My primary research interests are ancient Greek mathematics and metaphysics (especially Aristotle’s metaphysics, natural science, and philosophy of mathematics), as well as the question of how much we can understand about Aristotle’s predecessors and contemporaries from his discussions of their views. I am available to work with incoming graduate students as a committee member and/or teaching mentor.
“Does Frege Have Aristotle’s Number?”
Accepted for publication in the Journal of the American Philosophical Association. (I develop an interpretation of Aristotle’s number theory and show that it withstands Frege’s most powerful criticisms of empiricist number theories.)
“Aristotle’s Philosophy of Geometry: A Philosophical Defense"
Accepted for publication in Oxford Studies in Ancient Philosophy (expected to appear in vol. 61). (I defend the view that geometrical objects are “accidents”, for Aristotle. More specifically, geometrical objects are certain subjects just insofar as they have certain properties, i.e. they are so-called “kooky objects”. I also show that geometrical objects are not parts of sensible objects.)
“On Generation and Corruption II.3: The Number and Nature of the Primary Bodies,” in Panos Dimas, Andrea Falcon, and Sean Kelsey (eds.), Aristotle, On Generation and Corruption Book II. Introduction, Translation, and Interpretative Essays. Forthcoming (Ca
An interpretation of GC 2.3.
“What Numbers Could Not Be (for Aristotle).” Forthcoming in the Journal of the History of Philosophy 59 (2021), 193–219.
I argue that number for Aristotle is not a hylomorphic unity but rather a “measured heap.”
“Geometrical Objects as Properties of Sensibles: Aristotle’s Philosophy of Geometry.” Phronesis 64 (2019), 465–513.
A reconstruction of Aristotle’s philosophy of geometry.
“The Mixed Mathematical Intermediates.” Plato Journal 18 (2019), 83–96.
An analysis of two related Aristotelian arguments against Platonic mathematical substances.
“The Performance of Philosophizing in the Platonic Lovers” (with Ronald Polansky), American Journal of Philology 139 (2018), 397–421.
A close reading and interpretation of the Rival Lovers.
“Mathematical Substances in Aristotle’s Metaphysics B.5: Aporia 12 Revisited,” Archiv für Geschichte der Philosophie 100 (2018), 113–45.
This paper considers a metaphysical puzzle about whether geometrical objects and numbers are more substantial than sensible objects (because the former in some sense limit the latter).
“Ontological Separation in Aristotle’s Metaphysics,” Phronesis 62 (2017), 26–68.
While it is typically thought that Aristotle’s notion of ontological separation is merely non-symmetric, I find an additional, asymmetric notion in the Metaphysics. I argue that this notion allows Aristotle to prevent the proliferation of substance-kinds and thus to secure the unity of his metaphysical system.
“An Absurd Accumulation: Metaphysics M.2 1076b11-36,” Phronesis 59 (2014), 343–68.
I identify the motivations for and nature of Aristotle’s rejection of mathematical substances, as well as Aristotle’s own criteria for an adequate theory of mathematical objects.
“Aristotle’s Critique of Platonist Mathematical Objects: Two Test Cases from Metaphysics M.2,” Apeiron 46 (2013), 26–47.
This paper defends Aristotle’s (much maligned) criticisms of his predecessors’ views of mathematical objects.
“The Bad is Last but does not Last: Metaphysics Θ.9” (with Ronald Polansky), Oxford Studies in Ancient Philosophy 31 (2006), 233–42.
This paper shows that Aristotle’s Θ.9 argument that bad actualities are posterior to potentiality is valid, even though it apparently conflates priority in worth and priority in nature.