The Leibniz Review

Volume 14, December 2004

Wolfgang David Cirilo de Melo, James Cussens
Pages 31-41

Leibniz on Estimating the Uncertain
An English Translation of De incerti aestimatione with Commentary

Leibniz’s De incerti aestimatione, which contains his solution to the division problem, has not received much attention, let alone much appreciation. This is surprising because it is in this work that the definition of probability in terms of equally possible cases appears for the first time. The division problem is used to establish and test probability theory; it can be stated as follows: if two players agree to play a game in which one has to win a certain number of rounds in order to win the pool, but if they break the game off before either of them has won the required number of rounds, how should the pool be distributed? Our article has two aims: it provides the readers with the first published English translation of De incerti aestimatione, and it also gives them a brief commentary that explains Leibniz’s philosophical and mathematical concepts necessary in order to understand this work. The translation is as literal as possible throughout; it shows how Leibniz struggled at times to find a solution to the division problem and how he approached it from different angles. The commentary discusses Leibniz’s views on four key concepts: fairness, hope, authority and possibility. The commentary then outlines how Leibniz attempted to solve the problem of division.