John J. Cleary

Abstracting Aristotle’s Philosophy of Mathematics

In the history of science perhaps the most influential Aristotelian division was that between mathematics and physics. From our modern perspective this seems like an unfortunate deviation from the Platonic unification of the two disciplines, which guided Kepler and Galileo towards the modern scientific revolution. By contrast, Aristotle’s sharp distinction between the disciplines seems to have led to a barren scholasticism in physics, together with an arid instrumentalism in Ptolemaic astronomy. On the positive side, however, astronomy was liberated from commonsense realism for the conceptual experiments of Aristarchus of Samos, whose heliocentric hypothesis was not adopted by later astronomers because it departed so much from the ancient cosmological consensus. It was only in the time of Newton that convincing physical arguments were able to overcome the legitimate objections against heliocentrism, which had looked like a mathematical hypothesis with no physical meaning.

Cultivating Intellectual Virtue in Plato’s Philosopher-Rulers

This chapter discusses the intellectual virtues to be cultivated through mathematics and dialectic in the educational curriculum, which is prescribed for the philosopher-rulers. Yet, subsequently, an elaborate scheme of education is outlined for turning the natural capacity of human intelligence away from the sensible world and towards the intelligible realm. But, perhaps due to the historical influence of Plato, we would now describe this reorientation in terms of the cultivation of intellectual virtue. It considers how Plato understands mathematics and dialectic to be promoting intellectual virtue, which he often described in terms of phronesis. The chapter offers a reading of Republic VI VII in terms of Platos attempt to resolve a central problem of Socratic intellectualism, namely, to give some good reason why Socrates himself was motivated to inquire into virtue, so as to interpret the command of the god. Keywords:human intelligence; intellectual virtue; mathematics; philosopher-rulers; Plato; Socratic intellectualism

Back to the Texts Themselves

This chapter clarifies the challenge that Greek philosophical texts constitute for the discipline of hermeneutics. It illustrates the authors remarks with references to Platos Timaeus , which is one of the dialogues with the longest history of competing interpretations, beginning within the Old Academy itself. With respect to the Timaeus , one can establish a metaphorical interpretation of key doctrines from hints in the text itself. If one views the Timaeus through the eyes of Aristotle, who offers trenchant criticisms of the dialogue in his own inquiry about the heavens, it appears to be a treatise on cosmology. Despite its not having the literary form of a treatise, this is to treat the Timaeus as a prototype for Aristotles De Caelo , and to see Plato as anticipating some of Aristotles doctrines. The chapter considers some contentious questions about the Timaeus , which may have led Platos associates into disputes about its proper interpretation. Keywords:Aristotle; competing interpretations; Greek philosophical texts; Platos Timaeus

Plato’s Teleological Atomism

In De Caelo I, Aristotle makes it clear that not only in cosmology, but also in physics and mathematics, the choice between the finite and the infinite determines his whole system, just as a first principle dictates its consequences. In the case of Plato, the author finds a similar choice about the basic structure of matter being made in the Timaeus , where he parts company with the Atomists on the question of infinity, while accepting their conception of matter as discrete rather than as continuous. Timaeus explains such rational order in terms of a divine craftsman who generates the cosmos as a living creature with a soul and body, both of which are constructed according to the most perfect numerical proportion. Timaeus asserts that the universe is single by nature, even though he concedes that someone else may reach a different conclusion by considering other factors. Keywords:atomists; cosmology; Plato; Timaeus

The Personal and the Philosophical in Gadamer's Thought

In this review article I want to discuss a rather paradoxical publication, namely, an intellectual biography of a famous twentieth-century philosopher who himself doubted the value of biography as a guide to the most important ideas of any philosopher. 1 Thus one of the questions which I want to address is whether Jean Grondin’s semi-official biography of Hans-Georg Gadamer adds anything to our understanding of his work. From the outset, however, I should lay my own cards on the table by revealing that I attended Gadamer’s lectures at Boston College in the late 1970s and, subsequently, became both a colleague and a friend during the last quarter-century of his life. I am also personally acquainted with Grondin through our mutual connection with Gadamer, and I was a source for some of the information about his American sojourn. If any of these facts makes me a prejudiced reviewer, I hope that it is in the positive Gadamerian sense that all understanding is guided by some forejudgments based on personal history and experience. In any case, I am well placed to answer the question of whether Grondin’s biography of Gadamer captures the spirit of the man and the thinker whom I knew well, and whose work I admire. For the purposes of my review article, I will use the Gadamerian idea of ‘historically effected consciousness’ ( wirkungsgeschichtliches Bewusstsein ) as a leitmotif for the life of this central figure in twentieth-century German philosophy, while simultaneously subverting Gadamer’s own Heideggerean conviction that the life and personality of the philosopher is of no importance for understanding his philosophy.

Aristotle's Criticism of Plato's First Principles

In this paper I will discuss some puzzles about the first principles proposed by Plato and criticized by Aristotle in the course of his typical dialectical processs of developing his own first principles in metaphysics.

POWERS THAT BE: THE CONCEPT OF POTENCY IN PLATO AND ARISTOTLE

This chapter traces the conceptual role of the term dunamis as it was used by Plato and Aristotle for their own philosophical purposes. It focuses on how Plato used it for his own purposes in a quasi-technical way as a criterion for establishing the existence of things. The word dunamis provides us with a good illustration in Greek philosophy of the transition from ordinary talk about powers and capabilities to what we can recognise in Aristotle as a technical philosophical vocabulary. The chapter outlines a general way as a response to those modern scholars who reject all such talk as circular and uninformative, for instance, in his analysis of Aristotles theory of actuality, complains that the explanations given are uninformative because they merely redescribe the appearances. The main definition of the primary potency would be a principle of change in another thing, or in the same thing qua other. Keywords:Aristotle; dunamis ; Greek philosophy; Plato; potency