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).

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)

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)

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)

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)

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.

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.

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)

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)

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)

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)

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

The essays in this collection explore the idea that discursive norms-the norms governing our thought and talk-are profoundly social. Not only do these norms govern and structure our social interactions, but they are sustained by a variety of social and institutional structures. The chapters are divided into three thematic sections. The first offers historical perspectives on discursive norms, including a chapter by Robert Brandom on the way Hegel transformed Kant's normativist approach to representation by adding both a social and a (...) historicist dimension to it. Section II features four chapters that examine the sociality of normativity from within a broadly naturalistic framework. The third and final section focuses on the social dimension of linguistic phenomena such as online speech acts, oppressive speech, and assertions. The Social Institution of Discursive Norms will be of interest to scholars and advanced students working in philosophy of language, philosophy of mind, and social philosophy. (shrink)

The twenty-first century so far has seen the global rise of authoritarian populism, systematic racism, and dogmatic metaphysics. Even though these events demonstrate the growth of an age of 'unreason', in this original and compelling book John Roberts resists the assumption that such thinking displays an unthinking irrationality or loss of reason; instead he asserts that an important feature of modern reactionary politics is that it offers a supposedly convincing integration of the particular and the universal. This move is (...) defined by what Roberts calls the 'reasoning of unreason' and has deep roots in the history of Western thought and politics. Tracing the dark history of enlightenment-disenlightenment, John Roberts explores 'the reasoning of unreason' across centuries from Aquinas, William of Ockham, the most important treatise on witchcraft Malleus Maleficarum, Locke, Kant, and Count Arthur de Gobineau, to Social Darwinism, Nazism, Carl Schmitt, Leo Strauss, and Friedrich von Hayek. Roberts provides a new set of philosophical-political tools to understand the formation and denigration of the rational subject and the current reinvestment in various forms of political unreason globally. The Reasoning of Unreason is the first book to draw on the philosophy of reason, political philosophy, political theory and political history, in order to produce a dialectical account of the 'making of reason' internal to the forces of unreason and the limits of reason. (shrink)

The essays in this collection explore the idea that discursive norms--the norms governing our thought and talk--are profoundly social. Not only do these norms govern and structure of social interactions, but they are sustained by a variety of social and institutional structures. The chapters are divided into three thematic sections. The first offers historical perspectives on discursive norms, including a chapter by Robert Brandom on the way Hegel transformed Kant's normativist approach to representation by adding both a social and a (...) historicist dimension to it. Section II features four chapters that examine the sociality of normativity from within a broadly naturalistic framework. The third and final section focuses on linguistic phenomena such as online speech acts, oppressive speech, and assertions. The Social Institution of Discursive Norms will be of interest to scholars and advanced students working in philosophy of language, philosophy of mind, and social philosophy. (shrink)

Plato and the trial of Socrates -- What is philosophy? -- Euthyphro : defining philosophical terms -- The apology, Phaedo, and Crito : the trial, immortality, and death of Socrates -- Philosophy of religion -- Can we prove that God exists? -- St. Anselm : the ontological argument -- St. Thomas Aquinas : the cosmological argument -- William Paley : the teleological argument -- Blaisepascal : it is better to believe in God's existence than to deny it -- William James (...) : free choice is the basis of belief -- Does the idea of a good God exclude evil? -- Gottfried Wilhelm Leibniz : God can allow some evil -- David Hume : a good God would exclude evil -- Ethics -- Are ethics relative? -- Ruth Benedict : ethics are relative -- W.T. Stace : ethics are not relative -- Are humans always selfish? -- Humans are always selfish : Glaucon's challenge to Socrates -- James Rachels : humans are not always selfish -- Which is basic in ethics : happiness or obligation? -- Aristotle : happiness is living virtuously -- Jeremy Bentham : happiness is seeking the greatest pleasure for the greatest number of people -- Immanuel Kant : duty is prior to happiness -- Friedrich Nietzsche : happiness is having power -- Jean-Paul Sartre : existentialist ethics -- Rosemarie Tong : feminist ethics are different -- Contemporary moral problems : abortion, homosexuality, animal rights -- Jane English : are most abortions moral? -- Peter Singer : do animals have rights? -- Knowledge -- What is knowledge? -- Plato : knowledge is warranted, true belief -- What method is best for acquiring knowledge? -- Charles Sanders Peirce : four approaches to philosophy -- How do we acquire knowledge? -- René Descartes : knowledge is not ultimately sense knowledge -- John Locke : knowledge is ultimately sensed -- Immanuel Kant : knowledge is both rational and empirical -- How is truth established? -- Bertrand Russell : truth is established by correspondence -- Francis H. Bradley : truth is established by coherence -- William James : truth is established on pragmatic grounds -- Can we know the nature of causal relations? -- David Hume : cause means regular association -- David Hume : there are no possible grounds for induction -- Metaphysics -- Why is there something rather than nothing? -- Parmenides : being is uncaused -- Lao-Tzu : non-being is the source of being -- Is reality general or particular? -- Plato : universals are real -- David Hume : particulars are real -- Of what does reality consist? -- René Descartes : reality consists of mind and matter -- Paul Churchland : reality consists of matter -- George Berkeley : reality consists of ideas -- John Dewey : reality consists of mental and physical qualities -- Are humans free? -- Holbach : humans are determined -- Robert Kane : humans are free -- Social and political philosophy -- What is liberty? -- Fyodor Dostoevski : liberty and authority -- John Stuart Mill : liberty is independence from the majority's tyranny -- Martin Luther King, Jr. : liberty and racial prejudice -- Which government is best? -- Thomas Hobbes : monarchy is best -- John Locke : democracy is best -- Karl Marx : communism and nonalienated labor is best -- Alexis de Tocqueville : democracy can have serious problems -- Karl Popper : utopias lead to violence -- Aesthetics -- What constitutes the experience of beauty? -- Plotinus : beauty, sensuous, and ideal -- What is the function of art? -- Aristotle : the nature of tragedy -- Henri Bergson : the nature of comedy -- Philosophy and the good life -- Classic views of the good life -- Epicurus : Epicurus and the pleasant life -- Epictetus : Epictetus and the life of self-control -- What gives life meaning? -- Leo Tolstoy : faith provides life's meaning -- Albert Camus : each person determines his or her life's meaning -- What is the value of philosophy? -- Bertrand Russell : the value of philosophy. (shrink)

The paper illustrates how organic chemists dramatically altered their practices in the middle part of the twentieth century through the adoption of analytical instrumentation — such as ultraviolet and infrared absorption spectroscopy and nuclear magnetic resonance spectroscopy — through which the difficult process of structure determination for small molecules became routine. Changes in practice were manifested in two ways: in the use of these instruments in the development of ‘rule-based’ theories; and in an increased focus on synthesis, at the expense (...) of chemical analysis. These rule-based theories took the form of generalizations relating structure to chemical and physical properties, as measured by instrumentation. This ‘Instrumental Revolution’ in organic chemistry was two-fold: encompassing an embrace of new tools that provided unprecedented access to structures, and a new way of thinking about molecules and their reactivity in terms of shape and structure. These practices suggest the possibility of a change in the ontological status of chemical structures, brought about by the regular use of instruments. The career of Robert Burns Woodward provides the central historical examples for the paper. Woodward was an organic chemist at Harvard from 1937 until the time of his death. In 1965, he won the Nobel Prize in Chemistry. (shrink)