Curriculum Vitae: CV 2018.pdf

E-mail: ekatz@msu.edu

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 Mixed Mathematical Intermediates." Forthcoming in *Plato Journal *18, 83-96. An analysis of two related Aristotelian arguments against Platonic mathematical substances.

(2) “The Performance of Philosophizing in the Platonic *Lovers*.” *American Journal of Philology* 139, 397-421. A close reading and interpretation of the *Rival Lovers *(with Ron Polansky).

(3) “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).

(4) "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.

(5) “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.

(6) “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.

(7) “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 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)?