Minimizing Motivated Beliefs

In the last post, we noted that there is a conflict between the goal of accurate beliefs about your future actions, and your own goals about your future. More accurate beliefs will not always lead to a better fulfillment of those goals. This implies that you must be ready to engage in a certain amount of trade, if you desire both truth and other things. Eliezer Yudkowsky argues that self-deception, and therefore also such trade, is either impossible or stupid, depending on how it is understood:

What if self-deception helps us be happy?  What if just running out and overcoming bias will make us—gasp!—unhappy?  Surely, true wisdom would be second-order rationality, choosing when to be rational.  That way you can decide which cognitive biases should govern you, to maximize your happiness.

Leaving the morality aside, I doubt such a lunatic dislocation in the mind could really happen.

Second-order rationality implies that at some point, you will think to yourself, “And now, I will irrationally believe that I will win the lottery, in order to make myself happy.”  But we do not have such direct control over our beliefs.  You cannot make yourself believe the sky is green by an act of will.  You might be able to believe you believed it—though I have just made that more difficult for you by pointing out the difference.  (You’re welcome!)  You might even believe you were happy and self-deceived; but you would not in fact be happy and self-deceived.

For second-order rationality to be genuinely rational, you would first need a good model of reality, to extrapolate the consequences of rationality and irrationality.  If you then chose to be first-order irrational, you would need to forget this accurate view. And then forget the act of forgetting.  I don’t mean to commit the logical fallacy of generalizing from fictional evidence, but I think Orwell did a good job of extrapolating where this path leads.

You can’t know the consequences of being biased, until you have already debiased yourself.  And then it is too late for self-deception.

The other alternative is to choose blindly to remain biased, without any clear idea of the consequences.  This is not second-order rationality.  It is willful stupidity.

There are several errors here. The first is the denial that belief is voluntary. As I remarked in the comments to this post, it is best to think of “choosing to believe a thing” as “choosing to treat this thing as a fact.” And this is something which is indeed voluntary. Thus for example it is by choice that I am, at this very moment, treating it as a fact that belief is voluntary.

There is some truth in Yudkowsky’s remark that “you cannot make yourself believe the sky is green by an act of will.” But this is not because the thing itself is intrinsically involuntary. On the contrary, you could, if you wished, choose to treat the greenness of the sky as a fact, at least for the most part and in most ways. The problem is that you have no good motive to wish to act this way, and plenty of good motives not to act this way. In this sense, it is impossible for most of us to believe that the sky is green in the same way it is impossible for most of us to commit suicide; we simply have no good motive to do either of these things.

Yudkowsky’s second error is connected with the first. Since, according to him, it is impossible to deliberately and directly deceive oneself, self-deception can only happen in an indirect manner: “The other alternative is to choose blindly to remain biased, without any clear idea of the consequences.  This is not second-order rationality.  It is willful stupidity.” The idea is that ordinary beliefs are simply involuntary, but we can have beliefs that are somewhat voluntary by choosing “blindly to remain biased, without any clear idea of the consequences.” Since this is “willful stupidity,” a reasonable person would completely avoid such behavior, and thus all of his beliefs would be involuntary.

Essentially, Yudkowsky is claiming that we have some involuntary beliefs, and that we should avoid adding any voluntary beliefs to our involuntary ones. This view is fundamentally flawed precisely because all of our beliefs are voluntary, and thus we cannot avoid having voluntary beliefs.

Nor is it “willful stupidity” to trade away some truth for the sake of other good things. Completely avoiding this is in fact intrinsically impossible. If you are seeking one good, you are not equally seeking a distinct good; one cannot serve two masters. Thus since all people are interested in some goods distinct from truth, there is no one who fails to trade away some truth for the sake of other things. Yudkowsky’s mistake here is related to his wishful thinking about wishful thinking which I discussed previously. In this way he views himself, at least ideally, as completely avoiding wishful thinking. This is both impossible and unhelpful, impossible in that everyone has such motivated beliefs, and unhelpful because such beliefs can in fact be beneficial.

A better attitude to this matter is adopted by Robin Hanson, as for example when he discusses motives for having opinions in a post which we previously considered here. Bryan Caplan has a similar view, discussed here.

Once we have a clear view of this matter, we can use this to minimize the loss of truth that results from such beliefs. For example, in a post linked above, we discussed the argument that fictional accounts consistently distort one’s beliefs about reality. Rather than pretending that there is no such effect, we can deliberately consider to what extent we wish to be open to this possibility, depending on our other purposes for engaging with such accounts. This is not “willful stupidity”; the stupidity would to be engage in such trades without realizing that such trades are inevitable, and thus not to realize to what extent you are doing it.

Consider one of the cases of voluntary belief discussed in this earlier post. As we quoted at the time, Eric Reitan remarks:

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?

Here, Reitan is proposing that someone believe that “a transcendent good is at work redeeming evil” for the purpose of having “the sense that their lives have positive meaning.” If we look at this as it is, namely as proposing a voluntary belief for the sake of something other than truth, we can find ways to minimize the potential conflict between accuracy and this other goal. For example, the person might simply believe that “my life has a positive meaning,” without trying to explain why this is so. For the reasons given here, “my life has a positive meaning” is necessarily more probable and more known than any explanation for this that might be adopted. To pick a particular explanation and claim that it is more likely would be to fall into the conjunction fallacy.

Of course, real life is unfortunately more complicated. The woman in Reitan’s discussion might well respond to our proposal somewhat in this way (not a real quotation):

Probability is not the issue here, precisely because it is not a question of the truth of the matter in itself. There is a need to actually feel that one’s life is meaningful, not just to believe it. And the simple statement “life is meaningful” will not provide that feeling. Without the feeling, it will also be almost impossible to continue to believe it, no matter what the probability is. So in order to achieve this goal, it is necessary to believe a stronger and more particular claim.

And this response might be correct. Some such goals, due to their complexity, might not be easily achieved without adopting rather unlikely beliefs. For example, Robin Hanson, while discussing his reasons for having opinions, several times mentions the desire for “interesting” opinions. This is a case where many people will not even notice the trade involved, because the desire for interesting ideas seems closely related to the desire for truth. But in fact truth and interestingness are diverse things, and the goals are diverse, and one who desires both will likely engage in some trade. In fact, relative to truth seeking, looking for interesting things is a dangerous endeavor. Scott Alexander notes that interesting things are usually false:

This suggests a more general principle: interesting things should usually be lies. Let me give three examples.

I wrote in Toxoplasma of Rage about how even when people crusade against real evils, the particular stories they focus on tend to be false disproportionately often. Why? Because the thousands of true stories all have some subtleties or complicating factors, whereas liars are free to make up things which exactly perfectly fit the narrative. Given thousands of stories to choose from, the ones that bubble to the top will probably be the lies, just like on Reddit.

Every time I do a links post, even when I am very careful to double- and triple- check everything, and to only link to trustworthy sources in the mainstream media, a couple of my links end up being wrong. I’m selecting for surprising-if-true stories, but there’s only one way to get surprising-if-true stories that isn’t surprising, and given an entire Internet to choose from, many of the stories involved will be false.

And then there’s bad science. I can’t remember where I first saw this, so I can’t give credit, but somebody argued that the problem with non-replicable science isn’t just publication bias or p-hacking. It’s that some people will be sloppy, biased, or just stumble through bad luck upon a seemingly-good methodology that actually produces lots of false positives, and that almost all interesting results will come from these people. They’re the equivalent of Reddit liars – if there are enough of them, then all of the top comments will be theirs, since they’re able to come up with much more interesting stuff than the truth-tellers. In fields where sloppiness is easy, the truth-tellers will be gradually driven out, appearing to be incompetent since they can’t even replicate the most basic findings of the field, let alone advance it in any way. The sloppy people will survive to train the next generation of PhD students, and you’ll end up with a stable equilibrium.

In a way this makes the goal of believing interesting things much like the woman’s case. The goal of “believing interesting things” will be better achieved by more complex and detailed beliefs, even though to the extent that they are more complex and detailed, they are simply that much less likely to be true.

The point of this present post, then, is not to deny that some goals might be such that they are better attained with rather unlikely beliefs, and in some cases even in proportion to the unlikelihood of the beliefs. Rather, the point is that a conscious awareness of the trades involved will allow a person to minimize the loss of truth involved. If you never look at your bank account, you will not notice how much money you are losing from that monthly debit for internet. In the same way, if you hold Yudkowksy’s opinion, and believe that you never trade away truth for other things, which is itself both false and motivated, you are like someone who never looks at your account: you will not notice how much you are losing.

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Technology and Culture

The last two posts have effectively answered the question raised about Scott Alexander’s account of cultural decline. What could be meant by calling some aspects of culture “less compatible with modern society?” Society tends to change over time, and some of those changes are humanly irreversible. It is entirely possible, and in fact common, for some of those irreversible changes to stand in tension with various elements of culture. This will necessarily tend to cause cultural decay at least with respect to those elements, and often with respect to other elements of culture as well, since the various aspects of culture are related.

This happens in a particular way with changes in technology, although technology is not the only driver of such irreversible change.

It would be extremely difficult for individuals to opt out of the use of of various technologies. For example, it would be quite difficult for Americans to give up the use of plumbing and heating, and a serious attempt to do so might lead to illness or death in many cases. And it would be still more difficult to give up the use of clothes, money, and language. Attempting to do so, assuming that one managed to preserve one’s physical life, would likely lead to imprisonment or other forms of institutionalization (which would make it that much more difficult to abandon the use of clothes.)

Someone might well respond here, “Wait, why are you bringing up clothes, money, and language as examples of technology?” Clothes and money seem more like cultural institutions than technology in the first place; and language seems to be natural to humans.

I have already spoken of language as a kind of technology. And with regard to clothes and money, it is even more evident that in the concrete forms in which they exist in our world today they are tightly intertwined with various technologies. The cash used in the United States depends on mints and printing presses, actual mechanical technologies. And if one wishes to buy something without cash, this usually depends on still more complex technology. Similar things are true of the clothes that we wear.

I concede, of course, that the use of these things is different from the use of the machines that make them, or as in the case of credit cards, support their use, although there is less distinction in the latter case. But I deliberately brought up things which look like purely cultural institutions in order to note their relationship with technology, because we are discussing the manner in which technological change can result in cultural change. Technology and culture are tightly intertwined, and can never be wholly separated.

Sarah Perry discusses this (the whole post is worth reading):

Almost every technological advance is a de-condensation: it abstracts a particular function away from an object, a person, or an institution, and allows it to grow separately from all the things it used to be connected to. Writing de-condenses communication: communication can now take place abstracted from face-to-face speech. Automobiles abstract transportation from exercise, and allow further de-condensation of useful locations (sometimes called sprawl). Markets de-condense production and consumption.

Why is technology so often at odds with the sacred? In other words, why does everyone get so mad about technological change? We humans are irrational and fearful creatures, but I don’t think it’s just that. Technological advances, by their nature, tear the world apart. They carve a piece away from the existing order – de-condensing, abstracting, unbundling – and all the previous dependencies collapse. The world must then heal itself around this rupture, to form a new order and wholeness. To fear disruption is completely reasonable.

The more powerful the technology, the more unpredictable its effects will be. A technological advance in the sense of a de-condensation is by its nature something that does not fit in the existing order. The world will need to reshape itself to fit. Technology is a bad carver, not in the sense that it is bad, but in the sense of Socrates:

First, the taking in of scattered particulars under one Idea, so that everyone understands what is being talked about … Second, the separation of the Idea into parts, by dividing it at the joints, as nature directs, not breaking any limb in half as a bad carver might.”

Plato, Phaedrus, 265D, quoted in Notes on the Synthesis of Form, Christopher Alexander.

The most powerful technological advances break limbs in half. They cut up the world in an entirely new way, inconceivable in the previous order.

Now someone, arguing much in Chesterton’s vein, might say that this does not have to happen. If a technology is damaging in this way, then just don’t use it. The problem is that often one does not have a realistic choice not to use it, as in my examples above. And much more can one fail to have a choice not to interact with people who use the new technology, and interacting with those people will itself change the way that life works. And as Robin Hanson noted, there is not some human global power that decides whether or not a technology gets to be introduced into human society or not. This happens rather by the uncoordinated and unplanned decisions of individuals.

And this is sufficient to explain the tendency towards cultural decline. The constant progress of technology results, and results of necessity, in constant cultural decline. And thus we fools understand why the former days were better than these.

Scott Alexander on the Decline of Culture

From Scott Alexander’s Tumblr:

voximperatoris:

[This post is copied over from Stephen Hicks.]

An instructive series of quotations, collected over the years, on the theme of pessimism about the present in relation to the past:

Plato, 360 BCE: “In that country [Egypt] arithmetical games have been invented for the use of mere children, which they learn as pleasure and amusement. I have late in life heard with amazement of our ignorance in these matters [science in general]; to me we appear to be more like pigs than men, and I am quite ashamed, not only of myself, but of all Greeks.” (Laws, Book VII)

Catullus, c. 60 BCE: “Oh, this age! How tasteless and ill-bred it is!”

Sallust, 86– c. 35 BCE: “to speak of the morals of our country, the nature of my theme seems to suggest that I go farther back and give a brief account of the institutions of our forefathers in peace and in war, how they governed the commonwealth, how great it was when they bequeathed it to us, and how by gradual changes it has ceased to be the noblest and best, and has become the worst and most vicious.” About Rome’s forefathers: “good morals were cultivated at home and in the field; there was the greatest harmony and little or no avarice; justice and probity prevailed among them.” They “adorned the shrines of the gods with piety, their own homes with glory, while from the vanquished they took naught save the power of doing harm.” But Rome now is a moral mess: “The men of to‑day, on the contrary, basest of creatures, with supreme wickedness are robbing our allies of all that those heroes in the hour of victory had left them; they act as though the one and only way to rule were to wrong.” (The Catiline War)

Horace, c. 23-13 BCE: “Our fathers, viler than our grandfathers, begot us who are viler still, and we shall bring forth a progeny more degenerate still.” (Odes 3:6)

Alberti, 1436: Nature is no longer producing great intellects — “or giants which in her youthful and more glorious days she had produced so marvelously and abundantly.” (On Painting)

Peter Paul Rubens, c. 1620: “For what else can our degenerate race do in this age of error. Our lowly disposition keeps us close to the ground, and we have declined from that heroic genius and judgment of the ancients.”

Mary Wollstonecraft, c. 1790: “As from the respect paid to property flow, as from a poisoned fountain, most of the evils and vices which render this world such a dreary scene to the contemplative mind.”

William Wordsworth, 1802:
“Milton! thou should’st be living at this hour:
England hath need of thee: she is a fen
Of stagnant waters: altar, sword, and pen,
Fireside, the heroic wealth of hall and bower,
Have forfeited their ancient English dower
Of inward happiness. We are selfish men;
Oh! raise us up, return to us again;
And give us manners, virtue, freedom, power.”
(“London”)

John Stuart Mill, in 1859, speaking of his generation: “the present low state of the human mind.” (On Liberty, Chapter 3)

Friedrich Nietzsche, in 1871: “What else, in the desolate waste of present-day culture, holds any promise of a sound, healthy future? In vain we look for a single powerfully branching root, a spot of earth that is fruitful: we see only dust, sand, dullness, and languor” (Birth of Tragedy, Section 20).

Frederick Taylor, 1911: “We can see our forests vanishing, our water-powers going to waste, our soil being carried by floods into the sea; and the end of our coal and our iron is in sight.” (Scientific Management)

T. S. Eliot, c. 1925: “We can assert with some confidence that our own period is one of decline; that the standards of culture are lower than they were fifty years ago; and that the evidences of this decline are visible in every department of human activity.”

So has the world really been in constant decline? Or perhaps, as Gibbon put it in The Decline and Fall of the Roman Empire (1776): “There exists in human nature a strong propensity to depreciate the advantages, and to magnify the evils, of the present times.”

Words to keep in mind as we try to assess objectively our own generation’s serious problems.

I hate this argument. It’s the only time I ever see “Every single person from history has always believed that X is true” used as an argument *against* X.

I mean, imagine that I listed Thomas Aquinas as saying “Technology sure has gotten better the past few decades,” and then Leonardo da Vinci, “Technology sure has gotten better the past few decades”. Benjamin Franklin, “Technology sure has gotten better the past few decades”. Abraham Lincon, “Technology sure has gotten better the past few decades. Henry Ford, “Technology sure has gotten better the past few decades.”

My conclusion – people who think technology is advancing now are silly, there’s just some human bias toward always believing technology is advancing.

In the same way technology can always be advancing, culture can always be declining, for certain definitions of culture that emphasize the parts less compatible with modern society. Like technology, this isn’t a monotonic process – there will be disruptions every time one civilization collapses and a new one begins, and occasional conscious attempts by whole societies to reverse the trend, but in general, given movement from time t to time t+1, people can correctly notice cultural decline.

I mean, really. If, like Nietszche, your thing is the BRUTE STRENGTH of the valiant warrior, do you think that the modern office worker has exactly as much valiant warrior spirit as the 19th century frontiersman? Do you think the 19th century frontiersman had as much as the medieval crusader? Do you think the medieval crusader had as much as the Spartans? Pinker says the world is going from a state of violence to a state of security, and the flip side of that is people getting, on average, more domesticated and having less of the wild free spirit that Nietszche idealized.

Likewise, when people talk about “virtue”, a lot of the time they’re talking about chastity and willingness to remain faithful in a monogamous marriage for the purpose of procreation. And a lot of the time they don’t even mean actual chastity, they mean vocal public support for chastity and social norms demanding it. Do you really believe our culture has as much of that as previous cultures do? Remember, the sort of sharia law stuff that we find so abhorrent and misogynist was considered progressive during Mohammed’s time, and with good reason.

I would even argue that Alberti is right about genius. There are certain forms of genius that modern society selects for and certain ones it selects against. Remember, before writing became common, the Greek bards would have mostly memorized Homer. I think about the doctors of past ages, who had amazing ability to detect symptoms with the naked eye in a way that almost nobody now can match because we use CT scan instead and there’s no reason to learn this art. (Also, I think modern doctors have much fewer total hours of training than older doctors, because as bad as today’s workplace-protection/no-overtime rules are, theirs were worse)

And really? Using the fact that some guy complained of soil erosion as proof that nobody’s complaints are ever valid? Soil erosion is a real thing, it’s bad, and AFAIK it does indeed keep getting worse.

More controversially, if T.S. Eliot wants to look at a world that over four hundred years, went from the Renaissance masters to modern art, I am totally okay with him calling that a terrible cultural decline.

Scott’s argument is plausible, although he seems somewhat confused insofar as he appears to associate Mohammed with monogamy. And since we are discussing the matter with an interlocutor who maintains that the decline of culture is obvious, we will concede the point immediately. Scott seems a bit ambivalent in regard to whether a declining culture is a bad thing, but we will concede that as well, other things being equal.

However, we do not clearly see an answer here to one of the questions raised in the last post: if culture tends to decline, why does this happen? Scott seems to suggest an answer when he says, “Culture can always be declining, for certain definitions of culture that emphasize the parts less compatible with modern society.” According to this, culture tends to decline because it becomes incompatible with modern society. The problem with this is that it seems to be a “moronic pseudo-reason”: 2017 is just one year among others. So no parts of culture should be less compatible with life in 2017, than with life in 1017, or in any other year. Chesterton makes a similar argument:

We often read nowadays of the valor or audacity with which some rebel attacks a hoary tyranny or an antiquated superstition. There is not really any courage at all in attacking hoary or antiquated things, any more than in offering to fight one’s grandmother. The really courageous man is he who defies tyrannies young as the morning and superstitions fresh as the first flowers. The only true free-thinker is he whose intellect is as much free from the future as from the past. He cares as little for what will be as for what has been; he cares only for what ought to be. And for my present purpose I specially insist on this abstract independence. If I am to discuss what is wrong, one of the first things that are wrong is this: the deep and silent modern assumption that past things have become impossible. There is one metaphor of which the moderns are very fond; they are always saying, “You can’t put the clock back.” The simple and obvious answer is “You can.” A clock, being a piece of human construction, can be restored by the human finger to any figure or hour. In the same way society, being a piece of human construction, can be reconstructed upon any plan that has ever existed.

There is another proverb, “As you have made your bed, so you must lie on it”; which again is simply a lie. If I have made my bed uncomfortable, please God I will make it again. We could restore the Heptarchy or the stage coaches if we chose. It might take some time to do, and it might be very inadvisable to do it; but certainly it is not impossible as bringing back last Friday is impossible. This is, as I say, the first freedom that I claim: the freedom to restore. I claim a right to propose as a solution the old patriarchal system of a Highland clan, if that should seem to eliminate the largest number of evils. It certainly would eliminate some evils; for instance, the unnatural sense of obeying cold and harsh strangers, mere bureaucrats and policemen. I claim the right to propose the complete independence of the small Greek or Italian towns, a sovereign city of Brixton or Brompton, if that seems the best way out of our troubles. It would be a way out of some of our troubles; we could not have in a small state, for instance, those enormous illusions about men or measures which are nourished by the great national or international newspapers. You could not persuade a city state that Mr. Beit was an Englishman, or Mr. Dillon a desperado, any more than you could persuade a Hampshire Village that the village drunkard was a teetotaller or the village idiot a statesman. Nevertheless, I do not as a fact propose that the Browns and the Smiths should be collected under separate tartans. Nor do I even propose that Clapham should declare its independence. I merely declare my independence. I merely claim my choice of all the tools in the universe; and I shall not admit that any of them are blunted merely because they have been used.

Other Wagers

While no one believes the ridiculous position that only atheists go to heaven, not even Richard Carrier himself, many people do believe things which allow for the construction of wagers in favor of things besides Christianity.

Other real religions would be a typical example. Thus Muslims probably generally believe that you are more likely to go heaven if you become a Muslim, and some of them believe that all non-Muslims go to hell. So they can argue that you should choose to believe that Islam is true, in order to increase your chances of going to heaven, and to avoid going to hell.

Similarly, some Catholics who hold a Feeneyite position hold not only that you must be a Catholic, externally and literally, in order to be saved, but that you also cannot be saved unless you accept this position. Since there is some chance that they are right, they might argue, you should choose to accept their position, in order to be more sure of getting to heaven and avoiding hell.

Likewise, a Catholic could argue that the Church teaches that the religious life is better than married life. This probably means that people choosing to embrace religious life are more likely to go to heaven, since it is unlikely that the chances are completely equal, and if getting married made you more likely to go to heaven, it would be better in an extremely important way. So if you are a single Catholic, you should choose to believe that you have a religious vocation, in order to maximize your chances of going to heaven.

It is instructive to consider these various wagers because they can give some sort of indication of what kinds of response are reasonable and what kinds are not, even to Pascal’s original wager.

A Christian would be likely to respond to the Islamic wager in this way: it is more likely that Christianity is true than Islam, and if Christianity is true, the Christian would increase his chances of going to hell, and decrease his chances of going to heaven, by converting to Islam, and especially for such a reason. This is much like Richard Carrier’s response to Pascal, but it is reasonable for Christians in a way in which it is not for Carrier, because Christianity is an actually existing religion, while his only-atheists-go-to-heaven religion is not.

A Catholic could respond to the Feeneyite wager in a similar way. The Feeneyite position is probably false, and probably contrary to the teaching of the Church, and therefore adopting it would be uncharitable to other people (by assuming that they are going to hell), and unfaithful to the Catholic Church (since the most reasonable interpretation of the Church’s teaching does not allow for this position.) So rather than increasing a person’s chances of going to heaven, adopting this position would decrease a person’s chances of this result. Again, the possibility of this answer derives from the fact that there are two already existing positions, so this answer does not benefit someone like Carrier.

It is more difficult for a Catholic to reject the religious vocation wager in a reasonable way, because the Church does teach that the religious life is better, and in fact this most likely does imply that Catholics embracing this form of life are more likely to be saved.

A Catholic could respond, “But I don’t actually have a religious vocation, and so I shouldn’t choose to believe that I do.” This is no different from a unbeliever saying, “But Christianity is not actually true, and so I shouldn’t choose to believe that it is.” And this response fails in both cases, because the arguments do not purport to establish that you have a vocation or that Christianity is true. They only intend to establish that it is better to believe these things, and such a response does not address the argument.

The Catholic could insist, “But if I don’t actually have a religious vocation, God does not want me to do that. So if I choose to believe in a vocation and follow it, I will be doing something that God does not want me to do. So I will be less likely to be saved.” This seems similar to the unbeliever responding, “If God exists, he does not want people believing things that are false, and Christianity is false. So I will be less likely to get anything good from God by believing.”

Both responses are problematic, basically because they are inconsistent with the principles that are assumed to be true in order to consider the situation. In other words, the response here by the Catholic is probably inconsistent with the teaching of the Church on religious vocations, and likewise the response by the unbeliever is obviously inconsistent with Christianity (since it denies it.) The reason the Catholic response is likely inconsistent with the teaching of the Church on vocations is that given that someone asserts that he has a religious vocation, the Church forbids other people from dissuading him from it on the supposed grounds that he does not have a real vocation. But if it were true that someone who chooses to believe that he has a vocation, and then acts on it, is less likely to be saved given that he did not really have a vocation, then it would be extremely reasonable for people to dissuade him. Since the Church forbids such dissuasion, it seems to imply that this answer is not correct.

Both responses can be modified so that they will be consistent with the situation under consideration. The Catholic can respond, “I very much do not want to live the religious life. Granted that the religious life in general would make someone more likely to be saved, I would be personally extremely miserable in it. This would tempt me to various vicious things, either as consequences of it, as snapping angrily at people, or in order to relieve my misery, as engaging in sinful pleasures. So despite the general situation, I would be personally less likely to be saved if I lived the religious life.”

It is not clear how strong this response is, but at least it is consistent with accepting the general teaching of the Church on vocations. Likewise, the unbeliever can modify his response to the following: “Even if Christianity is true, it seems false to me, and from my point of view, choosing to believe it would be choosing to believe something false. The Bible makes clear that people rejecting the light and choosing darkness are doing evil, so that would mean God wouldn’t be pleased by this kind of behavior. So choosing to believe would make me less likely to go to heaven, even given that Christianity is true.”

Once again, it is not clear how strong this response is, but it is consistent with the claims of Christianity, and no less reasonable than the response of the single Catholic to the argument regarding vocations.

Scott Alexander, in the comment quoted previously, is dissatisfied with such arguments because they do not provide a general answer that would apply in all possible circumstances (e.g. if you were guaranteed that God did not object to your choosing to believe something you think to be false), and it seems to him that he personally would want to reject the wager in all circumstances. He concludes that his desire to reject it is objectively unreasonable. However, he does this under the assumption that the value of getting to heaven and avoiding hell is actually infinite. As we have seen, it is not infinite in the way that matters. However, he also assumes in his comment that the probability of Christianity is astronomically low. If this were correct, then since the value of salvation is not numerically infinite, it would be right to reject the wager in all circumstances. But since it is not correct to assign such a low probability, this does not follow.

The implication is that it is not possible to give a reasonable response to the wager which implies that it would never be reasonable to accept it. Likewise, the implication of the possible responses is that it is not possible to propose the wager in a form which ought to be compelling to anyone who is reasonable and under all circumstances. In this sense, Scott Alexander is right to suppose that his desire to reject the wager under all possible circumstances is irrational. Real life is complicated, and in real life a person could reasonably accept such a wager under certain circumstances, and a person could reasonably reject such a wager under certain circumstances.

Erroneous Responses to Pascal

Many arguments which are presented against accepting Pascal’s wager are mistaken, some of them in obvious ways. For example, the argument is made that the multiplicity of religious beliefs or potential religious beliefs invalidates the wager:

But Pascal’s argument is seriously flawed. The religious environment that Pascal lived in was simple. Belief and disbelief only boiled down to two choices: Roman Catholicism and atheism. With a finite choice, his argument would be sound. But on Pascal’s own premise that God is infinitely incomprehensible, then in theory, there would be an infinite number of possible theologies about God, all of which are equally probable.

First, let us look at the more obvious possibilities we know of today – possibilities that were either unknown to, or ignored by, Pascal. In the Calvinistic theological doctrine of predestination, it makes no difference what one chooses to believe since, in the final analysis, who actually gets rewarded is an arbitrary choice of God. Furthermore we know of many more gods of many different religions, all of which have different schemes of rewards and punishments. Given that there are more than 2,500 gods known to man, and given Pascal’s own assumptions that one cannot comprehend God (or gods), then it follows that, even the best case scenario (i.e. that God exists and that one of the known Gods and theologies happen to be the correct one) the chances of making a successful choice is less than one in 2,500.

Second, Pascal’s negative theology does not exclude the possibility that the true God and true theology is not one that is currently known to the world. For instance it is possible to think of a God who rewards, say, only those who purposely step on sidewalk cracks. This sounds absurd, but given the premise that we cannot understand God, this possible theology cannot be dismissed. In such a case, the choice of what God to believe would be irrelevant as one would be rewarded on a premise totally distinct from what one actually believes. Furthermore as many atheist philosophers have pointed out, it is also possible to conceive of a deity who rewards intellectual honesty, a God who rewards atheists with eternal bliss simply because they dared to follow where the evidence leads – that given the available evidence, no God exists! Finally we should also note that given Pascal’s premise, it is possible to conceive of a God who is evil and who punishes the good and rewards the evil.

Thus Pascal’s call for us not to consider the evidence but to simply believe on prudential grounds fails.

There is an attempt here to base the response on Pascal’s mistaken claim that the probability of the existence of God (and of Catholic doctrine as a whole) is 50%. This would presumably be because we can know nothing about theological truth. According to this, the website reasons that all possible theological claims should be equally probable, and consequently one will be in any case very unlikely to find the truth, and therefore very unlikely to attain the eternal reward, using Pascal’s apparent assumption that only believers in a specific theology can attain the reward.

The problem with this is that it reasons for Pascal’s mistaken assumptions (as well as changing them in unjustified ways), while in reality the effectiveness of the wager does not precisely depend on these assumptions. If there is a 10% chance that God exists, and the rest is true as Pascal states it, it would still seem to be a good bet that God exists, in terms of the practical consequences. You will probably be wrong, but the gain if you are right will be so great that it will almost certainly outweigh the probable loss.

In reality different theologies are not equally probable, and there will be one which is most probable. Theologies such as the “God who rewards atheism”, which do not have any actual proponents, have very little evidence for them, since they do not even have the evidence resulting from a claim. One cannot expect that two differing positions will randomly have exactly the same amount of evidence for them, so one theology will have more evidence than any other. And even if it did not have overall a probability of more than 50%, it could still be a good bet, given the possibility of the reward, and better than any of the other potential wagers.

The argument is also made that once one admits an infinite reward, it is not possible to distinguish between actions with differing values. This is described here:

If you regularly brush your teeth, there is some chance you will go to heaven and enjoy infinite bliss. On the other hand, there is some chance you will enjoy infinite heavenly bliss even if you do not brush your teeth. Therefore the expectation of brushing your teeth (infinity plus a little extra due to oral health = infinity) is the same as that of not brushing your teeth (infinity minus a bit due to cavities and gingivitis = infinity), from which it follows that dental hygiene is not a particularly prudent course of action. In fact, as soon as we allow infinite utilities, decision theory tells us that any course of action is as good as any other (Duff 1986). Hence we have a reductio ad absurdum against decision theory, at least when it’s extended to infinite cases.

As actually applied, someone might argue that even if the God who rewards atheism is less probable than the Christian God, the expected utility of being Christian or atheist will be infinite in each case, and therefore one will not be a more reasonable choice than another. Some people actually seem to believe that this is a good response, but it is not. The problem here is that decision theory is a mathematical formalism and does not have to correspond precisely with real life. The mathematics does not work when infinity is introduced, but this does not mean there cannot be such an infinity in reality, nor that the two choices would be equal in reality. It simply means you have not chosen the right mathematics to express the situation. To see this clearly, consider the following situation.

You are in a room with two exits, a green door and a red door. The green door has a known probability of 99% of leading to an eternal heaven, and a known probability of 1% of leading to an eternal hell. The red door has a known probability of 99% of leading to an eternal hell, and a known probability of 1% of leading to an eternal heaven.

The point is that if your mathematics says that going out the red door is just as good as going out the green door, your mathematics is wrong. The correct solution is to go out the green door.

I would consider all such arguments, namely arguing that all religious beliefs are equally probable, or that being rewarded for atheism is as probable as being rewarded for Christianity, or that all infinite expectations are equal, are examples of not very serious thinking. These arguments are not only wrong. They are obviously wrong, and obviously motivated by the desire not to believe. Earlier I quoted Thomas Nagel on the fear of religion. After the quoted passage, he continues:

My guess is that this cosmic authority problem is not a rare condition and that it is responsible for much of the scientism and reductionism of our time. One of the tendencies it supports is the ludicrous overuse of evolutionary biology to explain everything about life, including everything about the human mind. Darwin enabled modern secular culture to heave a great collective sigh of relief, by apparently providing a way to eliminate purpose, meaning, and design as fundamental features of the world. Instead they become epiphenomena, generated incidentally by a process that can be entirely explained by the operation of the nonteleological laws of physics on the material of which we and our environments are all composed. There might still be thought to be a religious threat in the existence of the laws of physics themselves, and indeed the existence of anything at all— but it seems to be less alarming to most atheists.

This is a somewhat ridiculous situation.

This fear of religion is very likely the cause of such unreasonable responses. Scott Alexander notes in this comment that such explanations are mistaken:

I find all of the standard tricks used against Pascal’s Wager intellectually unsatisfying because none of them are at the root of my failure to accept it. Yes, it might be a good point that there could be an “atheist God” who punishes anyone who accepts Pascal’s Wager. But even if a super-intelligent source whom I trusted absolutely informed me that there was definitely either the Catholic God or no god at all, I feel like I would still feel like Pascal’s Wager was a bad deal. So it would be dishonest of me to say that the possibility of an atheist god “solves” Pascal’s Wager.

The same thing is true for a lot of the other solutions proposed. Even if this super-intelligent source assured me that yes, if there is a God He will let people into Heaven even if their faith is only based on Pascal’s Wager, that if there is a God He will not punish you for your cynical attraction to incentives, and so on, and re-emphasized that it was DEFINITELY either the Catholic God or nothing, I still wouldn’t happily become a Catholic.

Whatever the solution, I think it’s probably the same for Pascal’s Wager, Pascal’s Mugging, and the Egyptian mummy problem I mentioned last month. Right now, my best guess for that solution is that there are two different answers to two different questions:

Why do we believe Pascal’s Wager is wrong? Scope insensitivity. Eternity in Hell doesn’t sound that much worse, to our brains, than a hundred years in Hell, and we quite rightly wouldn’t accept Pascal’s Wager to avoid a hundred years in Hell. Pascal’s Mugger killing 3^^^3 people doesn’t sound too much worse than him killing 3,333 people, and we quite rightly wouldn’t give him a dollar to get that low a probability of killing 3,333 people.

Why is Pascal’s Wager wrong? From an expected utility point of view, it’s not. In any particular world, not accepting Pascal’s Wager has a 99.999…% chance of leading to a higher payoff. But averaged over very large numbers of possible worlds, accepting Pascal’s Wager or Pascal’s Mugging will have a higher payoff, because of that infinity going into the averages. It’s too bad that doing the rational thing leads to a lower payoff in most cases, but as everyone who’s bought fire insurance and not had their house catch on fire knows, sometimes that happens.

I realize that this position commits me, so far as I am rational, to becoming a theist. But my position that other people are exactly equal in moral value to myself commits me, so far as I am rational, to giving almost all my salary to starving Africans who would get a higher marginal value from it than I do, and I don’t do that either.

While a far more reasonable response, there is wishful thinking going here as well, with the assumption that the probability that a body of religious beliefs is true as a whole is extremely small. This will not generally speaking be the case, or at any rate it will not be as small as he suggests, once the evidence derived from the claim itself is taken into account, just as it is not extremely improbable that a particular book is mostly historical, even though if one considered the statements contained in the book as a random conjunction, one would suppose it to be very improbable.