Rethinking Pascal's wager

This is another cut and paste from OT guys- enjoy.

I recently made a thread about Zeno's paradox which got me to thinking about this topic.

Pascal's wager for those who don't know it is basically a suggestion that everyone should live as though God exists. He claims that the possibility of eternal happiness or eternal misery in the afterlife, no matter how improbable, will always be statistically more significant than the possibility of just a finite existence on earth. The reasoning behind this is quite clear when it's expressed in terms of a probability matrix of expected outcome. For the sake of discussion lets put aside the bucketful of objections to this argument and just consider the proposition in terms of the maths with these points in mind.

1. You are a hedonist seeking to maximise the amount of time that you spend being happy and minimise the amount of time that you spend being miserable.

2. The probability of a God existing is equal to the probability of a God not existing.

3. If a theist is correct in his beliefs then he will always earn eternal happiness and if an atheist is wrong in his beliefs then he will always earn eternal misery.

With all of that taken as granted here is the expected outcome for a situation where a theistic lifestyle is demanding and brings about more misery than happiness during natural life and where the opposite is true of atheism. . A + sign indicates happiness while a - sign indicates misery.

---------------------------------------------------------Theist ----------------------------Atheist

A God exists (P=0.5)________________+infinity_______________-infinity

A God does not exist (P=0.5)_________ -finite_________________+finite

The result is quite clearly in the theist's favour. They gain infinite happiness (infinity - finite = infinity) while the atheist gains infinite misery (-infinity + finite = -infinity).

At this point the usual objection is to say "but how does the theist know that he has chosen the correct God". This is a valid point to bring up as multiple God's will diminish the probability that the theist has chosen correctly. Nevertheless it doesn't really seem to affect the conclusion of the equation at all. The great strength of Pascal's wager is that no matter how improbable it is that a theist's chosen God exists the expected outcome of a probability matrix will always equal infinity in his favour.

Let's examine that statement in regards to Zeno's paradox (copypasta from my other thread follows).....

The basic argument of Zeno's paradox is that if you fire an arrow at a target it will never reach that target. Here's how it works.

The movement of an arrow from the bow to the target can be divided into many increments e.g. the arrow can be half way to it's target, it can be 1/4th the way to the target it can be 1/8th the way to the target etc etc. The arrow takes a certain amount of time to reach each increment, obviously the time will be longer or shorter depending on the distance it has travelled but if it moves at all it takes at least some time to do so.

Simple enough right? Here's the cool bit.

The number of increments in the arrows path is infinite. That means that you can keep on dividing the distance it travels for an endless amount of times e.g. 1/16, 1/32, 1/64------->1/infinity.

If there is an infinite number of increments and each increment (no matter how small) takes time then that means that an infinite amount of time must pass before the arrow reaches its target. It is of course impossible for this to happen in in a finite amount of time and therefore the arrow never reaches its target.

Mathematically you could express Zeno's paradox like this 1/infinity * infinity = infinity

(end copypasta)

Now it's quite clear that the conclusion of Zeno's paradox is false. You can prove that to yourself by shooting an arrow at a target and seeing if it gets there or not. The problem with the argument is that it is hinging upon the proposition that a finite quantity (the time that it takes for the arrow to travel an infinitely small increment of its total distance) multiplied by infinity (the number of total increments along the arrows path of flight) will always be infinite. This is incorrect. In the case of the arrow and the target we can see that an infinitely small value multiplied infinitely will equal a finite value (i.e. the arrow travels an infinite amount of increments in a finite length of time).

The mathematical reality of Zeno's paradox therefore is more like this: 1/infinity * infinity = 1

Now let's take that piece of reasoning and apply it to the statement that was made earlier about Pascal's wager- "no matter how improbable it is that a theist's chosen God exists the expected outcome of a probability matrix will always equal infinity in his favour."

What if we say that the probability of the theist chosing the correct God is 1/infinity. That is to say, what if there is an infinite number of possible Gods to choose from with only one being correct? If that were to be the case then Pascal's wager would drastically change. A new matrix of expected outcomes with an infinitely improbable chance of picking the correct God would yield finite outcomes for both theist and atheist alike:

-----------------------------------------------------Theist----------------------------------- Atheist

A God exists (P=1/infinity)__________+finite___________________-finite

And in that way Pascal's wager can no longer favour the theist with the loophole of eternity. The playing field is even on both sides and in terms of mathematics you are free to bet on God or not.

Oh, Domatron you can try to reason with religious people in a reasonable manner, but they'll just come up with some "But the bible says so!" crap.

Oh, Domatron you can try to reason with religious people in a reasonable manner, but they'll just come up with some "But the bible says so!" crap.

felixlynch777

Not all of them. The ones who put any confidence in logical arguments for belief will also be obliged to look at logical arguments against belief.

[QUOTE="felixlynch777"]

Oh, Domatron you can try to reason with religious people in a reasonable manner, but they'll just come up with some "But the bible says so!" crap.

domatron23

Not all of them. The ones who put any confidence in logical arguments for belief will also be obliged to look at logical arguments against belief.

Their double standards on these matters though, logic sometimes just doesn't apply to them.

[QUOTE="domatron23"]

[QUOTE="felixlynch777"]

Oh, Domatron you can try to reason with religious people in a reasonable manner, but they'll just come up with some "But the bible says so!" crap.

felixlynch777

Not all of them. The ones who put any confidence in logical arguments for belief will also be obliged to look at logical arguments against belief.

Their double standards on these matters though, logic sometimes just doesn't apply to them.

If there's a double standard of logic applying then I'll let them know that and proceed to discontinue the discussion. Religious folk are only worth arguing with when they're ready to work on an even level.