Leibniz's laboratory of concepts
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In this dissertation I take up a reading of Leibniz’s metaphysics from the perspective of his mathematical reflections on the nature of infinitesimals. A longstanding tradition of interpreting Leibniz’s 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 Leibniz’s 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 Leibniz’s 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 Leibniz’s 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 Leibniz’s 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 Leibniz’s lifelong engagement with the infinite and infinitesimal. The second and third chapters treat the problem of the status of infinitesimals in Leibniz’s 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 Leibniz’s commitment to the reality of corporeal bodies and motion in the light of his mathematically embedded assertions about the actual infinite dividedness of reality.