Curriculum Vitae: CV 2018.pdf
My primary research interests are ancient Greek mathematics and metaphysics, Aristotle’s Metaphysics (in particular Books B, Θ, M and N), Aristotle’s notions of separation and priority, and the question of how much we can understand about Aristotle’s predecessors and contemporaries from his discussions of their views.
(Full abstracts available on academia.edu)
(1) “The Performance of Philosophizing in the Platonic Lovers.” Forthcoming in American Journal of Philology (second issue of 2018). A close reading and interpretation of the Rival Lovers (with Ron Polansky).
(2) “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).
(3) "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.
(4) “An Absurd Accumulation: Metaphysics M.2 1076b11-36”, Phronesis 59, 2014, 343–68. This paper identifies 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.
(5) “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.
(6) “The Bad is Last but does not Last: Metaphysics IX.9” (co-authored with Ron 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.
My current projects include:
(1) An analysis of the structure of M–N. The last two books of the Metaphysics are often treated as a mere appendix, and the consensus has long been that they are quite scattered. I show that the task Aristotle sets for himself in M–N is an important one, and that these two books form an organized unity (specifically, that they carry out, each in turn, the three inquiries outlined in M.1).
(2) An argument about the nature of Aristotelian mathematical objects. I develop an interpretation of Aristotle's philosophy of mathematics, taking into account both his texts and then-current geometrical practices. I argue that for Aristotle, mathematical objects are in sensible bodies, but not in a partlike way. Rather, they are combinations of properties (πάθη) of sensible things. This interpretation has implications for Aristotle's notion of intelligible matter (ὕλη νοητή).
(3) An examination of Aristotle's own reasoning about Platonic mathematical intermediates. I consider two closely related passages where Aristotle argues that Platonists will need intermediates not only for the pure mathematical sciences, but also for the mixed mathematical sciences, and ultimately for all sciences of sensibles. This is generally seen as mere polemics, and so of little interest. I show that the argument reveals a new reason a Platonic ontology needs intermediates (at least according to Aristotle), and that this is in fact a serious argument for him, as he is himself committed to its key premises. Consequently, a careful examination of the argument sheds light on Aristotle’s own view about mathematical objects, which should avoid the objections he raises against his opponents.
(4) An analysis of On Generation and Corruption II.3. I work out several interpretative puzzles, among which: what are "Plato's divisions", and what should we make of Aristotle's puzzling claim that fire (the element) is not fire, but "fiery" (πυροειδές)?