A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics and its similarities to modern views as well as its differences. It focuses on philosophical, foundational, and logical questions — rather than strictly historical and mathematical issues — and features several helpful appendixes.

Des Jardins (1976) and Dreher (1990) have suggested that Plato's Line should be thought of as divided in the mean and extreme ('golden') ratio. I examine their arguments, as well as other reasons that could be brought up in support of the 'golden division' of the Line, and show that all of them are wanting.

Dans un célèbre ouvrage surContemplation et Vie contemplative selon Platon, A.J. Festugière donnait de la dialectique platonicienne une interprétation selon laquelle celle-ci constituait une véritable expérience mystique possédant presque tous les traits de la contemplation chrétienne. La dialectique platonicienne y était présentée, surtout dans son acte final, comme une sorte d'extase, une union d'ordre mystique, un contact de l'âme perdue dans son objet, contact qui suscite en elle un sentiment qui dépasse tout l'ordre normal de la connaissance. Le Bien ou (...) l'Un en tant qu'objet dernier de l'ascension dialectique y était conçu comme quelque chose d'ineffable et d'indéfinissable. (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.

197: on logon didonai as giving a proof. In answer to Plato's charge that mathematicians take as their starting point certain unproved assumptions, and call upon them to "give an account" of them in the sense of deriving them from some more basic principle or principles.

Joe Sachs has followed up his brilliant translation of Aristotle's Physics with a new translation of Metaphysics. Sachs's translations bring distinguished new light onto Aristotle's works, which are foundational to history of science. Sachs translates Aristotle with an authenticity that was lost when Aristotle was translated into Latin and abstract Latin words came to stand for concepts Aristotle expressed with phrases in everyday Greek language. When the works began being translated into English, those abstract Latin words or their cognates were (...) used, thus suggesting a level of jargon and abstraction, and in some cases misleading interpretation, which was not Aristotle's language or style. These important new translations open up Aristotle's original thought to readers. (shrink)

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

No part ot Plato's writings has been more debated than the three similes in Books VI.-VII. of the Republic, and still there is a diversity of opinion about their meaning. I believe that most of these difficulties arise from certain assumptions about their purpose which need revision. The current view applies the Cave to the Line, as Plato seems to direct, and this application, which is itself attended by considerable difficulties, leads to an assimilation of the two figures till they (...) seem to have much the same content and purpose. Again, as this makes the lower line appear to be the phenomenal world, it is thought that the simile of the sun foreshadows the theme of the Line by hinting at a connexion between the intelligible and the sensible which is made more explicit in the Line. Thus the group of similes seem mainly intended to show the dependence of Becoming upon Being. This paper will argue that such a view depends upon the misrepresentation of the symbolism adopted by Plato, that two antithetical groups of symbols are confused with one another, and that symbols are even identified with antitypes. Owing to these misinterpretations the Form of the Good has been mistaken for a material cause; both the Line and the Cave have been thought to reveal Plato as embarrassed by a dualism between sense and intellect, and the purpose of the Cave in particular, since the error is cumulative, has been completely obscured. This paper will attempt to substitute for current accounts another interpretation which will relate the three similes closely with the political arguments of Book VI., and with the Platonic education which is set forth in close connexion with them. (shrink)

PREFACE: THE preparation of this volume was undertaken some years ago, but was interrupted by my work on the Lexicon Platonicum which has proved a more ...