"First published in this translation 1955; second edition (revised) 1974; reprinted with additional revisions 1987; reissued with new Further Reading 2003; reissued with new introduction 2007"--T.p. verso.

"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_.

Together these two dialogues contain Plato’s most important work on poetry and beauty.

Drawing on his extensive classroom experience and linguistic expertise, Paul Ryan offers a commentary that is both rich in detail and—in contrast to earlier, more austere commentaries on the Phaedrus—fully engaging. Line by line, he explains subtle points of language, explicates difficulties of syntax, and brings out nuances of tone and meaning that students might not otherwise notice or understand.

This article examines the reasons why Plato endorses obedience to absolute, unchangeable laws, despite the fact that Plato refers to it as only the second best method of rule. Plato's use of the myth, his definition of statesmanship, and the dramatic elements of the dialogue, including its relationship to the Apology, are used to discern why Plato affirms a method of rule so different from that of the Republic. It is argued that Plato's primary concern (...) in the Statesman is practical. Rather than looking for the best constitution, Plato is looking for the best constitution that can actually be put into practice. (shrink)

Offering a unique and wide-ranging examination of the theory of knowledge, the new edition of this comprehensive collection deftly blends readings from the foremost classical sources with the work of important contemporary philosophical thinkers. Human Knowledge: Classical and Contemporary Approaches, 3/e, offers philosophical examinations of epistemology from ancient Greek and Roman philosophy (Plato, Aristotle, Sextus Empiricus); medieval philosophy (Augustine, Aquinas); early modern philosophy (Descartes, Locke, Leibniz, Berkeley, Hume, Reid, Kant); classical pragmatism and Anglo-American empiricism (James, Russell, Ayer, Lewis, Carnap, (...) Quine, Rorty); and other influential Anglo-American philosophers (Chisholm, Kripke, Moore, Wittgenstein, Strawson, Putnam). Organized chronologically and thematically, Human Knowledge, 3/e, features exceptionally broad coverage and nontechnical selections that are easily accessible to students. An ideal text for both undergraduate and graduate courses in epistemology, it is enhanced by the editors' substantial general introduction, section overviews, and up-to-date bibliographies. The third edition offers expanded selections on contemporary epistemology and adds selections by Thomas Reid, Richard Rorty, David B. Annis, Richard Feldman and Earl Conee, Ernest Sosa, Barry Stroud, and Louise M. Antony. Human Knowledge, 3/e, offers an unparalleled introduction to our ancient struggle to understand our own intellectual experience. (shrink)

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)

In his account of Plato’s ideas in the first book of the “Transcendental Dialectic”, “On the concepts of pure reason”, Kant, in describing how for Plato ideas were “archetypes of things themselves”, adds that these ideas “flowed from the highest reason, through which human reason partakes in them”.1 Later, in the section of the Transcendental Dialectic treating the “ideals of pure reason”, he again attributes to Plato the notion of a “divine mind” within which the “ideas” exist. (...) An “ideal”, Kant says, “was to Plato, an idea in the divine understanding”.2 But as the editors of the Cambridge University Press translation of the Critique of Pure Reason point out, the idea of a divine mind as container of the ideas was not Plato’s and did not originate until the “syncretistic Platonism from the period of the Middle Academy”. From there it “was later adopted by Platonists as diverse as Philo of Alexandria, Plotinus and St Augustine, and became fundamental to later Christian interpretations of Platonism”. (shrink)

In _ Plato's Camera_, eminent philosopher Paul Churchland offers a novel account of how the brain constructs a representation -- or "takes a picture" -- of the universe's timeless categorical and dynamical structure. This construction process, which begins at birth, yields the enduring background conceptual framework with which we will interpret our sensory experience for the rest of our lives. But, as even Plato knew, to make singular perceptual judgments requires that we possess an antecedent framework of (...) abstract categories to which any perceived particular can be relevantly assimilated. How that background framework is assembled in the first place is the motivating mystery, and the primary target, of Churchland's book. Unexpectedly, this neurobiologically grounded account of human cognition also provides a systematic story of how such low-level epistemological activities are integrated within an enveloping framework of linguistic structures and regulatory mechanisms at the social level. As Churchland illustrates, this integration of cognitive mechanisms at several levels has launched the human race on an epistemological adventure denied to all other terrestrial creatures. (shrink)

In _ Plato's Camera_, eminent philosopher Paul Churchland offers a novel account of how the brain constructs a representation -- or "takes a picture" -- of the universe's timeless categorical and dynamical structure. This construction process, which begins at birth, yields the enduring background conceptual framework with which we will interpret our sensory experience for the rest of our lives. But, as even Plato knew, to make singular perceptual judgments requires that we possess an antecedent framework of (...) abstract categories to which any perceived particular can be relevantly assimilated. How that background framework is assembled in the first place is the motivating mystery, and the primary target, of Churchland's book. Unexpectedly, this neurobiologically grounded account of human cognition also provides a systematic story of how such low-level epistemological activities are integrated within an enveloping framework of linguistic structures and regulatory mechanisms at the social level. As Churchland illustrates, this integration of cognitive mechanisms at several levels has launched the human race on an epistemological adventure denied to all other terrestrial creatures. (shrink)

A resume and analysis of Plato's writings whith synopses and critical comment.

Für Natorp selbst stand seine Arbeit an Plato in unmittelbarem Zusammenhang mit der Arbeit an seiner eigenen Philosophie; sosehr sein großes Buch sich als Hinführung zu Plato verstand, sosehr bildet die Ausarbeitung von Platos Ideenlehre auch einen originären Teil der Philosophie Paul Natorps. Die Sonderausgabe dieses Standardwerkes zur Philosophie Platons bietet den Text nach der zweiten Auflage von 1921.

Paul Moser's book defends what has been an unfashionable view in recent epistemology: the foundationalist account of knowledge and justification. Since the time of Plato philosophers have wondered what exactly knowledge is. This book develops a new account of perceptual knowledge which specifies the exact sense in which knowledge has foundations. The author argues that experiential foundations are indeed essential to perceptual knowledge, and he explains what knowledge requires beyond justified true beliefs. In challenging prominent sceptical claims that (...) we have no justified beliefs about the external world, the book outlines a theory of rational belief. (shrink)

Paul Moser's book defends what has been an unfashionable view in recent epistemology: the foundationalist account of knowledge and justification. Since the time of Plato philosophers have wondered what exactly knowledge is. This book develops a new account of perceptual knowledge which specifies the exact sense in which knowledge has foundations. The author argues that experiential foundations are indeed essential to perceptual knowledge, and he explains what knowledge requires beyond justified true beliefs. In challenging prominent sceptical claims that (...) we have no justified beliefs about the external world, the book outlines a theory of rational belief. (shrink)

This paper examines Nietzsche’s concept of unified agency. A widespread consensus has emerged in the secondary literature on three points: (1) Nietzsche’s notion of unity is meant to be an analysis of freedom; (2) unity refers to a relation between the agent’s drives or motivational states; and (3) unity obtains when one drive predominates and imposes order on the other drives. I argue that these claims are philosophically and textually indefensible. In contrast, I argue that (1′) Nietzschean unity is an (...) account of the distinction between genuine actions and mere behaviors, rather than between free and unfree actions; (2′) unity refers to a relation between drives and conscious thought; and (3′) unity obtains when the agent’s attitude toward her own action is stable under the revelation of further information about the action’s etiology. I show that Nietzsche develops this notion of unity by drawing on Plato’s and Schiller’s accounts of unified agency. (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)

In this paper I argue that Plato's Apology is the principal text on which Kierkegaard relies in arguing for the idea that Socrates is fundamentally an ironist. After providing an overview of the structure of this argument, I then consider Kierkegaard's more general discussion of irony, unpacking the distinction he draws between irony as a figure of speech and irony as a standpoint. I conclude by examining Kierkegaard's claim that the Apology itself is “splendidly suited for obtaining a clear (...) concept of Socrates' ironic activity,” considering in particular Kierkegaard's discussion of Socrates' remarks about death and his use of Friedrich Ast's commentary to help his readers to discover the irony that he contends runs throughout Socrates' defense speech. (shrink)

Originally published in German as Platon: Seinswahrheit und Lebenswirklichkeit 2d edn, 1954; 3d edn, 1964 by W. de Gruyter & Co., Berlin.

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)

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)

The Theaetetus is one of the most widely studied of any of the Platonic dialogues because its dominant theme concerns the significant philosophical question, what is knowledge? In this book Paul Stern provides a full-length treatment of its political character in relationship to this dominant theme. He argues that this approach sheds significant light on the distinctiveness of the Socratic way of life, with respect to both its initial justification and its ultimate character. More specifically, he argues that Socrates' (...) revolutionary decision to subject political life to philosophic reflection, the decision that leads directly to his trial and execution, is based on his awareness of the elusiveness of comprehensive knowledge and the implications of that elusiveness for the validity of philosophic inquiry. This view of Socrates' rationale has important consequences for our understanding of political philosophy and of the validity of the life of reason itself. (shrink)

In this book, Livingston develops the political implications of formal results obtained over the course of the twentieth century in set theory, metalogic, and computational theory. He argues that the results achieved by thinkers such as Cantor, Russell, Godel, Turing, and Cohen, even when they suggest inherent paradoxes and limitations to the structuring capacities of language or symbolic thought, have far-reaching implications for understanding the nature of political communities and their development and transformation. Alain Badiou's analysis of logical-mathematical structures forms (...) the backbone of his comprehensive and provocative theory of ontology, politics, and the possibilities of radical change. Through interpretive readings of Badiou's work as well as the texts of Giorgio Agamben, Jacques Lacan, Jacques Derrida, Gilles Deleuze, and Ludwig Wittgenstein, Livingston develops a formally based taxonomy of critical positions on the nature and structure of political communities. These readings, along with readings of Parmenides and Plato, show how the formal results can transfigure two interrelated and ancient problems of the One and the Many: the problem of the relationship of a Form or Idea to the many of its participants, and the problem of the relationship of a social whole to its many constituents. (shrink)

Supporters of G.W.F. Hegel's philosophy have largely shied away from relating his logic to modern symbolic or mathematical approaches. While it has predominantly been the non-Greek discipline of algebra that has informed modern mathematical logic, philosopher Paul Redding argues that the approaches of Plato and Aristotle to logic were deeply shaped by the arithmetic and geometry of classical Greek culture. And by ignoring the fact that Hegel's logic also has this deep mathematical dimension, conventional Hegelians have missed some (...) of Hegel's greatest insights. In Conceptual Harmonies, Redding develops an account of Hegel's logic against a classical and modern historical background that is rarely considered. He stresses Hegel's attention to the Platonic background of Aristotle's original syllogistic and beyond. He then links these Platonic elements to Leibniz's modern revitalization of the logical tradition and then to new forms of algebraic geometry emerging in Hegel's lifetime. Redding thereby reestablishes aspects of Hegel's philosophy that are essential if Hegel is to be taken as a thinker relevant not only to contemporary philosophy, but also to current philosophical conceptions of logic. (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 account of the famous trial of Socrates in 399 b.c., appeals to historians, philosophers, political scientists, and classicists. It is also essential reading for students of ancient Greek. Paul Allen Miller and Charles Platter provide running commentary, glosses of unfamiliar words, introductions that address historical and philosophical issues, and thought-provoking essays on each chapter.

This article examines the significance of the image of the Chimera which Socrates invites Glaucon to mould in Book IX of Republic. It argues that the image, when explicitly intended to represent the just and rationally autonomous individual soul, must also, in keeping with Socrates’ methodological procedure in the dialogue, correspond to a political structure. We argue that, as it cannot correspond to or represent the structure of the Kallipolis, the city this soul would correspond to would be the approximately (...) just polis from which the Kallipolis could emerge. The question thus arises as to what kind of individual or which class of persons each part of the tripartite soul can be assigned in a political context. We conclude that the answer supplied and best supported by the dialogue is a rule of the philosopher over a demos or tyrant through the intermediary aid of a rhetorician. (shrink)

Pre-Socratic -- Socrates (469-399 B.C.) -- Plato (429-347 B.C.) -- Existentialism -- Aristotle (384-322 B.C.) -- The ship of Theseus -- Francis Bacon (1561-1626) -- The cow in the field -- David Hume (1711-1776) -- Hedonism -- Prisoner's dilemma -- St. Thomas Aquinas (1225-1274) -- Hard determinism -- Jean-Jacques Rousseau (1712-1778) -- The trolley problem -- Realism -- Immanuel Kant (1724-1804) -- Dualism -- Utilitarianism -- John Locke (1632-1704) -- Empiricism versus Rationalism -- Georg Wilhelm Friedrich Hegel (1770-1831) -- (...) René Descartes (1596-1650) -- A-Theory -- The liar paradox -- Thomas Hobbes (1588-1679) -- Philosophy of language -- Metaphysics -- Jean-Paul Sartre (1905-1980) -- Free will -- Philosophy of humor -- The Enlightenment -- Friedrich Nietzsche (1844-1900) -- The Sorites paradox -- Ludwig Wittgenstein (1889-1951) -- Aesthetics -- Philosoph of culture -- Epistemology -- Twin Earth -- Arthur Schopenhauer (1788-1860) -- Karl Marx (1818-1883) -- Martin Heidegger (1889-1976) -- Voltaire (1694-1778) -- Relativism -- Eastern philosophy -- Avicenna (980-1037) -- Bertrand Russell (1872-1970) -- Phenomenology -- Nominalism -- Gottfried Wilhelm Leibniz (1646-1716) -- Ethics -- Philosophy of science -- Baruch Spinoza (1632-1677) -- Philosopy of religion. (shrink)