Seraphim

Well, someone asked me to try and answer this "Wager" problem and I must say, I come out with something worth sharing. I'm not sure where too put, so I will dump it on Philosophy Section.

Based on this website :
<a href="http://plato.stanford.edu/entries/pascal-wager/" target="_blank">http://plato.stanford.edu/entries/pascal-wager/</a>

Overview
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"Suppose that you have two possible actions, A1 and A2, and the worst outcome associated with A1 is at least as good as the best outcome associated with A2; suppose also that in at least one state of the world, A1's outcome is strictly better than A2's. Let us say in that case that A1 superdominates A2. Then rationality surely requires you to perform A1."

Reply : True ... of the A1 is rational thing to do.

"In decisions under risk, the agent assigns subjective probabilities to the various states of the world. Assume that the states of the world are independent of what the agent does. A figure of merit called the expected utility, or the expectation of a given action can be calculated by a simple formula: for each state, multiply the utility that the action produces in that state by the state's probability; then, add these numbers. According to decision theory, rationality requires you to perform the action of maximum expected utility (if there is one). "

Reply : In another word (less complicated terms), the agent is performing a task which nets him the MOST profitable outcome/profit. Same as a businessman could do with his business - he will try to get as much profit as possible from the good and services he provides.

In term of Religion, a follower will follow a teaching more strictly than others IF he thinks that he will get more merit out of what he is following.

The Argument of Superdominance
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"Pascal maintains that we are incapable of knowing whether God exists or not, yet we must "wager" one way or the other. Reason cannot settle which way we should incline, but a consideration of the relevant outcomes supposedly can."

Reply : Pascal thought that humans unable to determine whether is such a force called God through studies of religion, and the only reason humans both to believe in God is because of the possible outcomes (going to heaven or hell for eternity).

This is a logical statement from him, SINCE he has no information on religion other than Christianity or maybe even Islam to help him make such assumption.

"God is, or He is not." But to which side shall we incline? Reason can decide nothing here. There is an infinite chaos which separated us. A game is being played at the extremity of this infinite distance where heads or tails will turn up...

Which will you choose then? Let us see. Since you must choose, let us see which interests you least. You have two things to lose, the true and the good; and two things to stake, your reason and your will, you knowledge and your happiness; and your nature has two things to shun, error and misery. Your reason is no more shocked in choosing one rather than the other, since you must of necessity choose... But your happiness? Let us weigh the gain and the loss in wagering that God is... If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is."

From Pascal's note.

Reply : Notice the last statement? If you gain, you gain all; if you lose, you lose NOTHING. Wager, then, without hesitation that HE is"

It simply means - if humans wage that there is a God, then they gain everything from their wager (assuming that they did good). If there is no God and yet humans believe in Him, then they still do not lose anything in believing Him since they will be dead and dead people do not receive anything if there is no heaven or hell. So which wager is better? Wage that there is a God or wage there is no God?

Argument from Expectation
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He (Pascal) continues:
Let us see. Since there is an equal risk of gain and of loss, if you had only to gain two lives, instead of one, you might still wager. But if there were three lives to gain, you would have to play (since you are under the necessity of playing), and you would be imprudent, when you are forced to play, not to chance your life to gain three at a game where there is an equal risk of loss and gain. But there is an eternity of life and happiness.

Reply : The lives he meant was simply means how many "throws" of dice we get in our wages. Since life is only one, and the wager is two, you are forced to make ONE bet/wager in one life time (one throw).

Same as the throw of a dice - you put down your bet in one of the numbers and throw a dice, if you win, you take ALL, if you lose, you lose ALL.

"So Pascal has now made two striking assumptions:
(1) The probability of God's existence is 1/2.
(2) Wagering for God brings infinite reward if God exists.

Morris 1994 is sympathetic to (1), while Hacking 1972 finds it "a monstrous premiss".

Reply : Hacking (1972) makes a wrong assumption by associating Pascal's assumption to that of a lottery. The reason Pascal said that the probability of God's existence is 1/2 is because that is probability chance of you get in ONE lifetime. There is no second chance after you dead.

It is TRUE that the chance of winning a lottery is 1/Million since there is a million people who is betting with the same odd as you would. In such context, you are betting against LUCK, not Logic. And you can always buy more lottery tickets to increase your chances - buying 10 tickets = 10/million. In life, there is no insurance or guarantee that you will come back alive (like a game character) once you are dead. In such context, Hacking is WRONG.

The Argument from Generalized Expectations : Pascal's Wager
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"But there is an eternity of life and happiness. And this being so, if there were an infinity of chances, of which one only would be for you, you would still be right in wagering one to win two, and you would act stupidly, being obliged to play, by refusing to stake one life against three at a game in which out of an infinity of chances there is one for you, if there were an infinity of an infinitely happy life to gain. But there is here an infinity of an infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite. It is all divided; wherever the infinite is and there is not an infinity of chances of loss against that of gain, there is no time to hesitate, you must give all..."

Reply : IF you could bet for infinity times (like in a lottery) then the best bet will be that which you could win and you will avoid betting on bets which is against you (winning).

But the problem is, your bet is just one (finite - 1 Life) and you have two wagers - Believe or not to Believe. Common sense suggests that you will bet on the most profitable bet you could find.
In religion's point of view, if a person is given a choice whether he is to believe in God or not to believe, he will believe in Him even so he doesn't believe in existence of a God (no evidence other than Religion) SINCE he rather be in heaven (the best bet) than in hell (worst bet) IF God did existed. This is simply because he has ONLY 1 chance to bet (1 life) against 2 possible outcomes.

Now for the MAIN show :


Objections to Pascal's Wager
-----------------------------------
1. Decision Matrix
1. Different matrices for different people.
"The argument assumes that the same decision matrix applies to everybody. However, perhaps the relevant rewards are different for different people. Perhaps, for example, there is a predestined infinite reward for the Chosen, whatever they do, and finite utility for the rest, as Mackie 1982 suggests. Or maybe the prospect of salvation appeals more to some people than to others, as Swinburne 1969 has noted."

Reply : The Pascal Wager could only apply to a Muslim or a Christian (or Atheist) since other religion such as Buddhism, Hindusm and Toast do not believe in a single life. In such context (try or wrong is not the matter here, but the belief that one has more than one chance at the dice/throw), there is an increase in Argument of Expectation since the throw is given has increase as well.

In another word, just as someone who doesn't know whether God doesn't exist yet willing to be He does, a person who believes in such concept as reincarnation will assume that the bet he made in One life time can be changed in the next.

2. The utility of salvation could not be infinite.
"One might argue that the very notion of infinite utility is suspect---see for example Jeffrey 1983 and McClennen 1994.[6] Hence, the objection continues, whatever the utility of salvation might be, it must be finite. Strict finitists, who are chary of the notion of infinity in general, will agree---see. Dummett 1978 and Wright 1987. Or perhaps the notion of infinite utility makes sense, but an infinite reward could only be finitely appreciated by a human being."

Reply : I don't very much understand this. It sounded like this guys argue that there should be more chance since the reward for a bet is infinite (betting in God in 1 lifetime - finite bet, could bring an infinitely reward - forever in heaven).

3. There should be more than one infinity in the matrix. There are also critics of the Wager who, far from objecting to infinite utilities, want to see more of them in the matrix. For example, it might be thought that a forgiving God would bestow infinite utility upon wagerers-for and wagerers-against alike---Rescher 1985 is one author who entertains this possibility. Or it might be thought that, on the contrary, wagering against an existent God results in negative infinite utility. (As we have noted, some authors read Pascal himself as saying as much.) Either way, f2 is not really finite at all, but or - as the case may be. And perhaps f1 and f3 could be or -. Suppose, for instance, that God does not exist, but that we are reincarnated ad infinitum, and that the total utility we receive is an infinite sum that does not converge.

Reply : This one has NO place in Pascal's wager. Pascal has only made two assumptions :
1. Life is only 1 - 1 throw of dice
2. There is only two bet - God exist or God doesn't exist

Try to add such a forgiving God doesn't change the bet (no chance to the original Wager) but only to assume that there is a God that feels. To an Atheist, such notion is useless in making a bet, thus such assumptions made by Rescher doesn't have place in Pascal's Wager.

At the same time, concept such as reincarnation does chance the Wager by increasing the "Throw" you will get in making a bet - more throws, more life. But, such concept is again is useless to a person who believes in Christianity or Islam (and some people who doesn't believe either in a soul or reincarnation) since they believe there is only one throw and it is back to Pascal's original concept.

4. The matrix should have more rows. Perhaps there is more than one way to wager for God, and the rewards that God bestows vary accordingly. For instance, God might not reward infinitely those who strive to believe in Him only for the very mercenary reasons that Pascal gives, as James 1956 has observed. One could also imagine distinguishing belief based on faith from belief based on evidential reasons, and posit different rewards in each case.

Reply : The original matrix has only two rows with two possible outcome, anything that adds to this rows should be entertained - such as the possibility of reincarnation. Such notion that God bestows anything is illogical since the bet is already made.

5. The matrix should have more columns: the many Gods objection. If Pascal is really right that reason can decide nothing here, then it would seem that various other theistic hypotheses are also live options. Pascal presumably had in mind the Catholic conception of God---let us suppose that this is the God who either 'exists' or 'does not exist'. By excluded middle, this is a partition. The objection, then, is that the partition is not sufficiently fine-grained, and the '(Catholic) God does not exist' column really subdivides into various other theistic hypotheses. The objection could equally run that Pascal's argument 'proves too much': by parallel reasoning we can 'show' that rationality requires believing in various incompatible theistic hypotheses. As Diderot 1875-77 puts the point: "An Imam could reason just as well this way".[7]

Reply : Again, there is an unsuccessful attempt to increase the column and rows with assumption that different religion follow different God thus the matrix should be increased. This has NO place in Pascal's Wager as well.

Assuming that ALL religion in the world plays the SAME role in a human life - bring the person following it to a God, the matrix doesn't change since there is no difference. A person who believe either in a God or Gods will still follow a religion, thus he only have one single choice - to believe in a God/Gods or not to believe in a God. The matrix doesn't change nor does the column increases.

2. Probability Assigned to God's Existence
1. Undefined probability for God's existence. Premise 1 presupposes that you should have a probability for God's existence in the first place

Reply : Stupidity in Action here. When Pascal made this concept, he ASSUMED there is two bets per person - whether to believe in God or not to believe in God. If one wonders whether there is a God, it shows that he already made a bet that there is no God available, thus the bet already made.

2. Zero probability for God's existence.
Reply : Another stupidity in action once again. Same as above, 1 life - 1 bet. Atheist already cast their bet, there is no reason they should study Pascal's Wagers anymore.

3.Rationality Requires Maximizing Expected Etility
"Finally, one might distinguish between practical rationality and theoretical rationality. One could then concede that practical rationality requires you to maximize expected utility, while insisting that theoretical rationality might require something else of you---say, proportioning belief to the amount of evidence available."

Reply : No idea what they are talking about here. As far as I could understand, it is like assuming that rationality is split into two - being rational means not accepting God and being theoretical means accepting God. I don't see what is rationality has to do with Pascal's Wager here.

"A number of authors who have been otherwise critical of the Wager have explicitly conceded that the Wager is valid---e.g. Mackie 1982, Rescher 1985, Mougin and Sober 1994, and most emphatically, Hacking 1972. That is, these authors agree with Pascal that wagering for God really is rationally mandated by Pascal's decision matrix in tandem with positive probability for God's existence, and the decision theoretic account of rational action."

Reply : Wrong. Pascal made the Wager based on most logical choice a person could make, and not because he was a Christian. Best way to look at it is by looking at the game show - "Who Wants to be a Millionaire? "

You sit on the hot seat with the host staring at you. The time is ticking away and you are required to make ONE choice out of 4 options available to you. Assuming you cannot make the choice, you will call someone to make for you and the host will ask whether to follow that choice or your own. Here is where Pascal's Wager comes in. You are to make 1 bet from 4 choice and you have your friend's choice (which you are not sure true or not) with you. Do you pick your own choice assuming your friend is wrong? Do you go with your friend's choice, assuming he or she is right about it?

"Even worse, suppose that you focus all your energy into avoiding belief in God. Still, you may well assign positive and finite probability to your efforts failing, with the result that you wager for God nonetheless. In that case again, your expectation is infinite again. So even if rationality requires you to perform the act of maximum expected utility when there is one, here there isn't one. Rather, there is a many-way tie for first place, as it were.[10]"

Reply : I have no idea why Expectation has anything to do with a choice we make or in Pascal's Wager. You either choose to accept something or you don't. If you choose to eat hamburger, than when you reach a burger shop, you will be expecting one - choice made, action made, result received. If you do not believe in God and if there is no God, do you still expect to go to heaven or hell? No.

Moral Objections to Wagering for God
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"One way of putting the argument is that wagering for God may require you to corrupt yourself, thus violating a Kantian duty to yourself. Clifford 1986 argues that an individual's believing something on insufficient evidence harms society by promoting credulity. Penelhum 1971 contends that the putative divine plan is itself immoral, condemning as it does honest non-believers to loss of eternal happiness, when such unbelief is in no way culpable; and that to adopt the relevant belief is to be complicit to this immoral plan. See Quinn 1994 for replies to these arguments. For example, against Penelhum he argues that as long as God treats non-believers justly, there is nothing immoral about him bestowing special favor on believers, more perhaps than they deserve."

Reply : Such notion is true IF it is applied to Islam and Christianity where treatment toward no-believers are different to those who believes. However, such is NOT the case when applying to Hindusm, Buddhism or Taoist.

What Does It Mean to "Wager for God"?
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"We find two main pieces of advice to the non-believer here: act like a believer, and suppress those passions that are obstacles to becoming a believer. And these are actions that one can perform at will."

Reply : In another word, ACT like you believe. Not sure what this will accomplish.
"Believing in God is presumably one way to wager for God. This passage suggests that even the non-believer can wager for God, by striving to become a believer. Critics may question the psychology of belief formation that Pascal presupposes, pointing out that one could strive to believe (perhaps by following exactly Pascal's prescription), yet fail. To this, a follower of Pascal might reply that the act of genuine striving already displays a pureness of heart that God would fully reward; or even that genuine striving in this case is itself a form of believing. "

Reply : in another word, even acting like you believe in God is an act of waging for God, and Pascal or his followers believers believe that such act is the first step toward God, since you have NOTHING to lose if God doesn't exist.

Corgan Sow

Don't step on me and I won't stomp on you.

Oh, god. That's not a good courtesy. You CAME here, remember?

Just advice...

Corgan Sow

Sorry for my previous post...Wrong topic...

Seraphim, uh..can you state what are you trying to argue?

K

Seraphim:

That was an excellent demonstration of the fact that Pascal's wager makes perfect sense for people who are certain that Christianity is true. But I always thought it was supposed to convince atheists.

You seem to have the idea that atheists are Christians who don't believe in the Christian God (whatever that means). Atheists don't believe in ANY god. Why in the world would an atheist agree that the only two choices are that there is no god or that the Christian God exists?

Pascal's wager ONLY makes sense if one has accepted the initial premise that Christianity is true. And it certainly isn't much utility in that case unless it is used to scare people from questioning their faith.

Yggdrasill

I have to agree with K, you even stated:
[Edited to expand the quote]

[ October 10, 2002: Message edited by: Yggdrasill ]</p>

galiel

Massimo Pigliucci presents a quite simple refutation of Pascal's wager.

<a href="http://fp.bio.utk.edu/skeptic/Essays/pascal_weager.htm" target="_blank">http://fp.bio.utk.edu/skeptic/Essays/pascal_weager.htm</a>

As he points out, the fundamental difference between the gullible and the skeptical boils down to the difference in modern statistics between wishing to minimize Type I errors and striving to minimize Type II errors.

Goliath

For Pascal's Wager to work in the xian's favor, xians must prove the following lemma:

If a god exists, then it is unique. Moreover, said god is the xian god.

Good luck!

Sincerely,

Goliath

Autonemesis

Man, you're almost as bellicose and arrogant as me. I like that.

Of course, PW is bull if it is much less likely that the Christian god exists, than that He does not exist. And that is the case. Buh-bye now.

HRG

Just one point.

If your do not increase the number of columns, then the matrix entries will be totally indeterminate. The results of believing in God X and of believing in God Y will in general be quite different (especially if X sees Y as a competitor and punishes Y-believers much more severely than atheists).

IOW, collapsing all the approx. 2500 gods that mankind has come up with into a single column leaves the matrix elements completely undefined.

Regards,
HRG.

Agnos1

Also, the columns increase greatly when once considers some more "non-Catholic" possibilities in a supreme being:

1) There could be a Supreme Creator of the universe that has absolutely no obligation nor intention of bringing humans into his domain (Heaven) and therefore the finiteness of human existence still exists.

2) Assuming this Supreme Being DID intend to bring humans into his "house," suppose that belief itself had nothing to do with entry--All were accepted? Just living your life would not jeopardize your "reward." It would be a natural occurance and part of ris "plan."

3) Assume there is a SB and honest belief is important. If one HONESTLY believes there is no God using rational argument based on informed observation to the best of ris ability, then honesy is rewarded, which is all one could ask. In other words, as Pascal's Wager is infinitely small, the thiest may say there is "STILL" chance, but this would be a chance for an infinitely merciless god (infinite penalty for a finite error in judgement) and one not worth worshipping.