There is a debate about whether particular properties are for Aristotle non-recurrent and trope-like individuals or recurrent universals. I argue that Physics I.7 provides evidence that he took non-substantial particulars to be neither; they are instead non-recurrent modes. Physics I.7 also helps show why this matters. Particular properties must be individual modes in order for Aristotle to preserve three key philosophical commitments: that objects of ordinary experience are primary substances, that primary substances undergo genuine change, and that primary substances are (...) ontologically fundamental. (shrink)

In this paper I argue that Aristotle's understanding of mathematical continuity constrains the mathematical ontology he can consistently hold. On my reading, Aristotle can only be a mathematical abstractionist of a certain sort. To show this, I first present an analysis of Aristotle's notion of continuity by bringing together texts from his Metaphysica and Physica, to show that continuity is, for Aristotle, a certain kind of per se unity, and that upon this rests his distinction between continuity and contiguity. Next (...) I argue briefly that Aristotle intends for his discussion of continuity to apply to pure mathematical objects such as lines and figures, as well as to extended bodies. I show that this leads him to a difficulty, for it does not at first appear that the distinction between continuity and contiguity can be preserved for abstract mathematicals. Finally, I present a solution according to which Aristotle's understanding of continuity can only be saved if he holds a certain kind of mathematical ontology. (shrink)

In this essay I use Socrates’s aside to Callicles at Gorgias 481c5-482b1 to argue that love is essential to philosophy on Plato’s conception. On my reading, Plato uses the drama of the dialogue to critique the discussion therein, against a standard for philosophy which is implicit in Socrates’s remarks. Plato suggests that Socrates’s exchange with Gorgias is the best of the three, since it best realizes the inseparable goals of pursuing truth and becoming more persuadable by reason. What makes it (...) so is that between Socrates and Gorgias alone does there seem to be a genuine good will and love leading to an effective partnership in the social activity which is philosophy. (shrink)