I wanted to wish a Happy Easter and a Happy Passover to all.

There’s an old joke, that goes something like this. A liberal is arguing with a conservative about the death penalty. Finally, exasperated, the conservative says to the liberal, “of course I’m in favor of the death penalty–without the death penalty, there’d be no Easter and no Easter Bunny!”

While this is an awful joke, it does remain true that in the two major capital punishment trials that we know about in history, Socrates and Jesus, as best we know, both were wrongfully convicted and sentenced to death. I won’t even get to the OJ trial, although as we all know, the glove didn’t fit and they had to acquit.

Obviously Socrates and Jesus could have used Johnny Cochran as their lawyer.

Socrates on dying, was reputed to have said something like, I die, you live, god knows who is going to the better place. Those of us who are religious of course believe that death brings us closer to a better place indeed, but Socrates provides a flash of insight that this short life is not the only one, that there is a spiritual and inner life that transcends death. Religion ministers to the soul, or at least to our conception of the soul, and consequently it is a vital part of our lives.

The Passover story about Moses leading the chosen people out of bondage and out of Egypt is a great story, as well as being an integral part of the old testament. “Exodus” is actually ancient greek for “Exothos” or “Exit” or “Leaving”. It’s the title of the book from the Ancient Greek Septuagint. The entire point of Exodus is the story of the Chosen People Leaving, “Exothos”, from Egypt and their bondage. God frees them from slavery and bondage through Moses and a series of miracles, each one greater than the last, which are celebrated each and every Passover.

It is such an important story because it gives hope to every oppressed peoples that God will redeem every one in bondage, free them and lead them to their own Promised Land. When Martin Luther King spoke of reaching the Promised Land, it was the Passover Story he was referring to. He didn’t need to explain that to his listeners, many of whom were careful Bible readers. The African-Americans of this country understood about bondage, redemption, and being led out of bondage and to the Promised Land.

On this Passover, we should think about these matters in considering President Obama, a man who has the potential to unite many different elements of society, and perhaps finally lead a people to the Promised Land. All oppressed peoples the world over hearken to the story of Exodus.

I’ve always had a strong faith in God and I don’t doubt God’s existence. Recently there’s been a spate of books and articles by respected scholars advocating atheism and the non-existence of God. I find this to be an awful waste of scholarly time, and especially of taxpayer and endowment money. Isn’t there something important these guys should be doing on our nickel?

Richard Dawkins, who once wrote a book called “The Selfish Gene,” is one of these. He used to teach at Harvard, now teaches in England, and appears to enjoy bashing God and religion in his books. Dawkins used to be a capable biologist. In his old age, he’s turned into a menacing crank who hates old ladies who go to church and pray to the saints and God for the memories of their dead husbands.

How mean can you possible get?

You might call him “The Selfish Dean” because he really seems only to care about himself. Is this what tenure breeds? Idiotic books about atheism? Pushed on us by editors and publishing houses?

Belief in God is a personal matter, but it also means a commitment to others, and to doing things for others, without considering the personal benefit to yourself. Sitting around the table at Easter, at Seder, at any family gathering, we give thanks to our creator and Lord for family, for health, for happiness. I can’t imagine a life without God or without prayer, a life without church or without friends from church or the church community.

I’ve looked at Dawkins’ books on atheism. They are poorly written, poorly argued, and basically are rants.

It’s not a careful argument.

A careful argument, for example, would be Aquinas’ Summa Contra Gentiles, or Martin Luther’s 95 Theses against the Catholic Church, or John Calvin’s immense work of theology criticizing the Roman Catholic Church and setting forth the tenets of Calvinism.

Those are careful and thoughtful books, which make their cases carefully, point by point.

Dawkins’ books by contrast are awful and poorly researched and poorly written. It’s embarassing to see a professor publish such awful work. Especially when he was able while younger to write such a good book on biology as “The Selfish Gene.” It’s readily apparent Dawkins’ writing and intellectual skills have sharply declined with age.

But assuming that Dawkins (and any of these other atheists) has/have any rational or reasonable points to make, I’d like to refute them with Pascal’s Wager, for one. I think Dawkins is already refuted by the Transcendental a priori arguments of Kant for God’s existence, but Blaise Pascal made a classic probability argument which is, in fact, irrefutable on mathematical and utility grounds, for God’s existence.

Pascal said you should believe in God, because if you did, even if there was only a 1 in a million chance of his existence, the benefits would be eternal salvation, whereas if you denied Him, the possible harm would be eternal damnation.

Consequently, it’s a lot like the nuclear calculus–the benefits are so great, that even if there’s only a slight chance of God existing, it’s worth going all in on God. If you win, you get eternal salvation forever. (the nukes argument goes like, if there’s a one in a million chance of starting World War III, the harm is so great, you have to avoid it, because it’s nuclear winter and the death of mankind, so the policy can’t be adopted).

If you lose the wager, you burn in hell forever. I kind of envision Dawkins burning in a really hot part of hell, by the way. The part where they keep Bernie Madoff, child molesters, child molesting catholic priests and every single convicted defendant whose story was the real basis for the plot line of a LAW AND ORDER:SVU episode. Those stories are really pretty awful. This is a digression, but it’s hard to believe that’s Jayne Mansfield’s daughter in that show, by the way. Mariska Hargitay, emmy winning actress, now approximately in her mid-40s, and still very beautiful, is the daughter of Mickey Hargitay (a former Mr. Universe) and Jayne Mansfield, the 1950s starlet/sex bomb. I think you’d have to say that Mariska Hargitay has really had a solid acting career.

As for all of those who doubt God’s existence or lack faith in God, I give you an extended discusion of Pascal’s Wager from the Stanford Encylopaedia of Philosophy.

Pascal’s Wager
By Alan Hajek, Stanford Encyclopedia of Philosophy

“Pascal’s Wager” is the name given to an argument due to Blaise Pascal for believing, or for at least taking steps to believe, in God. The name is somewhat misleading, for in a single paragraph of his Pensées, Pascal apparently presents at least three such arguments, each of which might be called a ‘wager’ — it is only the final of these that is traditionally referred to as “Pascal’s Wager”. We find in it the extraordinary confluence of several strands in intellectual thought: the justification of theism; probability theory and decision theory, used here for almost the first time in history; pragmatism; voluntarism (the thesis that belief is a matter of the will); and the use of the concept of infinity.

We will begin with some brief stage-setting: some historical background, some of the basics of decision theory, and some of the exegetical problems that the Pensées pose. Then we will follow the text to extract three main arguments. The bulk of the literature addresses the third of these arguments, as will the bulk of our discussion here. Some of the more technical and scholarly aspects of our discussion will be relegated to lengthy footnotes, to which there are links for the interested reader. All quotations are from §233 of Pensées (1910, Trotter translation), the ‘thought’ whose heading is “Infinite—nothing”.
• 1. Background
• 2. The Argument from Superdominance
• 3. The Argument from Expectation
• 4. The Argument from Generalized Expectations: “Pascal’s Wager”
• 5. Objections to Pascal’s Wager
• Bibliography
• Other Internet Resources
• Related Entries

1. Background
It is important to contrast Pascal’s argument with various putative ‘proofs’ of the existence of God that had come before it. Anselm’s ontological argument, Aquinas’ ‘five ways’, Descartes’ ontological and cosmological arguments, and so on, purport to give a priori demonstrations that God exists. Pascal is apparently unimpressed by such attempted justifications of theism: “Endeavour … to convince yourself, not by increase of proofs of God…” Indeed, he concedes that “we do not know if He is …”. Pascal’s project, then, is radically different: he seeks to provide prudential reasons for believing in God. To put it crudely, we should wager that God exists because it is the best bet. Ryan 1994 finds precursors to this line of reasoning in the writings of Plato, Arnobius, Lactantius, and others; we might add Ghazali to his list — see Palacios 1920. But what is distinctive is Pascal’s explicitly decision theoretic formulation of the reasoning. In fact, Hacking 1975 describes the Wager as “the first well-understood contribution to decision theory” (viii). Thus, we should pause briefly to review some of the basics of that theory.

In any decision problem, the way the world is, and what an agent does, together determine an outcome for the agent. We may assign utilities to such outcomes, numbers that represent the degree to which the agent values them. It is typical to present these numbers in a decision matrix, with the columns corresponding to the various relevant states of the world, and the rows corresponding to the various possible actions that the agent can perform.

In decisions under uncertainty, nothing more is given — in particular, the agent does not assign subjective probabilities to the states of the world. Still, sometimes rationality dictates a unique decision nonetheless. Consider, for example, a case that will be particularly relevant here. Suppose that you have two possible actions, A1 and A2, and the worst outcome associated with A1 is at least as good as the best outcome associated with A2; suppose also that in at least one state of the world, A1’s outcome is strictly better than A2’s. Let us say in that case that A1 superdominates A2. Then rationality surely requires you to perform A1.

In decisions under risk, the agent assigns subjective probabilities to the various states of the world. Assume that the states of the world are independent of what the agent does. A figure of merit called the expected utility, or the expectation of a given action can be calculated by a simple formula: for each state, multiply the utility that the action produces in that state by the state’s probability; then, add these numbers. According to decision theory, rationality requires you to perform the action of maximum expected utility (if there is one).

Example. Suppose that the utility of money is linear in number of dollars: you value money at exactly its face value. Suppose that you have the option of paying a dollar to play a game in which there is an equal chance of returning nothing, and returning three dollars. The expectation of the game itself is

0*(1/2) + 3*(1/2) = 1.5,

so the expectation of paying a dollar for certain, then playing, is

-1 + 1.5 = 0.5.

This exceeds the expectation of not playing (namely 0), so you should play. On the other hand, if the game gave an equal chance of returning nothing, and returning two dollars, then its expectation would be:

0*(1/2) + 2*(1/2) = 1.

Then consistent with decision theory, you could either pay the dollar to play, or refuse to

play, for either way your overall expectation would be 0.

Considerations such as these will play a crucial role in Pascal’s arguments. It should be admitted that there are certain exegetical problems in presenting these arguments. Pascal never finished the Pensées, but rather left them in the form of notes of various sizes pinned together. Hacking 1972 describes the “Infinite—nothing” as consisting of “two pieces of paper covered on both sides by handwriting going in all directions, full of erasures, corrections, insertions, and afterthoughts” (24).[1] This may explain why certain passages are notoriously difficult to interpret, as we will see. Furthermore, our formulation of the arguments in the parlance of modern Bayesian decision theory might appear somewhat anachronistic. For example, Pascal did not distinguish between what we would now call objective and subjective probability, although it is clear that it is the latter that is relevant to his arguments. To some extent, “Pascal’s Wager” now has a life of its own, and our presentation of it here is perfectly standard. Still, we will closely follow Pascal’s text, supporting our reading of his arguments as much as possible.

There is the further problem of dividing the Infinite-nothing into separate arguments. We will locate three arguments that each conclude that rationality requires you to wager for God, although they interleave in the text.[2] Finally, there is some disagreement over just what “wagering for God” involves — is it believing in God, or merely trying to? We will conclude with a discussion of what Pascal meant by this.

2. The Argument from Superdominance
Pascal maintains that we are incapable of knowing whether God exists or not, yet we must “wager” one way or the other. Reason cannot settle which way we should incline, but a consideration of the relevant outcomes supposedly can. Here is the first key passage:

“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… 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, you 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… But your happiness? Let us weigh the gain and the loss in wagering that God is… If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.

There are exegetical problems already here, partly because Pascal appears to contradict himself. He speaks of “the true” as something that you can “lose”, and “error” as something “to shun”. Yet he goes on to claim that if you lose the wager that God is, then “you lose nothing”. Surely in that case you “lose the true”, which is just to say that you have made an error. Pascal believes, of course, that the existence of God is “the true” — but that is not something that he can appeal to in this argument. Moreover, it is not because “you must of necessity choose” that “your reason is no more shocked in choosing one rather than the other”. Rather, by Pascal’s own account, it is because “[r]eason can decide nothing here”. (If it could, then it might well be shocked — namely, if you chose in a way contrary to it.)

Following McClennen 1994, Pascal’s argument seems to be best captured as presenting the following decision matrix:
God exists God does not exist
Wager for God Gain all Status quo
Wager against God Misery Status quo

Wagering for God superdominates wagering against God: the worst outcome associated with wagering for God (status quo) is at least as good as the best outcome associated with wagering against God (status quo); and if God exists, the result of wagering for God is strictly better that the result of wagering against God.

(The fact that the result is much better does not matter yet.) Pascal draws the conclusion at this point that rationality requires you to wager for God.

Without any assumption about your probability assignment to God’s existence, the argument is invalid. Rationality does not require you to wager for God if you assign probability 0 to God existing. And Pascal does not explicitly rule this possibility out until a later passage, when he assumes that you assign positive probability to God’s existence; yet this argument is presented as if it is self-contained. His claim that “[r]eason can decide nothing here” may suggest that Pascal regards this as a decision under uncertainty, which is to assume that you do not assign probability at all to God’s existence. If that is a further premise, then the argument is valid; but that premise contradicts his subsequent assumption that you assign positive probability. See McClennen for a reading of this argument as a decision under uncertainty.

Pascal appears to be aware of a further objection to this argument, for he immediately imagines an opponent replying:

“That is very fine. Yes, I must wager; but I may perhaps wager too much.”

The thought seems to be that if I wager for God, and God does not exist, then I really do lose something. In fact, Pascal himself speaks of staking something when one wagers for God, which presumably one loses if God does not exist. (We have already mentioned ‘the true’ as one such thing; Pascal also seems to regard one’s worldly life as another.) In other words, the matrix is mistaken in presenting the two outcomes under ‘God does not exist’ as if they were the same, and we do not have a case of superdominance after all.
Pascal addresses this at once in his second argument, which we will discuss only briefly, as it can be thought of as just a prelude to the main argument.

3. The Argument From Expectation
He continues:

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.

His hypothetically speaking of “two lives” and “three lives” may strike one as odd. It is helpful to bear in mind Pascal’s interest in gambling (which after all provided the initial motivation for his study of probability) and to take the gambling model quite seriously here. Recall our calculation of the expectations of the two dollar and three dollar gambles. Pascal apparently assumes now that utility is linear in number of lives, that wagering for God costs “one life”, and then reasons analogously to the way we did! This is, as it were, a warm-up. Since wagering for God is rationally required even in the hypothetical case in which one of the prizes is three lives, then all the more it is rationally required in the actual case, in which one of the prizes is eternal life (salvation).

So Pascal has now made two striking assumptions:

(1) The probability of God’s existence is 1/2.

(2) Wagering for God brings infinite reward if God exists.

Morris 1994 is sympathetic to (1), while Hacking 1972 finds it “a monstrous premiss”. It apparently derives from the classical interpretation of probability, according to which all possibilities are given equal weight. Of course, unless more is said, the interpretation yields implausible, and even contradictory results. (You have a one-in-a-million chance of winning the lottery; but either you win the lottery or you don’t, so each of these possibilities has probability 1/2?!) Pascal’s best argument for (1) is presumably that “[r]eason can decide nothing here”. (In the lottery ticket case, reason can decide something.) But it is not clear that complete ignorance should be modeled as sharp indifference. In any case, it is clear that there are people in Pascal’s audience who do not assign probability 1/2 to God’s existence. This argument, then, does not speak to them.
However, Pascal realizes that the value of 1/2 actually plays no real role in the argument, thanks to (2). This brings us to the third, and by far the most important, of his arguments.

4. The Argument From Generalized Expectations: “Pascal’s Wager”
We continue the quotation.

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; wherever 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…

Again this passage is difficult to understand completely. Pascal’s talk of winning two, or three, lives is at best misleading. By his own decision theoretic lights, you would not act stupidly “by refusing to stake one life against three at a game in which out of an infinity of chances there is one for you”—in fact, you should not stake more than an infinitesimal amount in that case (an amount that is bigger than 0, but smaller than every positive real number). The point, rather, is that the prospective prize is “an infinity of an infinitely happy life”.

In short, if God exists, then wagering for God results in infinite utility.

What about the utilities for the other possible outcomes? There is some dispute over the utility of “misery”. Hacking interprets this as “damnation”, and Pascal does later speak of “hell” as the outcome in this case. Martin 1983 among others assigns this a value of negative infinity. Sobel 1996, on the other hand, is one author who takes this value to be finite. There is some textual support for this reading: “The justice of God must be vast like His compassion. Now justice to the outcast is less vast … than mercy towards the elect”.

As for the utilities of the outcomes associated with God’s non-existence, Pascal tells us that “what you stake is finite”. This suggests that whatever these values are, they are finite.
Pascal’s guiding insight is that the argument from expectation goes through equally well whatever your probability for God’s existence is, provided that it is non-zero and finite (non-infinitesimal) — “a chance of gain against a finite number of chances of loss”.[3]

With Pascal’s assumptions about utilities and probabilities in place, he is now in a position to calculate the relevant expectations. He explains how the calculations should proceed:
… the uncertainty of the gain is proportioned to the certainty of the stake according to the proportion of the chances of gain and loss… [4]

Let us now gather together all of these points into a single argument. We can think of Pascal’s Wager as having three premises: the first concerns the decision matrix of rewards, the second concerns the probability that you should give to God’s existence, and the third is a maxim about rational decision-making. Specifically:
1. Either God exists or God does not exist, and you can either wager for God or wager against God. The utilities of the relevant possible outcomes are as follows, where f1, f2, and f3 are numbers whose values are not specified beyond the requirement that they be finite:

God exists God does not exist
Wager for God ∞ f1
Wager against God f2 f3

2. Rationality requires the probability that you assign to God existing to be positive, and not infinitesimal.

3. Rationality requires you to perform the act of maximum expected utility (when there is one).

4. Conclusion 1. Rationality requires you to wager for God.

5. Conclusion 2. You should wager for God.

We have a decision under risk, with probabilities assigned to the relevant ways the world could be, and utilities assigned to the relevant outcomes. The conclusion seems straightforwardly to follow from the usual calculations of expected utility (where p is your positive, non-infinitesimal probability for God’s existence):

E(wager for God) = ∞*p + f1*(1 − p) = ∞

That is, your expected utility of belief in God is infinite — as Pascal puts it, “our proposition is of infinite force”. On the other hand, your expected utility of wagering against God is

E(wager against God) = f2*p + f3*(1 − p)

This is finite.[5] By premise 3, rationality requires you to perform the act of maximum expected utility.

Therefore, rationality requires you to wager for God.

We now survey some of the main objections to the argument.

5. Objections to Pascal’s Wager
Premise 1: The Decision Matrix
Here the objections are manifold. Most of them can be stated quickly, but we will give special attention to what has generally been regarded as the most important of them, ‘the many Gods objection’ (see also the link to footnote 7).

1. Different matrices for different people.
The argument assumes that the same decision matrix applies to everybody. However, perhaps the relevant rewards are different for different people. Perhaps, for example, there is a predestined infinite reward for the Chosen, whatever they do, and finite utility for the rest, as Mackie 1982 suggests. Or maybe the prospect of salvation appeals more to some people than to others, as Swinburne 1969 has noted.
Even granting that a single 2 x 2 matrix applies to everybody, one might dispute the values that enter into it. This brings us to the next two objections.

2. The utility of salvation could not be infinite.
One might argue that the very notion of infinite utility is suspect — see for example Jeffrey 1983 and McClennen 1994.[6] Hence, the objection continues, whatever the utility of salvation might be, it must be finite. Strict finitists, who are chary of the notion of infinity in general, will agree — see Dummett 1978 and Wright 1987. Or perhaps the notion of infinite utility makes sense, but an infinite reward could only be finitely appreciated by a human being.

3. There should be more than one infinity in the matrix.
There are also critics of the Wager who, far from objecting to infinite utilities, want to see more of them in the matrix. For example, it might be thought that a forgiving God would bestow infinite utility upon wagerers-for and wagerers-against alike — Rescher 1985 is one author who entertains this possibility. Or it might be thought that, on the contrary, wagering against an existent God results in negative infinite utility. (As we have noted, some authors read Pascal himself as saying as much.) Either way, f2 is not really finite at all, but ∞ or -∞ as the case may be. And perhaps f1 and f3 could be ∞ or -∞. Suppose, for instance, that God does not exist, but that we are reincarnated ad infinitum, and that the total utility we receive is an infinite sum that does not converge.

4. The matrix should have more rows.
Perhaps there is more than one way to wager for God, and the rewards that God bestows vary accordingly. For instance, God might not reward infinitely those who strive to believe in Him only for the very mercenary reasons that Pascal gives, as James 1956 has observed. One could also imagine distinguishing belief based on faith from belief based on evidential reasons, and posit different rewards in each case.

6. The matrix should have more columns: the many Gods objection.
If Pascal is really right that reason can decide nothing here, then it would seem that various other theistic hypotheses are also live options. Pascal presumably had in mind the Catholic conception of God — let us suppose that this is the God who either ‘exists’ or ‘does not exist’. By excluded middle, this is a partition. The objection, then, is that the partition is not sufficiently fine-grained, and the ‘(Catholic) God does not exist’ column really subdivides into various other theistic hypotheses. The objection could equally run that Pascal’s argument ‘proves too much’: by parallel reasoning we can ‘show’ that rationality requires believing in various incompatible theistic hypotheses. As Diderot 1875-77 puts the point: “An Imam could reason just as well this way”.[7]

Since then, the point has been represented and refined in various ways. Mackie 1982 writes, “the church within which alone salvation is to be found is not necessarily the Church of Rome, but perhaps that of the Anabaptists or the Mormons or the Muslim Sunnis or the worshippers of Kali or of Odin” (203). Cargile 1966 shows just how easy it is to multiply theistic hypotheses: for each real number x, consider the God who prefers contemplating x more than any other activity. It seems, then, that such ‘alternative gods’ are a dime a dozen — or aleph one, for that matter.

Premise 2: The Probability Assigned to God’s Existence
There are four sorts of problem for this premise. The first two are straightforward; the second two are more technical, and can be found by following the link to footnote 8.
1. Undefined probability for God’s existence. Premise 1 presupposes that you should have a probability for God’s existence in the first place. However, perhaps you could rationally fail to assign it a probability — your probability that God exists could remain undefined. We cannot enter here into the thorny issues concerning the attribution of probabilities to agents. But there is some support for this response even in Pascal’s own text, again at the pivotal claim that “[r]eason 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…” The thought could be that any probability assignment is inconsistent with a state of “epistemic nullity” (in Morris’ 1986 phrase): to assign a probability at all — even 1/2 — to God’s existence is to feign having evidence that one in fact totally lacks. For unlike a coin that we know to be fair, this metaphorical ‘coin’ is ‘infinitely far’ from us, hence apparently completely unknown to us. Perhaps, then, rationality actually requires us to refrain from assigning a probability to God’s existence (in which case at least the Argument from Superdominance would be valid). Or perhaps rationality does not require it, but at least permits it. Either way, the Wager would not even get off the ground.

2. Zero probability for God’s existence. Strict atheists may insist on the rationality of a probability assignment of 0, as Oppy 1990 among others points out. For example, they may contend that reason alone can settle that God does not exist, perhaps by arguing that the very notion of an omniscient, omnipotent, omnibenevolent being is contradictory. Or a Bayesian might hold that rationality places no constraint on probabilistic judgments beyond coherence (or conformity to the probability calculus). Then as long as the strict atheist assigns probability 1 to God’s non-existence alongside his or her assignment of 0 to God’s existence, no norm of rationality has been violated.
Furthermore, an assignment of p = 0 would clearly block the route to Pascal’s conclusion. For then the expectation calculations become:

E(wager for God) = ∞*0 + f1*(1 − 0) = f1

E(wager against God) = f2*0 + f3*(1 − 0) = f3

And nothing in the argument implies that f1 > f3. (Indeed, this inequality is questionable, as even Pascal seems to allow.) In short, Pascal’s wager has no pull on strict atheists.[8]

Premise 3: Rationality Requires Maximizing Expected Etility
Finally, one could question Pascal’s decision theoretic assumption that rationality requires one to perform the act of maximum expected utility (when there is one). Now perhaps this is an analytic truth, in which case we could grant it to Pascal without further discussion — perhaps it is constitutive of rationality to maximize expectation, as some might say. But this premise has met serious objections. The Allais 1953 and Ellsberg 1961 paradoxes, for example, are said to show that maximizing expectation can lead one to perform intuitively sub-optimal actions. So too the St. Petersburg paradox, in which it is supposedly absurd that one should be prepared to pay any finite amount to play a game with infinite expectation. (That paradox is particularly apposite here.)[9]

Finally, one might distinguish between practical rationality and theoretical rationality. One could then concede that practical rationality requires you to maximize expected utility, while insisting that theoretical rationality might require something else of you — say, proportioning belief to the amount of evidence available. This objection is especially relevant, since Pascal admits that perhaps you “must renounce reason” in order to follow his advice. But when these two sides of rationality pull in opposite directions, as they apparently can here, it is not obvious that practical rationality should take precedence. (For a discussion of pragmatic, as opposed to theoretical, reasons for belief, see Foley 1994.)

Is the Argument Valid?

A number of authors who have been otherwise critical of the Wager have explicitly conceded that the Wager is valid — e.g. Mackie 1982, Rescher 1985, Mougin and Sober 1994, and most emphatically, Hacking 1972. That is, these authors agree with Pascal that wagering for God really is rationally mandated by Pascal’s decision matrix in tandem with positive probability for God’s existence, and the decision theoretic account of rational action.

However, Duff 1986 and Hájek 2001 argue that the argument is in fact invalid. Their point is that there are strategies besides wagering for God that also have infinite expectation — namely, mixed strategies, whereby you do not wager for or against God outright, but rather choose which of these actions to perform on the basis of the outcome of some chance device. Consider the mixed strategy: “Toss a fair coin: heads, you wager for God; tails, you wager against God”. By Pascal’s lights, with probability 1/2 your expectation will be infinite, and with probability 1/2 it will be finite. The expectation of the entire strategy is:

1/2*∞ + 1/2[f2*p + f3*(1 − p)] = ∞

That is, the ‘coin toss’ strategy has the same expectation as outright wagering for God. But the probability 1/2 was incidental to the result. Any mixed strategy that gives positive and finite probability to wagering for God will likewise have infinite expectation: “wager for God iff a fair die lands 6”, “wager for God iff your lottery ticket wins”, “wager for God iff a meteor quantum tunnels its way through the side of your house”, and so on.

The problem is still worse than this, though, for there is a sense in which anything that you do might be regarded as a mixed strategy between wagering for God, and wagering against God, with suitable probability weights given to each. Suppose that you choose to ignore the Wager, and to go and have a hamburger instead. Still, you may well assign positive and finite probability to your winding up wagering for God nonetheless; and this probability multiplied by infinity again gives infinity. So ignoring the Wager and having a hamburger has the same expectation as outright wagering for God. Even worse, suppose that you focus all your energy into avoiding belief in God. Still, you may well assign positive and finite probability to your efforts failing, with the result that you wager for God nonetheless. In that case again, your expectation is infinite again. So even if rationality requires you to perform the act of maximum expected utility when there is one, here there isn’t one. Rather, there is a many-way tie for first place, as it were.[10]

Moral Objections to Wagering for God

Let us grant Pascal’s conclusion for the sake of the argument: rationality requires you to wager for God. It still does not obviously follow that you should wager for God. All that we have granted is that one norm — the norm of rationality — prescribes wagering for God. For all that has been said, some other norm might prescribe wagering against God. And unless we can show that the rationality norm trumps the others, we have not settled what we should actually do.

There are several arguments to the effect that morality requires you to wager against God. Pascal himself appears to be aware of one such argument. He admits that if you do not believe in God, his recommended course of action will “deaden your acuteness.” One way of putting the argument is that wagering for God may require you to corrupt yourself, thus violating a Kantian duty to yourself. Clifford 1986 argues that an individual’s believing something on insufficient evidence harms society by promoting credulity. Penelhum 1971 contends that the putative divine plan is itself immoral, condemning as it does honest non-believers to loss of eternal happiness, when such unbelief is in no way culpable; and that to adopt the relevant belief is to be complicit to this immoral plan. See Quinn 1994 for replies to these arguments. For example, against Penelhum he argues that as long as God treats non-believers justly, there is nothing immoral about him bestowing special favor on believers, more perhaps than they deserve. (Note, however, that Pascal leaves open in the Wager whether the payoff for non-believers is just, even though as far as his argument goes, it may be extremely poor.)

Finally, Voltaire protests that there is something unseemly about the whole Wager. He suggests that Pascal’s calculations, and his appeal to self-interest, are unworthy of the gravity of the subject of theistic belief. This does not so much support wagering against God, as dismissing all talk of ‘wagerings’ altogether.

What Does It Mean to “Wager for God”?

Let us now grant Pascal that, all things considered (rationality and morality included), you should wager for God. What exactly does this involve?

A number of authors read Pascal as arguing that you should believe in God — see e.g. Quinn 1994, and Jordan 1994a. But perhaps one cannot simply believe in God at will; and rationality cannot require the impossible. Pascal is well aware of this objection: “[I] am so made that I cannot believe. What, then, would you have me do?”, says his imaginary interlocutor. However, he contends that one can take steps to cultivate such belief:

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…

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

We find two main pieces of advice to the non-believer here: act like a believer, and suppress those passions that are obstacles to becoming a believer. And these are actions that one can perform at will.
Believing in God is presumably one way to wager for God. This passage suggests that even the non-believer can wager for God, by striving to become a believer. Critics may question the psychology of belief formation that Pascal presupposes, pointing out that one could strive to believe (perhaps by following exactly Pascal’s prescription), yet fail. To this, a follower of Pascal might reply that the act of genuine striving already displays a pureness of heart that God would fully reward; or even that genuine striving in this case is itself a form of believing.

Pascal’s Wager vies with Anselm’s Ontological Argument for being the most famous argument in the philosophy of religion. As we have seen, it is also a great deal more besides.


• Allais, Maurice. 1953. “Le Comportment de l’Homme Rationnel Devant la Risque: Critique des Postulats et Axiomes de l’École Américaine”, Econometrica 21: 503-546.
• Broome, John. 1995. “The Two-Envelope Paradox”, Analysis 55: 1, 6-11.
• Brown, Geoffrey. 1984. “A Defence of Pascal’s Wager”, Religious Studies 20: 465-79.
• Cain, James. 1995. “Infinite Utility”, Australasian Journal of Philosophy, Vol. 73, No. 3, 401-404.
• Cargile, James. 1966. “Pascal’s Wager”, Philosophy, 35: 250-7.
• Castell, Paul and Diderik Batens. 1994. “The Two-Envelope Paradox: the Infinite Case”, Analysis 54: 46-49.
• Chalmers, David. 1997. “The Two-Envelope Paradox: A Complete Analysis?”, manuscript, http://ling.ucsc.edu/~chalmers/papers/envelope.html (and envelope.ps)
• Clifford, William K. 1986. “The Ethics of Belief”, The Ethics of Belief Debate, ed. Gerald D. McCarthy, Scholars Press.
• Conway, John. 1976. On Numbers and Games, Academic Press.
• Cutland, Nigel, ed. 1988. Nonstandard Analysis and its Applications, London Mathematical Society, Student Texts 10.
• Diderot, Denis. 1875-1877. Pensées Philosophiques, LIX, Oeuvres, ed. J. Assézat, Vol. I.
• Duff, Antony. 1986. “Pascal’s Wager and Infinite Utilities”, Analysis 46: 107-9. n
• Dummett, Michael. 1978. “Wang’s Paradox”, in Truth and Other Enigmas, Harvard University Press.
• Ellsberg, D.. 1961. “Risk, Ambiguity and the Savage Axioms”, Quarterly Journal of Economics 25: 643-669.
• Feller, William. 1971. An Introduction to Probability Theory and its Applications, Vol. II, 2nd edition, Wiley.
• Flew, Anthony. 1960. “Is Pascal’s Wager the Only Safe Bet?”, The Rationalist Annual, 76: 21-25.
• Foley, Richard. 1994. “Pragmatic Reasons for Belief”, in Jordan 1994b.
• Hacking, Ian. 1972. “The Logic of Pascal’s Wager”, American Philosophical Quarterly 9/2, 186-92. Reprinted in Jordan 1994b.
• Hacking, Ian. 1975. The Emergence of Probability, Cambridge University Press.
• Hájek, Alan. 1997a. “Review of Gambling on God” (Jordan 1994b), Australasian Journal of Philosophy, Vol. 75, No. 1, March 1997, 119-122.
• Hájek, Alan. 1997b. “The Illogic of Pascal’s Wager”, Proceedings of the 10th Logica International Symposium, Liblice, ed. T. Childers et al, 239-249.
• Hájek, Alan. 2000. “Objecting Vaguely to Pascal’s Wager”, Philosophical Studies, vol. 82.
• Hájek, Alan. 2001. “Waging War on Pascal’s Wager: Infinite Decision Theory and Belief in God”, manuscript.
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• Lewis, David. 1981. “Causal Decision Theory”, Australasian Journal of Philosophy 59, 5-30; reprinted in Philosophical Papers, Volume II, Oxford University Press, 1986.
• Lindstrom, Tom. 1988. “Invitation to Non-Standard Analysis”, in Cutland 1988.
• Mackie, J. L.. 1982. The Miracle of Theism, Oxford.
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• Martin, Michael. 1990. Atheism: a Philosophical Justification, Temple University Press.
• McClennen, Edward. 1994. “Finite Decision Theory”, in Jordan 1994b.
• Morris, T. V. 1986. “Pascalian Wagering”, Canadian Journal of Philosophy 16, 437-54.
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Copyright © 1998, 2001
Alan Hájek

Stanford Encyclopedia of Philosophy

See also, Stephen R. Welch’s page on Pascal’s Wager

It probably isn’t news to anyone currently breathing that every newspaper owning corporation in the United States is currently in bankruptcy Chapter 11 proceedings. Here in Philadelphia, after sinking more that 500 million bucks to take the Philadelphia Inquirer and the Philly Daily News off the hands of the guys who bought them from Knight Ridder, the purchasing group headed by Brian Tierney et al. ended more than eleven months of negotiations with creditors by filing for Chapter 11 protection with the United States Bankruptcy Court, meaning reorganization and possible liquidation. There are serious rumors that only one of the two newspapers will survive, probably the Inquirer.

In a way, this is strange, because there was a time in Philadelphia, and I don’t mean going back to Ben Franklin, when it was obvious that the Inquirer was the worst and most pitiful newspaper in town. The Philadelphia Public Ledger was the newspaper of record (its building still stands at 6th & Chestnut) for many decades, while the Philadelphia Bulletin was clearly the better of the two papers while the Bulletin and Inquirer were the two main papers in the second half of the 20th century.

Of course, the Public Ledger went under in the Great Depression; it died in a court-ordered liquidation in 1941 or 1942. This may just be history repeating itself. The Public Ledger was owned jointly by the owners of the NY Times, incidentally.

For a complete list of ALL newspapers ever printed in Philadelphia, go to this website pdf of newspapers held by the free library of philadelphia;


you’ll be shocked and amazed how many newspapers there have been and how many small ones there still are other than the inquirer and daily news even now.

But then again, the Philadelphia Athletics won five world series and too many pennants to count between 1901 and 1953, and were the main baseball team in Philadelphia for more than fifty years. No one gave a fig about the Phillies. It was only after Connie Mack died and the A’s moved away that the Phillies finally developed a fan base, and even then not really until the 1964 pennant run with Dick Allen and Jim Bunning did they really draw any fans. But who remembers the A’s today in Philly? Where are they today? No one in Philadelphia remembers them at all.

There’s a small museum in one of the counties, and a small bronze plaque at the new ballpark. That’s about it for the team that in the first half of the 20th century was the second best ballclub in the American League, and by far the best professional sports team in Philadelphia.

Getting back to newspapers, the point is that you can’t understand history by looking at it now. If you looked around now and saw humans, you’d never know that dinosaurs once ruled the earth. Likewise, looking around and seeing the Inquirer being the main newspaper, you’d never know that once there was a Public Ledger, a Bulletin, and probably a dozen other papers. Even the Saturday Evening Post, the nation’s number one women’s magazine, was published right here in Philadelphia, but it died too. That building is still around also. We have seen the end of magazines like Life, the Saturday Evening Post, and most recently, U.S. News & World Report, in the past forty years. Now newspapers are dying as well.

There were a lot of great movies about newspapers. The best movie of all time is about newspapers. Here I refer to Citizen Kane (1941), which is a thinly veiled biopic of William Randolph Hearst and his media empire.

There’s also Meet John Doe (1936) and let’s not forget All the President’s Men (1974).

I’d throw in Broadcast News (1980s) as well, even though it’s really a TV movie, just because it’s flat out hysterically funny and not at all dated, and because Brooks is one of my favorite comics in the world other than Mike Reiss. Just looking at Brooks makes you laugh.

But history does repeat itself. The Hearst media empire was bankrupted by the Great Depression—so much so that Hearst himself, so rich that he could build the Heart mansion—the famous “Xanadu” in the Kane movie—in San Simeon, California—now a famous museum—actually lost all his money to his creditors in bankruptcy proceedings and lost control of his newspaper holdings. No one today has heard of the New York newspapers that Hearst made his fortune from.

Now, we are going through another serious economic dislocation which is again severely affecting media badly. As badly as Hearst was affected by the Depression and War years, that’s how badly newspapers and old media will be affected this time around. Add to that the free news which is available on the internet, and on every persons’ telephone, and one would be silly to expend money for a newspaper.

It’s quite obvious that within another twenty years, there will be no more magazines or newspapers in print at all, that everything will be delivered right to your computer, tv or phone via internet. Maybe (and I often futurize about this) the convergence of nanotechnology and biotechnology will eventuate in a chip being implanted in your brain or neural net, so that you can visualize the images yourself without a machine mediating at all. Perhaps we’ll all be connected to the internet and to each other one day in such a fashion. It’s difficult to make radical predictions, but then again, in 1910, no one could have predicted that baseball, then a deadball sport based on bunting, stealing and pitching, would in the 1920s and thereafter become a sport of sitting around waiting for someone to hit a three run home run.

I will miss the Philadelphia Daily News. For the last forty years, it’s been the best sports paper in the country, and I’ve read all the other papers around, including the Boston Globe, the Chicago, the LA, the NY and SF papers. NY has tabloids basically and no good writing at all; the Boston Globe for a long time had great writers, but they’ve all gone to ESPN or national outlets where the money really is; and no other city really had good sports writing. Philly might be the last town in which there’s been good beat writing and sports writing for a long time now.

If the Daily News goes, that will probably be the end of it, though it may survive on line since there’s an online edition of the daily news that’s pretty good, and even better, available nationally to all former philly residents who follow their teams. So when they throw the last daily news into the fire and you see the sled burning with the name “rosebud,” remember you read it here—this was all a story about Charley Foster Kane, who wanted to be the world’s greatest newspaperman, and succeeded all too well.

By the way, I mentioned in a prior post that GE was way off about Jimmy Fallon? GE stock is now trading at five dollars a share. That’s right, five dollars a share. they made a big deal about this on one of the network news shows while i was working out on the elliptical at the gym. whoa nellie! The stock apparently has completely crashed.

Jack and Suzy Welch, would you buy this company’s stock? It was trading at $40 just last year. And now it’s down to $5 a share and dropping like a rock. Pretty soon it will be worth, say, 1923 German deutsche marks, which is to say, nothing.

Oh yes I would says the Wizard of OZ. You can get a thousand shares in this company now for the price of a song. Heck, the only place the stock can go is a little down, or a lot up.

I said they should have bumped Leno three years ago. While I recognize most of their problems are with GE Capital, entertainment is the division that’s always recession proof.

If you’re not sure about that, check out the fact that 1930s and 1970s are the greatest eras of film history.

Jimmy Fallon had another great show–Jon Bon Jovi did a duet with one of his fans, while Tina Fey sat and rooted the two of them on. I think it was the girls’ dream moment of her life, all caught on camera. You can bet that will be on youtube.

Art Kyriazis
Philly/South Jersey
Home of the World Champion Philadelphia Phillies
You can