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)

The first part of this paper argued that the traditional application of the Cave to the Line was not intended by Plato, and led to a misunderstanding of both similes. The Cave, it was said, is attached to the simile of the Sun and the Line by the visible region outside the cave, which is a reintegration of the symbolism of sun, originals and images in the sunlight, and the new system of objects inside the cave is compared and (...) contrasted with the natural objects in the visible outside. As we know that the natural symbolism illustrates the Platonic education, our main task in this paper will be to find the meaning of the cave, untrammelled by the associations of the lower line. (shrink)

In Varia Socratica Professor A. E. Taylor devotes his first chapter to a proof that the impiety for which Socrates was condemned consisted in his connection with an Orphic-Pythagorean cult. This argument has more than historical interest, for it is the first step in an attempt to attribute to Socrates, and ultimately to Pythagorean sources, doctrines hitherto regarded as Platonic. Much of Dr. Taylor′s new evidence seems to rest on passages which in their context contradict or greatly modify his inferences; (...) other arguments have no better basis than the dubious principle that any fact shown to be related to Orphism in one connection is always so related; and, above all, the enquiry which set out to give precise legal grounds for the charge of impiety tails away lamentably into a mere discussion of doctrine. I propose, after examining the wording of the charge, to analyze the evidence for regarding Socrates′ offence as the importation of a foreign cultus, then to enquire how far Dr. Taylor′s discussion of doctrine is relevant to the legal charge, and, lastly, to ask whether the Apology of Plato and the Memorabilia really do preserve so suspicious a silence about the impiety as to justify a totally new theory to account for their reticence. (shrink)

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)

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)

This book is an excellent collection of papers which partly spring from, and partly bear on the Study Group on the Unity of Knowledge held in various universities, October, 1967-March, 1970. The papers all bear on the problem of reduction. In "Unity of Physical Law and Levels of Description," Ilya Prigogine argues that organized structures need physical laws of organization, not of entropy only, to explain their genesis and operation." The editor’s paper, "Reducibility: Another Side Issue," argues, following Polanyi, that (...) living things as machines already transcend physics, since they demand both chemical and engineering principles for their explanation." "How is Mechanism Conceivable?" points out that ordinary ways of talking about and explaining behavior, i.e., as involving intention and purpose, differs in logic from mechanistic explanation. But this difference in logic of the two languages is "never an obstacle to the reduction of one theory to another, indeed, there is always such a noncongruence of the conceptual mesh." Anthony J. P. Kenny’s "The Homunculus Fallacy" argues against "the reckless application of human-being predicates to insufficiently human-like objects." In "Behavior, Belief, and Emotion," A. C. MacIntyre argues for the thesis that "there is no necessary connection between at least some emotions and particular forms of behavior." In "The Critique of Artificial Reason," H. Dreyfus criticizes both the empirical and a priori arguments for optimism underlying the work in artificial intelligence. It displays the underlying philosophical assumption inherent in Western philosophical tradition since Plato. The last two papers concern Polanyi’s theory of knowledge. In "Tacit Knowledge and the Concept of Mind," W. T. Scott shows how Ryle’s "Concept of Mind can be significantly extended by considering certain features of the philosophical position that Michael Polanyi has developed around the concept of tacit knowing." R. S. Cohen’s "Tacit, Social and Hopeful" discusses the difficulties in Polanyi’s epistemology and the merits of the logical reconstruction work in science. Only the papers by Dreyfus and Scott have been previously published. Throughout the collection, the editor has provided useful introductory remarks focusing upon the unifying themes in the collection.—A. S. C. (shrink)

In Varia Socratica Professor A. E. Taylor devotes his first chapter to a proof that the impiety for which Socrates was condemned consisted in his connection with an Orphic-Pythagorean cult. This argument has more than historical interest, for it is the first step in an attempt to attribute to Socrates, and ultimately to Pythagorean sources, doctrines hitherto regarded as Platonic. Much of Dr. Taylor′s new evidence seems to rest on passages which in their context contradict or greatly modify his inferences; (...) other arguments have no better basis than the dubious principle that any fact shown to be related to Orphism in one connection is always so related; and, above all, the enquiry which set out to give precise legal grounds for the charge of impiety tails away lamentably into a mere discussion of doctrine. I propose, after examining the wording of the charge, to analyze the evidence for regarding Socrates′ offence as the importation of a foreign cultus, then to enquire how far Dr. Taylor′s discussion of doctrine is relevant to the legal charge, and, lastly, to ask whether the Apology of Plato and the Memorabilia really do preserve so suspicious a silence about the impiety as to justify a totally new theory to account for their reticence. (shrink)

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)

єί μέƲ ο$$v$$Ʋ ήμєȋς μέƲ ƲλακЃκ ώς άληθς ποіομєƲ, кіστα КαКоύρονς Τςs πóλєѡς, ό δ' κєîƲo גέγѡƲ γєѡργούς τιƲς καì σπєρ έƲ παƲƞΥύρєі άλλ' ο᧻ ÉƲ πόλєі έσΤιάΤορας єύδαίµοƲας, ȁλιƲ ȁƲ ΤΙ πóλιƲ λέλoi. ‘More simply expressed,’ write Jowett and Campbell, ‘the sense is as follows: “If the idea of a state requires the citizens to be guardians, he who converts them into rustic holiday-workers will mean something that is not a state.“’ This rendering, which seems to be necessary if (...) the traditional text is retained, is difficult to reconcile with the preceding argument. Although this note will suggest an emendation, its chief purpose is to indicate the connexion of this passage with the argument of which it is the closing sentence. (shrink)

This article tackles the sole surviving ancient commentary on what was perhaps the second most important Platonic work, with special interest for the manner in which the ancients tackled the setting of Plato's dialogues, Socratic ignorance, Socratic eros, the central myth-like Palinode, and the question of oral as against written teaching.

I desire to invite the attention of students of Plato and of Greek mathematics to a solution of a passage which has long been a field of controversy for critics. For brevity's sake I shall take for granted an acquaintance with the two solutions which at present dispute the field, and further adopt certain positions which previous enquirers have established beyond reasonable doubt.

The ideal city of Plato could only come true if three great and unlikely changes were made in the state. Neither Plato's contemporaries nor later generations have been able to breast the second of these ‘waves,’ which brings in a new order of marriage for guardians. The scheme is condemned as not only not good or possible—the Platonic tests—but as inconsistent with itself and with the account given in the Timaeus. The parts under censure are the so-called table (...) of prohibited affinities and the sanction of infanticide. It would be strange to find discrepancies in a proposal so important for Plato's state that details cannot well be left to some Damon, and I hope to show that difficulties arise only when critics do not place themselves exactly at Plato's point of view. He conceived a certain problem with sharp outlines, and his answer is precisely adapted to that. The first wave left the guardians as a family of men and women living in common. How was it possible to preserve this communal life and provide for the future of the guardian class? If the rulers failed to choose aright here, an oracle foretold the decay of the city . Therefore Plato's rigid preoccupation in the second wave is to secure for the archons entire control over the birth of guardian children. Otherwise the community will sink into mere promiscuity and the stock will degenerate. In short, Plato tries to ensure that, apart from the necessary getting of children for the state, the guardians shall be friends and not lovers. Our special problems arise from the two questions—πως παδοποιήσονtαι, καì γεκομÉνους πως θρÉψουσι; . Let us begin with the first of these. (shrink)

The ideal city of Plato could only come true if three great and unlikely changes were made in the state. Neither Plato's contemporaries nor later generations have been able to breast the second of these ‘waves,’ which brings in a new order of marriage for guardians. The scheme is condemned as not only not good or possible—the Platonic tests—but as inconsistent with itself and with the account given in the Timaeus. The parts under censure are the so-called table (...) of prohibited affinities and the sanction of infanticide. It would be strange to find discrepancies in a proposal so important for Plato's state that details cannot well be left to some Damon, and I hope to show that difficulties arise only when critics do not place themselves exactly at Plato's point of view. He conceived a certain problem with sharp outlines, and his answer is precisely adapted to that. The first wave left the guardians as a family of men and women living in common. How was it possible to preserve this communal life and provide for the future of the guardian class? If the rulers failed to choose aright here, an oracle foretold the decay of the city. Therefore Plato's rigid preoccupation in the second wave is to secure for the archons entire control over the birth of guardian children. Otherwise the community will sink into mere promiscuity and the stock will degenerate. In short, Plato tries to ensure that, apart from the necessary getting of children for the state, the guardians shall be friends and not lovers. Our special problems arise from the two questions—πως παδοποιήσονtαι, καì γεκομÉνους πως θρÉψουσι;. Let us begin with the first of these. (shrink)

Do the later Platonic dialogues abandon the earlier doctrine of forms? If not, do the forms, as the objects or contents of thought, have any relation to experienced things? Schipper, in this lucid and scholarly study of the Parmenides, Theaetetus, Sophist, Philebus, and Timaeus, maintains that Plato continues to assume the essentials of the earlier doctrine of forms, and that while he offers no complete and explicit answer to the second question, the later dialogues do provide clues which are (...) consistent with each other. In formulating this answer, Schipper suggests that sensible things can be considered in two aspects: as immediately sensed and as known by means of the forms; the two aspects are united by the perceiving and knowing mind. However, this seems to be merely a restatement of the problem. Her other, more provocative suggestion is that forms are not discovered by an intellectual perception, but are assumed or posited as demanded by logos or argument in order to explain and define experienced things. Thus the interrelated forms can apply to things without being immanent in them. Although the treatment of the dialogues is careful, the book is primarily a spiritless exegesis of the text, together with an account of what other scholars have said. It is bereft of an index.—S. A. S. (shrink)

This book is an excellent collection of papers which partly spring from, and partly bear on the Study Group on the Unity of Knowledge held in various universities, October, 1967-March, 1970. The papers all bear on the problem of reduction. In "Unity of Physical Law and Levels of Description," Ilya Prigogine argues that organized structures need physical laws of organization, not of entropy only, to explain their genesis and operation." The editor’s paper, "Reducibility: Another Side Issue," argues, following Polanyi, that (...) living things as machines already transcend physics, since they demand both chemical and engineering principles for their explanation." "How is Mechanism Conceivable?" points out that ordinary ways of talking about and explaining behavior, i.e., as involving intention and purpose, differs in logic from mechanistic explanation. But this difference in logic of the two languages is "never an obstacle to the reduction of one theory to another, indeed, there is always such a noncongruence of the conceptual mesh." Anthony J. P. Kenny’s "The Homunculus Fallacy" argues against "the reckless application of human-being predicates to insufficiently human-like objects." In "Behavior, Belief, and Emotion," A. C. MacIntyre argues for the thesis that "there is no necessary connection between at least some emotions and particular forms of behavior." In "The Critique of Artificial Reason," H. Dreyfus criticizes both the empirical and a priori arguments for optimism underlying the work in artificial intelligence. It displays the underlying philosophical assumption inherent in Western philosophical tradition since Plato. The last two papers concern Polanyi’s theory of knowledge. In "Tacit Knowledge and the Concept of Mind," W. T. Scott shows how Ryle’s "Concept of Mind can be significantly extended by considering certain features of the philosophical position that Michael Polanyi has developed around the concept of tacit knowing." R. S. Cohen’s "Tacit, Social and Hopeful" discusses the difficulties in Polanyi’s epistemology and the merits of the logical reconstruction work in science. Only the papers by Dreyfus and Scott have been previously published. Throughout the collection, the editor has provided useful introductory remarks focusing upon the unifying themes in the collection.—A. S. C. (shrink)

The fulfillment of the pedagogical intention of this work takes the form of developing a specific conception of metaphysics. The author’s conception is not the original one in terms of the object of metaphysics, but one that encompasses as well the various philosophical developments that affect the original conception of it, including critiques of it. The author conceives metaphysics in terms of "motives" of thought, originally articulated by Plato, namely, 1) the knowledge of principles of being; 2) the standard (...) of true knowledge; and 3) the way in which this knowledge is attained. According to the author, the first definitive treatment of the first of these themes is given by Aristotle, in the conception of the essences of things as the principles of being. In subsequent treatments, these themes undergo various transformations, which are presented by the author as being the result of critical reflections on prior treatments. In fact, they are the result of shifts in perspective, the most fundamental of which is, as the author himself notes, the introduction of perspectivity as a category in the sense of a condition of knowledge. The author traces the function of this category in the thought of various philosophers from Augustine to Nietzsche, suggesting, though not explicitly establishing, its theological origin. (shrink)

You'd never know Athens was locked in a life-or-death struggle from the tranquil and leisurely philosophical discussion that unfolds through the pages of the Republic...Plato's masterpiece continues to inform our questions and our thinking when it comes to being, truth, beauty, goodness, justice, community, the soul, and more." -From Dr. Littlejohn's Introduction. On the way back from a festival, Socrates is waylaid by some friends who compel him to go home with them. There he and his companions engage in (...) a long discussion about whether it is worse to suffer evil or to commit it. Far from being dry or abstract, Plato's dialogue is full of practical questions about the nature of justice, education, power, and virtue, and it ends with two of the most vivid myths ever devised by man. This Canon Classic is translated clearly by Benjamin Jowett, and unlike all other works of philosophy, it's actually fun to read. The Canon Classics series presents the most definitive works of Western literature in a colorful, well-crafted, and affordable way. Unlike many other thrift editions, our classics are printed on thicker text stock and feature individualized designs that prioritize readability by means of proper margins, leading, characters per line, font, trim size, etc. Each book's materials and layout combine to make the classics a simple and striking addition to classrooms and homes, ideal for introducing the best of literary culture and human experience to the next generation. This Worldview Edition features an introduction divided into sections on The World Around, About the Author, What Other Notables Said, Setting, Characters, & Plot Summary, Worldview Analysis, 21 Significant Questions & Answers, and Further Discussion & Review. (shrink)

DigiCat Publishing presents to you this special edition of "Socratic Discourses" by Plato, Xenophon. DigiCat Publishing considers every written word to be a legacy of humankind. Every DigiCat book has been carefully reproduced for republishing in a new modern format. The books are available in print, as well as ebooks. DigiCat hopes you will treat this work with the acknowledgment and passion it deserves as a classic of world literature.

Plato is one of the key ancient authors studied by both classicists and philosophers. This long-awaited new edition contains seven of the dialogues of Plato, and is the first in the five-volume complete edition of his works in the Oxford Classical Texts series. The result of many years of painstaking scholarship, the new volume will replace the now nearly 100 year old original edition, and is destined to become just as long-lasting a classic.

Republic is the central work of the Western world's most famous philosopher. Essentially an inquiry into morality, Republic also contains crucial arguments and insights into many other areas of philosophy. It is also a literary masterpiece: the philosophy is presented for the most part for the ordinary reader, who is carried along by the wit and intensity of the dialogue and by Plato's unforgettable images of the human condition. This new, lucid translation by Robin Waterfield is complemented by full (...) explanatory notes and an up-to-date critical introduction. (shrink)

This long-awaited new edition contains eight of the dialogues of Plato, and is the first in a new five-volume complete edition of his works in the OCT series.

A lively dialogue between a foreign philosopher and a powerful statesman, Plato's Laws reflects the essence of the philosopher's reasoning on political theory and practice. It also embodies his mature and more practical ideas about a utopian republic. Plato's discourse ranges from everyday issues of criminal and matrimonial law to wider considerations involving the existence of the gods, the nature of the soul, and the problem of evil. Translated by the distinguished scholar Benjamin Jowett, this edition is an (...) authoritative choice for students of philosophy, political science, and literature. (shrink)

Both an ideal entrée for beginning readers and a solid text for scholars, the second edition of Peter Kalkavage's acclaimed translation of Plato's _Timaeus_ brings enhanced accessibility to a rendering well known for its faithfulness to the original text. An extensive essay offers insights into the reading of the work, the nature of Platonic dialogue, and the cultural background of the _Timaeus_. Appendices on music, astronomy, and geometry provide additional guidance. A brief outline of the themes of the work, (...) a detailed glossary, and a selected bibliography are also included. (shrink)

In addition to its interest as one of Plato's most brilliant dramatic masterpieces, the Protagoras presents a vivid picture of the crisis of fifth-century Greek thought, in which traditional values and conceptions of man were subjected on the one hand to the criticism of the Sophists and on the other to the far more radical criticism of Socrates. The dialogue deals with many themes which are central to the ethical theories which Plato developed under the influence of Socrates, (...) notably the nature of human excellence, the relation of knowledge to right conduct, and the place of pleasure in the good life. This translation of the Protagoras was originally published in 1976. In this revised edition, C. C. W. Taylor has made a number of changes in the translation and commentary, and has added a new Preface and Introduction. The Bibliography has also been extended to include titles published up to 1990. (shrink)

Stylometry can be defined as the use of numerical methods for the solution of literary problems, most often problems of authorship, integrity, and chronology. As stylometry has been described it seems hardly more than the application of common sense to a literary situation. For example: It consists in collecting as many peculiarities of style and grammar as possible from these works [the dialogues of Plato], particularly the Laws, which are known, or for good reasons supposed to belong to the (...) author's latest period, and observing the frequency with which these occur in other dialogues. If it is then found, e.g., that one dialogue uses commonly 100 of these, another but 60, it is reasonable to suppose the former to be nearer in time to the Laws, i.e. later. (shrink)

Stylometry can be defined as the use of numerical methods for the solution of literary problems, most often problems of authorship, integrity, and chronology. As stylometry has been described it seems hardly more than the application of common sense to a literary situation. For example: It consists in collecting as many peculiarities of style and grammar as possible from these works [the dialogues of Plato], particularly the Laws, which are known, or for good reasons supposed to belong to the (...) author's latest period, and observing the frequency with which these occur in other dialogues. If it is then found, e.g., that one dialogue uses commonly 100 of these, another but 60, it is reasonable to suppose the former to be nearer in time to the Laws, i.e. later. (shrink)

This edition of Martin Ostwald's revised version of J. B. Skemp's 1952 translation of _Statesman_ includes a new selected bibliography, as well as Ostwald's interpretive introduction, which traces the evolution in Plato's political philosophy from _Republic_ to _Statesman to Laws_--from philosopher-king to royal statesman.

Plato's dialogues frequently criticize traditional Greek myth, yet Plato also integrates myth with his writing. Daniel S. Werner confronts this paradox through an in-depth analysis of the Phaedrus, Plato's most mythical dialogue. Werner argues that the myths of the Phaedrus serve several complex functions: they bring nonphilosophers into the philosophical life; they offer a starting point for philosophical inquiry; they unify the dialogue as a literary and dramatic whole; they draw attention to the limits of language and (...) the limits of knowledge; and they allow Plato to co-opt cultural authority as a way of defining and legitimating the practice of philosophy. Platonic myth, as a species of traditional tale, is thus both distinct from philosophical dialectic and similar to it. Ultimately, the most powerful effect of Platonic myth is the way in which it leads readers to participate in Plato's dialogues and to engage in a process of self-examination. (shrink)

Plato's Phaedo, written by legendary author Plato, is widely considered to be one of the greatest classic texts of all time. This great classic will surely attract a whole new generation of readers. For many, Plato's Phaedo is required reading for various courses and curriculums. And for others who simply enjoy reading timeless pieces of classic literature, this gem by Plato is highly recommended. Published by Classic Books International and beautifully produced, Plato's Phaedo would make (...) an ideal gift and it should be a part of everyone's personal library. (shrink)

Is virtue teachable? What should we value as an ideal? Is pleasure or perception the highest good that ought to be the object of our lives? Three of Plato's most important dialogues are brought together in a single volume to address these concerns which continue to occupy serious minds today. In the Protagoras Plato attempts to answer questions about the nature of virtue and whether it is inherent in humans or a subject capable of being taught. In the (...) Philebus he addresses the nature and content of the good and whether wisdom or pleasure is to be preferred. The Gorgias applies what is learned from the previous discussions to address larger issues, such as the proper functioning of society and the state and the individual's appropriate place within them. (shrink)

Given its brevity, Plato's Meno covers an astonishingly wide array of topics: politics, education, virtue, definition, philosophical method, mathematics, the nature and acquisition of knowledge and immortality. Its treatment of these, though profound, is tantalisingly short, leaving the reader with many unresolved questions. This book confronts the dialogue's many enigmas and attempts to solve them in a way that is both lucid and sympathetic to Plato's philosophy. Reading the dialogue as a whole, it explains how different arguments are (...) related to one another and how the interplay between characters is connected to the philosophical content of the work. In a new departure, this book's exploration focuses primarily on the content and coherence of the dialogue in its own right and not merely in the context of other dialogues, making it required reading for all students of Plato, be they from the world of classics or philosophy. (shrink)

Gentzen's original proof of the Hauptsatz used a rule of multicut in the case that the right premiss of cut was derived by contraction. Cut elimination is here proved without multicut, by transforming suitably the derivation of the premiss of the contraction.

This is a commentary on selected texts of Plato concerned with poetry: the Ion and relevant sections of the Republic. It is the first commentary to present these texts together in one volume, and the first in English on Republic 2 and 3 and Ion for nearly 100 years. The introduction sets Plato's views in their Greek context and outlines their influence on later aesthetic thought. An important feature of the commentary is its exploration of the ambivalence of (...) Plato's pronouncements through an analysis of his own skill as a writer. (shrink)

Republic is the central work of the western world's most famous philosopher. Essentially an inquiry into morality, Republic also contains crucial arguments and insights into many other areas of philosophy. It is also a literary masterpiece: the philosophy is presented for the most part for the ordinary reader, who is carried along by the wit and intensity of the dialogue and by Plato's unforgettable images of the human condition. This new, lucid translation by Robin Waterfield is complemented by full (...) explanatory notes and an up-to-date critical introduction. (shrink)

Gentzens natural deduction. Thereby the appearance of the cuts in translation is explained.

Ostensibly a discussion about love, the debate in the Phaedrus also encompasses the art of rhetoric and how it should be practised. This new edition contains an introductory essay outlining the argument of the dialogue as a whole and Plato's arguments about rhetoric and eros in particular. The Introduction also considers Plato's style and offers an account of the reception of the dialogue from its composition to the twentieth century. A new Greek text of the dialogue is accompanied (...) by a select textual apparatus. The greater part of the book consists of a Commentary, which elucidates the text and makes clear how Plato achieves his philosophical and literary objectives. Primarily intended for advanced undergraduates and graduate students of ancient Greek literature and philosophy, it will also benefit scholars who want an up-to-date account of how to understand the text, argument, style and background of the work. (shrink)

In Plato's Gorgias, Gorgias of Leontini, a famous teacher of rhetoric, has come to Athens to recruit students, promising to teach them how to become leaders in politics and business. A group has gathered at Callicles' house to hear Gorgias demonstrate the power of his art. This dialogue blends comic and serious discussion of the best human life, providing a penetrating examination of ethics, the foundations of knowledge, and the nature of the good.

Gentzen's systems of natural deduction and sequent calculus were byproducts in his program of proving the consistency of arithmetic and analysis. It is suggested that the central component in his results on logical calculi was the use of a tree form for derivations. It allows the composition of derivations and the permutation of the order of application of rules, with a full control over the structure of derivations as a result. Recently found documents shed new light on the discovery of (...) these calculi. In particular, Gentzen set up five different forms of natural calculi and gave a detailed proof of normalization for intuitionistic natural deduction. An early handwritten manuscript of his thesis shows that a direct translation from natural deduction to the axiomatic logic of Hilbert and Ackermann was, in addition to the influence of Paul Hertz, the second component in the discovery of sequent calculus. A system intermediate between the sequent calculus LI and axiomatic logic, denoted LIG in unpublished sources, is implicit in Gentzen's published thesis of 1934—35. The calculus has half rules, half “groundsequents,” and does not allow full cut elimination. Nevertheless, a translation from LI to LIG in the published thesis gives a subformula property for a complete class of derivations in LIG. After the thesis, Gentzen continued to work on variants of sequent calculi for ten more years, in the hope to find a consistency proof for arithmetic within an intuitionistic calculus. (shrink)