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Pascal's Wager
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lacavin
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PostPosted: Mon Mar 16, 2009 9:09 am    Post subject: Reply with quote

John Theta wrote:
0.5 * Infinity = Infinity
You can't do that. Infinity is not a number.


I'm not a mathematician, but according to the Extended Real Numbers on Wikipedia, the algebra of this group that consists of all real numbers (R) plus infinity and -infinity (R-dash) allows it.

The extended algebra is:
a + Inf = Inf + a = Inf if a is not -Inf
a - Inf = -Inf + a = -Inf if a is not Inf
a * Inf = Inf * a = Inf if a belongs to (0, Inf]
a * Inf = Inf * a = -Inf if a belongs to [-Inf, 0)
and so on...

So it looks like 0.5 * Inf = Inf, as 0.5 belongs to (0, Inf].

You can prove it ad absurdum by defining infinity as larger than the largest number you can think of. If 0.5*Inf is not infinite but equal to a, than obviously you can think of a larger number: (a+1)*2. Therefore Inf was not the largest number you could think of, and hence by definition not Inf at all.

It also looks like Inf - Inf = undefined.

On top of it, it that would be wrong, than the whole Pascal's wager would be because it is based on the formula p*Inf = Inf for all nonzero positive p.
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Bezman
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PostPosted: Mon Mar 16, 2009 2:55 pm    Post subject: Reply with quote

Actually, after reading all the reasoning from both parties, I must draw another, quite depressing, but nevertheless, mathematically correct, assumption.

Pascal's wager makes suicide the only reasonable option.

Why?

Do the maths again.
No matter what value you give your earthly life (currently theoretically maximum of 1.0, most likely less), when you compare it to eternity, it means NOTHING. This is the outcome of the original wager and also what you have both shown with your equations.
Not even a perfect (earthly) life will mean SQUAT in the long run (1.0/Inf).
Thus, the only reasonable thing to do is to .become a true believing monotheist ASAP, then go kill yourself.
Why live a life (especially if it is not superb) which will be divided by infinity in comparison and most likely forgotten already when you enter the (alleged) afterlife.

Or: are we then wasting something? Not if the possible reward is paradise in eternity. And if it isn't? Well as long as that chance is not exactly zero... Wink

Thus, I deduct from the mathematics of Pascal's wager that suicide is the only reasonable decision you can make of it. Anything else would be futile.

(Yep, there is a small amount of .irony. in this post, but it IS mathematically true. It is mainly meant to point at the absurdity of infinity in a decision model.
And no, I don't plan to suicide and I strongly appeal to anyone reading this to not even think of doing it either.)
EDIT: Changed the word "glee" which could be misinterpreted.
EDIT2: Changed "pray like h*ll for x period of time" to "become a montheist..."

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lacavin
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PostPosted: Mon Mar 16, 2009 3:28 pm    Post subject: Reply with quote

Bezman wrote:
Pascal's wager makes suicide the only reasonable option.

Not really.
Assuming that suicide does not exclude you from heaven, suicide or continuing to live are equivalent on the long view.
Feel better? You can be reasonable and keep on living Wink...

But I agree that it is absurd.
And that you should not suicide.
Really.

Because it's a sin and there is a probability that it will send you to hell. Because Hell has a value of -Inf, this option evaluates to -Inf. Of course it is still possible that God will understand and send you to paradise. Therefore it evaluates also to +Inf.
Mmmm... +Inf = -Inf...???? Twisted Evil

Just don't.
Really.
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Bezman
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PostPosted: Mon Mar 16, 2009 4:27 pm    Post subject: Reply with quote

lacavin wrote:
...suicide or continuing to live are equivalent on the long view.

Mathematically yes, but everything you do (except strengthen your belief) will be futile. So why go on doing it?
And I hold your statement for "not true" if you assign a (relatively) negative value to continuing to live after you come to that conclusion.

Or: Do you consider it equally good to wait for your bus, in pouring cold rain, without an umbrella, for 30 (or x) years, or to have it come right now - if you know you will come to the exact same destination at the exact same time and that the journey will be exactly 5 minutes in either case? (Temporally impossible yes, but that's what this is about.)

And no, it does not make me feel a squat better about Pascal's wager! Very Happy

lacavin wrote:
...there is a probability that it will send you to hell.
Hey, this topic is about a wager - where are your guts, man? Wink Laughing
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lacavin
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PostPosted: Mon Mar 16, 2009 4:58 pm    Post subject: Reply with quote

Bezman wrote:
lacavin wrote:
...suicide or continuing to live are equivalent on the long view.

Mathematically yes, but everything you do (except strengthen your belief) will be futile. So why go on doing it?
And I hold your statement for "not true" if you assign a (relatively) negative value to continuing to live after you come to that conclusion.

Well, obviously, if you assign to your life a negative value, suicide is a logical option. If you think your life is worth living (positive value), then not.
I prefer not waiting for the bus, of course. Unless I am with a friend or a nice lady... again positive or negative value for your time...

This independantly from afterlife. Actually the presence of afterlife cancel the value (positive or negative) of your temporal life and hence cancel any incentive to live longer and any incentive to suicide. Razz

But don't.
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TFBW
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PostPosted: Tue Mar 17, 2009 3:02 am    Post subject: Reply with quote

lacavin wrote:
So it looks like 0.5 * Inf = Inf, as 0.5 belongs to (0, Inf].

In the system of Extended Real Numbers, what you say is true. That particular system is not preferred by mathematicians for most purposes, since it lacks many of the properties we take for granted in other systems -- thus your earlier error of assuming that "inf - inf = 0". Bear in mind that "truth" in mathematics is relative to the system in which the equation is expressed.

We should question whether the system of Extended Real Numbers is appropriate for reasoning about the wager. I suggest that your examples demonstrate that it is not. Although it's true that someone who receives either eternal life or oblivion on the basis of a coin toss has an expected outcome of infinity (given "eternal life is infinitely valuable"), it's also clear that this is not equal to a guarantee of eternal life: it is precisely half as valuable.

Fortunately we can express this using the much more conventional Real Number system, and speak of limiting behaviour as things approach infinity, rather than treat infinity as a number. Using that approach, it is clear that in the expression "0.5 * x = y", although x approaches infinity as y does, the equality holds only when x is twice the value of y. Thus, in terms of the wager, we might say that the expected outcome of someone who receives either eternal life or oblivion on the basis of a coin toss is the same as the expected outcome of someone who receives a guarantee of eternal life of half the quality.

That is my intuitive evaluation of the situation, and the Real Number system supports it, while the Extended Real Number system contradicts it. I therefore prefer the Real Number system for reasoning about the wager. If you insist on the Extended Real Numbers, that is your prerogative, but it means we can not agree on the significance of infinite values.
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TFBW
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PostPosted: Tue Mar 17, 2009 3:19 am    Post subject: Reply with quote

Bezman wrote:
Thus, I deduct from the mathematics of Pascal's wager that suicide is the only reasonable decision you can make of it. Anything else would be futile.

You haven't shown that futility makes suicide a better option, mathematically speaking. Your reasoning is emotional: something along the lines of, "futility is depressing, and I'm going to kill myself because I'm depressed." If you've shown anything mathematical, it's that whether your life is very short or very long makes little difference in the overall (eternal) scheme of things, and I agree with that assertion.

It's also a major assumption on your part that our actions in this life have no bearing on the quality of our afterlife. That's not an assumption you can take for granted where monotheism is concerned: some believe that suicide precludes a person from receiving eternal life. Such nuances are outside the scope of Pascal's Wager, however.
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lacavin
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PostPosted: Tue Mar 17, 2009 9:40 am    Post subject: Reply with quote

TFBW wrote:
We should question whether the system of Extended Real Numbers is appropriate for reasoning about the wager.

Well, it is the only system we have that allow arithmetic with the infinity. It is also not so strange. It behaves similarly to normal real, with few difference and fewer undefined operations (e.g. Inf - Inf, or 0 * Inf).

Infinity behaves like zero for multiplication - it is an "absorber". Anything times zero is zero. Anything time infinity is infinity.
So if you say, that yes, it is infinite but only half as big, than you must accept that a contract that promise you 150% of a base salary of zero is better than a contract with only 100% of the zero base salary. because it's zero, but a bigger zero...

TFBW wrote:
Fortunately we can express this using the much more conventional Real Number system, and speak of limiting behaviour as things approach infinity, rather than treat infinity as a number. Using that approach, it is clear that in the expression "0.5 * x = y", although x approaches infinity as y does, the equality holds only when x is twice the value of y. Thus, in terms of the wager, we might say that the expected outcome of someone who receives either eternal life or oblivion on the basis of a coin toss is the same as the expected outcome of someone who receives a guarantee of eternal life of half the quality.

OK. But if y is not equal to x, it means y is not infinite (when does a "smaller" infinity become finite? - never according to mathematics, but with your logic, if 0.5* Inf < Inf, the logical consequence is that it will...).
Then I guess 0.9* Infinitiy is not infinite either. So a * Infinity < Infinity if a <1, I guess. (Funnily, if a > 1, then it becomes bigger than infinity. What's bigger then infinite? God's God? Wink)

This means that as soon as I assign a probability lower than 100% for "the existence of a God that will provide an eternal life of bliss if I believe in him", then the reward of belief becomes finite.

Then it becomes really important to judge the rewards of an atheist lifetime, because while any finite number was nothing compared to infinity (hence the choice of "1"), all finite numbers are significant compared to another finite number.

So Pascal's wager is reduced to: If you assume that it is better to have (insert probability) chances for paradise compared to have a better lifetime, then you should believe in God.
This assertion is correct; if you do, then you should. But atheist do not, so they should not. The wager will only convince the convinced.

TFBW wrote:
speak of limiting behaviour as things approach infinity
OK. Let's go: whatever the (finite) reward, if the probability to get it tends to zero, then the expected value tends to zero. At the limit, it is zero. So people thinking that the probability of God's existence is very, very small (but cannot prove it is exactly zero), i.e. atheists, have a wager where atheism dominates with its sure value of 1.
Or did you want to apply the "limiting behavior" only to the numbers that support your opinion?


Damn, I guess I promised not to react anymore. Mmmm. Bad, bad. But it is difficult to resists, because it is just incorrect: you cannot take infinity (or pass to the limit) when you like it (so that whatever the probability, religion has a better payoff) and assume infinity behaves unlike infinity (suddenly you take the probabilities into account) when it disturbs you. This is just wrong.
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Bezman
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PostPosted: Tue Mar 17, 2009 5:29 pm    Post subject: Reply with quote

TFBW wrote:
Bezman wrote:
Thus, I deduct from the mathematics of Pascal's wager that suicide is the only reasonable decision you can make of it. Anything else would be futile.

You haven't shown that futility makes suicide a better option, mathematically speaking.

Let's see about that then. IMO, the not-so-modest Blaise did not think this one through properly - at least not this aspect of it.

First we have Pascal's wager decision theory table. I will use the notations from Wikipedia, where B is "act is if God exists" (Believe) and G is "God does indeed exist". The negatives of these are then ~B and ~G ("not B" and "not G").
Code:

                                       God exists (G) | God does not exist (~G)
Living as if God exists (B)                      +∞   |             f1
Living as if God does not exist (~B)             f2   |             f3


Now what are the broken down EVs (Expected Values) of these four alternatives?
for BG = (qB * 1) + (qAL(B) * +∞ * pB)
for B~G = (qB * 1) + (0)
for ~BG = (q~B * 1) + (qAL(~B) * +∞ * p~B)
for ~B~G = (q~B * 1) + (0)

where:
q = Quality of life (0.0-1.0, average value for (the remainder of) your life, starting now)
AL = Afterlife
p = the chance (0.0-1.0) of making it to AL
1 = assumed value of the length of your remaining earth-life, see note at bottom

This also assumes to apply to anyyou at anyyou's present time of life.


{Unimportant trivia:
Well. Both the X~G cases boil down to whether you prefer B or ~B lifestyle.

Also we can
not outrule that even prodigal sons and alike can make it to AL, although p~B is most likely a tiny fraction of pB. Thus, in my opinion, "f2" should also be "+∞" in the table.}

Now, down to my showing and explaining.
For either of the cases, the value of the (q?B * 1) is in the range 0.0-1.0.
I am not a mathematician and I don't want to make a mathematical error for you to gloat in when moving the +∞ part around, so I'll leave that to anyone that actually likes doing such work.
It should however be fully clear to anyone that studies the equation that no matter what value you assign to (qB * 1) or (q~B * 1), it will never be greater than 1, and when you compare it to (divide it by) the value on the right side of the plus sign, it is near zero (0.0 to 1.0 divided by {some fraction of Infinity}). This translates to: whatever you do in your earthly life, it will be worth zero and nothing in the Pascal-based EV equation. Regardless if you end up with "1.0" or "0.0" in that part, it will be worth zero. Thus, why do you want to spend time and effort on doing something worth ZERO? Or, as I previously called it, "futile".

And; Using common sense, if you spend your time and effort on doing something that you know has no value, you are either brain dead, or you will know that you are wasting your time and efforts and therefore suffer from doing it; "Why am I doing this? There is no use! Why even try?".
Thus, NOT doing it will save you from named suffering/thoughts and IS a better option. "Apathy (and belief) until God chooses to pull me away from this existence" appears to me as the optimized choice - zero effort, same reward.

Oh. You want that mathematically too? OK. *groans* Smile

PqL = Perceived quality of your (remaining) earthly life
VoWYD = Value of What You Do during the of the rest of your earthly life (...which we have already established to be nearly ZERO in the equation and reasoning above.)
E = efforts in a negative meaning - (Energy you spend on) things you do that you don't want to do and can (at least theoretically) choose not to do. (You can also replace it with "suffering" and get an equally valid equation.)
G = Good deeds and any other positive value creating actions

PqL = (G * VoWYD) - (E * Time)

Since VoWYD is (nearly) 0, the more effort you spend, and the more Time you spend doing it, the lower your PqL will be. Thus don't.

OK, that'll have to do for now - I'm totally whacked after typing, proof-reading and editing this for nearly/over(?) two hours. Please tell me if this is unclear or incorrect somewhere, and I'll try to fix the holes.
Tomorrow. Wink


Note that the "1" in (qB * 1) may be worth a little more than just "1", since they statistically may live longer than ~B, but I will leave that speculation out of the formula. I also note that x / Inf is "undefined", but if you try with higher and higher numbers, you will see that the result approaches zero.

Also please note that I have left out all reasoning of "living a good life", "doing the right thing", "helping others onto the right path and thus saving them" etc and other moral and important considerations, since they are simply not part of the original decisionmaking table, and certainly not part of or even suitable in this specific discussion topic.
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TFBW
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PostPosted: Tue Mar 17, 2009 5:50 pm    Post subject: Reply with quote

lacavin wrote:
TFBW wrote:
We should question whether the system of Extended Real Numbers is appropriate for reasoning about the wager.

Well, it is the only system we have that allow arithmetic with the infinity.

Perhaps it's the only one that you've heard of, but there are numerous arithmetic systems which include a concept of the infinite. As I said earlier, "truth" in mathematics is relative to the system in which the equation is expressed. My analysis is true when the system of Hyperreal numbers is used. Under that system "infinity" is not a number -- it is a class of numbers: the infinites. Different infinites can be bigger or smaller than each other, but every infinite is bigger than every finite, and every infinitesimal is greater than zero but smaller than every positive finite.

It's no big deal that you weren't aware of this -- you've said that you're not a mathematician, and this is pretty obscure stuff. At the same time, however, you are making a lot of extremely bold claims about advanced mathematical concepts and suggesting that I'm manipulating the figures to suit my agenda. Specifically, you said:

lacavin wrote:
But it is difficult to resists, because it is just incorrect: you cannot take infinity (or pass to the limit) when you like it (so that whatever the probability, religion has a better payoff) and assume infinity behaves unlike infinity (suddenly you take the probabilities into account) when it disturbs you. This is just wrong.

Please reflect on this, and ask yourself whether your comments were justified in retrospect. I've found that I tend to produce a better argument when I take a charitable view of my opponents' arguments: that is, I assume perhaps that they have a point, and know what they're talking about. Maybe you could use a little more of that.

Most of your argument above was based on the idea that the extended real numbers are the only way to reason about infinity. Now that you are aware of the broader possibilities, would you like to retract or modify any of your objections and comments?
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lacavin
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PostPosted: Tue Mar 17, 2009 9:49 pm    Post subject: Reply with quote

TFBW wrote:
My analysis is true when the system of Hyperreal numbers is used.

Thanks for showing those different systems. I indeed did not know them. Embarassed

While I agree now that there are formal systems where 0.5*Inf < Inf but still infinite, this does not really help for our problem. With hyperreal numbers, if one assign an infinitesimal probability to God's existence, the product p*Inf is apparently undefined (see on this text p.31), except in special situations that do not apply here.

This is normal. Only a system with a "true" infinity - larger as any other number you can think of - will give you a defined, infinite, result for any non-zero multiplication. And such systems have by definition that a fraction of this infinite remains the same infinite. It is circular. If 0.5*Inf is not equal to Inf, than obviously p*Inf may become small even if p is non-zero.

You need however p*Inf to be infinite for any non-zero p in order to convince an atheist (that by definition considers p to be very, very small) of this logic - only so can you inverse the burden of proof: "atheism is irrational unless you are sure that the probability of God's existence is really zero!".

I don't know - perhaps some mathematicians did invent some more complex systems where what you want is possible, but I doubt it. Unless proven otherwise:
  1. Either a*Inf = Inf for all non zero a and in this case reward of heaven is infinite, but it is as rational to toss a coin than to become monothesit,
  2. Or a*Inf is not equal to Inf for all non zero a, and in this case the wager will be dominated by atheism if the probability for God's existence and paradise is deemed infinitesimal - at best it will be undefined and hence have no value.
My core statement is therefore that you must use the same rules for all discussions of the wager, so you cannot use rule #1 to say that expected value of heaven is infinite, and than rule #2 to say that my option to remain atheist with an open mind is not as rational.


TFBW wrote:
Please reflect on this, and ask yourself whether your comments were justified in retrospect.

Therefore, I regretfully consider that while I was obviously factually wrong in the assertion of "only system to deal with infinity", the core critic is and remain justified. Can you find a rule system that supports infinite reward for infinitesimal probability but discriminate between monotheism and decision on a coin-toss?

TFBW wrote:
I've found that I tend to produce a better argument when I take a charitable view of my opponents' arguments: that is, I assume perhaps that they have a point, and know what they're talking about. Maybe you could use a little more of that.

Well, I am sorry for the insults. You may (I quote a certain TFBW) not be "wilfully obtuse" but be honestly mistaken. Razz
In the heat of discussion, both our tongues may slip. As you well know after several month of participation, I usually also try to be - if not charitable, than respectful - with my opponents. Please accept my excuses for the slip; I look forward to keep debating, this is highly interesting and I keep learning.


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lacavin
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PostPosted: Tue Mar 17, 2009 10:03 pm    Post subject: Reply with quote

Bezman wrote:
IMO, the not-so-modest Blaise did not think this one through properly - at least not this aspect of it.
To defend my tongue-brother Blaise, he certainly did not think this through as completely as he wanted. The pensées are notes published after his untimely death, not finished and polished publications.

Bezman wrote:
PqL = (G * VoWYD) - (E * Time)

Since VoWYD is (nearly) 0, the more effort you spend, and the more Time you spend doing it, the lower your PqL will be. Thus don't.

If E * Time > G * VoWYD, than PqL is indeed negative.
If however, VoWYD * G is deemed larger, than you should keep living.

VoWYD may be close to zero on an infinite perspective, but so is also E, and of course Time.

This is independent of Pascal's wager and any thoughts on afterlives, therefore it is not a consequence of Pascal's wager.
In words, you say: "Does the sufferings in my life gets compensated by the good moments?", and Pascal's wager just tell you that both sufferings and good moments are anyway small compared to afterlife, which does not impact on the answer.

For me, by the way, the formula should be a bit different:
PqL = (F - E) * Time + VoWYD*G
F is fun. E is your suffering. For me, F>E so suicide is anyway a stupid option. If E>F and (F-E)*Time > VoWYD*G, than suicide can be a rational option.
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Bezman
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PostPosted: Tue Mar 17, 2009 10:07 pm    Post subject: Reply with quote

lacavin wrote:
...and I keep learning.

Me too. I like the concept of Hyperreals - easy to understand.
Still thinking about if I need to change anything I wrote though.

Keep it coming, TFBW!
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PostPosted: Wed Mar 18, 2009 1:08 am    Post subject: Reply with quote

lacavin wrote:
You need however p*Inf to be infinite for any non-zero p in order to convince an atheist (that by definition considers p to be very, very small) of this logic - only so can you inverse the burden of proof: "atheism is irrational unless you are sure that the probability of God's existence is really zero!".

I'd consider it progress if we could agree that Pascal's Wager illustrates that it's irrational for an agnostic (who assents to the possibility of God's existence with finite, non-zero probability) to live an atheist lifestyle. At the very least, that would allow me to present such agnostics with a trilemma: admit that you're irrational, admit that you're an atheist (not an agnostic), or get busy researching possible afterlife scenarios (give up the atheist lifestyle).

I don't need Pascal's Wager to address hard-core atheists -- those who do not assent to the possibility of God's existence, or admit only an infinitesimal possibility of such (whatever that means in practical terms). In a situation such as that, I can simply inquire as to the source of their remarkable certainty. If such a position is rational, there must be some way to demonstrate it. If, on the other hand, it's not rational, I have no reason to challenge it.
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Leorobin
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PostPosted: Wed Mar 18, 2009 4:06 am    Post subject: Reply with quote

Jhon is right, but we can use infinity as a number for some conceptual relations.
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Bezman
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PostPosted: Wed Mar 18, 2009 2:31 pm    Post subject: Reply with quote

Just a few short comments:
lacavin wrote:

Bezman wrote:
PqL = (G * VoWYD) - (E * Time)

Since VoWYD is (nearly) 0, the more effort you spend, and the more Time you spend doing it, the lower your PqL will be. Thus don't.

If E * Time > G * VoWYD, than PqL is indeed negative.
If however, VoWYD * G is deemed larger, than you should keep living.

VoWYD may be close to zero on an infinite perspective, but so is also E, and of course Time.

Well, in that case we can replace the infinitesimals in the equation with zeroes like this:
PqL = (G * 0) - (0 * 0) = 0
Thus the special case still gives PqL = 0, which was my point.
(And if you can make do with using less than an infinitesimal (G * VoWYD) of effort to complete your life, you are indeed economic! Wink)

lacavin wrote:

For me, by the way, the formula should be a bit different:
PqL = (F - E) * Time + VoWYD*G
F is fun. E is your suffering. For me, F>E so suicide is anyway a stupid option. If E>F and (F-E)*Time > VoWYD*G, than suicide can be a rational option.


I understand what you meant, but I think you got it wrong in the underlined part... Smile
Hint: if E>F, then (F-E) is negative and not likely to be bigger than the right side of the formula... Wink

(In my subjective opinion, E is always at least twice, most often ten times, and not seldom more than 100 times the F or G you get from it, but that is just the way life is, and has always been, at least for me. I see it as "the normal state of life" and I have never considered suicide because of that. I just seek to get as much F as possible to keep the F/E ratio at an as high level as possible. Smile)
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PostPosted: Wed Mar 18, 2009 2:41 pm    Post subject: Reply with quote

TFBW wrote:
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.

Actually, NO. It depends on what value you put into the "1". For this equation, it is equal to "the maximum value you could ever get out of earthly life", namely 1.0. You wouldn't consider one who dedicated his or her entire life to theism "being a hard-core dead-certain atheist as [he/she] can be without actually being one", would you?
Once again, I say the numbers are flawed, or rather, stacked unfairly.
It is the same unfairness and abuse of power that the Spanish Inquisition used to judge alleged heretics in the past.
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PostPosted: Wed Mar 18, 2009 4:34 pm    Post subject: Reply with quote

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.
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PostPosted: Wed Mar 18, 2009 8:28 pm    Post subject: Reply with quote

TFBW wrote:
I'd consider it progress if we could agree that Pascal's Wager illustrates that it's irrational for an agnostic (who assents to the possibility of God's existence with finite, non-zero probability) to live an atheist lifestyle.

I guess we can throw a party right now. We agree on this one. Laughing

As soon as you don't target atheists, then my third objection is answered. Of course, the wager looses also a significant part of his interest...

This reformulates the wager as: If you assume that there is a real (albeit small) chance to have a God which grant eternal paradise to those that believe in him and not to those that do not believe, then you should believe in this God.
It is a correct assertion and I think an interesting argument for agnostics.

Now, of course, as usual, the first term "if" will be the hard one. Because accepting a finite, non-zero probability for the presence of a God is one step, but the agnostic still have to judge reasonable the assumptions about this God (some examples are mentioned in my summary post). Even many christians don't accept those hypothesis. This was my second objection.

Finally, the last - or first - objection remains for me (but there were some interesting arguments already) the fatal one - I don't believe in voluntary belief.

TFBW wrote:
At the very least, that would allow me to present such agnostics with a trilemma: admit that you're irrational, admit that you're an atheist (not an agnostic), or get busy researching possible afterlife scenarios (give up the atheist lifestyle).

Therefore we are not there yet... because the trilemma has several other ways out - I am still not an atheist, because while I am not believing in a God such as the one you assume, I still have doubts about other concepts of Gods, such as the calvinist one Rolling Eyes .
And if I cave in and accept a real probability for your God to exist - OK, I accept it would be rational to believe. But I cannot choose to believe. Hence I cannot rationally do anything else then searching evidence by participating to discussion about God's existence on the forum of Beyond the Fourth Wall. Hey - looks I am rational after all... Cool

TFBW wrote:
I don't need Pascal's Wager to address hard-core atheists [...] In a situation such as that, I can simply inquire as to the source of their remarkable certainty. If such a position is rational, there must be some way to demonstrate it. If, on the other hand, it's not rational, I have no reason to challenge it.

Of course, as atheism is the position by default as it just does not assume the existence of anything unmeasurable, the burden of proof lies in your hands - YOU have to prove that you are not irrational as a believer, if you want to see it like this.

Otherwise I will require you to prove me that superman does not exist (actually, he does, but he is very timid so he stays hidden as Clark Kent - he uses actually another cover name and work as a countryside latin teacher - without doing anything with his powers - no miracles Wink). And Father Christmas (Bez - saw him in Sweden lately?)
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PostPosted: Wed Mar 18, 2009 8:48 pm    Post subject: Reply with quote

Bezman wrote:
Well, in that case we can replace the infinitesimals in the equation with zeroes like this:
PqL = (G * 0) - (0 * 0) = 0
Thus the special case still gives PqL = 0, which was my point.

Indeed we all agree that compared to an infinite paradise, a finite temporal lifetime has close to no value. But this still does not mean it is worth avoiding it - living it through and not living it through have the same infinitesimal value, in this sense. So it gives no rationale for the decision to suicide.

Bezman wrote:
Hint: if E>F, then (F-E) is negative and not likely to be bigger than the right side of the formula... Wink

Sure, I meant the absolute value of (F-E)*Time in my head.

Bezman wrote:
(In my subjective opinion, E is always at least twice, most often ten times, and not seldom more than 100 times the F or G you get from it, but that is just the way life is, and has always been, at least for me. I see it as "the normal state of life" and I have never considered suicide because of that. I just seek to get as much F as possible to keep the F/E ratio at an as high level as possible. Smile)

I am sorry to hear that - I guess sometimes life is really hard; but you can find so many positive things...
For me, really, F is so much higher than E. Of course there are pains and worries. But just to be here and see a sunset is wonderful, not to speak about having friends or love in your life. Perhaps it's also an attitude?
I sincerely wish you more F... in the future, it helps to keep positive! (I mean Fun, of course Twisted Evil)
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PostPosted: Thu Mar 19, 2009 3:00 am    Post subject: Reply with quote

lacavin wrote:
As soon as you don't target atheists, then my third objection is answered. Of course, the wager looses also a significant part of his interest...

Given that the wager assumes uncertainty in relation to the afterlife, I don't think it was ever applicable to fully convinced atheists. How could it be?

lacavin wrote:
This reformulates the wager as: If you assume that there is a real (albeit small) chance to have a God which grant eternal paradise to those that believe in him and not to those that do not believe, then you should believe in this God.

I don't see that as much of a reformulation. The relevant parts of Pensées show that Pascal was rather more assertive about our knowledge (or lack thereof) of God's existence: he says we have no clue one way or the other. Other than that, you've summarised the wager quite well.

lacavin wrote:
...the agnostic still have to judge reasonable the assumptions about this God (some examples are mentioned in my summary post). Even many christians don't accept those hypothesis. This was my second objection.

That's a separate issue. So long as we agree that it's rational to repudiate the atheist lifestyle, we've made about as much progress as can be expected from the present discussion. The question of how to go about attaining eternal life is much broader: all we've determined here is that the effort is worthwhile.

lacavin wrote:
Finally, the last - or first - objection remains for me (but there were some interesting arguments already) the fatal one - I don't believe in voluntary belief.

This is still a point of some confusion for me. On the one hand you seem to have asserted that you can not believe because you are a slave to reason. But Pascal's Wager provides the rational basis for belief, so if not a slave to reason, then perhaps a slave to evidence? But evidence is equivocal when it comes to a matter so large as the existence of God: we can only imagine what a universe looks like with and without a God, and thereby judge which of those ours resembles. Such a judgement is intuitive, because the evidence is interpreted purely on the basis of imagination. So are you a slave to your own intuitions? That I can understand, but it suggests that your inability to believe is itself a product of your imagination.

lacavin wrote:
Of course, as atheism is the position by default as it just does not assume the existence of anything unmeasurable, the burden of proof lies in your hands - YOU have to prove that you are not irrational as a believer, if you want to see it like this.

Ah, yes. A popular refrain. I'm not even slightly persuaded, though. God either exists or does not, but a lack of proof one way is not sufficient to prove the other. The rational choice is not "atheist until theism is proved", nor for that matter "theist until atheism is proved", but rather "agnostic until proof is given". Atheism does not assume the existence of anything unmeasurable, but it asserts the nonexistence of the unmeasurable, which is no better. The position of "atheist until theism is proved" is a statement of prejudice, pure and simple. Your prejudices are not my burden of proof, except in your own prejudiced mind.

Nobody likes to be called "prejudiced", of course, and if I could say it without the associated overtones of racism and other socially unacceptable behaviour, I would. It's hard enough to keep the debate cool and calm without using pejoratives like that. My point is that you claim to identify a burden of proof, and I challenge whether that alleged "burden of proof" exists as a matter of pure reason as you suggest, or whether it is actually a matter of personal pre-rational inclination to a particular view (i.e. "prejudice").
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PostPosted: Thu Mar 19, 2009 9:54 am    Post subject: Reply with quote

As a general view, you cannot prove an inexistence (unless you make hypotheis about necessary effects) - at most you may be able to illustrate convincingly the absence of effects and infer the likely absence of cause - i.e. of existence.
But nobody will ever be able to prove that unicorns do not exist - only there is until now no proof that they do. The more so if you define the object as not measurable: how can you prove that there are no invisible, intangible, inaudible unicorns roaming around in Manhattan? You cannot.
Therefore it is rational to believe that something does not exist (while being aware that it is not proven, but likely due to absence of evidence) as long as no positive proofs are given.
If you hold the opposite, than you must believe that there are unicorns, or that superman exists, or that the sky is full of small invisible birds that carry the clouds and guide the rain drop by drop (and sometime have fun making snow by blowing their freezing exhalation on rain).

I think this is the core of rational behavior. I guess we will not agree on it, but I would like to have your argumentation on whether you believe in unicorns or superman, and if not, how you can rationally do so.

Of course, I accept that you may personally have evidence of God's existence (I mentioned that having Faith may be ironically enough evidence) and that therefore you may be a rational believer. But you cannot put the burden of proof to the non-believer.

TFBW wrote:
Given that the wager assumes uncertainty in relation to the afterlife, I don't think it was ever applicable to fully convinced atheists. How could it be?

It would have been the beauty of the wager - because you need an exactly zero probability otherwise monotheism dominate, and because rational atheists know that they cannot prove a zero probability, they are in a tough corner where they must either be irrational by remaining atheist or irrational in accepting a zero probability without possible proof. At this point, atheists become as "irrational" as they hold the monothesits to be.

TFBW wrote:
So long as we agree that it's rational to repudiate the atheist lifestyle, we've made about as much progress as can be expected from the present discussion.

No, no, you misunderstand what I meant.
The wager may not hold for agnostics, because they can say (and think honestly) that while they admit a real probability for the exitence of a God, they do not accept the expected value table presented in the wager.

Calvinism, for instance, teaches that we are so imperfect, that only the sovereign grace of God can save us. What we do in our life is +/-1 and to earn the grace we need +Inf. Unreachable. So even a Calvinist would not accept the expected values of the wager, because both terms are equal - the infinite heaven is foreordained and independant from your acts, i.e. from your chosen lifestyle.
For a agnostic that finds the calvinist's view of God more probable than the (may I say "Catholic"? Not sure) view assumed in Pascal's wager, therefore, the wager brings no help in deciding.

So while my third objection has now been accepted and hence the wager does not anymore hold for atheists, my second objection say that it must also not hold for any people having another "view" - make other assumptions - on God's nature.

Therefore we are still very far from agreing that it's rational to repudiate the atheist lifestyle!

TFBW wrote:
lacavin wrote:
Finally, the last - or first - objection remains for me (but there were some interesting arguments already) the fatal one - I don't believe in voluntary belief.

This is still a point of some confusion for me. On the one hand you seem to have asserted that you can not believe because you are a slave to reason.
Perhaps I am not a slave to reason - I am a smoker, that show how unreasonable I can be sometimes (and not proud of it!). But rational belief is a slave to reason. Reason may be mistaken of course, but to rationally hold a belief you must believe that you have reasons for it.
TFBW wrote:
But Pascal's Wager provides the rational basis for belief,
we are not there yet... See above.

TFBW wrote:
evidence is equivocal when it comes to a matter so large as the existence of God: we can only imagine what a universe looks like with and without a God, and thereby judge which of those ours resembles. Such a judgement is intuitive, because the evidence is interpreted purely on the basis of imagination. So are you a slave to your own intuitions? That I can understand, but it suggests that your inability to believe is itself a product of your imagination.

I accept your argument that in presence of equivocal information, intuition and tastes may become predominant and use reason as a mask. But as seen with my introduction - when unsure, when not able to rationally make a decision, doubt.
Without positive proof, in my views the rational behavior is not to believe in the existence but keep an open mind for the case where proof/evidence is brought.


TFBW wrote:
lacavin wrote:
Of course, as atheism is the position by default...

Ah, yes. A popular refrain. I'm not even slightly persuaded, though. God either exists or does not, but a lack of proof one way is not sufficient to prove the other. The rational choice is [...] "agnostic until proof is given".

You are perfectly right. My mistake.
The position by default is agnostism - the "open mind" part. I got myself lost because we use the same word for different meaning.

An agnostic has an "atheist" lifestyle. An agnostic will not bow to the rules of a religion, will not pray, will not effectively believe in God. For all practical purposes, they will behave like atheists, except they should not feel the drive to evangelize...

As definition:
  • People living the "atheist" lifestyle
    • Strong atheist = certain that God does NOT exist - Pascal's wager does not apply (see above)
    • Weak atheist, agnostic = no certainty, but no belief.
    • Strong agnostic = are certain that it will never be possible to know whether a god exists.
  • People living like "monotheist" lifestyle
    • Monotheist = certain that God does exist. Lifestyle include bending to religious rules.
    • Weak-monotheist = bends to the rules, monotheist lifestyle, but not really believing (probably many people in countries with a hard social pressure to be religious).

TFBW wrote:
Nobody likes to be called "prejudiced", of course, and if I could say it without the associated overtones of racism and other socially unacceptable behaviour, I would.

I have no problems in being called prejudiced - perhaps because I don't understand the connotations, being from a foreign-language. We are all prejudiced, because we had no time to think about everything, and for all the things we had no time or no desire to really think about, than we are reducted to our prejudices.
Of course I would have a bit more problem to be called prejudiced with regards to the religious question, because I did think about it, so I think that my position is well considered - even if it may be wrong.

TFBW wrote:
My point is that you claim to identify a burden of proof, and I challenge whether that alleged "burden of proof" exists as a matter of pure reason as you suggest, or whether it is actually a matter of personal pre-rational inclination to a particular view (i.e. "prejudice").

With regards to the burden of proof, see my introduction.
I agree with you - somebody that asserts the certain inexistence of God has a burden of proof (and he will loose! - usually to seem like winning, they make hypothesis about necessary effects; but those hypotheis are not proven themselves) that the probability is exactly zero.
Somebody that asserts the certain existence of God has similarly the burden of proof (and I guess he will loose too).
The agnostic, or weak atheist has no burden of proof. The one that want to change his mind - either to make him an hard atheist or to make him a monotheist - has the burden of proof.

This explain my statement - without any proof in one side or the other, the normal, default position is weak atheism = agnostism and therefore atheist lifestyle (for the effective behavior in life). So when you speak to such a person, you do have the burden of proof.

By the way, I guess there are very few strong atheists - even if they make noise because they publish books. There are probably many more - like me - "weak atheist", or agnostic. They do not believe in God; they live the atheist lifestyle. But they are not certain of God's inexistence.
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PostPosted: Fri Mar 20, 2009 5:31 am    Post subject: Reply with quote

lacavin wrote:
As a general view, you cannot prove an inexistence...

I have responded to this aspect of the issue over in the Proof of God thread.

lacavin wrote:
TFBW wrote:
Given that the wager assumes uncertainty in relation to the afterlife, I don't think it was ever applicable to fully convinced atheists. How could it be?

It would have been the beauty of the wager - because you need an exactly zero probability otherwise monotheism dominate, and because rational atheists know that they cannot prove a zero probability, they are in a tough corner where they must either be irrational by remaining atheist or irrational in accepting a zero probability without possible proof. At this point, atheists become as "irrational" as they hold the monothesits to be.

I said Pascal's Wager doesn't apply to fully convinced atheists. By that I mean those who do assign an "exactly zero" (or infinitesimal) probability to the existence of God. The wager does apply to those who assign a non-zero, finite probability to the existence of God -- just as a simple matter of mathematics. So the observation that you make above is correct, and exactly the point of the wager. On the other hand, you don't seem to have any difficulty in shrugging off those very same implications through special pleading like "belief is not voluntary".

lacavin wrote:
For a agnostic that finds the calvinist's view of God more probable than the (may I say "Catholic"? Not sure) view assumed in Pascal's wager, therefore, the wager brings no help in deciding.

I've tried to explain this before, so I apologise in advance to those for whom this is nothing but annoying repetition. The mathematics of Pascal's Wager can also solve this problem. In this case we weigh up the Calvinist view of predestination (in which nothing you do makes any difference to your salvation) against the alternative that action is required on our part. Let us grant your assertion that the agnostic in question finds the Calvinist model more probable for some reason (probability p > 0.5), but this leaves "not Calvinism" possible (with probability 1 - p < 0.5). Here, note that there is nothing whatsoever that one can do to increase or decrease the chances of success if Calvinism is true, but success under not-Calvinism may be influenced in some way. The rational thing to do (in order to maximise your expected outcome) is ignore Calvinism, and come up with a strategy for maximising your expected outcome under not-Calvinism.

I hope that the logic of that strategy is clear. The general strategy is that you need to positively influence all the factors over which you have control. The Calvinist model of things leaves no room for positive influence, so there's no point thinking about it: if it's true, you're either going to win or lose as a matter of unyielding fate. It may not be true, however, and you should work on improving your chances in that case. This is all relatively straightforward: things only start to get really tricky when possible courses of action become mutually exclusive. Calvinism presents no such difficulty.

Pascal's technique for maximising expected outcomes applies where truth is not certain. It applies to the uncertainty of God's existence, and it applies to the uncertainty of Calvinist predestination. So long as you are not fully convinced of the truth of atheism or the truth of Calvinism, rational self interest dictates that you should proceed as though they are false.

lacavin wrote:
Without positive proof, in my views the rational behavior is not to believe in the existence but keep an open mind for the case where proof/evidence is brought.

That's a false dichotomy. Nothing prevents you from tentatively adopting a belief, while being open to the possibility of contrary proof. Scientists do it all the time with scientific theories -- or so I'm told. It's perfectly reasonable to adjust one's behaviour in accordance with the evidence that one has at hand. In the case of Pascal's Wager we take it as given that God's existence is unknown, and observe that it's more profitable to assume that he does exist. So make "God exists" your working assumption until it is disproved.

lacavin wrote:
The position by default is agnostism - the "open mind" part. I got myself lost because we use the same word for different meaning.

Indeed we do. "Agnostic" does not mean "open-minded" -- it means "without knowledge". An agnostic asserts that he does not know whether God exists -- he professes ignorance. A strong agnostic is quite closed-minded about this, insisting that the existence of God is completely unknowable, and that anyone who claims to know whether God exists is irrational or mistaken.

lacavin wrote:
An agnostic has an "atheist" lifestyle.

Most who profess to be agnostic are atheist in practice. Pascal's Wager shows this to be irrational behaviour, or at least unprofitable behaviour. ("Irrational" follows if the agnostic believes that his effectively atheistic lifestyle is a profitable one.) Technically speaking, I'm a fairly strong agnostic in that I don't believe there will ever be valid, conclusive proof one way or the other (in this lifetime) of God's existence, and that whatever "evidence" exists is dominated by our prejudices. I have chosen to be Christian in practice. I consider this to be a matter of choice precisely because reason does not compel one belief or the other.

Douglas Adams had a funny section in the Hitchhiker's Guide to the Galaxy about a proof of God's existence that proved that God didn't exist. It started out like this. "I refuse to prove that I exist, says God, for proof denies faith, and without faith I am nothing." Here's an alternative that occurs to me. "I refuse to prove that I exist, says God, for proof denies choice, and without choice you are not free."

lacavin wrote:
Weak atheist, agnostic = no certainty, but no belief.

They aren't the same, technically. An atheist asserts the non-existence of God. A strong atheist asserts it with greater confidence than a weak atheist. An agnostic makes no assertions, since an agnostic claims not to know.

In practice, however, there are no clear dividing lines between these positions. We can say that someone who thinks that God exists with probability p = 0 is a strong atheist, and someone who thinks that God exists with probability p = 0.5 is an agnostic, but all the points in between these two are fuzzy. We're better off talking in terms of probabilities than we are in terms of labels like "atheist" and "agnostic" when it comes to a mathematical analysis like Pascal's Wager.

lacavin wrote:
Of course I would have a bit more problem to be called prejudiced with regards to the religious question, because I did think about it, so I think that my position is well considered - even if it may be wrong.

It's not a question of whether you thought about it. It's a question of whether your conclusion was dominated by your prejudices or not. Would you have come to a different conclusion if you'd started with a different set of prejudices?
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PostPosted: Fri Mar 20, 2009 6:06 am    Post subject: Reply with quote

Quote:
Thanks for showing those different systems. I indeed did not know them.


Don't feel bad...I have a masters degree in mathematics, and was unaware of the concept of hyperreal numbers. I am familiar with the extended reals, because we used them in my 600-level real analysis class. There's also the one-point compactification of the real number line, which has just one point at infinity, rather than one positive and one negative. It's like the line becomes a gigantic circle, but it's an infinite distance from 0 to infinity, in either direction.

However, this is definitely off topic, and since I don't have the time to process all the arguments here in order to discuss them intelligently, I'll stop trying to hijack the thread into a discussion of mathematics. Smile
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PostPosted: Fri Mar 20, 2009 4:03 pm    Post subject: Reply with quote

TFBW wrote:
On the other hand, you don't seem to have any difficulty in shrugging off those very same implications through special pleading like "belief is not voluntary".
My "special pleading" is fundamental and hence my first objection. These implications would have been true assuming good answers to my 3 objections - so I don't have to shrug off the implications, as the implications are not acceptable yet.

TFBW wrote:
I've tried to explain this before, so I apologise in advance to those for whom this is nothing but annoying repetition. The mathematics of Pascal's Wager can also solve this problem. [...] Let us grant your assertion that the agnostic in question finds the Calvinist model more probable for some reason (probability p > 0.5), but this leaves "not Calvinism" possible (with probability 1 - p < 0.5). [...] come up with a strategy for maximising your expected outcome under not-Calvinism.

Let me also apologize to repeat the same arguments - apparently I was not clear enough.
I understand what you mean, and it is clear that you can come to this conclusion with calvinism or different table whether either the result is the same, or where the result is undefined. This was however but one illustrative example - and in retrospect not the best - sorry if it mislead you.
But the core of my message is different:

There are an immense (infinite?) number of expected values tables that can be drawn with different assumptions about God. Those tables may lead to different conclusions upon the best choice in life. Hence the wager is invalid.

Let me give you another example: assume a God that reward honesty more than belief. Now unbelievers that do not act as if they believed go to paradise, and unbelievers that act as if they believed do not. From such a table, which is as possible as the one of Pascal supposing a God rewarding only belief, the rational behavior for somebody that does not believe is not to change anything.

If you combine this table with Pascal's table, you see suddenly no possibility to take a decision for unbelievers like me:
Pretend to believe: +Inf (God reward belief) 0 (God reward honesty)
Do not Pretend to: 0(God reward belief) +Inf (God reward honesty)
Combination with Infinity show equal expectations on both sides. Without infinity, put a instead if you want, it requires probabilities to be computed - which we do not have.

That's exactly what I want to illustrate. Add many more tables and you just get no single dominating behavior.

Now don't discuss the proposed table above (again only an illustration). Discuss these questions:
  1. Do you agree that there can be different table based on different assumptions of God?
  2. Do you agree that such tables may lead to different winning behaviors?
  3. 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?
  4. Do you agree therefore that you cannot use Pascal's wager for somebody that has no preferred assumptions about God's behavior?
  5. 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?
  6. Do you agree that therefore the wager cannot be used for its target audiance?

TFBW wrote:
So long as you are not fully convinced of the truth of atheism or the truth of Calvinism, rational self interest dictates that you should proceed as though they are false.
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.

TFBW wrote:
lacavin wrote:
Without positive proof, in my views the rational behavior is not to believe in the existence but keep an open mind for the case where proof/evidence is brought.

That's a false dichotomy. Nothing prevents you from tentatively adopting a belief, while being open to the possibility of contrary proof. Scientists do it all the time with scientific theories -- or so I'm told. It's perfectly reasonable to adjust one's behaviour in accordance with the evidence that one has at hand.
Tentatively adopting a belief is not the same as believing. When, as a scientist, I am tentatively adopting a theory, that means either that I make a thought experiment (put myself in the situation where it holds and hence can design experiments to try to make it fail). Or that I actually believe it (leap of Faith? intuition?) but know I must wait for more evidence in oder to prove that my belief is correct and to sell it as truth to my peers.
I may with my will try to think as if I would believe in God, but that does not make me believe.

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. Do you? Do you have in your life examples where you decided against what your heart was saying at that time to change your belief and it worked?
Remember that as a person with an "atheist" lifestyle, in your heart you do not believe in the existence - you admit simply that you are not sure of the inexistence. At least that's me. Perhaps other people call themselves agnostic or atheist when they actually do believe, but that sounds sort of funny.

TFBW wrote:
Technically speaking, I'm a fairly strong agnostic in that I don't believe there will ever be valid, conclusive proof one way or the other (in this lifetime) of God's existence, and that whatever "evidence" exists is dominated by our prejudices. I have chosen to be Christian in practice. I consider this to be a matter of choice precisely because reason does not compel one belief or the other.
Have you been "non-christian" (not just not going to church, but without "Faith") and did you decide one morning that you would become chirstian and then had belief/faith grow into you?
Or did you have Faith to begin with? Did you believe in the christian God in the beginning and decided to become a practising christian?

These are rather private questions. Don't feel that you have to answer, but this is exactly the core question about voluntarily belief.

TFBW wrote:
"I refuse to prove that I exist, says God, for proof denies choice, and without choice you are not free."

That could indeed be a very good argument to explain why God behaves like he does. IMVHO he goes to far however. Indeed "proof" may be too much - but you still have the freedom to honor him or not. Moreover nothing forbids him to give at least some evidence...

TFBW wrote:
"It's not a question of whether you thought about it. It's a question of whether your conclusion was dominated by your prejudices or not. Would you have come to a different conclusion if you'd started with a different set of prejudices?

Sure. But when I think about something, I actively try to go over my prejudices. So when you think (honestly) about something, it should make you unprejudiced. Sometimes you fail to fight against them. Perhaps I did. Perhaps you did. We can but do our best...
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