Substance and Essence in Aristotle is a close study of Aristotle's most profound-and perplexing-treatise: Books VII-IX of the Metaphysics. These central books, which focus on the nature of substance, have gained a deserved reputation for their difficulty, inconclusiveness, and internal inconsistency. Despite these problems, Witt extracts from Aristotle's text a coherent and provocative view about sensible substance by focusing on Aristotle's account of form or essence. After exploring the context in which Aristotle's discussion of sensible substance takes place, Witt turns to his analysis of essence. Arguing against the received interpretation, according to which essences are classificatory, Witt maintains that a substance's essence is what causes it to exist. In addition, Substance and Essence in Aristotle challenges the orthodox view that Aristotelian essences are species-essences, defending instead the controversial position that they are individual essences. Finally, Witt compares Aristotelian essentialism to contemporary essentialist theories, focusing in particular on Kripke's work. She concludes that fundamental differences between Aristotelian and contemporary essentialist theories highlight important features of Aristotle's theory and the philosophical problems and milieu that engendered it.

Substance and Essence in Aristotle: An Interpretation of Metaphysics VII-IX

This Ph.D. thesis aims at a novel reconstruction of the metaphysical and epistemological theories of the first two successors of Plato, Speusippus and Xenocrates. By advancing a new methodology for the selection and evaluation of the evidence and putting it to the test, this thesis will offer a picture of Speusippus’ and Xenocrates’ theories as grounded in the privileged testimony of Aristotle.
The Early Academy has always been a riddle and a challenge for modern scholars. Indeed, for Plato’s immediate successors, Speusippus and Xenocrates, the sources at our disposal do not often encourage the project of a coherent reconstruction of their thought. Any exegesis of them faces the following difficulty: on the one hand, the earliest preserved chronological sources approach their doctrines polemically; on the other hand, later testimonia are to be found in authors who appropriated and reshaped Early Academic doctrines in their own philosophical frameworks.
Through an in-depth analysis of Aristotelian testimonia, this thesis will show that Speusippus’ and Xenocrates’ doctrines can be better understood in the context of the Academy, and, in particular, with respect to the discussions undertaken with Aristotle. By exposing a set of problems the two philosophers target in order to defend Platonic theories from the inconsistencies detected by Aristotle, Speusippus’ and Xenocrates’ Platonic inheritance is finally revealed.

Aristotle’s account of Speusippus’ and Xenocrates’ Metaphysical and Epistemological Theories

Abstract: 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 that mathematicals are separate; but the B.5 mathematicals are inherent. I argue that the B.5 inherence is compatible with the M.2 separateness, and further, that aporia 12 is more than just a puzzle about the hypostatization of mathematicals. It is also a puzzle about the ontological status of mathematicals relative to sensibles.

Mathematical Substances in Aristotle’s Metaphysics B.5: Aporia 12 Revisited

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 notion allows Aristotle to prevent the proliferation of substance-kinds and thus to secure the unity of his metaphysical system.

Ontological Separation in Aristotle’s Metaphysics

Brentanian continua and their boundaries Arthur Heller Britto This dissertation focuses on how a specific conceptual thread of the history of mathematics unfolded throughout the centuries from its original account in Ancient Greece to its demise in the Modern era due to new mathematical developments and, finally, to its revival in the work of Brentano. In particular, we shall discuss how the notion of continuity and the connected notion of continua and boundaries developed through the ages until Brentano’s revival of the original Aristotelian account against the by then established mathematical ortodoxy. Thus, this monograph hopes to fill in a gap in the present state of Brentanian scholarship as well as to present a thorough account of this specific historical thread.

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Brentanian continua and their boundaries

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.

Geometrical Objects as Properties of Sensibles: Aristotle’s Philosophy of Geometry

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 mathematical objects. I hope to persuade readers of Metaphysics M.2 that Aristotle is a more thoughtful critic than he is often taken to be.

Emily Katz

Papers

Ontological Separation in Aristotle’s Metaphysics

Geometrical Objects as Properties of Sensibles: Aristotle’s Philosophy of Geometry

An Absurd Accumulation: Metaphysics M.2, 1076b11-36