Blaise Pascal · Mathematics
Pascal turns reason on the probability of <em>belief</em>: the <em>Provincial Letters</em> demolish the lax ‘probabilism’ of the casuists, and the Wager of the <em>Pensées</em> applies the mathematics of expectation - which Pascal helped invent - to the ultimate decision under uncertainty, whether to believe in God.
In 1656 and 1657, Pascal entered a bitter religious controversy on the side of his friends at the convent of Port-Royal, who were under attack for their austere, ‘Jansenist’ Christianity. Writing anonymously under the name Louis de Montalte, he published a series of eighteen open letters, the Provincial Letters, aimed at the moral teaching of the Jesuit casuists. With devastating wit and mock innocence, Pascal exposed what he saw as a system for excusing sin - above all the doctrine of probabilism, which held that one may lawfully follow any morally ‘probable’ opinion, meaning one backed by even a single reputable theologian, even when the weightier opinion forbids the act. Pascal showed how this let a clever casuist find some authority to permit almost anything. The Letters were a sensation, a masterpiece of French prose, and a turning point: they married rigorous argument to satire and made moral laxity look ridiculous.
Pascal was gripped, in two very different registers, by the problem of how to act when you cannot be certain. In the Provincial Letters he attacked a corrupt use of probability: the casuists’ trick of calling an opinion ‘probable’ in order to excuse doing what you want. But in the Pensées, his unfinished defence of the Christian faith, he put probability to a rigorous use, reasoning carefully about the greatest uncertainty of all - whether God exists - and how one ought rationally to act in the face of it. Here he reached for the very mathematics he had helped invent for gamblers: the theory of expectation. If we cannot know the answer, perhaps we can still calculate the smartest bet. This is the argument the world remembers as the Wager, and it is the moment when the mathematics of chance, born over a card game, was turned on eternity.
It is vital to see what the Wager is and is not. It is not an argument that God exists; Pascal explicitly grants that reason can settle nothing about that. It is an argument about how a rational person should act given that they cannot know. Because the possible gain (an eternity of happiness) is infinite, while the possible loss (some earthly indulgences) is finite, the calculation comes out overwhelmingly one way, and prudence itself counsels belief. Pascal anticipates the natural objection - ‘but I cannot simply decide to believe’ - and answers with psychology rather than logic: begin by acting as believers act, follow the practices and habits of faith, and belief will tend to follow, for we are creatures of custom as much as of reason. The Wager is meant not to compel assent but to move a wavering, worldly person to start seeking, to get off the fence they falsely imagine to be neutral ground.
This is the opening of the lesson. The rest — the dialogue, the primary source, and the recall — is in the app.
You learned that the Provincial Letters attacked the casuists’ ‘probabilism’ (that one may follow any opinion made ‘probable’ by a single authority), and that the Wager applies mathematical expectation to belief in God - the first use of expected value in a decision problem. Explain both in your own words.
Leads to Christiaan Huygens.
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