Abstract

This study examines Gottfried Wilhelm Leibniz's proposal for a mathematical discipline which he variously referred to as "analysis situs", "calculus situs", and "characteristica geometrica". In addition to discussing analysis situs per se, several concepts from Leibniz's proposal are shown to be related to, and in some cases prior both temporally and conceptually to, similar developments in his metaphysics and in his logical theory. In this way, the concept of "situs" is shown to have been an important philosophical concept in Leibniz's thought. ;After an introductory chapter, Chapter 2 investigates analysis situs qua mathematical science. This includes a study of its primary concepts, theorems, methodology, relationship to Euclid's geometry, and relationship to Descartes' geometry. ;In Chapter 3, several of these same features of analysis situs are shown to have occurred in the development of Leibniz's metaphysics. More specifically, Leibniz's criticism of Descartes' metaphysics, including his analysis of Descartes' concepts of extension and motion, used principles, concepts and theorems from analysis situs. In Leibniz's own characterization of a monad, situs was introduced to explain non-extensive monadic relations. In Leibniz's theory of space, after a comparison with Descartes' and Newton's theories, situs is shown to have been a pivotal concept upon which both the Leibnizian concepts of space and place are dependent. ;In Chapter 4, Leibniz's pre-1679 and circa 1679 logical writings are examined in order to establish two points. Historically, analysis situs and certain aspects of Leibniz's logical theory developed concurrently during this 1679 period. Philosophically, it was Leibniz's analogy of logic to analysis situs, not to Euclid's Elements, which constituted the essentially geometrical aspect of Leibniz's mathematization of logic which has been referred to by B. Russell, L. Couturat, I. Bochenski, G. Martin, and others. ;In the concluding Chapter 5, based upon the previous analysis of Leibniz's mathematical, metaphysical, and logical uses of "situs", a generalization of the concept of "situs" as it must have been understood by Leibniz is given. Also certain similarities between Plato's and Leibniz's theories of the relationship between mathematics and philosophy is discussed based on this entire investigation of analysis situs