Leibniz’s Mereology in the Essays on Logical Calculus of 1686–1690

Abstract

Mereology, the doctrine of the relations of part to whole and of parts to parts, has so far awoken the interest of only a small number of Leibniz’s scholars. Since the publication of the pioneering paper of Hans Burkhardt and Wolfgang Degen (Topoi 9(1):3–13, 1990), entirely devoted to Leibniz’s mereology, very few works have been published on the same topic. Moreover, these works tend to consider mereology in the general setting of Leibniz’s metaphysics and do not pay due attention to those essays where Leibniz systematically develops a mereological calculus. In the years 1686–1690, indeed, Leibniz wrote a series of essays, concerning the so-called ‘plus-minus calculus’, where a very interesting mereological doctrine is developed. While several scholars have investigated the ancient and medieval attempts to develop a more or less embryonic mereology, modern theories of parthood are less explored. In this paper my aim is to fill at least partially this gap, focusing on Leibniz’s mereological ideas. Leibniz, indeed, just in the Dissertation on Combinatorial Art (1666) elaborated the project of constructing a very general mereological doctrine, which evolved later in a series of papers centered on the logical operation of ‘real addition’. Leibniz considered the real addition as a kind of non restricted sum, capable of being applied to any sort of things and satisfying the conditions of ‘idempotence’, ‘reflexivity’ and ‘transitivity’. With the real addition, the relation of containment (reflexive, transitive and anti-symmetric), and the notion of proper parthood, Leibniz elaborates a quite interesting mereology. My main purpose is to offer an exhaustive analysis of the essays (written around 1690) in which Leibniz proposes his mereological calculi based on ‘real addition’.