The Christian game theorist Jack Holgroth, whose OBJECTIVE: Ministries (an activist Christian site full of right wing propaganda) wrote this Game theory payoff matrix to show why Pascal's wager is such a... *heh-hem*... strong argument against atheism.
The matrix shows the atheist will lose infinitely while the believer in God will win infinitely.
If you think it sounds like the game might be rigged, then you'd be correct (for reasons I shall shortly explain).
I was actually surprised to see this on an actual "Game theorists" page, because anyone who actually is calculating a payoff matrix, such as betting on a horse at a horse race, has to calculate the chances of all the horses in that race, not just the top rated and the least rated.
Also, if introducing infinitude into the wager also seems peculiar, again you'd be right.
Objection 1: Other Probable Gods
The above game wager payoff matrix fails to consider each and every possible contender in the race. That is, it fails to account for all the alternative god possibilities that exist or ever will exist. Because this game isn't about just one set of horses. It is a game which is betting against all the horses in existence, that have ever existed, or that will ever exist. That's the nature of the god-probability-game. Without accounting for all possible gods, the matrix will be incorrect and the results will therefore also be incorrect.
Monotheism is not an assumption which can simply be made a priori. In order to get to monotheism, one has to demonstrate there are no other gods. If the demonstration isn't made, then belief in other gods is equal to belief in a monotheistic God since the a priori assumptions are equal. So the matrix needs to be revised to account for this.
The matrix should therefore read:
- God Exists +1 infinity*(Believer) -1 infinity (atheist)
- Other Gods Exist +1 infinity*(Believer) -1 infinity (atheist)
- No God or god(s) Exist -1 infinity*(Believer) +1 infinity (atheist)
Since the revised matrix properly includes other gods, as monotheism is not an assumption which can simply be made, and the probability of other gods existing is equal to the Christian God, it is an infinite gain to believe in other gods.
Being a monotheism, however, Christianity says there are no other gods. This claim needs to be validated otherwise the matrix is meaningless when other Gods are thrown into the mix. Why is it meaningless? Because a Christian cannot believe in the Christian God and other gods simultaneously, as this nullifies what it means to be a Christian--and Christian belief becomes irrelevant. Which is why objection one succeeds in demonstrating Pascal's wager to be erroneous.
Thus when all other gods (past, present, and still to come) are properly considered, the probability of the Christian god existing is negated by the equally probable existence of *other possible gods.
This is why, logically speaking, Pascal's wager doesn't work.
Objection 2: Contradictions in Terms
Like most Christians, the author has misunderstood the nature of infinity as it applies to reality and not surreal numbers. It seems, as a game theorist, he was talking in terms of mathematics. That is, the theoretical framework by which infinity can be described. But the problem should, I hope, be obvious.
God is said to exist infinitely. Theologians typically mean that God exists without limit. Even so, let's not forget that infinity is really only a duration of time. How much time? An infinite amount. Time without limit, one could say. To say God exists as a limitless being (note: God's supposed existence is what distinguishes him apart from a surreal number) is to say he exists within the frame work of space time and not outside of it. Therefore to claim God is both infinite and transcendent is a contradiction.
Let me explain.
As Albert Einstein showed us, nature is a little more complicated and less intuitive than we commonly are lead to believe. According to Einstein's theory of *special relativity, Einstein was able to show that time is relative and that infinity has a finite beginning at the beginning of all space and time, i.e. the big bang.
In Einstein's law of special relativity there was no dimension of *time before the big bang--as the big bang is what created time as we understand it. Time itself is merely the fourth dimension of physical reality.
An *infinite being cannot exist outside of space time because that would mean it would be existing outside of *infinity.
You may want to read that last sentence again as it is vitally important to get clear.
Time cannot exists outside of time, as far as Einstein is concerned. Therefore, it makes no sense to designate infinitude to the property of belief in the Christian god. Why? Because the Christian god, according to those who believe in him, is a transcendent being.
Why does objection 2 apply in the first place? If we are talking only about God's infinite nature, then why would God's transcendence haven any sway on the outcome of the wager?
It's like this. The payoff matrix states one will gain infinitely if they chose to believe in God and are right, while those who do not believe will lose finitely.
Regardless, the only way to say one can gain infinitely by choosing God is to *assume God is infinite in nature. According to the assumptions of Christian theologians, we come into God, whatever that could mean, and our gains would be infinite as God is an infinite in being. This is what the assumption is making prior to the wager is made and before anything gets calculated.
But can we allow theologians to ignore God's other properties when describing the Christian God? I would argue no. Not when theologians are simply selecting from a priori assumptions. If you ignore God's specific attributes of God then you are not describing the *Christian God, but rather, you are talking about a generic deistic being. If so, then objection 1 is even more pertinent than I initially thought.
If Pascal's wager only describes God in generic terms, and all generic deistic entities are equally probable, then it is an infinite gain to believe in any or all of them. So in order to specify belief in the Christian God modifiers are used to differentiate him from other God. Modifiers like the Christian God being *infinite. The question becomes, why does the above matrix include one modifier and not another?
Because when you get specific, as I have, you find contradictions in terms. A god that exists for an infinite duration of time outside of time itself does not make any sense. It is a negation of terms. The possibility of such a being is ZERO.
So even if you choose to write belief in God's existence as +1 infinity, it doesn't actually matter. We cannot ever get that far. The very belief in such a being is based on arbitrary selecting attributes which negate each other before the math can be done.
If you persist on writing out Pascal's wager anyway, taking into account contradictory terms, then it's not +1 infinity for the existence of God. Rather, seeing as how the existence of such a being is equal to zero, the math should reflect this and be written as (+1 x 0) * infinity. I kept the +1 to keep with the format of the above math. However, it is simpler just to write 0 instead.
You cannot multiply infinity by zero. All you get is
0 * ∞ = c. It's an undefined, or indeterminate, number. Limitless, sure. But also meaningless when attached to descriptions of God. The question becomes: what do you think you are betting on?
A contradiction in terms complicates Pascal's wager to the point of making it moot. Which is why certain terms are frequently ignored in favor of ones which suit the purpose of the theologian. This only goes to show that Pascal's wager is rigged from the start.
Objection 3: A Moral Conundrum
I mentioned briefly that according to Pascal's wager one could bet on God without actually believing in him. This problem arises when one overlooks objection 1 and simply agrees with the math as written. Although the math by itself is correct, it once again neglects to consider the other attributes of God. Why is this problematic? Because it is technically describing a different God than Christians actually believe. Which is why it is important to not overlook the properties of God when weighing the wager.
The problem is like this, God being omniscient he would *know whether or not you were lying. Since the Christian God views lying as a sin, feigned belief would not likely do you any good. Therefore Pascal's wager, and this is kind of funny, only works for Christians as only true Christians *full of conviction could gain from it. If it only applies to Christians, then the wager becomes irrelevant.
It would be like taking bets on a Boston Red Sox vs. New York Yankees baseball game, only to say, it doesn't matter who you bet on because only those who are true Red Sox fans will win. Everyone else will lose--for no other reason than they are not genuine Red Sox fans. How is that not a rigged bet?
This creates a moral dilemma, for obvious reasons. You get forced into having to believe the Red Sox are the best, only true, baseball team worth believing in. Even when that is not what you can honestly believe. What if the Red Sox suck that year? What if the Yankees upset them to go on to win the World Series? There are always other factors which need to be considered before putting down on a wager.
In religious terms, then, these other factors are just as important to consider before betting on the existence of God.
Granted, Pascal's wager is designed to rationally convince the atheist that it is safer to err on the side of caution and bet on the existence of God than not to. But even though this appeals to our rational brain, the reasoning if flawed. There are many other, independent, reasons why it is impossible to believe in the Christian God. Yet none of these reasons are accounted for in Pascal's wager, which means, if an atheist has other reasons for not believing then they will not likely be convinced by the probability that they would gain anything in a false, or feigned, belief--given what we know about the nature of God.
Like in real life, it is always good to have all the information available before you throw down on a wager--whether it is a Red Sox vs. Yankees game or belief in God vs. atheism. The thing is, however, in the case of God vs. atheism, once all the information is considered, the wager becomes erroneous. It's not so simple as Pascal would have us believe.
The objections I raise here are devastating to Pascal's wager. Objection 1 shows that any payoff matrix has to include other Gods as monotheism is not an assumption that can simply be made without a valid demonstration. When other gods are thrown into the mix the wager becomes absurd.
Objection 2 shows that contradictory terms will seek to make Pascal's wager moot, and therefore Pascal's wager is designed to ignore the various properties of God in favor of a simplified math, proving the wager is rigged from the start. Consequently, it seems to be an over simplification as it renders the Christian God into a generic one. As such, objection 1 becomes all the more pertinent.
Objection 3 ignores the math but deals with the implications of the wager. If the wager is taken for granted, then it can be believed. But when it is properly scrutinized, however, it reveals itself to be an immoral proposition.
Taken together, all three objections reveal why Pascal's wager should be rejected.