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What does Plato mean in saying that, for all forms, “F-ness is F”? In such claims, I argue, ‘F’ is being used metonymically to refer to the property of being productive of F-ness rather than to the property of being F, in a way consistent with univocity and the rejection of a genuine Self-Predication Assumption. I explain and defend this productive metonymy reading and show how it can resolve the troubling argument at Phaedo 74b7-c6.

I examine the reasons Aristotle presents in Physics VIII 8 for denying a crucial assumption of Zeno’s dichotomy paradox: that every motion is composed of sub-motions. Aristotle claims that a unified motion is divisible into motions only in potentiality (δυνάμει). If it were actually divided at some point, the mobile would need to have arrived at and then have departed from this point, and that would require some interval of rest. Commentators have generally found Aristotle’s reasoning unconvincing. Against David Bostock and Richard Sorabji, inter alia, I argue that Aristotle offers a plausible and internally consistent response to Zeno. I defend Aristotle’s reasoning by using his discussion of what to say about the mobile at boundary instants, transitions between change and rest. There Aristotle articulates what I call the Changes are Open, Rests are Closed Rule: what is true of something at a boundary instant is what is true of it over the time of its rest. By contrast, predications true of something over its period of change are not true of the thing at either of the boundary instants of that change. I argue that this rule issues from Aristotle’s general understanding of change, as laid out in Phys. III. It also fits well with Phys. VI, where Aristotle maintains that there is a first boundary instant included in the time of rest, but not a “first in which the mobile began to change.” I then show how this rule underlies Aristotle’s argument that a continuous motion cannot be composed of actual sub-motions. Aristotle distinguishes potential middles, points passed through en route to a terminus, from actual middles. The Changes are Open, Rests are Closed Rule only applies to actual middles, because only they are boundaries of change that the mobile must arrive at and then depart from. On my reading, Aristotle argues that the instant of arrival, the first instant at which the mobile has come to be at the actual middle, cannot belong to the time of the subsequent motion. If it did, the mobile would already be moving towards the next terminus and thus, per Phys. VI 6, would have already left. But it cannot have moved away from the midpoint at the very same moment it has arrived there. This means that the instant of arrival must be separated from the time of departure by an interval of rest. I show how Aristotle’s reasoning applies generally to rule out any continuous reflexive motion or continuous complex rectilinear motion. On my interpretation, however, the argument does not apply to every change of direction. When, as in the case of projectile motion, multiple movers and their relative powers explain why the mobile changes directions, distinct sub-motions are not involved. Aristotle holds that such motions cannot be continuous, not because they involve intervals of rest, but because they involve multiple causes of motion. My interpretation of the Changes are Open, Rests are Closed Rule allows us to make better sense of Aristotle’s argument than any previous interpretation.

One of three basic types of desire, claims Aristotle, is thumos (‘spirit,’ ‘passion,’ ‘heart,’ ‘anger,’ ‘impulse’). The other two are epithumia (‘appetite’) and boulêsis (‘wish,’ ‘rational desire’). Yet, he never gives us an account of thumos ; it has also received relatively little scholarly attention. I argue that thumos has two key features. First, it is able to cognize what I call ‘social value,’ the agent’s own perceived standing relative to others in a certain domain. In human animals, shame and honor are especially important manifestations of social value. Second, thumos provides non-rational motivation to pursue what affirms the agent’s social value and avoid what denies it. Interpretations that hold thumos just is anger, or that its object is the fine ( kalon ), I argue, are mistaken. My account also explains the role of thumos in moral education. In a virtuous agent thumos will be affectively attuned to the correct social rankings; it will take the practically wise, the lovers of the fine, or moral exemplars, as authorities.

In the last two books of the Politics , Aristotle articulates an education program for his best regime in contrast to what he takes to be the goal and practices of Sparta’s educational system. Although Aristotle never refers to his program as liberal education, clearly he takes its goal to be the production of free male and female citizens. By contrast, he characterizes the results of the Spartan system as ‘crude’ (φορτικός), ‘slavish’ (ἀνδραποδώδης), and ‘servile’ (βάναυσος). I argue that Aristotle’s criticisms of Spartan education elucidate his general understanding of Sparta and provide an interpretative key to understanding Politics 7–8. But although Aristotle contrasts the goals and methods of Spartan education with that of his own best regime, the citizens of his best regime are more like Spartan citizen-soldiers than Athenian participatory-citizens.