This book presents an English translation of a classic Russian text on duality theory for Heyting algebras. Written by Georgian mathematician Leo Esakia, the text proved popular among Russian-speaking logicians. This translation helps make the ideas accessible to a wider audience and pays tribute to an influential mind in mathematical logic. The book discusses the theory of Heyting algebras and closure algebras, as well as the corresponding intuitionistic and modal logics. The author introduces the key notion of a hybrid that (...) “crossbreeds” topology and order, resulting in the structures now known as Esakia spaces. The main theorems include a duality between the categories of closure algebras and of hybrids, and a duality between the categories of Heyting algebras and of so-called strict hybrids. Esakia’s book was originally published in 1985. It was the first of a planned two-volume monograph on Heyting algebras. But after the collapse of the Soviet Union, the publishing house closed and the project died with it. Fortunately, this important work now lives on in this accessible translation. The Appendix of the book discusses the planned contents of the lost second volume. (shrink)

Even after the masterly studies of Leo Sternbach following on the paper by Hilberg1 there are still some small points to be noted on the historical poems of George of Pisidia. In what follows I have, of course, presupposed a knowledge of Sternbach's work which has happily rendered superfluous the new text which he was to have edited for Methuen's Series of Byzantine Texts.

Leo Strauss articulates the conflict between reason and revelation as he explores Spinoza's scientific, comparative, and textual treatment of the Bible. Strauss compares Spinoza's Theologico-political Treatise and the Epistles, showing their relation to critical controversy on religion from Epicurus and Lucretius through Uriel da Costa and Isaac Peyrere to Thomas Hobbes. Strauss's autobiographical Preface, traces his dilemmas as a young liberal intellectual in Germany during the Weimar Republic, as a scholar in exile, and as a leader of American philosophical thought. (...) "[For] those interested in Strauss the political philosopher, and also those who doubt whether we have achieved the 'final solution' in respect to either the character of political science or the problem of the relation of religion to the state." -- Journal of Politics "A substantial contribution to the thinking of all those interested in the ageless problems of faith, revelation, and reason." -- Kirkus Reviews Leo Strauss (1899-1973) was the Robert Maynard Hutchins Distinguished Service Professor Emeritus of political science at the University of Chicago. His contributions to political science include The Political Philosophy of Hobbes, The City and the Man, What is Political Philosophy?, and Liberalism Ancient and Modern. (shrink)

The article which was published for the first and single time in 1939, is the starting point of Leo Strauss’ “esoteric” scholarship. While devoted to the investigation of Xenophon’s treatise called Constitution of the Lacedemonians the article, using it as an example, shows reasons, techniques, and the meaning of writing “between the lines”. Strauss sequentially shows how Xenophon hides his critique of the Spartan constitution behind the facade of an encomium. But what may be even more important, in the piece (...) Strauss clearly tries to overcome the established 19th-century view that Xenophon was a mediocre and charged with laconophilia historian; he tries to reinstate Xenophon’s position as that of a serious thinker: a Socratic philosopher. He shows how meticulously Xenophon studies the Spartan constitution and that this apparently very successful and very stable regime, in fact, deserves serious politico-philosophic critique. Thereby he partially reveals the essence of classical political philosophy to careful readers. (shrink)

Leo Strauss's Philosophy and Law contains a groundbreaking study of the political philosophy of Maimonides and his Islamic predecessors, and it offers an argument on behalf of that philosophy which is also a profound critique of modern philosophy. Here is an entirely new and complete English translation of Strauss's work, which takes as its ideal the exacting standards of accuracy that Strauss himself emphasized in his own work. It includes a prefatory essay introducing the argument of each of the four (...) sections of Philosophy and Law. This is a fresh and challenging treatment of the perennial conflict between reason and revelation, or philosophy and religion. Strauss's key contention in this book is that the most influential modern approaches to this conflict have run aground in ways that reflect their loss of key insights developed by the medieval philosophers of Islam and their Jewish pupils, especially Maimonides. Strauss challenges the modern view that scientific enlightenment must ultimately amount to atheism, and that therefore there can be no such thing as enlightened religion. Through a careful, original, and detailed treatment of central works of the medieval Islamic-Jewish tradition, especially Maimonides' Guide of the Perplexed, Strauss aims to recover their key insights into this question. (shrink)

This paper presents an argument against the A-Theory of time. Briefly, I shall contend that the A-Theorist has no explanation for why the present moment in particular has the metaphysical privilege she accords it, and that this puts the theory at a disadvantage. In what follows, I shall begin by presenting this argument. I will follow that with some potential explanations for why the present moment is privileged and reasons militating against them, in addition to some other possible objections to (...) my argument and my responses to them. The conclusion will be that the A-Theorist fails to provide either an obvious or a theoretical explanation of the present time’s privileged status and is thereby at a theoretical disadvantage to theories that do not posit a metaphysically privileged present time. Topics covered include the purported analogy between times and worlds, the possibility that times are individuated by what is true at them, and the semantic status of titles for date-times. (shrink)

Die Quellen der Aristoteles-Rezeption bzw. der aristotelischen Logik im byzantinischen Mittelalter sind nur teilweise oder gering erforscht. Eine der wichtigen Autoritäten dieser Tradition stellt Leon Magentenos (12. Jh.?) dar. Magentenos war Metropolit von Mytilene sowie ein Gelehrter, der Kommentare zu allen sechs Traktaten des aristotelischen Organon (Categoriae, De Interpretatione, Analytica Priora, Analytica Posteriora, Topica, Sophistici Elenchi) verfasst hat. Hier wird die kritische Edition des Kommentars zum zweiten Buch der Ersten Analytik zusammen mit seiner Übersetzung ins Englische vorgelegt. Untersucht werden auch (...) die dem Kommentar angehängten syllogistischen Diagramme. Kommentare zu Analytica Priora II nach der Spätantike und vor Magentenos waren eher eine Rarität, daher ist sein Kommentar eine wichtige Quelle für alle Forscher, die sich mit der Geschichte der byzantinischen Logik und der aristotelischen Kommentierung befassen. (shrink)

Among the central meanings in Büchner's Woyzeck, there is one that comes clear only when we read the play in the context of the history of ideas—specifically in the light of certain currents of thought about human history and eschatology. Aspects of the play's expression are thereby elucidated, that are forcefully brought forward through the organization and compositional procedures of Berg's Wozzeck. Near the end of the long third scene of the opera, Wozzeck appears suddenly at Marie's window and alludes (...) cryptically to the mysterious signs that had come to him in the field the scene before, confiding to her that he is "on the track of something big." As those signs had first been presented through Wozzeck's eyes, they seemed like the imaginings and fears of a simple man about Freemasons and who knows what other objects of superstition, But now in the third scene he gives them a scriptural context, as though through a sudden insight: "Isn't it written, 'And behold, the smoke went up from the land, as the smoke from a furnace'?" What Wozzeck has recalled here is a passage in the Book of Genesis, chapter 19: "Then the Lord rained upon Sodom brimstone and fire from the Lord out of heaven. . . . and, behold, the smoke went up from the Land as the smoke from a furnace." The image is repeated in the New Testament Book of Revelation , chapter 9: "And the fifth angel sounded, and I saw a star fall from heaven unto the earth; and to him was given the key of the bottomless pit; and there arose a smoke out of the pit as the smoke of the great furnace; and the sun and the air were darkened by reason of the smoke of the pit." Both passages are about a holocaust visited by a wrathful God upon a corrupt and debauched people, and that is the idea that begins to form in Wozzeck's mind as he stands for the first time on the stage before his mistress. And he asks, "What will it all come to?" The answer to this thematic question lies in the strange unfolding of the drama, pressed forward by forces that lie, as Büchner had once put it, "Outside of ourselves"1 and by Wozzeck, who guarantees the outcome as he imagines himself becoming aware of what it must be. · 1. Letter to his family, February 1834: "I scorn no one, least of all because of his understanding or his education, for it lies in no one's power not to become a dumbbell or a criminal—because we have all become alike through like circumstances, and because the circumstances lie outside of ourselves . . ." Werner Lehmann, George Büchner: Sämtliche Werke und Briefe , 2:422. Leo Treitler, professor and chairman of the department of music at the State University of New York at Stony Brook, is the author of, among other works, "Dufay the Progressive" and "Homer and Gregory: The Transmission of Epic Poetry and Plainchant.". (shrink)