Pascal vs. Paulos, The Final Round: All Bets Are Off

Previous Entries:

Pascal vs. Paulos, Setting the Stage

Pascal vs. Paulos, Round 1: Pascal’s Wager

Pascal vs. Paulos, Round 2: Paulos Ups the Ante

Here is a concise summary of the objections raised by Paulos that I plan on responding to (For a more thorough treatment of the objections Paulos raises against Pascal’s Wager, please see the previous post):

  1. The wager argument can be used to justify heinous acts by people who judge human penalties to be inconsequential in comparison to their heavenly rewards.
  2. The concept of “betting on God” is ambiguous and can be used by people of various faiths.
  3. The phrase “the probability of God’s existence” is nonsensical because the universe is a singularity.

I would also like to respond to Paulos’ comments on ethics. To be fair, Paulos notes that his discussion of ethics is being given as an aside and it is not the primary focus of the chapter. However, there is another chapter in the book in which his discussion does center around morality. So then, I will save the discussion of ethics, morality and mathematics for a future posting.

In regards to objection 1: I believe this comment ultimately stems from a misunderstanding of Pascal’s Wager. Pascal’s argument is given as a response to the question: “Supposing the evidence for God’s existence is inconclusive, then is it rational to remain in unbelief?” The premise of this question is crucial to understanding the argument. The Wager argument is only useful for a person who isn’t sure one way or the other that God exists. Pascal would openly say that if the evidence is indisputably in favor for God, then believe in God. If the evidence is indisputably in favor against God, then don’t believe in God (though Pascal himself would personally say that the evidence indeed favors God’s existence).

People who would use a line of reasoning similar to Pascal’s Wager in order to justify horrible acts of violence are certainly not people who are in doubt about God’s existence. They are people who are already 100% sold on his existence. They are also people who are 100% misinformed about the nature of God and the desires He has for His creation.

It is not my desire to go into great prose here in addressing the atrocities that evil people commit in the name of religion. Just because evil people perform evil acts in the name of some religion, it does not justify their actions nor does it make that religion inherently evil (since it seems to me that people in this category have largely warped the religion they claim). Similarly, it should be stated, just because evil people perform evil acts in the name of non-religion (atheists), it does not justify their actions nor do their actions alone make atheism inherently evil. All this line of argument does is show that people are evil. ALL people. All people, when left to their own devices, are at their core depraved. We are all in need of redemption and the grace of God.

In regards to objection 2: It is certainly true that with Pascal’s Wager alone you cannot arrive at an argument for the God of Christianity. But the fact remains, if the argument can succeed in persuading a person to simply theistic belief over atheism, then the leap to specific Christian belief is not nearly as great.

There also arises the question of what does it mean to “bet on God.” By betting on God, Pascal does not mean that you can make yourself believe. Salvation remains a work of the Spirit and not the will. Perhaps it is instructive to again quote here Pascal’s own understanding of any argument for God.

That is why those to whom God has given religious faith by moving their hearts are very fortunate, and feel quite legitimately convinced, but to those who do not have it we can only give such faith through reasoning, until God gives it by moving their heart, without which faith is only human and useless for salvation. (Pensees, 282)

What Pascal means by betting on God is that you can put yourself in situations that are more conducive to belief. For instance you can attend church, you can pray, and you can leave behind your present lifestyle. Putting yourself in those situations places you in a seemingly better position to be open to the working of the Spirit, though it is no guarantee of salvation.

And without faith it is impossible to please Him, for he who comes to God must believe that He is and that He is a rewarder of those who seek Him. (Hebrews 11:6, Italics mine)

We can be comforted in knowing that God rewards those who seek Him.

In regards to objection 3: While I certainly do not claim to have a complete understanding of statistics or the use of religious language claims, I see no reason why the phrase “the probability of God’s existence” should fail to make since simply because we cannot count the number of universes there are and how many of those universes have gods, or something along those lines (even if we could count the total number of universes in existences, the claim is still that there exists one God who is over all of them).

One of the more popular examples that statistics students bring to me is the infamous sock drawer. Questions read along the lines of: “You are getting ready for school and your sock drawer has four argyle socks, two polka-dotted socks, and one blue-striped sock (since you lost one). What is the probability that you select two socks that match?”

If there was only sock in the drawer, would it be nonsensical to ask “what is the probability of one sock existing in the drawer?” I hardly think so. The probability is either 1 (meaning there is absolutely one sock in the drawer), or it is 0 (meaning there is absolutely not one sock in the drawer).

To extend the metaphor, it would seem that Paulos believes “the probability of God” does not make sense because we cannot open the drawer (on his view) to see if God is really there. Either God exists or He doesn’t (but He does), so the probability is either 1 or 0 (but it’s 1). So then, the phrase “the probability of God’s existence” seems to me to make perfect sense.

In Summary: While this post has certainly not been exhaustive in the treatment of the topic at hand (though those of you are still reading at this point may disagree), my critique of Paulos essentially boils down to this: Paulos’ critiques of Pascal’s Wager stem from a restatement of the argument that Pascal never originally intended. Pascal simply intended to demonstrate through sound mathematical reasoning that if you aren’t sure whether God exists or He doesn’t, it makes more sense for you to believe in Him than to not so believe.

I don’t fault Paulos for this approach. I simply offer it up as evidence that the presuppositions we bring to a subject (in this case Paulos’ atheism) always affect the way we reason through an argument.


Pascal vs. Paulos, Round 2: Paulos Ups the Ante

Previous Entries:

Pascal vs. Paulos, Setting the Stage

Pascal vs. Paulos, Round 1: Pascal’s Wager

Here is a brief summary of John Allen Paulos’ critique of Pascal’s wager in his book Irreligion: A Mathematician Explains why the Arguments for God Just Don’s Add Up. I believe there are very sound responses to each of his points mentioned below and I plan on discussing them in the next post. For now, you can read the previous entry in which I summarized Pascal’s Wager, read what Paulos has to say, and think for yourself how valid his reasoning is and how you might respond.

If you pay attention you will notice how the presuppositions Paulos brings to this matter affect the way he reasons and the way he discusses mathematics. I think this book is a clear demonstration that religious beliefs affect the discipline of mathematics, be they Christian, atheist, or something else entirely. So the real question then, is why should an atheistic or naturalistic worldview be more appropriate for mathematics than a Christian one? But I digress, a topic for another time. Back to the book…

Paulos’ Summary of the Pascal Wager Argument for God (133):

  1. We can choose to believe God exists, or we can choose not to so believe.
  2. If we reject God and act accordingly, we risk everlasting agony and torment if He does exist but enjoy fleeting earthly delights if He doesn’t.
  3. If we accept God and act accordingly, we risk little if He doesn’t exist but enjoy endless heavenly bliss if He does.
  4. It’s in our self-interest to accept God’s existence.
  5. Therefore God exists.

The first problem that Paulos finds with the argument is that:

The argument itself has little to do with Christianity and could just as readily be used by practitioners of Islam and other religions to rationalize other already existing beliefs (134).

In summarizing the mathematics behind expected values, Paulos’ first critique becomes even more apparent by his own parenthetical comments:

If we multiply whatever huge numerical payoff we put on endless heavenly bliss by even a tiny probability, we obtain a product that trumps all other factors, and gambling prudence dictates that we should believe (or at least try hard to do so) (135).

In essence, the first problem with Pascal’s Wager is that it is not faith specific and it very vague in its description of how one actually bets on God’s existence.

As an aside Paulos even brings into doubt the ability to assign a probability to God’s existence. He notes that the statement “the probability of a God” is unlike “the probability of a royal flush.” We can calculate the number of poker hands and royal flushes that are possible and determine that all hands are equally likely but, unlike a deck of cards, the universe is unique. Since we cannot calculate the number of universes there are and how many of them have a God and how equally likely they are, the statement “the probability of a God” is nonsensical.

The second problem that Paulos finds with the argument is that while it can be used to argue for a rational belief in God, by assigning such large values to the payout of God’s existence the argument can also be used to rationalize horrible actions.

Killing thousands or even millions of people might be justified in some devout believers’ eyes if in doing so they violate only mundane human laws and incur only mundane human penalties while upholding higher divine laws and earning higher divine approbation (135).

Paulos uses this notion to relate Psacal’s Wager to an argument from fear, summarized as follows (137):

  1. If God doesn’t exist, we and our loved ones are going to die.
  2. This is sad, dreadful, frightening.
  3. Therefore God exists.

This prompts a sound lampooning of religious and political leaders who lead by fear-mongering. His critique then moves into a discussion of ethics, largely focused on demonstrating that atheists and agnostics are at least if not more moral that devout religious believers.

An atheist or agnostic who acts morally simply because it is the right thing to do is, in a sense, more moral than someone is trying to avoid everlasting torment or, as is the case with martyrs, to achieve eternal bliss. He or she is making the moral choice without benefit of Pascal’s divine bribe (140).

Extrinsic rewards undercut intrinsic interest and this is a reason not to base ethics on religious teaching (141).

Tune in next time for a response to Paulos’ critique.

Pascal vs. Paulos, Round 1: Pascal’s Wager

Previous Entry: Pascal vs. Paulos, Setting the Stage

Like all good mathematicians of the 17th century, Blaise Pascal’s life was characterized by three primary activities: gambling, drinking, and womanizing. After coming to Christ in a dramatic way, Pascal set out to persuade his contemporaries (who were caught up in a similar lifestyle) to follow him in Christian belief. So Pascal’s wager argument is set in the context of being presented to an audience that is familiar with gambling theory.

It should be noted that Pascal’s coming to faith was not based upon this argument. In fact, Pascal did not believe any argument was sufficient for faith. In the Pensees (which is a collection of his thoughts), when speaking of the relationship between reason and faith, he concluded by stating:

That is why those to whom God has given religious faith by moving their hearts
are very fortunate, and feel quite legitimately convinced, but to those who do not have it we can only give such faith through reasoning, until God gives it by moving their heart, without which faith is only human and useless for salvation. (Thought 282)

Now, you may be asking, “how does gambling theory apply to religious belief?” An excellent question, thank you for asking. Pascal offers two keen insights into the nature of life. First, he notes that life itself is a risk. Everyday you have to make decisions have before you have all the evidence on a given topic. This is particularly true in regards to religious belief. A decision for God or against God must be made during this life, prior to having indisputable evidence for His existence.

The second insight that Pascal offers is that we always develop strategies when making decisions that serve to maximize our potential for gain, and minimize our potential for loss. So then, based on these two insights, applying an argument based around gambling theory seems like a sound approach to the question of religious belief.

Pascal’s wager argument is based on calculating expected values. Suppose you find yourself at a local fair or carnival and there is booth that says “Dice Game.” To play this game you must pay $3 (a relative bargain for local fair prices). Once you have paid you get one roll of a standard six-sided die. If you roll any number between 1 and 5 then you lose (sorry), but if you roll a 6 then you win $15 (a profit of $12)!

Expect Value (EV) of “Dice Game” = (Event of Winning $12) x (Probability of Rolling 6) – ($3 Cost of Playing) x (Probability of Losing)

EV(Dice Game) = ($12) x (1/6) – ($3) x (5/6) = -1/2 (or -$0.50)

This means that if you played this game over and over for an extended period of time, you would average losing $0.50 per game. Though this example is simplified, this is essentially why casinos are profitable businesses.

So then, in general the formula for an expected value can be given as follows: the expected value of an event E equals the probability of winning multiplied by the payout amount, minus the cost. In other words:

EV (E) = Pr(Winning) x Payout – Cost

Pascal then poses the question, “supposing the evidence for God’s existence is inconclusive, then is it rational to remain in unbelief?” What if you aren’t sure if God exists or if He doesn’t? In that case, suppose the probability of God’s existence is 50/50 (any numbers result in the same outcome, even if it is 99/1, but we’ll discuss this further in another post).

Pascal then supposes to paint belief in God in the worst possible light, to show that his argument still demonstrates that one should believe in God over atheism. So then, suppose the cost of believing in God is significant, such as the hardships you would endure in life and supposed freedoms you would have to forgo for your faith. Even if the cost is significant, ultimately if God exists, then the cost is only finite and temporary; whereas the payout for betting on God if He exists is infinite and eternal.

For atheism, the cost might be zero (in reality it probably isn’t, but again, just to paint the argument most favorably toward atheism, we’ll assume this is the case). The payout for betting on atheism could be significant if God doesn’t exist, in terms of the freedoms you could indulge in during life. But even if it is significant, if God doesn’t exist then this life is all you have, so the payout no matter how large is always finite. So then returning to the formula for expected value we have:

EV (Theism) = 0.5 x Infinite Payout – Significant but Finite Cost

EV (Atheism) = 0.5 x Significant but Finite Payout – 0 Cost

The result then is that the expected value of theism is infinite. Any number times infinity is infinity, and subtracting any finite number from that still yields infinity (the concept of infinity will be taken up in future posts).

The expected value of atheism could be significant, but is ultimately a finite number. You get this same result no matter the probabilities you insert into the equation. Even if the probability against God is 99/1, the result still holds. The expected value of theism is always greater.

Therefore you should bet on God. What exactly that means is a topic for another day.

Recommended Reading:

You can read Pensees for free here.

Tim Rogalsky, “Blaise Pascal – Mathematician, Mystic, Disciple”