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)

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)

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)

R.E. Allen's superb new translations of four Socratic dialogues—_Ion_, _Hippias Minor_, _Laches_, and _Protagoras_—bring these classic texts to life for modern readers. Allen introduces and comments on the dialogues in an accessible way, inviting the reader to reexamine the issues continually raised in Plato's works. In his detailed commentary, Allen closely examines the major themes and central arguments of each dialogue, with particular emphasis on _Protagoras_. He clarifies each of Plato's arguments and its refutation; places the themes in (...) historical perspective; ties each theme to interpretations of rival translations; and links the philosopher's thought to trends in late modern philosophy. Topics discussed include: whether virtue is an art, whether wisdom and courage are logically equivalent, whether virtue is knowledge, and whether to know the good is to do it. Allen connects his discussion of these issues to the Benthamite tradition of hedonism and utilitarianism and to the ethical theories of Mill, Sidgwick, Moore, and Freud. (shrink)

This chapter focuses on the development of Gerhard Gentzen's structural proof theory and its connections with intuitionism. The latter is important in proof theory for several reasons. First, the methods of Hilbert's old proof theory were limited to the “finitistic” ones. These methods proved to be insufficient, and they were extended by infinitistic principles that were still intuitionistically meaningful. It is a general tendency in proof theory to try to use weak principles. A second reason for the importance of intuitionism (...) for proof theory is that the proof-theoretical study of intuitionistic logic has become a prominent part of logic, with applications in computer science. (shrink)

Presents outstanding translations of the Greek philosopher's works by leading British and American scholars of the last century.

The edition includes a select bibliography, a synopsis of each book, a glossary of terms, a glossary and index of names, and a general index.

The second edition of _Five Dialogues_ presents G. M. A. Grube's distinguished translations, as revised by John Cooper for Plato, _Complete Works_. A number of new or expanded footnotes are also included along with an updated bibliography.

The Phaedo is acknowledged to be one of Plato's greatest masterpieces, showing him both as a philosopher and as a dramatist at the height of his powers. For its moving account of the execution of Socrates, the Phaedo ranks among the supreme literary achievements of antiquity. It is also a seminal document for many ideas deeply ingrained in western culture, and provides one of the best introductions to Plato's thought. This new edition is a revised version of the (...) Clarendon Press translation, and is eminently suitable for readers new to Plato, and ideal for classroom use, thanks to the provision of Stephanus page and letter numbering. ABOUT THE SERIES: For over 100 years Oxford World's Classics has made available the widest range of literature from around the globe. Each affordable volume reflects Oxford's commitment to scholarship, providing the most accurate text plus a wealth of other valuable features, including expert introductions by leading authorities, helpful notes to clarify the text, up-to-date bibliographies for further study, and much more. (shrink)

The structure of derivations in natural deduction is analyzed through isomorphism with a suitable sequent calculus, with twelve hidden convertibilities revealed in usual natural deduction. A general formulation of conjunction and implication elimination rules is given, analogous to disjunction elimination. Normalization through permutative conversions now applies in all cases. Derivations in normal form have all major premisses of elimination rules as assumptions. Conversion in any order terminates.Through the condition that in a cut-free derivation of the sequent Γ⇒C, no inactive weakening (...) or contraction formulas remain in Γ, a correspondence with the formal derivability relation of natural deduction is obtained: All formulas of Γ become open assumptions in natural deduction, through an inductively defined translation. Weakenings are interpreted as vacuous discharges, and contractions as multiple discharges. In the other direction, non-normal derivations translate into derivations with cuts having the cut formula principal either in both premisses or in the right premiss only. (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.

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)

'What exactly is knowledge?' The Theaetetus is a seminal text in the philosophy of knowledge, and is acknowledged as one of Plato's finest works. Cast as a conversation between Socrates and a clever but modest student, Theaetetus, it explores one of the key issues in philosophy: what is knowledge? Though no definite answer is reached, the discussion is penetrating and wide-ranging, covering the claims of perception to be knowledge, the theory that all is in motion, and the perennially tempting (...) idea that knowledge and truth are relative to different individuals or states. The inquirers go on to explore the connection between knowledge and true judgement, and the famous threefold definition of knowledge as justified true belief. Packed with subtle arguments, the dialogue is also a work of literary genius, with an unforgettable portrait of Socrates as a midwife of wisdom. This new edition uses the acclaimed translation by John McDowell. It includes a valuable introduction that locates the work in Plato's oeuvre, and explains some of the competing interpretations of its overall meaning. The notes elucidate Plato's arguments and draw connections within the work and with other philosophical discussions. ABOUT THE SERIES: For over 100 years Oxford World's Classics has made available the widest range of literature from around the globe. Each affordable volume reflects Oxford's commitment to scholarship, providing the most accurate text plus a wealth of other valuable features, including expert introductions by leading authorities, helpful notes to clarify the text, up-to-date bibliographies for further study, and much more. (shrink)

Gentzen writes in the published version of his doctoral thesis Untersuchungen über das logische Schliessen that he was able to prove the normalization theorem only for intuitionistic natural deduction, but not for classical. To cover the latter, he developed classical sequent calculus and proved a corresponding theorem, the famous cut elimination result. Its proof was organized so that a cut elimination result for an intuitionistic sequent calculus came out as a special case, namely the one in which the sequents have (...) at most one formula in the right, succedent part. Thus, there was no need for a direct proof of normalization for intuitionistic natural deduction. The only traces of such a proof in the published thesis are some convertibilities, such as when an implication introduction is followed by an implication elimination [1934–35, II.5.13]. It remained to Dag Prawitz in 1965 to work out a proof of normalization. Another, less known proof was given also in 1965 by Andres Raggio.We found in February 2005 an early handwritten version of Gentzen's thesis, with exactly the above title, but with rather different contents: Most remarkably, it contains a detailed proof of normalization for what became the standard system of natural deduction. The manuscript is located in the Paul Bernays collection at the ETH-Zurichwith the signum Hs. 974: 271. Bernays must have gotten it well before the time of his being expelled from Göttingen on the basis of the racial laws in April 1933. (shrink)

Plato's dialogues frequently treat several topics and show their connection to each other. The Phaedrus is a model of that skill because of its seamless progression from examples of speeches about the nature of love to mythical visions of human nature and destiny to the essence of beauty and, finally, to a penetrating discussion of speaking and writing. It ends with an examination of the love of wisdom as a dialectical activity in the human mind. Phaedrus lures Socrates outside (...) the walls of Athens, where he seldom goes, by promising to share a new work by his friend and mentor Lysias, a famous writer of speeches. This dialogue provides a powerful example of the dialectical writing that Plato uses to manifest ideas that are essential to human existence and to living a good life. The Phaedrus shows how oral and written forms of language relate to each other and to philosophy. It simultaneously embodies the entire process in some of the greatest poetry ever written. (shrink)

Plato's Republic, one of the great works in the history of philosophy, is presented here as it was written - as a dramatic performance exploring various perspectives on justice, truth, knowledge, and the good. Plato wrote each book of The Republic to be performed by actors playing the characters of Socrates, Glaucon, Adeimantus, Thrasymachus, and the others. When Book One was performed, he then invited his students—the brightest and best young people in Athens—to respond to each and every (...) argument, issue, and question posed by the characters. Rather than passively listening, they were lured into the process and challenged to evaluate and improve on the ideas presented in the performance. Based on their responses, Plato then wrote Book Two. The same process was repeated, and Book Three was generated. In this way all ten books evolved as part of a dynamic and creative dialectic intended to take place in the souls of each and every participant—including Plato himself. This dramatized version is an adaptation of the Benjamin Jowett translation. (shrink)

With a masterful sense of the place of rhetoric in both thought and practice and an ear attuned to the clarity, natural simplicity, and charm of Plato's Greek prose, James H. Nichols Jr., offers precise yet unusually readable translations of two great Platonic dialogues on rhetoric. The Gorgias presents an intransigent argument that justice is superior to injustice: To the extent that suffering an injustice is preferable to committing an unjust act. The dialogue contains some of Plato's most (...) significant and famous discussions of major political themes, and focuses dramatically and with unrivaled intensity on Socrates as a political thinker and actor. Featuring some of Plato's most soaringly lyrical passages, the Phaedrus investigates the soul's erotic longing and its relationship to the whole cosmos, as well as inquiring into the nature of rhetoric and the problem of writing. Nichols's attention to dramatic detail brings the dialogues to life. Plato's striking variety in conversational address is carefully reproduced, as is alteration in tone and implication even in the short responses. The translations render references to the gods accurately and non-monotheistically for the first time, and include a fascinating variety of oaths and invocations. A general introduction on rhetoric from the Greeks to the present shows the problematic relation of rhetoric to philosophy and politics, states the themes that unite the two dialogues, and outlines interpretive suggestions that are then developed more fully for each dialogue. The twin dialogues reveal both the private and the political rhetoric emphatic in Plato's philosophy, yet often ignored in commentaries on it. Nichols believes that Plato's thought on rhetoric has been largely misunderstood, and he uses his translations as an opportunity to reconstruct the classical position on right relations between thought and public activity. (shrink)

Gentzen writes in the published version of his doctoral thesis Untersuchungen über das logische Schliessen that he was able to prove the normalization theorem only for intuitionistic natural deduction, but not for classical. To cover the latter, he developed classical sequent calculus and proved a corresponding theorem, the famous cut elimination result. Its proof was organized so that a cut elimination result for an intuitionistic sequent calculus came out as a special case, namely the one in which the sequents have (...) at most one formula in the right, succedent part. Thus, there was no need for a direct proof of normalization for intuitionistic natural deduction. The only traces of such a proof in the published thesis are some convertibilities, such as when an implication introduction is followed by an implication elimination [1934–35, II.5.13]. It remained to Dag Prawitz in 1965 to work out a proof of normalization. Another, less known proof was given also in 1965 by Andres Raggio.We found in February 2005 an early handwritten version of Gentzen's thesis, with exactly the above title, but with rather different contents: Most remarkably, it contains a detailed proof of normalization for what became the standard system of natural deduction. The manuscript is located in the Paul Bernays collection at the ETH-Zurichwith the signum Hs. 974: 271. Bernays must have gotten it well before the time of his being expelled from Göttingen on the basis of the racial laws in April 1933. (shrink)

This pedagogical reader of the Greek text of Plato?s Gorgias, originally published for students in Victorian England, is an immensely helpful textbook for the student of the Greek language and literature. Edited by the prominent W. H. Thompson.

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)

A fluent and accurate new translation of the dialogue that, all of Plato's works, has seemed to speak most directly to the interests of contemporary analytical philosophers. White's extensive introduction explores the dialogue's center themes, its connection with related discussions in other dialogues, and its implication for the interpretation of Plato's metaphysics.

ABSTRACTThough the perennial problem of consciousness has outlasted the idealists, the reductivist turn in contemporary naturalistic philosophy of mind and the non-reductivist reactions to it provoke us to re-think post-Kantian idealism. Fichte's Wissenschaftslehre makes for a classical case of non-reductivist approach to mind and his critique of ‘dogmatism’ is all the more relevant in this context. This article contains four sections. The first section is an introduction that explains why post-Kantian idealism is relevant to contemporary philosophy of mind. The second (...) section pinpoints the placement issue that confronts not only current philosophers but also partially motivated Fichte's own philosophy. The third section is a short but essential remark about the normative and practical valence of ‘knowledge’ and ‘science’ in Fichte's traditional understanding of them. In the fourth section, I provide a reconstructive analysis of Fichte's understanding and critique of physicalism. Fichte's argument can be analyzed into two horns with each targeting reductivism and epiphenomenalism respectively. The final section is a brief but positive exposition on a necessary feature, namely reflexivity, of mind and the first-person perspective. Fichte's appropriation of intellectual intuition exemplifies a non-representationalist picture that connects content transparency with the active nature of mind. (shrink)

Ion -- Meno (Menon) -- Symposium (The banquet) -- The republic -- The apology (The defence of Socrates) -- Crito (Criton) -- Phaedo (Phaidon) -- The Greek alphabet -- Pronouncing index.

A normalization procedure is given for classical natural deduction with the standard rule of indirect proof applied to arbitrary formulas. For normal derivability and the subformula property, it is sufficient to permute down instances of indirect proof whenever they have been used for concluding a major premiss of an elimination rule. The result applies even to natural deduction for classical modal logic.

'The god wanted everything to be good, marred by as little imperfection as possible.'Timaeus, one of Plato's acknowledged masterpieces, is an attempt to construct the universe and explain its contents by means of as few axioms as possible. The result is a brilliant, bizarre, and surreal cosmos - the product of the rational thinking of a creator god and his astral assistants, and of purely mechanistic causes based on the behaviour of the four elements. At times dazzlingly clear, at (...) times intriguingly opaque, this was state-of-the-art science in the middle of the fourth century BC. The world is presented as a battlefield of forces that are unified only by the will of God, who had to do the best he could with recalcitrant building materials.The unfinished companion piece, Critias, is the foundational text for the story of Atlantis. It tells how a model society became corrupt, and how a lost race of Athenians defeated the aggression of the invading Atlanteans. This new edition combines the clearest translation yet of these crucial ancient texts with an illuminating introduction and diagrams. (shrink)

This volume contains new translations of two dialogues of Plato, the Protagoras and the Meno, together with explanatory notes and substantial interpretive essays. Robert C. Bartlett's translations are as literal as is compatible with sound English style and take into account important textual variations. Because the interpretive essays both sketch the general outlines of the dialogues and take up specific theoretical or philosophic difficulties, they will be of interest not only to those reading the dialogues for the first time (...) but also to those already familiar with them. The Protagoras and the Meno are linked by the attention each pays to the idea of virtue: the latter dialogue focuses on the fundamental Socratic question, "What is virtue?"; the former on the specific virtue of courage, especially in its relation to wisdom. An appendix contains a short extract from Xenophon's Anabasis of Cyrus that vividly portrays the figure of Meno. (shrink)

This paper discusses different interpretations of probability in relation to determinism. It is argued that both objective and subjective views on probability can be compatible with deterministic as well as indeterministic situations. The possibility of a conceptual independence between probability and determinism is argued to hold on a general level. The subsequent philosophical analysis of recent advances in classical statistical mechanics (ergodic theory) is of independent interest, but also adds weight to the claim that it is possible to justify an (...) objective interpretation of probabilities in a theory having as a basis the paradigmatically deterministic theory of classical mechanics. (shrink)

"Gill's and Ryan's Parmenides is, simply, superb: the Introduction, more than a hundred pages long, is transparently clear, takes the reader meticulously through the arguments, avoids perverseness, and still manages to make sense of the dialogue as a whole; there is a fine selective bibliography; and those parts of the translation I have looked at in detail suggest that it too is very good indeed." --Christopher Rowe, _Phronesis_.

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)

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.

Recently Ekman gave a derivation in natural deduction such that it either contains a substantial redundant part or else is not normal. It is shown that this problem is caused by a non-normality inherent in the usual modus ponens rule.

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

Elementary geometry can be axiomatized constructively by taking as primitive the concepts of the apartness of a point from a line and the convergence of two lines, instead of incidence and parallelism as in the classical axiomatizations. I first give the axioms of a general plane geometry of apartness and convergence. Constructive projective geometry is obtained by adding the principle that any two distinct lines converge, and affine geometry by adding a parallel line construction, etc. Constructive axiomatization allows solutions to (...) geometric problems to be effected as computer programs. I present a formalization of the axiomatization in type theory. This formalization works directly as a computer implementation of geometry. (shrink)

The way from linearly written derivations in natural deduction, introduced by Jaskowski and often used in textbooks, is a straightforward root-first translation. The other direction, instead, is tricky, because of the partially ordered assumption formulas in a tree that can get closed by the end of a derivation. An algorithm is defined that operates alternatively from the leaves and root of a derivation and solves the problem.

Gentzen's “Untersuchungen” [1] gave a translation from natural deduction to sequent calculus with the property that normal derivations may translate into derivations with cuts. Prawitz in [8] gave a translation that instead produced cut-free derivations. It is shown that by writing all elimination rules in the manner of disjunction elimination, with an arbitrary consequence, an isomorphic translation between normal derivations and cut-free derivations is achieved. The standard elimination rules do not permit a full normal form, which explains the cuts in (...) Gentzen's translation. Likewise, it is shown that Prawitz' translation contains an implicit process of cut elimination. (shrink)