Examining Pascal's Wager

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Examining Pascal's Wager

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Post by Paul of Tarsus »

(My treatment of Pascal's Wager will be a bit technical in this OP, but please bear with me because my examination of Pascal's Wager should be informative.)

According to Wikipedia:
Pascal's wager is an argument in philosophy presented by the seventeenth-century French philosopher, theologian, mathematician and physicist, Blaise Pascal (1623–1662).[1] It posits that humans bet with their lives that God either exists or does not.

Pascal argues that a rational person should live as though God exists and seek to believe in God. If God does not actually exist, such a person will have only a finite loss (some pleasures, luxury, etc.), whereas if God does exist, he stands to receive infinite gains (as represented by eternity in Heaven) and avoid infinite losses (eternity in Hell).
What decision should we make regarding the existence of God, and what are the potential consequences of that decision?

To answer this question, we should start with the "null hypothesis" (so named because of it's negation, "not.")

H0: God does not exist.

Note that this null hypothesis can be true or false, and we can reject it or fail to reject it. A summary of the four combinations of these possibilities are the following:

We reject the null hypothesis (we believe in God) and
A. The null hypothesis is true in saying God does not exist, and we make a "Type I" error.
B. The null hypothesis is false in saying God does not exist, and we make a "Type B correct decision."

We fail to reject the null hypothesis (we don't believe in God) and
C. The null hypothesis is true in saying God does not exist, and we make a "Type A correct decision."
D. The null hypothesis is false in saying God does not exist, and we make a "Type II" error.

So if theists err because God doesn't exist, then they commit a Type I error. If atheists err (God does exist), then they commit a Type II error.

Which of these two errors has more serious consequences? As pascal points out in his wager, the gains of believing in God are infinite while the gains of doubt are finite. So if we doubt God's existence, then we better make darn sure we are right. If we believe in God, on the other hand, then the probability of being wrong need not be so low. So contrary to Pascal, I won't tell anybody that it's better to believe in God or not; it's just best to make sure you are making the correct decision whether you believe in God or not. Atheists appear to need to make sure that the probability of being wrong is lower than the theist's probability of being wrong.

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Re: Examining Pascal's Wager

Post #241

Post by Ionian_Tradition »

[Replying to Paul of Tarsus in post #1]

While it does seem intuitively correct that the potential losses incurred by a lack of belief in God would be infinitely more severe than those incurred by belief, this conclusion will continue to be conjectural so long as the term "God" remains ill-defined. After all, the consequences of not believing in God on something like Taoism, for example, are quite distinct from those which obtain within the Christian context. For this reason, the Pascalian Wager, in its classical form, necessarily requires appeals to external evidence/arguments supporting the truth of Christianity (or something approximating it) in order to give the wager its bite. However, if these appeals to external support for Christianity prove successful, Pascal's Wager becomes unnecessary. I suspect this is why Pascal's Wager appears to have fallen out of fashion with the majority of contemporary apologists.

That being said, I've wondered if it is possible to modify Pascal's Wager in a manner which avoids the aforementioned difficulties. Tentatively, I've developed the following (admittedly unpolished) modification:

1. It is incumbent upon all rational persons to select, and live in accordance with, a worldview.
2. A rational person will select only that worldview which most probably entails the greatest potential gains (if true) and least potential losses (if false).
3. The (mere) Christian worldview most probably entails the greatest potential gains (if true) and least potential losses (if false).
4. From 2 & 3, a rational personal will select, and live in accordance with, the (mere) Christian worldview.

------------------------------------------------------------------------------------------------------------------------------------------
I suspect that detractors of this variation of the Wager will most likely take issue with premise 3. Here is my preemptive defense:

Firstly, I define mere Christianity as a worldview which holds to the most basic/foundational doctrines of Christian theology (i.e. 1st Corinthians 15 coupled with a theology of hell which entail eternal separation from God).

That mere Christianity (if true) entails infinite potential gains is, I think, more or less self-evident. That Christianity (if false) entails the least potential losses is less evident. It is clear that if an atheistic metaphysic is true, then Christianity entails very little loss. However, would the same also be true if another religious worldview were correct? To answer this question, I begin by considering the falsity of Christianity with the context of four major world religions: Hinduism, Buddhism, Islam, and Taoism.

Hinduism: If Christianity is false on Hinduism, then the potential losses are most likely negligible. After all, once karmic debts are paid, all Atman return to Brahman. Sure, the Christian may need to take another spin or two around the proverbial mountain of reincarnation (assuming one's Dharma cannot be properly instantiated within the Christian walk), but so would many practicing Hindus. In the end, as they say, all dogs go to "heaven".

Buddhism: The the potential losses incurred by a practicing Christian are considerably low if Buddhism is true. In its theistic form, the consequences for the Christian are not dissimilar to those which obtain under Hinduism. In its non-theistic form, the consequences are similar to those which obtain on atheism.

Islam: Per the most primary, and foundational Islamic text (the Quran), Christians are classified as "Children of the Book" and are (with certain qualifications) looked upon in a generally favorable way within Islam (see 2:62, 5:69, and 61:14 for reference). While Christianity is certainly not the optimal religious stance within the Islamic context, the potential losses incurred by the Christian are appreciably low if Islam is true. (as an aside, something similar would also apply within the context of Judaism).

Taoism: Within the pantheistic context of Taoism, Christianity is neither wrong or right but instead is a necessary feature of the Tao by which other things are made manifest in contrast according to the principle of yin and yang. On this view, the potential losses incurred by the Christian are not dissimilar from those incurred within the context of metaphysical naturalism.

It would seem that, at least with respect to the major religions of the world, that the potential losses incurred by practicing Christians is considerably low if any one of the aforementioned religions is true. Interestingly, if Christianity is true, the potential loss incurred by each of these religions is substantial. We may conclude, therefore, that Christianity entails the greatest potential gain, and least potential loss, with respect to the major world religions. But what of some obscure worldview known only to a select few? Is it possible that there exists a largely unknown religion which usurps Christianity as the worldview entailing the greatest potential gains and least potential losses?

I cannot deny the possibility that such a worldview exists. However if it does, it is currently unknown to me (and I suspect most of those who will read this post). Never the less, what concerns us is not whether such a worldview exists, but whether it is most probable (prima facie). I would contend that such an obscure worldview would have its work cut out for it if it sought to show itself more prima facie probable than Christianity in particular. The staggering number of individuals (both past and present) who provide anecdotal attestation of the veracity and impact of Christianity in their daily lives elevates the prior probability of Christianity being true well beyond a non-negligible value. So long as the prior probability of Christianity remains higher than any of its obscure competitors, (which its status as humanity's largest global religion ensures) the Wager holds.

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Re: Examining Pascal's Wager

Post #242

Post by Paul of Tarsus »

Ionian_Tradition wrote: Wed Mar 17, 2021 2:56 am [Replying to Paul of Tarsus in post #1]

While it does seem intuitively correct that the potential losses incurred by a lack of belief in God would be infinitely more severe than those incurred by belief, this conclusion will continue to be conjectural so long as the term "God" remains ill-defined. After all, the consequences of not believing in God on something like Taoism, for example, are quite distinct from those which obtain within the Christian context. For this reason, the Pascalian Wager, in its classical form, necessarily requires appeals to external evidence/arguments supporting the truth of Christianity (or something approximating it) in order to give the wager its bite. However, if these appeals to external support for Christianity prove successful, Pascal's Wager becomes unnecessary. I suspect this is why Pascal's Wager appears to have fallen out of fashion with the majority of contemporary apologists.

That being said, I've wondered if it is possible to modify Pascal's Wager in a manner which avoids the aforementioned difficulties. Tentatively, I've developed the following (admittedly unpolished) modification:

1. It is incumbent upon all rational persons to select, and live in accordance with, a worldview.
2. A rational person will select only that worldview which most probably entails the greatest potential gains (if true) and least potential losses (if false).
3. The (mere) Christian worldview most probably entails the greatest potential gains (if true) and least potential losses (if false).
4. From 2 & 3, a rational personal will select, and live in accordance with, the (mere) Christian worldview.

------------------------------------------------------------------------------------------------------------------------------------------
I suspect that detractors of this variation of the Wager will most likely take issue with premise 3. Here is my preemptive defense:

Firstly, I define mere Christianity as a worldview which holds to the most basic/foundational doctrines of Christian theology (i.e. 1st Corinthians 15 coupled with a theology of hell which entail eternal separation from God).

That mere Christianity (if true) entails infinite potential gains is, I think, more or less self-evident. That Christianity (if false) entails the least potential losses is less evident. It is clear that if an atheistic metaphysic is true, then Christianity entails very little loss. However, would the same also be true if another religious worldview were correct? To answer this question, I begin by considering the falsity of Christianity with the context of four major world religions: Hinduism, Buddhism, Islam, and Taoism.

Hinduism: If Christianity is false on Hinduism, then the potential losses are most likely negligible. After all, once karmic debts are paid, all Atman return to Brahman. Sure, the Christian may need to take another spin or two around the proverbial mountain of reincarnation (assuming one's Dharma cannot be properly instantiated within the Christian walk), but so would many practicing Hindus. In the end, as they say, all dogs go to "heaven".

Buddhism: The the potential losses incurred by a practicing Christian are considerably low if Buddhism is true. In its theistic form, the consequences for the Christian are not dissimilar to those which obtain under Hinduism. In its non-theistic form, the consequences are similar to those which obtain on atheism.

Islam: Per the most primary, and foundational Islamic text (the Quran), Christians are classified as "Children of the Book" and are (with certain qualifications) looked upon in a generally favorable way within Islam (see 2:62, 5:69, and 61:14 for reference). While Christianity is certainly not the optimal religious stance within the Islamic context, the potential losses incurred by the Christian are appreciably low if Islam is true. (as an aside, something similar would also apply within the context of Judaism).

Taoism: Within the pantheistic context of Taoism, Christianity is neither wrong or right but instead is a necessary feature of the Tao by which other things are made manifest in contrast according to the principle of yin and yang. On this view, the potential losses incurred by the Christian are not dissimilar from those incurred within the context of metaphysical naturalism.

It would seem that, at least with respect to the major religions of the world, that the potential losses incurred by practicing Christians is considerably low if any one of the aforementioned religions is true. Interestingly, if Christianity is true, the potential loss incurred by each of these religions is substantial. We may conclude, therefore, that Christianity entails the greatest potential gain, and least potential loss, with respect to the major world religions. But what of some obscure worldview known only to a select few? Is it possible that there exists a largely unknown religion which usurps Christianity as the worldview entailing the greatest potential gains and least potential losses?

I cannot deny the possibility that such a worldview exists. However if it does, it is currently unknown to me (and I suspect most of those who will read this post). Never the less, what concerns us is not whether such a worldview exists, but whether it is most probable (prima facie). I would contend that such an obscure worldview would have its work cut out for it if it sought to show itself more prima facie probable than Christianity in particular. The staggering number of individuals (both past and present) who provide anecdotal attestation of the veracity and impact of Christianity in their daily lives elevates the prior probability of Christianity being true well beyond a non-negligible value. So long as the prior probability of Christianity remains higher than any of its obscure competitors, (which its status as humanity's largest global religion ensures) the Wager holds.
Thanks for the response, but I'm a little shaky on your answer to the question for debate. I understand that you favor belief in the Christian God because that belief entails the largest potential reward if that God exists but the least loss if that God does not exist. Is that correct? What I'm most interested in knowing, though, is how much the probability of that God's existence might affect your faith in that God. Even if the potential rewards for faith in God and punishment for unbelief are enormous, how much does it matter if the odds of God's existence are slim?

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Re: Examining Pascal's Wager

Post #243

Post by Ionian_Tradition »

Paul of Tarsus wrote: Sun Mar 21, 2021 7:16 pm What I'm most interested in knowing, though, is how much the probability of that God's existence might affect your faith in that God. Even if the potential rewards for faith in God and punishment for unbelief are enormous, how much does it matter if the odds of God's existence are slim?
I suppose the answer to your question will depend upon whether, and to what degree, pragmatic considerations play a role in influencing our response to the Wager. One could argue, I think without contradiction, that if the Christian worldview entails the most favorable ratio of risk to reward among all competing worldviews, then Christianity is to be rationally (or pragmatically) preferred, even if the probability of Christianity being true is lower than that of its competitors. That being said, it would be erroneous to assume that probabilities have no bearing whatsoever on the Wager. After all, a sufficiently clever person could, I’m sure, cook up a wildly improbable worldview which boasts a better risk/reward ratio than any conceivable alternative. I think we’d both agree that such a worldview is still not to be preferred.

To avoid such antics, I appealed to Bayesian prior probability as a possible method for filtering out bogus/contrived worldviews. Ideally, worldviews with a sufficiently low prior probability will be discarded in favor of those whose prior probability is, shall we say, “more respectable”.

I use prior probability specifically (and not the full Bayesian value) because Pascal’s Wager is, at its core, an argument from pragmatism, not probability. Indeed, if the primary goal were merely to demonstrate to the honest worldview seeker that Christianity is most likely to be true, then the apologist would most certainly be better served by employing a different argument. However, if the primary aim is to assist the honest worldview seeker in identifying the best possible worldview according to its cost/benefit characteristics (which is by no means an invalid approach), then Pascal’s Wager does a suitable job in showing Christianity to be a top contender among competing worldviews.

Interestingly, Christianity’s status as humanity’s largest ever global religion serves, I think, to place its prior probability in the upper register.

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Re: Examining Pascal's Wager

Post #244

Post by Tcg »

Ionian_Tradition wrote: Wed Mar 24, 2021 4:11 am
Interestingly, Christianity’s status as humanity’s largest ever global religion serves, I think, to place its prior probability in the upper register.
Only if one relies on the "Argumentum ad populum" logical falacy:
Argumentum ad populum

Description

Argumentum ad populum is a type of informal fallacy,[1][13] specifically a fallacy of relevance,[14][15] and is similar to an argument from authority (argumentum ad verecundiam).[13][3][8] It uses an appeal to the beliefs, tastes, or values of a group of people,[11] stating that because a certain opinion or attitude is held by a majority, it is therefore correct.[11][16]

Appeals to popularity are common in commercial advertising that portrays products as desirable because they are used by many people[8] or associated with popular sentiments[17] instead of communicating the merits of the products themselves.

The inverse argument, that something that is unpopular must be flawed, is also a form of this fallacy.[7]

https://en.wikipedia.org/wiki/Argumentu ... escription

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Re: Examining Pascal's Wager

Post #245

Post by Kylie »

Paul of Tarsus wrote: Mon Feb 01, 2021 10:06 am (My treatment of Pascal's Wager will be a bit technical in this OP, but please bear with me because my examination of Pascal's Wager should be informative.)

According to Wikipedia:
Pascal's wager is an argument in philosophy presented by the seventeenth-century French philosopher, theologian, mathematician and physicist, Blaise Pascal (1623–1662).[1] It posits that humans bet with their lives that God either exists or does not.

Pascal argues that a rational person should live as though God exists and seek to believe in God. If God does not actually exist, such a person will have only a finite loss (some pleasures, luxury, etc.), whereas if God does exist, he stands to receive infinite gains (as represented by eternity in Heaven) and avoid infinite losses (eternity in Hell).
What decision should we make regarding the existence of God, and what are the potential consequences of that decision?

To answer this question, we should start with the "null hypothesis" (so named because of it's negation, "not.")

H0: God does not exist.

Note that this null hypothesis can be true or false, and we can reject it or fail to reject it. A summary of the four combinations of these possibilities are the following:

We reject the null hypothesis (we believe in God) and
A. The null hypothesis is true in saying God does not exist, and we make a "Type I" error.
B. The null hypothesis is false in saying God does not exist, and we make a "Type B correct decision."

We fail to reject the null hypothesis (we don't believe in God) and
C. The null hypothesis is true in saying God does not exist, and we make a "Type A correct decision."
D. The null hypothesis is false in saying God does not exist, and we make a "Type II" error.

So if theists err because God doesn't exist, then they commit a Type I error. If atheists err (God does exist), then they commit a Type II error.

Which of these two errors has more serious consequences? As pascal points out in his wager, the gains of believing in God are infinite while the gains of doubt are finite. So if we doubt God's existence, then we better make darn sure we are right. If we believe in God, on the other hand, then the probability of being wrong need not be so low. So contrary to Pascal, I won't tell anybody that it's better to believe in God or not; it's just best to make sure you are making the correct decision whether you believe in God or not. Atheists appear to need to make sure that the probability of being wrong is lower than the theist's probability of being wrong.
This would seem to indicate we should believe in whichever God has the worst Hell, and then hope that such a God isn't the kind of God who will punish us for believing for purely selfish reasons.

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Re: Examining Pascal's Wager

Post #246

Post by Paul of Tarsus »

[Replying to Kylie in post #246]

Yes, different gods complicate the wager. But for the sake of simplicity, let's assume Pascal's God.

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Re: Examining Pascal's Wager

Post #247

Post by Paul of Tarsus »

Ionian_Tradition wrote: Wed Mar 24, 2021 4:11 am
Paul of Tarsus wrote: Sun Mar 21, 2021 7:16 pm What I'm most interested in knowing, though, is how much the probability of that God's existence might affect your faith in that God. Even if the potential rewards for faith in God and punishment for unbelief are enormous, how much does it matter if the odds of God's existence are slim?
I suppose the answer to your question will depend upon whether, and to what degree, pragmatic considerations play a role in influencing our response to the Wager. One could argue, I think without contradiction, that if the Christian worldview entails the most favorable ratio of risk to reward among all competing worldviews, then Christianity is to be rationally (or pragmatically) preferred, even if the probability of Christianity being true is lower than that of its competitors.
If the probability that Christianity is a genuine divine plan was thought to be close to zero, then those who think so would probably disregard its grand promises and frightening threats of punishment. Many atheists no doubt think that way.
That being said, it would be erroneous to assume that probabilities have no bearing whatsoever on the Wager. After all, a sufficiently clever person could, I’m sure, cook up a wildly improbable worldview which boasts a better risk/reward ratio than any conceivable alternative. I think we’d both agree that such a worldview is still not to be preferred.
Yes, I've been arguing all along that the probability of God's existence makes or breaks Pascal's wager. Any prudent person considers how likely threats and punishments are before heeding them
...if the primary aim is to assist the honest worldview seeker in identifying the best possible worldview according to its cost/benefit characteristics (which is by no means an invalid approach), then Pascal’s Wager does a suitable job in showing Christianity to be a top contender among competing worldviews.
In other words, Christianity is the most promising and scariest of all religions.
Interestingly, Christianity’s status as humanity’s largest ever global religion serves, I think, to place its prior probability in the upper register.
I suppose if God exists, then yes, his religion would be the most popular of all religions.

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Re: Examining Pascal's Wager

Post #248

Post by Bust Nak »

Ionian_Tradition wrote: Wed Mar 24, 2021 4:11 am ...After all, a sufficiently clever person could, I’m sure, cook up a wildly improbable worldview which boasts a better risk/reward ratio than any conceivable alternative. I think we’d both agree that such a worldview is still not to be preferred...
How probable worldview has to be (assuming you can even objectively evaluate how probable a particular worldview is), before you would let it past your filter? Presumably that would just be an arbitrary standard?

Isn't it better to figure out exactly what the mathematically best bet is?

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Re: Examining Pascal's Wager

Post #249

Post by TRANSPONDER »

Paul of Tarsus wrote: Thu Mar 25, 2021 8:18 pm
Ionian_Tradition wrote: Wed Mar 24, 2021 4:11 am
Paul of Tarsus wrote: Sun Mar 21, 2021 7:16 pm What I'm most interested in knowing, though, is how much the probability of that God's existence might affect your faith in that God. Even if the potential rewards for faith in God and punishment for unbelief are enormous, how much does it matter if the odds of God's existence are slim?
I suppose the answer to your question will depend upon whether, and to what degree, pragmatic considerations play a role in influencing our response to the Wager. One could argue, I think without contradiction, that if the Christian worldview entails the most favorable ratio of risk to reward among all competing worldviews, then Christianity is to be rationally (or pragmatically) preferred, even if the probability of Christianity being true is lower than that of its competitors.
If the probability that Christianity is a genuine divine plan was thought to be close to zero, then those who think so would probably disregard its grand promises and frightening threats of punishment. Many atheists no doubt think that way.
That being said, it would be erroneous to assume that probabilities have no bearing whatsoever on the Wager. After all, a sufficiently clever person could, I’m sure, cook up a wildly improbable worldview which boasts a better risk/reward ratio than any conceivable alternative. I think we’d both agree that such a worldview is still not to be preferred.
Yes, I've been arguing all along that the probability of God's existence makes or breaks Pascal's wager. Any prudent person considers how likely threats and punishments are before heeding them
...if the primary aim is to assist the honest worldview seeker in identifying the best possible worldview according to its cost/benefit characteristics (which is by no means an invalid approach), then Pascal’s Wager does a suitable job in showing Christianity to be a top contender among competing worldviews.
In other words, Christianity is the most promising and scariest of all religions.
Interestingly, Christianity’s status as humanity’s largest ever global religion serves, I think, to place its prior probability in the upper register.
I suppose if God exists, then yes, his religion would be the most popular of all religions.
The reason Pascal's wager fails is because it assumed that Christianity - or not - is the only option on the table. It wasn't even in Pascal's day; there was Islam, and still is. There are of course other religions but they aren't so scarey. Islam is. Indeed Pascal assumed that only one version of Christianity is the valid option. If you choose the wrong Christian denomination, then your bet is no better than that of the atheist.

Of course, here you have to start studying form - not just on the logical parameters of the bet but assessing which of the other runners are likely to be true.

That is what these debates are all about and Pascal's wager really doesn't carry a lot of force, these days.

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Re: Examining Pascal's Wager

Post #250

Post by Paul of Tarsus »

TRANSPONDER wrote: Tue May 11, 2021 5:45 pmThe reason Pascal's wager fails is because it assumed that Christianity - or not - is the only option on the table. It wasn't even in Pascal's day; there was Islam, and still is. There are of course other religions but they aren't so scarey. Islam is. Indeed Pascal assumed that only one version of Christianity is the valid option. If you choose the wrong Christian denomination, then your bet is no better than that of the atheist.

Of course, here you have to start studying form - not just on the logical parameters of the bet but assessing which of the other runners are likely to be true.

That is what these debates are all about and Pascal's wager really doesn't carry a lot of force, these days.
While I agree with your criticisms of Pascal's wager, I'm not really interested in examining the wager for logical validity. Pascal raised the question of making a decision regarding God's existence and the consequences of making an error in that decision. I'm asking how the probability of God existing should impact that decision, something Pascal neglected to do. While I agree that rejecting a wrathful and vengeful God entails very dire consequences, those consequences become trivial if the probability of God existing is very low, and an atheist might then wisely continue to disbelieve in God.

Allow me to illustrate with an example. Say you and I go hiking in Yellowstone Park, and I make a wager with you. If we see a black bear first, I will pay you $10, but if the first bear is a grizzly, you must pay me $1,000. You'd wisely decline the wager realizing that the probability of spotting either bear is about equal. However, if I make the same wager except that the bear we must see for you to pay me $1,000 is a polar bear. In that case you should agree to the wager because even though you risk $1,000, the chances of seeing a polar bear is so low that you realize the bet is worth the risk.

So for the wise atheist, God is like seeing that polar bear in Yellowstone Park. If he's there, then he's expensive, but he's probably not there, so take the bet!

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