Examining Pascal's Wager

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Paul of Tarsus
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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 #271

Post by Purple Knight »

Paul of Tarsus wrote: Thu May 13, 2021 9:56 pmWhat is your null hypothesis? A type I error is to decide that the null hypothesis is false when it's true, and a type II error is to decide the null hypothesis is true when it's false.
So going back to your original post...
Paul of Tarsus wrote: Mon Feb 01, 2021 10:06 amWhat 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.
If God does exist, but he rewards for atheism (perhaps he set the universe up to leave no evidence of his existence and he's testing for rationality and punishing credulity) the errors aren't necessarily reversed (that was my bad) but the consequences of them are. We can now construct a Pascal's Wager that proves you ought to be an atheist.

But we can also construct Wagers that prove you ought to believe in any other religion. That's saying nothing of the fact that there are many sects of Christianity, each considering itself correct about what God wants and will punish for.
Paul of Tarsus wrote: Thu May 13, 2021 9:56 pmThere's really no mathematical mistakes in Pascal's wager. Pascal was a brilliant mathematician. He just didn't consider the probability of God's existence and how that probability affects the wisdom of being an atheist.
And so he shouldn't because we can't assess that probability. We can only guess. So far the Wager is sound. But likewise we can't give in to every statement of the form, "There might be this being that rewards you for believing in it and punishes you eternally for not" because there are infinite possible of these beings, and a lot of them are jealous (they insist you believe in that one alone). Lucifer might be the good guy and the Bible might be a load of lies designed to make him look bad. Or maybe in the end he wins and gets God's throne.

If the main thing is true (a very powerful being that can reward and punish), any number of things may also be true about the nature of what we're rewarded for and why. So we have an infinite number of Wagers all proving we should do different and sometimes diametrically opposite things. Therefore, the Wager cannot be sound.

One thing alone could salvage it: Add the premise that God is fair. Whether the powerful being is fair or not is of no consequence, but now we have a potentially sound Wager. I'll call it the Purple Wager. If the powerful being is fair, it wouldn't punish us for arbitrary things, create no-win scenarios, or force us to guess making the choice between good and evil more of a gameshow than a moral decision. So if it's Lucifer, and he's fair, he will not punish me for taking God's side unless there was a good reason not to take it (*cough* Job *cough*). If it's Bonoweebeeponimoke, and he's fair, he knows I have no way of knowing about him and he won't punish me for not worshiping him.

The Purple Wager is potentially sound, because 1) all the infinite Wagers converge on a fair God 2) we can actually follow a fair god's wishes, because, by definition, he wouldn't have any expectations that were unreasonable or required guesses and finally 3) all those infinite unfair gods... we can't do what they want anyway, unless we guess correctly. The question is, is it actually sound, not just potentially?

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Re: Examining Pascal's Wager

Post #272

Post by JoeyKnothead »

Miles wrote: Mon Feb 01, 2021 6:02 pm
Paul of Tarsus wrote: Mon Feb 01, 2021 5:38 pm
Miles wrote: Mon Feb 01, 2021 2:10 pm .


So which god is it that I should seek to believe in?


Image


And why that one and not another?


.
You should believe in the one, true God, of course. Other gods don't exist and can do you no good.

Fine, but which one is it, and why?



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That one I'm me extra special me proud of.

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Re: Examining Pascal's Wager

Post #273

Post by Ionian_Tradition »

Tcg wrote: Wed Mar 24, 2021 6:57 pm
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:
To be clear, I'm not arguing that because Christianity boasts a greater number of professing adherents that it is therefore true, or even that it is the superior worldview. If I were, then indeed I could be rightly charged with Argumentum ad populum. In point of fact however, I'm arguing a more subtle point, namely that Christianity's status as the world largest religion supports a sufficiently high prior probability so as to be taken seriously when performing the type of (pragmatic) worldview cost/benefit analysis the Wager seeks to perform.

For additional context on why I feel a sufficiently high prior probability is important to the Wager, I'll direct you to my previous response to Paul of Tarsus.

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Re: Examining Pascal's Wager

Post #274

Post by Tcg »

Ionian_Tradition wrote: Sat May 22, 2021 5:55 pm
In point of fact however, I'm arguing a more subtle point, namely that Christianity's status as the world largest religion supports a sufficiently high prior probability so as to be taken seriously when performing the type of (pragmatic) worldview cost/benefit analysis the Wager seeks to perform.
You're still arguing that since Christianity is popular it has a higher probability of being true. This quite clearly isn't valid.


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Re: Examining Pascal's Wager

Post #275

Post by Goat »

Paul of Tarsus wrote: Mon Feb 01, 2021 5:35 pm
The Barbarian wrote: Mon Feb 01, 2021 1:19 pm
Paul of Tarsus wrote: Mon Feb 01, 2021 10:06 am 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 is very true, but only if you accept Paschal's assumption that those with disbelief will be eternally punished if God exists, and those with belief will always be rewarded with eternal bliss, if God exists. Neither is necessarily true. Certainly, it's not true for Christianity.
I don't wish to get into a debate about the nature of hell, but whatever hell is like, I think it's obviously a fate that nobody wishes to suffer. Or to look at it another way, to reject God and to deny him is not without very serious consequences. At the very least the denier foregoes the good that God has to offer. If you compare such consequences to the consequences of believing in a nonexistent God, the latter are trivial.

So atheists, make sure that the probability of your being wrong is very, VERY low! To play it safe you want to reject any hypothesis that if false, can land you in a lot of trouble.
Of course, that is making an assumption that hell exists. There are a number of religions that believe in God that do not believe in Hell. So, that makes Pascal's wager much narrower, and less likely.
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Re: Examining Pascal's Wager

Post #276

Post by Ionian_Tradition »

Bust Nak wrote: Fri Apr 16, 2021 2:02 pm
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?
This is a fair objection. Speaking personally, I would certainly prefer a more precise mathematical figure. However, it seems to me that in order to perform the full Bayesian analysis, we'd need to begin collecting various bits of evidence which, in turn, would take us far afield from what I believe is the actual intent of the Wager. As near as I can tell, the Wager isn't precisely concerned with whether Christianity is true, or even whether it is likely to be true. Instead, the Wager (particularly my version) assesses the potential risks and rewards of treating various worldviews as true or false, and then invites us to act in our ultimate best interest (viz. live as if Christianity were true). In this way, the Wager functions more as a pragmatic worldview “cost/benefit analysis” than it does a robust argument for the truth of Christianity.

Nevertheless, I feel we do need some method for filtering out overly contrived worldviews from our list of candidates. Prior probability is one proposed method for doing just that. Granted, whatever the acceptable value is which allows a candidate worldview to “make the cut”, it will be arbitrary. Even so, it’s not evident to me that this is altogether problematic. To illustrate, consider the following:

Suppose you’re interested in taking a much-needed holiday to a relaxing Hawaiian resort. Knowing that the possible number of resorts you could visit is vast, you’ve decided to limit the options by composing a list of the 3 best resorts in Hawaii. To determine which resorts should make it on your list, you’ve asked for recommendations from all the people you personally know who have stayed at a Hawaiian resort.

Now, how many recommendations would be necessary in order for a particular resort to qualify for your list? Two? Five? Twenty?...Whatever the number is, it will necessarily be arbitrary. Never the less, it is by no means clear that you would have been irrational for relying upon this method to compose your list and to filter out non-viable candidates.

In the same way, though the acceptable value for my “prior probability filter” is arbitrary (and subject to some measure of intuition), it’s not clear that this method of refining our data set is therefore invalid or without useful merit.

For my part, I believe Christianity’s status as the world’s largest religion, coupled with the (often under-appreciated) peculiarity of its rise to prominence, is sufficient (at the very least) to secure a prior probability which warrants a place on our list of top worldview candidates.

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Re: Examining Pascal's Wager

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Post by Paul of Tarsus »

Goat wrote: Sat May 22, 2021 7:17 pm
Paul of Tarsus wrote: Mon Feb 01, 2021 5:35 pm
...atheists, make sure that the probability of your being wrong is very, VERY low! To play it safe you want to reject any hypothesis that if false, can land you in a lot of trouble.
Of course, that is making an assumption that hell exists. There are a number of religions that believe in God that do not believe in Hell. So, that makes Pascal's wager much narrower, and less likely.
Yes, I agree with your criticism of Pascal's wager. Which God exists determines the severity of not believing in that God. However, Pascal was referring to his version of the Christian God, and for the purposes of discussion I have decided to focus our attention on that God and the consequences of doubting he exists.

Now, the risk that is taken by doubting that God exists involves two important considerations:
1. The Severity of the Risk
2. The Probability of the Risk
Note that Pascal only considered 1, the severity of not believing in God, while not considering 2, the probability of God's existence. I'm "correcting" Pascal's wager by considering both of these factors.

The values of either of these two factors can serve to determine the risk of atheism. Let's say the severity of unbelief runs from 0, no severity, to 10, eternal punishment. We can compute the risk using an expected value by simply multiplying the "severity index" by the assumed probability of God's existence. For example, if the presumed severity of unbelief is 10, God condemns atheists to hell, but we can safely assume that God cannot exist, then the risk is:

Risk = 0 X 10 = 0

or no risk at all in atheism! On the other hand, if the severity of unbelief is 5, and there's an even chance of God existing, then the atheist's risk is:

Risk = 0.5 X 5 = 2.5

a significantly greater risk.

But how do we know the values of the severity and the probability? We really don't know those values, but the prudent person will study the Bible and use her best judgment to determine the severity of unbelief, and she should also consider the evidence and reasons to believe God exists to conclude what the probability of his existence might be.

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Re: Examining Pascal's Wager

Post #278

Post by Ionian_Tradition »

Tcg wrote: Sat May 22, 2021 6:12 pm
Ionian_Tradition wrote: Sat May 22, 2021 5:55 pm
In point of fact however, I'm arguing a more subtle point, namely that Christianity's status as the world largest religion supports a sufficiently high prior probability so as to be taken seriously when performing the type of (pragmatic) worldview cost/benefit analysis the Wager seeks to perform.
You're still arguing that since Christianity is popular it has a higher probability of being true. This quite clearly isn't valid.


Tcg
You seem to be conflating prior probability with posterior probability. The former is a variable in Bayes theorem which represents the initial likelihood of an outcome within a particular data set (prior to examination of the evidence). Posterior probability, on the other hand, represents the probability of an outcome given all the relevant evidence.

For our purposes, Christianity's status as the worlds largest religion is the back drop (not the evidence) from which we derive our prior. Or put another way, there is a prima facie likelihood that Christianity is true in a world where Christianity is the largest religion; this is our prior probability.

In terms of prior probabilities, Christianity's popularity is no more evidence of its probable truth than a fire on the side of the road is evidence of probable arson. Both Christianity's popularity and the fire on the roadside are outcomes which require explanation. Many explanations could be posited to explain these outcomes and each one has its own prior probability.

To summarize, Christianity being true is one possible explanation for the outcome of its own immense popularity, and this explanation has an initial likelihood which we call its prior probability. I would contend that this prior probability is greater, for example, than the prior probability of Greco-Roman Polytheism being true.

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Re: Examining Pascal's Wager

Post #279

Post by Goat »

Paul of Tarsus wrote: Sat May 22, 2021 8:45 pm
Goat wrote: Sat May 22, 2021 7:17 pm
Paul of Tarsus wrote: Mon Feb 01, 2021 5:35 pm
...atheists, make sure that the probability of your being wrong is very, VERY low! To play it safe you want to reject any hypothesis that if false, can land you in a lot of trouble.
Of course, that is making an assumption that hell exists. There are a number of religions that believe in God that do not believe in Hell. So, that makes Pascal's wager much narrower, and less likely.
Yes, I agree with your criticism of Pascal's wager. Which God exists determines the severity of not believing in that God. However, Pascal was referring to his version of the Christian God, and for the purposes of discussion I have decided to focus our attention on that God and the consequences of doubting he exists.

Now, the risk that is taken by doubting that God exists involves two important considerations:
1. The Severity of the Risk
2. The Probability of the Risk
Note that Pascal only considered 1, the severity of not believing in God, while not considering 2, the probability of God's existence. I'm "correcting" Pascal's wager by considering both of these factors.

The values of either of these two factors can serve to determine the risk of atheism. Let's say the severity of unbelief runs from 0, no severity, to 10, eternal punishment. We can compute the risk using an expected value by simply multiplying the "severity index" by the assumed probability of God's existence. For example, if the presumed severity of unbelief is 10, God condemns atheists to hell, but we can safely assume that God cannot exist, then the risk is:

Risk = 0 X 10 = 0

or no risk at all in atheism! On the other hand, if the severity of unbelief is 5, and there's an even chance of God existing, then the atheist's risk is:

Risk = 0.5 X 5 = 2.5

a significantly greater risk.

But how do we know the values of the severity and the probability? We really don't know those values, but the prudent person will study the Bible and use her best judgment to determine the severity of unbelief, and she should also consider the evidence and reasons to believe God exists to conclude what the probability of his existence might be.
Apparently, the risk is imaginary. It also assumes that there is no risk in not believing in other gods. .. it is specifically geared to believing in the Christian God, with Christian rhetoric. What if there is a bigger risk in belieiving in the Christian God , because the God that exists would rather someone not believe in God verses the Christian God?
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Re: Examining Pascal's Wager

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Post by Paul of Tarsus »

Goat wrote: Sat May 22, 2021 9:30 pmApparently, the risk is imaginary.
While I'm not sure what you mean here, risk is for practical purposes very real. What we might base the risk on, on the other hand, can be imaginary. If Pascal's God is not real, for example, then recognizing the risk of unbelief in that God is to base that risk on what is imaginary.
It also assumes that there is no risk in not believing in other gods.


Assuming you are referring to Pascal's wager, I wouldn't say it assumes anything about other gods. Other gods are simply not considered.
.. it is specifically geared to believing in the Christian God, with Christian rhetoric. What if there is a bigger risk in belieiving in the Christian God , because the God that exists would rather someone not believe in God verses the Christian God?
If I understand what you're saying, in the case of that non-Christian God existing, you had better not believe in the Christian God.

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