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.

[Bust Nak]

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.

You can try arguing that, I'd like to see how you even go about assigning a value to the probability of either deity's existence. More to the point, the probability (as long as it is non-zero) doesn't matter all that much when the consequences can be infinite. Any non-zero possibility multiplied by infinity is still infinity, the strength of Pascal's wager is the ability to avoid having to evaluate the odds of God's existence.

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

That's exactly my point, whether atheism or Christianity is the less risky (and hence the wiser) proposition depends on which testing you are performing, so looking at one test in isolation is unhelpful.

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 a decision really be called "wise" if it is only good under one test, but worse under another test? It's like saying investing in project A is wise without taking into account that the money could be better invested in project B.

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.

Similarly, if people don't understand the obvious fact that a seemingly wise decision might not be so wise after all under different considerations, then their souls are in trouble.

[1213]

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?

In that case I would first ask, why do you think so. If you could not come up with any intelligent reason, I would ignore it.

[Bust Nak]

In that case I would first ask, why do you think so. If you could not come up with any intelligent reason, I would ignore it.

Why do I think what exactly? Why do I think there are little green man living on Mars? I don't think that. I made that up to prove a point. The point being, the fact that I made that up out of thin air, does not imply one way or the other, whether there are any green man living on Mars. Whether you ignore my story or not, also doesn't imply one way or the other, whether there are any green man living on Mars.

The existence or lack there of, of green men on Mars does not depend in anyway on what I am telling you.

While there isn't any significant potentials in ignoring little green man, the potential cost of ignoring my other made up story is huge, as outlined by Paul of Tarsus' analysis on my null hypothesis here. You would be prudent to make sure that the probability of my H0 being false is very low - your eternal soul depends on you getting it right.

[Paul of Tarsus]

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.

You can try arguing that, I'd like to see how you even go about assigning a value to the probability of either deity's existence.

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?

More to the point, the probability (as long as it is non-zero) doesn't matter all that much when the consequences can be infinite. Any non-zero possibility multiplied by infinity is still infinity, the strength of Pascal's wager is the ability to avoid having to evaluate the odds of God's existence.

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. A probability of infinite value is not defined.

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

That's exactly my point, whether atheism or Christianity is the less risky (and hence the wiser) proposition depends on which testing you are performing, so looking at one test in isolation is unhelpful.

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.

Can a decision really be called "wise" if it is only good under one test, but worse under another test? It's like saying investing in project A is wise without taking into account that the money could be better invested in project B.

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.

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.

Similarly, if people don't understand the obvious fact that a seemingly wise decision might not be so wise after all under different considerations, then their souls are in trouble.

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

[Haven0]

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.

[Haven]

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

[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

[William]

...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

Which would be to say - no weight at all.

"God" - as a largely undefined Christian mythology representing The Creator of this Reality Simulation, is no more proven to being the actual Creator of said Reality Simulation than any other Creator concept know to humanity.

So there is literally no weight to the argument the Christian god which they call "God" is the representation of the actual Creator of this Reality Simulation.

[Miles]

...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.

Just as an FYI, atheism almost always centers around belief, not knowledge. So very rarely will will you see an atheist claim god does not exist, but rather that they don't believe he exists. However, agnosticism does concern itself with knowledge; "I don't know if god exists or not."



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[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. Pascal's Wager says that one should believe (in a narrowly defined form of Christianity) because of Heaven and Hell. This argument fails because:

1. The default position on any claim is skepticism, until it meets its burden of proof. A non-theist will contend that god claims have not met their burden of proof.

2. Pascal's Wager assumes only two options (atheism and conservative Christianity), but in reality there are far more god claims, many of which are mutually exclusive.

3. Given 1 and 2, Pascal's Wager fails as an argument.

One does not need to have absolute knowledge of a god's nonexistence to be justified in lacking belief of its existence. This is because skepticism is (or at least, should be) the default position.