Robert I. Soare, Automorphisms of the Lattice of Recursively Enumerable Sets. Part I: Maximal Sets.Manuel Lerman, Robert I. Soare, $d$-Simple Sets, Small Sets, and Degree Classes.Peter Cholak, Automorphisms of the Lattice of Recursively Enumerable Sets.Leo Harrington, Robert I. Soare, The $\Delta^0_3$-Automorphism Method and Noninvariant Classes of Degrees.

The Anthropology of Sport and Human Movement represents a collection of work that reveals and explores the often times dramatic relationship of our biology and culture that is inextricably woven into a tapestry of movement patterns. It explores the underpinning of human movement, reflected in play, sport, games and human culture from an evolutionary perspective and contemporary expression of sport and human movement.

We give a proof of a theorem of Harrington that there is no orbit of the lattice of recursively enumerable sets containing elements of each nonzero recursively enumerable degree. We also establish some degree theoretical extensions.

The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, ε, such that the question of membership in this orbit is ${\Sigma _1^1 }$ -complete. This result and proof have a number of nice corollaries: the Scott rank of ε is $\omega _1^{{\rm{CK}}}$ + 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of ε; for all finite α ≥ 9, there is a properly $\Delta (...) _\alpha ^0 $ orbit (from the proof). (shrink)

We announce and explain recent results on the computably enumerable (c.e.) sets, especially their definability properties (as sets in the spirit of Cantor), their automorphisms (in the spirit of Felix Klein's Erlanger Programm), their dynamic properties, expressed in terms of how quickly elements enter them relative to elements entering other sets, and the Martin Invariance Conjecture on their Turing degrees, i.e., their information content with respect to relative computability (Turing reducibility).

In lieu of an abstract, here is a brief excerpt of the content:John Robert Leo CRITICISM OF CONSCIOUSNESS IN SHELLEY'S A DEFENCE OF POETRY IN his "Ode to Liberty" Shelley locates by encircling and enfolding metaphors a mythic Hellenic moment, one in which verse was yet "speechless" and philosophy still burdened with "lidless eyes." Greece— always for Shelley either the displaced Garden of prethematic unity or the mythic dream of integrated civic and aesthetic life—is about to inaugurate Athens and (...) the "wrinkled image" of historical consciousness.1 Poetry, thinking, and the tilling of an earth "to human use" are implicitly related and foreseen as destiny: from their enchanted caves Prophetic echoes flung dim melody. On the unapprehensive wild The vine, the corn, the olive mild, Grew savage yet, to human use unreconciled; And, like unfolded flowers beneath the sea, Like the man's dark thought in the infant's brain, Like aught that is which wraps what is to be, Art's deathless dreams lay veiled by many a vein Of Parian stone; and, yet a speechless child, Verse murmured, and Philosophy did strain Her lidless eyes for thee... (11. 49-60). Shelley could be describing the reading or speaking of a text, for poetic experience is an originating moment which unfolds our reflections and anticipations. Poetry elides speechlessness and the empty gaze. Its goings are all returnings, its experience is always inventive before meanings codify and resolve: "Every original language near to its source," we find in the Defence (p. 279), "is in itself the chaos of a cyclic poem; the copiousness of lexicography and the distinctions of grammar are the works of a later age and are merely the catalogue and the form of the creations of poetry." What was dark to experience is now illumined, 46 John Robert Leo47 as different regions in experience are uncovered or redistributed by language across our shifting horizons. Thus this bringing-foward-intoclarity, this moving of the previously inexpressed into articulation, is the pattern not only behind Shelley's view ofGreece producing a "sun-fire garlanded" Athens (1. 68), but also the more pervasive design describing other regarded experience. James Edie puts it this way: "We... can learn to make distinctions in our experience by attending to differences of meaning which are normally below the level of our own cultural threshold. By attending to a given region of experience, we can lower the differential thresholds already sedimented in our language almost indefinitely and make what was implicit in our experience more and more explicit."2 Edie's comments may be taken as responses to questions emerging from modernist readings of Shelley and other visionary poets—Blake, Hart Crane, or Charles Olson are instances—who sense the poetic project as a criticism of consciousness, within the lived body, as it struggles to make a world. How do language and the imagination consort in the critical regeneration of our lives? In what sorts of ways is renascence the uncovering and unfolding of an indefinite wholeness by the unlayering of fixed habits and attitudes? How does Shelley's Defence of Poetry, both a text on aesthetics and a reading of the world, suggest their alignment? What methods from critical discourse make Shelley's poetics present to our experience and thought? The adjustment of these issues is the task of the remainder of my article. First I examine Shelley's organization of consciousness into "reason" and "imagination" and trace the meanings of these functions in their immediate social context. A brief dispute with the reductive idealism of Platonic tradition allows for my third procedure, which is a phenomenological description of the imaginative field according to Husserl. Finally, I try to explicate Shelley's understanding of imaginative "decentering" within our experience. I Poetry and prose are saturated with references to phenomena. Texts refer to interior and exterior events (memory, rain), which are objects ofandfor consciousness. Shelley grasps this co-givenness of consciousness and world, their correlativity, as a condition revealed and strengthened by metaphor, which itself arrests us as "that of which we are speaking through words."3 But if it is the nature of language to be both perceptual and yet transcendental, both present and absent, it still exists as the imagination's voice in... (shrink)

Post in 1944 began studying properties of a computably enumerable set A such as simple, h-simple, and hh-simple, with the intent of finding a property guaranteeing incompleteness of A . From the observations of Post and Myhill , attention focused by the 1950s on properties definable in the inclusion ordering of c.e. subsets of ω, namely E = . In the 1950s and 1960s Tennenbaum, Martin, Yates, Sacks, Lachlan, Shoenfield and others produced a number of elegant results relating ∄-definable properties (...) of A , like maximal, hh-simple, atomless, to the information content of A . Harrington and Soare gave an answer to Post's program for definable properties by producing an ∄-definable property Q which guarantees that A is incomplete and noncomputable, but developed a new Δ 3 0 -automorphism method to prove certain other properties are not ∄-definable. In this paper we introduce new ∄-definable properties relating the ∄-structure of A to deg, which answer some open questions. In contrast to Q we exhibit here an ∄-definable property T which allows such a rapid flow of elements into A that A must be complete even though A may possess many other properties such as being promptly simple. We also present a related property NL which has a slower flow but fast enough to guarantee that A is not low, even though A may possess virtually all other related lowness properties and A may simultaneously be promptly simple. (shrink)

A set X of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. Let ε denote the structure of the computably enumerable sets under inclusion, $\varepsilon = (\{W_e\}_{e\in \omega}, \subseteq)$ . We previously exhibited a first order ε-definable property Q(X) such that Q(X) guarantees that X is not Turing complete (i.e., does not code complete information about c.e. sets). Here we show first that Q(X) implies that X has (...) a certain "slowness" property whereby the elements must enter X slowly (under a certain precise complexity measure of speed of computation) even though X may have high information content. Second we prove that every X with this slowness property is computable in some member of any nontrivial orbit, namely for any noncomputable A ∈ ε there exists B in the orbit of A such that X ≤ T B under relative Turing computability (≤ T ). We produce B using the Δ 0 3 -automorphism method we introduced earlier. (shrink)

By constructing a maximal incomplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees and of the ω-r.e. degrees.

This paper compares two explanations of the process by which human communication systems evolve: iterated learning and social collaboration. It then reports an experiment testing the social collaboration account. Participants engaged in a graphical communication task either as a member of a community, where they interacted with seven different partners drawn from the same pool, or as a member of an isolated pair, where they interacted with the same partner across the same number of games. Participants’ horizontal, pair‐wise interactions led (...) “bottom up” to the creation of an effective and efficient shared sign system in the community condition. Furthermore, the community‐evolved sign systems were as effective and efficient as the local sign systems developed by isolated pairs. Finally, and as predicted by a social collaboration account, and not by an iterated learning account, interaction was critical to the creation of shared sign systems, with different isolated pairs establishing different local sign systems and different communities establishing different global sign systems. (shrink)

By constructing a maximal incomplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees and of the ω-r.e. degrees.

A transcript of Leo Strauss’s key seminars on Plato’s Protagoras. This book offers a transcript of Strauss’s seminar on Plato’s Protagoras taught at the University of Chicago in the spring quarter of 1965, edited and introduced by renowned scholar Robert C. Bartlett. These lectures have several important features. Unlike his published writings, they are less dense and more conversational. Additionally, while Strauss regarded himself as a Platonist and published some work on Plato, he published little on individual dialogues. In (...) these lectures Strauss treats many of the great Platonic and Straussian themes: the difference between the Socratic political science or art and the Sophistic political science or art of Protagoras; the character and teachability of virtue, its relation to knowledge, and the relations among the virtues, courage, justice, moderation, and wisdom; the good and the pleasant; frankness and concealment; the role of myth; and the relation between freedom of thought and freedom of speech. In these lectures, Strauss examines Protagoras and the sophists, providing a detailed discussion of Protagoras as it relates to Plato’s other dialogues and the work of modern thinkers. This book should be of special interest to students both of Plato and of Strauss. (shrink)

_Examines the German and Jewish sources of Strauss's thought and the extent to which his philosophy can shed light on the crisis of liberal democracy._.

In this classic work, Leo Strauss examines the problem of natural right and argues that there is a firm foundation in reality for the distinction between right and wrong in ethics and politics. On the centenary of Strauss's birth, and the fiftieth anniversary of the Walgreen Lectures which spawned the work, _Natural Right and History_ remains as controversial and essential as ever. "Strauss... makes a significant contribution towards an understanding of the intellectual crisis in which we find ourselves... [and] brings (...) to his task an admirable scholarship and a brilliant, incisive mind."—John H. Hallowell, _American Political Science Review_ Leo Strauss was the Robert Maynard Hutchins Distinguished Service Professor Emeritus in Political Science at the University of Chicago. (shrink)

Leo Strauss is known to many people as a thinker of the right, who inspired hawkish views on national security and perhaps even advocated war without limits. Moving beyond gossip and innuendo about Strauss's followers and the Bush administration, this book provides the first comprehensive analysis of Strauss's writings on political violence, considering also what he taught in the classroom on this subject. In stark contrast to popular perception, Strauss emerges as a man of peace, favorably disposed to international law (...) and skeptical of imperialism - a critic of radical ideologies (right and left) who warns of the dangers to free thought and civil society when philosophers and intellectuals ally themselves with movements that advocate violence. Robert Howse provides new readings of Strauss's confrontation with fascist/Nazi jurist Carl Schmitt, his debate with Alexandre Kojève about philosophy and tyranny, and his works on Machiavelli and Thucydides and examines Strauss's lectures on Kant's Perpetual Peace and Grotius's Rights of War and Peace. (shrink)

On Tyranny is Leo Strauss's classic reading of Xenophon's dialogue, Hiero or Tyrannicus, in which the tyrant Hiero and the poet Simonides discuss the advantages and disadvantages of exercising tyranny. This edition includes a translation of the dialogue, a critique of the commentary by the French philosopher Alexandre Kojève, Strauss's restatement of his position in light of Kojève's comments, and finally, the complete Strauss-Kojève correspondence. "Through [Strauss's] interpretation Xenophon appears to us as no longer the somewhat dull and flat author (...) we know, but as a brilliant and subtle writer, an original and profound thinker. What is more, in interpreting this forgotten dialogue, Strauss lays bare great moral and political problems that are still ours." —Alexandre Kojève, Critique "On Tyranny is a complex and stimulating book with its 'parallel dialogue' made all the more striking since both participants take such unusual, highly provocative positions, and so force readers to face substantial problems in what are often wholly unfamiliar, even shocking ways." —Robert Pippin, History and Theory "Every political scientist who tries to disentangle himself from the contemporary confusion over the problems of tyranny will be much indebted to this study and inevitably use it as a starting point."—Eric Voegelin, The Review of Politics Leo Strauss (1899-1973) was the Robert Maynard Hutchins Distinguished Service Professor of Political Science at the University of Chicago. (shrink)

"-- M. J. Silverthorne,The Humanities Association Review Leo Strauss (1899-1973) was the Robert Maynard Hutchins Distinguished Service Professor Emeritus of ...

ExcerptAfter emigrating to the United States, Leo Strauss taught political philosophy for thirty years, first at the New School for Social Research in New York and then at the University of Chicago, before retiring at St. John's College. Richard Wolin observes that he “seems to have deeply mistrusted day-to-day politics—a very strange stance, to be sure, for someone who made his living teaching political philosophy.”1 But is it really so strange? What in his German Gymnasium education, or his participation in (...) the Zionist movement, would have prepared him for the peculiarities of day-to-day American politics? Strauss did not underestimate the…. (shrink)

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)