Blaise Pascal and Pascal's Wager
By Joseph Mark Haykov
May 18, 2024
Introduction
Blaise Pascal (1623-1662) was a French mathematician, philosopher, scientist, and inventor known for his significant contributions to probability theory, Pascal's Triangle, and various practical achievements. Pascal is credited with inventing an early digital calculator, a syringe, a hydraulic press, and the roulette wheel. However, this discussion will focus on his famous philosophical argument known as Pascal's Wager.
Pascal's Wager
Pascal's Wager addresses the rationality of belief in God, framing the decision to believe or not believe in God as a bet. The wager can be summarized as follows:
If God exists and you believe in God, you gain infinite happiness (heaven).
If God exists and you do not believe in God, you suffer infinite loss (hell).
If God does not exist and you believe in God, you lose very little (a finite amount of time, resources, etc.).
If God does not exist and you do not believe in God, you gain very little (a finite amount of time, resources, etc.).
Given these outcomes, it is rational to believe in God because the potential gain (infinite happiness) outweighs the potential loss (finite resources). Even if the probability of God's existence is low, the infinite value of the reward justifies belief (Pascal, 1670).
Dually Defined Null Hypothesis
An interesting aspect of this wager is the construction of null and alternative hypotheses. Pascal posits an axiom (an educated guess), known as H0 in hypothesis testing, that God, as well as hell and heaven, are real. In the context of the wager, the number of gods is a natural number: 0, 1, 2, 3, and so on. Because of this, there is an inherent duality in the hypothesis H0 because there are two ways in which it could turn out to be true. Therefore, we must consider two null hypotheses, H0a and H0b:
H0a: There are no gods at all, except for Yahweh, the God specifically referenced in the wager, as Pascal was a devout believer in Christ, meaning the God he was referring to specifically was Yahweh, also referred to as “the Father” (or The Godfather, to be more accurate—akin to a good version of Marlon Brando).
H0b: There are multiple gods, but Yahweh is the only one we should worship, before all others. This is akin to advice to diversify to spread risk, but in reverse.
Mathematically, let N denote the number of gods. The prior estimate of N, given our lack of knowledge, could be infinitely many—not just 0 or 1. This is an important consideration when discussing probability, aligning with Nassim Taleb's observation that just because we have never seen a black swan, it does not mean one does not exist.
Having two different alternative hypotheses is a potential problem because, in mathematics, just like on Wall Street, we don't throw darts at the board—we only bet on sure things. Absolute certainty in the objective reality we all live in and share is strictly limited to things that can be independently verified, which means we can only ever be absolutely certain about empirical facts and deductive reasoning. Logical deduction guarantees with absolute certainty that as long as our axioms are true, the theorems will also be true, because the accuracy of deductive logic in mathematics—showing that if A (axioms) is true, then B (theorems) must logically follow—can be independently verified (e.g., proving the Pythagorean Theorem in middle school).
However, axioms are nothing but educated guesses, accepted as true without proof and based on being 'self-evidently' true to those who first propose them—in this case, ourselves. This prompts us to consider which of the alternative hypotheses, H0a or H0b, should be utilized. We can avoid guessing by consulting the original sources that Pascal in fact referenced. According to the Torah, Yahweh, the deity Pascal discusses, commands: 'You shall have no other gods before me' (Exodus 20:3, NIV). This directive indicates that we should support H0b, which posits Yahweh as the primary deity, deserving of exclusive worship ahead of any other gods. This acknowledgment of Yahweh as the foremost deity aligns with the concept of multiple gods found in the Bhagavad Gita within Indian culture, where a hierarchy of divine beings can coexist.
Addressing Common Objections
The Sincerity Objection
Believing in God simply to avoid hell may seem insincere, potentially resulting in that very outcome. However, even attempting to believe in God lowers the relative risk of going to hell. Thus, this objection does not hold in a rational argument about God.
The Infinite Utility Problem
This objection highlights issues with using infinite rewards (heaven) and punishments (hell) in rational decision-making, arguing that infinite values make all finite outcomes seem irrelevant.
Response: Pascal's argument relies on the belief in the infinite nature of the rewards and punishments. Questioning the infinite nature of these outcomes undermines the fundamental premise of the wager itself. Therefore, this objection misunderstands the framework of Pascal's argument, which requires accepting the infinite stakes as a starting point (Pascal, 1670).
The Moral Objection
Believing in God purely out of self-interest is morally questionable, suggesting that such belief reduces faith to a selfish gamble.
Response: Even if initial belief is insincere, it is still better than non-belief in terms of potential consequences. Pascal's Wager posits that pragmatic belief can lead to genuine faith and moral growth over time (Pascal, 1670).
The Probability Objection
This objection questions the assumption that even a small probability of God's existence justifies belief due to the infinite reward, arguing that assigning probabilities to metaphysical claims is problematic.
Response: With zero knowledge about the true probability of God's existence, the initial estimate should be 50%, aligning with the principle of indifference. Thus, the probability of God's existence is not inherently low, and the potential infinite reward still justifies belief (Pascal, 1670).
The Cost Objection
This objection highlights that Pascal's Wager underestimates the potential costs of belief, such as sacrifices in time, resources, and personal freedoms.
Response: One does not need to spend excessive resources to hold a belief in God. Simple and moderate religious practices can be integrated into one's life without significant sacrifices, minimizing potential costs while still gaining the potential infinite reward (Pascal, 1670).
The Agnosticism Objection
This objection points out that Pascal's Wager presents belief as a binary choice without addressing the rational stance of agnosticism.
Response: The wager is based on the premise that the objective reality is binary: God either exists or does not. Agnosticism does not change this binary fact. Pascal's Wager encourages a proactive decision in the face of this reality, arguing that the potential infinite reward of belief outweighs the finite costs (Pascal, 1670).
The Many Gods Objection
This objection argues that given the multitude of belief systems, believing in the "wrong" God might still result in damnation.
Response: While there are many belief systems with many gods, Pascal advocated for belief in Yahweh, the God referred to in the Ten Commandments: "You shall have no other gods before me" (Exodus 20:3, NIV). Yahweh, also known as "The Father" in the New Testament and "Allah" in the Koran, is the one God we should believe in according to Pascal's Wager. Here, we cannot help but quote Mark Twain, who said, “It’s not what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so.” Check your sources more carefully before jumping to conclusions!
Conclusion
Further research should begin with the axiomatic assumption that many gods exist, starting with early source material such as the Emerald Tablets and the Hermetic principle "as above, so below." Researchers should aim to identify which of the earlier gods Yahweh corresponds to and understand what specific attributes allowed Yahweh to evolve into the dominant deity.
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In passing, it is worth noting that, regardless of individual opinions about the Jewish people, they have an empirical track record of winning Nobel prizes and generally hold a direct belief in Yahweh. This is an intriguing point to consider.
Oh, and by the way, what motivated me to write this little essay is the forex exchange rate matrix E, which is the transpose of the Hadamard inverse of itself. This not only demystifies Einstein’s equation but does so according to the “as above, so below” principle. This finding in mathematical economics is available on 🧨 tnt.money too!
References
Pascal, Blaise. Pensées. 1670.
Twain, Mark. “It’s not what you don’t know that gets you. It’s what you know for sure, that just ain’t so.”
The Holy Bible, New International Version, Exodus 20:3.
Hájek, Alan. “Waging War on Pascal's Wager.” Philosophical Review, vol. 112, no. 1, 2003, pp. 27-56.
Jordan, Jeff. “Pascal's Wager: Pragmatic Arguments and Belief in God.” Philosophy and Phenomenological Research, vol. 52, no. 2, 1992, pp. 439-453.
Mackie, J.L. The Miracle of Theism: Arguments For and Against the Existence of God. Oxford University Press, 1982.