Leibniz, Weigel and the birth of binary arithmetic

Abstract

In recent years, Leibniz’s previously unpublished writings have cast a new light on his relationship with Erhard Weigel, from a mere influence during the early years to an exchange of ideas that lasted at least until Weigel’s death in 1699. In this paper I argue that Weigel’s De supputatione multitudinis a nullitate per unitates finitas in infinitum collineantis ad deum is one of the most important influences on Leibniz’s development of binary arithmetic. This work published in 1679, the same year of Leibniz’s De progressione dyadica, contains some fundamental ideas adopted by Leibniz both in mathematics and metaphysics. The controversial theories expressed in these writings will also help in understanding why Leibniz tried to hide Weigel’s influence during his life.