Abstract

This fascinating and expertly edited little volume brings to light some hitherto neglected works, illustrating Leibniz’s lifelong interest in the calculus of combinations, and in the problem of the progress of human culture. In fact both interests are united in these works in a characteristically Leibnizian way. Leibniz’s project in De l’Horizon de la Doctrine Humaine is well expressed in its lengthy subtitle: “Meditation on the number of all possible truths and falsities, enunciable by humanity such as we know it to be; and on the number of feasible books. Wherein it is demonstrated that these numbers are finite, and that it is possible to write, and easy to conceive, a much greater number. To show the limits of the human spirit [l’esprit humain], and to know the extent of these limits”. Following in the tradition of the mathematical curiosities of Clavius, Mersenne, and Guldin, Leibniz offers a formula for the calculation of the number of possible words, significant or nonsignificant, pronounceable or unpronounceable, which can be generated from an alphabet of 23 letters. Even though the product of this calculation is prodigiously great, it is finite, and given a sufficiently lengthy lifespan of the species all truths would very likely be exhausted, and novelty give way to repetition. This observation yields the notion of a “horizon of human doctrine”, an extrinsic limit to the number of truths statable in language, and confirms the “vulgar expression that 'nothing is said which has not been said already’”.