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.

[JehovahsWitness]

...a god wanting people to believe ...would have strong motivation to leave evidence of her/his/its existence and desires in the universe. ... no such evidence exists...

Nobody could possibly be in a position to know what is or is not in existence without becoming the very thing atheists claim does not exist. The most one can do is present a statement of belief, ie say is they do not believe they have seen any evidence of God's existence.

Which would carry no more weight than the beliefs of those that say they have.

JW

The point under debate is not absolute knowledge, it is (non)belief and the consequences thereof.

I know what the debate is about. Unless your statement is irrelevant to said debate - in which case why did you make it - it is an unproven premise offered in support of your argument , and can obviously be questioned.




JW

[Haven]

...a god wanting people to believe ...would have strong motivation to leave evidence of her/his/its existence and desires in the universe. ... no such evidence exists...

Nobody could possibly be in a position to know what is or is not in existence without becoming the very thing atheists claim does not exist. The most one can do is present a statement of belief, ie say is they do not believe they have seen any evidence of God's existence.

Which would carry no more weight than the beliefs of those that say they have.

JW

The point under debate is not absolute knowledge, it is (non)belief and the consequences thereof.

I know what the debate is about. Unless your statement is irrelevant to said debate - in which case why did you make it - it is an unproven premise offered in support of your argument , and can obviously be questioned.




JW

I’m not sure what you mean here, could you clarify? You were suggesting that one would have to be a god to rationally disbelieve in Christian god claims, and my response was explaining why that is not, in fact, the case.

[Bust Nak]

In hypothesis testing you assign a probability to an error that you're willing to risk. If you fail to reject the hull hypothesis in this case, how much risk are you willing to take that you are wrong and God exists? Or in other words, as an atheist how much of a probability will you accept that God does exist for you to continue to doubt? If you think the probability that he exists is fifty percent, for example, would you risk it and remain an unbeliever? How about five percent?

Given the premise that there is no real downside to Christianity and no real upside to atheism, I would not risk anything beyond 0% chance of God's existence. The problem here is of course the premise itself, looking at just one null hypothesis fails to take into all the potential cost and benefit to the two wager.

More to the point, here you are talking about what percentage chance I was willing to risk, where as previously you were talking about the percentage of God existing, I don't see what chance I am willing risk help you estimate the chance of God existing.

The probability of your being wrong is very subjective, and you can pick any probability you want as long as it's greater than zero and less than one.

Is it really subjective given the seriousness of the potential outcome? Why would anyone not go all in on a sure win?

A probability of infinite value is not defined.

I was referring to the expected value, while the probability has to be between zero and one, the expected value is not bounded.

But in this discussion we are examining the hypothesis, H0: God does not exist. If we examine a different hypothesis, then we are changing the subject. The topic I started in the OP is how much atheists and theists risk by their respective doubt and belief in the Christian God. Your hypothesis was about a different god.

My objection is that one particular hypothesis alone doesn't give the full picture, pointing out that the full picture involves examining hypotheses beyond that one hypothesis isn't much of a counter-argument.

I suppose how you determine a wise decision would vary from one test to another, but the "test" did not change. Again, you asked me to examine a different null hypothesis using the same terms and logic as I used to examine the null hypothesis in the OP. The different conclusions I arrived at resulted from testing a different null hypothesis--not from using a different test.

Whether the same terms and logic on different null hypotheses counts as different tests or not is just semantic. The point is still that the "wise" decision flip flops depending on the hypothesis being tested, which means the result is useless in isolation.

I'm considering the consequences of belief in the Christian God. Let's stick with that topic.

Let me try a different tack, if you could bear with a little role play.

Boss: "We have this war chest, what should invest in project A?"
Employee 1: "Investing in project A would yield 7% over two years. Interest alone is extremely unlikely to come close to matching that return. It's a no brainer, the number says the wise decision is to invest in project A."
Employee 2: "But project B would yield 15%!"
Employee 1: "I am considering the consequences of investing in project A, project B is a different project, lets stick to the topic."

The Boss isn't gonna be very happy with Employee 1.

[JehovahsWitness]

I’m not sure what you mean here, could you clarify? You were suggesting that one would have to be a god to rationally disbelieve in Christian god claims, and my response was explaining why that is not, in fact, the case.

No, I am saying one would have to be a god to be in a position to know there exists no evidence for a god, regardless of the nature of the god under discussion.

The fact that no evidence for such a god exists is exactly what one would expect to find given the nature of the being.

[Paul of Tarsus]

Paul, the problem that I see with Pascal’s Wager is that it only accounts for one view of God — the conservative Christian view (Pascal’s use of Heaven and Hell illustrate this clearly).

There are thousands of god concepts believed in by human beings. Even if Pascal specifically referred to the god of classical theism, there are still dozens of concepts that fit the god of classical theism (the one in which I assume you believe), many of which do not have heavens or hells as you seem to understand them.

How is one to decide between these god concepts, in light only of Pascal’s Wager? One can’t rationally distinguish between them, as all have fervent believers and the same amount of evidence in favor of them (that is, very little). Therefore, one must conclude that Pascal’s Wager is a flawed argument, as it offers no means by which to distinguish the various god claims made by humanity.

Yes, obviously Pascal did not consider other Gods when he proposed his wager. I agree with what you're saying here, but I'm not defending Pascal's wager. I'm just examining the decisions and the error's a person might make regarding their belief in the existence of God and how sure they should be that they are right.

[Paul of Tarsus]

Moreover, Paul, to address your second H0 (//there is no god that rewards atheists with heaven and punishes theists with hell//): there is no way to assign a probability to such a god existing (given the lack of evidence for it). Furthermore, there is no way to assign probability to the hypothesis in the OP (that is, Pascal’s wager), given the lack of evidence and the multiplicity of possibilities.

Given these parameters, rejection of the null hypothesis in both cases seems unjustified.

However, there is something else that should be considered, something that will shift the balance toward your second Ha. That is, a god that rewards people for being atheistic (that is, for not believing in a god) will be highly unlikely to reveal him/her/itself, in order to facilitate non belief. The fact that no evidence for such a god exists is exactly what one would expect to find given the nature of the being. Meanwhile, a god wanting people to believe (even so far as going to torture nonbelievers eternally) would have strong motivation to leave evidence of her/his/its existence and desires in the universe.

Since no such evidence exists, it seems inescapable that one would be more justified in rejecting your second H0 (that is, the one from your Reverse Pascal’s Wager) than in rejecting your original H0 (that is, the one in Pascal’s Wager).

~Haven

You may wish to take up these issues with Bust Nak. It was he who came up with the "second" null hypothesis.

[Haven]

I know what the debate is about. Unless your statement is irrelevant to said debate - in which case why did you make it - it is an unproven premise offered in support of your argument , and can obviously be questioned.




JW

I don’t think you understand the nature of evidence. Evidence is defined by what we know. By definition, something can only be evidence if it is known to exist. New evidence can be found, but it cannot be considered evidence until it is discovered.

[Paul of Tarsus]

The problem here is of course the premise itself, looking at just one null hypothesis fails to take into all the potential cost and benefit to the two wager.

You are welcome to check any null hypothesis you wish. I'm just focusing on the null hypothesis, H0: God does not exist, because it's the null hypothesis that Pascal was referring to in his wager. If you do consider other null hypotheses, don't confuse your results with the results of my null hypothesis.

More to the point, here you are talking about what percentage chance I was willing to risk, where as previously you were talking about the percentage of God existing, I don't see what chance I am willing risk help you estimate the chance of God existing.

They're the same probabilities but are just worded differently. If you fail to reject my null hypothesis by assigning a probability to your being wrong that you find acceptably low, then that probability is the same probability as God existing. In other words, if you are wrong then God exists, and the probability of your being wrong is the same as the probability of God existing.

The probability of your being wrong is very subjective, and you can pick any probability you want as long as it's greater than zero and less than one.

Is it really subjective given the seriousness of the potential outcome?

Yes. As far as I know there's no way to objectively choose a probability value for the chance that you will accept for being wrong.

Why would anyone not go all in on a sure win?

There are no "sure wins." That's why we even bother with hypothesis testing.

I was referring to the expected value, while the probability has to be between zero and one, the expected value is not bounded.

Correct me if I'm wrong, but as far as I know expected values are not used in hypothesis testing.

My objection is that one particular hypothesis alone doesn't give the full picture, pointing out that the full picture involves examining hypotheses beyond that one hypothesis isn't much of a counter-argument.

Yes, but I'd rather just focus on the issues I raised in the OP.

The point is still that the "wise" decision flip flops depending on the hypothesis being tested, which means the result is useless in isolation.

Actually, the "flip-flop" we ran into resulted from your coming up with a null hypothesis about belief in a different god. That is a weakness of Pascal's wager (he didn't consider other gods), but I'm looking to see if he was even right about belief in the Christian God. He might be wrong even then--to the delight of atheists everywhere!

Boss: "We have this war chest, what should invest in project A?"
Employee 1: "Investing in project A would yield 7% over two years. Interest alone is extremely unlikely to come close to matching that return. It's a no brainer, the number says the wise decision is to invest in project A."
Employee 2: "But project B would yield 15%!"
Employee 1: "I am considering the consequences of investing in project A, project B is a different project, lets stick to the topic."

The Boss isn't gonna be very happy with Employee 1.

I'd say that the "Boss" should finish his consideration of project A by using a hypothesis test. Once that work is done, then he may wish to test Employee 2's hypothesis.

So let's finish considering the null hypothesis in the OP.

Let me conclude that a hypothesis test normally involves numerical values. For example, if project A is hoped to increase the pressure that a part will endure, then the null hypothesis might be:

H0: Project A will not increase the average maximal pressure on the part of an average of 1,000 pounds per square inch.

To test this hypothesis would involve measurements and calculating an average to see if that average falls into the "critical region" of the assigned probability under the normal curve.

Unfortunately, we can't do that with God.

[Haven]

I just wanted to clarify something on the nature of H0–Paul (and Pascal’s Wager) heavily imply it, but don’t explicitly state it.

H0 is not “God [an undefined omnimax entity] does not exist.” It is “God, as defined by conservative Christian theology, does not exist.”

A very important distinction.

[Bust Nak]

This seem like a big deal, I want to focus on this:

To test this hypothesis would involve measurements and calculating an average to see if that average falls into the "critical region" of the assigned probability under the normal curve.

Unfortunately, we can't do that with God.

Then why are we even talking about testing the hypothesis? Though out this thread you've been talking about the consequence of getting the result wrong, which doesn't seem to have much to do with preforming the test itself.