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Abstract
In this dissertation I take up a reading of Leibnizs metaphysics from the perspective of his mathematical reflections on the nature of infinitesimals. A longstanding tradition of interpreting Leibnizs treatment of infinitesimals has focused on the problem of its logical consistency as the key to unlocking its relation to the rest of his philosophy. Scholarly inquiry around the status of infinitesimals throughout Leibnizs work has thus tended toward logical reduction. By pointing to some key moments where this approach runs into difficulty, I develop an alternative where the speculative consequences of Leibnizs infinitesimals can be viewed through the lens of the mathematical, rather than logical, concepts produced through his mathematical work. The issue of the status of infinitesimals thus provides a means by which to understand important aspects of his metaphysics which is often misunderstood. In turn, this exploration allows a rereading of important developments in Leibnizs treatment of the structure of reality as an actual infinitely divided one. This rereading provides a different means to understand the role that the reality of bodies and their motion plays in his mature metaphysics. As such, I suggest that Leibnizs mathematical reflections serve as a laboratory of concepts which not only have profound consequences for his own means of thinking through problems but can also guide us in understanding aspects of his method and scope of his work. The first chapter sets the stage for the rest of the dissertation by a cursory examination of the short-comings of logical reduction in order to underline the nature of the speculations afforded by Leibnizs lifelong engagement with the infinite and infinitesimal. The second and third chapters treat the problem of the status of infinitesimals in Leibnizs work through a critique of contemporary interpretations and underlining the importance of his mathematical reflections through epistemological and metaphysical lenses. The fourth and fifth chapters treat the development of Leibnizs commitment to the reality of corporeal bodies and motion in the light of his mathematically embedded assertions about the actual infinite dividedness of reality.