Table of Contents
Logical Consistency and Usefulness as an Argument for the Existence of God
There are only four possibilities, four and only four. The question being ‘Should I believe that a Christian Theistic God exists?’ The possibilities are, simply put; I believe and such a God does exist, I believe and such a God does not exist, I do not believe and such a God does exist, or I do not believe and such a God does not exist. This far is simple logic, either a Christian Theistic God exists or not and either I believe or not. Pascal’s wager analyzes these possibilities and concludes that one possibility has such a greater reward than the others as to make it alone worth following.
Blaise Pascal was born in the year 1623 in the French city of Clermont. His father, Etienne, was a well-educated and successful lawyer. His mother died when Blaise was three years old, leaving his father to raise the three children. It is apparent that Etienne did a good job with the education of his children, as they all seem to have become successful at their various ventures in life. He insisted that they be schooled at home and he took the lead role in their instruction, using tutors only when by necessity he could not fulfill the job at hand. Blaise had a sound grounding in Latin, Greek, mathematics and science. “Also important were the people he met through his father, united by a common interest in mathematics and science. . . . Descartes (mathematician and philosopher) . . . the Parisian members of the Mersenne circle (Pere Mersenne was the unofficial agent in Paris for Descartes). . . Desargues and Fermat the most famous mathematicians in
In order to understand Pascal and his religious thought two major influences in his life must be mentioned. First, in 1646 his father was injured in an accident and had to have continual medical help for an extended period of time. The two brothers that were employed to assist were deeply religious and had a profound effect on Blaise and his family. The brothers were followers of Saint-Cyran who expounded on the ideas of the Jansenists and had been influential at the spiritual retreat known as Port-Royal. Blaise Pascal “experienced at this time what is usually called his ‘first conversion.’” The Jansenists were a reforming movement within the French Roman Catholic Church. Their beliefs “entailed an austere form of piety and a rigorously puritanical morality. Also Jansen argued in favor of absolute Predestination, in which humans are perceived as incapable of doing good without God’s unsolicited grace and only a chosen few are believed to receive Salvation.” The effect on Blaise Pascal was a personal “awareness of man’s wretchedness” and his own sinful nature, along with a total “dependence on divine grace” as over and against the majority teaching of the church of his day, that man could have a “comfortable optimism and reliance on human means for salvation.”
The second major influence in Pascal’s life that needs to be mentioned is his receiving of Jesus Christ as his personal savior. This is often referred to as his second conversion but in reality is his first and only conversion. “Quite suddenly on the night of 23 November 1654, he had an experience, . . . On that night he felt at last reconciled with Christ and resolved thenceforth to give himself wholeheartedly to the service of God and others.” Since his so called first conversion Blaise Pascal had become more and more aware of the obstacles that blocked his full commitment of love for God through Christ.
Pascal saw his intellectual pride and selfishness as great barriers that kept him from total commitment. But on that November evening he gave himself to Jesus Christ not by his works or best efforts but by the Grace of God. The result of Pascal’s conversion was an intense desire to show others the way to the Lord. He realized that many of his friends, both from the Jansenists and the group of his gambling buddies in Paris, had a need to find Jesus Christ.
It is in this context that Blaise Pascal began to work on an “Apology for the Christian Religion.” His means of work was to set down numerous ideas and ‘thoughts’ on scraps of paper, with the intent to organize them into one outline and thus produce a book on apologetics. The Wager as it is so called was one such thought on one of Pascal’s scraps of paper. However, Pascal’s death in 1662 left this work unfinished, many scraps of paper with notes and a partial outline are all that were found of his apologetic efforts. Over the years several scholars have undertaken to finish Pascal’s work. Thus today we have the book entitled Pensees credited to the authorship of Blaise Pascal but with much of the organizational work done by the different translators / editors. This paper will use the Penguin Classics edition compiled and translated by A.J. Krailsheimer for all quotes and references.
Now let us return to the possible ways to answer the question ‘Should I believe that a Christian Theistic God exists?’
‘Either God is or he is not.’. . . Since you must necessarily choose, your reason is no more affronted by choosing one rather than the other. That is one point cleared up. But your happiness? Let us weigh up the gain and the loss involved in calling heads that God exists. Let us assess the two cases: if you win you win everything, if you lose you lose nothing. Do not hesitate then; wager that he does exist.
Pascal in these few words puts forth the heart of his wager.
A point raised among the commentators on the wager is why bet at all, why not be agnostic and thus avoid this whole debate. Pascal pursues this line of thought when in his rhetorical form he says, “The fact is that they are both at fault, (the one who calls heads and the other) the right thing to do is not to wager at all. Yes, but you must wager. There is no choice, you are already committed.” He refers to the fact that by virtue of life one is committed to either believe in God or not, there is no in-between, no neutral ground on which to stand and observe. To live is to believe there is a God or not. Thus it is that “besides being, sometimes, detached inquirers we also are and have to be agents. It is an ineluctable part of our human predicament that we have to act, to live our lives.”
Pascal’s wager argument itself can be thought of in the following simplified form.
|God Exists||God does not Exist|
I receive an infinity of happiness
I lose very little
|I do not Believe
I Receive an infinity of despair
I gain very little
Some who comment on Pascal’s wager argue that there are several parts to the one wager argument while others think that there are multiple arguments within the few pages of the wager while still others argue for both views. Typical of these thoughts are the expressions of Jeff Jordan in his work Gambling on God. “There is not just one, but at least three wager arguments” yet, “all versions share three constitutive features.” Ian Hacking introduces the wager saying, “Pascal’s wager is the name of some game-theoretic considerations that concern belief in God. I shall show that Pascal briefly presents three distinct arguments.” Most of the commentators agree that Pascal’s wager is quite complex even though it can be stated quite simply.
Pascal’s wager can be analyzed as a “decision situation in which the possible gain or benefit involved in one of the outcomes swamps all others.” Suppose a state of affairs S1 that has the gain or benefit of U1 (U for utility which is a more comprehensive term than ‘gain’ or ‘benefit’) if a certain action A1 is performed. Also suppose that there is within S1 a utility U2 derived from the action A2. It is found that U1 is greater than U2 and upon investigation it is further found that for any SX it is the case that U1 always is greater than U2. This would lead to the conclusion that A1 swamps or dominates A2. “If one act dominates all others, the solution to our decision problem is ‘perform the dominant act’.” Applying this to Pascal’s wager, as charted above, it can be readily seen that the action of believing in God’s existence is of far more utility than not believing and this would seem to be true in any given state of affairs. Thus ‘believing’ dominates over ‘non-belief’ and the dominant act should be performed; a person, any person, even every person should believe that God exists. This is a valid conclusion in the strict sense of logic where the conclusion must follow from the premises. However, as Hacking comments, “Nowhere do I imply that Pascal’s arguments are persuasive. But this is not because they are invalid (in the logician’s sense) but because the premises of the arguments are, at best, debatable.” The problems of the wager will be looked at later in this paper.
Another analyses of Pascal’s wager can be done from an inductive logical perspective rather than using the deductive logic just presented. In this sense probability enters into the discussion. “Most philosophers and commentators have understood the logic of the relevant passages in the Pensees to be urging us to do with respect to theism and atheism what we normally do, mostly without explicitly conscious reflective awareness, in all parallel decision making contexts, namely, to place our bets on the available option with the highest … expectation.” The basic formula, commonly in use, for the expectation to gain profit is:
“Expectation (E) = [Probability (p) X Payoff (U)] – Cost (C).”
Alan Hajek carries the discussion further as he expresses his interest in Pascal’s Wager “largely for the questions it raises in the philosophy of probability theory.” Hajek sees three premises contained in the wager. The first premise being that a positive probability must be assigned to God’s existence. Pascal can be seen to do this when he states that “We know that the infinite exists without knowing its nature, . . . Therefore we may well know that God exists without knowing what he is.” Premise two is “Either God exists or God does not exist, and you can either believe in God or not believe in God.” The third premise is similar to the one stated before by Hacking namely that “Rationality requires you to perform the action that maximizes expected utility.” To draw a conclusion the expediency formula can be used as follows:
“Expectation (E) = [Probability (p) X Payoff (U)] – Cost (C)."
E1 (believe in God) = p X ¥ (infinity) – (very little) = ¥
E2 (do not believe in God) = (1-p) X (a finite amount) - (a finite amount) = (a finite amount).
Therefore since E1 expects an infinite return and E2 expects only a finite return then “Rationality requires you to believe in God.” Hajek however offers objections to both premises one and two and contends that the argument is invalid. But if the premises are true the conclusion would follow as valid. Again, objections will be analyzed later.
A third way to view Pascal’s wager is to see it as a pragmatic argument. “A pragmatic argument is any argument which has premises which are prudentially-directed rather than truth-directed.” Richard Foley suggests
That the pragmatic benefits of having a belief do give us a reason to have that belief . . . This conclusion fits well with Pascal’s proposed wager because precisely what Pascal claims is that there are huge benefits in the offing from belief in God and that these benefits make it rational for us to believe in God.
Nicholas Rescher in his work on Pascal’s wager develops this pragmatic dimension with an in-depth study of practical reasoning. Rescher would contrast the prudentially-directed pragmatic argument not as over and against ‘truth-directed’ arguments, as mentioned in the definition given above, but as alongside evidence-directed arguments. Rescher establishes a “Taxonomy of Reason” as follows:
Theoretical (Probative: Acceptance-Oriented) Reasoning
- formal (mathematics, logic, language, etc.)
- evidential (factual “inductive” reasoning in science and common life)
Practical (Pragmatic: Choice-Oriented) Reasoning
- axiological (value-oriented)
- prudential (interest-oriented)
- instrumental (“value-free” means-ends reasoning)
It can be concluded from Rescher’s formulation that he sees prudential arguments as different than formal (deductive) or evidential (inductive) arguments but as no less valid forms of reasoning. A person would be evidentially justified in believing a thesis if the evidence is substantial and the thesis fits with all other beliefs that the person holds. By contrast, but no less valid, a person would be pragmatically justified in believing a thesis if:
1. the probability of the thesis is nonzero, and
2. the thesis is not incompatible with any or all evidentially justified believes, (there is no evidence to the contrary, not a lack of evidence but no actual contradictory evidence), and
3. the person has cogent reason to think that adopting the thesis is demanded for the realization of some proper and legitimate aim or goal (pragmatic arguments are always in a context and as such can not be abstract and it is necessary that the context be reasonable and appropriate), and
4. the thesis is compatible with any and all other pragmatically justified beliefs that are held by the person. 
Then applying this to the wager “Pascal does not want us to avert our eyes from the distinction between what we know to be true and what we are well advised to think (be it for prudential or moral or other reasons). Indeed his (Pascal’s) whole argument pivots on this distinction. What matters for the wager argument is simply that evidence does not have a corner on the market of good reasons.” Rescher believes that Pascal makes this very same point when Pascal states, “It is the heart that perceives God and not the reason. That is what faith is: God perceived by the heart, not by reason.”
Point one of the definition of a pragmatic argument as set out by Rescher is fulfilled by Pascal in the wager, as noted earlier, when he states “We know that the infinite exists without knowing its nature, just as we know that it is untrue that numbers are finite. . . Therefore we may well know that God exists without knowing what he is.” Propositions (2) and (4) of Rescher’s definition seem to be addressed by Pascal’s statements in his thoughts on ‘Submission and the Use of Reason’ (chapter XIII in the Penguin Classics edition). Where Pascal concludes “If we submit everything to reason our religion will be left with nothing mysterious or supernatural. If we offend the principles of reason our religion will be absurd and ridiculous.” The third part of Rescher’s definition of a pragmatic argument, which is the foundation of the whole argument form, would be fulfilled when Pascal makes statements such as the following:
For my part, I confess that as soon as the Christian religion reveals the principle that men are by nature corrupt and have fallen away from God, this opens one’s eyes so that the mark of this truth is everywhere apparent: for nature is such that it points at every turn to a God who has been lost, both within man and without, and a corrupt nature.
Without any doubt after this, considering the nature of life and of this religion, we ought not to resist the inclination to follow it if our hearts are so inclined.
And again from the heart of the wager:
Let us weigh up the gain and the loss involved in calling heads that God exists. Let us assess the two cases: if you win you win everything, if you lose you lose nothing. Do not hesitate then; wager that he does exist. 
Thus, with the four premises of Rescher’s definition of the pragmatic argument fulfilled he asserts that Pascal’s wager substantiates that it is prudent to believe that God exists.
Pascal’s wager is an appeal neither to man’s scientific prowess (to competence at factual inquiry) nor to his “better self” (to human idealism), but to rational self-interest. As he saw it, the religious journey will no doubt eventually lead to a certainty of higher principle but can (and for many must) begin in the moral certitude of man’s practical affairs.
As suggested already there exist many objections to Pascal’s wager argument, several of which shall now be considered. Let us begin by considering the Moral Objection to Pascal’s Wager. William James captures the essences of one part of this objection when he translates Pascal as saying “Go, then, and take holy water and have masses said; belief will come and stupefy your scruples.” It seems that some people must act “unthinkingly and mechanically, to wager on theism.” The objection as stated is that Pascalian wagering also known as stepping out on faith sets aside the evidence, or lack thereof, and will harm the individuals powers of reasoning. The human being has certain intellectual abilities that are to be used in the pursuit of knowledge. If these abilities are not used or are ‘stupefied’, then they will form habits that corrupt the cognitive faculties. Pascal is seen as encouraging all mankind to stop testing and inquiring about belief statements and simply wager or do religion before or without reasoning. Some have even suggested that this habit of using insufficient evidence will lead not just to individual wrong beliefs but also may harm the whole of society, because it must cause us to “sink back into savagery.”
An extension of the moral objection is to see a basic immorality in the wager’s dealing with the non-believer. He is doomed to receive an infinity of despair when it can not be shown that he is to be blamed for his unbelief. “It seems immoral to condemn anyone . . . for not believing something unless such unbelief is culpable.” “Unbelief will always be something for which one can rightly be blamed only if unbelief always amounts to self-deception.” However, some unbelievers “on examining the evidence for and against theism, remain convinced, without in any way being at fault, that their unbelief is epistemically rational.” So the objection would run that since they are not self-deceived then it would be immoral to condemn them for their unbelief.
Pascal would answer this moral objection by insisting that “if you are unable to believe, it is because of your passions, since reason impels you to believe and yet you cannot do so.” Pascal throughout the Pensees gives argument after argument for the reasonableness of Christianity and belief in God. The thrust of Pascal’s writing is that there is evidence that anyone should be able to see clearly and believe. When a person does not come to this same conclusion there must be a problem within themselves. This Pascal names as one’s passions or concupiscence, what is more commonly referred to as sin. The nature of the person is so corrupted by sin that they will not recognize what is obvious, Pascal knew this to be true from his study of the Scriptures and his own experience with his personal sin.
There are only two classes of persons who can be called reasonable: those who serve God with all their hearts because they know him and those who seek him with all their heart because they do not know him. As for those who live without either knowing or seeking him, . . . I hope that they will be satisfied, and convinced by the proofs of so divine a religion which I have collected here.
Yet, Pascal goes further to say “It should be apparent that those who follow it [the proofs and evidence he gives throughout the Pensees] are prompted to do so by grace and not by reason, and those who evade it are prompted by concupiscence and not by reason.
The moral objections seem to be set aside by Pascal in that he in no way wants to avoid evidence nor to stupefy anyone’s scruples, on the contrary he offers chapter upon chapter of ‘proofs’. Neither is anyone condemned for that which they are not able to understand, but rather for being totally self-deceiving due to the sin in their hearts that they are not even willing to admit. “Behind all this, of course, lies Pascal’s commitment to an Augustinian account of original sin” which is itself a part of the Augustinian doctrine of predestination, the doctrinal stand that Pascal adhered to from the Jansenists. Pascal instructs a person, to take up the habits of religion and shed their doubts, not to evade reason but to incline the person to seek God while shedding off one’s sins. There is certainly nothing immoral with these intentions. They are the same as the views of others who follow the Augustinian way of theology. “The moral law [for example the Ten Commandments] is of use to all men, . . . binding them to walk accordingly; to convince them of their disability to keep it, and of the sinful pollution of their nature, hearts, and lives: . . . and thereby help them to a clearer sight of the need they have of Christ."
Another objection to Pascal’s wager accuses the argument of being one from self-interest. George Schlesinger goes so far as to speak of the wager as a reliance on greed.
It is common knowledge that many well-intentioned individuals reject the wager for reasons that do not require much philosophical sophistication. They find it mercenary. They believe it appeals to the scheming, calculating self and are repelled by it. . . . The essence of religion is generally perceived as the conviction that all profane, self-seeking ambitions are incompatible with the quest for piety. The religious seeker is not one to be mired in self indulgent pursuits but passionately devotes oneself to much nobler and more ultimate concerns.
Pascal might counter by agreeing that wagering will indeed provide “an eternity of life and happiness” for the individual, however, “what harm will come to you from choosing this course? You will be faithful, honest, humble, grateful, full of good works, and a sincere friend.” This is hardly a list of ‘self-seeking ambitions’ and ‘mercenary’ causes, but if an even nobler and more ultimate concern is needed then Pascal could add “that he [God] might bring your being also to submit to him [God] for your own good and for his [God’s] glory.” Or, Pascal might have quoted from the Gospel of Mark where Jesus declares that the greatest commands are “Love the Lord your God with all your heart and with all your soul and with all your mind and with all your strength.' and the second is this: 'Love your neighbor as yourself’." Surely no one would charge Jesus with promoting self-interest by these words, in the same way neither is Pascal with his wager argument.
R. G. Swinburne states the Probability objection in a concise manner when he states “Pascal supposes (by his remarks ‘There are equal risks of gain and loss’ and ‘Reason can decide nothing here’) that the probabilities of his two alternative states are equal. This claim is, to say the least, arguable.” Morris adds to the objection by asking if the injection of ‘infinite value’ and ‘non-repetitive wagering’ will change the normal betting situation.
Can (E) [the probability of expectation as quoted above see page 6] be expected to serve its ordinary function with such an extraordinary assignment to one of its variables? . . . Also it is clear that in the bet concerning God we do not have a situation of repetitive wagering [as in normal betting situations] in which gain is compatible with numerous losses along the way. And so it can be argued that conditions do not obtain in which the rational bettor is best guided by (E). But of course, if (E) is not used, this popular form of the Wager does not work.
Alan Hajek adds to the probability objection by stating that the Wager “presupposes that you assign a probability to God’s existence. . . . I am happy to grant Pascal that you should assign probability to God’s existence. What I am less happy to grant is that this probability should be positive.” Taking these together they would seem to be calling into question one part or another of the common probability formula for the expectation of gain or loss, “Expectation (E) = [Probability (p) X Payoff (U)] – Cost (C).” as applied to the wager argument. These challenges to Pascal’s wager certainly have the potential to nullify his intended use, unless answered or proven wrong. So, let us revisit some of Pascal’s assertions in an attempt to clear up these potential problems. Pascal claims that “Either God is or he is not. Reason cannot decide this question.” By this statement Pascal does not mean that there are no reasons to believe in God nor that there could be good reasons to not believe, but that there is, as Morris states the position, “a rough epistemic parity.” If indeed there were no reasons to believe in God and/or there were good reasons to not believe then reason could decide the issue. If Hajek wants to assert a less then positive probability for God’s existence then he must show an argument against the existence of God that is reasonable, which he cannot do. If this is true then “there cannot be a clear preponderance of purely epistemic considerations either way. Thus there cannot be a great disparity between the assigned probability values of theism and atheism.” Pascal then seems to take the correct route by saying that reason cannot decide the issue by itself.
The hesitation to use the common probability formula for the expectation of gain or loss (E) with an infinite value for one of its variables seems to be based on additional assumptions not found in Pascal nor necessary to the Wager. The formula can be properly used for any finite calculation no matter how high the numbers become, thus the size of a finite wager would never invalidate a person’s expectation. Mathematically the infinite is simply the end of the line of the finite numbers, and what works for the finite should work for the infinite.
Morris says that “a moment’s consideration will show that the only problematic and absurd consequences of applying (E) with an infinite payoff value are displayed in the famous Many Claimants problem, a problem which results only from additional assumptions. . . . But if these assumptions are rejected . . . the importation of an infinite value into (E) has no clearly problematic results.
This leads directly to the fourth and final major objection to Pascal’s Wager that shall be considered, the Many God’s objection. “The problem is that despite appearances, Pascal’s betting partition is not exhaustive.” “The range of betting options is not limited solely to Christianity because one could formulate a Pascalian wager for Islam, certain sects of Buddhism, or for any of the sects found within Christianity itself.” This line of thought has even been carried to the extent that a “Perverse God who infinitely rewards all and only those who fail to believe in any God” and even worse concepts of god are assumed to be able to fit into Pascal’s wager argument. However, it must be understood that the many gods objection to have any creditability must deal with only ‘The Wager’ section of Pascal’s Pensees, and that would be only five pages out of almost three-hundred pages in the total book. Pascal in the entire sweep of the Pensees argues only for the Christian understanding of God. In reply to Jordan and others Pascal has a section of the Pensees entitled “Falseness of other religions,” in which he argues against ‘other religions’ in general and against Islam in particular. “It is not by what is obscure in Mahomet [Mohammed] that I want him to be judged, but by what is clear, by his paradise and all the rest. That is what is ridiculous about him.” Pascal explains why those of other religions do not understand saying “It is like people who use a certain obscure language amongst themselves; those who cannot understand it only make nonsense of it.” Pascal further claims that the “falseness of other religions [is] they have no witnesses. God challenges other religions to produce such signs. Isaiah 43:9-44:8.” It is quite clear that Pascal did not put forth a ‘Wager argument’ that he believed could be used for ‘Many Gods.’
Yet, others still have made the claim and it must therefore be analyzed. In dealing with the Many Gods objection a main assertion is that every possibility must also be given a positive nonzero probability.
“When one tosses a coin considered fair, it is possible that it land on its edge, remain suspended in midair, or disappear, or any number of bizarre but possible events might occur. Yet, because there is no reason to believe that these events are plausible, one quite properly neglects their possibility and considers the partition of heads and tails jointly to exhaust the possibilities.”
Thus the bizarre and grossly implausible can be assigned if not a zero probability at least a probability so small as to be neglected.
To come at this from the positive side, if there is a faithful, just and righteous God whose attributes attract a person and is thus worthy of emulation it would be reasonable to assign this God a higher probability of existence. Schlesinger continues this point by stating “It should seem sensible to hold that the greater those sublime properties, the greater the likelihood the one exemplifying them exists. Hence, the being greater than which is inconceivable, who possesses them to a maximum degree, is to be regarded more probable than any other deity.” Thus, if one and only one out of the many gods is far more probable than the others then there is not a problem for Pascal’s Wager with many gods.
The many gods objection needs to be viewed from a more practical side as well. What of the gods of the non-Christian major religions of the world, which many adherents would think plausible? To answer this let us keep in mind the nature and purpose of Pascal’s argumentation. The Wager is presented to a target audience who have a very definite view of God, people who are exploring the Christian idea of God, but are hesitant to believe in Him. Nicholas Rescher has been asked “What if the gambling theist finds that he has backed the wrong horse.” Rescher responds;
The person who is worried about all those myriad of gods is indeed going to find Pascal’s Wager unconvincing. But the fact remains the argument is simply not addressed to this person. It is addressed to those nominal Christians, [Christians in name only, calling themselves Christian but with out a true conversion experience] who do indeed espouse the god-conception on which the argument is premised. For most people the idea of God has its limits - the range of god-possibilities they are prepared to consider as real possibilities is one at most.”
Pascal’s Wager presupposes an audience that has a Christian tradition that will determine the sort of God that they think of as possible. “Thus the fact that others take a different view of the matter is simply beside the point for us.”
The common idea of the Many Gods objection is that there may be other relevant possibilities that could render the wager useless. However, if the Wager is taken in the proper context and formulation, as set out in our discussion of this objection, then the “many-gods objection is not a conclusive criticism of Pascal’s Wager. It is also likely that no new version of the many-gods objection will be forthcoming that could render the wager useless.”
Pascal’s Wager as an argument for God’s existence does have a logical consistency to it if (and this is a large if) the Wager is somewhat narrowly defined and the audience to which it is addressed is very narrowly defined. But this is exactly what Pascal meant to put forth in his Pensees. He was a Jansenist and as such Pascal believed in predestination so he knew that the results of The Wager were in the control of God at all times. His apologetic intention is to incite a desire for the things of the Lord within people who called themselves Christian yet had no conversion experience. Pascal’s method is simply to encourage them to make a wager for God that he knows they can not lose and whose results are infinite in value. Is the Wager a definitive argument for God? The answer would be no. Yet, perhaps it could be given a rightful place in a cumulative group of arguments for God’s existence. “There is nothing wrong with reaching a decision based on a cumulative argument. . . . Our judgment in such matters is seldom the result of one argument or piece of evidence.” Thus at the right time and directed to the right audience Pascal’s Wager may along with other arguments have an apologetic appeal in establishing a belief in the existence of God.
 A. J. Krailsheimer, Pascal, (New York: Hill and Wang, 1980), 3.
 Hugh M. Davidson, Blaise Pascal, (Boston: Twayne Publishers, 1983),6.
 T. Tackett, Catholic Encyclopedia (on-line), 2001 ed., available from http://mb-soft.com/believe/txc/jansenis.htm; Internet.
 Krailsheimer, Pascal, 6.
 Ibid., 9.
 A. J. Krailsheimer, “Introduction,” in Pensees, Blaise Pascal, ed. A.J. Krailsheimer (New York: Penguin Books, 1995), xv.
 Blaise Pascal, Pensees, ed. A.J. Krailsheimer (New York: Penguin Books, 1995), 122-3, Sec. 418:14,16.
 Ibid., 123, Sec. 418:15,16.
 Antony Flew, God and Philosophy (New York: Harcourt, Brace & World, Inc., 1966), 183, Sec. 9.7 see also Sec. 9.10.
 Pascal, Pensees, 123, Sec. 418:16,17.
 Ibid., 136,7, Sec. 432:6,434.
 Jeff Jordan, Gambling On God, Essays on Pascal’s Wager (Lanham, Maryland: Rowman & Littlefield Publishers, Inc., 1994),2.
 Ian Hacking, “The Logic of Pascal’s Wager,” American Philosophical Quarterly 9:2 (April 1972): 186.
 Hacking, “The Logic of Pascal’s Wager,” 187.
 Ibid., 187.
 Thomas V. Morris, “Wagering and the Evidence” in Gambling On God, Essays on Pascal’s Wager, ed. Jeff Jordan, (Lanham, Maryland: Rowman & Littlefield Publishers, Inc., 1994), 48,9.
 Thomas V. Morris, “Pascalian Wagering,” Canadian Journal of Philosophy 16, no. 3 (September 1986): 439.
 Alan Hajek, “Objecting Vaguely to Pascal’s Wager,” Philosophical Studies 98, no. 1 (March 2000): 1.
 Pascal, Pensees, 121, Sec. 418:4,5.
 Hajek, “Objecting Vaguely,” Philosophical Studies, 1.
 Ibid., 2.
 Morris, “Pascalian Wagering,” Canadian Journal of Philosophy, 439.
 Hajek, “Objecting Vaguely,” Philosophical Studies, 2.
 Richard Foley, “Pragmatic Reasons for Belief” in Gambling On God, Essays on Pascal’s Wager, ed. Jeff Jordan, (Lanham, Maryland: Rowman & Littlefield Publishers, Inc., 1994), 44.
 Nicholas Rescher, Pascal’s Wager: A Study of Practical Reasoning in Philosophic Theology (Notre Dame, Indiana: University of Notre Dame Press, 1985), 51.
 Taken and restated from Rescher, Pascal’s Wager, 46,7.
 Rescher, Pascal’s Wager,50.
 Pascal, Pensees, 127, Sec. 424
 Ibid., Pensees, 121, Sec. 418:4,5.
 Ibid., Pensees, 54, Sec. 173.
 Ibid., Pensees, 152, Sec. 471.
 Ibid., Pensees, 153, Sec. 482:2.
 Ibid., Pensees, 123, Sec. 418:16.
 Rescher, Pascal’s Wager, 38.
 William James, The Will to Believe and Other Essays in Popular Philosophy (New York: Longmans, Green & Co., 1897; reprint, Atlanta: Scholars Press, 1986), 57.
 Philip L. Quinn, “Moral Objections to Pascalian Wagering” in Gambling On God, Essays on Pascal’s Wager, ed. Jeff Jordan, (Lanham, Maryland: Rowman & Littlefield Publishers, Inc., 1994), 63.
 Ibid., “Moral Objections” in Gambling On God, 65.
 Ibid., “Moral Objections” in Gambling On God, 66.
 Ibid., “Moral Objections” in Gambling On God, 66.
 Ibid., “Moral Objections” in Gambling On God, 67.
 Pascal, Pensees, 124, Sec. 418:20.
 Ibid., Pensees, 132,33, Sec. 427:18,19.
 Ibid., Pensees, 260, Sec. 835.
 See in the Pensees Section One Chapters: 22,23 and 24 and in Section Two Chapters 11-13,16,17 and 18.
 Quinn, “Moral Objections” in Gambling On God, 75.
 The Westminster Larger Catechism, Question 95.
 George Schlesinger, “A Central Theistic Argument” in Gambling On God, Essays on Pascal’s Wager, ed. Jeff Jordan, (Lanham, Maryland: Rowman & Littlefield Publishers, Inc., 1994), 83,4.
 Pascal, Pensees, 123, Sec. 418:17.
 Ibid., Pensees, 125, Sec. 418:21.
 Ibid., Pensees, 125, Sec. 418:24.
 R. G. Swinburne, “The Christian Wager,” Religious Studies 4, no. 2 (April 1969): 220.
 Morris, “Pascalian Wagering,” Canadian Journal of Philosophy, 441.
 Hajek, “Objecting Vaguely,” Philosophical Studies, 3.
 Morris, “Pascalian Wagering,” Canadian Journal of Philosophy, 439.
 Pascal, Pensees, 122, Sec. 418:14.
 Morris, “Pascalian Wagering,” Canadian Journal of Philosophy, 443.
 Ibid., “Pascalian Wagering,” Canadian Journal of Philosophy, 443.
 Ibid., “Pascalian Wagering,” Canadian Journal of Philosophy, 443,4.
 Jeff Jordan, “The Many-Gods Objection” in Gambling On God, Essays on Pascal’s Wager, ed. Jeff Jordan, (Lanham, Maryland: Rowman & Littlefield Publishers, Inc., 1994), 101.
 Ibid., “The Many-Gods Objection” in Gambling On God, 101.
 Graham Oppy, “Pascal’s Wager is a possible bet (but not a very good one): Reply to Harmon Holcomb III,” International Journal for Philosophy of Religion 40, (1996): [article on-line] available from http://www.infidels.org/library/modern/graham_oppy/p_wager.html; 11.
 Pascal, Pensees, 70, Sec. 218.
 Ibid., Pensees, 70, Sec. 217:3.
 Ibid., Pensees, 66, Sec. 204:1,2, see also Pensees, 169,70, Sec. 489:19ff.
 Ibid., “The Many-Gods Objection” in Gambling On God, 107.
 Schlesinger, “A Central Theistic Argument” in Gambling On God, 91,2.
 Rescher, Pascal’s Wager, 97.
 Ibid., Pascal’s Wager, 93.
 Nash, Ronald H., Faith and Reason: Searching for a Rational Faith, (Grand Rapids: Zondervan Publishing House, 1988) 115.
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