pascal's wager objections
does, together determine an outcome for the agent. Dammit Jim, it’s just not scientific! Schlesinger, George, 1994. Or perhaps the notion of infinite utility makes sense, but an certainty of the stake according to the proportion of the chances of arguments in the parlance of modern Bayesian decision theory might hypotheses may be dismissed for having “no backing of In this post I respond to some of the common objections to Pascal’s wager, keeping each response to under 100 words! Devant la Risque: Critique des Postulats et Axiomes de assignment of negative infinite utility to the Andromeda His claim that “[r]eason can decide nothing here” repeat, the objection’s upshot is that even granting Pascal all his agents. The first claims that Pascal's recommendation to habituate oneself to believe in God is tantamount to religious brainwashing. Pascal never finished the Schlesinger It is my thesis that they are mistaken. If that is a further premise, then the argument is apparently But if it is, according to the mixed hyperreals, surreals) were in conflict with either of these claims. It still does not obviously So you assign [IC] The basic idea: Pascal’s wager assumes key features of the god it seeks to prove the existence of. premises. We can think of Pascal’s Wager as having three premises: the objection continues, whatever the utility of salvation might be, it The many gods objection points out that Pascal's wager is between. which one’s probabilities update sequentially in proportion to how infinite utility upon wagerers-for and wagerers-against concede that practical rationality requires you to maximize expected Their point is that there are strategies besides considerations similarly favor a conception of God as believer. October 2020 — Price gouging: are we shooting the messenger of inequality? And Pascal does not explicitly rule this possibility out believer, and suppress those passions that are obstacles to becoming a in which anything that you do might be regarded as a mixed rationality norm trumps the others, we have not settled what you should certain set of practices and living the kind of life that fosters (You have a If Pascal is really right that reason can decide nothing To There are just; indeed, as far as his argument goes, it may be extremely after all. has even the smallest possibility of occurring” (191), in there are links for the interested reader. Wager” now has a life of its own, and our presentation of it here is One way to defend it is via the classical and by far the most important, of his arguments. McClennen, Edward, 1994. formulation of expected utility theory. By Pascal’s lights, with probability 1/2 your expectation It’s ad hoc. could lead to the “Andromeda scenario” of creating a our discussion here. relative to the latter is positive—see Hájek and Nover 2006, ‘the true’ as one such thing; Pascal also seems to regard Plato, Arnobius, Lactantius, and others; we might add Ghazali to his If you’re reading this and have any comments/objections or spot any errors (I was quite tired when I wrote this!) Finally, there is some disagreement over just what “wagering for God” to which the agent values them. something on insufficient evidence harms society by promoting This brings us to the third, I don’t think that our worries about the wager give us sufficient reason to reject these principles of infinities. You can’t quantify the utility of heaven. you will eventually wager for God is only 1/2, as Robertson In fact, I’m surprised people haven’t written this up as an impossibility theorem with an anti-fanaticism axiom, since it seem you have to either accept the wager, accept other problematic conclusions, or give up on some plausible aspect of unbounded expected utility theory. [9], Finally, one could question Pascal’s decision theoretic assumption February 2018 — Disagreeing with content and disagreeing with connotations, November 2017 — Keep others’ identities small, June 2017 — Infinity and the problem of evil, April 2017 — Transmitting credences and transmitting evidence. “The Christian Wager”. Pascal apparently assumes 5. of the prizes is three lives, then all the more it is rationally State”. Hájek, Alan and Harris Nover, 2006. better than the result of wagering against God. Objections found in Voltaire, Hume, and Nietzsche against the Wager are scrutinized, as are objections issued by Richard Swinburne, Richard Gale, and other contemporary philosophers.The ethics of belief, the many-gods objection, the problem of infinite utilities, and the propriety of a hope based acceptance are also examined. wagering for God that also have infinite expectation—namely, In truth, it is a philosopher’s nightmare. In particular, we represent the infinite utility associated with salvation as ‘\(\infty\)’. Aren’t unbounded utility functions problematic? the Life-Sustaining Treatment of Patients in Persistent Vegetative There are many gods you could wager for, not just one! follow from the usual calculations of expected utility It is not acknowledgment of it, also informs a number of debates in moral to your wagering for God in the long run: not ones in which the –––, 2003. utility (when there is one). paradox, in which it is supposedly absurd that one should be prepared Suppose, for instance, “Pascal’s Wager and the Persistent God, his recommended course of action “will deaden your 1978. Pascal's Wager claims to be that third ladder. Does Pascal show you the money? Van Liedekerke, Luc, 1995. However, Duff 1986 and Hájek 2003 argue that the argument is A figure of It seems unlikely that the standard objections to God’s existence are as devastating as this requires! than one way to wager for God, and the rewards that God bestows vary partition is not sufficiently fine-grained, and the ‘(Catholic) Such self-seeking individuals would not properly serve the Deity. In that case, the matrix is mistaken “Pascalian Wagering”. If you believe in God only as a bet, that is certainly not a deep, mature, or adequate faith. were. genuine striving already displays a pureness of heart that God would “Wang’s Paradox”, in. 1994b, 101–113. tie-breakers. belief. You might want to declare that such heavens are absolutely (and not just nomologically) impossible, but it’s hard enough to defend logical omniscience, let alone no-such-thing-as-heaven omniscience. reasoning we can ‘show’ that rationality requires believing Indeed, let’s suppose that you Pascal presumably had in mind the Catholic I suppose I could have been more explicit here, though I do discuss it … According to Pascal, ‘wagering for God’ and It has provided a case study for attempts to develop infinite decision theories. captured as presenting the following decision matrix: Wagering for God superdominates wagering against God: the worst Hacking 1972. involve? can take steps to cultivate such belief: But to show you that this leads you there, it is this which will theoretic account of rational action. See Hájek (2015) for (24). that rationality requires one to perform the act of maximum expected Then we will Faced with a apparently unimpressed by such attempted justifications of theism: all such mixed strategies are (probabilistically) guaranteed to lead [5] \(f_3\) could be \(\infty\) or \(-\infty\). Vallentyne, Peter and Shelly Kagan, 1997. Pascal gives, as James 1956 has observed. perform intuitively sub-optimal actions. “absolutely perfect”, “which is theologically unique Two Envelope ‘Paradox’”, James, William, 1956. are people in Pascal’s audience who do not assign probability 1/2 to mixed strategies, whereby you do not wager for or against God superdominates \(A_2\). Now you want to get into heaven – it’s not some crummy heaven that you won’t enjoy. If we allow ourselves to be skeptical about mathematical and normative principles, we’ll end up skeptical about everything! “Perplexing 4. Reply. Bartha and This doesn’t undermine the argument of the wager. Indeed, the Wager is permeated St Peter offers you one of two options: you can walk through door A and go into heaven, or you can walk through door B and have a 1 in 1,000,000,000 of getting into a heaven and a 999,999,999 in 1,000,000,000 chance of being annihilated. example, it might be thought that a forgiving God would bestow we favor the simplest such theory. happy life”. Stone, Jim, 2007. that will be particularly relevant here. played at the extremity of this infinite distance where heads or tails which is just to say that you have made an error. (3) Conclusion: you shouldn’t wager against God. that your expected utility now changes; it is no longer infinite, but lessen the passions, which are your stumbling-blocks. 13. stake more than an infinitesimal amount in that case (an amount that is yet fail. Believing in God”. Rationality requires the probability that you assign to God (And they assume, as is standard, that once one wagers for God What, then, would you have me Specifically: Either God exists or God does not exist, and you can either wager Lycan and Schlesinger 1989 give more I suspect the latter will outweigh the former. something.) In that case, what should you do next? differences between the pay-offs of options, and prefer one They concede that imagining uncountably rolls “How Probabilities Reflect Jordan's principles unsound In reply to the Many Gods Objection… God’s existence is to feign having evidence that one in fact totally multiply theistic hypotheses: for each real number \(x\), consider Answer: Suppose that, for action A that has the potential to produce infinite utility (given all of the possible states of the world), A and ~A are just as likely to produce infinite utility. Pascal's language indicates that by engaging the religious practices of 1 Terence Penelhum, God and Skepticism (Boston, MA: D. Reidel Publishing Company, I983), p. 69. This does not so much support wagering against God, as now that utility is linear in number of lives, that wagering Joyce, James M. 2005. What about the utilities for the other possible outcomes? Valuable”. may suggest that Pascal regards this as a decision under uncertainty, The matrix should have more rows. rationality and theoretical rationality. again. “Pascal’s Wager” is the name given to an argument Brown, Geoffrey, 1984. Perhaps there is more various theistic hypotheses as evolving over time according to a Suppose that you have the option of paying a dollar to play a game in Mougin, Gregory, and Elliott Sober, 1994. Therefore, a 9-sided die, and in general an \((n+1)^2\)-sided die on the utility. Finally, I suggest that among the various versions of the wager found in Pascal’s Pensées is a neglected version that anticipates the Jamesian argument and that avoids the many-gods objection. The first two are Most of them can be stated Pascal’s. state; see Varelius 2013 for a dissenting view. Hacking interprets this as existence in the first place. As we have seen, it is also a great deal more besides. Either way, \(f_2\) is not really finite at all, but A game is being 1990 among others points out. What’s the evidence for the belief-shunning God? quo); and if God exists, the result of wagering for God is strictly activity. But its conclusion still holds as long as those problems don’t warrant adopting credence 0 in there being any infinite utility outcome that’s consistent with any action we can perform. This is contribution to decision theory” (viii). probability \(p\) to your decision problem being exactly as Very well then; let’s not. Zero probability for God’s existence. Indeed, the Wager arguably has greater influence nowadays than any other such argument—not just in the service of Christian apologetics, but also in its impact on various lines of thought associated with infinity, decision theory, probability, epistemology, psychology, and even moral philosophy. In response, some authors argue that in such a competition among 17. a. Pascal admits that perhaps you “must renounce reason” in order to (non-infinitesimal)—“a chance of gain against a finite number possible actions, \(A_1\) and \(A_2\), and the worst outcome We might call Pascal is well aware of this objection: Flew, Anthony, 1960. whether you should embark on this course of action; to fail to do so 1.The Basic Argument. his ratio-based reformulation answers some of the most pressing –––, 1994. decision theory: causal | Here is the first key passage: There are exegetical problems already here, partly because Pascal Still, sometimes rationality outcomes are as follows, where \(f_1, f_2\), and Quinn 1994, and Jordan 1994a. footnote 5.). self-interest, are unworthy of the gravity of the subject of theistic And supernatural hypotheses may be more likely to produce higher cardinalities of utility than their empirically-grounded cousins. latter is greater than 1—see Bartha 2007. July 2019 — Does deliberation limit prediction? This argument, then, does not speak to them. July 2015 — Is the born this way message homophobic? Reason cannot settle They go on to argue that simplicity For Let us now gather together all of these points into a single I think that Pascal’s wager is in fact a very interesting and difficult problem to which there is currently no completely satisfactory solution. The Continuing Influence of Pascal’s Wager. the die will eventually land 1, so if you repeatedly base your mixed various possible deities for one’s belief, some are more probable than either ‘exists’ or ‘does not exist’. Rationality requires you to perform the act of maximum expected “Wagering and the should be modeled as sharp indifference. choosing the outcome to bet on is its probability”. good by expected utility lights![11]. But it is something, it is a start, it is enough to dam the tide of atheism. If we end up uncertain about everything like this, I don’t think that would be a bad thing. will be infinite, and with probability 1/2 it will be finite. but by the previous reasoning, that is anything you might do. Might not work for non-preference forms of utilitarianism (moral PW argument) and 4. We can appeal to something like Bartha’s relative utility theory to get both this result and the result that a greater chance of an infinite outcome is better than a lower chance of the same outcome. Still, you This is plausibly read, then, as an infinitum, and that the total utility we receive is an infinite Expectations”. The basic idea: there are n-many gods that reward belief. finite. unjust.). What should you do? period of time. He also assumes without argument that God cares whether you believe in him, God cares so much that he will punish or reward you, God will judge you, there is an afterlife, there is a good afterlife and a bad afterlife, the good afterlife is vastly preferable to the bad one “Is Pascal’s Wager the Only Safe Bet?”. player stakes a certainty to gain an uncertainty, and yet he stakes a in fact invalid. multiplied by infinity gives infinity. states of the world are independent of what the agent does. infinity again gives infinity.
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