Actual and Ideal Infinitesimals in Leibniz’s Specimen Dynamicum

This article aims to treat the question of the reality of Leibniz’s infinitesimals from the perspective of their application in his account of corporeal motion. Rather than beginning with logical foundations or mathematical methodology, I analyze Leibniz’s use of an allegedly “instantiated” infinitesimal magnitude in his treatment of dead force in the Specimen Dynamicum. In this analysis I critique the interpretive strategy that uses the Leibnizian distinction, drawn from the often cited 1706 letter to De Volder, between actual and ideal for understanding the meaning of Leibniz’s infinitesimal fictionalism. In particular, I demonstrate the ambiguity that results from sticking too closely with the idea that ideal mathematical terms merely “represent” concrete or actual things. In turn I suggest that, rather than something that had to be prudentially separated from the realm of actual things, the mathematics of infi nitesimals was part of how Leibniz conceived of the distinction between the actual and ideal within the Specimen Dynamicum.