Pascal's Wager

Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory (...) to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives. (shrink)

Among recent objections to Pascal's Wager, two are especially compelling. The first is that decision theory, and specifically the requirement of maximizing expected utility, is incompatible with infinite utility values. The second is that even if infinite utility values are admitted, the argument of the Wager is invalid provided that we allow mixed strategies. Furthermore, Hájek has shown that reformulations of Pascal's Wager that address these criticisms inevitably lead to arguments that are philosophically unsatisfying and historically unfaithful. Both the objections (...) and Hájek's philosophical worries disappear, however, if we represent our preferences using relative utilities rather than a one-place utility function. Relative utilities provide a conservative way to make sense of infinite value that preserves the familiar equation of rationality with the maximization of expected utility. They also provide a means of investigating a broader class of problems related to the Wager. (shrink)

J.L. Schellenberg argues that divine hiddenness provides an argument for the conclusion that God does not exist, for if God existed he would not allow non-resistant non-belief to occur, but non-resistant non-belief does occur, so God does not exist. In this paper, I argue that the stakes involved in theistic considerations put pressure on Schellenberg’s premise that non-resistant non-belief occurs. First, I specify conditions for someone’s being a resistant non-believer. Then, I argue that many people fulfill these conditions because, given (...) some plausible assumptions, there is a very good pragmatic reason to be a theist rather than an atheist. I assume it is more likely that theists go to heaven than atheists, and I argue there is a non-zero probability that one can receive infinite utility and a method of comparing outcomes with infinite utilities in which the probability of each outcome affects the final expected values. Then, I show how this argument entails there is no good reason to think that there are very many non-resistant non-believers. (shrink)

This paper defends a principle I call Equal Treatment, according to which the rationality of a belief is determined in precisely the same way as the rationality of any other state. For example, if wearing a raincoat is rational just in case doing so maximizes expected value, then believing some proposition P is rational just in case doing so maximizes expected value. This contrasts with the popular view that the rationality of belief is determined by evidential support. It also contrasts (...) with the common idea that in the case of belief, there are two different incommensurable senses of rationality, one of which is distinctively epistemic. I present considerations that favor Equal Treatment over these two alternatives, reply to objections, and criticize some arguments for Evidentialism. I also show how Equal Treatment opens the door to a distinctive kind of response to skepticism. (shrink)

This paper is a critical review of Howard Sobel’s ’Logic and Theism’. I discuss his analyses of ontological arguments, cosmological arguments, teleological arguments, and arguments from evil, and comment upon his accounts of Pascal’s wager and Hume on miracles. My overall judgment is that this is the very best book on arguments about the existence of God that has yet appeared.

Gdzieś w ciemnej uliczce... Bandyta: Ej ty, dawaj portfel! Pascal: A niby dlaczego miałbym to zrobić? Bandyta: Bo w przeciwnym razie cię zastrzelę. Pascal: Ale przecież nie masz broni. Bandyta: A niech to! Wiedziałem, że zapomniałem o czymś. Pascal: No to zapomnij też o moim portfelu. Miłego wieczoru. Bandyta: Stój! Pascal: Co znowu? Bandyta: Jest interes do zrobienia... Co ty na to, żebyś jednak oddał mi portfel? W zamian obiecuję przyjść do ciebie jutro i dać ci dwukrotność kwoty, którą w (...) nim masz. Nieźle, co? 200 procent zwrotu z inwestycji w 24 godziny. (shrink)

Some recent work in philosophy of religion addresses what can be called the “axiological question,” i.e., regardless of whether God exists, would it be good or bad if God exists? Would the existence of God make the world a better or a worse place? Call the view that the existence of God would make the world a better place “Pro-Theism.” We argue that Pro-Theism is not implausible, and moreover, many Theists, at least, (often implicitly) think that it is true. That (...) is, many Theists think that various good outcomes would arise if Theism is true. We then discuss work in cognitive science concerning human cognitive bias, before discussing two noteworthy attempts to show that at least some religious beliefs arise because of cognitive bias: Hume’s, and Draper’s and Nichols’s. We then argue that, as a result of certain cognitive biases that result when good outcomes might be at stake, Pro-Theism causes many Theists to inflate the epistemic probability that God exists, and as a result, Theists should lower the probability they assign to God’s existence. Finally, based our arguments, we develop a novel objection to Pascal’s wager. (shrink)

According to conventionalist accounts of personal identity, persons are constituted in part by practices and attitudes of certain sorts of care. In this paper, we concentrate on the most well-developed and defended version of conventionalism currently on offer (namely, that proposed by David Braddon-Mitchell, Caroline West, and Kristie Miller) and discuss how the conventionalist appears forced either (1) to accept arbitrariness concerning from which perspective to judge one's survival or (2) to maintain egalitarianism at the cost of making “transfiguring” decisions (...) such as Pascal's Wager rationally intractable. We consider three ways the egalitarian conventionalist could make these choices tractable and show that each one comes at significant cost to the view. We end the paper by considering whether accepting arbitrariness would be a better move for the conventionalist and conclude that, even here, she runs the risk of transfiguring choices being rationally intractable. (shrink)

Lately, there has been an explosion of literature exploring the the relationship between one’s practical situation and one’s knowledge. Some involved in this discussion have suggested that facts about a person’s practical situation might affect whether or not a person knows in that situation, holding fixed all the things standardly associated with knowledge (like evidence, the reliability of one’s cognitive faculties, and so on). According to these “pragmatic encroachment” views, then, one’s practical situation encroaches on one’s knowledge. Though we won’t (...) endorse pragmatic encroachment here, we find the view intriguing, and it’s popularity warrants carefully considering it’s implications. One potential avenue of exploration concerns religious epistemology, in particular, whether pragmatic encroachment has consequences concerning the epistemic requirements of atheism. We begin the journey down that avenue by connecting Pascal’s Wager to pragmatic encroachment in order to defend this conditional: If there is pragmatic encroachment, then it is ceteris paribus more difficult to know that atheism is true (if it is) than it is to know that God exists (if God does exist). (shrink)

Using “brute reason” I will show why there can be only one valid interpretation of probability. The valid interpretation turns out to be a further refinement of Popper’s Propensity interpretation of probability. Via some famous probability puzzles and new thought experiments I will show how all other interpretations of probability fail, in particular the Bayesian interpretations, while these puzzles do not present any difficulties for the interpretation proposed here. In addition, the new interpretation casts doubt on some concepts often taken (...) as basic and unproblematic, like rationality, utility and expectation. This in turn has implications for decision theory, economic theory and the philosophy of physics. (shrink)

Konserwatywni przeciwnicy prowadzenia badań naukowych na ludzkich embrionach argumentują, że od momentu poczęcia mają one status moralny równy statusowi ludzi dorosłych: zarodki mają takie samo prawo do życia jak dorośli. W artykule przedstawiam oryginalną argumentację za tym stanowiskiem, której źródła można znaleźć w XVII-wiecznej teologii moralnej i współczesnej teorii decyzji. Argumentacja ta nie odwołuje się do statusu ontologicznego embrionów, ale do pewnego typu rozumowania praktycznego na temat tego, co należy robić w rozmaitych sytuacjach niepewności. Na pierwszy rzut oka wydaje się (...) ona wzmacniać stanowisko konserwatywne, ponieważ nie zależy od kontrowersyjnych metafizycznych założeń na temat statusu zarodków czy kwestii ich potencjalności. W artykule pokażę jednak, że argumentacja ta obarczona jest poważnymi wadami, które sprawiają, że nie da się jej zastosować do uzasadnienia sprzeciwu wobec moralnej czy prawnej dopuszczalności np. badań na zarodkowych komórkach macierzystych. (shrink)

The Many Gods Objection (MGO) is widely viewed as a decisive criticism of Pascal’s Wager. By introducing a plurality of hypotheses with infinite expected utility into the decision matrix, the wagerer is left without adequate grounds to decide between them. However, some have attempted to rebut this objection by employing various criteria drawn from the theological tradition. Unfortunately, such defenses do little good for an argument that is supposed to be an apologetic aimed at atheists and agnostics. The purpose of (...) this paper is to offer a defensive strategy of a different sort, one more suited to the Wager’s apologetic aim and status as a decision under ignorance. Instead of turning to criteria independent of the Wager, it will be shown that there are characteristics already built into its decision theoretic structure that can be used to block many categories of theological hypotheses including MGO’s more outrageous “cooked-up” hypotheses and “philosophers’ fictions”. -/- Please note that there are editorial errors in the published version. They have been corrected in the attached. (shrink)

Pascal’s Wager holds that one has pragmatic reason to believe in God, since that course of action has infinite expected utility. The mixed strategy objection holds that one could just as well follow a course of action that has infinite expected utility but is unlikely to end with one believing in God. Monton (2011. Mixed strategies can’t evade Pascal’s Wager. Analysis 71: 642–45.) has argued that mixed strategies can’t evade Pascal’s Wager, while Robertson (2012. Some mixed strategies can evade Pascal’s (...) Wager: a reply to Monton. Analysis 72: 295–98.) has argued that Monton is mistaken. We show that Monton is correct, highlight the crucial assumptions that he relies on, and shed some light on the role of mixed strategies in decision theory. (shrink)

I defend Pascal's Wager from a particular way of evading it, the mixed strategy approach. The mixed strategies approach suggests that Pascal's Wager does not obligate one to believe in God, because one can get the same infinite expected utility from other strategies besides the strategy of believing in God. I will show that while there's nothing technically wrong with the mixed strategy approach, rationality requires it to be applied in such a way that Pascal's Wager doesn't lose any force.

I argue that a version of Pascal's Wager applies to the persistent vegetative state with sufficient force that it ought to part of advance directives.

Arthur Falk has proposed a new construal of faith according to which it is not a mere species of belief, but has essential components in action. This twist on faith promises to resurrect Pascal’s Wager, making faith compatible with reason by believing as the scientist but acting as the theist. I argue that Falk’s proposal leaves religious faith in no better shape; in particular, it merely reframes the question in terms of rational desires rather than rational beliefs.