Aristotle's Philosophy of Mathematics.

Aus der Bibliothek von Prof. Wolfgang Haase, langj�igem Herausgeber der ANRW und des International Journal of the Classical Tradition (IJCT) / From the library of Prof. Wolfgang Haase, long-time editor of ANRW and the International Journal of the Classical Tradition (IJCT). - altersgem�sehr guter Zustand / very good condition - NONE if Aristotle�s extant treatises deals specifically with mathematics. References to mathematics in many of his works indicate, however, that he held a definite view of the subject and that it had an important place in his philosophy. H. G. Apostle, in Aristotle�s Philosophy of Mathematics, presents a detailed and systematic account of this philosophy. The body of material is drawn from Aristotle�s treatises and is organized in accordance with Aristotle�s own method of presenting the philosophy of a science. Chapter i deals with the nature of mathematics as a science, method in mathematics, and principles of mathematics. Chapters II and III examine the two fundamental branches of mathematics�arithmetic and geometry-and chapter IV is concerned with those sciences which are applications of mathematics to particular physical problems; e.g., harmonics, optics, astronomy, mechanics, etc. The final chapter discusses the mathematical views of the Pythagoreans, Plato, Speusippus, and Xenocrates, with respect to the difficulties to which their theories lead and the criticisms which Aristotle makes of these theories. -- TABLE OF CONTENTS -- Universal Mathematics -- Mathematics Is a Theoretical Science -- Mathematics Investigates the Properties of Quantities -- Nature of Quantity -- Accidental Quantities -- Manner of Existence of Quantities -- Motion, Generation, Place, Position, Not Essential Attributes of Quantities -- How Quantities Are Known -- Method in Mathematics -- Causes in Mathematics -- Mathematical Definition -- Common Attributes of Quantities -- Nature of Mathematical Axioms -- The Infinite , First Division of the Mathematical Sciences -- Arithmetic -- Arithmetic Is More Accurate than Geometry -- The Unit as Principle of Number -- Number -- Geometry -- Only Three Dimensions in Geometry -- The Limit Is Prior in Definition to the Limited -- The Limited Is Prior in Substance to the Limit -- Whether the Kinds of Magnitudes Are Simultaneous by Nature or Not -- Order of Scientific Knowledge in Magnitudes -- Material Cause and Definition in Magnitudes -- Magnitudes Are Not Composed of Indivisible Elements -- Composite Sciences -- Composite Sciences Are Possible Because Quantity Is Present in Physical Bodies -- Kinds of Subordination in Composite Sciences -- Principles of Composite Sciences -- Demonstration in Composite Sciences -- Criticism of Various Views on Mathematics -- Statement of Various Views -- Criticism of First Principles of Things -- Criticism of Generation from Principles -- Criticism of Nature and Existence of Things.