Xeno's wager



There is a well-known thought problem called X(z)eno's Paradox, or the Dichotomy Paradox. The essential base of Xeno's dichotomy is what I allude to, while the basic conclusions and premises behind the argument I push aside as they are not relevant.

The dichotomy is this, to travel any distance, say 10m, you must first travel half that distance before you can travel 10m. Thus you must travel 5m. To travel the remaining 5m, you must first travel 2.5m, and to travel the remaining 2.5m you must travel 1.25m first and so on. The gist of the argument is that motion is an illusion; one cannot travel, or begin to travel any finite distance without making an infinite number of smaller trips.

The interesting thing about Xeno's Paradox is that the more half-moves you make, the closer you move toward 0m until, at some point, the differentiation is pointless and from a pragmatic position, there is no longer a division between the remainder and 0.

How does this apply to Pascal's Wager?

The sliding scales of halving work in opposition to one another as you place your wager for god's existence and I place mine against. Since we know there are more possible gods than one, and since any argument in the absence of evidence applies equally to all gods, we like Xeno, must half the probabilities of a god existing, while increasing the possibility of no gods existing by a half.

So, if we allow the existence of gods an equal starting probability (50/50) and place our wagers, first through Pascal's method, then wager accordingly with the Dichtomy Paradox, it becomes apparent that non-existence quickly moves toward a probability of 1.0 and non-existence towards 0.

Pacal's Wagers:


Yahweh + Jesus = 0.50/2 or 0.25
Vishnu + Shiva = 0.25/2 or 0.125
Allah + holy spirit = 0.125/2 or 0.0625
Brahma + Kali = 0.0625/2 or 0.03125
Ganesha + wu wei = 0.03125/2 or 0.015625


Considering if we counted or attempted to account for every variation of god that exists, we would likely end up some where over 4 billion possible deities. If that seems high, you must remember that:

  • Most Christians have their own version of god with bits they like, bits they don't
  • Hinduism would account for a large portion with official public deities and individual house hold deities
  • You would also have to include every god that had existed, but are no longer worshiped


The number of 4 billion is entirely reasonable, but lets cut that in half just to give those positing god the strongest possible argument. That equates to:

0.50/2,000,000,000 = 0.00000000025


The number is so low, it might as well be zero. But lets be even more generous and include only those denominations within one religion, Christianity. Presently, there are somewhere between 38,000 to 55,000 versions, each claiming to be correct, and each claiming three separate gods exist, are equal but one. So lets not multiply their number of possible gods by three, even though we ought to since the chance of Yahweh existing is equal to the holy spirit existing as it is to Jesus existing as a man-god – don't believe me? Ask a Muslim or Jew.

So, best case scenario, using the minimum possible bets, we arrive at:

0.50/38000 = 0.0000131579


Not as improbable, but the resulting number is also close to, if not zero, pragmatically, which I will address later before moving on to the ontological apology.

Xeno's Wagers:

0.50/38000 = 0.0000131579
0.0000131579 – 1.0 = .9999868421


Just in this case, we can see wagering against Pascal's gods, we come close to arriving at 1 without actually reaching it, nor can we ever, regardless of how many gods we might add. Example:

0.50/2000000000 = 0.00000000025
0.00000000025 -1.0 = 0.99999999975


This of course might embolden the agnostic or believer who insists god exists in the very small margins described, after all, if the chance isn't 0 and isn't 1, then there is a possibility, even if there is little to no probability.

Views: 21

Tags: Bayes, Christianity, dichotomy, hell, infinite, pascal's, reason, statistics, wager, xeno, More…zeno

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Comment by Jo Jerome on October 6, 2010 at 6:27pm
On evolutionary advantage - with recent readings and studies, I've started to latch onto the notion that humans have a tendency to perceive a 'will' in everything. That somewhere in the part of our brain that searches for patterns when confronted with an unknown, we also have a tendency not to ask "What" made that noise in the brush but "Who." I can see this as an evolutionary advantage in being ever so slightly more paranoid/cautious about approaching that unknown lurking in the brush.

There is also the psychological advantage to belief. Prayer works if only by means of a very powerful placebo effect. I believe some supernatural something is going to make me better, help me win the battle, whatever, and my psyche/body responds with a boosted healing process, more self-confidence, whatever.

Those simple, psychological processes spurred on by superstition far, FAR outlive their usefulness when it translates into subjugating classes and races in the name of that superstition, or putting yourself in the role of eternal victim, doomed to suffer.
Comment by Glen Rosenberg on October 6, 2010 at 10:44am
Free, I have also wondered whether there is an evolutionary advantage. I think that it must be social cohesion. How? It gets the group on the same page. Religion makes the world intelligible. That was true for stone age man. It is true for pc man.
I have also wondered why weddings have greater significance to the fairer sex. I think it relates to the same impulse. Birth and life stages and ceremonies and sacraments and the afterlife. It is all part of the story. I hypothesize atheist women attach less importance on weddings. It is funny how the fairer sex is more pious and thereby cement their second class role.
I aint drinkin n can feel a ramble comin so i am stoppin.
Comment by Atheist Exile on October 6, 2010 at 9:06am
Hey Jo,

If we're right and there ultimately is no God, then the whole notion of God -- which we can't even disprove -- was an entirely human construct. Our preoccupation with God is a defining human characteristic. As such, there must be an evolutionary advantage -- some survival value -- to such a belief. If so, that advantage appears to have lost its impetus. Perhaps our material progress is outstripping our evolutionary progress and religiosity is a vestige of our primitive selves: much like an appendix or coccyx.

I sometimes wonder how much of a waste religion is. If a person is devoutly religious (like my wife), have they wasted their lives? My wife is happy and loving and her children will always adore her. People trust her easily and she has friends all over the world. One could live a far less fulfilling life, whether or not one believes in God.

Anyway, I'm rambling . . . which happens when I drink :-).
Comment by Atheist Exile on October 6, 2010 at 8:42am
Hi goodthink,

Yes, you're right. I was only suggesting some likely responses that a true believer might proffer.
Comment by goodthink on October 6, 2010 at 3:09am
@free thinker

I know Xeno's Dichotomy is flawed, which is why I didn't get into the the specific details of Paradox and focused only on 1 element the Paradox highlights.

As for other gods and one god, the probability of 1 god is the same for 10 billion in the absence of evidence. It wouldn't matter if the person assert their god was the only one, since that is special pleading. Unless they can prove their god is the one and only god, you have to consider all gods equally. Thus, Xeno's Wagers. You quickly approach 1, meaning absolute probability there is no god. The only defense against this, is for the the apologist to prove their god exists and that it is somehow more probable than others.
Comment by Jo Jerome on October 6, 2010 at 12:31am
I've pointed this out many a time when confronted with Pascal's Wager. (By the way; I've yet to have a Theist confront me with this defense and actually know that it has a name - Pascal's Wager. Anyway...)

I'll point out that it's closer to a lottery gamble. Consider all the gods, all the denominations of various religions, and it's million/billion to one odds of getting it right.

The theist, sometimes after a lot of stuttering and grasping at straws, will often come back with saying God isn't that picky - as long as you believe in "something" and will give broader parameters. Anything from "So long as you're one of the Protestant denominations" up to any belief in higher deity.

My comeback to that is if God is that liberal/forgiving of my getting the details wrong, then God surely won't mind if I fail to believe altogether.

I'll also point out that Atheists have far greater "faith" in this context. The point of Pascal's Wager is to hedge your bets. Like the lottery: You can't win if you don't play. You can't go to heaven if you don't believe in something. Ergo, we Atheists are "betting" our eternal souls that there is no god(s) to the point of not taking the bet at all.
Comment by Atheist Exile on October 5, 2010 at 11:53pm
Hi goodthink,

A true believer might argue that god(s) that don't actually exist are irrelevant. Additionally, there can only be one Creator. This presumes their God exists and, probably, is the only one they will admit exists. Statistically diminishing returns would apply equally well to their God's existence as well as to their God's non-existence . . . canceling each other out. That leaves us at square one: either God exists or he doesn't.

Another point would be that Xeno's wager is obviously flawed . . . something you can confirm, personally, if you've ever overshot your destination. Ever been absorbed in thought and walk right past your destination?

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