Scott Alexander

Other Wagers

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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

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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.