Silsbee 1 Betting on God: Pascal, Probability Theory and Theology Blaise Pascal, born in 17 th century France, was a mathematician and physicist who nevertheless made surprising contributions to the field of religious philosophy. In spite of suffering, from an early age, with an undetermined illness and dying of stomach cancer before reaching 40, Pascal was instrumental in establishing both the mathematical theory of probability and understanding atmospheric pressure in terms of weight ( Blaise Pascal ). Among those in the general population, however, he is probably best remembered for his Wager. Pascal, fascinated by mathematics, created the Wager by attempting to apply mathematical probability to the choice of whether or not one should believe in God. His conclusion was that one should believe because, by believing, one loses nothing if it turns out that God does not exist, but stands to gain infinite rewards if it turns out God does exist. Choosing not to believe, in contrast, provides no particular benefit if God does not exist, and equally provides no benefit indeed, makes one a great deal worse off if it turns out one was wrong (Hájek sec. 4). Though the logic may seem both valid and sound, Pascal's Wager has some serious issues, among them these three: the problem of choosing between competing faiths, the question how becoming it is for a religion to encourage converts based on greed, and the potential objection of whether or not one can choose one's beliefs. There are also some modern responses to Pascal which attempt to address these and other obstacles, two of which I will examine in some depth. The most common objection and one of the simplest, since it does not require an extended examination of the mathematics involved in probability theory raised against Pascal's Wager by non-believers and philosophers is that it assumes that one's choice in religion is binary
Silsbee 2 (Hájek sec. 5). Pascal's logic can be sound if the only choice is between believing in the Christian God or not believing in any God, but there are myriad religions in the world, even leaving aside the question of whether Christianity can truly be considered a single religion that worships a single deity. Most religions claim to hold some ultimate and saving truth that the others do not, meaning that an individual cannot, in most cases, choose to wager on more than one set of beliefs, and certainly cannot wager on unlimited sets of belief. Given this reality, while it may be wise to wager on some kind of religion, at best one might attempt to piece together two or three non-contradictory creeds and attempt to believe all of them in order to maximize the chances of whatever salvation each has on offer. Moreover, even the conclusion that one ought to wager on a religion is suspect in a world with seemingly infinite numbers of gods, each with contradictory attributes, it is difficult to make any assumptions about the supernatural and whether it exists at all. It is just as likely that any god or gods that exist would prefer honest agnosticism or atheism to an attempt to adhere to a set of religious beliefs strictly for reasons related to one's own self-interest (Amesbury sec. 2.2.1). In the absence of any demonstrable truth, it may truly be wisest to refrain from making any decision at all. Currently there is only a single defense presented against the many Gods objection. Authors George Schlesinger and William Lycan argue that not all deities are equally likely to exist, and so the two scholars attempt to prescribe a method for assigning probability to various gods. Schlesinger and Lycan compare the probability of a deity existing to the problem of choosing between competing theories in science (Hájek sec. 5). In science, if we have multiple theories which might explain a data-set or a collection of evidence, we always choose the
Silsbee 3 simplest until and unless additional evidence forces us to complicate it. This approach is preferred for two particularly important reasons: first, a simpler hypothesis is always more easily tested and therefore more falsifiable. Second, based on simple probability, fewer assumptions introduce fewer possibilities for error. Attempting to appropriate this reasoning without, apparently, fully understanding it, Lycan and Schlesinger assert that the simplest deity is the most probable (Hájek sec. 5). This assertion begins on shaky ground: one could argue that the nonexistence of any deity is even simpler, and that their argument is therefore invalid from the start. Ignoring this potential objection, however, they persevere, claiming the simplest concept for a deity is one that is perfect, and that this therefore makes the Christian God both the simplest and most probable, meaning that one ought to wager on that deity out of all those available (Hájek sec. 5). It hardly needs to be said that Lycan and Schlesinger's conclusion is riddled with problems, among them a disturbing degree of ethnocentrism. Conceptions of perfection necessarily vary from culture to culture, and in the argument the two authors assign primacy to one particular traditional Western definition without even acknowledging that others might exist in competition with it. Their definition of simplicity also leaves a great deal to be desired how, for instance, is their conception of the perfect God quantitatively or qualitatively simpler than, say, the Hindu conception of reality as a single source and destination, and individuals as mere manifestations of that underlying truth? They unfortunately make no attempt to justify the claim further. Thus we must conclude that, while it may be true that the existence of some deities is more or less probable than that of others, this consideration can only do so much to narrow the field. Schlesinger and Lycan's argument fails to demonstrate Pascal's
Silsbee 4 God as significantly more probable than any other, and even a single deity left in competition with his, renders the Wager logically unsound. The second objection to Pascal's Wager, which was touched on obliquely earlier, comes primarily from other Christians. Voltaire was unimpressed by the Wager, finding the entire idea of betting for or against God based purely on self-interest to be contrary to Christianity's stated intention (Hájek sec. 5). William James said of the Wager: When religious faith expresses itself thus, in the language of the gaming-table, it is put to its last trumps, and one cannot deny the validity of his reasoning. Making an argument in favor of religion based only on practical concerns seems to imply that the faith in question has nothing better to offer. Though Schlesinger weighs in again in defense of Pascal, calling self-interest in the search for piety a noble greed, one might be tempted to reply to him in the words of T.S. Eliot's Thomas Becket: The last temptation is the greatest treason: To do the right deed for the wrong reason (Hájek sec. 5; 44). While it is always possible that what begins in greed or fear may be transformed to more noble motives in time which is undoubtedly what Pascal intended encouraging nonbelievers to adopt a religion from base considerations seems more likely to corrupt the church than to purify the false converts. The question of false versus sincere converts moves us along to the third objection: Pascal seems to be under the impression that one can simply choose to believe in God or not. Philosophically, the belief that people have either direct or indirect voluntary control over at least some of their beliefs is known as doxastic voluntarism. Pascal espouses the less controversial indirect doxastic voluntarism in matters of religious belief that is, he does not expect a nonbeliever to simply decide to believe in God and from that point on have a firm and
Silsbee 5 unshakable faith: You would like to attain faith and do not know the way...learn of those who have been bound like you...follow the way by which they began; by acting as if they believed, taking the holy water, having the masses said, etc. (Pascal 233). Pascal suggests here that one who wants to believe for self-interested reasons ought to go through the motions of faith, and that, eventually, that person is likely to begin believing. While this particular version of doxastic voluntarism is certainly less controversial in the sense of whether or not it is achievable, there is still something a bit distasteful and even dishonest about people more or less tricking themselves into believing in a god or anything against their instincts and judgment. Doing so to gain a reward or avoid punishment seems particularly shallow and manipulative. Due to all these objections and several others that are mathematical in nature, Pascal's Wager is generally considered to have been discredited in philosophical circles. There are, however, more modern strategies which owe their existences to greater or lesser degrees to the general bent of Pascal's thought. One version, put forth by Joshua Golding, sidesteps the problem of doxastic voluntarism by discussing the value of a religious lifestyle rather than belief in God. Golding emphasizes the importance of living in relationship with God rather than believing, and asserts that this relationship can be built almost regardless of one's beliefs by living in accordance with God's law. Unlike Pascal, Golding also does not make claims about the value of salvation, but instead argues that there is benefit to be had merely in the living of a religious life (Amesbury sec. 2.2.1). One of the primary mathematical objections to Pascal's Wager deals with the fact that he sets the possible gain from choosing to believe in God as being infinite, which leads to questions about whether the claim is logically valid by certain constructions, all
1 outcomes go to infinity and the math ceases to work (Hájek sec. 5). Golding avoids that particular mathematical problem by dealing only with the finite here-and-now benefits of religious lifestyles (Amesbury sec. 2.2.1). In this way, he does manage to answer two of the Silsbee 6 challenges which ultimately caused most scholars to reject Pascal's Wager as invalid, unsound or both. Unfortunately, in restricting his value to a finite number, Golding creates the flaw in his argument: because he constructs the payoff given by a relationship with God as finite, he must wrestle with the probability of God's existence. Pascal, by setting the value of salvation as infinite, could argue that no matter how improbable God's existence might be, any possibility at all makes it more rational to wager on God than on any other option (Hájek sec. 4). Golding attempts to patch this problem by claiming that the payoff from a good relationship with God is not simply better than the payoff from any other pursuit, but that it is qualitatively different. This move allows him to claim that no amount of good from other pursuits could be added together to equal the value to be found in a religious lifestyle. In claiming a qualitative difference, however, he injects a novel mathematical problem into his claim: the probability matrix used to evaluate these wagers is incapable of evaluating qualitative differences (Amesbury sec. 2.2.1). Golding's math therefore does not work, and one must choose either to believe or not that a religious lifestyle offers benefits which cannot be equaled through any other pursuit which defeats the purpose of attempting to give a mathematical reason for choosing religion in the first place. Perhaps the most successful offspring of Pascal's Wager is William James' much more modest claim: that, in the absence of sufficient evidence, it is permissible to believe based on 1 For background information on probability theory and the equation used by Pascal, see Hájek sections 1-4.
Silsbee 7 faith. The connection between the Wager and James' thesis is not immediately obvious, but James, in spite of his recognition of the limitations of and problems with Pascal's Wager, nevertheless sees value in arguing matters of faith from the standpoint of probability and mathematics. The argument he makes draws on the philosophical traditions surrounding the Wager even if he does not attempt to construct a wager himself. Moreover, the question he is driving at is the same: what does reason tell us about what we should or shouldn't believe? Pascal was convinced that it told us we ought to believe, if for no other reasons than prudential ones. James makes the argument that it says we may believe, at least in the absence of evidential reasons to avoid doing so. The answers to the question may be different and may be arrived at in different ways, but both men are still addressing the same question. James laid out his claim in his essay, The Will to Believe, a response to an argument made by 19 th century philosopher and agnostic W.K. Clifford, who asserted that there can be no justification for ever believing anything without sufficient evidence (Amesbury sec. 2.2.3). Clifford saw all of civilization as being founded upon skepticism, and believed that no progress could be made without it. His conclusion was that believing anything in error was, in essence, a moral transgression that regressed society, and so every attempt should be made to avoid making such errors. James, on the other hand, saw situations in which missing out on potential truths would be a greater evil than occasionally being wrong. James' example of how this might function practically was social cooperation one must extend faith that others are acting with good intentions before relationships can be built (Jordan sec. 3). James acknowledged that avoiding error might be of primary importance in science, but argued that in other circumstances it is necessary to put the fear of error aside lest one miss out on important truths (Amesbury sec.
Silsbee 8 2.2.3). Here again we see a connection to Pascal, for whom missing out on a positive good salvation was infinitely more important than simply avoiding an inaccuracy. In terms of religion, James saw faith as more akin to social cooperation than science. He outlined two claims made by religion: first, that things are better the more eternal they are, and, second, that believing confers immediate benefits (25-26). James contends that choosing to believe is a perfectly rational choice for three reasons: in the first place, the claims made by religion can, to some degree, only be evaluated experientially. In the second, there is no consensus on whether there is enough evidence to validate or invalidate any major religion. In the third, refraining from making a choice amounts to choosing not to believe. He argues, in fact, that choosing to refrain from believing is driven just as much by emotion as the choice to believe the former is a choice made in fear of being wrong, and the latter a choice made in the hope of being right (Amesbury sec. 2.2.3). Of course, since James considers it permissible to believe as one pleases only in the absence of evidence, the claim that religion is one such case is open to criticism. There are many non-believers who would argue that there is sufficient evidence for reaching the conclusion that there are no gods, and that believers, in defiance of James' principle, willfully ignore the evidence. James does not, indeed, attempt to define what sufficient evidence means, which is problematic. If one were arguing against Christianity, for example, one might cite the actual age of the Earth against the genealogical calculations to be gleaned from the Bible as a factual error that makes suspect the reliability of all other Biblical accounts. Physical facts ought to be easier to get right than metaphysical facts, after all. This one error would be enough evidence for some to say that Christianity, at least, can be dropped from the roster of potentially true religions. This
Silsbee 9 example demonstrates the difficulty in determining just what sufficient evidence means, since it can vary wildly from person to person though this is a criticism which can certainly be leveled against Clifford as well as James. Other than that single critique, James' more modest answer to the question presented by Pascal's Wager seems largely sound. Reason may not demand that one believe in God or in any other deity but James makes a good case for reason failing to demand that one reject religion. Could Pascal have foreseen this humbling of his original claim, he might have been disappointed. Even so, it seems unfair to expect a purely natural phenomenon like reason to be able to pass definitive judgment on issues which lie outside the realm of nature. If reason can be used to defend supernatural beliefs as permissible, that is likely the best outcome that a believer can legitimately hope for.