Examining Pascal's Wager

[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.

[Paul of Tarsus]

Yes your clarification is helpful.

That's good to hear. Hypothesis testing is not easy to understand, and it's not easy to explain. What it boils down to is rejecting or failing to reject a hypothesis and the seriousness of both decisions.

I reject the hypothesis that "A creator doesn't exist/we do not exist within a creation." because I think it is unfalsifiable. I am always open to being shown this is not the case.

How serious would you say your decision to reject that hypothesis might be? You appear to reject hypotheses if they are unfalsifiable. Is that correct? The philosopher Karl Popper argued that scientific hypotheses should be falsifiable. Over the years that idea has caught on, but some scientists disagree.

"God" is a name given to a particular image of a being which is claimed by those presenting said image to the world, that the being presented is - in Truth - The Creator of The Creation.

The claim is that this is The Truth.

It could be The Truth but I think it is unlikely to be The Whole Truth.

Can you be more specific regarding the creator? Is the Christian God the creator?

[William]

Yes your clarification is helpful.

That's good to hear. Hypothesis testing is not easy to understand, and it's not easy to explain. What it boils down to is rejecting or failing to reject a hypothesis and the seriousness of both decisions.

I reject the hypothesis that "A creator doesn't exist/we do not exist within a creation." because I think it is unfalsifiable. I am always open to being shown this is not the case.

How serious would you say your decision to reject that hypothesis might be?

As my subjective experience over my lifetime amounts to the overall realization that it is likely I am existing within a reality simulation [creation] I am serious in that realization. Apart from that, how serious can serious get?

You appear to reject hypotheses if they are unfalsifiable. Is that correct? The philosopher Karl Popper argued that scientific hypotheses should be falsifiable. Over the years that idea has caught on, but some scientists disagree.

Scientific examination can only be applied to things which are [or can be made] visible. As such, scientists would not claim that we DO, or do NOT exist within a reality simulation [creation] but in that, they cannot falsify either position.
Mind you, I accept that I may not be understanding what 'falsifiable/unfalsifiable' actually means. I am open to being educated on that if I am incorrect ...

"God" is a name given to a particular image of a being which is claimed by those presenting said image to the world, that the being presented is - in Truth - The Creator of The Creation.

The claim is that this is The Truth.

It could be The Truth but I think it is unlikely to be The Whole Truth.

Can you be more specific regarding the creator?

IF we do exist within a creation [such as a reality simulation] THEN [at the very least] this implies there is a creator/creators. By examining the nature of the reality simulation we should be able to ascertain the abilities of said creator, but would we also be able to ascertain the nature of said creator?

Is the Christian God the creator?

Impossible to answer, as Christians appear to have various versions as to their ideas of The Creator.

For example, while most believe that the old testament idea of The Creator is the same being as Jesus refers to as his Father [The Father] other Christians think the OT entity is the entity Jesus referred to as "The Devil" when critiquing the religious leaders if his day.

John 8:44
English Standard Version
You are of your father the devil, and your will is to do your father's desires. He was a murderer from the beginning, and does not stand in the truth, because there is no truth in him. When he lies, he speaks out of his own character, for he is a liar and the father of lies.

So, while I have reason to think I exist within a creation and therefore it was created, I do not think any religious organizations ideas regarding The Creator are necessarily the truth of the matter.

[Bust Nak]

So theists would be prudent to make sure that the probability of H0 being false is very low.

Which means theists and atheists alike are in the same boat as far as having to be prudent to make sure the respective probability being very low. Hypothesis testing doesn't make one position more appealing than the other.

[Purple Knight]

IMO Pascal's Wager fails in its intended use because we have to assume at least one of these two things and thing three and thing four in the case that God does exist:

1. You can somehow turn a belief designed and concocted only to benefit yourself into a true belief that is honest... or... God doesn't even care.
2. God doesn't care why you believe in him at all. If you do it out of fear of being punished or out of merely wanting the reward, he's like, well, you did the thing, don't care why, here's a ticket to Heaven.
3. You also have to assume that God doesn't hate gambling, because gambling, in order to win, is exactly what you're doing here.
4. You also have to assume that there's some reason to pick Christianity over any other religion someone concocts that also has belief as a prerequisite for eternal reward in the afterlife. (See, unless we do make that assumption, there are infinite, equally valid, Pascal's Wagers for every possible religion with this believe-in-me clause.)

However, I think Pascal's Wager succeeds in the case of a person who genuinely wants to do the right thing and doesn't know what that is, when that person is faced with one or many people who do claim to know what good is. He's forced into a Hell of servitude to them, forced to follow as many of their commandments as he can, because any of them could be correct. Even in the case of someone obviously self-interested who says, "be my slave" - that could actually be good. The person without innate knowledge of good and evil has no way to know.

[1213]

...
I presented a counter-example against this premise in my last post, making up a story based on my imagination does not imply I know it is not true. ... ...Is that not enough to dismantle this claim of yours?

Sorry, it is not. But it is interesting, if you could choose things that are not based on anything real and think it as reliable as thing that has even something to support it.

[Paul of Tarsus]

So theists would be prudent to make sure that the probability of H0 being false is very low.

Which means theists and atheists alike are in the same boat as far as having to be prudent to make sure the respective probability being very low.

When you consider different null hypotheses, the results of the test will be different, of course. That's why the test results of your null hypothesis differed markedly from the null hypothesis I tested in the OP: the two hypotheses assumed the nonexistence of very different gods. The god you made up is of little significance because almost nobody believes in such a god. The Christian God, on the other hand, has billions of believers and therefore is of great significance. The hypothesis testing of the Christian God is then far more important than the testing of any "lesser" gods.

Hypothesis testing doesn't make one position more appealing than the other.

While I'm not sure what you mean by "appealing," hypothesis testing does clarify the potential risks and benefits of deciding to reject or fail to reject a null hypothesis. That's why business managers, for example, often make use of hypothesis testing to make decisions about risky business ventures. And as I have shown, atheism is riskier than Christianity, but if you're very sure there is no God, then there's no need to worry.

[Bust Nak]

Sorry, it is not. But it is interesting, if you could choose things that are not based on anything real and think it as reliable as thing that has even something to support it.

Okay, let me make something up contrary to anything real with less than zero support: there are little green man living on Mars. Does the fact that I made that story up imply there are no green man living on Mars?

[Bust Nak]

The god you made up is of little significance because almost nobody believes in such a god. The Christian God, on the other hand, has billions of believers and therefore is of great significance. The hypothesis testing of the Christian God is then far more important than the testing of any "lesser" gods.

The god I've made up is significant in one sense: as you've concluded, the test result of that null hypothesis has shown that Christianity is riskier than atheism; Christians would be prudent to make sure that the probability my made up god existing is very low, where as atheists don't have to worry the odds at all.

While I'm not sure what you mean by "appealing," hypothesis testing does clarify the potential risks and benefits of deciding to reject or fail to reject a null hypothesis. That's why business managers, for example, often make use of hypothesis testing to make decisions about risky business ventures.

When business managers use hypothesis testing for decision making, they are hoping to figure out which alternative has the best utility in terms of risk vs reward. That best option is the "appealing" one.

And as I have shown, atheism is riskier than Christianity...

You have also shown the exact opposite, that Christianity is riskier than atheism when you analysed my H0. Can Christianity be both riskier and less risky than atheism? If it can be both, then how would a business manager make a decision when an option is both riskier and less risky than it's alternative?

[Paul of Tarsus]

The god you made up is of little significance because almost nobody believes in such a god. The Christian God, on the other hand, has billions of believers and therefore is of great significance. The hypothesis testing of the Christian God is then far more important than the testing of any "lesser" gods.

The god I've made up is significant in one sense: as you've concluded, the test result of that null hypothesis has shown that Christianity is riskier than atheism; Christians would be prudent to make sure that the probability my made up god existing is very low, where as atheists don't have to worry the odds at all.

You aren't considering the probability of the god under consideration actually existing. Since you obviously made him up, then the odds of his existing is close to zero and arguably much lower than the odds of the Christian God's existing.

And as I have shown, atheism is riskier than Christianity...

You have also shown the exact opposite, that Christianity is riskier than atheism when you analysed my H0.

You are comparing the "test" results of two different null hypotheses. That's why my look at the two hypotheses resulted in different conclusions.

By the way, technically I'm not really testing hypotheses. Hypothesis testing is much more involved than what I've posted. What I am doing is laying out the decisions and the possible errors of rejecting null hypotheses. Those are the very important first steps in hypothesis testing. Nevertheless, I am clarifying wise decisions to make after considering the probability of being wrong about a null hypothesis.

Can Christianity be both riskier and less risky than atheism? If it can be both, then how would a business manager make a decision when an option is both riskier and less risky than it's alternative?

The risk of Christianity versus atheism depends on the null hypothesis under consideration. Different conclusions may result from different hypotheses as we have seen. Business managers should understand this obvious fact. If they don't, then their businesses are in trouble.

[The Barbarian]

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

That assumes that God will punish you even if you seek to follow Him, if you're wrong about some of His attributes. I see very little reason to believe that.

"The Catholic Church rejects nothing that is true and holy in these religions. She regards with sincere reverence those ways of conduct and of life, those precepts and teachings which, though differing in many aspects from the ones she holds and sets forth, nonetheless often reflect a ray of that Truth which enlightens all men."
Nostra Aetate