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17The Concept of Motion in Ancient Greek Thought: Foundations in Logic, Method, and MathematicsPhilosophical Review 131 (4): 503-506. 2022.
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285Aristotle's Actual InfinitiesOxford Studies in Ancient Philosophy 59. 2021.Aristotle is said to have held that any kind of actual infinity is impossible. I argue that he was a finitist (or "potentialist") about _magnitude_, but not about _plurality_. He did not deny that there are, or can be, infinitely many things in actuality. If this is right, then it has implications for Aristotle's views about the metaphysics of parts and points.
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159Zeno BeachPhronesis 65 (4): 467-500. 2020.On Zeno Beach there are infinitely many grains of sand, each half the size of the last. Supposing Aristotle denied the possibility of Zeno Beach, did he have a good argument for the denial? Three arguments, each of ancient origin, are examined: the beach would be infinitely large; the beach would be impossible to walk across; the beach would contain a part equal to the whole, whereas parts must be lesser. It is attempted to show that none of these arguments was Aristotle’s. Indeed, perhaps Arist…Read more
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70Review of Marko Malink, Aristotle's Modal Syllogistic (review)Notre Dame Philosophical Reviews. 2014.Malink’s interpretation is designed to validate Aristotle’s claims of validity and invalidity of syllogistic-style arguments, as well as his conversion claims. The remaining sorts of claims in Aristotle's text are allowed to fall out as they may. Thus, not all of Aristotle’s examples turn out correct: on some occasions, Aristotle claims that a given pair of terms yields a true (false) sentence of a given type although, under Malink’s interpretation, the sentence in question is false (true). Simi…Read more
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100Physics V–VI vs. VIII: : Unity of Change and Disunity in the PhysicsIn Mariska Leunissen (ed.), Aristotle's Physics: a critical guide, Cambridge University Press. 2015.Aristotle offers several arguments in Physics viii.8 for his thesis that, when something moves back and forth, it does not undergo a single motion. These arguments occur against the background of a sophisticated theory, expounded in Physics v—vi, of the basic structure of motions and of other continuous entities such as times and magnitudes. The arguments in Physics viii.8 stand in a complex relation to that theory. On the one hand, Aristotle evidently relies on the theory in a number of crucial…Read more
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2Review of Sarah Broadie, Aristotle and Beyond: Essays on Metaphysics and Ethics (review)Notre Dame Philosophical Reviews 2008 (6). 2008.
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3A method of modal proof in AristotleIn Brad Inwood (ed.), Oxford Studies in Ancient Philosophy, Oxford University Press. 2012.
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26Motion and Change in Aristotle’s Physics 5. 1Phronesis 57 (1): 63-99. 2012.Abstract This paper illustrates how Aristotle's topological theses about change in Physics 5-6 can help address metaphysical issues. Two distinctions from Physics 5. 1 are discussed: changing per se versus changing per aliud ; motion versus change. Change from white to black is motion and alteration, whereas change from white to not white is neither. But is not every change from white to black identical with a change from white to not white? Theses from Physics 6 refute the identity. Is change f…Read more
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8Proof by Assumption of the Possible in Prior Analytics 1.15Mind 122 (488): 953-986. 2013.In Prior Analytics 1.15 Aristotle undertakes to establish certain modal syllogisms of the form XQM. Although these syllogisms are central to his modal system, the proofs he offers for them are problematic. The precise structure of these proofs is disputed, and it is often thought that they are invalid. We propose an interpretation which resolves the main difficulties with them: the proofs are valid given a small number of intrinsically plausible assumptions, although they are in tension with som…Read more
Areas of Specialization
Ancient Greek and Roman Philosophy |
Areas of Interest
1 more
Metaphysics |
Meta-Ethics |
Logic and Philosophy of Logic |
Aristotle |
Gottfried Wilhelm Leibniz |
Ancient Greek and Roman Logic |