Published Works

Internal Applications and Puzzles of the Applicability of Mathematics
2023. Philosophia Mathematica:  1-20. doi: 10.1093/philmat/nkad109  

Abstract:  Just as mathematics helps us to represent and reason about the natural world, in its internal applications one branch of mathematics helps us to represent and reason about the subject matter of another.  Recognition of the close analogy between internal and external applications of mathematics can help resolve two persistent philosophical puzzles concerning its applicability:  a platonist puzzle arising from the abstractness of mathematical objects; and an empiricist puzzle arising from mathematical propositions’ lack of empirical factual content.  In order to see how this is the case, we will examine what it is to apply mathematics internally and describe examples.

Review of The Language of Nature: Reassessing the Mathematization of Natural Philosophy in the Seventeenth Century 
2017. HOPOS: 383-386. doi: 10.1086/693426

First Paragraph: This anthology of 12 contributed papers is the ultimate outcome of a workshop held in the autumn of 2012 and organized jointly by the Minnesota Center for the Philosophy of Science and the Rotman Institute of Philosophy. The goal of the workshop and the anthology is to reassess a received way of telling the history of  seventeenth-century science that relies on two central theses, thesis 1 being that “there was a transformation in the sciences of the seventeenth century brought about by a mathematization of nature,” and thesis 2 being that “the project of mathematizing nature guided the seventeenth century scientific enterprise.” 

Galileo’s Defense of the Application of Geometry to Physics in the Dialogue 
2013. Studies in the History and Philosophy of Science: 178-187. doi: 10.1016/j.shpsa.2013.02.001

Abstract: Alessandro Piccolomini and several other prominent 16th-century Aristotelians claimed that while a sphere touches a plane at a point in geometry, a material sphere touches a plane not at a point but over a small surface. These thinkers thereby called into question the reliability of geometric reasoning in physics. In this article I provide a detailed analysis of Galileo’s reply to such worries about geometry in the Second Day of his Dialogue Concerning the Two Chief World Systems. Because his infamous extrusion argument relies on the premise that a sphere touches a plane at a point, Galileo takes the opportunity to defend the argument and to attack geometry’s critics. According to the account I propose, Galileo argues for the applicability of geometry to physics by defending the legitimacy of geometric approximations and by advocating an expansive notion of geometric curve.

Leibniz: Geometry, Physics, and Idealism 
2011. Leibniz Review: 9-32. doi: 10.5840/leibniz2011212

Abstract: Leibniz holds that nothing in nature strictly corresponds to any geometric curve or surface.Yet on Leibniz’s view, physicists are usually able to ignore any such lack of correspondence and to investigate nature using geometric representations. The primary goal of this essay is to elucidate Leibniz’s explanation of how physicists are able to investigate nature geometrically, focussing on two of his claims: (i) there can be things innature which approximate geometric objects to within any given margin of error; (ii) the truths of geometry state laws by which the phenomena of nature are governed. A corollary of Leibniz’s explanation is that physical bodies do have boundaries with which geometric surfaces can be compared to very high levels of precision. I argue that the existence of these physical boundaries is mind-independent to such an extent as to pose a significant challenge to idealist interpretations of Leibniz.