Pascal's wager

thumb|Blaise Pascal (1623–1662)

Pascal's wager is a philosophical argument advanced by Blaise Pascal (1623–1662), a French mathematician, philosopher, physicist, and theologian. This argument posits that individuals essentially engage in a life-defining gamble regarding the belief in the existence of God.

Pascal contends that a rational person should adopt a lifestyle consistent with the existence of God and should strive to believe in God. The reasoning for this stance involves the potential outcomes: if God does not exist, the believer incurs only finite losses, potentially sacrificing certain pleasures and luxuries; if God does exist, the believer stands to gain immeasurably, as represented for example by an eternity in Heaven in Abrahamic tradition, while simultaneously avoiding boundless losses associated with an eternity in Hell.

The first written expression of this wager is in Pascal's Pensées ("Thoughts"), a posthumous compilation of previously unpublished notes. Pascal's wager is the first formal application of decision theory, existentialism, pragmatism, and voluntarism.

Critics of the wager question the ability to provide definitive proof of God's existence. The argument from inconsistent revelations highlights the presence of various belief systems, each claiming exclusive access to divine truths. Additionally, the argument from inauthentic belief raises concerns about the genuineness of faith in God if it is motivated solely by potential benefits and losses.

The wager

The wager uses the following logic (excerpts from Pensées, part III, §233):

"God is, or God is not. Reason cannot decide between the two alternatives"
"A Game is being played ... where heads or tails will turn up"
"You must wager; it is not optional"
"Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing"
"Wager, then, without hesitation that He is. ... There is here an infinity of an infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite. And so our proposition is of infinite force when there is the finite to stake in a game where there are equal risks of gain and of loss, and the infinite to gain."
"But some cannot believe. They should then 'at least learn your inability to believe...' and 'Endeavour then to convince' themselves."

Pascal asks the reader to analyze humankind's position, where our actions can be enormously consequential, but our understanding of those consequences is flawed. While we can discern a great deal through reason, we are ultimately forced to gamble. Pascal cites a number of distinct areas of uncertainty in human life:

{| class="wikitable"

!width="180"|Category

!Quotation(s)

| Uncertainty in all

| "This is what I see, and what troubles me. I look on all sides, and everywhere I see nothing but obscurity. Nature offers me nothing that is not a matter of doubt and disquiet."

| Uncertainty in man's purpose

| "For after all what is man in nature? A nothing in relation to infinity, all in relation to nothing, a central point between nothing and all and infinitely far from understanding either."

"We understand nothing of the works of God unless we take it as a principle that He wishes to blind some and to enlighten others."

Pascal begins by painting a situation where both the existence and non-existence of God are impossible to prove by human reason. So, supposing that reason cannot determine the truth between the two options, one must "wager" by weighing the possible consequences. Pascal's assumption is that, when it comes to making the decision, no one can refuse to participate; withholding assent is impossible because we are already "embarked", effectively living out the choice.

We only have two things to stake, our "reason" and our "happiness". Pascal considers that if there is "equal risk of loss and gain" (i.e. a coin toss), then human reason is powerless to address the question of whether God exists. That being the case, then human reason can only decide the question according to possible resulting happiness of the decision, weighing the gain and loss in believing that God exists and likewise in believing that God does not exist.

He points out that if a wager were between the equal chance of gaining two lifetimes of happiness and gaining nothing, then a person would be a fool to bet on the latter. The same would go if it were three lifetimes of happiness versus nothing. He then argues that it is simply unconscionable by comparison to bet against an eternal life of happiness for the possibility of gaining nothing. The wise decision is to wager that God exists, since "If you gain, you gain all; if you lose, you lose nothing", meaning one can gain eternal life if God exists, but if not, one will be no worse off in death than if one had not believed. On the other hand, if you bet against God, win or lose, you either gain nothing or lose everything. You are either unavoidably annihilated (in which case, nothing matters one way or the other) or miss the opportunity of eternal happiness. In note 194, speaking about those who live apathetically betting against God, he sums up by remarking, "It is to the glory of religion to have for enemies men so unreasonable".

Inability to believe

Pascal addressed the difficulty that reason and rationality pose to genuine belief by proposing that "acting as if [one] believed" could "cure [one] of unbelief":

Analysis with decision theory

The possibilities defined by Pascal's wager can be thought of as a decision under uncertainty with the values of the following decision matrix.

{| class="wikitable" style="margin:1em auto; text-align:center;width100%;"

! God exists (G)

! God does not exist (¬G)

! Belief (B)

| +∞ (infinite gain)

| −c (finite loss)

! Disbelief (¬B)

| −∞ (infinite loss)

| +c (finite gain)

Given these values, the option of living as if God exists (B) always has a greater expected value than the option of living as if God does not exist (¬B), as long as one assumes a positive probability that God exists.

In fact, according to decision theory, the only value that matters in the above matrix is the +∞ (infinitely positive). Any matrix of the following type (where f1, f2, and f3 are all negative or finite positive numbers) results in (B) as being the only rational decision.

To be put at the beginning of Pascal's planned book, the wager was meant to show that logical reasoning cannot support faith or lack thereof:

Frederick Copleston writes that Pascal did not intend the wager as proof of God's existence or even a substitute for such proofs. He argues that the wager must be understood in the context of Pascal addressing the wager to those who "though they are also unconvinced by the arguments of sceptics and atheists" also "remain in a state of suspended judgment". Pascal's aim was to prepare "their minds and the production of dispositions favourable to belief".

Criticism

Failure to prove the existence of God

Voltaire (another prominent French writer of the age of Enlightenment), a generation after Pascal, regarded the idea of the wager as a "proof of God" as "indecent and childish", adding, "the interest I have to believe a thing is no proof that such a thing exists". Pascal, however, did not advance the wager as a proof of God's existence but rather as a necessary pragmatic decision which is "impossible to avoid" for any living person. He argued that abstaining from making a wager is not an option and that "reason is incapable of divining the truth"; thus, a decision of whether to believe in the existence of God must be made by "considering the consequences of each possibility".

Voltaire's critique concerns not the nature of the Pascalian wager as proof of God's existence, but the contention that the very belief Pascal tried to promote is not convincing. Voltaire hints at the fact that Pascal, as a Jansenist, believed that only a small, and already predestined, portion of humanity would eventually be saved by God.

Voltaire explained that no matter how far someone is tempted with rewards to believe in Christian salvation, the result will be at best a faint belief. Pascal, in his Pensées, agrees with this, not stating that people can choose to believe (and therefore make a safe wager), but rather that some cannot believe.

As Étienne Souriau explained, in order to accept Pascal's argument, the bettor needs to be certain that God seriously intends to honour the bet; he says that the wager assumes that God also accepts the bet, which is not proved; Pascal's bettor is here like the fool who seeing a leaf floating on a river's waters and quivering at some point, for a few seconds, between the two sides of a stone, says: "I bet a million with Rothschild that it takes finally the left path." And, effectively, the leaf passed on the left side of the stone, but unfortunately for the fool Rothschild never said "I [will take that] bet".

Argument from inconsistent revelations

Since there have been many religions throughout history, and therefore many conceptions of God (or gods), some assert that all of them need to be factored into the wager, in an argumentation known as the argument from inconsistent revelations. This, its proponents argue, would lead to a high probability of believing in "the wrong god" and would eliminate the mathematical advantage Pascal claimed with his wager. Denis Diderot, a contemporary of Voltaire, expressed this opinion when asked about the wager, saying "an Imam could reason the same way". J. L. Mackie writes that "the church within which alone salvation is to be found is not necessarily the Church of Rome, but perhaps that of the Anabaptists or the Mormons or the Muslim Sunnis or the worshipers of Kali or of Odin."

Pascal considers this type of objection briefly in the notes compiled into the Pensées, and dismisses it: