# Between the Lines: Pascal’s Wager

—> Reader beware: this post is going to be a long read full of deductive logic and working to challenge postulations.

[What is Between the Lines? Read how it got started here.]

Before we start, this is not a deconstruction of Pascal’s Wager itself. This is a deconstruction of a random INTJ’s argument rejecting Pascal’s Wager as logically sound.

The INTJ’s thesis statement is as follows:

In my opinion, Pascal’s Wager is an emotional, persuasive and dangerously weaselly argument, which is likely to appeal to any non-Rational (NT). I hope to in this post debunk this argument and hopefully free a few minds in the process.

It’s likely to appeal to other types… why? We’ll never know; INTJ assumes it’s self-evident and doesn’t explain. Moving on, INTJ summarizes for us:

What is Pascal’s Wager? The argument goes as such:

A) Either God exists, or he does not exist.
B) If he does not exist, and I do not believe in him, I gain no benefit.
C) If he does not exist, and I believe in him, I suffer no detriment.
D) If he exists, and I do not believe in him, I suffer infinite detriment (eternal hell).
E) If he exists, and I believe in him, I gain infinite benefit (eternal heaven).

This is, if you checked the Wiki summary of Pascal’s Wager, accurate but crucially incomplete.

I love game theory, adore it, but I’m not so well-versed in it that I can spell it out in laymen’s terms for what this game structure would look like with the agents involved.

So instead, let me attempt to summarize the Wager using some formal logic language:

Rule 1. If Is God, then God has a quality [infinitely incomprehensible]. We are incapable of knowing what God is or if God is.

Rule 2. Either Is God or Isn’t God. There are only two states in this argument, God either is or isn’t. (Reminder: we can’t know if God is or isn’t based on the first postulation.)

Rule 3. You must choose Believe in God or Don’t Believe in God. You must wager, participation not optional.

• If Is God and Believe, then infinite gain.
• If Is God and Don’t Believe, then infinite loss.
• If Isn’t God and Believe, then no effect.
• If Isn’t God and Don’t Believe, then no effect.

This is the crux of the argument. There is a succinct summary of the logic here in the Wiki article section Inability to believe as outlined here. The logical answer, strictly speaking, is to Believe.

Fabulous, let’s move on:

What is wrong with this argument? Many things, though it may not be obvious at first.

Firstly, this argument assumes that if God does not exist, nothing matters either way, meaning that the atheist and Christian will have equal utility values. I submit that this is wrong.

No, it’s not “nothing matters either way”. The entire sum of the decision matrix in the Inability to believe section outlines why this isn’t the case. There is a rational, logically deduced optimal decision here.

It seems clear to me that a life without religion will have far more earthly happiness than a life with religion.

This is subjective, and outside of the scope of the argument.

If anyone’s ever worked on tangent curves with a limit of infinity, you will have an extra layer of understanding: even if it were the case that one could live life on earth with a large but finite amount of happiness, that finite amount of happiness would numerically pale in comparison to the infinite happiness of the afterlife in the case that Is God and Believe.

Infinity is a rather large number.

This is the implied trade many believers make and are willing to make, on the chance that they will get a far larger payoff in heaven. It can be seen that if it were indeed blindingly obvious that the Christian’s and atheist’s lifetime utility were equal, no rational person would even need to stop to consider which path to take. The fact that there exists doubt, is prima facie evidence for the atheist having greater quality of life and lifetime utility than the Christian. Therefore, if God does not exist, the atheist wins out in terms of lifetime utility, instead of being arbitrarily placed on equal footing with the Christian, as this argument conveniently ignores.

So, logically speaking, INTJ is trying to say:

IF
A: Christian and Christian has quality [lifetime utility]
B: Atheist and Atheist has quality [lifetime utility]
C: Christian’s [lifetime utility] is equivalent to Atheist [lifetime utility]
THEN
D: Correct choice (Believe or Don’t Believe) is obvious

IF
E: Doubt in postulation C
THEN
F: Atheist [quality of life] and [lifetime utility] greater than Christian [quality of life] and [lifetime utility]

So then we get a conclusive sentence like “If there’s doubt that a Christian and an Atheist have different lifetime utilities, then the Atheist has a greater quality of life and lifetime utility than the Christian.”

Wait, what was INTJ’s conclusive sentence?

"if God does not exist, the atheist wins out in terms of lifetime utility"

Huh.

When we spell out INTJ’s argument like that in bare terms, you can see how the structure makes no sense, and the conclusion doesn’t follow from the postulates. Let’s continue:

Secondly, this argument is circular, as its core assumptions imply the truth of its conclusions. To assume that God is good, will grant believers heaven, created hell, etc. is to assume that Christianity is the sole correct religion, ignoring all other possible religions. Whether the argument is circular or not rests on the validity of this “many-religions objection”.

INTJ is invoking the idea of assumptions made about who or what God is — when we explicitly stated in the argument that we can’t know as such. This is a good objection to Pascal’s Wager: if we can’t know anything about God, then how can we assume or conclude the outcome of Believe and Is God will be infinite happiness?

Pascal opines that those who “rest content with the many-religions objection are people whose skepticism has seduced them into a fatal ‘repose’. If they were really bent on knowing the truth, they would be persuaded to examine ‘in detail’ whether Christianity is like any other religion, but they just cannot be bothered(via Wikipedia).” I submit that here Pascal makes a gaping error. The atheist dismisses all religions equally because they are equally unprovable. Christian doctrine may be more comprehensive, more thought-out, but it is no more provable than any other religion’s.

Pascal’s going off into the deep end here with appealing to the hypothetical motivation for “knowing the truth” so focus on the statement INTJ made that “Christian doctrine … is no more provable than any other religion’s.” Pascal is derailing his own scope of the original argument by appealing to an assumption as fact, that Christianity is the truth.

INTJ points out that you can’t prove as much:

The only material  difference that could make Christianity ‘not like any other religion’ would be its deductive provability, or such a high strength of its inductive claims that it would be virtually certain that Christianity was correct. Pascal himself implicitly admits that this is not so, as seen from his own core assumption in making the Wager that “reason alone cannot defend either proposition (that God exists, or does not exist). If reason alone is not sufficient to confirm that Christianity is not the correct religion, then we have no logical basis on which to make the Wager a Christian one either.

If you notice, what he tried to quote was actually text from the Wikipedia article, and not Pascal. The (questionable) logic here:

IF
A: The argument {Reason and Only Reason} does not satisfy the argument whose conclusion is {Christianity is Not Correct Religion}
THEN
B: The Wager is Not Christian.

This is a bit of language gymnastics: if reason alone is not enough to conclude that Christianity is NOT the correct religion (where being correct means to be the rules by which we are determining that God is a benevolent being who will provide infinite happiness to us in the event Is God and Believe), then the Wager is NOT bound within Christianity (meaning the Wager’s God isn’t the benevolent being who will provide infinite happies).

Why would it follow that if reason’s not enough to determine that Christianity isn’t the correct religion, subsequently the Wager’s not a Christian one? If we can’t use reason to prove a negative, isn’t the burden of proof then on the claimant (Pascal) to provide the evidence required?

This argument was unnecessary, we just got done going over this, and if you’re struggling with the logic here, that’s because there isn’t any.

Onward:

This argument is also circular by virtue of the fact that the knowledge of how much exactly one is staking, depends directly on the conclusion. If the Christian’s assumptions are right, you are staking a finite life for infinite benefit, but if the atheist is right, you are staking an infinite life (because it is all we have to trade), for finite benefit (that can only be accrued during your lifetime). There is a clear logical impasse that cannot be resolved without leaving Pascal’s Wager aside. This spanner in the argumentative works alone should be enough to convince one to discard the Wager as a serious argument.

Oh man.

IF
A: Christian’s assumptions (which are what?) are true
THEN
B: Trading finite life for infinite benefit

IF
C: Atheist’s assumptions (we don’t know what these are either) are true
THEN
D: Trading infinite life for finite benefit

Note that both of these arguments assume Is God. It also ignored the fact that the result of Is God and Don’t Believe results in infinite bad.

Look at how simple that was comparative to INTJ’s language pretzels earlier!

Lastly, according to Pascal, the Wager should only be played if one assumes that ‘the existence or non-existence of God cannot be proved by reason’. However, this is false and very sneaky. It does not and should not logically follow that if we cannot prove or disprove God by reason, we should then engage in the Wager. Everyday, we make choices like those in the Wager.

Didn’t we just make an argument based off reason being insufficient to prove a negative (that Christianity is not the correct religion by which we are determining if our God in the Wager will deliver the infinite happies)?

IF
A: We can’t prove or disprove Is God
THEN
B: We should choose to participate in the Wager

Nowhere in any of the Wager was this ever stated. Rule 3 as summarized above: playing the game isn’t optional. We didn’t reason our way into deciding to participate. (Going outside of this and into abstaining from deciding Believe or Don’t Believe is part of arguments from others elsewhere, and is mentioned in the Wikipedia article.)

You, dear reader, surely go about your daily life acting as if there were no crazy axe murderer lurking in the shadows waiting to kill you. Can you categorically prove this? No, you cannot. But you go about your life as if you have nonetheless. This is because based on your empirical observations, which in turn affect the balance of probability between both outcomes, you have assessed that the chance of the axe crazy murderer waiting to kill you is almost zero, at least close enough to zero that you should act as if it is zero.

There is no material difference between the axe crazy murderer, and God.

IF
A: Chances of X bad thing happening is near zero
THEN
B: It’s ok to act as if X won’t happen

Hmm.

The line of reasoning you take for the murderer should be the exact same one you take to God (assuming you accept that there is as little empirical evidence for him as there is for the murderer, which frankly is hard to disagree with). If you take a different line, it is for only one reason: fear. Fear of the high stakes, and of the unknown. However, this is not logical! The stakes at hand should logically do absolutely nothing to credit or discredit an argument. [emphasis mine]

You said it, not me.

if you are fearful, it is because you have not examined the evidence (or lack thereof) enough. In addition, going back to the murderer example, the stakes aren’t exactly low either: your life is at stake! Yet one almost surely engages in the (logical) line of reasoning that the axe murderer’s existence is empirically indistinguishable from the one who does not exist. Again, observe the lack of material difference between the two examples. I reiterate that the only possible logical rebuttal one could make against this line is to challenge the probabilities based on evidence, and I submit that this is impossible to do. In summary, to draw an inexorable link between the inability to prove or disprove God and engaging in the Wager is purely fallacious.

There are other objections, but these three deal only in the argument’s axioms and logic, thus refraining from delving into theology, as does the “fake belief’ objection, where one has to contemplate if God would let a fake believer into heaven.

Obviously, there are criticisms to Pascal’s Wager that invoke nature, the definitions of what the rules are or require of the agent playing the Wager game, options for abstaining from the Wager (which is against the canon rules as we went over). You can read more

Anyway, I hope you guys enjoyed examining this with me, hopefully it gave you some things to mentally cut your teeth on.

1. intjadvice posted this