The Second Mistake

The second mistake that we mentioned at the end of this post was that given the thesis that God is hidden, arguments against a religion become arguments in favor of it. Pascal suggests such a position when he says, “that darkness in which they are, and with which they upbraid the Church, establishes only one of the things which she affirms, without touching the other, and, very far from destroying, proves her doctrine?”

This is not completely wrong, but there is less truth than error in it. If you explain a difficulty by adding something to your account, as the Mormon does in this example, then technically the difficulty does support the new account. The problem is, as was said there, that the new account overall remains less probable than the original account was without the addition. And the difficulty remains evidence that the original account was simply wrong; it does not “change sides” to support only the new account.

There are several things that need to be considered in the present case. The first is in what sense it is an additional explanation when one says that the explanation for the existence of difficulties is the hiddenness of God. It is somewhat different from the example of the Mormon, and in a way that favors Christianity. The Mormon may have been aware of all widely known facts about his religion, without being aware of the problem regarding the Book of Abraham. But this could not be true of the Christian in the case under discussion. It may be a Christian does not realize that his religion implies that God is hidden; but this is on account of a lack of consideration. The very things that he already knows and believes imply that this must be true in order for his religion to be true. In the Mormon case, on the contrary, nothing about the Mormon religion implies there needs to be some special explanation regarding the Book of Abraham. So when the Mormon adds a special explanation, this is a real addition that must reduce the probability of his general claim. But the Christian in the case under discussion is simply explaining what was implicit in his claim in the first place. In this sense it does not reduce the probability of his claim, but leaves it as it is.

On the other hand, if one has not yet considered the fact that Christianity requires the thesis of hiddenness, it may be that the prior probability for Christianity should be less than what one supposed, when one was judging it without this consideration. In this sense, it may reduce the probability for a particular individual who has not yet fully considered the situation.

Finally, this does not in fact imply that concrete difficulties with Christianity are not evidence against it, because even if the difficulties fit with the claim that Christianity is true but hidden, they may sometimes fit even better with the claim that Christianity is false. For example, suppose there were no historical evidence for the Virgin Birth (this is a counterfactual, since in reality there is historical evidence for it, even if weak relative to the strength of the claim, namely the assertions of the Gospels); such an absence of evidence would fit with the idea that the doctrine is true but hidden, but it would fit even better with the idea that the doctrine is false. Consequently, the evidence would make “the doctrine is true but hidden” more probable relative to “the doctrine is true and not hidden,” but overall the evidence would be likely to make “the doctrine is false” more probable than it was initially before checking the evidence.

 

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The First Mistake

At the end of the last post, I mentioned two opposed errors. The first was to say that the Christian thesis that God is hidden is a mere excuse, one given because someone realizes that his position is basically unsupported. This is not true, because as I indicated even in the last post, the thesis is a basic principle of Christian theology, and always has been, much as Pope Benedict XVI pointed out that the principles of development, and of interpretation relative to Christ, have always been at work within the Church.

More generally, the idea that God is hidden is a basic principle of any and every religion or theology. In a previous discussion I showed how motivations other than truth affect our beliefs more in matters more remote from the senses, and I included religious beliefs in this area. And this is in fact how the world is. But it is easy enough to imagine a world where religion is not remote from the senses, and where substantial disagreement about religion would not exist. The Garden of Eden as described would be one such world, but it is easy to imagine this in other ways as well. The point is that such a world is evidently not the actual world, and real religions do not posit such a world.

Blaise Pascal discusses this situation:

194. … Let them at least learn what is the religion they attack, before attacking it. If this religion boasted of having a clear view of God, and of possessing it open and unveiled, it would be attacking it to say that we see nothing in the world which shows it with this clearness. But since, on the contrary, it says that men are in darkness and estranged from God, that He has hidden Himself from their knowledge, that this is in fact the name which He gives Himself in the Scriptures, Deus absconditus; and finally, if it endeavours equally to establish these two things: that God has set up in the Church visible signs to make Himself known to those who should seek Him sincerely, and that He has nevertheless so disguised them that He will only be perceived by those who seek Him with all their heart; what advantage can they obtain, when, in the negligence with which they make profession of being in search of the truth, they cry out that nothing reveals it to them; and since that darkness in which they are, and with which they upbraid the Church, establishes only one of the things which she affirms, without touching the other, and, very far from destroying, proves her doctrine?

In order to attack it, they should have protested that they had made every effort to seek Him everywhere, and even in that which the Church proposes for their instruction, but without satisfaction. If they talked in this manner, they would in truth be attacking one of her pretensions. But I hope here to show that no reasonable person can speak thus, and I venture even to say that no one has ever done so. We know well enough how those who are of this mind behave. They believe they have made great efforts for their instruction when they have spent a few hours in reading some book of Scripture and have questioned some priests on the truths of the faith. After that, they boast of having made vain search in books and among men. But, verily, I will tell them what I have often said, that this negligence is insufferable. We are not here concerned with the trifling interests of some stranger, that we should treat it in this fashion; the matter concerns ourselves and our all.

The immortality of the soul is a matter which is of so great consequence to us and which touches us so profoundly that we must have lost all feeling to be indifferent as to knowing what it is. All our actions and thoughts must take such different courses, according as there are or are not eternal joys to hope for, that it is impossible to take one step with sense and judgment unless we regulate our course by our view of this point which ought to be our ultimate end.

Thus our first interest and our first duty is to enlighten ourselves on this subject, whereon depends all our conduct. Therefore among those who do not believe, I make a vast difference between those who strive with all their power to inform themselves and those who live without troubling or thinking about it.

I can have only compassion for those who sincerely bewail their doubt, who regard it as the greatest of misfortunes, and who, sparing no effort to escape it, make of this inquiry their principal and most serious occupation.

But as for those who pass their life without thinking of this ultimate end of life, and who, for this sole reason that they do not find within themselves the lights which convince them of it, neglect to seek them elsewhere, and to examine thoroughly whether this opinion is one of those which people receive with credulous simplicity, or one of those which, although obscure in themselves, have nevertheless a solid and immovable foundation, I look upon them in a manner quite different.

This carelessness in a matter which concerns themselves, their eternity, their all, moves me more to anger than pity; it astonishes and shocks me; it is to me monstrous. I do not say this out of the pious zeal of a spiritual devotion. I expect, on the contrary, that we ought to have this feeling from principles of human interest and self-love; for this we need only see what the least enlightened persons see.

We do not require great education of the mind to understand that here is no real and lasting satisfaction; that our pleasures are only vanity; that our evils are infinite; and, lastly, that death, which threatens us every moment, must infallibly place us within a few years under the dreadful necessity of being for ever either annihilated or unhappy.

There is nothing more real than this, nothing more terrible. Be we as heroic as we like, that is the end which awaits the world. Let us reflect on this and then say whether it is not beyond doubt that there is no good in this life but in the hope of another; that we are happy only in proportion as we draw near it; and that, as there are no more woes for those who have complete assurance of eternity, so there is no more happiness for those who have no insight into it.

Surely then it is a great evil thus to be in doubt, but it is at least an indispensable duty to seek when we are in such doubt; and thus the doubter who does not seek is altogether completely unhappy and completely wrong. And if besides this he is easy and content, professes to be so, and indeed boasts of it; if it is this state itself which is the subject of his joy and vanity, I have no words to describe so silly a creature.

How can people hold these opinions? What joy can we find in the expectation of nothing but hopeless misery? What reason for boasting that we are in impenetrable darkness? And how can it happen that the following argument occurs to a reasonable man?

“I know not who put me into the world, nor what the world is, nor what I myself am. I am in terrible ignorance of everything. I know not what my body is, nor my senses, nor my soul, not even that part of me which thinks what I say, which reflects on all and on itself, and knows itself no more than the rest. I see those frightful spaces of the universe which surround me, and I find myself tied to one corner of this vast expanse, without knowing why I am put in this place rather than in another, nor why the short time which is given me to live is assigned to me at this point rather than at another of the whole eternity which was before me or which shall come after me. I see nothing but infinites on all sides, which surround me as an atom and as a shadow which endures only for an instant and returns no more. All I know is that I must soon die, but what I know least is this very death which I cannot escape.

“As I know not whence I come, so I know not whither I go. I know only that, in leaving this world, I fall for ever either into annihilation or into the hands of an angry God, without knowing to which of these two states I shall be for ever assigned. Such is my state, full of weakness and uncertainty. And from all this I conclude that I ought to spend all the days of my life without caring to inquire into what must happen to me. Perhaps I might find some solution to my doubts, but I will not take the trouble, nor take a step to seek it; and after treating with scorn those who are concerned with this care, I will go without foresight and without fear to try the great event, and let myself be led carelessly to death, uncertain of the eternity of my future state.”

Who would desire to have for a friend a man who talks in this fashion? Who would choose him out from others to tell him of his affairs? Who would have recourse to him in affliction? And indeed to what use in life could one put him?

In truth, it is the glory of religion to have for enemies men so unreasonable; and their opposition to it is so little dangerous that it serves, on the contrary, to establish its truths. For the Christian faith goes mainly to establish these two facts: the corruption of nature, and redemption by Jesus Christ. Now I contend that, if these men do not serve to prove the truth of the redemption by the holiness of their behaviour, they at least serve admirably to show the corruption of nature by sentiments so unnatural.

Nothing is so important to man as his own state, nothing is so formidable to him as eternity; and thus it is not natural that there should be men indifferent to the loss of their existence, and to the perils of everlasting suffering. They are quite different with regard to all other things. They are afraid of mere trifles; they foresee them; they feel them. And this same man who spends so many days and nights in rage and despair for the loss of office, or for some imaginary insult to his honour, is the very one who knows without anxiety and without emotion that he will lose all by death. It is a monstrous thing to see in the same heart and at the same time this sensibility to trifles and this strange insensibility to the greatest objects. It is an incomprehensible enchantment, and a supernatural slumber, which indicates as its cause an all-powerful force.

There must be a strange confusion in the nature of man, that he should boast of being in that state in which it seems incredible that a single individual should be. However, experience has shown me so great a number of such persons that the fact would be surprising, if we did not know that the greater part of those who trouble themselves about the matter are disingenuous and not, in fact, what they say. They are people who have heard it said that it is the fashion to be thus daring. It is what they call “shaking off the yoke,” and they try to imitate this. But it would not be difficult to make them understand how greatly they deceive themselves in thus seeking esteem. This is not the way to gain it, even I say among those men of the world who take a healthy view of things and who know that the only way to succeed in this life is to make ourselves appear honourable, faithful, judicious, and capable of useful service to a friend; because naturally men love only what may be useful to them. Now, what do we gain by hearing it said of a man that he has now thrown off the yoke, that he does not believe there is a God who watches our actions, that he considers himself the sole master of his conduct, and that he thinks he is accountable for it only to himself.? Does he think that he has thus brought us to have henceforth complete confidence in him and to look to him for consolation, advice, and help in every need of life? Do they profess to have delighted us by telling us that they hold our soul to be only a little wind and smoke, especially by telling us this in a haughty and self-satisfied tone of voice? Is this a thing to say gaily? Is it not, on the contrary, a thing to say sadly, as the saddest thing in the world?

If they thought of it seriously, they would see that this is so bad a mistake, so contrary to good sense, so opposed to decency, and so removed in every respect from that good breeding which they seek, that they would be more likely to correct than to pervert those who had an inclination to follow them. And, indeed, make them give an account of their opinions, and of the reasons which they have for doubting religion, and they will say to you things so feeble and so petty, that they persuade you of the contrary. The following is what a person one day said to such a one very appositely: “If you continue to talk in this manner, you will really make me religious.” And he was right, for who would not have a horror of holding opinions in which he would have such contemptible persons as companions!

Thus those who only feign these opinions would be very unhappy, if they restrained their natural feelings in order to make themselves the most conceited of men. If, at the bottom of their heart, they are troubled at not having more light, let them not disguise the fact; this avowal will not be shameful. The only shame is to have none. Nothing reveals more an extreme weakness of mind than not to know the misery of a godless man. Nothing is more indicative of a bad disposition of heart than not to desire the truth of eternal promises. Nothing is more dastardly than to act with bravado before God. Let them then leave these impieties to those who are sufficiently ill-bred to be really capable of them. Let them at least be honest men, if they cannot be Christians. Finally, let them recognise that there are two kinds of people one can call reasonable; those who serve God with all their heart because they know Him, and those who seek Him with all their heart because they do not know Him.

But as for those who live without knowing Him and without seeking Him, they judge themselves so little worthy of their own care, that they are not worthy of the care of others; and it needs all the charity of the religion which they despise, not to despise them even to the point of leaving them to their folly. But because this religion obliges us always to regard them, so long as they are in this life, as capable of the grace which can enlighten them, and to believe that they may, in a little time, be more replenished with faith than we are, and that, on the other hand, we may fall into the blindness wherein they are, we must do for them what we would they should do for us if we were in their place, and call upon them to have pity upon themselves, and to take at least some steps in the endeavour to find light. Let them give to reading this some of the hours which they otherwise employ so uselessly; whatever aversion they may bring to the task, they will perhaps gain something, and at least will not lose much. But as for those who bring to the task perfect sincerity and a real desire to meet with truth, those I hope will be satisfied and convinced of the proofs of a religion so divine, which I have here collected, and in which I have followed somewhat after this order…

195. Before entering into the proofs of the Christian religion, I find it necessary to point out the sinfulness of those men who live in indifference to the search for truth in a matter which is so important to them, and which touches them so nearly.

Of all their errors, this doubtless is the one which most convicts them of foolishness and blindness, and in which it is easiest to confound them by the first glimmerings of common sense and by natural feelings.

For it is not to be doubted that the duration of this life is but a moment; that the state of death is eternal, whatever may be its nature; and that thus all our actions and thoughts must take such different directions, according to the state of that eternity, that it is impossible to take one step with sense and judgement, unless we regulate our course by the truth of that point which ought to be our ultimate end.

There is nothing clearer than this; and thus, according to the principles of reason, the conduct of men is wholly unreasonable, if they do not take another course.

On this point, therefore, we condemn those who live without thought of the ultimate end of life, who let themselves be guided by their own inclinations and their own pleasures without reflection and without concern, and, as if they could annihilate eternity by turning away their thought from it, think only of making themselves happy for the moment.

Yet this eternity exists, and death, which must open into it and threatens them every hour, must in a little time infallibly put them under the dreadful necessity of being either annihilated or unhappy for ever, without knowing which of these eternities is for ever prepared for them.

This is a doubt of terrible consequence. They are in peril of eternal woe and thereupon, as if the matter were not worth the trouble, they neglect to inquire whether this is one of those opinions which people receive with too credulous a facility, or one of those which, obscure in themselves, have a very firm, though hidden, foundation. Thus they know not whether there be truth or falsity in the matter, nor whether there be strength or weakness in the proofs. They have them before their eyes; they refuse to look at them; and in that ignorance they choose all that is necessary to fall into this misfortune if it exists, to await death to make trial of it, yet to be very content in this state, to make profession of it, and indeed to boast of it. Can we think seriously of the importance of this subject without being horrified at conduct so extravagant?

This resting in ignorance is a monstrous thing, and they who pass their life in it must be made to feel its extravagance and stupidity, by having it shown to them, so that they may be confounded by the sight of their folly. For this is how men reason, when they choose to live in such ignorance of what they are and without seeking enlightenment. “I know not,” they say…

Pascal is surely right about the importance of religious truth. He is also right to say that the idea that this truth is somewhat hidden from men is not foreign to religion, but an essential part of every real religion. The argument that “if religion is true, it should be obvious to everyone,” is evidently invalid, because religions not only do not claim this, but explicitly deny it. If a religion were obviously true to everyone, it would be a very different religion from any that exists, and a very different world.

Rather than attacking such a non-existent religion, he says,

In order to attack it, they should have protested that they had made every effort to seek Him everywhere, and even in that which the Church proposes for their instruction, but without satisfaction. If they talked in this manner, they would in truth be attacking one of her pretensions. But I hope here to show that no reasonable person can speak thus, and I venture even to say that no one has ever done so.

But here he is almost certainly going too far. It may be that “they would in truth be attacking one of her pretensions,” but only to the degree that they believe that ultimately it is more reasonable to think that religious beliefs are untrue. They would not be attacking the Church’s claims, or at least any claim truly important to the Church, simply by saying that some individual may do his best to seek the truth, and may come to the conclusion that religious truth is not present in the Church.

I touched on this earlier when discussing the suggestion of Leo XIII that it is easy to see that Catholicism is true. If this is taken to apply to the real world in any concrete way, he is mistaken, and this in fact would be the claim that Pascal says is obviously wrong and obviously not the Church’s claim. On a very similar topic, Newman says:

Starting then with the being of a God, (which, as I have said, is as certain to me as the certainty of my own existence, though when I try to put the grounds of that certainty into logical shape I find a difficulty in doing so in mood and figure to my satisfaction,) I look out of myself into the world of men, and there I see a sight which fills me with unspeakable distress. The world seems simply to give the lie to that great truth, of which my whole being is so full; and the effect upon me is, in consequence, as a matter of necessity, as confusing as if it denied that I am in existence myself. If I looked into a mirror, and did not see my face, I should have the sort of feeling which actually comes upon me, when I look into this living busy world, and see no reflexion of its Creator. This is, to me, one of those great difficulties of this absolute primary truth, to which I referred just now. Were it not for this voice, speaking so clearly in my conscience and my heart, I should be an atheist, or a pantheist, or a polytheist when I looked into the world. I am speaking for myself only; and I am far from denying the real force of the arguments in proof of a God, drawn from the general facts of human society and the course of history, but these do not warm me or enlighten me; they do not take away the winter of my desolation, or make the buds unfold and the leaves grow within me, and my moral being rejoice. The sight of the world is nothing else than the prophet’s scroll, full of “lamentations, and mourning, and woe.”

To consider the world in its length and breadth, its various history, the many races of man, their starts, their fortunes, their mutual alienation, their conflicts; and then their ways, habits, governments, forms of worship; their enterprises, their aimless courses, their random achievements and acquirements, the impotent conclusion of long-standing facts, the tokens so faint and broken of a superintending design, the blind evolution of what turn out to be great powers or truths, the progress of things, as if from unreasoning elements, not towards final causes, the greatness and littleness of man, his far-reaching aims, his short duration, the curtain hung over his futurity, the disappointments of life, the defeat of good, the success of evil, physical pain, mental anguish, the prevalence and intensity of sin, the pervading idolatries, the corruptions, the dreary hopeless irreligion, that condition of the whole race, so fearfully yet exactly described in the Apostle’s words, “having no hope and without God in the world,”—all this is a vision to dizzy and appall; and inflicts upon the mind the sense of a profound mystery, which is absolutely beyond human solution.

What shall be said to this heart-piercing, reason-bewildering fact? I can only answer, that either there is no Creator, or this living society of men is in a true sense discarded from His presence. Did I see a boy of good make and mind, with the tokens on him of a refined nature, cast upon the world without provision, unable to say whence he came, his birthplace or his family connexions, I should conclude that there was some mystery connected with his history, and that he was one, of whom, from one cause or other, his parents were ashamed. Thus only should I be able to account for the contrast between the promise and the condition of his being. And so I argue about the world;—if there be a God, since there is a God, the human race is implicated in some terrible aboriginal calamity. It is out of joint with the purposes of its Creator. This is a fact, a fact as true as the fact of its existence; and thus the doctrine of what is theologically called original sin becomes to me almost as certain as that the world exists, and as the existence of God.

And now, supposing it were the blessed and loving will of the Creator to interfere in this anarchical condition of things, what are we to suppose would be the methods which might be necessarily or naturally involved in His purpose of mercy? Since the world is in so abnormal a state, surely it would be no surprise to me, if the interposition were of necessity equally extraordinary—or what is called miraculous. But that subject does not directly come into the scope of my present remarks. Miracles as evidence, involve a process of reason, or an argument; and of course I am thinking of some mode of interference which does not immediately run into argument. I am rather asking what must be the face-to-face antagonist, by which to withstand and baffle the fierce energy of passion and the all-corroding, all-dissolving scepticism of the intellect in religious inquiries? I have no intention at all of denying, that truth is the real object of our reason, and that, if it does not attain to truth, either the premiss or the process is in fault; but I am not speaking here of right reason, but of reason as it acts in fact and concretely in fallen man. I know that even the unaided reason, when correctly exercised, leads to a belief in God, in the immortality of the soul, and in a future retribution; but I am considering the faculty of reason actually and historically; and in this point of view, I do not think I am wrong in saying that its tendency is towards a simple unbelief in matters of religion. No truth, however sacred, can stand against it, in the long run; and hence it is that in the pagan world, when our Lord came, the last traces of the religious knowledge of former times were all but disappearing from those portions of the world in which the intellect had been active and had had a career.

Newman takes the existing situation to be a strong argument for the doctrine of original sin. This is not as strong an argument as it seems to him; the existing situation is a likely result of the order of the world. In any case, his point is that one way or another, in the real world, it is not easy to come to the conclusion that a religion is true. In fact, he says that the natural tendency is to come to the opposite conclusion.

It is possible and reasonable to say in a sense that human beings in general are dishonest and unreasonable, and that this is the main explanation for why they disagree substantially in such important matters.

But it is quite unreasonable to say, “Human beings are divided into two kinds: the honest and reasonable ones, and the dishonest and unreasonable ones. The honest and reasonable ones are those who agree with me, and the dishonest and unreasonable ones are those who disagree with me.” And this is basically what Pascal asserts when he claims that no one can say that he has made every effort to discover the truth about religion, and has concluded that it is not present in the Church. He says even more: “I hope here to show that no reasonable person can speak thus, and I venture even to say that no one has ever done so.” Here he says that “no one has ever done so,” that is, no one has even claimed to make such an investigation. He is mistaken in both respects: in whatever sense there exist reasonable people, there are reasonable non-Catholics. And surely some of them have investigated Catholicism, come to the conclusion that it was not true, and said that they have done so.

Gwern Branwen explains the history of his religious opinions:

For I count being refuted a greater good, insofar as it is a greater good to be rid of the greatest evil from oneself than to rid someone else of it. I don’t suppose that any evil for a man is as great as false belief about the things we’re discussing right now…

I think religion was the first subject in my life that I took seriously. As best as I can recall at this point, I have no “deconversion story” or tale to tell, since I don’t remember ever seriously believing – the stories in the Bible or at my Catholic church were interesting, but they were obviously fiction to some degree. I wasn’t going to reject religion out of hand because some of the stories were made-up (any more than I believed George Washington didn’t exist because the story of him chopping down an apple tree was made-up), but the big claims didn’t seem to be panning out either:

  1. My prayers received no answers of any kind, not even a voice in my head
  2. I didn’t see any miracles or intercessions like I expected from a omnipotent loving god

There is a basic flaw in Gwern’s thinking here, and it is basically a naive concept of God, much like that of Richard Dawkins. The result is that he is falling into the error that Pascal condemns. The Church does not expect such things, at least on a regular basis, and if you think that it follows from the concept of an omnipotent loving God, then your concept of that being is not a Christian concept. In this sense, his whole mistake is that he fails to understand the idea that God is hidden. Nonetheless, it is wrong to say that the reason for Gwern’s mistake is that he was dishonest and unreasonable, and it is especially wrong to say that it was because he did not care about religious truth:

So I never believed (although it was obvious enough that there was no point in discussing this since it might just lead to me going to church more and sitting on the hard wooden pews), but there was still the troubling matter of Heaven & Hell: those infinities meant I couldn’t simply dismiss religion and continue reading about dinosaurs or Alcatraz. If I got religion wrong, I would have gotten literally the most important possible thing wrong! Nothing else was as important – if you’re wrong about a round earth, at worst you will never be a good geographer or astronomer; if you’re wrong about believing in astrology, at worst you waste time and money; if you’re wrong about evolution and biology, at worst you endanger your life; and so on. But if you’re wrong about religion, wasting your life is about the least of the consequences. And everyone accepts a religion or at least the legitimacy of religious claims, so it would be unspeakably arrogant of a kid to dismiss religion entirely – that sort of evidence is simply not there. (Oddly enough, atheists – who are not immediately shown to be mistaken or fools- are even rarer in books and cartoons than they are in real life.)

Kids actually are kind of skeptical if they have reason to be skeptical, and likewise will believe all sorts of strange things if the source was previously trustworthy. This is as it should be! Kids cannot come prewired with 100% correct beliefs, and must be able to learn all sorts of strange (but true) things from reliable authorities; these strategies are exactly what one would advise. It is not their fault that some of the most reliable authorities in their lives (their parents) are mistaken about one major set of beliefs. They simply have bad epistemic luck.

So I read the Bible, which veered from boring to incoherent to disgusting. (I became a fan of the Wisdom literature, however, and still periodically read the Book of Job, Ecclesiastes, and Proverbs.) That didn’t help much. Well, maybe Christianity was not the right religion? My elementary school library had a rather strange selection of books which included various Eastern texts or anthologies (I remember in particular one anthology on meditation, which was a hodge-podge of religious instruction manuals, essays, and scientific studies on meditation – that took me a long time to read, and it was only in high school and college that I really became comfortable reading psychology papers). I continued reading in this vein for years, in between all my more normal readings. The Koran was interesting and in general much better than the Bible. Shinto texts were worthless mythologizing. Taoism had some very good early texts (the Chuang-tzu in particular) but then bizarrely degenerated into alchemy. Buddhism was strange: I rather liked the general philosophical approach, but there were many populist elements in Mahayana texts that bothered me. Hinduism had a strange beauty, but my reaction was similar to that of the early translators, who condemned it for sloth and lassitude. I also considered the Occult seriously and began reading the Skeptical literature on that and related topics (see the later section).

It is clear from this that he did in fact care about getting the truth about religion, much for the reasons that Pascal says it is important to care about it.

More generally, in the real world there are honest and reasonable people, in the sense in which there are such people at all, belonging to every religion, and some belonging to none. And if we think about it carefully, this is a necessary effect of the thesis of the hidden God. Perhaps, as Pascal says, “God has set up in the Church visible signs to make Himself known to those who should seek Him sincerely, and that He has nevertheless so disguised them that He will only be perceived by those who seek Him with all their heart.” The purpose might be to distinguish between people who care and those who don’t. And this may succeed to some extent, but the net will inevitably catch some of the wrong people and miss some of the right people: some people who do not care, will believe anyway, and some people who do, will end up not believing.

 

Numbering The Good

The book Theory of Games and Economic Behavior, by John Von Neumann and Oskar Morgenstern, contains a formal mathematical theory of value. In the first part of the book they discuss some objections to such a project, as well as explaining why they are hopeful about it:

1.2.2. It is not that there exists any fundamental reason why mathematics should not be used in economics. The arguments often heard that because of the human element, of the psychological factors etc., or because there is allegedly no measurement of important factors, mathematics will find no application, can all be dismissed as utterly mistaken. Almost all these objections have been made, or might have been made, many centuries ago in fields where mathematics is now the chief instrument of analysis. This “might have been” is meant in the following sense: Let us try to imagine ourselves in the period which preceded the mathematical or almost mathematical phase of the development in physics, that is the 16th century, or in chemistry and biology, that is the 18th century. Taking for granted the skeptical attitude of those who object to mathematical economics in principle, the outlook in the physical and biological sciences at these early periods can hardly have been better than that in economics, mutatis mutandis, at present.

As to the lack of measurement of the most important factors, the example of the theory of heat is most instructive; before the development of the mathematical theory the possibilities of quantitative measurements were less favorable there than they are now in economics. The precise measurements of the quantity and quality of heat (energy and temperature) were the outcome and not the antecedents of the mathematical theory. This ought to be contrasted with the fact that the quantitative and exact notions of prices, money and the rate of interest were already developed centuries ago.

A further group of objections against quantitative measurements in economics, centers around the lack of indefinite divisibility of economic quantities. This is supposedly incompatible with the use of the infinitesimal calculus and hence (!) of mathematics. It is hard to see how such objections can be maintained in view of the atomic theories in physics and chemistry, the theory of quanta in electrodynamics, etc., and the notorious and continued success of mathematical analysis within these disciplines.

This project requires the possibility of treating the value of things as a numerically measurable quantity. Calling this value “utility”, they discuss the difficulty of this idea:

3.1.2. Historically, utility was first conceived as quantitatively measurable, i.e. as a number. Valid objections can be and have been made against this view in its original, naive form. It is clear that every measurement, or rather every claim of measurability, must ultimately be based on some immediate sensation, which possibly cannot and certainly need not be analyzed any further. In the case of utility the immediate sensation of preference, of one object or aggregate of objects as against another, provides this basis. But this permits us only to say when for one person one utility is greater than another. It is not in itself a basis for numerical comparison of utilities for one person nor of any comparison between different persons. Since there is no intuitively significant way to add two utilities for the same person, the assumption that utilities are of non-numerical character even seems plausible. The modern method of indifference curve analysis is a mathematical procedure to describe this situation.

They note however that the original situation was no different with the idea of quantitatively measuring heat:

3.2.1. All this is strongly reminiscent of the conditions existent at the beginning of the theory of heat: that too was based on the intuitively clear concept of one body feeling warmer than another, yet there was no immediate way to express significantly by how much, or how many times, or in what sense.

Beginning the derivation of their particular theory, they say:

3.3.2. Let us for the moment accept the picture of an individual whose system of preferences is all-embracing and complete, i.e. who, for any two objects or rather for any two imagined events, possesses a clear intuition of preference.

More precisely we expect him, for any two alternative events which are put before him as possibilities, to be able to tell which of the two he prefers.

It is a very natural extension of this picture to permit such an individual to compare not only events, but even combinations of events with stated probabilities.

By a combination of two events we mean this: Let the two events be denoted by B and C and use, for the sake of simplicity, the probability 50%-50%. Then the “combination” is the prospect of seeing B occur with a probability of 50% and (if B does not occur) C with the (remaining) probability of 50%. We stress that the two alternatives are mutually exclusive, so that no possibility of complementarity and the like exists. Also, that an absolute certainty of the occurrence of either B or C exists.

To restate our position. We expect the individual under consideration to possess a clear intuition whether he prefers the event A to the 50-50 combination of B or C, or conversely. It is clear that if he prefers A to B and also to C, then he will prefer it to the above combination as well; similarly, if he prefers B as well as C to A, then he will prefer the combination too. But if he should prefer A to, say B, but at the same time C to A, then any assertion about his preference of A against the combination contains fundamentally new information. Specifically: If he now prefers A to the 50-50 combination of B and C, this provides a plausible base for the numerical estimate that his preference of A over B is in excess of his preference of C over A.

If this standpoint is accepted, then there is a criterion with which to compare the preference of C over A with the preference of A over B. It is well known that thereby utilities, or rather differences of utilities, become numerically measurable. That the possibility of comparison between A, B, and C only to this extent is already sufficient for a numerical measurement of “distances” was first observed in economics by Pareto. Exactly the same argument has been made, however, by Euclid for the position of points on a line in fact it is the very basis of his classical derivation of numerical distances.

It is important to note that the the things being assigned values are described as events. They should not be considered to be actions or choices, or at any rate, only insofar as actions or choices are themselves events that happen in the world. This is important because a person might very well think, “It would be better if A happened than if B happened. But making A happen is vicious, while making B happen is virtuous, so I will make B happen.” He prefers A as an outcome, but the actions which cause these events do not line up, in their moral value, with the external value of the outcomes. Of course, just as the person says that A happening is a better outcome than B happening, he can say that “choosing to make B happen” is a better outcome than “choosing to make A happen.” So in this sense there is nothing to exclude actions from being included in this system of value. But they can only be included insofar as actions themselves are events that happen in the world.

Von Neumann and Morgenstern continue:

The introduction of numerical measures can be achieved even more directly if use is made of all possible probabilities. Indeed: Consider three events, C, A, B, for which the order of the individual’s preferences is the one stated. Let a be a real number between 0 and 1, such that A is exactly equally desirable with the combined event consisting of a chance of probability 1 – a for B and the remaining chance of probability a for C. Then we suggest the use of a as a numerical estimate for the ratio of the preference of A over B to that of C over B.

So for example, suppose that C is an orange (or as an event, eating an orange). is eating a plum, and is eating an apple. The person prefers the orange to the plum, and the plum to the apple. The person prefers a combination of a 20% chance of an apple and an 80% chance of an orange to a plum, while he prefers a plum to a combination of a 40% chance of an apple and a 60% chance of an orange. Since this indicates that his preference changes sides at some point, we suppose that this happens at a 30% chance of an apple and a 70% chance of an orange. All the combinations giving more than a 70% chance of the orange, he prefers to the plum; and he prefers the plum to all the combinations giving less than a 70% chance of the orange. The authors are suggesting that if we assign numerical values to the plum, the apple, and the orange, we should do this in such a way that the difference between the values of the plum and the apple, divided by the difference between the values of the orange and the apple, should be 0.7.

The basic intuition here is that since the combinations of various probabilities of the orange and apple vary continuously from (100% orange, 0% apple) to (0% orange, 100% apple), the various combinations should go continuously through every possible value between the value of the orange and the value of the apple. Since we are passing through those values by changing a probability, they are suggesting mapping that probability directly onto a value. Thus if the value of the orange is 1 and the value of the apple is 0, we say that the value of the plum is 0.7, because the plum is basically equivalent in value to a combination of a 70% chance of the orange and a 30% chance of the apple.

Working this out formally in the later parts of the paper, they show that given that a person’s preferences satisfy certain fairly reasonable axioms, it will be possible to assign values to each of his preferences, and these values are necessarily uniquely determined up to the point of a linear transformation.

I will not describe the axioms themselves here, although they are described in the book, as well as perhaps more simply elsewhere.

Note that according to this system, if you want to know the value of a combination, e.g. (60% chance of A and 40% chance of B), the value will always be 0.6(value of A)+0.4(value of B). The authors comment on this result:

3.7.1. At this point it may be well to stop and to reconsider the situation. Have we not shown too much? We can derive from the postulates (3:A)-(3:C) the numerical character of utility in the sense of (3:2:a) and (3:1:a), (3:1:b) in 3.5.1.; and (3:1:b) states that the numerical values of utility combine (with probabilities) like mathematical expectations! And yet the concept of mathematical expectation has been often questioned, and its legitimateness is certainly dependent upon some hypothesis concerning the nature of an “expectation.” Have we not then begged the question? Do not our postulates introduce, in some oblique way, the hypotheses which bring in the mathematical expectation?

More specifically: May there not exist in an individual a (positive or negative) utility of the mere act of “taking a chance,” of gambling, which the use of the mathematical expectation obliterates?

The objection is this: according to this system of value, if something has a value v, and something else has the double value 2v, the person should consider getting the thing with value v to be completely equal with a deal where he has an exactly 50% chance of getting the thing with value 2v, and a 50% chance of getting nothing. That seems objectionable because many people would prefer a certainty of getting something, to a situation where there is a good chance of getting nothing, even if there is also a chance of getting something more valuable. So for example, if you were now offered the choice of $100,000 directly, or $200,000 if you flip a coin and get heads, and nothing if you get tails, you would probably not only prefer the $100,000, but prefer it to a very high degree.

Morgenstern and Von Neumann continue:

How did our axioms (3:A)-(3:C) get around this possibility?

As far as we can see, our postulates (3:A)-(3:C) do not attempt to avoid it. Even that one which gets closest to excluding a “utility of gambling” (3:C:b) (cf. its discussion in 3.6.2.), seems to be plausible and legitimate, unless a much more refined system of psychology is used than the one now available for the purposes of economics. The fact that a numerical utility, with a formula amounting to the use of mathematical expectations, can be built upon (3:A)-(3:C), seems to indicate this: We have practically defined numerical utility as being that thing for which the calculus of mathematical expectations is legitimate. Since (3:A)-(3:C) secure that the necessary construction can be carried out, concepts like a “specific utility of gambling” cannot be formulated free of contradiction on this level.

“We have practically defined numerical utility as being that thing for which the calculus of mathematical expectations is legitimate.” In other words, the reason for the strange result is that calling a value “double” very nearly simply means that a 50% chance of that value, and a 50% chance of nothing, is considered equal to the original value which was to be doubled.

Considering the case of the $100,000 and $200,000, perhaps it is not so strange after all, even if we think of value in the terms of Von Neumann and Morgenstern. You are benefited if you receive $100,000. But if you receive $100,000, and then another $100,000, how much benefit do you get from the second gift? Just as much? Not at all. The first gift will almost certainly make a much bigger change in your life than the second gift. So even by ordinary standards, getting $200,000 is not twice as valuable as getting $100,000, but less than twice as valuable.

There might be something such that it would have exactly twice the value of $100,000 for you in the Von Neumann-Morgenstern sense. If you care about money enough, perhaps $300,000, or $1,000,000. If so, then you would consider the deal where you flip a coin for this amount of money just as good (considered in advance) as directly receiving $100,000. If you don’t care enough about money for such a thing to be true, there will be something else that you do consider to have twice the value, or more, in this sense. For example, if you have a brother dying of cancer, you would probably prefer that he have a 50% chance of survival, to receiving the $100,000. This means that in the relevant sense, you consider the survival of your brother to have more than double the value of $100,000.

This system of value does not in fact prevent one from assigning a “specific utility of gambling,” even within the system, as long as the fact that I am gambling or not is considered as a distinct event which is an additional result. If the only value that matters is money, then it is indeed a contradiction to speak of a specific utility of gambling. But if I care both about money and about whether I am gambling or not, there is no contradiction.

Something else is implied by all of this, something which is frequently not noticed. Suppose you have a choice of two events in this way. One of them is something that you would want or would like, as small or big as you like. It could be having a nice day at the beach, or $100, or whatever you please. The other is a deal where you have a virtual certainty of getting nothing, and a very small probability of some extremely large reward. For example, it may be that your brother dying of cancer is also on the road to hell. The second event is to give your brother a chance of one in a googolplex of attaining eternal salvation.

Of course, the second event here is worthless. Nobody is going to do anything or give up anything for the sake of such a deal. What this implies is this: if a numerical value is assigned to something in the Von Neumann-Morgenstern manner, no matter what that thing is, that value must be low enough (in comparison to other values) that it won’t have any significant value after it is divided by a googolplex.

In other words, even eternal salvation does not have an infinite value, but a finite value (measured in this way), and low enough that it can be made worthless by enough division.

If we consider the value to express how much we care about something, then this actually makes intuitive sense, because we do not care infinitely about anything, not even about things which might be themselves infinite.

Pascal, in his wager, assumes a probability of 50% for God and for the truth of religious beliefs, and seems to assume a certainty of salvation, given that you accept those beliefs and that they happen to be true. He also seems to assume a certain loss of salvation, if you do not accept those beliefs and they happen to be true, and that nothing in particular will happen if the beliefs are not true.

These assumptions are not very reasonable, considered as actual probability assignments and actual expectations of what is going to happen. However, some set of assignments will be reasonable, and this will certainly affect the reasonableness of the wager. If the probability of success is too low, the wager will be unreasonable, just as above we noted that it would be unreasonable to accept the deal concerning your brother. On the other hand, if the probability of success is high enough, it may well be reasonable to take the deal.

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.

Pascal’s Wager

Blaise Pascal, in his Pensees, proposes his wager:

Let us now speak according to natural lights.

If there is a God, He is infinitely incomprehensible, since, having neither parts nor limits, He has no affinity to us. We are then incapable of knowing either what He is or if He is. This being so, who will dare to undertake the decision of the question? Not we, who have no affinity to Him.

Who then will blame Christians for not being able to give a reason for their belief, since they profess a religion for which they cannot give a reason? They declare, in expounding it to the world, that it is a foolishness, stultitiam; and then you complain that they do not prove it! If they proved it, they would not keep their word; it is in lacking proofs that they are not lacking in sense. “Yes, but although this excuses those who offer it as such and takes away from them the blame of putting it forward without reason, it does not excuse those who receive it.” Let us then examine this point, and say, “God is, or He is not.” But to which side shall we incline? Reason can decide nothing here. There is an infinite chaos which separated us. A game is being played at the extremity of this infinite distance where heads or tails will turn up. What will you wager? According to reason, you can do neither the one thing nor the other; according to reason, you can defend neither of the propositions.

Do not, then, reprove for error those who have made a choice; for you know nothing about it. “No, but I blame them for having made, not this choice, but a choice; for again both he who chooses heads and he who chooses tails are equally at fault, they are both in the wrong. The true course is not to wager at all.”

Yes; but you must wager. It is not optional. You are embarked. Which will you choose then? Let us see. Since you must choose, let us see which interests you least. You have two things to lose, the true and the good; and two things to stake, your reason and your will, your knowledge and your happiness; and your nature has two things to shun, error and misery. Your reason is no more shocked in choosing one rather than the other, since you must of necessity choose. This is one point settled. But your happiness? Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is. “That is very fine. Yes, I must wager; but I may perhaps wager too much.” Let us see. Since there is an equal risk of gain and of loss, if you had only to gain two lives, instead of one, you might still wager. But if there were three lives to gain, you would have to play (since you are under the necessity of playing), and you would be imprudent, when you are forced to play, not to chance your life to gain three at a game where there is an equal risk of loss and gain. But there is an eternity of life and happiness. And this being so, if there were an infinity of chances, of which one only would be for you, you would still be right in wagering one to win two, and you would act stupidly, being obliged to play, by refusing to stake one life against three at a game in which out of an infinity of chances there is one for you, if there were an infinity of an infinitely happy life to gain. But there is here an infinity of an infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite. It is all divided; where-ever the infinite is and there is not an infinity of chances of loss against that of gain, there is no time to hesitate, you must give all. And thus, when one is forced to play, he must renounce reason to preserve his life, rather than risk it for infinite gain, as likely to happen as the loss of nothingness.

For it is no use to say it is uncertain if we will gain, and it is certain that we risk, and that the infinite distance between the certainly of what is staked and the uncertainty of what will be gained, equals the finite good which is certainly staked against the uncertain infinite. It is not so, as every player stakes a certainty to gain an uncertainty, and yet he stakes a finite certainty to gain a finite uncertainty, without transgressing against reason. There is not an infinite distance between the certainty staked and the uncertainty of the gain; that is untrue. In truth, there is an infinity between the certainty of gain and the certainty of loss. But the uncertainty of the gain is proportioned to the certainty of the stake according to the proportion of the chances of gain and loss. Hence it comes that, if there are as many risks on one side as on the other, the course is to play even; and then the certainty of the stake is equal to the uncertainty of the gain, so far is it from fact that there is an infinite distance between them. And so our proposition is of infinite force, when there is the finite to stake in a game where there are equal risks of gain and of loss, and the infinite to gain. This is demonstrable; and if men are capable of any truths, this is one.

“I confess it, I admit it. But, still, is there no means of seeing the faces of the cards?” Yes, Scripture and the rest, etc. “Yes, but I have my hands tied and my mouth closed; I am forced to wager, and am not free. I am not released, and am so made that I cannot believe. What, then, would you have me do?”

True. But at least learn your inability to believe, since reason brings you to this, and yet you cannot believe. Endeavour, then, to convince yourself, not by increase of proofs of God, but by the abatement of your passions. You would like to attain faith and do not know the way; you would like to cure yourself of unbelief and ask the remedy for it. Learn of those who have been bound like you, and who now stake all their possessions. These are people who know the way which you would follow, and who are cured of an ill of which you would be cured. Follow the way by which they began; by acting as if they believed, taking the holy water, having masses said, etc. Even this will naturally make you believe, and deaden your acuteness. “But this is what I am afraid of.” And why? What have you to lose?

But to show you that this leads you there, it is this which will lessen the passions, which are your stumbling-blocks.

The end of this discourse.–Now, what harm will befall you in taking this side? You will be faithful, humble, grateful, generous, a sincere friend, truthful. Certainly you will not have those poisonous pleasures, glory and luxury; but will you not have others? I will tell you that you will thereby gain in this life, and that, at each step you take on this road, you will see so great certainty of gain, so much nothingness in what you risk, that you will at last recognise that you have wagered for something certain and infinite, for which you have given nothing.

Pascal is not arguing that here God exists, or that Christian doctrines are true. He is making a moral argument that it is better to believe these things, whether they are true or not. But in this process he states or suggests a number of things which are not in fact the case.

First, he suggests that the probability that God exists is 50%. It is unlikely that this is a reasonable subjective probability for someone to assign, however he understands the idea of God. If God is understood as the first cause, a reasonable probability could be much higher than this. If God is understood in a significantly more concrete sense, a reasonable probability might be lower than this. But it would be unlikely for the reasonable probability to be exactly 50%, however God is understood.

He also implies that this probability of 50% is also the probability that the body of Christian and Catholic doctrine taken as a whole is true. This is basically inconsistent with the previous point, because if the existence of God has a certain probability, the probability that “God exists and these other statements are true as well,” will necessarily be lower than the probability of God.

He is also implying an extremely strong version of the doctrine of extra Ecclesiam nulla salussince he presumes that the infinite gain will necessarily be lost if you do not believe. The most reasonable reading of Catholic teaching is not consistent with this interpretation, which is a flaw in his argument, given that he is arguing specifically for people to become Catholics.

Despite these errors, however, there is a moral argument here which should be taken seriously, something that is rarely done.