The introduction of probability into mathematics

Abstract

The coincidence of two independent developments led to the mathematization of probability from Pascal to de Moivre. On the one hand there are the changing implications of probabilitas ending in a quantifiable concept, and on the other, the mathematization of chance within the area of games of chance. Probabilitas from Cicero to Thomas Aquinas largely takes its meaning from a pre-scientific dialectical method which dates back to the rhetoric of Aristotle. In this tradition probabilitas used synonymously with verisimilitudo can mean provable argument, credibility and convincing power. The use of the comparative probabilior in this connection has nothing to do with an order-relation. During the probabilism dispute the Jansenists postulated the quantifiability of probabilitas. This was done for the first time in the Port Royal Logic, based on simple methods for solving problems in games of chance. The conditions for the creations of such methods had been developed in Italy between 1450 and 1550. They were 1) a high standard of mathematics compared with the Middle Ages, combined with an optimistic estimation concerning the scope of application of mathematical methods, 2) a considerably increased intensity of gaming, 3) a growing emancipation from the church, and 4) the overcoming of the scholastic conviction that money is sterile. The attempts of the church to prohibit games of chance interrupted the process of mathematization. Favourable circumstances in France in the middle of the 17th century provided for a new beginning which led continuously to the creation of a theory of probability. © 1976.