•  12
    Colloquium 5 Aristotle’s Rejection of Mathematized Metaphysics
    Proceedings of the Boston Area Colloquium of Ancient Philosophy 37 (1): 167-189. 2023.
    According to Aristotle, those who seek mathematical principles of sensible things are looking in entirely the wrong place. But despite his strong opposition to mathematized metaphysics, Aristotle does not outright reject mathematical explanation of the natural world. In fact, he argues that mathematics does explain certain sensible phenomena, that the natural world has many mathematical patterns and features, and that this is often not mere coincidence. That he devotes two books of his Metaphysi…Read more
  •  18
    Why Aristotle Can’t Do without Intelligible Matter
    Ancient Philosophy Today 5 (2): 123-155. 2023.
    I argue that intelligible matter, for Aristotle, is what makes mathematical objects quantities and divisible in their characteristic way. On this view, the intelligible matter of a magnitude is a sensible object just insofar as it has dimensional continuity, while that of a number is a plurality just insofar as it consists of indivisibles that measure it. This interpretation takes seriously Aristotle's claim that intelligible matter is the matter of mathematicals generally – not just of geometri…Read more
  •  31
    Does Frege Have Aristotle's Number?
    Journal of the American Philosophical Association 9 (1): 135-153. 2023.
    Frege argues that number is so unlike the things we accept as properties of external objects that it cannot be such a property. In particular, (1) number is arbitrary in a way that qualities are not, and (2) number is not predicated of its subjects in the way that qualities are. Most Aristotle scholars suppose either that Frege has refuted Aristotle's number theory or that Aristotle avoids Frege's objections by not making numbers properties of external objects. This has led some to conclude that…Read more
  •  58
    What Numbers Could Not Be
    Journal of the History of Philosophy 59 (2): 193-219. 2021.
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  •  16
    The Mixed Mathematical Intermediates
    Plato Journal 18 83-96. 2018.
    In Metaphysics B.2 and M.2, Aristotle gives a series of arguments against Platonic mathematical objects. On the view he targets, mathematicals are substances somehow intermediate between Platonic forms and sensible substances. I consider two closely related passages in B2 and M.2 in which he argues that Platonists will need intermediates not only for geometry and arithmetic, but also for the so-called mixed mathematical sciences, and ultimately for all sciences of sensibles. While this has been …Read more
  •  81
    There is little agreement about Aristotle’s philosophy of geometry, partly due to the textual evidence and partly part to disagreement over what constitutes a plausible view. I keep separate the questions ‘What is Aristotle’s philosophy of geometry?’ and ‘Is Aristotle right?’, and consider the textual evidence in the context of Greek geometrical practice, and show that, for Aristotle, plane geometry is about properties of certain sensible objects—specifically, dimensional continuity—and certain …Read more
  •  19
    The Performance of Philosophizing in the Platonic Lovers
    American Journal of Philology 139 (3): 397-421. 2018.
  •  23
    Mathematical Substances in Aristotle’s Metaphysics B.5: Aporia 12 Revisited
    Archiv für Geschichte der Philosophie 100 (2): 113-145. 2018.
    : Metaphysics B considers two sets of views that hypostatize mathematicals. Aristotle discusses the first in his B.2 treatment of aporia 5, and the second in his B.5 treatment of aporia 12. The former has attracted considerable attention; the latter has not. I show that aporia 12 is more significant than the literature suggests, and specifically that it is directly addressed in M.2 – an indication of its importance. There is an immediate problem: Aristotle spends most of M.2 refuting the view th…Read more
  •  26
  •  87
    Books M and N of Aristotle's Metaphysics receive relatively little careful attention. Even scholars who give detailed analyses of the arguments in M-N dismiss many of them as hopelessly flawed and biased, and find Aristotle's critique to be riddled with mistakes and question-begging. This assessment of the quality of Aristotle's critique of his predecessors (and of the Platonists in particular), is widespread. The series of arguments in M 2 (1077a14-b11) that targets separate mathematical object…Read more
  •  21
  •  152
    Ontological Separation in Aristotle’s Metaphysics
    Phronesis 62 (1): 26-68. 2017.
    Ontological separation plays a key role in Aristotle’s metaphysical project: substances alone are ontologically χωριστόν. The standard view identifies Aristotelian ontological separation with ontological independence, so that ontological separation is a non-symmetric relation. I argue that there is strong textual evidence that Aristotle employs an asymmetric notion of separation in the Metaphysics—one that involves the dependence of other entities on the independent entity. I argue that this not…Read more
  •  109
    An Absurd Accumulation: Metaphysics M.2, 1076b11-36
    Phronesis 59 (4): 343-368. 2014.
    The opening argument in the Metaphysics M.2 series targeting separate mathematical objects has been dismissed as flawed and half-hearted. Yet it makes a strong case for a point that is central to Aristotle’s broader critique of Platonist views: if we posit distinct substances to explain the properties of sensible objects, we become committed to an embarrassingly prodigious ontology. There is also something to be learned from the argument about Aristotle’s own criteria for a theory of mathematica…Read more