truth, multiple independent witnesses could in principle establish any degree of probability whatsoever.

The basic problem here seems to be Hume’s mathematically incorrect understanding of probability. If something has never been seen to happen, he says, this is a full proof that it cannot happen. Thus he seems to imply that there is a 0% chance of it happening. But this is evidently unreasonable. In reality, of course, we often see particular things happen which never happened before. And similarly, it is simply not true that a miracle is only called a miracle because it “has never been observed in any age or country.” There have been many reports, in many ages and many countries, of dead people coming to life again. So the only way Hume could say that a dead person coming to life is a miracle in this sense, is by assuming that all of these reports are false. This is simply to assume what he is trying to prove, and in any case we think that resurrection is a miracle whether or not these reports are true. In other words, to say that resurrection is a miracle is not to say that these reports are false, but that if they are true, they are reports of miracles.

Taken in another way, Hume seems to be saying, “A miracle requires a suspension of natural laws. But false testimony does not. Therefore if we have the choice of believing that there was a miracle or of believing that there was false testimony, we should always choose to believe that there was false testimony.” The problem is that, again, if you evaluate this in terms of probabilities, the suspension of natural laws might well be more probable than a particular possibility which does not suspend natural laws. If someone predicts the result of a coin flip 100,000 times in a row, it does not violate natural laws to think that this happened by chance, with a fair coin. But it is much more probable that natural laws were violated, than that this happened by chance with a fair coin.

While it would only relate to Hume personally, we might also note that according to Hume, induction cannot even establish a probability, let alone a necessity.  So according to his position, the experience of dead people remaining dead does not make it improbable that one would rise, let alone excluding it as impossible.

Hume himself seems to sense that there is something wrong with his position, even if he cannot quite work out what it is, again probably on account of the lack of a mathematical theory of probability. Consequently he adds a number of arguments:

For first, there is not to be found, in all history, any miracle attested by a sufficient number of men, of such unquestioned good sense, education, and learning, as to secure us against all delusion in themselves; of such undoubted integrity, as to place them beyond all suspicion of any design to deceive others; of such credit and reputation in the eyes of mankind, as to have a great deal to lose in case of their being detected in any falsehood; and at the same time, attesting facts performed in such a public manner and in so celebrated a part of the world, as to render the detection unavoidable: all which circumstances are requisite to give us a full assurance in the testimony of men.
Secondly. We may observe in human nature a principle which, if strictly examined, will be found to diminish extremely the assurance, which we might, from human testimony, have in any kind of prodigy. The maxim, by which we commonly conduct ourselves in our reasonings, is, that the objects, of which we have no experience, resembles those, of which we have; that what we have found to be most usual is always most probable; and that where there is an opposition of arguments, we ought to give the preference to such as are founded on the greatest number of past observations. But though, in proceeding by this rule, we readily reject any fact which is unusual and incredible in an ordinary degree; yet in advancing farther, the mind observes not always the same rule; but when anything is affirmed utterly absurd and miraculous, it rather the more readily admits of such a fact, upon account of that very circumstance, which ought to destroy all its authority. The passion of surprise and wonder, arising from miracles, being an agreeable emotion, gives a sensible tendency towards the belief of those events, from which it is derived. And this goes so far, that even those who cannot enjoy this pleasure immediately, nor can believe those miraculous events, of which they are informed, yet love to partake of the satisfaction at second-hand or by rebound, and place a pride and delight in exciting the admiration of others.
With what greediness are the miraculous accounts of travellers received, their descriptions of sea and land monsters, their relations of wonderful adventures, strange men, and uncouth manners? But if the spirit of religion join itself to the love of wonder, there is an end of common sense; and human testimony, in these circumstances, loses all pretensions to authority. A religionist may be an enthusiast, and imagine he sees what has no reality: he may know his narrative to be false, and yet persevere in it, with the best intentions in the world, for the sake of promoting so holy a cause: or even where this delusion has not place, vanity, excited by so strong a temptation, operates on him more powerfully than on the rest of mankind in any other circumstances; and self-interest with equal force. His auditors may not have, and commonly have not, sufficient judgement to canvass his evidence: what judgement they have, they renounce by principle, in these sublime and mysterious subjects: or if they were ever so willing to employ it, passion and a heated imagination disturb the regularity of its operations, their credulity increases his impudence: and his impudence overpowers their credulity.
Eloquence, when at its highest pitch, leaves little room for reason or reflection; but addressing itself entirely to the fancy or the affections, captivates the willing hearers, and subdues their understanding. Happily, this pitch is seldom attains. But what a Tully or a Demosthenes could scarcely effect over a Roman or Athenian audience, every Capuchin, every itinerant or stationary teacher can perform over the generality of mankind, and in a higher degree, by touching such gross and vulgar passions.
The many instances of forged miracles, and prophecies, and supernatural events, which, in all ages, have either been detected by contrary evidence, or which detect themselves by their absurdity, prove sufficiently the strong propensity of mankind to the extraordinary and the marvellous, and ought reasonably to beget a suspicion against all relations of this kind. This is our natural way of thinking, even with regard to the most common and most credible events. For instance: There is no kind of report which rises so easily, and spreads so quickly, especially in country places and provincial towns, as those concerning marriages; insomuch that two young persons of equal condition never see each other twice, but the whole neighbourhood immediately join them together. The pleasure of telling a piece of news so interesting, of propagating it, and of being the first reporters of it, spreads the intelligence. And this is so well known, that no man of sense gives attention to these reports, till he find them confirmed by some greater evidence. Do not the same passions, and others still stronger, incline the generality of mankind to believe and report, with the greatest vehemence and assurance, all religious miracles?
Thirdly. It forms a strong presumption against all supernatural and miraculous relations, that they are observed chiefly to abound among ignorant and barbarous nations; or if a civilized people has ever given admission to any of them, that people will be found to have received them from ignorant and barbarous ancestors, who transmitted them with that inviolable sanction and authority, which always attend received opinions. When we peruse the first histories of all nations, we are apt to imagine ourselves transported into some new world; where the whole frame of nature is disjointed, and every element performs its operations in a different manner, from what it does at present. Battles, revolutions, pestilence, famine and death, are never the effect of those natural causes, which we experience. Prodigies, omens, oracles, judgements, quite obscure the few natural events, that are intermingled with them. But as the former grow thinner every page, in proportion as we advance nearer the enlightened ages, we soon learn, that there is nothing mysterious or supernatural in the case, but that all proceeds from the usual propensity of mankind towards the marvellous, and that, though this inclination may at intervals receive a check from sense and learning, it can never be thoroughly extirpated from human nature.
It is strange, a judicious reader is apt to say, upon the perusal of these wonderful historians, that such prodigious events never happen in our days. But it is nothing strange, I hope, that men should lie in all ages. You must surely have seen instances enough of that frailty. You have yourself heard many such marvellous relations started, which, being treated with scorn by all the wise and judicious, have at last been abandoned even by the vulgar. Be assured, that those renowned lies, which have spread and flourished to such a monstrous height, arose from like beginnings; but being sown in a more proper soil, shot up at last into prodigies almost equal to those which they relate.

Hume is making some reasonable points here. But note that all of these things are contingent. They could have been otherwise in general, and they might well be otherwise in particular cases, even actual ones. Consequently they cannot possibly amount to a full proof that miraculous accounts should not be accepted. The fact that Hume feels the need to point to these contingent facts shows that at some level he is aware of the fact that his argument is not conclusive, although he wishes it to be.

In the end, Hume’s argument does not establish anything, but only expresses his own incredulity, as in this example:

There is also a memorable story related by Cardinal de Retz, which may well deserve our consideration. When that intriguing politician fled into Spain, to avoid the persecution of his enemies, he passed through Saragossa, the capital of Arragon, where he was shewn, in the cathedral, a man, who had served seven years as a doorkeeper, and was well known to every body in town, that had ever paid his devotions at that church. He had been seen, for so long a time, wanting a leg; but recovered that limb by the rubbing of holy oil upon the stump; and the cardinal assures us that he saw him with two legs. This miracle was vouched by all the canons of the church; and the whole company in town were appealed to for a confirmation of the fact; whom the cardinal found, by their zealous devotion, to be thorough believers of the miracle. Here the relater was also contemporary to the supposed prodigy, of an incredulous and libertine character, as well as of great genius; the miracle of so singular a nature as could scarcely admit of a counterfeit, and the witnesses very numerous, and all of them, in a manner, spectators of the fact, to which they gave their testimony. And what adds mightily to the force of the evidence, and may double our surprise on this occasion, is, that the cardinal himself, who relates the story, seems not to give any credit to it, and consequently cannot be suspected of any concurrence in the holy fraud. He considered justly, that it was not requisite, in order to reject a fact of this nature, to be able accurately to disprove the testimony, and to trace its falsehood, through all the circumstances of knavery and credulity which produced it. He knew, that, as this was commonly altogether impossible at any small distance of time and place; so was it extremely difficult, even where one was immediately present, by reason of the bigotry, ignorance, cunning, and roguery of a great part of mankind. He therefore concluded, like a just reasoner, that such an evidence carried falsehood upon the very face of it, and that a miracle, supported by any human testimony, was more properly a subject of derision than of argument.

This is a distorted account of the miracle of Calanda. Ironically, Hume’s position is actually supported to some extent by the errors contained in his own account of the miracle: we cannot “trace its falsehood,” in the sense that we cannot determine whether the account has been distorted by Hume himself, by the Cardinal, by the residents of Zaragoza, or by others, or some combination of these, but it is easy enough to determine the fact that it has been so distorted. Nevertheless, Hume is not proving anything here, but simply asserting that he would not believe in a miracle no matter how good the testimony brought in its favor.

This is not a reasonable attitude, but sheer stubbornness.