Theokritos Kuremenos Knihy

In Phys. 8.10 and Cael. 1.7, 3.2 Aristotle establishes theses central to his physical theory by relying on proportions he sets out in Phys. 7.5 without, though, giving any clue as to their character or even their role in the argument he develops in Phys. 7. The author seeks to determine the nature of the problematic Phys. 7.5 proportions, which have been traditionally understood out of any context as Aristotle’s flawed mathematical laws of motion, in the light of their applications in Phys. 8.10 and Cael. 1.7, 3.2. He argues that Aristotle conceived these proportions as purely mathematical assumptions which, though, do not compromise the arguments in Phys. 8.10 and Cael. 1.7, 3.2, for there is strong evidence that for Aristotle these arguments do not turn on any proportionality assumption. This is the first comprehensive study of the important arguments in which Aristotle makes use of the Phys. 7.5 proportions and sheds light on a rather neglected side of his physics.

Plato’s view that mathematics paves the way for his philosophy of forms is well known. This book attempts to flesh out the relationship between mathematics and philosophy as Plato conceived them by proposing that in his view, although it is philosophy that came up with the concept of beings, which he calls forms, and highlighted their importance, first to natural philosophy and then to ethics, the things that do qualify as beings are inchoately revealed by mathematics as the raw materials that must be further processed by philosophy (mathematicians, to use Plato’s simile in the Euthedemus , do not invent the theorems they prove but discover beings and, like hunters who must hand over what they catch to chefs if it is going to turn into something useful, they must hand over their discoveries to philosophers). Even those forms that do not bear names of mathematical objects, such as the famous forms of beauty and goodness, are in fact forms of mathematical objects. The first chapter is an attempt to defend this thesis. The second argues that for Plato philosophy’s crucial task of investigating the exfoliation of the forms into the sensible world, including the sphere of human private and public life, is already foreshadowed in one of its branches, astronomy.

In his Republic Plato considers grasping the unity of mathematics as the ultimate goal of the mathematical studies in which the future philosopher-rulers must engage before they turn to philosophy. How the unity of mathematics is supposed to be understood is not explained, however. This book argues that Plato conceives of the unity of mathematics in terms of the mutually benefiting links between its branches, just as he conceives of the unity of the state outlined in the Republic in terms of the common benefit for all citizens. Evidence for this view is provided by a discussion of his conception of astronomy as a propedeutic to philosophy, which can be best understood as hinting at a historically possible link between fourth-century-BC astronomy and solid geometry. The monograph also includes a detailed discussion of two well-known stories about Plato: not only he motivated Greek mathematicians to solve a difficult problem in solid geometry with his interpretation of a Delphic oracle given to the inhabitants of the island of Delos but he also posed the question which led to the development of the astronomical theory of homocentric spheres. It is argued that these stories are best understood as fictional episodes in Plato's life, constructed from passages in his works.

This is the first full-scale commentary on Aristotle's de Caelo III to appear in recent decades. de Caelo III can serve as a good introduction to Aristotle's physics and its character. In it he answers some very general questions about the elements of all material things except celestial objects: how many these elements are, why they cannot be infinitely many but must be more than one, whether they are eternal or can be generated and decay, and, if the second, how. His discussion is often framed as a critique of rival theories, and he argues systematically against the geometrical theory of the elements in Plato's Timaeus, which adds greatly to the interest of the work. The commentary adduces many parallel passages from Aristotle's other works to round off the readers understanding, and the introduction offers a brief but comprehensive overview of the Aristotelian theory of the elements, which de Caelo III often takes for granted.

This book offers a reappraisal of basic aspects of Aristotelian cosmology. Aristotle believed that all celestial objects consist of the same substance that pervades the heavens, a stuff unlike those found near the center of the cosmos that compose us and everything in our immediate surroundings. Kouremenos argues that, contrary to the received view, Aristotle originally introduced this heavenly stuff as the matter of the stars alone, the remotest celestial objects from the Earth, and as filler of the outermost part of the heavens, forming a diurnally rotating spherical shell whose fixed parts are the stars, the crust of the cosmos which has the Earth at its center. The author also argues that, contrary to another common view, at no point in the development of his cosmological thought did Aristotle believe the heavens to be structured according to the theory of homocentric spheres developed by his older contemporary Eudoxus of Cnidus, in which the other celestial objects, the five planets known in antiquity, the Sun and the Moon, were hypothesized to move uniformly in circles, as if they were fixed stars.