“On the Unviability of Interpreting Leibniz's Infinitesimals through Non-standard analysis”

Abstract

Non-standard analysis has often been presented as the proper framework for expressing rigorously Leibniz's conception of infinitesimals. This paper intends to study this interpretation from an historical point of view and to dispel a series of misunderstandings on which it rests. In order to do so, we propose to go back to Leibniz's conception of quantity, number and magnitude, an approach which has not been developed yet in the literature.