ABSTRACT
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book examines the relation between philosophy and the individual sciences from the perspective of the ancients themselves, in so far as this is possible. It discusses the way in which Galen appeals to mathematics as an example of rigorous intellectual method and an answer to scepticism. The book shows how the mathematical study of music formed part of an increasing emphasis on mathematics in the philosophy of late antiquity, and describes how music was seen as being valuable both in moral and in theoretical terms. It argues that the proper principles of a specific science, though derived from common principles or from the principles of a higher science, are none the less primitive and underived in the context of the specific science.
