Using Me!

Pascal's Wager (Part the third)

Jumile recently blogged about Pascal’s Wager, here and here, and I read the comments on his thread with some interest. It seems the phrasing of the wager caused some confusion. Distinguishing between ‘a god’ and ‘God’ seems to be at the root of it.

I thought I might rewrite the Wager using ‘a deity’ and ‘The Supreme Being’ but being a maths geek I thought a matrix (or spreadsheet!) might be better (and then went silly with Integration). In the table below I’ve illustrated what happens to you after death based on:

I actually reworked all the above as equations that I integrated over the P(Supreme Being Exists) from 0 to 1 and I’ll post the work at the bottom of this article purely for mathematical amusement.

I’ve argued before as to the un-likelihood of any actual God sending good people to Hell. In which case True Faith is irrelevant but where True Faith is not required Atheists are better off because the the price for misplaced Atheism has to be less than that of misplaced Belief – they didn’t waste any effort cowtowing to the wrong god. A minor point once you’re dead and in Heaven anyway but it could be quite a price during life.

However the important point is that where True Faith is required things are complicated. On the one hand it depends on how much value an Atheist would give to an afterlife in Heaven versus validating their Atheism. More importantly though it all comes down to whether the person of Faith has the true faith. Even if you only consider the main religions of the world the chance of you being in the right one is no more than 1:5 or so. If you consider the various interpretations of that religion to be important then it’s more like 1:20 or 1:50. If you consider all the deities that have ever been worshipped – and many of them still are worshipped by small numbers of people – then you have a snowball’s chance in hell of finding the right one.

That is to say that when picking apart Pascal’s wager the most important ‘variable’ is whether or not a Deity demands True Faith in him/her/it. If they do then you might as well just pick the one who’s notion of an afterlife you like the most. If you’re in the armed forces I’d go for Odin if I were you!

As the number of potential Supreme Beings rises the value of having faith diminishes and the value of being an Atheist rises – where True Faith is required. Where it is not required the value of faith still diminishes and the value of being an Atheist remains the same.

This leads to an interesting tangent. At some point religions changed. They changed from accepting that other people had other gods and the belief was simply that these were your ‘local’ gods and possibly that yours were better than anyone else’s; and they changed to stating that yours was the only real god and everyone else was simply deluded. And from this we simply conclude that religion is about power and control (and wealth). There is no other reason that I can come up with for why this change would occur. Any argument that the true faith became apparent is fallacious because there is no explanation as to why it didn’t exist beforehand nor any explanation let alone proof of which this true faith is. Christians love to talk about events prior to Christ being the Devil’s handiwork to confuse the believer. This is such unbelievable poppycock as it can be applied just as easily as to their own religion!

Anyway there’s my little exploration of Pascal’s Wager, now here comes the silly maths.

We can make an expected value of ‘belief’ from integrating the outcome values over a probability of the Supreme Being existing from 0 to 1. This is a sum of all possibilities along the P(Supreme Being) spectrum.

For most people V(Hell) and V(Misplaced Belief) will be negative which is why all solutions are additive not subtractive.

For an Atheist where the Supreme Being demands true Faith we can say:

Value = Integral of [ ( P(Supreme Being) * V(Hell) ) + ( P(!Supreme Being) * V(Valid Atheism) ) ]

The result is:

Value = ( V(Hell) + V(Valid Atheism) ) / 2

For an Atheist where true Faith is not required:

Value = Integral of [ ( P(Supreme Being) * V(Heaven) ) + ( P(!Supreme Being) * V(Misplaced Atheism) ) ]
Value = ( V(Heaven) + V(Misplaced Atheism) ) /2

For a Deist where True Faith is required:

Value = Integral of [ ( P(Supreme Being) * V(Heaven) * P(Belief in Correct Deity) ) + ( P(!Supreme Being) * V(Misplaced Belief) ) ]
Value = ( V(Heaven)*P(Velief in Correct Deity) + V(Misplaced Belief) ) / 2

For a Deist where True Faith is not required:

Value = Integral of [ ( P(Supreme Being) * V(Heaven) ) + ( P(!Supreme Being) * V(Misplaced Belief)) ) ]
Value = ( V(Heaven) + V(Misplaced Belief) ) /2

Plug in your own number is you like!