Mathematical justification for Atheism

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Mathematical justification for Atheism

Postby eebamxela » Thu Aug 09, 2007 2:11 pm

We've all been through the Pascal's wager discussions. How you gatta accept the 50/50 chance, yet side with one just because the outcome would be better, yada yada yada. I won't get into that.

Image

This is how the wager is portrayed. Pretty straight forward. If your goal is to go with what is right, and since neither side can be proven, then really you should go for believing that there is a god right? Heaven sounds like a nice place.

But of course this assumes that there is only one god to believe in. Theists seem to think that it is possible to choose between yes-god and no-god, but not possible to choose between godA and godB and godC. Given the miriad of religions and ideas of various gods, there is necessarily at least one party who is wrong.

Because it is a binary reality (either there is a god or there is not) and also since neither option can be proven true or false by any means, it is necessary to maintain 50/50 proportions for the probability of yes-god and no-god. However, the "yes-god" part is where the shit hits the fan. Pascal's Wager does not account for the different types of gods. This is what I think it really should look like:

Image

Seems to me that this would be a dead give away for those middle of the road people. If you really want to base your decision on what's most likely, how is it that you justify going with GodA? It's slice of pie is so tiny. In fact the slices on the right should be infinitesimal, given the ability to instantly claim the existence of an entire "new" god.

Is my logic sound? If a middle of the road person saw this what would they say to it? Help me hone my thought processes here.
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Postby Sans_Deity » Thu Aug 09, 2007 3:53 pm

Don't get me wrong, I like what you've done here and I think it could prove useful...but Pascal's wager (to my understanding) has nothing to do with the probability of a god existing.

The wager is basically a cost/benefit analysis that presumes that one should believe in a god - no matter how unlikely its existence is - because the risk of not believing makes disbelief too risk (or because the reward for believing makes belief the best choice).

Someone arguing Pascal's wager might try to claim that a .0001% chance at eternal bliss is enough to justify belief. Scott Adams, creator of Dilbert and certifiable nutjob, made a similar argument last week.
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Postby eebamxela » Thu Aug 09, 2007 4:41 pm

Yeah I guess the use of pascal's wager in lieu of probability is not the best way to go. But how do we convince the masses to take pride in embracing reality over fantasy? That's the ultimate question. And the answer better not be "42".

I can't think of any other way to bring this argument down to a level that most can understand without using something that people have heard before like PW. Is there any other way that this idea can be better expressed?
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Postby Marathon » Thu Aug 09, 2007 11:19 pm

One way I think you could present this argument would be to equate it to flipping a coin. People mistakenly think of it as on one side of the coin, god exists and on the other he does not.

In reality it should be more like the roll of a dice (of if you are really nerdy a d20, or a d1000+ if you take into account all the gods) where each side represents a different god.

Of course that would seem to legitimize the idea of god, but it would mainly indicate that it's just as probable that Zeus or Odin exist as does the Christian god.
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Postby imperium2000 » Fri Aug 10, 2007 12:26 am

Pascal's Wager is inherently about weighing cost and benefit. It is the assumption by the theist that the benefit of eternal life in heaven is infinitely more beneficial then an eternity in hell. This is essentially a false dichotomy since it assumes:

God Exist, Heaven Exist, Merely believing leads to Heaven, No other religion is true, a false belief is not harmful etc.
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Postby Whosawhatsis » Sat Aug 11, 2007 5:51 am

People assume that even if there's a 50% chance of a god, that god must resemble the god of some religion. It's tempting to divide the god side according to the world's religions, or even the individual (and unique!) concepts of god that each believer holds, but without consistent revelation, these gods are no more likely than any other conceivable gods. Herein lies, I believe, the real achilles heel of Pascal's Wager.

Let's assume that there is a god that is aware of you, gives a damn about what you believe, and will punish you for believing the wrong things. The probability of this is already far below 50%, but for the sake of argument, we'll assume that these are necessary properties of a god, and that deism and the like fall into the no-god side of the equation. This god is at least as likely to value skepticism and evidence-based belief as blind faith. Add the fact that if there is a god, it goes to great lengths to hide its presence (as evidenced by the fact that we have to ask the question), and the benefit of pleasing the skepticism god is better than that of the faith god, as the latter would obviously be a sadistic psychopath. In fact, in the watered-down theologies in which the punishment is only annihilation or separation from the god, I'd say that the punishment is better than the reward.

When you look at it this way, the greatest benefit possible comes from pleasing a god that values skepticism. Skepticism also offers the greatest chance of a benefit because you would have a roughly 75% chance of either being right or being wrong but gaining the favor of a god that values skepticism, therefore skepticism is the only logical choice.

You've inspired me to go into this issue a bit more in-depth in my blog, including a quick refutation of Scott Adams' objection (Adams, BTW, is at worst a pantheist, and says some stupid things that he doesn't believe in his otherwise enjoyable blog just to "make the monkeys dance").
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Postby eebamxela » Sat Oct 27, 2007 5:15 am

I came up with a good analogy that can justify why when it comes to PW you might as well not believe in god.

Believing in god for the sake of being right to reap the benefits is kinda like playing the lottery.

You have two options: buy a ticket, or don't buy a ticket. If you do not buy a ticket you are guaranteed to not win. If you buy a ticket your chances of winning increase from zero to some value greater than zero. However because there is only one correct combination of numbers, and because there are a LARGE number of incorrect combination of numbers, statistically speaking you probably will not win. If you probably will not win, you might as well not even buy a ticket.

Some might argue that if the lottery were free that you should go ahead and get a ticket and play. But the lottery is not free. Since it is a business it requires a renewable source of money to fund the jackpots (and in florida at least, my tuition at my college).

Some might also argue that believing in a deity costs nothing so you might as well do it. Well, thats not exactly free either. Making a conscious effort to accept an idea as true costs something. Mainly time and brainpower (sometimes even money). It is rational to spend time and energy on the things that have been cut the thinnest by Occam's razor.
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Re: Mathematical justification for Atheism

Postby Carneades » Sat Oct 27, 2007 6:37 am

eebamxela wrote:Is my logic sound? If a middle of the road person saw this what would they say to it? Help me hone my thought processes here.


Well your logic isn't really sound. Perhaps I can explain the problem most easily through a counterexample. Imagine that a Christian considers the question by saying...

"Either the Christian God exists or He doesn't so I assign a 50% probability to each possibility. But in the event that the Christian God doesn't exist, atheism isn't the only possible winner. The Hindu gods could be the real rulers of the universe, or the Greek gods, or the Mormon God, etc. So atheism ends up as one infinitesimally thin slice of the pie while the Christian God still has half the pie. Obviously any sensible person can see that their best chance of being right is to bet on the Christian God."

A Muslim could make the same sort of argument to support his religion, as could a Hindu, a Jew, a wiccan, etc. So your approach doesn't really help us to determine the likelihood of any particular position being true.
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Re: Mathematical justification for Atheism

Postby Whosawhatsis » Sat Oct 27, 2007 4:09 pm

Carneades wrote:"Either the Christian God exists or He doesn't so I assign a 50% probability to each possibility. But in the event that the Christian God doesn't exist, atheism isn't the only possible winner. The Hindu gods could be the real rulers of the universe, or the Greek gods, or the Mormon God, etc. So atheism ends up as one infinitesimally thin slice of the pie while the Christian God still has half the pie. Obviously any sensible person can see that their best chance of being right is to bet on the Christian God."

A Muslim could make the same sort of argument to support his religion, as could a Hindu, a Jew, a wiccan, etc. So your approach doesn't really help us to determine the likelihood of any particular position being true.

The second paragraph of that paragraph answers the first. Without consistent revelation, we have no way to say that any internally-consistent concept of god is appreciably more likely than any other, therefore any specific concept of god has a negligible probability of being correct.

I think it's perfectly fair to assume that atheism has at least a 50% chance of being correct, but the argument doesn't stand or fall on that point. Because a god is as likely to value honest inquiry (and really, any number of other things) over blind faith in the correct god (out of an infinite number of possibilities), honest inquiry is infinitely more likely to be the correct course of action, even if atheism is not considered to be any more likely than any specific god belief.

How about this to demonstrate the idea:

"All hail the god who rewards logic, scientific inquiry, and intellectual honesty; punishes faith; and whose favorite number is -1,370,863,452.38500042! All other gods, including one with the same values for every other possible favorite number, are false!"

I have just posited an infinite number of conceivable gods who punish faith and reward atheistic values, each of which each of which is just as likely to be the one true god as any of the gods that reward faith. Without solid evidence, the probability of a god that values faith can never exceed 50% minus half of whatever probability is assigned to the possibility that there is no god. As long the latter probability is non-zero, the atheistic values are at least infinitesimally more likely to be better than faith, therefore faith cannot be the logical choice.
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Postby donnyton » Sat Oct 27, 2007 8:02 pm

Suppose you went to the store and asked for a lottery ticket, and the cashier hands you a ticket for "Christianity #2098". The ticket costs all of your life savings.


You: "How much do I win if my ticket is the winning ticket?"
Cashier: "I'm not sure, but it must be really great. You are paying your life's savings, after all!"

"Has anyone actually won this lottery before?"
"On I'm sure people have! Not that I actually know of, but there must have been SOMEBODY that got lucky!"

"Who pays the prize to me?"
"That company that manages all the lotteries."

"What's the company's name?"
"They've changed it from Yahweh to Jehovah to Lord to Jesus. I'm not sure what they are today."

"How do I know this company exists?"
"Just read the back of the ticket! It's right there in the rules."

"When will the drawings occur?"
"Could occur at any time, really."

"Who do I go to if I've won?"
"Don't worry, the prize will come to you!"


If you add up the probabilities of all these ridiculous claims, you eventually come to a pie chart with the lottery even existing taking up half the chart, and your individual ticket taking up an insignificant point. Which sums up the problem with Pascal's wager: it's not a 1/2 chance of winning the God lottery. It's a 1/infinity chance.
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Postby bugsoup » Sat Oct 27, 2007 10:45 pm

Russell recently discussed the long list of assumptions one must make to continue belief in a god. What if this idea was applied to the mathematical proof? For instance, suppose for every assumption there exists two possibilities. Namely true or false.

1) an omnipotent god

2) an omnibenevolent god

3) an omniscient god

4) ...

Granted these chances might not actually be 50/50 but I'm being generous and simplistic to start with. Now for every set of assumptions you make, you must compound the value of all chances. So, if you want to claim 1 and 2 are true, then your overall chance of that particular god existing is 25%. (50% of 50%). Now, if any one of your assumptions contradict another, you immediately have a 0% chance. If you picked 1, 2, and 3, then you do have a 0% chance.

Continue this "compound likelihood" calculation for every assumption. If you think your god wants us to be happy and be 1 and 2, then you are 12.5% likely to be correct. Note that since the actual existence isn't provable, this isn't included in the 50/50 list. This calculation is used to determine how likely it is that your particular version of god is true. Any time one of your assumptions can be verified, it's probability becomes 100% and the conversely false option is 0%.

What do you guys think of this?
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Postby donnyton » Sun Oct 28, 2007 12:39 am

Well if you want to go at it that way, you could continue...

God is omniscient?

- God knows what I ate for dinner last night? 50%
- God knows what I will eat tonight? 50%
- God knows how often I clip my toenails? 50%
- God knows if he can make a rock so big he can't lift it? 50%
etc.

God is omnipotent?

- God can smite people at will?
- God created the earth?
- And the stars?
- And dark matter?
- And neutrinos?
- And black holes?


The probabilities just get ridiculous.
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limited by presumptions

Postby eFree » Mon Dec 03, 2007 10:18 pm

People seem to never ask if this 'wager' had any impact on Pascal's faith. I would take a wager against his 'faith' being influenced by his 'wager'--James 'will to believe' has a good analysis of this.

As well, few seem to question the premise. As you wrote:
Sans_Deity wrote:The wager is basically a cost/benefit analysis that presumes that one should believe in a god - no matter how unlikely its existence is - because the risk of not believing makes disbelief too risk (or because the reward for believing makes belief the best choice)..

Why presume eternal life hinges on 'belief' any more than presuming eternal life hinges on being smart enough to figure out holy books are crap?

Sans_Deity wrote:Someone arguing Pascal's wager might try to claim that a .0001% chance at eternal bliss is enough to justify belief. Scott Adams, creator of Dilbert and certifiable nutjob, made a similar argument last week.


This uncovers another implied presumption, that belief 'benefits' one on earth even if wrong about eternal life (more moral, happier, etc.) Most who have 'faith' take this for granted. Undoubtedly, for some imaginary friends are fun
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Postby eebamxela » Wed Mar 26, 2008 7:36 am

bugsoup wrote:Russell recently discussed the long list of assumptions one must make to continue belief in a god. What if this idea was applied to the mathematical proof? For instance, suppose for every assumption there exists two possibilities. Namely true or false.
1) an omnipotent god
2) an omnibenevolent god
3) an omniscient god
4) ...
Granted these chances might not actually be 50/50 but I'm being generous and simplistic to start with. Now for every set of assumptions you make, you must compound the value of all chances. So, if you want to claim 1 and 2 are true, then your overall chance of that particular god existing is 25%. (50% of 50%). Now, if any one of your assumptions contradict another, you immediately have a 0% chance. If you picked 1, 2, and 3, then you do have a 0% chance.

Continue this "compound likelihood" calculation for every assumption. If you think your god wants us to be happy and be 1 and 2, then you are 12.5% likely to be correct. Note that since the actual existence isn't provable, this isn't included in the 50/50 list. This calculation is used to determine how likely it is that your particular version of god is true. Any time one of your assumptions can be verified, it's probability becomes 100% and the conversely false option is 0%.

What do you guys think of this?


I missed this reply the first time around.

I like your approach to the whole thing but its not quite the direction i was going in. If the assumption was made that "a god exists", and no matter where you are on the pie theres a god there, then the only attribute that matters is whether or not the god wants you to believe that he gives a shit about what you do.

If you call into question benevolance and presence, those are only different versions of the god and have no bearing on what will happen to you when you die (for the most part).

Omnipresent? Don't know? 50% that you'll pick the right one.
Omnibenevolant? don't know? 25% that you'll pick the right one.
Omnipresent? 12.5%
Male? 6.25%
Of humanoid form? 3.125%
All Just? 1.5625%
Yada? .781%
Yada? .39%
Yada? .195%
Blah? .097%
Blah? .0488%
Blah? .0244%
ad infinitum... ad nausium... ad bullshitium...

All of these sorts of traits are meaningless to the individual human, compared to the one trait i left off the list. The odds that you will pick the right set of attributes that accurately describe the god are 0%. Theres only one trait that really affects a person (eg, where they will go when they die), and thats whether or not he will punish or reward you for your various deeds, actions, or thoughts. And since you don't know, its 50%. So you better follow the rules regardless of whether or not god is a douche bag, or if he's the greatest role model of all time. (Keep in mind that this was assuming that there is a god).

<rant_mode>
This is why I get frustrated with people's use of the "problem of evil" to talk about why they think god doesn't exist. Yes there is this alleged "evil" in the world, however it is not a valid point to make against god's existence because A) you don't know if he exists for one thing and B) if he does exits.... get the fuck over it, he's evil AND he exists. Theres nothing you can do about it. Your disapproval of a behavior of a deity doesn't have anything to do with the probability of the god's existence. If you say "i can't believe a god would do such evil things, therefore I'm an atheist" thats a pretty lame way to go.
</rant_mode>

As far as that excel pie chart goes, I meant for it to be used in a Yahweh v. Zeus v. FSM v. Isis v. A, B, C, etc, versus "none exist". However all those minor attributes (the "omni-" ones) only decrease the size of each pie slice.

The one thing that concerned me the most about this argument for believing that no god exists, was how big to make the "none exist" slice. Regardless of how big the "none exist" slice goes, it still holds that the other slices are infinitely small, therefore all still have a probability of 0%. The only reason there's a pie in the first place is because someone came along and said "there's a god" and immediately would have had to show how likely they were to be true.

Seeing as how there is nor ever was a reason to have sliced the pie in the first place, i would argue that its an almost 100% (if not exact) probability that there is no god. The reason for making the yes/no possibility a 50/50 odds thing was actually not founded upon anything but straight up compromise with theistic thought, just to simplify things and get the ball started on the argument. The more I think about it, the more comfortable I get in saying that there are no gods, as opposed to saying that there probably are no gods.

How big do you think the "none exist" slice should be?
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Postby dromedaryhump1 » Wed Mar 26, 2008 2:32 pm

eebam , I think your original pie chart with the multiple gods made a very important point, which denegrates if not invalidates Pascal's Wager.

If there are an infinite number of possible God's to worship, then the likelyhood of worshipping the wrong god exponentially increases your chances of damnation.

I propose that an omnicient, omni-benevolent being would be more lilkely to prefer to have its creations remain "uncommitted" than to invest their praise and worship in a false god. Thus, rejecting all gods/ not worshipping any god , can be as likely, or better, a path to "salvation" than any one god choice.

Homer Simpson said it best: "But Marge, what if we chose the wrong religion? Each week we just make God madder and madder."
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