Business Ethics, Commercial Mathematics, and the Origins of Mathematical Probability

The origins of mathematical probability are usually traced to the 1654 correspondence of Blaise Pascal and Pierre de Fermat about games of luck, and then to Christiaan Huygens's 1657 On Reckoning in Games of Luck, which was motivated by the work of Pascal and Fermat. This essay argues rather that the conceptual context within which Huygens developed probability mathematics was, ultimately, that of ethical business practice as it was embodied in commercial mathematics.

In choosing to use Huygens's work on games of luck, along with his own comments, as part 1 of his The Art of Conjecturing (published posthumously in 1713, but largely completed in the 1680s), Jacob Bernoulli also operated within the framework of ethics and commercial mathematics. When in part 4 of his book Bernoulli extended the art of conjecturing from games to civil, moral, and economic decision making, he applied the mathematics of games of luck to epistemic probability, bringing games of luck into conjunction with the preexisting concept of probable opinion, something Pascal, Fermat, and Huygens had not done.¹ In this way the conceptual context of probability came full circle, from ethical business practice to prudent decision making, all within the compass of concepts of the moral oeconomy (cf. Daston 1983 on the relationship of classical mathematical probability and the moral sciences).

In his 1711 "De mensura sortis, seu, de Probabilitate Eventuum in Ludis a Casu Fortuito Pendentibus" [On the measure of chance, or, on the probability of outcomes in games depending on contingency] and his 1718 The Doctrine of Chances; or A Method of Calculating the Probability of Events in Play, Abraham De Moivre, like Bernoulli, brought the word probability into conjunction with games of luck, but, at the same time, he shifted the foundations of mathematical probability from ethical business partnerships to relative frequencies. Thus almost at the moment when mathematical probability was first developed, it received a new foundation.² This has encouraged historians of probability to read De Moivre's frequentist conceptual framework into their interpretations of Huygens and Bernoulli and to overlook its origins in concepts of the moral oeconomy.

This article results from my wish to understand in its historical particularity the conceptual framework within which Jacob Bernoulli proposed to develop an art of conjecture, a wish that arose in the process of my trying to choose the best English words for translating the key technical terms of Bernoulli's Ars Conjectandi from Latin into English.³ Clearly, there is no reasonable alternative to translating the Latin probabilitas by the English probability, even though probabilitas in Bernoulli's Latin did not have the strong connotations of relative frequency that probability now inevitably has. But problems of translation also arose for the words alea, sors, and casus. Should all three of these words be translated chance, and, if so, why were three words used for a single meaning? Moreover, why, as became obvious to me in the course of my translation, did Huygens and Bernoulli often use sors and expectatio interchangeably?⁴ It was in trying to resolve my translation problems that I was led to see the connection of Huygens's and Bernoulli's work to business ethics and the related commercial arithmetic.

The background of early mathematical probability theory in the mathematics of ethical business practice has been obscured by histories of economics that overemphasize the Catholic Church's condemnation of usury while failing to recognize that the same theologians and lawyers who frowned on usury could smile on profit-making business relationships based on just contracts pursued in an ethical way (cf. Noonan 1957 and Munro 2001–3). There are a number of excellent recent books and articles that attempt to construct a different and more diverse narrative of medieval economic ethics.⁵ What I want to do here is to link this recent scholarship to the work...