Justin Li


Pascal's Wager

2008-10-29

NOTE: I wrote this around the end of October, but I never finished it. I have since realized that Pascal's Wager is a valid argument for belief in God, but it doesn't supply any proof of His existence. It would seem that rationality (here defined as maximizing benefits to the individual) argues for God's non-existence and belief in God at the same time. I'm no expert (and even that is an overstatement), but perhaps this is somehow related to Godel's incompleteness theorem despite it not being a direct contradiction?

The first thing you should know is that I'm now a Shelfari user. It's a book keeper's bookkeeping site. I've tried LibraryThing, but that has a limit of 200 books for free accounts. I have another list at WorldCat, but I'm putting only complex systems related books there.

Anyway, if you look at my Shelfari, I'm currently reading Daniel Dennett's Breaking the Spell: Religion as a Natural Phenomenon. Dennett is actually speaking at Northwestern tomorrow, as part of a series on evolution. I had planned on finishing his book before going, but chances are I won't have time to do that. For most of the book Dennett develops a theory of why religion exists, and how it came to be as widespread as it is now. He first focuses on why people believe in God, then on why people believe in belief in God. Between these two sections, he spends a short chapter on why for but mostly against God's existance.

While I was reading that, I didn't really pay attention to the arguments he gave, since I've encountered most of them before. Rather, my mind was on another argument I've been having trouble with: Pascal's Wager. The argument looks at belief in God as a utility calculation. Assuming the basic heaven/hell in afterlife, the utility of belief can be summarized:

God Exists God Doesn't Exist
Believe in God +Infinity 0
Don't Believe in God -Infinity 0

Eternity in heaven or hell gives positive or negative infinity, and if nothing happens in afterlife, then there is no value in either belief or non-belief.

Richard Dawkins, Dennett's colleage at Oxford, made the argument there is a cost to believing in God if God doesn't exist: the time spent worshiping and the money paid to churches could be used for something else. However, since the time and money spent is finite, and the time in heaven or hell is infinite, this still doesn't offset the utility in case God exists.

A more interesting argument is that we are all atheists - with regard to at least all but one religion which has ever existed. Because religions are (or at least tend to be) mutually exclusive, the probability of believing in the right God is minimal. In fact, if the above table was modified to say "Believe in the Right God" and "Right God Exists", the previously inifinite utility would actually be undefined. This is due to the number of religions being infinite, and infinity over infinity is undefined (I wonder if you can take rephrase that as a limit, and apply l'Hopital's rule... just kidding).

Another curious note on this argument against the wager is that there seems to be a vague parallel with the lottery paradox in epistemology.

Regardless, this doesn't exactly solve the problem. Even if the utility is undefined, it is still larger than 0 (since both infinities are positive). This means there is still a higher utility to believe than not to believe, and this has been bugging me for the past 2 weeks.

Then today when I read Dennett's chapter, I suddenly realized that Pascal's wager is not actually about the existance of God. It's about the believe in the existance of God, which is something entirely different. As Dennett repeats several times, it's possible to believe in God but believe in the belief in God, and vice versa. That is, one can believe God exists, and yet be ashamed of it as

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