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Pascal's Wager
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TFBW
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PostPosted: Fri Mar 20, 2009 5:51 pm    Post subject: Reply with quote

lacavin wrote:
Do you agree that there can be different table based on different assumptions of God?

Yes. Tables of that sort are subjective.

lacavin wrote:
Do you agree that such tables may lead to different winning behaviors?

Of course.

lacavin wrote:
Do you agree that the combination of several such tables is either possible (use of infinity) but then several/all behaviors lead to an infinite expected value or require probabilities we do not have?

I don't understand the question. I hope it doesn't matter.

lacavin wrote:
Do you agree therefore that you cannot use Pascal's wager for somebody that has no preferred assumptions about God's behavior?

Yes. Pascal's Wager is also not appropriate for people who have undefined beliefs as to the possibility of God's existence. If any of the values are undefined, then the person has no rational means for reaching any sort of conclusion. If such a person wishes to pursue a rational course of action, his first order of business should be to fill in the blanks.

lacavin wrote:
Do you agree finally that the target audiance of the wager is the unbelievers, and that it is unlikely that unbelievers will have preferred assumptions about God's behavior?

In my experience, the range of beliefs is fairly varied. No doubt some people will have given the matter little thought, as you say.

lacavin wrote:
Do you agree that therefore the wager cannot be used for its target audiance?

No. If a party is an atheist only because he has considered no alternatives, then the wager should at least alert him to the fact that his belief is pure prejudice. If, in an attempt to draw up a table of possibilities, he realises that he does not know what probabilities to assign things, this merely identifies the need for research. The table can be simplified by eliminating those alternatives where the person's own actions have no impact on the outcome (e.g. Calvinism, Universalism), and those alternatives which are overshadowed by the presence of infinites (should any be present). This is known as "creating a short list". Anything which survives the short-listing process can be the subject of further investigation. Should new information arrive, this can be considered in light of what is already known.

I can see what you're trying to get at, but it sounds like, "there are, in principle, an infinite number of possible religions, and I can't possibly analyse all that, so I'm just going to stick with my present lifestyle because I happen to like it." That amounts to a denial that rational behaviour is possible. After all, if it's true, the person in question has no possible way to demonstrate that his lifestyle has any property other than "I like it". Rational self-interest isn't possible, so self-indulgence takes its place.

lacavin wrote:
Therefore I rewrite you sentence as: as long as you are convinced that any probable God will either ignore your actions or prefer you to act like a believer whatever your core beliefs, then rational self interest dictates that you should proceed to act like a believer.

And you think that's a bad thing because you would prefer people to act in accordance with their beliefs, even if it's not rational self interest to do so? Frankly, if belief is involuntary (as you say), then we have a dilemma here: either rational self-interest, or obedience to involuntary beliefs. What do you think about that dilemma?

lacavin wrote:
Tentatively adopting a belief is not the same as believing.

Tentatively adopting a belief is not the same as committing to it. It is still believing, however -- and voluntarily, at that.

lacavin wrote:
I may with my will try to think as if I would believe in God, but that does not make me believe.

Perhaps we should start a different thread on the nature of belief. I'd like to see you argue in favour of this idea of yours that belief is involuntary. It should, of course, include a description of that involuntary mechanism. That will give us a much clearer idea as to whether this belief barrier of yours can be addressed.

lacavin wrote:
I guess this issue of voluntarily belief is really a philosophical question where we will find no answer. I cannot think of an example where I was able to adopt a belief willfully.

Can you think of an example where you actually tried?

Meh... this is getting off topic. Start a new topic on the nature of belief if you really want to discuss it. The topic here is Pascal's Wager.
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lacavin
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PostPosted: Sun Mar 22, 2009 9:41 pm    Post subject: Reply with quote

TFBW wrote:
lacavin wrote:
Do you agree therefore that you cannot use Pascal's wager for somebody that has no preferred assumptions about God's behavior?

Yes. Pascal's Wager is also not appropriate for people who have undefined beliefs as to the possibility of God's existence. If any of the values are undefined, then the person has no rational means for reaching any sort of conclusion. If such a person wishes to pursue a rational course of action, his first order of business should be to fill in the blanks.

I guess your formulation is not what you meant: Pascal's wager is made for people without defined beliefs about God's existence... I meant: it will not give a defined answer on the rational behavior for people having no clear assumption about the God's behavior assuming He exists.

This means even if I accept the uncertainty that a God may exist, because of the uncertainty about how He will act, and the resulting diverging tables, I cannot draw a rational conclusion out of a Pascal-type decision-making calculation.

I guess we are there. Because it is not possible to "fill in the blanks" without accepting the teaching of one religion, then obviously you must think one religion is correct beforehand, and if you do... well, the wager is moot.

TFBW wrote:
In my experience, the range of beliefs is fairly varied. No doubt some people will have given the matter little thought, as you say.
That's not what I meant - not ignorance, but uncertainty. Even when thinking about it, still you do not have evidence to conclude on a good set of assumptions about God's behavior.

TFBW wrote:
lacavin wrote:
Do you agree that therefore the wager cannot be used for its target audiance?

No. If a party is an atheist only because he has considered no alternatives, then the wager should at least alert him to the fact that his belief is pure prejudice.

Yeah, but he has nothing else as prejudices, in this case. As you cannot rationally determine which table is correct and hence that a given behavior dominates, the wager is just no help at all.

TFBW wrote:
I can see what you're trying to get at, but it sounds like, "there are, in principle, an infinite number of possible religions, and I can't possibly analyse all that, so I'm just going to stick with my present lifestyle because I happen to like it."

Yeah, at the end I agree it is similar to multiple religions (even if that may be multiple theological interpretation of the same - e.g. christian - religion). The result is however NOT "I'm going to stick with my present lifestyle because I like it", even if it may be the most rational to do what you like when you have no proven reason to change.
My conclusion is similar to yours - you need to do more research because you know that you don't know. Hence the discussion on God's existence thread.


In this thread, we are discussing Pascal's wager - this just prove that Pascal's wager is no help to decide. That's all. I will not use Pascal's wager to prove that you should remain atheist, I only want to demonstrate that YOU cannot use it to prove that all people with atheist lifestyles are irrational.

Let's list what we agreed on already:
- Not using infinity because it becomes absurd,
- Hence inapplicability to atheists even when they are not sure of exactly zero probability of God's existence (but assume a very, very low probability - that's why they are atheists),
- Multiple, contradictory, expected-values tables are possible,
- Hence need of more research to select the correct table - if at all possible rationally.

Can we agree now that Pascal's wager is an excellent tool to make people aware of the question and of the importance of it, but not a tool that per se allows to judge which behavior is rational or not?


If we agree on the statement above, this will be the end of the thread I guess - at least for the bilateral TFBW-lacavin debate. If not, I'll answer your further arguments in another posts.
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TFBW
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PostPosted: Mon Mar 23, 2009 3:12 am    Post subject: Reply with quote

lacavin wrote:
This means even if I accept the uncertainty that a God may exist, because of the uncertainty about how He will act, and the resulting diverging tables, I cannot draw a rational conclusion out of a Pascal-type decision-making calculation.

No, you're still missing my point. Pascal's Wager is a rational way to deal with uncertainty, so uncertainty is not a problem. The uncertainty is expressed in terms of probabilities. Pascal's Wager does not provide you with a rational way to assign probabilities to alternatives -- you have to provide your own best estimate there -- but it tells you which of those alternatives is the best choice given that you want to maximise your expected outcome. This is true whether the alternatives are "does God exist or not?" or "which kind of behaviour does God want from us?" The only difference between the two is that the former question has only two possible answers (unless you adopt some unconventional logic), whereas the latter question is more fuzzy.

lacavin wrote:
Because it is not possible to "fill in the blanks" without accepting the teaching of one religion, then obviously you must think one religion is correct beforehand, and if you do... well, the wager is moot.

I disagree completely. One can take the teachings of religions X, Y, and Z and assign them equal probability, or any other weighting of probability that seems approximately fair. Such a judgement will be purely subjective, but then again, so is the assignment of probability in the "does God exist" question. Similarly, some of the religions may dominate the table thanks to enormous potential rewards, rendering their actual probability mostly irrelevant. For example, compare those religions which offer Heaven to something like Buddhism which offers Nirvana. The kind of atheist who starts out with "get the most out of life" as his aim is unlikely to rate the reward of Nirvana very highly: it's "emptiness" is not much different from oblivion, and takes a lot more work to get there.

In fact, it's pretty obvious up front that religions which offer a Heaven or paradise are going to be the only ones worth considering if "get the most out of life" is your aim. Where you go from there in your investigations is a matter of personal choice: you have to construct a research programme. You might reason, "if there is a God and he wants people to find Heaven, then he probably has passed the needed information to mankind in some way." That being so, you might conduct a survey of things which claim to be inspired scriptures, but you'll also need to come up with a technique of sorting the wheat from the chaff. By this stage, I think Pascal's Wager has done all it can to help you.

lacavin wrote:
I will not use Pascal's wager to prove that you should remain atheist, I only want to demonstrate that YOU cannot use it to prove that all people with atheist lifestyles are irrational.

Well, I'm still leaning towards the view that if your goal is "get the most out of life" (which seems to be the common rationalisation atheists use for their lifestyle), then the rational thing to do is focus your mind on finding heaven, not live it up here and now. You're excused from this only if you think it can't succeed for some reason, otherwise you're really not following the course of action which is most likely to meet your goals.

lacavin wrote:
Let's list what we agreed on already:
- Not using infinity because it becomes absurd,

I don't agree with that. One can reason about infinities using the hyperreals. If you want to avoid infinites in your mathematics, that's your choice, but I'm not going to join you in a blanket ban on them. To me that just sounds like ad-hoc rulemaking designed to eliminate one of the known advantages the Wager offers Christianity.

lacavin wrote:
- Hence inapplicability to atheists even when they are not sure of exactly zero probability of God's existence (but assume a very, very low probability - that's why they are atheists),

If you can fill in the blanks in such a way that the expected outcome of atheism is better than the alternatives, then fine. You're going to wind up with some strangely arbitrary assumptions in order to justify the outcome, but so be it.

lacavin wrote:
- Multiple, contradictory, expected-values tables are possible,

This was never a problem. Table choice is subjective. You pick the one that you find most credible given the information that you have. If you're particularly clever, you can observe that multiple "conflicting" tables actually collapse to the same outcome, so much of the apparent conflict is irrelevant.

lacavin wrote:
- Hence need of more research to select the correct table - if at all possible rationally.

An informed choice is better than an uninformed one, clearly. It's not possible to determine the "correct" probabilities, however. The "correct" answer is not a probability at all: probabilities are used in lieu of certain knowledge about the correct answer.
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lacavin
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PostPosted: Mon Mar 23, 2009 12:44 pm    Post subject: Reply with quote

TFBW wrote:
No, you're still missing my point. Pascal's Wager is a rational way to deal with uncertainty, so uncertainty is not a problem.
The wager is a way to deal with uncertainty indeed - I understand this very well. But the way to deal with uncertainty and still obtain a certain outcome is only possible because the chosen hypothesis.
Uncertainty is indeed not a problem if and only if all alternatives lead to the same conclusion or the expected value of one alternative dominates regardless of probabilities (infinity).

Pascal works with the domination of one alternative, based on the hypothesis that God will not save unbelievers. If I give you the following value table:

Code:
(a>>1)                God exists           God exists           God does
                      rewards honesty      rewards belief       not exist

I am a believer

A.1) act as a believer     a                    a                   1
A.2) act as an atheist     0                    0                   1

I am an unbeliever

B.1) act as a believer     0                    a                   0
B.2) act as an atheist     a                    0                   1

it is clear that assuming you believe in God, you should act as a believer. But assuming you do not believe in God, how does this table help you to decide?
Whether "a" is infinite or not, whether you use the common extended real or the hyperreals, nothing will discriminate between B.1 and B.2 as long as you do not attribute at least relative probabilities to God's rewarding honesty or belief.

With this table (one of thousands of possible tables), the best bet is to be and act as a believer - the thread on voluntary belief will tell us if it is a feasible option (I don't think so) for an unbeliever. But if you do not believe, this table does not help to determine the rational lifestyle!

Of course, other tables could be created (they would however probably require antagonists view of what "act as a believer" means, i.e. uncompatible rules to follow in several possible views of God) that would even put the believer at the same level, make A.x options comparable to B.x.

This is why I mean that even with Pascal's wager, uncertainty is a problem.

TFBW wrote:
The uncertainty is expressed in terms of probabilities. Pascal's Wager does not provide you with a rational way to assign probabilities to alternatives -- you have to provide your own best estimate there

Therefore it is a personal judgement as the result depends on your personal estimates which cannot be measured. Therefore you cannot use Pascal's wager to say that it is irrational to behave like an atheist - it is only irrational within your personal subjective estimates of probabilities.
That's all I want you to accept.

TFBW wrote:
I disagree completely. One can take the teachings of religions X, Y, and Z and assign them equal probability, or any other weighting of probability that seems approximately fair. Such a judgement will be purely subjective, [...]Where you go from there in your investigations is a matter of personal choice: you have to construct a research programme. [...] you'll also need to come up with a technique of sorting the wheat from the chaff. By this stage, I think Pascal's Wager has done all it can to help you.

You confirm that you need lot's of subjective research and personal opinion. You need to use your personal judgement to sort the wheat from the chaff. That means Pascal's wager is effectively not helping to take an objective decision of lifestyle, as it is based on subjective judgements.

Can we really not agree that:
Pascal's wager is an excellent tool to make people aware of the question and of the importance of it, but not a tool that per se allows to judge objectively which behavior is rational or irrational for anybody else then yourself (within your own subjective assumptions)?

My only intention (no secret agenda here) is to help you not glide down the soapy slope of judging your opponents irrational using Pascal's wager. I (and you too) try always (even if sometimes weak formulation can give the opposite impression Embarassed) not to judge our opponents irrational and to have a discussion without judgement...
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TFBW
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PostPosted: Mon Mar 23, 2009 3:22 pm    Post subject: Reply with quote

lacavin wrote:
...it is clear that assuming you believe in God, you should act as a believer. But assuming you do not believe in God, how does this table help you to decide?

Whether "a" is infinite or not, whether you use the common extended real or the hyperreals, nothing will discriminate between B.1 and B.2 as long as you do not attribute at least relative probabilities to God's rewarding honesty or belief.

Emphasis added. So there's your solution. Make a judgement as to which scenario you consider to be more likely. If, in all honesty, you believe these three alternatives are precisely equally probable, then the rational choice is to act as an atheist, since the expected outcome is a/3 + 1/3 (for Real or Hyperreal values of a). If, on the other hand, you believe that the relative probability of God rewarding "belief" (as you put it) is even the slightest bit higher than him rewarding honest atheism, then the scales tip the other way.

lacavin wrote:
Of course, other tables could be created (they would however probably require antagonists view of what "act as a believer" means, i.e. uncompatible rules to follow in several possible views of God) that would even put the believer at the same level, make A.x options comparable to B.x.

Yes, there are an infinite number of possible tables. Some of them justify atheism, and some of them justify theism. Show me your table, and I will tell you whether your actions are consistent with what you profess to believe and what you claim to be trying to achieve.

Now that you know how it's done, you can fill in the blanks in such a way that atheism is the rational choice, thereby demonstrating that your actions follow rationally from your beliefs! Of course, in order to do that, you have to be very careful about choosing the degree to which you concede each possibility. Or, in other words, you have to choose your beliefs.

lacavin wrote:
Therefore it is a personal judgement as the result depends on your personal estimates which cannot be measured. Therefore you cannot use Pascal's wager to say that it is irrational to behave like an atheist - it is only irrational within your personal subjective estimates of probabilities.
That's all I want you to accept.

Oh, sure -- I insist on it, even. It's just that most atheists don't get past the sheer improbability (in their subjective opinion) of God existing as justification for their atheism, as though that in itself justifies the atheist lifestyle. The classic formulation of Pascal's Wager shows that to be irrational, because the question of God's existence is almost completely irrelevant to the expected value calculations. Additional beliefs are necessary to prop up the rationality of atheistic behaviour, and few of the candidate beliefs pass the laugh test, so they don't get aired in public much.

So if we're trading concessions, can I ask you to concede that the question of whether God actually exists or not has almost no bearing on whether atheism is a profitable lifestyle choice?

lacavin wrote:
My only intention (no secret agenda here) is to stop you from the slope you were gliding on of judging your opponents irrational using Pascal's wager. I try always (even if sometimes weak formulation can give the opposite impression Embarassed) not to judge believers irrational and to have a discussion without judgement.

Well, my on-going challenge has been, "demonstrate how atheism can be rational in light of Pascal's Wager." I've already made a couple of suggestions in that regard -- right as far back as my first post, even -- but the general response (from you and Bezman in particular) has been to challenge Pascal's mathematics as a basis for rational thinking, rather than come up with reasons that work within the mathematics to make atheism a rational choice.

Atheists tend to be proud of their rational thinking, and often accuse "religious" folks of all sorts of epistemic infelicities -- also known as "stupidity". All I'm really looking for here is a good solid example of that sharp atheistic reasoning. I really didn't expect the process to be this hard: I expected at least one clear-thinking rational atheist to jump up and share his reasons.

So far all I've been able to gather is that you're a sort of Calvinist atheist -- predestined to disbelieve, and constitutionally incapable of seeing anything as evidence for God's existence. That's not a reasoned approach to atheism -- it's a fatalist one. I don't have a problem with that -- fatalism is not irrational in and of itself -- but I was hoping someone would offer a reasoned response.
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Bezman
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PostPosted: Mon Mar 23, 2009 6:38 pm    Post subject: Reply with quote

TFBW wrote:
I think we have a misunderstanding as to the meaning of terms, Bez. Pm is a value between zero and one which represents a person's degree of willingness to believe that there may be a God. If you've assigned Pm an infinitesimal value, you're talking about a near-certain atheist.

Beyond that, I really can't reply because I can't follow your argument at all.

Then I believe that you must be really really mad at me, and/or deliberately choosing to misunderstand.

Just to clarify my point: I apologize if I made an unclear statement. I tried to write that IMO, your statement that Pm is a value between 0 and 1 is incorrect. I say it should be a value between 0/Inf and 1/Inf, since there are infinitely many possibilities out there.
(An "as close to being a hard-core dead-certain atheist as you can be" would thus have the Pm value of (1/Inf)/Inf, or 1/(Inf squared))

Please ask if there is something in particular that you don't understand in my reasoning, and bear in mind that I'm also struggling with a 2nd language.
*humble*

EDIT:
On second thought, I think I should refine what I've written a bit here.
Yes, you (TFBW) have already mentioned that focus is {monotheist religions that DO promise an eternal heaven}, because this was part of what I was unawaredly aiming at;

if we assume that
A = An eternal heaven/paradise does in fact exist
B = A monotheist creator God does in fact exist

then it would be rather safe to assume "if A then B", but it would NOT be safe to assume "if B, then A",
which happens to be what Pascal's wager in fact does.

In my suggested change to Pm above, I change my statement to be "Pm (or that entire side of the formula, really) should be multiplied with one more variable, namely 'P(exists)A'", where P(exists)A is the probability that such a heavenly reward actually does exist.

This is of course where subjectivity comes into the picture. I think it would be a common error to use your heart here and assume that this would have a probability value widely spread across the 0.0 to 1.0 range, whereas EVIDENCE most likely will put this value close to the one I have suggested: 1/Infinity. Thus I stick to my statement that the formula shows that the value is at best equal, and that Infinity has been wrongfully inserted into the formula to disbalance it. This re-balances it.
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PostPosted: Mon Mar 23, 2009 6:46 pm    Post subject: Reply with quote

lacavin wrote:
And Father Christmas (Bez - saw him in Sweden lately?)

Nah, he lives in Finland - Rovaniemi. Wink Very Happy
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PostPosted: Mon Mar 23, 2009 7:51 pm    Post subject: Reply with quote

Now, to another question, that REALLY gives me doubt about the validity of Pascal's wager. I have read (most of Smile) both lacavin's and TFBW's arguments back and forth, and I have come to this question, which I hope the two of them (or somebody else) can help me with:

Assume, hypothetically, that I claim/say/state/preach, to all of humankind:
"Donate 10% of all your money to me, and you will be granted eternal life in paradise".

Now, explain to me why not all that do not comply to that are not irrational, using the same reasoning as in Pascal's wager. As long as the probability of my hypothetical statement being true is not exactly zero (which it isn't), then everyone on this planet that does not obey it is irrational as soon as I say it - right?
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PostPosted: Mon Mar 23, 2009 8:45 pm    Post subject: Reply with quote

TFBW wrote:
lacavin wrote:
Therefore you cannot use Pascal's wager to say that it is irrational to behave like an atheist - it is only irrational within your personal subjective estimates of probabilities.
That's all I want you to accept.

Oh, sure -- I insist on it, even.


Party time. We are on the same wavelength!

TFBW wrote:
So if we're trading concessions, can I ask you to concede that the question of whether God actually exists or not has almost no bearing on whether atheism is a profitable lifestyle choice?

I agree on this statement.
The fact that chances are very low or very high has no logical impact on the lifestyle you should rationally choose.

There are a couple of small print attached to the statement.
Of course, for instance, a definite proof would change matter. Also this does not hold for people believing (i.e. being convinced) that God does not exist (zero probability). Most important: The vision that one individual has about this potential God has however a large impact.
Illustratively, it is rational to go to church (or give Bez 10% of your money) if you believe that God will reward people going to church (or those that give Bez 10% of their money). It is not rational do go to church, or give a copper to Bez, if you believe that God don't care (i.e. exists and don't care or does not exist at all).


TFBW wrote:
Well, my on-going challenge has been, "demonstrate how atheism can be rational in light of Pascal's Wager." I've already made a couple of suggestions in that regard -- right as far back as my first post, even -- but the general response (from you and Bezman in particular) has been to challenge Pascal's mathematics as a basis for rational thinking, rather than come up with reasons that work within the mathematics to make atheism a rational choice.

That's not fair. Many of the reasons we gave you are within the same mathematics excellent reason to judge that atheism is the rational choice. The alternative tables. The fact that remaining atheist with a non-zero probability to change your mind is as rational as opting for monotheism and that because temporal rewards are higher, the resulting expected value dominates.
You chose to ignore all our attempts. Perhaps because we were not always fully serious about them...

Because I guess both Bez and myself did not really want to use the methodology to convince people to become skeptical because we both see that as soon as we can prove the opposite using the same system... well... the system just looses its value. So we just had to convince you as well of the fact that your expectation are unreasonable and then we can close the chapter of Pascal's wager and keep discussing about the rationality of atheism in a broader perspective if this is of interest.


TFBW wrote:
So far all I've been able to gather is that you're a sort of Calvinist atheist -- predestined to disbelieve, and constitutionally incapable of seeing anything as evidence for God's existence. That's not a reasoned approach to atheism -- it's a fatalist one. I don't have a problem with that -- fatalism is not irrational in and of itself -- but I was hoping someone would offer a reasoned response.

That's not correct. I used Calvinism to illustrate because I happen to know it, but I am definitely not accepting Calvin's views. I cannot accept for instance his predetermination's views (pretty much at the core).
Of course, I have not a reasoned approach to atheism, because I am not atheist - I said already that I believe in a "first cause"-God. I am however not believing in a personal God such as the christian one. Therefore I am agnostic with regards to a personal God, but not really with regards to the existence of something supernatural.

My approach is not more "fatalist" than yours. We both have opinions and will change them only if new evidence is given. I am rational about it (meaning: rational about being mostly in a "waiting position"), because I have proven that the burden of proof lies in God's hands and that if he does not reveal himself, it is rational to not believe in him; and if He punishes me for that, then it just shows He is not benevolent. Are you as rational in being so confident in your monotheism?

Now I guess it is not intended as an insult, but being "constitutionally incapable of seeing anything as evidence for God's existence" does not really sound like a compliment. Neither does the fact that you consider I offered no reasoned response. Care to precise what you mean?

Anyway, IMNSHO, I offered pretty rational and reasoned arguments to prove that Pascal's wager is not valid. And therefore that it cannot be used to prove the irrationality of atheism nor the irrationality of theism (and hence that your expectations of getting a "reasoned atheist view within Pascal's wager" are unreasonable expectations). It is pretty on-topic - and more reasoned that just dump a table where atheists are winning...

Bezman wrote:
then it would be rather safe to assume "if A then B", but it would NOT be safe to assume "if B, then A",
which happens to be what Pascal's wager in fact does.
This is of course where subjectivity comes into the picture.

Yeah, that's exactly what I mean with assumptions about God's behavior. Pascal had certain assumptions which we may not share.

Bezman wrote:
I think it would be a common error to use your heart here and assume that this would have a probability value widely spread across the 0.0 to 1.0 range, whereas EVIDENCE most likely will put this value close to the one I have suggested: 1/Infinity. Thus I stick to my statement that the formula shows that the value is at best equal, and that Infinity has been wrongfully inserted into the formula to disbalance it. This re-balances it.

However I don't agree with you on this one. Putting 1/Inf is exactly as prejudiced than putting 1.0 or 0.314159265. It is also a subjective assumption on your part as how God is actually behaving. Of course we have no evidence that paradise exists, but that does not imply an infinitesimal probability.
As an example, until about a decade in the past, we had no evidence that extra-solar planets did exist - but every astrophysicist (and every SciFi fan) was pretty sure the probability was high. And indeed since then many have been spotted thanks to new instruments/techniques.
Absence of evidence is not evidence of absence...
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TFBW
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PostPosted: Tue Mar 24, 2009 2:00 am    Post subject: Reply with quote

Bezman wrote:
I say it should be a value between 0/Inf and 1/Inf, since there are infinitely many possibilities out there.

Oh, I see. That complaint again. I responded to similar remarks from lacavin a few posts back, like so.

TFBW wrote:
I can see what you're trying to get at, but it sounds like, "there are, in principle, an infinite number of possible religions, and I can't possibly analyse all that..."

If I accept your assertion that I must consider every conceivable possibility in my table, then my table will in fact be infinite, and there will be no possible way for me to analyse it exhaustively. I can, however, make a general observation about the entries: only those options which offer the possibility of attaining a good quality of eternal life are worth considering, because only entries with a potentially infinite reward survive multiplication with infinitesimal probability (i.e. produce a finite result). This eliminates one infinite set of possibilities -- the set of lifestyles which promise no eternal reward -- and leaves another infinite set of possibilities -- the set of lifestyles which offer the possibility of heaven or its equivalent.

Not that this helps very much. If we allow every conceivable lifestyle choice to have some possibility of leading to heaven, then we haven't eliminated any lifestyle choices -- not even atheism. Our only hope for rational decision-making here is the relative probabilities of these alternatives, which you allow to vary between 0/inf and 1/inf. On reflection, I'm not sure that this restriction is mathematically valid, since the sum of all the probabilities must be equal to one. That means that the average probability must be 1/inf, and it doesn't preclude the existence of finite probabilities. Still, that's a side issue: the core problem is that we are faced with an infinite set, not that we are faced with infinitesimal probabilities.

So, as I was saying, the only hope for rational decision-making is the relative probability of the alternatives. There are infinitely many of them, but since we are making this table up based on our own knowledge (we only insist that rational behaviour follow our own knowledge of things), then perhaps we know the top ten most likely things in the infinite set of possible paths to heaven? In fact, if we judge any one of the possibilities to be slightly more probable than all the rest, then that is our rational choice.

I will allow for one loophole in this reasoning, based on a limitation of reasoning with infinite values. If you sincerely believe that there are an infinite number of possible paths to heaven, each of which has an infinitesimal probability of being the right one, then the expected value of those possibilities can't be compared against the expected value of a finite life. That's because there are two infinities at play here: the infinite length of an eternal life, and the infinite number of possible paths to heaven. As I understand it, we can't assume that these are the same Hyperreal value, so we don't know what one divided by the other is, and so we have no basis to compare the value with the expected value of a finite life associated with a finite probability. Given these conditions, it's not irrational to prefer maximising one's finite life over an attempt to find eternal life. It's not rational, either -- there is no rational basis for decision-making that I can see under these conditions.

So, in summary, I don't fully accept your argument. In particular, analysis suggests that your restriction of Pm to a value between 0/inf and 1/inf (based on the assertion that a table must express infinitely many possibilities) is mistaken. Given that assertion, the average probability must be 1/inf, but the full range of restrictions is still between zero and one. Furthermore, if we believe that one of the possible paths to heaven has probability which is (a) finite, and (b) strictly greater than all other heaven-bound probabilities, then we have a clear winner. Of course, it's easy to imagine a table which does not meet these requirements. Such a table offers no rational basis for decision-making.

Conclusion: if rational decision-making is possible at all in an infinite table, it is dominated by the most probable path to heaven. By implication, if you assert that your choice of lifestyles is rational under these conditions, you assert, "I believe that my lifestyle choice is more likely than any other to get me to heaven."

This doesn't strike me as a line of reasoning that the average "non-religious" person would want to embrace. The alternative seems to be denial that a reasoned lifestyle choice is possible, or denial that the table of values must necessarily include every conceivable possibility.

I seriously doubt that this is the conclusion you had in mind, Bez. Maybe you could clarify further where I've gone off track in my analysis.
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TFBW
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PostPosted: Tue Mar 24, 2009 2:20 am    Post subject: Reply with quote

Bezman wrote:
Assume, hypothetically, that I claim/say/state/preach, to all of humankind:
"Donate 10% of all your money to me, and you will be granted eternal life in paradise".

Now, explain to me why not all that do not comply to that are not irrational, using the same reasoning as in Pascal's wager. As long as the probability of my hypothetical statement being true is not exactly zero (which it isn't), then everyone on this planet that does not obey it is irrational as soon as I say it - right?

Your claim sits alongside all other claims which offer infinite rewards. Pascal's reasoning dictates that such claims must be weighed on the basis of their relative probability. If, for some unfathomable reason, I consider your claim to be the most credible claim on the market, then it follows that I should promptly send you 10% of my bank balance, since that's a pretty sweet deal.

Of course, I have no special reason to grant your claim any credibility. You're up against the likes of Jesus Christ, who claimed to be "the way, the truth, the life", the sole means of access to God, and he was also willing to assert this when hauled into court and charged with blasphemy, ultimately resulting in his execution. (This forms the basis of the C. S. Lewis "Lord, Liar, or Lunatic" trilemma, but that's a different story.) That's stiff competition, Bez, so please excuse me if I assign your claim a relatively low probability and, quite rationally, keep my money. Feel free to get back to me after you've earned some credibility, though.
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PostPosted: Tue Mar 24, 2009 11:28 am    Post subject: Reply with quote

TFBW wrote:
I seriously doubt that this is the conclusion you had in mind, Bez. Maybe you could clarify further where I've gone off track in my analysis.

Thank you for the enlighting, honest and open-minded answer. You make a few assumptions that I must digest, but the maths behind most of your statements seem solid enough. I'll see if I have anything to add.
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Bezman
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PostPosted: Tue Mar 24, 2009 12:27 pm    Post subject: Reply with quote

TFBW wrote:
...I assign your claim a relatively low probability...


Ah, that's a rather good analysis, but it does not get you out of it. You are now at our end of the table. Wink

Even "a relatively low probability" multiplied with the benefits of eternal paradise - same as Pascal's wager - dictates that you should (must, if you take a strictly rational approach) do what is most beneficial in the long run. (highest EV)
And as long as the credibility/likelyness is non-zero, the "give your money" is most beneficial to anyone. Making all other behaviour irrational, right?

(Oh, do remember that we are talking of a hypothetical claim here. Smile Let's say that I, no let's call "me" ZEB in this hypothetical matter - ZEB also has a book, named "The Book", with lots of stories in it, to enhance his credibility.)

Now please explain why it is reasonable or rational to accept a statement that could give you, say 10 tickets to get into paradise, and then reject another one that could give you 5 more tickets to the 10 you already have?
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TFBW
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PostPosted: Tue Mar 24, 2009 1:29 pm    Post subject: Reply with quote

Bezman wrote:
Even "a relatively low probability" multiplied with the benefits of eternal paradise - same as Pascal's wager - dictates that you should (must, if you take a strictly rational approach) do what is most beneficial in the long run. (highest EV)

I am doing exactly that. I'm favouring Christianity over Bezmanism because although they offer the same infinite reward, I find Christianity's claims immensely more credible. The EV is infinite in both cases, but using the Hyperreal model of infinites, I can still say that Christianity's EV is much higher. Why would I back the horse with the lower perceived chance of success?

Bezman wrote:
Now please explain why it is reasonable or rational to accept a statement that could give you, say 10 tickets to get into paradise, and then reject another one that could give you 5 more tickets to the 10 you already have?

In general, it's not, but Christianity isn't a religion where you can hedge your bets like that. The first commandment (of the well-known Ten Commandments) is to have no other gods but Him. That's a point to consider, I suppose: if several religions aren't mutually exclusive, you could combine their EVs by following their superset. Of course, there's a clear limit on how much of that you can do when the religions in question are, for example, asking for ten percent of your money.
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TFBW
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PostPosted: Tue Mar 24, 2009 3:54 pm    Post subject: Reply with quote

lacavin wrote:
Illustratively, it is rational to go to church (or give Bez 10% of your money) if you believe that God will reward people going to church (or those that give Bez 10% of their money). It is not rational do go to church, or give a copper to Bez, if you believe that God don't care (i.e. exists and don't care or does not exist at all).

Hooray! More common ground.

lacavin wrote:
That's not fair. Many of the reasons we gave you are within the same mathematics excellent reason to judge that atheism is the rational choice. The alternative tables.

I'm fully aware that some tables favour atheism. I have yet to see an atheist produce such a table and say, "this is my table, and as you can see, the atheist lifestyle has the highest expected value." This, more than anything else, is what I hope to see, particularly since the atheist lifestyle is supposed to be about maximising value in life. Surely it must be possible to illustrate this maximisation process mathematically?

lacavin wrote:
The fact that remaining atheist with a non-zero probability to change your mind is as rational as opting for monotheism and that because temporal rewards are higher, the resulting expected value dominates.

I take exception to that line of reasoning. It's only true for infinite expected values using the Extended Real Numbers. It's false for all finite values, and for infinites using the Hyperreals. If you want to insist on this point, then fine, but it entails the idea that a 99.9% chance of winning an infinite prize is exactly the same as a 0.01% chance of winning an infinite prize. Would you seriously tell me that these two things are exactly the same? That the EV in both cases is infinite, so it makes no difference which you choose?

lacavin wrote:
You chose to ignore all our attempts. Perhaps because we were not always fully serious about them...

I'm not ignoring them, but as you can see, I have unresolved issues with them. The possibility of alternative tables doesn't invalidate the reasoning process: in fact, it allows a rational defence of atheism so long as you choose a table carefully. The challenge is to produce such a table that can be taken seriously. Similarly, the mathematical trick where being an atheist with an option to become a monotheist results in a high EV entails some pretty weird reasoning. Rest your case on that logic if you like, but I want to offer you a chance to back away from it, given the logical implications of the position.

lacavin wrote:
Of course, I have not a reasoned approach to atheism, because I am not atheist - I said already that I believe in a "first cause"-God. I am however not believing in a personal God such as the christian one. Therefore I am agnostic with regards to a personal God, but not really with regards to the existence of something supernatural.

Fine, but you're effectively atheist in terms of lifestyle, aren't you? I'd use the term "godless" instead of "atheist" to make the distinction, but I don't want to sound pejorative. The question is whether you have a reasoned approach to your lifestyle. Are you trying to maximise what you get out of life? How do your beliefs justify your actions? Maybe you are... read on.

lacavin wrote:
I am rational about it (meaning: rational about being mostly in a "waiting position"), because I have proven that the burden of proof lies in God's hands and that if he does not reveal himself, it is rational to not believe in him; and if He punishes me for that, then it just shows He is not benevolent.

So... if I'm following this correctly, the key to your apathy is that you are quite certain that heaven can only be attained by an act of God -- namely, the bestowing of either sufficient evidence or sufficient faith on a person. You are quite certain that nothing you can say or do will make any difference, and that the outcome is entirely in God's hands. Furthermore, you are quite certain that nothing you can do will make God any more likely to bestow that gift or not: his decisions in that regard are arbitrary, or at least completely beyond your power to influence.

Those particular beliefs do lead, rationally speaking, to "live life as you please" having the greatest EV. A few well-placed certainties can work around Pascal's Wager quite nicely. I do, however, describe that set of beliefs as "fatalistic", primarily because it categorically denies people any power to influence their own destiny in this matter. You said you weren't fatalist: is that because I've misunderstood your beliefs, or because you thought I meant something else by "fatalist"?

lacavin wrote:
Now I guess it is not intended as an insult, but being "constitutionally incapable of seeing anything as evidence for God's existence" does not really sound like a compliment. Neither does the fact that you consider I offered no reasoned response. Care to precise what you mean?

Well, I've attempted to re-write your ideas into a more carefully reasoned response above, so that's the kind of "reasoned response" I sought. The "constitutionally incapable" is in reference to your denial that belief is or can be voluntary. That is, your assertion that your unbelief is not caused by wilfully choosing to interpret evidence in a certain way: rather, it is an aspect of your being that you have no more control over than your eye colour. (I'm still not sure I buy that argument, but we're discussing it elsewhere, so I won't argue here. Also, I note that it's another fatalist position: a denial that you have any influence over things.)
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lacavin
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PostPosted: Tue Mar 24, 2009 10:33 pm    Post subject: Reply with quote

TFBW wrote:
Hooray! More common ground.

I guess that's the end of this particular debate.
We both agree on the most important, and therefore I will proceed now to try to give you a possible rational explanation within Pascal's wager to follow an atheist lifestyle - I'll do that by mostly quoting previous examples I gave.

I tried to make my argument such that monotheists have also the optimal solution! I don't want them to be convinced, to renounce religion, and to go to hell. Razz

Let me start with the reasoning to prove that the burden of proof lies in God's hand (in Proof of God thread). This shows that God will give us evidence if he wants us to believe in him (and more, such as honor him).
Obviously, therefore, if God does not give any evidence, he won't expect us to believe in him. What does he expect in this case? Of course that we behave rationally and use or free will rationally - this is how he meant us to be.

The logical Pascal-equivalent table is therefore:

Code:
                            Personal God         No God or
                                                 impersonal God

God gave me evidence*

A.1) act as a believer           a                    0
A.2) act as an atheist           0                    1

God did not give me evidence

B.1) act as a believer           0                    0
B.2) act as an atheist           a                    1

*) In the case of no God or impersonal God, the evidence was wrong - the "believer" has made a false interpretation.
Note: for this table, if you assume that it is possible to voluntary change your belief, you can remove the "act as" in every alternative without changing the interpretation.

This truth table is perfectly logical. God made us in his image as rational beings that can reason on abstract tables like Pascal's wager. I cannot imagine that God would be expecting from his creature to renounce rationality. Rational behavior is to act according to your beliefs.

We are there. For atheists (people that don't believe in god because they had no evidence and use Occam's razor to remove unnecessary hypothesis), the rational behavior is to live like an atheist. If a is larger than 1, for monotheists (they believe in God because they received sufficient evidence), the rational behavior is to give Bez 10% of your... euh... sorry... to go to church.

Of course monotheists should be sure of their evidence. If God actually did not send them sufficient evidence and they irrationally behaved like believers, they may miss the payoff! Therefore if you think it is only possible that there is a personal God, the rational behavior is to remain atheist...


TFBW - is this a rational enough approach to show that atheist lifestyle is rational? Do you understand why it can be reasoned to have such a lifestyle? You may consider it mistaken, but probably not irrational...

I hope you did not expect a table with infinity paybacks in the column without God, because by definition for atheists, there is no infinite payback... as there is no afterlife.


TFBW wrote:
So... if I'm following this correctly, the key to your apathy is that you are quite certain that heaven can only be attained by an act of God -- namely, the bestowing of either sufficient evidence or sufficient faith on a person. You are quite certain that nothing you can say or do will make any difference, and that the outcome is entirely in God's hands. Furthermore, you are quite certain that nothing you can do will make God any more likely to bestow that gift or not: his decisions in that regard are arbitrary, or at least completely beyond your power to influence.

Therefore I am quite certain - that heaven - if it exists at all, I am really not certain it does - can only be attained by following God's plan for us - i.e. use our free will rationally.
I am also quite certain that we cannot prove the existence of such a personal God with science or logic, i.e. with our human means; therefore that only God can give us sufficient evidence of His existence, and therefore belief in Him and as a consequence belief in His messages and wishes (if any).
Assuming such a personal God, I am quite certain that behaving with honesty - i.e. rationally following your beliefs and not pretend, lie - is the best way to please Him. I also assume that searching for the truth will please him (you expect it from rational beings) and may be the best way to influence (if at all possible) his decision to give evidence.

So yes, I can do something to make a difference: be rational. Being rational means don't believing without sufficient evidence, and looking for evidence when in doubt.

All in all, that's not so fatalistic - why would I discuss on the 4th wall if I would be fatalistic?
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Bezman
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PostPosted: Thu Mar 26, 2009 10:54 pm    Post subject: Reply with quote

TFBW wrote:
...Bezmanism...

Oh PLEASE guys! Its ZEBMANISM, remember? Wink

Other than that, my head is to tired than to judge otherwise than that you snuck your way out of it rather nicely. Dangd, missed that backdoor. I'll have to look at that again tomorrow though - don't hold your breath! Wink
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PostPosted: Fri Apr 10, 2009 1:38 pm    Post subject: Reply with quote

No comments - does this mean this was fulfilling TFBW's expectations?
Are you now convinced that there is a rational version of Pascal's wager where unbelief is a rational solution?
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PostPosted: Sun Apr 12, 2009 1:17 am    Post subject: Reply with quote

I'm convinced.
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TFBW
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PostPosted: Sun Apr 12, 2009 4:15 am    Post subject: Reply with quote

The question remains, of course, as to whether you agree with all the premises on which that argument is based, such as the idea that an honest, rational lack of belief in God is the best way for a natural doubter to please Him.
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PostPosted: Sun Apr 12, 2009 8:45 pm    Post subject: Reply with quote

TFBW wrote:
The question remains, of course, as to whether you agree with all the premises on which that argument is based, such as the idea that an honest, rational lack of belief in God is the best way for a natural doubter to please Him.

This I can confirm.

Assuming a God created humans purposefully, what do we have that is different from animals? Of course, it is not completely unseen in the other animals (some chimpanzee do use crude tools), but I would guess it is our reason, and the resulting capability to take our own destiny under our control and to progress, personally as well as globally from generation to generation.

If a God created us thus, I would assume He would be pleased to have us behave in such a way - i.e. basing our acts on reason more than instincts. In my views, much more than He would be pleased by blind adoration - what does such a superior being need adoration? If He did, He could strike blindly with thunder and we would fall in line.
I can imagine He would be even more pleased by Love, but you cannot love really somebody you don't know - and we cannot know Him in this life. He may be interested in morality, perhaps. But moral behavior does not require belief.

Therefore, assuming a personal God exists and is interested in us, I would guess Him to be mostly interested in the application of reason.

All this is not facts, of course, it is only an opinion. But I see it as more probable than the others within my understanding (and I can not reason beyond my understanding, can I?).
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PostPosted: Wed Jun 02, 2010 9:11 am    Post subject: Reply with quote

Just wanted to add to show my appreciation of Pascal even if I don't agree:

I had a son last month. His name is Pascal.

Very Happy
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PostPosted: Sun Sep 26, 2010 9:27 am    Post subject: Reply with quote

"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"

This 'conflict' in Christianity can easily be explained through a short story.

Three blind men are walking along a road and they come across an elephant. They reach out to touch it, trying to figure out what it is. A while later they are arguing about what sort of creature it is.

You see, one of the men touched the tusk, and he can't possibly understand how the animal was wrinkly... it was smooth!

Another man touched the tail, and he argues even more, saying it was incredibly hairy.

And the third man was in the middle, who had touched the leg.

All three men touched the elephant, all three view were accurate. But their problem was how each perspective was 'blown out' of proportion, or simply misunderstood. God is understanding of different churches. There will not just be Mormons or Catholics in heaven, but a combination consisting of those who are trying.
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PostPosted: Mon Sep 27, 2010 2:53 pm    Post subject: Reply with quote

Once Upon a Time wrote:
There will not just be Mormons or Catholics in heaven, but a combination consisting of those who are trying.


Those who are trying what?

If it is those that are trying to understand, then there will be also lot's of agnostics and atheists on top of the mormons, hindu, muslims and other taoists in heaven...

By the way, I like your story - it is an excellent illustration!
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