Sunday, September 18, 2011

I Wager Pascal Should Stick to Science

Much has been said about Pascal's famous wager and since its flaws are plainly clear to me, I find it difficult to comprehend why many theologians use this as a defense of their faith (sometimes a main defense). The obvious problems seem to have been discussed ad nauseam such as the ignoring of many other mutually exclusive possible worlds in which it would be "infinitely" detrimental to hold a belief in any particular deity and may be "infinitely" beneficial to hold no theistic beliefs whatsoever.

I would like to bring up another possible problem with Pascal’s Wager, namely the issue of something being "infinitely" beneficial and "infinitely" detrimental. It is on the basis of appealing to some sort of "infinite" reward/punishment that Pascal argues that no benefits gained from a life of non-belief in a particular deity or religion (particularly Christianity for Pascal) can offset the potential gain or loss in the afterlife. I contend that such an understanding is not necessarily the case.

Often in debates about religion the terms infinity or perfection are thrown around willy-nilly without fully comprehending the consequences applying such terms. Infinitude is a term that doesn't apply well outside the realm of pure mathematics and into the real world. What does it mean to get an infinite amount of pleasure? An infinite amount of pain?

The economic concept of diminishing marginal utility may help inform our approach to Pascal’s Wager. The law of diminishing marginal utility states that as a person receives more and more units of a particular item the amount utility they receive per unit diminishes. To illustrate this imagine a poor person getting $100. That $100 will be worth much more to the poor person than it would be worth to a billionaire receiving the same amount. Ultimately depending on the persons preference receiving additional rewards will level out and any additional reward received will be effectively worthless. Therefore it isn’t correct to say that infinite rewards/punishment may await us in the afterlife since effectively there is only a finite amount value we can actually receive or lose.

Another thing to consider is what a person is willing to risk in order to receive an “infinite” reward. A person may very well be willing to take a bet to get an infinite amount of money with an almost zero probability of winning if it will only cost them a dollar. They may likely still take the bet if it cost them $10, $100, $1,000 or even $10,000 depending on the persons current wealth. But under the logic of Pascal’s Wager there shouldn’t be any fixed amount of money no matter how high a person shouldn’t risk to try to achieve this infinite amount of wealth since the expected value of any such wager is still infinity:

Expected Value = (Reward) x (Probability of Winning)
                             – (Cost) x (Probability of Losing)

                             = ($ Infinite) x 0.0001% - ($1,000,000,000) x (99.9999%)

                             = $ Infinite

Now consider a real life scenario, would any reasonable person risk their entire life savings on a bet like this? I would not. It is even likely that I wouldn’t even take this bet if it were 50-50. If there is too much at stake it becomes less and less likely for me to take very risky bets even if the expected value of such bets are positive. This is the major aspect missing from Pascal’s analysis. Pascal doesn’t take into account the inherent risks and costs involved with his wager. Not all decisions are based on total expected benefit vs. rewards, they also take into account risks/uncertainty as well as the actual utility of the potential benefits.

2 comments:

  1. Pascal’s Wager doesn’t work in the real world because, as you say, he assumes that there are only two options, Catholicism and atheism, and because he fails to recognize the costs of being religious. There’s also the problem that he treats belief as a choice, as if you could start believing that, say, the sky is green simply by an act of will. And the problem that God, especially the Christian version, may take kindly to a mercenary bet on His existence, when people are supposed to come to Him through faith.

    The oddest thing is seeing Pascal’s Wager used in defense of Judaism. For example, in his book “Beyond a Reasonable Doubt” Rabbi Waldman ends the introduction by saying that the whole book is really superfluous, because if Judaism is right, and you are frum, you can look forward to eternal reward, while if Judaism is wrong, you’ve haven’t lost anything by being frum, so you might as well be frum. Besides for all of the standard problems with Pascal’s Wager, there’s the added absurdity of using an argument formally formulated by a Catholic theologian in defense of Catholicism as an argument for Orthodox Judaism.

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  2. Rabbi yochanan ben avrohomSeptember 25, 2011 at 6:48 PM

    Orthodoxy in it self is wrong. When man and religion get in the way of the will of Hashem we have a problem. The Romans and Greeks reached deep into both religions of Judaism and Christianity to use it for their worldly gains. What we have in today's religions are sheeple. Defined, it is the unenlightened masses that follow blindly the cunning of the few. Name the organized religion and i can give you a example. I think there is a valid argument to be made for doing away with the ism and schism of institutions, and bringing the sanctity of G-d back down to earth in a call of Love. As John Lennon said, IMAGINE all the people living as one, no religion, no reasons to kill, just Being is a hard thing for man to do. Just know there is a G-d, that is indescribable by man, yet ever present in our lives that wants us to live in peace and share the bounty of his blessing without reasons for separations caused by RELIGION.
    Shalom Aleichem

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