Originally published in 1955, this book presents a detailed discussion regarding aspects of Plato's ethics. The text is divided into three main parts, covering 'The Personal Ideal', 'The Ethical Society' and 'The Growth of a Reality Principle'. It was based upon the author's Fellowship Dissertation for a position at Christ Church College, Oxford. A bibliography is also included and detailed notes are incorporated throughout. This book will be of value to anyone with an interest in Plato and his ethical standpoint.

Anyone who has read Plato’s Republic knows it has a lot to say about mathematics. But why? I shall not be satisfied with the answer that the future rulers of the ideal city are to be educated in mathematics, so Plato is bound to give some space to the subject. I want to know why the rulers are to be educated in mathematics. More pointedly, why are they required to study so much mathematics, for so long?

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

A model for the ideal state includes discussions of the nature and application of justice, the role of the philosopher in society, the goals of education, and the effects of art upon character.

A comprehensive introduction to the theory of knowledge.

The similes of the Sun, Line, and Cave in the Republic remain a reproach to Platonic scholarship because there is no agreement about them, though they are meant to illustrate. I propose to analyse the form of the argument, a clue that has never been properly weighed. The Greek theory and practice of analogia and diairesis give good evidence about the method that Plato adopted; if this usage were respected, the analogical argument would not be so loosely interpreted, and the (...) double diairesis and proportion that the Line actually is could not be mistaken for a classification. I hope also to show that Plato's terminology is definite and consistent; here too ancient usage helps to establish his meaning. (shrink)

The purpose is to clarify and explain plato's theory of the forms. discussion on the theory: varieties of paradigmata, image and reality and predicates. the forms of paradigmata fill a wide range of philosophical roles. forms should be spoken of as forms rather then as structures or patterns, sets or universals, fregean concepts or eternal possibilities. (staff).

Reprint of the original, first published in 1860.

An account of how the mathematical sciences turn the mind away from becoming and towards being. There are four main conclusions. 1. The study of numbers, when treated independently of the other sciences, uses a particular conception of the nature of numbers to detach the mind from the influence of perceptible objects. 2. The study of ratios and proportions, explicitly the core of Plato's harmonics, is fundamental also to plane and solid geometry and astronomy. 3. Ratios and proportion form the (...) basis for the synoptic vision of all the mathematical sciences. This vision is an essential preparation for dialectic because it makes mathematicians become aware of the limitations of the mathematics they have been engaged in but it also shows them how they can begin to overcome those limitations. 4. The main purpose of the study of numbers, treated finally in relation to the other sciences, is to calculate ratios. (shrink)

This interpretive introduction provides unique insight into Plato's Republic. Stressing Plato's desire to stimulate philosophical thinking in his readers, Julia Annas here demonstrates the coherence of his main moral argument on the nature of justice, and expounds related concepts of education, human motivation, knowledge and understanding. In a clear systematic fashion, this book shows that modern moral philosophy still has much to learn from Plato's attempt to move the focus from questions of what acts the just person ought to perform (...) to the more profound questions of what sort of person the just person ought to be. (shrink)

Following strict rules of interpretation, this book focuses on the ideas in Plato's early and middle dialogues that lie within the fields now called logic and methodology, specifically elenchus and dialectic and the method of hypothesis.

A step by step, passage by passage analysis of the complete Republic. White shows how the argument of the book is articulated, the important interconnections among its elements, and the coherent and carefully developed train of though which motivates its complex philosophical reasoning. In his extensive introduction, White describes Plato's aims, introduces the argument, and discusses the major philosophical and ethical theories embodied in the Republic. He then summarizes each of its ten books and provides substantial explanatory and interpretive notes.

Finds in Plato's dialogue not only a discussion, but also a demonstration of his philosophical principles.

Available from UMI in association with The British Library. ;Plato's philosophy of mathematics must be a philosophy of 4th century B.C. Greek mathematics, and cannot be understood if one is not aware that the notions involved in this mathematics differ radically from our own notions; particularly, the notion of arithmos is quite different from our notion of number. The development of the post-Renaissance notion of number brought with it a different conception of what mathematics is, and we must be able (...) to see the differences before we can begin to appreciate Plato's views, which must never be seen as applying to a revolutionary notion of mathematics . For this reason the first part of this dissertation must comprise a detailed analysis of these differences, along with some criticisms of those of Plato's modern interpreters who have not taken this point. Much of what will be found here can be found in Jacob Klein's Greek Mathematics and the Origin of Algebra, which will be extensively quoted and interpreted. This book is often quoted, but very seldom understood; or at least, those lessons which should be taken from it are rarely applied to Platonic exegesis. In the second part I attempt a better explanation of Plato's mathematical ontology, beginning with the most extensive passage in the dialogues, the triple image of Sun, Line and Cave in Republic. This reveals a relation between sensibles and forms which is at odds with the traditional view that mathematical objects are never precisely accurate instances of their forms--but this view can be refuted. Plato's view of the nature of mathematical objects will be seen to be a metaphorical way of saying what Aristotle says logically, and is entirely appropriate to the aims and methods of his contemporary mathematicians. Aristotle's criticism of Plato's views is examined and found to make sense and to be appropriate to views which Plato could consistently have held. (shrink)

At the end of the Sixth Book of the Republic Plato explains the Idea of Good by means of the Figure of the Sun. As the sun is the cause both of the becoming of that which is subject to becoming and of our apprehension of it and of its changes through the eye, so the idea of good is the cause of the being of that which is and also of our knowledge of it. As the sun is beyond (...) γxs22EFνεσις, so the Idea of Good is beyond Being. Glaucon says he does not understand. The simile is further elucidated by means of a line, divided into two parts, of which one stands for the νιητxs22EFν γxs22EFνος τε καxs22EF τxs22EFπος, where the Idea of Good bears rule, the other for the xs22EFρατxs22EFν γxs22EFνος τε καxs22EF τxs22EFπος, over which the sun is lord. The line is to be divided unequally , and subdivided in the same proportions. Thus we get a line consisting of four parts in the ratio 4 : 6 : : 6 : 9. Let us call the four parts A B C D respectively, A being the smallest, D the greatest, B and C necessarily equal. A stands for εxs1F31κxs22EFνες, shadows, images in water and on polished surfaces, and the like: B stands for animals, plants, and the creations of human industry: C for the objects of that enquiry in which the objects denoted by B are treated as images, i.e. mathematical enquiries: D for the objects apprehended by dialectic, the Ideas themselves. The first equation asserted is—The objects of opinion : objects of knowledge : : representation : original . There follows an explanation of the inferiority of mathematical to philosophical reasoning, and an explanation of the statement that the objects denoted by B are used as images or symbols by the enquiry concerned with C; as a result of which Glaucon perceives that the general distinction between C and D is that between the τxs22EFχναι , i.e. those sciences in which the Guardians were to be educated, and Philosophy or Dialectic. Finally a special πxs22EFθημα or affection of the soul is allotted to each of the four divisions of the line, to A εxs1F31κασxs22EFα, to B πxs22EFστις, to C διxs22EFνοια, to D νxs22EFησις, each πxs22EFθημα being clear in the same degree in which the objects it is concerned with are true. (shrink)

This book is an anthology of Plato's writings, connected with sections of commentary.