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April 18 2014 03:46 PDT

Blaise Pascal 1632-1662 halftone 
	detail of painting by Philippe de Champangne, Library of Congress 

Blaise Pascal, painting by Philippe de Champangne


since 01.01.06

Introduction to Philosophy

Pascal's Wager

Abstract: Since Pascal does not think a sound argument can be given for God's existence, he proposes a pragmatically persuasive consideration.

  1. According to Pascal, how much can be known about God?
  2. Reconstruct Pascal's Wager as carefully as possible.
  3. Explain whether you consider Pascal's Wager a proof of God's existence or not?
  4. What major objections can you construct to the Wager? Can the objections be countered?
  5. Clarify the meaning of Pascal's sentence, "The heart has its reasons which reason does not know."
  1. Blaise Pascal (1632-1662).
    1. Several biographical points should be briefly mentioned.
      1. With no formal education, Pascal studied languages at home until he became fascinated with Euclid's Elements.
      2. At sixteen Pascal wrote an important essay on the geometry of conic sections for a group of mathematicians who later formed part of the French Academy.
      3. He studied and made contributions to the physics of gases and liquids.
      4. By correspondence with Fermat, Pascal helped form the origin of probability theory. His final work solved several important problems raised by the cycloid: a mathemathical curve formed by the path taken by a point on the circumference of a circle as it rolls along a straight line.
      5. The Pensées from which "The Wager" is taken is a collection of fragments reconstructed by editors who might not accurately reflect the original writing of Pascal.
    2. William James's thesis in "The Will to Believe" is similar to Pascal's Wager; even so for James, Pascal's Wager would not constitute a momentous option and does not represent a method of how belief is established.
  2. The Wager
    1. Notes are arranged in response to the questions stated above in reference to Pascal's chapter "The Wager" from Pensées in Reading for Philosophical Inquiry.
      1. According to Pascal, how much can be known about God?
        1. God is so completely different from us that there is no way for us to comprehend him.
        2. We can know that God is, but we cannot know what God is.
        3. Ordinary human descriptions are futile and paradoxical when applied beyond the bounds of everyday application when we say God is all-powerful, all-good, and all-knowing. These predicates are beyond our experience.
      2. Reconstruct Pascal's Wager as carefully as possible.
        1. Pascal does not think that the atheist or the believer would be convinced by his Wager. Instead, he directs the Wager to the curious and unconvinced.
        2. I have a choice: either first I believe God exists or second I do not believe God exists.
        3. First, if I believe God exists, and God in fact does exist, then I will gain infinite happiness. However, if I believe God exists, and God in fact does not exist, then I will have no payoff.
        4. Second, if I do not believe God exists, and God in fact does exist, then I will gain infinite pain. However, if I believe God does not exist, and God in fact does not exist, then I will have no payoff.
        5. Thus, I have everything to gain and nothing to lose by believing in God, and I have everything to lose and nothing to gain by not believing in God. On these grounds, one would be foolish not to believe.
      3. Explain whether you consider Pascal's Wager a proof of God's existence or not?
        1. I come to have faith in God by "acting as if I believed." I, in effect, change my attitude, not my reason.
        2. In much the same manner as Tolstoy would write several centuries later, Pascal indicates we learn from those who believe and become like them. As a result of the Wager, we have nothing to lose and everything to gain.
        3. By rational decision theory, one can calculate the expected return of a payoff. Suppose I wonder whether I should enter the Family Publisher's Sweepstakes with a possible payoff of 20 million dollars. I look in the fine print and see that the chance of winning the payoff is 1 in 450 million. I can calculate my "expected" return by doing a thought-experiment. Suppose I enter the contest an indefinite number of times; I will win on the average the amount calculated by the following formula:

          [the probability of winning] X [the payoff] = [the expected return].
          1. So, doing the math ...

            [1 / 450,000,000] X [$2,000,000] = [$0.0044] or less than a half of a penny.
          2. Obviously, if I return my entry by mail I would normally lose money because of the cost of the stamp, the opportunity cost of my time, and, among other things, the shoe leather used on the way to the post office.
        4. With God's promise of an afterlife, however, the payoff is so large that the expected return makes it almost irrational not to believe, even if the probability were low. Even so, of course, there is no certainty there would be a payoff.
        5. The everyday beliefs we act on are the things we believe the strongest. We never bother to prove these beliefs. We do not try to prove the existence of the external world, that the sun will rise tomorrow, that the floor will remain under our feet, or that we are awake.
        6. It is little matter that we can, or cannot, prove these beliefs, so likewise, it is little matter that we prove God's existence. We simply assume life will go on, without proof; otherwise, it would be disastrous to our everyday existence if we were occupied with proving these ordinary things.
        7. In sum, Pascal's Wager is not intended to be a philosophical proof; the Wager is just intented as a persuasive, pragmatic consideration directed to the agnostic.
      4. What major objections can you construct to the Wager? Can the objections be countered?
        1. Two main objections are often raised to Pascal's Wager.
        2. (1) To believe in God simply for the payoff is the wrong motive for belief. Such self-seeking individuals would not properly serve the Deity.
        3. (2) In order to be sure of a payoff, an individual would not know which God or gods to believe in to cover the conditions of the wager. Would the Wager also hold for Zeus, Odin,or Mithra? One would have to believe in all gods to be sure, but if there were only one God in fact, then this strategy would defeat itself.
        4. Pascal could argue objection (1) isn't about subjective intentions; it's about objective probabilities.
        5. Pascal could argue for objection (2) the different conceptions of different religions could refer to the same God.
      5. Clarify the meaning of Pascal's sentence, "The heart has its reasons which reason does not know."
        1. Human beings live not by reason alone. Without heart, feeling, emotion, life would lose its value.
        2. Our uniqueness as a species might be the ability to think, but let not that blind ourselves to the fact that our whole value individually or as a group is not in reason alone.
    2. W. W. Rouse Ball points out with respect of the Wager: "Pascal made an illegitimate use of the new theory in the seventh chapter of his Pensées. In effect, he puts his argument that, as the value of eternal happiness must be infinite, then, even if the probability of a religious life ensuring eternal happiness be very small, still the expectation (which is measured by the product of the two) must be of sufficient magnitude to make it worth while to be religious. The argument, if worth anything, would apply equally to any religion which promised eternal happiness to those who accepted its doctrines. If any conclusion may be drawn from the statement, it is the undersirability of applying mathematics to questions of morality of which some of the data are necessarily outside the range of an exact science. It is only fair to add that no one had more contempt than Pascal for those who changes their opinions according to the prospect of material benefit, and this isolated passage is at variance with the spirit of his writings."
Further Reading:
  • Blaise Pascal (1623-1662). A mathematical biography transcribed from W. W. Rouse Ball's A Short Account of the History of Mathematics by D.R. Wilkins.
  • Decision Theory: The Wikipedia's entry article summarizing some of the major approaches to choice under uncertainty including mention of Pascal together with extensive references is an excellent starting place to learn something of decision theory.
  • Pascal's Wager. A clear and precise summary of the cluster of issues surrounding the Wager including super-dominance, expectation, genuine option, and paradox-objections by Paul Saka in The Internet Encyclopedia of Philosophy
  • Pascal's Wager: A thorough account of Pascal's Wager including the argument from superdominance and probabilistic expected value together with objections and extensive bibliography is provided by Alan Hájek in the Stanford Encyclopedia of Philosophy.
  • Religious Language. A student handout by Scott Moore of Baylor University summarily lists some of the major philosophical approaches to the problem of reference in religious language.
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“Pascal's reasoning may have been theologically simplistic, but it was mathematically intriguing. It illustrated the kind of reasoning that goes into calculation the ‘mathematical expectation’ of an economic decision—you miltiply he probability of an outcome by the value of that outcome. The reaitonal choice is the decision that computes to give the highest expected value. Pascal's wager is often cited as the earliest example of a math-based approach to decision theory.” Tom Siegfried, A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature (Washington, D. C.: Joseph Henry Press, 2006), 198.

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