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 geometricals. I also show that (...) intelligible matter has the same meaning in all three places where it is explicitly invoked: Z.10, Z.11, and H.6. Since the H.6 passage involves a mathematical definition, this requires determining what the mathematician defines and how she defines it. I show that, as with natural scientific definitions, there must be a matterlike element in mathematical definitions. This element is not identical with, but rather refers to, intelligible matter. (shrink)

Aristotle's inquiry into the definitional question “what is substance?” in the central books of the Metaphysics is constrained by the unity requirement. Roughly, a particular hylomorphic compound substance, such as this human, ought to be a unified whole and not just a heap of material parts and form. A similar claim applies to the substance‐kind, human, which Metaphysics ΖΗΘ characterises as a hylomorphic compound taken universally. I raise the following question about this picture of unity: Is a compound's unity basic (...) or is it derived from the form's unity? Reading closely Metaphysics Z.12 and H.6, I argue that the form is explanatorily basic for the compound's unity. (shrink)

Discussions of Aristotle’s Metaphysics Z tend to treat it either as an independent treatise on substance and essence or as preliminary to the main conclusions of the Metaphysics. I argue instead that Z is central to Aristotle’s project of first philosophy in the Metaphysics: the first philosopher seeks the first causes of being qua being, especially substances, and in Z, Aristotle establishes that essences or forms are the first causes of being of perceptible substances. I also argue that the centrality (...) of Z to first philosophy is compatible with its status as theology. (shrink)

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 properties possessed by actual and potential compass-and-straightedge drawings qua quantitative and (...) continuous. For their part, the objects of stereometry are potential sensible three-dimensional figures qua quantitative and continuous. (shrink)

Aristotle is sometimes committed to a pattern of inference that moves from complexity offunctioning to complexity in the entity's metaphysical structure. This article argues that Aristotle rejects this inference in the case of the basic essence, the ultimate differentia that determines the kind to which the entity belongs. Specifically, the functional difference between active and passive reasoning in humans is not matched in the structure of the basic human essence. The basic essence is an immediate unity in the strong sense (...) that it is wholly without structural parts. Complex rational functioning emerges from a metaphysically simple basic essence. (shrink)

This book discusses Aristotle’s notions of essence and substance as they are developed in Metaphysics ZH. I examine Aristotle's argument at length and defends an unorthodox interpretation according to which his motivation is to provide an answer against a conflation between criteria for existential priority (delivering substances as primary beings) and criteria for explanatory priority (delivering essences as primary principles).

Aristotle's conception of being is dynamic. He believes that a thing is most itself when engaged in its proper activities, governed by its nature. This paper explores this idea by focusing on Metaphysics , a text that continues the investigation of substantial being initiated inMetaphysics Z. Q.1 claims that there are two potentiality-actuality distinctions, one concerned with potentiality in the strict sense, which is involved in change, the other concerned with potentiality in another sense, which he says is more useful (...) for the present project. His present project is the investigation of substantial being, and the relevant potentiality is the potentiality for activity, the full manifestation of what a thing is. I explore Aristotle's two potentiality-actuality distinctions AND argue that the second distinction is modeled on the first, with one crucial modification. Whereas a change is brought about by something other than the object or by the object itself considered as other (as when a doctor cures himself), an activity is brought about byte object itself considered as itself. This single modification yields an important difference: whereas a change leads to a state other than the one an object was previously in, an activity maintains or develops what an object already is. (shrink)

I argue that Metaphysics H.6 is not an isolated chapter but the conclusion of an argument begun in H.3. This view will provide further and better arguments for the following view about long-standing interpretative debates: first, Aristotle provides a substantive account of the unity of the composite substance (although he also briefly addresses the unity of the form); second, neither Aristotle’s conception of matter nor his account of form changes between H.1–5 and H.6; and third, H does not rely on (...) and is not completed by book Θ in any significant way. (shrink)