Dissertation

Investigations into the Applicability of Geometry
2011. Harvard University 
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Abstract: Philosophical reflection about the sciences from Aristotle onwards has given rise to worries that mathematics, while true of its own special objects, is inapplicable to the physical world. Drawing on the histories of philosophy and science, I articulate a series of challenges to the applicability of geometry based on the general idea that geometry fails to fit nature. I then examine how two early modern thinkers, Galileo and Leibniz, develop notions of approximation as a way of overcoming these challenges. I conclude with an argument that the applicability of geometry—which by present-day standards is an established fact in need of explanation—imposes substantial constraints on the relationship between geometry and nature.