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Pascal's Wager
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PostPosted: Mon Mar 09, 2009 4:00 pm    Post subject: Pascal's Wager Reply with quote

The conversation regarding Pascal's wager in the "proof of God" thread has become a little fragmented and messy, so I'm going to reply in general and in a new topic rather than quoting specifics. (It's also straying off topic, because Pascal's wager is not a proof of God.)

The first thing I'd like to emphasise is that Pascal's wager is a wager between two specific conflicting lifestyle alternatives and their underlying rationales, not a general evaluation of all possible alternatives. Thus, we pose the choice between philosophical atheism, being the pursuit of life without deference to a divine authority or belief in an afterlife, and a generic monotheism which includes a God and heaven for those who act appropriately. Thus, "atheism" incorporates more specific outlooks like secular humanism, scientific rationalism, hedonism (so long as it is devoid of an afterlife), and even Buddhism. Monotheism as formulated covers obvious alternatives like Christianity, Judaism, Islam, and Mormonism. I think it's uncontroversial that these categories are mutually exclusive, but not comprehensive: you can be in one or the other, or something else entirely, but not in both.

To the extent that it's been discussed in the "proof of God" thread, we've had disagreement over some of the numbers, but there's general consensus that an eternal life of good quality is infinite in value compared to a finite life (of any quality). This is pretty straightforwardly mathematical in nature: it just results from an eternal life being infinite. We assume that the "heaven" of our generic monotheism alternative incorporates eternal life of good quality, and thus offers a technically infinite reward. Fill in the other blanks as you will with finite numbers.

There's a little bit of disagreement as to whether it's a good idea to maximise your expected gains. The general vibe I'm getting is that it's wise to maximise your own happiness if atheism is true, but somehow unacceptable to be so self serving if there's a God who offers a reward of eternal life. I'm not sure how to address this objection other than to dodge it by definition: let us suppose that the God of our generic monotheism does not reward those with "bad motives" (for some value of that term). Let us suppose that it's fair to choose the generic monotheism over atheism purely on the basis of rational costs/benefits analysis, but that the actual process of gaining the reward of eternal life filters out those of impure motives. The important thing to note here is that the reward is a goal one chooses to pursue, not simply a matter of saying "monotheism, I choose you" and thereby obtaining a pass to heaven. This actually applies to atheism just as much as it does to monotheism: an atheist doesn't automatically get a better life just for choosing to disbelieve in all things supernatural -- it's just a framework for how he conducts his affairs; part of a larger set of values. A choice to be atheist or monotheist will have implications for how one conducts oneself, but does not guarantee results in and of itself.

Bear in mind also that the wager is presented to those who claim to be agnostic, professing that the factual claims made by both alternatives are possible, and that we do not know with certainty where the truth lies. Uncertainty as to which framework offers true beliefs (if any) is key to the wager: if you assign a probability of zero to either one, then this discussion is not for you. For the sake of simplicity, however, we're only considering the two possibilities of atheism and generic monotheism relative to each other, not relative to every other possibility. This is simple enough to do, mathematically speaking, so long as the two probabilities in question are both non-zero. Think of this comparison as an elimination match: we're pitting these two lifestyles against each other first, to see if we can eliminate one as not rationally viable. The winner can take on the rest later if needs be.

There's one last thing to consider: the mathematics of expected outcomes. This is where Pascal was rather well placed to pose the problem, being a bit of a probability and games-of-chance buff. Cutting to the chase, we need to multiply the possible winnings by the chances of success. Let's go a step further and be a little more realistic about our expected winnings, since we've already admitted that simply choosing the option with the correct general assumptions isn't enough: if you're right about atheism, you still have to work at having a good life, and if you're right about theism, you still have to work at doing whatever it is that God requires. Each of the two options thus has three relevant factors: the relative probability (of the two mutually exclusive factual frameworks underlying theism and atheism), the value of the potential reward (given the truth of the alternative), and the degree or likelihood of success in pursuing the reward (given an attempt to do so).

For those who are inclined to the use of formal symbols, let us use the subscripts "a" and "m" to denote atheism and monotheism, with "P" to denote the (subjective) probability that the alternative is factually accurate (whether God exists and offers a heaven), "S" to denote the expected chances or degree of success in pursuing the goal (given the truth of the associated beliefs), "V" to denote the ideal value of the option (the possible reward), and "E" to denote the expected value (computed from the other elements). We then formalise the earlier remarks with Ex = Px * Sx * Vx, and note that Pa + Pm = 1, while Sx is between zero and one inclusive, being a measure of probability or degree. We also note that Vm has been generally regarded as infinite (eternal life), whereas Va is finite.

To be thorough, we should also consider expected values for each alternative when the associated beliefs are false (e.g. the expected value of monotheism given the truth of atheism, and vice versa), but let's leave that aside for the moment because there is a dominant feature in this picture which deserves our immediate attention. Vm, the possible reward for believing in God (eternal life), completely dominates the show because it is infinite. As a consequence of this, Em, the expected value of pursuing monotheism, is also infinite unless Pm and/or Sm are zero. Pm is only zero if you are quite certain (for whatever reason) that monotheism is false, and if that is true of you, then you're not agnostic in the sense that is required for this wager to be of relevance to you. Sm is only zero if you are certain that the terms and conditions for achieving eternal life are impossible (for you, at least).

Or, in plain English, if you grant the possibility that there might be a heaven and you might be able to get there, you'd be nuts not to try.

I'm not a great believer in the powers of human reasoning in general, but I'm still struck by the number of professing agnostics who are "atheist" in practice, given this evaluation of the situation. How can one believe that there is a possible infinite reward in monotheism, yet spurn it in practice for the finite reward of atheism? It doesn't add up! A purely rational analysis of the situation should provide compelling reason for any professing agnostic to get busy with the study of religion like it's a hunt for the mother of all treasures. Yet what do we see in actual practice? Apathetic agnostics: agnostics who claim not to know and seem not to care. Why is this?

Maybe it stems from our complete non-appreciation of infinite values -- values too big to comprehend. While that's at least plausible, I doubt this explanation: I think that the results would still be the same if Em were finite in value (but still conspicuously larger than Ea). I mean, would people be more likely to pursue the monotheism path if the promise were not "eternal life in paradise", but an ephemeral heaven where you got to live for a thousand years in extreme luxury? I'm not convinced.

I can, however, think of another factor which may be sneaking into the equation here. Monotheism entails the recognition that there is a Higher Authority, and the ostensibly infinite value of eternal life is tainted by the fact that it's eternal life under God. If atheism has something to offer, it's the kind of freedom which can claim "nobody is my boss". Atheism offers autonomy. So my best theory as to why people would profess the uncertainty of agnosticism yet be outwardly atheist rather than pursue monotheism is this: they place infinite value on their independence from God. It's their way of saying, "better a finite life under my own rule than eternity under God's."

To me, that particular insight explains a lot. It makes apathetic agnosticism ("don't know and don't care") that much more comprehensible from a purely rational perspective. If a person really does hold an attitude of "better a finite life under my own rule than eternity under God's", then a "don't know, don't care" attitude towards God's existence is perfectly reasonable because such a person is simply not interested in what God has to offer, infinite though it may be.

I'm particularly interested in hearing from "effectively atheist" agnostics as to whether there's anything in my evaluation of expected outcomes here, or whether I've missed some other consideration. How do you justify your lack of religious pursuits, given Pascal's analysis? Please bear in mind that we are posing a choice between two alternatives here: many other alternatives may exist, but they aren't factors in the choice between these two alternatives, so they aren't relevant to this discussion.
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lacavin
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PostPosted: Mon Mar 09, 2009 9:26 pm    Post subject: Reply with quote

I will not repeat here all the arguments presented in the other thread.

I just want to explain why in my opinion Pascal's wager is not of any help to choose a philosophy of life, even if it is a very nice theoretical construct - it was an incredible think to write this at that time; probabilities were new, infinity in mathematics was pretty new, applying such type of reasoning to philosophical questions... So my comments do not in anyway belittle the wonderful work of Pascal (I advise to read his "Pensées").

The basic assumptions of Pascal are (perhaps among others), the following:
  1. Pascal's wager target audience are rational humans with free-will. Rational, because they can understand such a wager and act based on it, with free-will because the assumption is that humans can choose how they live their life.
  2. The wager should help you choose to be monotheist or not. The assumption is hence that it is possible to choose to be monotheist. Because we are rational, however, we cannot believe in something without supporting evidence. In the absence of evidence, I can not choose to become monotheist - I just don't believe it! I can only choose to act as if I were a believer (go to church, obey the rules, ...); I agree with TFBW that pretending has few chances to open the door of Heaven.
  3. The wager assumes certain hypothesis with regards to the action of God. First that there is an infinite "good" afterlife. It assumes also for instance that "believing" increases your chance to this infinite paradise - i.e. that God judges according to philosophical belief. These assumptions are not universal among monotheist religion - why should they be true. Even within Christianity: Calvinist say that the Grace is foreordained by God and fully independent of your belief or behavior. Mormon think that you can be saved after death - you get another chance. And so on.
  4. Of course, mostly due to the century when Pascal was active, he thinks only to christianity. I do not agree with TFBW that the fact that there are alternatives is not important. Alternative religions may have incompatible rules (that these rules are made by God or by the men managing the religion is not important). Muslims should not drink alcohol, Christians should during the Holy meal. Catholics say women cannot make sacraments, Protestants have female priest (and hence according to catholic views invalid sacraments - e.g. you are not married, pal, but you live in sin). So which rules should you bow to to get closer to God?

Pascal actually more or less agrees with (b) above, I let you savor a citation (english translation from Wikipedia): "Follow the way [...] by acting as if they believed, bless yourself with holy water, have Masses said, and so on; by a simple and natural process this will make you believe, and will dull you—will quiet your proudly critical intellect...". So Pascal actually means you should be rational enough to understand the wager, and henceforth try to dull your spirit to make you believe. Interesting. Does it work like this and you become dumb when visiting churches? From the (mostly calvinist) priests and even one catholic bishop I know (most very intelligent and sharp people) I doubt it...

At this point the use of drugs may be safer than going to church to dull your critical intellect. Because as a non-believer, by the way, in which church are you going? As only one is probably true (is God schizophrenic?), that means the "rules" of the others may be untrue (incompatible with the true rules) and may not bring you closer, but further, to God...

Therefore my main complain to Pascal's wager is that it does not help to decide, because first it is not really a decision you can take. Secondly, everybody can put other expected values according to his opinion, having different views on those critical assumptions above. Finally, it would not help you to choose the "right" church or to select between different, incompatible, ways of live anyway because of the many competing theologies which you cannot discriminate as an unbeliever.
I would also add another critic: I personally dislike the use of infinity. It is always dangerous. The exampe from Bezman is a good illustration: if there is a non-zero probability that e.g. paradise gets boring over time, the infinite expected values can quickly become negative (i.e. paradise = hell).


As a side note using TFBW notation (personal opinion): as long as I don't believe, I consider Sm to be equal to zero (or more precisely, I consider that the chances of being "saved" are equal whether you live without religious rules or whether you pretend to believe and go to church) because I cannot choose to believe and hence cannot be judge culprit by a benevolent God for this unbelief; hence my best bet is to have the best possible lifetime - assuming this philosophical choice makes a difference, for instance that atheism is better because it has less constraints.

As soon as God provides Faith or sufficient evidence, being not anymore an agnostic, I don't need the wager. And then it's obvious that I better be friendly with the most powerful guy in the universe, isn't it?
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Bezman
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PostPosted: Tue Mar 10, 2009 2:11 pm    Post subject: Reply with quote

Nice equation, but I would like to object to it. However, there were so many algebraic variables that I choose to leave them out.

If there is an afterlife, then the "maximum value" is infinity times x.
IF there is NO such afterlife, then the maximum value is 1 in your equation.

I think that is wrong. If there is no afterlife, then you may just as well put the maximum value as infinity times x, since it is equal in value - the alternative is infinity times zero = ZERO. And there are no values higher than 1, so it is technically comparable to infinity in that scenario.

That would also answer your question of why apathetic agnostics act like they do - I think the mind works to get "an as high PERCENTAGE of the maximum possible value available". If I disregard this life in pursue of a non-existent afterlife, ie get a low percentage of it, I lose out on the maximum value. If I have even the slightest chance of getting a piece of the afterlife - well, then the percentage I put into it really doesn't matter... (i.e. since it will be multiplied by infinity anyways).

I don't know if I made my theory clear, I feel it may be poorly explained, so please feel free to ask about the parts that are obscure/garbled/unclear.
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PostPosted: Tue Mar 10, 2009 2:24 pm    Post subject: Reply with quote

Another thing that disqualifies the "infinity" as a likely part of the equation is this;

Will there be different qualities of life in the afterlife?
Because when it all adds up, or rather multiplies up - with infinity - even a lousy afterlife value of 0.000001 will be equal with one of value 0.99999...

Therefore I think you must add in "expected quality of afterlife" in the equation to get a more reasonable value of the afterlife instead of (1 times) infinity. That will also help explain why people forsake it.
If they expect the value of afterlife to a 4 on a scale from 1 to 10, they will go "apathetic agnostic" and pursue a 6 in "real life" instead. (And they know that they may STILL win the "4" or better in an afterlife.)
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PostPosted: Wed Mar 11, 2009 5:15 am    Post subject: Reply with quote

I'm not sure about the assumption that atheists are generally happier in this life. Are they?
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lacavin
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PostPosted: Wed Mar 11, 2009 8:27 am    Post subject: Reply with quote

Bezman wrote:
If there is an afterlife, then the "maximum value" is infinity times x.
IF there is NO such afterlife, then the maximum value is 1 in your equation.

I think that is wrong.
I think this is right - because whatever the reality is, it is better to have an infinite afterlife of hapiness then to have no afterlife at all. So it is correct to say that we should hope that there is a God that provides an infinite afterlife of hapiness, because it dominates the absence of God in terms of expectations. However, we cannot control this, of course.

The "quality" of afterlife in your second post is correct if you assume that maximum value is 1 both for scenarios with and without afterlife. As I mentionned above, I don't think so, so I don't agree.

John Theta wrote:
I'm not sure about the assumption that atheists are generally happier in this life. Are they?
This is based on the fact that if you want to maximize your chances for the afterlife, you have to bend to external rules of religion, so you have less freedom to pursue your own hapiness. This does not mean you become unhappy, but you can less maximize, so potentially are less happy.

Let me give an illustrative example. Suppose your religion say you should go to church every Sunday at 10am. You have probably fun in church, but sometimes - when you had a nice party on Saturday - you don't really want to be up and going so early.

If you follow Pascal's wager, you should always go to church on sunday, because you maximize your chances for the infinite reward. But the other hand of the alternative is going to church when you want it (we assumed it to be "fun", at least because of the contacts in the community), so if the desire of sleeping longer is stronger than the desire of visiting church, you just keep sleeping. This being your choice, it makes your temporal life better.

What this does not mean is that you must be unhappy when you target at salvation! And this does not mean that being unflexibly atheist is better (you loose the "fun" part of going to church).

In my case, for instance, I go sometimes (rarely) to church - to participate in important moments of the community (baptisms, weddings, burials), enjoy the music, or even enjoy the preaches (in my native place (not where I live now) we have an excellent priest with very good theological knowledge and the capacity to explain it clearly). But when I don't want to, I don't go. So I maximize my "happiness" by doing what I want.
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TFBW
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PostPosted: Wed Mar 11, 2009 3:54 pm    Post subject: Reply with quote

I see that nobody is in a hurry to espouse my "better a finite life under my own rule than eternity under God's" line of thinking -- so far, at least. Nor is anyone professing to misunderstand infinite reward. There's still a little bit of smoke being blown around, though, and I'll need to clear the air again.

Once again, I must stress that Pascal's Wager is a two way bet. You might even call it Pascal's Razor: it gives you a rational way to compare two alternatives and decide which of them you prefer over the other. There may be a very large number of possibilities, but in order to apply Pascal's Razor (if I may use the term), you need to pair them off against each other rather than considering all of them at once. Well, you don't strictly need to pair them off, mathematically speaking, but it's highly advisable from a complexity management perspective. Even if we are modestly rational beings, we tend to get befuddled when confronted with too much information. We learn in school how to multiply large numbers together by breaking it into small steps: this is the same kind of idea.

The next thing that I must reiterate is that you should pair off two things which you believe to be possible. Specifically, pair off your most plausible evaluation of "there is no afterlife" against your most plausible evaluation of "there is an afterlife". You should consider the afterlife scenario to be both possible and attainable. There's no point in considering options which certainly don't exist or certainly aren't reachable, since these have no value, and there's no point introducing an alternative with no value.

It's also preferable that the alternative require some kind of specific difference in action on your part, since the wager is pointless if there's no difference in conduct between the two alternatives. It's fair to say, "I think it probable that there's no afterlife, but my second most likely alternative is that everyone goes to heaven," but it renders the Razor irrelevant, since there's no question of how one conducts oneself. It's a valid stance, and something of a trump card against Pascal's Wager -- does anyone want to sincerely claim it as their excuse? We can always have a separate argument over whether this kind of heaven is a reasonable thing in which to believe.

If application of the Razor persuades you that the afterlife is worth pursuing, you will then face another problem: you need to choose which of several possible mutually exclusive afterlife scenarios is correct, given what you know. That's a totally separate discussion, however, so I'll ignore it completely here and now.

Now, on to specific responses.

lacavin wrote:
The wager should help you choose to be monotheist or not. The assumption is hence that it is possible to choose to be monotheist. Because we are rational, however, we cannot believe in something without supporting evidence. In the absence of evidence, I can not choose to become monotheist - I just don't believe it! I can only choose to act as if I were a believer (go to church, obey the rules, ...); I agree with TFBW that pretending has few chances to open the door of Heaven.

I'm still a little confused by this line of reasoning. If the evidence precluded belief in a God, then you'd call yourself an atheist, such that Pa = 1, Pm = 0. This isn't the case, though, is it? Therefore there must be some favourable or at least compatible evidence. You speak as though your mind is a scale that tips one way or the other based purely on the weight of evidence placed upon it. That is not a reasoning mind: beliefs and evidence are complex interwoven things which influence each other. We influence our beliefs by who we choose to listen to, where we invest our thoughts. This is why Pascal prescribes Christian activity for the doubter, as you noted...

lacavin wrote:
"Follow the way [...] by acting as if they believed, bless yourself with holy water, have Masses said, and so on; by a simple and natural process this will make you believe, and will dull you—will quiet your proudly critical intellect...". So Pascal actually means you should be rational enough to understand the wager, and henceforth try to dull your spirit to make you believe. Interesting. Does it work like this and you become dumb when visiting churches? From the (mostly calvinist) priests and even one catholic bishop I know (most very intelligent and sharp people) I doubt it...

It's not about dulling your intellect -- it's about exposing yourself to an environment which fosters the right kind of thinking. Expose yourself to intelligent and sharp believers rather than to intelligent and sharp doubters. We are influenced by our environment, and a wise person will therefore choose to dwell in an environment which is a positive influence. I go to the gym to exercise in the hope that I will improve my health and physique. I go to university to study in the hope that I will improve my mind and produce insightful ideas. Think of church along similar lines: a place to go if you want to achieve a particular personal result. If your problem is that you lack faith, where else do you think you'll get it?

lacavin wrote:
The wager assumes certain hypothesis with regards to the action of God. First that there is an infinite "good" afterlife.

The wager as originally expressed is between atheism and Christianity. It provided a certain set of parameters for that. It was never intended to present these as the only two actual alternatives: the very point of the exercise is that we don't know what the afterlife holds, so we line up those scenarios that we think are possible and evaluate them rationally. These two particular alternatives are used in the wager because they were the most relevant at the time. They are still extremely relevant, particularly to those who want to defend atheism as a rational choice.

lacavin wrote:
I do not agree with TFBW that the fact that there are alternatives is not important.

The alternatives are not important to the wager. We can evaluate things two at a time. When we are evaluating A against B, the other alternatives (C, D, E, ...) are just a distraction from the issue at hand.

lacavin wrote:
Secondly, everybody can put other expected values according to his opinion, having different views on those critical assumptions above.

Quite so, but that's a feature, not a fault. The wager helps you to act rationally on your own beliefs. It does not pretend to offer truth. If we knew the truth, there would be no need for the wager.

lacavin wrote:
I personally dislike the use of infinity. It is always dangerous.

Sometimes its usefulness outweighs its dangerousness. In any case, it's up to you to estimate a value of an afterlife. I don't insist on the use of infinity anywhere; I simply note that infinity is a good representation of eternity, and that infinity dominates the equation when present.

Bezman wrote:
If there is an afterlife, then the "maximum value" is infinity times x.
IF there is NO such afterlife, then the maximum value is 1 in your equation.

The number "one" is not mine, and I don't insist on it. You can valuate life any way you like: per day, per year, multiply by a "quality of life" factor -- whatever. I don't need you to conform to a standard of any sort, it just needs to be a numeric representation of perceived worth (like a price tag). My point with "infinity" is that an eternal life (of average quality greater than zero) is going to have infinite value if you let time be a factor in your computation.

Beyond that I can't say that I really understood your post, sorry. I'm not entirely sure I've understood the part I quoted.

Bezman wrote:
If they expect the value of afterlife to a 4 on a scale from 1 to 10, they will go "apathetic agnostic" and pursue a 6 in "real life" instead. (And they know that they may STILL win the "4" or better in an afterlife.)

You're saying that some people would prefer a short, high-quality life over a long so-so quality life? That's surprising on two levels. The first is that anyone expects an afterlife to be merely so-so. The only afterlife story I know that fits that mould involves reincarnation, and even then the supposedly wise thing to do is work off karma rather than accumulate more of it.

The other surprising thing is that anyone seriously prefers short over long. If the devil were to make you an offer -- you get to have absolutely whatever you want for one year, then you die with no afterlife -- would you think it a good offer? Suppose that you're not expecting to die soon in this scenario: you have some decades to go yet before you reach average life expectancy. Your existence for that one year would be as good as your imagination could make it. Tempted?

Not that it matters, really. If you can come up with some way to rate the alternatives, then that's all you need. If you think heaven is an eternal tent in a slum, then find some number that expresses your perception of what that's worth compared to seventy years of middle-class mediocrity in a first-world country (or whatever you expect to get out of life). Just be sure that something twice as good is double the value (and so on), otherwise the mathematics doesn't work.

John Theta wrote:
I'm not sure about the assumption that atheists are generally happier in this life. Are they?

The operative assumption, as lacavin has more or less pointed out, is that most atheists feel that their quality of life will be degraded by whatever it is God requires them to do to pursue eternal life. Whether or not that is a good assumption is open to question, but it's at least understandable. Even assuming it's perfectly true, however, it's not really relevant: heaven is supposed to massively overcompensate for this loss. Bezman seems to doubt that it will: he's heavily discounting heaven, and suggesting that maybe eternal life isn't infinitely valuable. I'm not sure if he's in earnest, or just stretching credibility in an effort to make a loophole.
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TFBW
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PostPosted: Thu Mar 12, 2009 4:43 am    Post subject: Reply with quote

It's just come to my attention that various Atheist groups, starting with the British Humanist Association (BHA), have been running an ad campaign on buses to promote the atheist lifestyle (which forms a key part of the discussion here). The original BHA bus ad said, "There's probably no God. Now stop worrying and enjoy your life."

That pretty much sums up the atheist lifestyle, doesn't it? Of course, Pascal's Wager renders this line of thinking quite dubious from a rational perspective. If there were certainly no God, or certainly no heaven, it would be a different matter. "Probably" just doesn't cut the mustard when it comes to putting eternal life at stake. That level of nuance and factual accuracy almost invariably gets lost in an ad campaign, of course, and I'm sure most of the atheists behind the campaign feel that they have a satisfactory answer to Pascal's Wager.

Even so, this has brought another aspect of the wager to my attention. The atheist lifestyle attempts to maximise the value of the here and now on the basis that it's the only life you are going to get. Thanks to the nature of time and human existence, however, this trade-off becomes progressively worse and worse. When you're young, you might feel like you have a lot to lose; if you're old or terminally ill, your potential gains from persisting in the atheist lifestyle are small at best.

The curious thing about the wager is that it's not a once and for all bet: it's a daily choice. In the game of roulette, you may continue to place bets or change bets until the croupier declares "no more bets". In the game of life, "no more bets" occurs at death. By that stage, the atheist has already won everything he can possibly win, so to persist in the atheist lifestyle right until the bitter end seems crazy.

Death isn't always something of which one receives advance notice, but sometimes it's obviously close at hand, and the probability is always climbing. Those who commit to atheism seem fairly intent to take it with them to the grave, however. How can this not be crazy?
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Bezman
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PostPosted: Thu Mar 12, 2009 4:10 pm    Post subject: Reply with quote

I think I found the flaws in the equation.

1. Give "quality of life" a value range from -1 to +1.
Also, you might want to consider the scenario if giving your current life an index value of 0 and 0.5 respectively. How will this value change if you pursue either options IRL, and how will it change in afterlife? Just assuming that it is "1.0" in an afterlife does at least not make sense to me, even if I do not exclude it from what I think is possible.
Now, don't spend too much time thinking about this one, instead read number 2 here:

2. If we should insist on using Infinity as a factor, then I personally hold that Pm is 1/Inf. (Or 10.000.000.000.000/Inf, but then we are allowing "high numbers" alongside with Infinity and 1, which I consider to be unfair - then these numbers should be allowed in both sides of the equation. So lets keep it to 1/Inf for the sake of justice.)
That gives Em = 1/Inf * Sm * Inf = 1 * 1 * (Inf/Inf(*1*1)=1) = 1
(given a maximized value of 1.0 for S)
And: Ea = (1-(1/Inf)) * Sa * 1 = 1 (too!)

Amazing? Not. Just quite logical. So the above breaks it down to what I (unknowingly) have been aiming at all the time: whether Sm or Sa are likely to be higher. And thus, the expected value of life.

I think there is one more flaw, but I have to work now, and I think the above pose more than enough to ponder about for a while.
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lacavin
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PostPosted: Thu Mar 12, 2009 4:12 pm    Post subject: Reply with quote

TFBW wrote:
You speak as though your mind is a scale that tips one way or the other based purely on the weight of evidence placed upon it. That is not a reasoning mind: beliefs and evidence are complex interwoven things which influence each other. We influence our beliefs by who we choose to listen to, where we invest our thoughts. This is why Pascal prescribes Christian activity for the doubter, as you noted...

The key point is: can you really choose to become monotheist.
My opinion is that you cannot. You need a gift from God. Either a gift of Faith, or sufficient evidence. This is an opinion shared by major theologists (e.g. Calvin), so not just an "atheist-wrongheaded-opinion".
This ends the discussion because there is no alternatives and hence no bets for unbelievers. So Pascal's wager is just irrelevant for them. Of course this does not end the discussion because you may not agree that you need God' help...
For believers, now, the situation is different, because as you believe there is a God, you can choose to honor him or not.

Whether good influance makes you more receptive to the "evidence" is possible, but anyway I repeat that you need a gift from God - He is all powerful so does not need a specific receptivity.

But OK, you are right that we are not analytical machines and that our tastes and moods color the evidence. I agree with this. But still if you assume we are rational enough to follow Pascal's Wager, then please consider us as rational enough to accept sufficient evidence of God's existence.

TFBW wrote:
I go to the gym to exercise in the hope that I will improve my health and physique. I go to university to study in the hope that I will improve my mind and produce insightful ideas. Think of church along similar lines: a place to go if you want to achieve a particular personal result. If your problem is that you lack faith, where else do you think you'll get it?

Well - I go to the gym to make sport, not to be with those people. Actually, in my case, I go to the gym to meet people and have a beer with them and funnily I keep not loosing much weight although I have lot's of good influence Rolling Eyes ...
I go to the university to study and learn. In this case, the intellectual stimulation also helps, I agree. But again the student that just hang up in the coffee-room of the campus will probably not gets his degrees because of the good influence.
All-in-all, the influence may help when you do an activity to make it better, but work is what really gets the results. In the case of belief, however, no amount of work will help - it must come from God. So I discuss with you, with priests, with religious friends, but all this good influence does not make a difference.

TFBW wrote:
lacavin wrote:
I do not agree with TFBW that the fact that there are alternatives is not important.

The alternatives are not important to the wager. We can evaluate things two at a time. When we are evaluating A against B, the other alternatives (C, D, E, ...) are just a distraction from the issue at hand.

This is just wrong. When I come at a cross-road, all the options are presented at the same time, and I have to consider them all.

What you probably mean is that first you ask the question whether you should have any religion or not, and this is Pascal's wager that forces you to go for religion. On a second turn you must choose your religion, and this is not the topic of Pascal.

Perhaps. But again the Wager suppose only 2 alternatives with given expected values. If I consider (and history, at least, shows that this view is the usual view of most churches) that follower of another religions are going straight to hell (so you kill them for their own good), I can imagine that being a honest man without religion but that tried always to investigate and get answers may just have no afterlife (if not have better chances to have the infinite reward).
In this case, the truth table is different:
Code:
                  A      B      C     None    Expected Value

Believe A        Inf   -Inf   -Inf     0        -Inf
Believe B       -Inf    Inf   -Inf     0        -Inf
Believe C       -Inf   -Inf    Inf     0        -Inf
Unbeliever        1      1      1      1          1

In this case the rational option is to be atheist.

Of course the hypothesis of an infinite hell for believer of another religion is just a hypothesis. But without proof, it is an hypothesis as good as the one from Pascal... not that I believe it, but it's also a possibility with non-
zero probability, and hence because we use infinity must be treated as seriously as any other!
So we should merge all the possible combinations of possible reactions from God...

TFBW wrote:
lacavin wrote:
Secondly, everybody can put other expected values according to his opinion, having different views on those critical assumptions above.

Quite so, but that's a feature, not a fault. The wager helps you to act rationally on your own beliefs. It does not pretend to offer truth. If we knew the truth, there would be no need for the wager.

You are joking... So we agree the wager just means that everybody is right. Wonderful and useful tool!
Because I put other expected values (see the example above) the rational act on my own belief is the opposite of yours - so one of us is wrong, so this line of reasoning can lead to wrong decisions, so it is not a good decision-making tool.

TFBW wrote:
lacavin wrote:
I personally dislike the use of infinity. It is always dangerous.

Sometimes its usefulness outweighs its dangerousness. In any case, it's up to you to estimate a value of an afterlife. I don't insist on the use of infinity anywhere; I simply note that infinity is a good representation of eternity, and that infinity dominates the equation when present.

Exactly - only infinity dominates. So you should insist on using it, because with any other value, then you would need a probability for God existence before you can compute the expected values. If the reward is not infinity the wager don't say anything.

TFBW wrote:
You're saying that some people would prefer a short, high-quality life over a long so-so quality life? [...] The other surprising thing is that anyone seriously prefers short over long.

Well, that's philosophically an option. I for one prefer drinking 1 small glass of good Whiskey than a bottle of bad one. But whiskey is not life, so... But I would not exclude this frame of mind a priori.
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PostPosted: Thu Mar 12, 2009 4:50 pm    Post subject: Reply with quote

lacavin wrote:
In this case, the truth table is different:
Code:
                  A      B      C     None    Expected Value

Believe A        Inf   -Inf   -Inf     0        -Inf
Believe B       -Inf    Inf   -Inf     0        -Inf
Believe C       -Inf   -Inf    Inf     0        -Inf
Unbeliever        1      1      1      1          1

In this case the rational option is to be atheist.

That's in fact a good point in the discussion.
(For clarity, I think it should be "Believer A/B/C" (or even "Belief A/B/C" or "Religion A/B/C" would make sense)

lacavin wrote:
...[any] follower of another religions are going straight to hell (so you kill them for their own good)

LOL, wouldn't this act send them straight to hell, and thus make you a "bad person"? Laughing
Unless your religion gives a "free pass" for this type of act, which happens to be common, unfortunately. This fact is one of the reasons that I do not confess to any particular earthly religion. What I believe about the existence of our universe, and what is "universally right", that's another story...
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PostPosted: Thu Mar 12, 2009 5:24 pm    Post subject: Reply with quote

lacavin wrote:
The key point is: can you really choose to become monotheist.
My opinion is that you cannot. You need a gift from God. Either a gift of Faith, or sufficient evidence.

Congratulations! You just proved that God exists.

Really, I'm serious.

You don't see it, do you?

Well look: I believe in God. I don't have sufficient evidence (or I would have shared it), so according to you it must be a gift of Faith from God. This is only possible if God actually exists, so my belief in God is itself irrefutable evidence that God exists!

OR, maybe people can choose to believe things after all. It's your call. The way I see it, you can either accept my proof, or give up the idea that belief requires divine intervention.

I'll reply to other points later, but I thought that this part was worth mentioning immediately. Take your time thinking about it.
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PostPosted: Thu Mar 12, 2009 8:02 pm    Post subject: Reply with quote

TFBW wrote:
lacavin wrote:
The key point is: can you really choose to become monotheist.
My opinion is that you cannot. You need a gift from God. Either a gift of Faith, or sufficient evidence.

Congratulations! You just proved that God exists.

Well look: I believe in God. I don't have sufficient evidence (or I would have shared it), so according to you it must be a gift of Faith from God. This is only possible if God actually exists, so my belief in God is itself irrefutable evidence that God exists!

OR, maybe people can choose to believe things after all. It's your call. The way I see it, you can either accept my proof, or give up the idea that belief requires divine intervention.

Touché! Smile

Even if you forget some other alternatives:
OR you are nuts, an irrational lunatic.
OR you lie to me (because I have only your word that you believe).
OR you are honest, but mistaken.
OR you are rational and correct and some divine power exist, but irrational in being christian.

So I fear this is not yet time to publish in the Acta Theologica that we did what d'Acquino could not do! Crying or Very sad

But I share somewhat you opinion; why do you think I am discussing?
* I don't believe so there is no God. End of discussion.
* Ooops... wait a minute - there are a couple of billion people that believe in God. That cannot be so easy.
* 2 options: they are all irrational lunatics or there is something behind religions.
* Billions of lunatic and just me rational Cool is possible but improbable,
* Therefore it is not the end of the discussion after all.
* Therefore I spend time (among others) on the 4th Wall!

Of course, I already mentioned that I believe in a super-natural force, which does not need to be personal.

So it may be those billions people are not fully nuts, but just exaggerating... seeing a bit more than a purely rational mind would see, because of eduction, or indoctrination, or wishes. Most of those billions certainly never thought about it, and are religious by "habit".
If education and indoctrination are responsible, that would explain why whenever "freedom" is given (no socially obligation to go to church, to follow its rules, but more important laic education), more and more people leave the historical church (and stop believing in a God such as described in the scriptures, if not atheists).

But also perhaps the existing God is personal, but don't share all the characteristics that large religions teach.

Anyway we have limited options:
  1. Billions of people are nuts,
  2. There is something (I did not write someone) out there, but it does not fulfill the job description - perhaps just impersonal, perhaps personal but not interested in us (not benevolent, no paradise); those billions people just follow the trend and after getting the proof/intuition of this something, just accept the whole menu of one of the churches,
  3. There is a God such as described in the scriptures.
And there come my "proof" - if God is like described in the scriptures, then he will give me Faith or sufficient evidence. If he does not, that means he is not like described in the scriptures. So (c) is to be considered (by me) wrong until somebody tells me that my proof is wrong and hence (c) remains a serious possibility. Note that I do not jeopardize my chances of paradise, because by not believing now, I'm still ready to fall in line if God decides to give me Faith or Proof in the future.

Between (a) and (b), well, this remains to be discussed. I think it is (b), personally.
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PostPosted: Fri Mar 13, 2009 12:56 pm    Post subject: Reply with quote

Bezman wrote:
2. If we should insist on using Infinity as a factor, then I personally hold that Pm is 1/Inf.

That gives Em = 1/Inf * Sm * Inf = 1 * 1 * (Inf/Inf(*1*1)=1) = 1
(given a maximized value of 1.0 for S)
And: Ea = (1-(1/Inf)) * Sa * 1 = 1 (too!)

Amazing? Not. Just quite logical.

If you're assigning Pm = 1/Inf, then you are as close to being a hard-core dead-certain atheist as you can be without actually being one. Your mathematics demonstrates that even under these conditions, the expected value of your net existence is the same whether you decide to pursue the atheist lifestyle or the monotheist one. This illustrates what, exactly? That you have to be literally as near as possible to certain that atheism is true before it becomes rationally defensible in terms of expected values?

Even in this scenario, however, the atheist is a fool to take his atheism to the grave if he can avoid it. When your expected reward in life is 1 and you've already received 0.99 of it, you're wagering your remaining 0.01 against another 1. So even under these conditions, the atheist only makes a rationally defensible choice when his whole life is ahead of him: it's a slow downhill slide into irrationality all the way after that.
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PostPosted: Fri Mar 13, 2009 3:21 pm    Post subject: Reply with quote

Back to the wager, here is an interesting thought:

In Pascal's wager, the expected value of atheism is 1 (or so). The expected value of montheism is +Inf.

Let us investigate what the expected value of deciding to decide based on a coin toss is.
It is 0.5*1+0.5*Inf = Inf.

Therefore it is exactly as rational to decide to become monotheist, or to decide to let a coin toss decide. Now this is ridiculous, is it not? Well, let's push a bit further:
I decide now to keep being atheist knowing that there is a non zero chance in the future that I will change my mind (as TFBW said, because I become for instance terminally ill). Guess what? Same expected value as becoming monotheist now. Except I get all the fun of having no "religious" constraints longer; so I maximize without loosing any expected value of paradise my value (and not expected value. Real value, because I get it whatever the probability of God's existence is!) of temporal life...

So the rational decision is to stay atheist for now but not exlude to become monotheist in the future. Exactly me.
Thank you Pascal for you help! Twisted Evil

By the way - as you don't know the exact hour of your death, the rational decision always remains to keep being atheist and not exlude to change your mind. Down to the end where this option and the monotheist option finally converge. That the beauty or the stupidity of decision theory when using infinity...
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PostPosted: Fri Mar 13, 2009 4:27 pm    Post subject: Reply with quote

lacavin wrote:
TFBW wrote:
The alternatives are not important to the wager. We can evaluate things two at a time. When we are evaluating A against B, the other alternatives (C, D, E, ...) are just a distraction from the issue at hand.

This is just wrong. When I come at a cross-road, all the options are presented at the same time, and I have to consider them all.

Yes, but if you don't have to consider them all at once. If your options are A, B, and C, then you can first compare A and B, completely ignoring C. If you clearly decide that A is better than B, you can then compare A and C.

For those of you who prefer analogies, here's how it works. Imagine that you do a service for a rich man, and he says you can take one bag of gold from his treasure room as a reward. All the bags look fairly similar, but you pick up a couple and discover that some feel heavier than others. Of course, you want to take the heaviest one, but you don't have a scale. The best that you can do is hold one in each hand and judge whether the left one or right one is heavier.

In order to find the heaviest one, start with any two bags, put the lighter of the two down in a "bags that I've already tried" pile, and pick up another from the "bags that I haven't tried" pile. Repeat until you're only holding one bag and there's nothing left to pick up. The heaviest bag is the one you're still holding -- assuming your ability to judge relative weight is good enough.

lacavin wrote:
What you probably mean is that first you ask the question whether you should have any religion or not, and this is Pascal's wager that forces you to go for religion. On a second turn you must choose your religion, and this is not the topic of Pascal.

The mathematics behind Pascal's Wager is quite general and doesn't require the subject to be religion at all. It's simply an application of the mathematics of expected outcomes to two outcomes which you think are possible. In applying the mathematics to religion, Pascal starts with atheism and Christianity, demonstrating that you can eliminate atheism on rational grounds not because it's false, but because it's a terrible bet. You can apply the same approach to other competing ideas. Where the requirements and rewards are similar, it won't help you very much, though. That's why it's particularly useful in comparing atheism to systems in which there is an afterlife of some kind: the afterlife makes a big difference.

lacavin wrote:
In this case, the truth table is different:
Code:
                  A      B      C     None    Expected Value

Believe A        Inf   -Inf   -Inf     0        -Inf
Believe B       -Inf    Inf   -Inf     0        -Inf
Believe C       -Inf   -Inf    Inf     0        -Inf
Unbeliever        1      1      1      1          1

In this case the rational option is to be atheist.

You've made an implicit assumption in relation to probability: namely, that all of these are equally likely -- or at least that A, B, and C are equally likely. If you seriously believed that these were the possible outcomes, and each had equal probability, then atheism would be a rational choice. But even here, if you thought that the probability of A was greater than B+C, say, then A would be the rational option, even if you thought that A was highly unlikely relative to the "none" option.

You've constructed a very artificial table here that's deliberately favourable to atheism -- atheists can't go to hell, while everyone else can, and that's what I call stacking the deck! Even so, atheism has nothing to offer except being the safe way out if none of the monotheism options is sufficiently probable relative to the others. A rational person would still choose A, B, or C if he felt the odds were right.

lacavin wrote:
Because I put other expected values (see the example above) the rational act on my own belief is the opposite of yours - so one of us is wrong, so this line of reasoning can lead to wrong decisions, so it is not a good decision-making tool.

The mathematics of expected outcomes are a very good decision making tool. The problem is that you are looking for absolute certainty where none exists. You have to make decisions based on your own judgement and incomplete information. Life is like that: you do it all the time. Business do it all the time.

Proper application of expected outcomes will help you to choose rationally between options given what you believe about the possibilities. It can't tell you whether your beliefs are right or not: it can only tell you what your beliefs imply. If you think that makes it useless, then so be it. Perhaps you have some other idea as to how we should deal with uncertainty.

lacavin wrote:
Exactly - only infinity dominates. So you should insist on using it, because with any other value, then you would need a probability for God existence before you can compute the expected values. If the reward is not infinity the wager don't say anything.

Sure it will. If the reward offered by heaven is one hundred times better than the reward offered by an atheist lifestyle, then you'd want to be more than 99% sure about atheism relative to monotheism before it made sense to live like an atheist.

Maybe what you're having trouble with here is my application of probability. Probability here represents the uncertainty of our knowledge, not the statistical likelihood of something happening. The probability of God existing is either one or zero: he either does or does not. If you're a perfect agnostic about the existence of God, then you understand that he either exists or does not, but represent your lack of knowledge about whether it is one or the other by saying he exists with 50% probability.
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PostPosted: Fri Mar 13, 2009 5:11 pm    Post subject: Reply with quote

lacavin wrote:
That the beauty or the stupidity of decision theory when using infinity...

So stop using "infinity" like it's a number and see what the trend is when you use finite numbers as they approach infinity.

But you don't need me to explain that to you. You've made it clear that you're being wilfully obtuse.
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PostPosted: Fri Mar 13, 2009 7:52 pm    Post subject: Reply with quote

TFBW wrote:
lacavin wrote:
That the beauty or the stupidity of decision theory when using infinity...

So stop using "infinity" like it's a number and see what the trend is when you use finite numbers as they approach infinity.

But you don't need me to explain that to you. You've made it clear that you're being wilfully obtuse.

I respect you and don't say nor think that you are willfully trying hard to be stupid and that's why you don't bow to my arguments, even when your post shows that you don't understand fully the role of infinity.
Please show other people the same respect.

I really think that Pascal's wager is flawed and hence does not help in the debate about God's existence, that's why I did not really want to discuss it before it became the main argument. But when you use it as main argument (and hence say atheism is irrational and actually as a consqeuence begin hinting that your opponents are lunatics), than I have to explain you why I think it is flawed. Proofs ad absurdum are legitimate proofs, but I had much more arguments already. Of course, that Pascal's wager is flawed does not change anything to the question of God's existence, and the flaw is not an argument to deny possibility of a God.

With regards to infinity: as soon as you remove infinity, the reasoning does NOT hold. Pascal's wager can only hold WITHOUT having a probability for God's existence BECAUSE of infinity.

If I put 1 million:1 the reward, then if I have less than 1/1mio chances for God's existence, then the expected value is higher for atheism. Quite easy really: x = reward for paradise; 1/x = minimum probability of God's existence to make the decision lead toward monotheism - less and atheism wins. If x=Inf, then (and only then) 1/x = zero; and less then zero does not exist for probabilities (hence atheism can never win).

With infinity you can argue that for any probability except exactly zero monotheism dominates. You can say "if you are not absolutely, completely sure, without any doubts, that God does not exist, then you should become monotheist". The burden of proof lies now by the atheist, that needs to prove a negative, which is impossible (the absence of evidence is not the evidence of absence). Therefore he cannot prove that he would not gain by becoming monotheist.

Without infinity you are back at square one and have to discuss the odds, because the only think you can have is "if you think that the probability of God's existence is higher than (insert number), than you should be monotheist". But atheists will not put this (insert number) probability and argue it, and hence the wager looses its validity to convince them. The burden of proof lies now by the monotheist that want to convince the atheist: he has to prove that this probability is reasonable.
On top of it, putting infinity for eternity sort of makes sense to most people, atheists alike. Putting just a high number becomes a question of judgment and opinion...

You understand?

By the way "you use finite numbers as they approach infinity" means passing at the limit which is infinity, so it does not make a difference at all...

And because you need infinity, than my reasoning holds, because you cannot use the math only when it helps you and refuse them otherwise. The math below is the same that Pascal uses. So if the rules used by Pascal are correct, then so is also the following:
lacavin wrote:
In Pascal's wager, the expected value of atheism is 1 (or so). The expected value of montheism is +Inf.

Let us investigate what the expected value of deciding to decide based on a coin toss is.
It is 0.5*1+0.5*Inf = Inf.

Therefore it is exactly as rational to decide to become monotheist, or to decide to let a coin toss decide. Now this is ridiculous, is it not? Well, let's push a bit further:
I decide now to keep being atheist knowing that there is a non zero chance in the future that I will change my mind (as TFBW said, because I become for instance terminally ill). Guess what? Same expected value as becoming monotheist now. Except I get all the fun of having no "religious" constraints longer; so I maximize without loosing any expected value of paradise my value (and not expected value. Real value, because I get it whatever the probability of God's existence is!) of temporal life...

So the rational decision is to stay atheist for now but not exlude to become monotheist in the future. Exactly me.
Thank you Pascal for you help! Twisted Evil
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PostPosted: Fri Mar 13, 2009 9:03 pm    Post subject: Reply with quote

TFBW wrote:
Yes, but if you don't have to consider them all at once. If your options are A, B, and C, then you can first compare A and B, completely ignoring C. If you clearly decide that A is better than B, you can then compare A and C.

Yes you can, but as the fact that there is another possibility changes the rewards, than you have to include the consequences of A, B and C before starting the comparison.
In the expectation table I gave, you can effectively see that atheism dominates. Or that A=B, then B=C, then C<atheism, and - o surprise - global decision remains atheism. Wink

In you example, if one bag contains diamonds instead of gold (like of a new option), than obviously you can still compare each bag one by one, but you have to take the description of the content (gold, diamond?) into consideration for each comparison. The weight is not enough anymore. So the one-by-one comparison must include the new fact.


TFBW wrote:
You've made an implicit assumption in relation to probability: namely, that all of these are equally likely -- or at least that A, B, and C are equally likely.

Wrong. Because of infinite expectations (see previous post) the probabilities are not relevant, so there is no implicit assumption, except that you cannot prove that the probability of my table being true is exactly zero. Burden of proof is in your hands.

TFBW wrote:
You've constructed a very artificial table here that's deliberately favourable to atheism -- atheists can't go to hell, while everyone else can, and that's what I call stacking the deck!

Of course I did make a table on purpose where atheists win (that's why I used 3 incompatible religions. With 2 it does not work).

But the fact that I can draw this table using the same rules as Pascal and that you cannot prove me that this table is impossible shows that the wager is not valid. Many tables + many diverging conclusions = no help in decision.

I am not trying to convince anybody to be atheist with this table that I don't think represent the truth more than the one of Pascal. I am just showing that such proofs have no value.

TFBW wrote:
The mathematics of expected outcomes are a very good decision making tool. The problem is that you are looking for absolute certainty where none exists. You have to make decisions based on your own judgement and incomplete information. Life is like that: you do it all the time. Business do it all the time.

hem... yeap, I'm quite aware of such decision making tools, I use them frequently in my job; funnily a core topic of my PhD was decision-making under uncertainty with several conflicting objectives. So believe me, I'm not looking for certainty because I know it does not exist in most practical situations.

And I know that while such tools are very helpful for supporting decision making, they are in almost every real life situation not proofs that the decision is right because rewards and probabilities are always a subjective question. And of course, you never mess with infinity which breaks up all calculation.

Therefore you use them to judge a situation, to clarify the odds and rewards and to communicate in order to take hard decisions, but not to prove that people that don't share your opinion are irrational lunatics.
In some perfectly defined cases, you can use them as proofs. This is the case for casino or lottery because odds and rewards are objective facts. This is why I don't play lottery Laughing.

TFBW wrote:
Maybe what you're having trouble with here is my application of probability. Probability here represents the uncertainty of our knowledge, not the statistical likelihood of something happening. The probability of God existing is either one or zero: he either does or does not. If you're a perfect agnostic about the existence of God, then you understand that he either exists or does not, but represent your lack of knowledge about whether it is one or the other by saying he exists with 50% probability.

I have troubles indeed. Because in this case it is wrong to compute an expected value. The probability must be the probability of God existing (and sending believers to an eternal paradise) in order for the expected values to be calculated.

If you are agnostic, you put an undefined as probability, which is higher than zero and lower than one. If you are christian you say it is one. If you are (strong) atheist, than it is zero.
Because the wager actually targets at non believers, what it does is only to put on them the burden of proof - saying they must be real sure of their assumption of a zero probability otherwise they will loose much.

It is very elegant and I admire Pascal a lot for his wager.
But as I mentioned in my previous posts, it is regrettably flawed, which explains why some people since 400 years are still not monotheists while being rational and smart people.
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PostPosted: Sat Mar 14, 2009 3:10 am    Post subject: Reply with quote

lacavin, my apologies for insulting you if you are not being wilfully obtuse, but I'm afraid that this conversation has (in my opinion) reached a stage of hopeless degeneracy. I've tried very hard to explain myself, but you have been extremely resilient to my attempts. I seriously doubt that anyone else is following this conversation with interest any more, because (in the words of Monty Python) it's not an argument, it's just contradiction. I say X, you say not X, and we both insist that we are right. So, for example...

lacavin wrote:
TFBW wrote:
You've made an implicit assumption in relation to probability: namely, that all of these are equally likely -- or at least that A, B, and C are equally likely.

Wrong. Because of infinite expectations (see previous post) the probabilities are not relevant, so there is no implicit assumption, except that you cannot prove that the probability of my table being true is exactly zero. Burden of proof is in your hands.

You think I've made a mistake, and I think you've made a mistake. Pure reason isn't all that it's made out to be when the practitioners are flawed.

But... for what it's worth... here's an attempt to show you that you are mistaken when you say that probabilities are not relevant. Let's replace your infinities with x so that the mathematics is general and doesn't rely on any particular value (such as infinity) to be valid. This changes the table so that each of the monotheistic religions has three outcomes, one of +x, the other two of -x. Now, assuming that each of the four outcomes is equally likely, this means that the expected value of A, B, and C is x/4 - x/4 - x/4 + 0 = -x/4. As x approaches infinity, the expected value of each option approaches negative infinity, just as your table suggests. Similarly the expected value of atheism is 1/4 + 1/4 + 1/4 + 1/4 = 1, as per your table.

If we change the assumptions in relation to probability, the outcome is different. In the above calculation, each outcome has P=1/4. Let's change this so that the atheist option is 70% certain, the A option is 20% certain, and the other two are 5% each. The expected value of A is now as follows: 0.2x - 0.05x - 0.05x + 0 = 0.1x. As x approaches infinity, so does the expected value of A. The expected value of atheism doesn't change: 0.2 + 0.05 + 0.05 + 0.7 = 1 (same as before).

So, as you can see, your table assumed equal probability for all possible outcomes, and changing the probability ratio changes the outcome -- even if I increase the probability of the atheist option and decrease all the others.

Of course, I fully expect you to reassert that I've got it wrong. I'll reserve comment on the remainder until we can get this disagreement sorted out. If we can't agree on what constitutes valid mathematical reasoning in relation to such choices, we're wasting our combined time anyhow.
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lacavin
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PostPosted: Sat Mar 14, 2009 9:02 pm    Post subject: Reply with quote

TFBW wrote:
lacavin, my apologies for insulting you if you are not being wilfully obtuse, but I'm afraid that this conversation has (in my opinion) reached a stage of hopeless degeneracy. I've tried very hard to explain myself, but you have been extremely resilient to my attempts.

No issues... and I must say you have been similarly exactly as resilient to my attempts. Wink

Now to be quick, I agree there may be a mistake in my math.

I guess it is not allowed to subtract infinities.
Because multiplications have higher precedence, we have a sum of terms like p*Inf which is equal whatever the probabilities (because of infinity. With any other number you are perfectly right!) to a sum of terms like Inf.
Problem is that they have different signs, like Inf - Inf - Inf + 0 and this is most probably not equal to -Inf but to undefined.
(see wikipedia under Arithmetic Operations, the second line below the formulas).

However this does not change the core of my reasoning, as with the "undefined" as result, my table just result in the impossibility to make a rational decision based on this table. Unless you can prove me that the hypothesis underlying my table are wrong, then it is enough to show that different hypothesis bring another result, and hence that Pascal's wager is not the solution proving that atheism is irrational.
I really do not mean at all that I could use a similar wager to prove that atheism is the rational choice - that was not the purpose of my table. Again, for me the wager just does not prove anything because it is based on hypothesis that atheists would not agree on.

But let's forget about this table, because my last argument is in my eyes even better, the ad absurdum argument. Let me begin with the beginning again and see if we can reach an agreement on this point:

Do you agree that you need infinity for Pascal's Wager to be a valid argument for atheists?

I repeat below the argumentation for easy reference:
lacavin wrote:
If I put 1 million:1 the reward, then if I have less than 1/1mio chances for God's existence, then the expected value is higher for atheism. Quite easy really: x = reward for paradise; 1/x = minimum probability of God's existence to make the decision lead toward monotheism - less and atheism wins. If x=Inf, then (and only then) 1/x = zero; and less then zero does not exist for probabilities (hence atheism can never win).

With infinity you can argue that for any probability except exactly zero monotheism dominates. You can say "if you are not absolutely, completely sure, without any doubts, that God does not exist, then you should become monotheist". The burden of proof lies now by the atheist, that needs to prove a negative, which is impossible (the absence of evidence is not the evidence of absence). Therefore he cannot prove that he would not gain by becoming monotheist.

Without infinity you are back at square one and have to discuss the odds, because the only think you can have is "if you think that the probability of God's existence is higher than (insert number), than you should be monotheist". But atheists will not put this (insert number) probability and argue it, and hence the wager looses its validity to convince them. The burden of proof lies now by the monotheist that want to convince the atheist: he has to prove that this (insert number) probability is reasonable.
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TFBW
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PostPosted: Sun Mar 15, 2009 4:43 am    Post subject: Reply with quote

lacavin wrote:
Without infinity you are back at square one and have to discuss the odds, because the only think you can have is "if you think that the probability of God's existence is higher than (insert number), than you should be monotheist". But atheists will not put this (insert number) probability and argue it, and hence the wager looses its validity to convince them. The burden of proof lies now by the monotheist that want to convince the atheist: he has to prove that this (insert number) probability is reasonable.

No, I don't agree that "infinity" is in any way necessary for Pascal's Wager to hold force. Furthermore, I don't have to provide you with an estimate of the probability of God's existence, or any other probability for that matter: I can ask you for your estimates of these probabilities. The wager is about whether your choices actually seek maximum value, given what you believe about the environment. We've seen here that the popular excuse among those living an atheist lifestyle is that they're trying to get the most value out of life. This is perfectly rational if you are quite certain that there is no possibility of a life beyond this one. It may not be rational under some other circumstances.

So here's another way of taking Pascal's Wager. Let A be a value which represents what you expect to get out of life if you live an atheist lifestyle. Let B be the value you think you'll get out of life if you live a Christian lifestyle. Let C be the value you place on going to heaven, and let D be a value between zero and one which represents the degree of confidence you have that living the Christian lifestyle will actually get you to heaven. Multiply C by D and add the result to B. If that number is bigger than A, then your estimates imply that the Christian lifestyle will bring better results, overall.

The potential for irrationality exists here in that a person can assert "I believe that such-and-such an alternative maximises my possible value in life" while simultaneously holding beliefs which mathematically contradict that view. For example, if you were to assert that "atheism is the winning lifestyle", while also believing A=100, B=10, C=1,000,000, D=0.001, your beliefs can be shown to contradict each other, because B+C*D=1010, which is substantially greater than A.
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lacavin
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PostPosted: Sun Mar 15, 2009 12:30 pm    Post subject: Reply with quote

TFBW wrote:
I can ask you for your estimates of these probabilities.

If the wager is used to convince an atheist, it must apply to a situation where the views for God's existence's probability is close to zero. You can use the wager (with infinity) to trap him because you can use it to show that if it is not exactly zero, he looses.

In any other cases, the atheist will tell you that he sees the probability of God's existence as infinitesimal (that's why he is atheist). Hence for whatever value of the paradise-reward, as long as the temporal life reward is higher when being atheist (it is for the atheist, of course), atheism wins.

Your version of the wager can be boiled up to: if you think there is a significant (even very small) probability that God exists, you do better in becoming monotheist. This assertion is correct, but atheists will not agree on the condition. Hence it is a circular argument which will not convince atheists.


Because I agree that obviously we won't agree, and hence discussion should keep going only if more people are involved I will make a new post with my position. Perhaps you want to make a similar statement as your conclusion (please do not answer directly to mine, that would spurn a new round of rebuttal, just write a summary of your own position).


Last edited by lacavin on Sun Mar 15, 2009 8:46 pm; edited 2 times in total
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PostPosted: Sun Mar 15, 2009 1:15 pm    Post subject: Reply with quote

A skeptical view on Pascal's wager

While Pascal's wager was incredibly advanced 400 years ago, and remain an admirable piece of work for it breakthrough in decision theory, it is in my opinion not an argument that will convince any atheist to become monotheist.
Because of its weaknesses, it is also not an argument that carry much weight for an agnostic.

The main weaknesses are listed below - each of them separately is in my view enough to discard Pascal's wager as the ultimate decision tool.
Of course, that the wager is not a good decision tool does not imply anything about the best lifestyle - it just say we will have to decide without Pascal's help. Note that there are some other weaknesses that are in my view less important, such as the inclusion of alternative, incompatible, religions.


1. Basic Assumption of voluntarily belief
The most basic assumption is that belief or Faith is voluntary; this mean that we can choose to believe in something.
My view is that belief is not voluntary but rational and needs supporting evidence: Are you able to believe that Superman does exist? Or does the lack of evidence and general low probability stops you?

Significant christian theologists, including Pascal, share this view. Pascal therefore precises just after the wager in his Pensées: "Follow the way [...] by acting as if [you] believed, bless yourself with holy water, have Masses said, and so on; by a simple and natural process this will make you believe, and will dull you—will quiet your proudly critical intellect...".
How can one appeal to reason for the wager and then propose a method to ignore your reason?


2. Assumptions about God
The wager is based on assumptions about God. For example:
- We can impact on God's decision about salvation by our behavior/beliefs.
- Believers can go to an eternal paradise, whatever their motives for belief.
- Unbelievers can not go to an eternal paradise, whatever their moral behavior.
These assumptions are not compatible with all the theological thinking even in the christian Faith (for examples: Calvin and many protestants don't share the first hypothesis - Acts cannot save you, only Grace can and this is God' sovereign and foreordained decision; Mormons don't share the third - you get another chance to become christian after death), not to say anything about other Faiths.
It is possible to generate based on other (possible) assumptions other forms of the wager which do not lead to the same conclusions.

This is a key issue because the target of the wager (atheists, agnostics) will probably not share these assumptions, and hence not recognize the wager as reasonable.


3. Use of Infinity
The use of infinity is required in order for the wager to carry his weight.

The wager's aim is to convince an atheist, therefore it must apply to a situation where the views for God's existence's probability is close to zero. You can use the wager (with infinity) to trap atheists because you can use it to show that if the probability of God's existence is not exactly zero, he looses. The ball is in the atheist's hands that must now justify this zero probability - and proving a negative is impossible.

The atheist sees the probability of God's existence as infinitesimal (that's why he is atheist). Hence for whatever finite value of the paradise-reward, as long as the temporal life reward is higher when being atheist (it is for the atheist, of course), atheism wins. Without infinity, the wager boils down to: if you think there is a significant (even very small) probability that God exists, you do better in becoming monotheist. This assertion is correct, but atheists will not agree on the condition, therefore it will not convince them.

Why is the use of infinity problematic? Because infinity actually evens out every non-zero probability. Therefore it is mathematically exactly as rational to decide to believe or to decide to toss a coin and believe only if a head comes up., because 0.5 * Infinity = Infinity...
Therefore it is mathematically exactly as good to become monotheist or to stay atheist while keeping open a possible (probability p > 0) change of mind in the future (because p * Inf = Inf | p > 0). As the monotheist has a "better" life (in his view, and whatever the truth is about God's existence), the atheism actually dominates the wager.

Thus even within Pascal's hypothesis, different conclusions can be drawn.


With this post I tried to clarify my position as well as possible. I will of course keep following up this thread, but not actively answers to people having different views (except if there are questions) unless they bring killer arguments against these three sufficient weaknesses.
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PostPosted: Mon Mar 16, 2009 8:34 am    Post subject: Reply with quote

0.5 * Infinity = Infinity

You can't do that. Infinity is not a number.
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