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Antoine Arnauld

b.  6 February 1612 Paris, France
d.  6 August 1694 Brussels, Belgium

Pierre Nicole

b. 16 October 1625 Chartes, France
d.  16 November 1695 Paris

Antoine Arnauld, surnamed the Great, studied at the Sorbonne, first at the college Calvi and then at Liseux. He earned a bachelor's degree in theology in 1635, was ordained a priest and earned a doctorate in theology in 1641. Two years later he entered the Sorbonne as a member of the faculty. His early education was influenced by the Abbé of Saint-Cyran and at this time he became a leader of French Jansenism. Arnauld was infamous for his support of Jansenism and his opposition to the Jesuits. For his Jansenist views he was expelled from the Sorbonne in 1656. Pascal came to his aid with his Provincial Letters written under the pseudonym of Montalte. He fled to the Netherlands in 1679.

His collected works fill 45 volumes. He corresponded with the intellectuals of the time, including Leibnitz and Descartes.

Pierre Nicole, although taking but a bachelor of theology, was a distinguished theologian and a staunch defender of the Jansenists in its battle with the Roman Catholic Church.

Arnauld is closely identified with the Port-Royal school which produced three important works: the Port-Royal Grammar (Grammaire générale et raisonnée, 1660), the Port-Royal Logic (La logique ou l'art de penser, 1662) and the Elements (Nouveaux élèmens de géomètrie, 1667).

The Logic especially bears notice. This work was written jointly with Pierre Nicole and published anonymously in 1662. The definitive version of the Logic appeared in 1683. The authors were deeply influenced by Descartes' Regulae and Pascal's Méthode.  The fourth part of this work, On the Method, which is attributed to Arnauld, presents clear indications of Pascal's influence.

The final chapters of Part IV, namely chapters 13 through 16, are concerned with probability. These may have been written by Pascal himself. Chapter 13 presents a rule for accepting human authority. Chapters 14, 15 and 16 consider, in order, application of the rule to miracles, to historical events and to future events. Here too may be observed a form of Pascal's wager.

In the first of these chapters a clear distinction is made between intrinsic and extrinsic evidence. The authors wrote,

To judge the truth of an Event, and to persuade myself into a Resolution to believe, or not to believe a thing; it must not be considered nakedly, and in itself, like a Proposition in Geometry; but all the Circumstances that accompany it, as well internal as external, are to be weighed with the same consideration; I call Internal Circumstances such as belong to the Fact itself; and external, those that relate to the Persons, whose Testimonies induce us believe it.

Chapter 16 of the Port Royal Logic considers reasoning with respect to future events. The reader is cautioned to consider not only an anticipated reward but also how likely it is to realize that reward.

Sometimes there is a little likelihood in the success of a thing, that how advantageous soever it be, and how small soever the hazard of winning, it is better not to hazard. Thus it would be a foolish thing to play twenty Sols against ten Millions of Livres, or against a Kingdom, upon condition he should not win, unless such an Infant taking out the Letters out of a Printers Case by accident, did also of a sudden Compose the first twenty Verses of Virgil's Aeneid. For indeed there are few Moments scape us, wherein we do not run the Risk of losing more, than a King that should stake his Kingdom to such a Condition.

Near the end of this same chapter, the author, after having considered finite rewards, now wrote

There are nothing but Infinite things that can be equaled by any temporal advantage, and therefore they are never to be put in the Balance with any of the things of this World. And therefore the least degree of Facility for a Man to save himself is worth all the felicities of this World joined together. And the least danger of losing it is more considerable than all temporal mischiefs, if only looked upon as Misfortunes.

The Logic, Part IV, Chapters 13-16.