Es werden zwei Bedeutungen von „Infinitesimal“ unterschieden und zwei Thesen verteidigt: (1) Leibniz glaubte, das Infinitesimale in einer der beiden Bedeutungen sei nicht nur eine nützliche Erdichtung, sondern es sei sogar notwendig fur die Differentialrechnung; (2) die moderne Nichtstand-Analysis rechtfertigt weder Leibniz's Griinde fur die Einführung des Infinitesimalen noch seinen Gebrauch desselben.

In this paper I challenge the usual interpretations of Newton's and Leibniz's views on the nature of space and the relativity of motion. Newton's ‘relative space’ is not a reference frame; and Leibniz did not regard space as defined with respect to actual enduring bodies. Newton did not subscribe to the relativity of intertial motions; whereas Leibniz believed no body to be at rest, and Newton's absolute motion to be a useful fiction. A more accurate rendering of the opposition between (...) them, I argue, leads to a wholly different understanding of Leibniz's theory of space, one which is not susceptible to the objections Newton had raised against Descartes regarding the representation of motion. This in turn suggests a new approach for contemporary theory of space, one which neither hypostatizes space nor tries to reduce it to relations among actual things. * This work was generously supported by the National Endowment for the Humanities, with a Fellowship for College Teachers and Independent Scholars (FB-26897-89), and also by a sabbatical leave from my institution, Middlebury College. Iam very grateful to various members of faculty of York University for their appreciative reception of an earlier one-week-old version of this paper. ‘Relative Space in Newton and Leibniz’, read to the Department of Philosophy there in January 1990, and to Robert Rynasiewicz for criticisms of an extract read at the 1991 History of Science meeting. (shrink)

Because of their vastness and rather fragmentary character, the writings of Leibniz leave the student unusually dependent on secondary literature for guidance. That the literature on Leibniz is exceptionally good is all the more reason to welcome the kind of orientation to the riches of both primary and secondary sources that this Companion aims to provide. Announcing itself as “the most accessible and comprehensive guide to Leibniz currently available” for nonspecialists and “a conspectus of recent developments in the interpretation of (...) Leibniz” for specialists, it lives up to both aspirations remarkably well. (shrink)

In my introduction to Kontinuität und Mechanismus, I expressed surprise at the lack of work which was being done at the time on the young Leibniz in spite of the fact that conditions for investigating the period up to 1676 are almost ideal—certainly in Leibnizian terms. Most of the letters and papers from this period of immediate philosophical significance have now been published in the Akademie-Ausgabe so that there is here an incomparably better starting point for detailed studies than in (...) the case of his later work. (shrink)