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.

We show that there exists a properly Σ2 minimal degree b, and moreover that b can be chosen to join with 0′ to 0″ – so that b is a 0″ complement for every degree a such that 0′ ≤ a < 0″.

We prove that there exists a nonzero recursively enumerable Turing degree possessing a strong minimal cover.

Computability theory concerns information with a causal–typically algorithmic–structure. As such, it provides a schematic analysis of many naturally occurring situations. Emil Post was the first to focus on the close relationship between information, coded as real numbers, and its algorithmic infrastructure. Having characterised the close connection between the quantifier type of a real and the Turing jump operation, he looked for more subtle ways in which information entails a particular causal context. Specifically, he wanted to find simple relations on reals (...) which produced richness of local computability-theoretic structure. To this extent, he was not just interested in causal structure as an abstraction, but in the way in which this structure emerges in natural contexts. Post’s programme was the genesis of a more far reaching research project. In this article we will firstly review the history of Post’s programme, and look at two interesting developments of Post’s approach. The first of these developments concerns the extension of the core programme, initially restricted to the Turing structure of the computably enumerable sets of natural numbers, to the Ershov hierarchy of sets. The second looks at how new types of information coming from the recent growth of research into randomness, and the revealing of unexpected new computability-theoretic infrastructure. We will conclude by viewing Post’s programme from a more general perspective. We will look at how algorithmic structure does not just emerge mathematically from information, but how that emergent structure can model the emergence of very basic aspects of the real world. (shrink)

Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary (...) computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The book includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable and lively way. (shrink)

The Planteome project provides a suite of reference and species-specific ontologies for plants and annotations to genes and phenotypes. Ontologies serve as common standards for semantic integration of a large and growing corpus of plant genomics, phenomics and genetics data. The reference ontologies include the Plant Ontology, Plant Trait Ontology, and the Plant Experimental Conditions Ontology developed by the Planteome project, along with the Gene Ontology, Chemical Entities of Biological Interest, Phenotype and Attribute Ontology, and others. The project also provides (...) access to species-specific Crop Ontologies developed by various plant breeding and research communities from around the world. We provide integrated data on plant traits, phenotypes, and gene function and expression from 95 plant taxa, annotated with reference ontology terms. (shrink)

We prove the following three theorems on the enumeration degrees of ∑20 sets. Theorem A: There exists a nonzero noncuppable ∑20 enumeration degree. Theorem B: Every nonzero Δ20enumeration degree is cuppable to 0′e by an incomplete total enumeration degree. Theorem C: There exists a nonzero low Δ20 enumeration degree with the anticupping property.

The Plant Ontology (PO; http://www.plantontology.org/) is a publicly-available, collaborative effort to develop and maintain a controlled, structured vocabulary (“ontology”) of terms to describe plant anatomy, morphology and the stages of plant development. The goals of the PO are to link (annotate) gene expression and phenotype data to plant structures and stages of plant development, using the data model adopted by the Gene Ontology. From its original design covering only rice, maize and Arabidopsis, the scope of the PO has been expanded (...) to include all green plants. The PO was the first multi-species anatomy ontology developed for the annotation of genes and phenotypes. Also, to our knowledge, it was one of the first biological ontologies that provides translations (via synonyms) in non-English languages such as Japanese and Spanish. There are about 2.2 million annotations linking PO terms to over 110,000 unique data objects representing genes or gene models, proteins, RNAs, germplasm and Quantitative Traits Loci (QTLs) from 22 plant species. In this paper, we focus on the plant anatomical entity branch of the PO, describing the organizing principles, resources available to users, and examples of how the PO is integrated into other plant genomics databases and web portals. We also provide two examples of comparative analyses, demonstrating how the ontology structure and PO-annotated data can be used to discover the patterns of expression of the LEAFY (LFY) and terpene synthase (TPS) gene homologs. (shrink)

We show that every nonzero $\Delta _{2}^{0}$ e-degree bounds a minimal pair. On the other hand, there exist $\Sigma _{2}^{0}$ e-degrees which bound no minimal pair.

A proof is given that 0′ is definable in the structure of the degrees of unsolvability. This answers a long-standing question of Kleene and Post, and has a number of corollaries including the definability of the jump operator.

Turing’s paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure comprehensively hosting causality at the physical level and beyond. On the other, it can give an insight into the way in which higher order information arises and leads to loss of computational control—while demonstrating how the control can be re-established, in special circumstances, via suitable type reductions. (...) We examine the classical computational framework more closely than is usual, drawing out lessons for the wider application of information–theoretical approaches to characterizing the real world. The problem which arises across a range of contexts is the characterizing of the balance of power between the complexity of informational structure and the means available to bring this information back into the computational fold. We proceed via appropriate mathematical modelling to a more coherent view of the computational structure of information, relevant to a wide spectrum of areas of investigation. (shrink)

History ended, according to Hegel according to Kojève, with the establishment and proliferation in Europe of states organized along Napoleonic lines: rational, bureaucratic, homogenous, atheist. This state lives in some tension with the popular slogan that helped give it birth: Liberty, Equality, Fraternity. But there is now also totalitarianism – the only new kind of regime, according to Arendt, created since the national state. Man is now in charge of nature, technology, and society; much of political life has become a (...) gavotte elaborating the meaning of the Napoleonic model. This interpretation, however opposed it seems to common sense, has been influential, particularly in France where the course of existentialism is unintelligible without taking it into account. Professor Cooper argues that it is inherently plausible and examines the arguments of Hegel and Kojève to reveal its consistency and explanatory power. And he applies it to more contemporary events – the experience of the atomic bomb, the Gulag system of extermination, and the growth of multinational corporations. The work concludes by pulling together the presuppositions and theories of the totalitarian system, the Hegelian version of the Napoleonic state, and our contemporary technological society. Overall, the reader will find here a complete and challenging presentation of how the modern world understands its collective life. (shrink)

Although his contributions to philosophy are revered and his writings have been collected, Eric Voegelin’s persona will inevitably fade with the memories of those who knew him. This book preserves the human element of Voegelin by capturing those valuable personal recollections. Barry Cooper and Jodi Bruhn conducted intensive interviews with Voegelin’s wife, his closest friends, and his first-generation students—many of whom have since passed on—in order to bring to print everything important about his life and personality. American scholars (...) will especially appreciate the glimpses provided by Voegelin’s German colleagues into his life in Munich, as well as the thoughts of his students in Vienna. Reflections of people such as Paul Caringella, Bruno Schlesinger, and Heinz Barazon capture Voegelin’s greatness and shortcomings alike and also shed new light on his philosophical quest for truth. By descending progressively further into the past, the book takes readers deeper into the essence of Voegelin as reminiscences become more dramatic. Ranging widely from America back to Germany—with recollections of Gestapo intimidation and eventual emigration—the accounts interweave episodes of pathos, humor, fear, rivalry, and ambition. We witness Voegelin’s persistent and partly self-imposed communication problems and impatience with administrative duties, his respect for prudent political actors and public servants, and his genuine affection not only for his colleagues and best students but also for diligent secretaries and empathetic nurses. Through these recollections, key elements of his personality repeatedly emerge: his intelligence, optimism, and integrity, combined with an acute perception of the significance of his work. This is the most revealing and comprehensive biographical work yet available on a man known to be captivating as a thinker—and now shown to be equally fascinating as a human being. His own publications attest to his mind and methods; _Voegelin Recollected_ provides a deeper understanding of the man himself. (shrink)

In addition to gestalt psychology and phenomenology, merleau-ponty's first book was influenced decisively by hegel. more precisely, it is argued that his critical remarks concerning reflexology as well as idealism and empiricism were inspired in large measure by the interpretation of hegel that merleau-ponty learned from alexandre kojeve.

This important new work is a major analysis of the foundation of Eric Voegelin's political science.

We say that a computably enumerable (c.e.) degree b is a Lachlan nonsplitting base (LNB), if there is a computably enumerable degree a such that a > b, and for any c.e. degrees w,v ≤ a, if a ≤ w or; v or; b then either a ≤ w or; b or a ≤ v or; b. In this paper we investigate the relationship between bounding and nonbounding of Lachlan nonsplitting bases and the high /low hierarchy. We prove that there (...) is a non-Low2 c.e. degree which bounds no Lachlan nonsplitting base. (shrink)

*Introduction by Joseph R. Strayer\n(ix-x) Not that Bloch was the greatest French historian of his generation, though he would certainly rank high in any list. Not even that he was the most widely read—others excelled in that art of combining exact knowledge with readability which has distinguished French scholarship for many years. Others have talked about the narrowness of purely political history, the evils of excessive specialization, and the unreality of the conventional periodization of history—without ever leaving their own limited (...) fields. Bloch not only said that history was a whole, that no period and no topic could be understood except in relation to other periods and topics, but he constantly taught [p.x] and wrote in accordance with this belief. …He worked constantly for a “wider, more human history,” for a history which described how and why people live and work together. He saw life as a whole, as a complicated interplay of ideals and realities, of conscious innovation and unconscious conservation. … Throughout the two volumes he sought, above everything else, to understand and explain the state of mind and the habits of life which could produce and support feudal organization.\n(32-33) It is very like the illusion of certain old etymologiests who thought they had said all when they set down the oldest known meaning of a word opposite its present sense, having shown… As if the main problem were not to understand how and why the transition had taken place. As if, above all, the meaning of any word were influenced more by its own past than by the contemporary state of the vocabulary which, in its turn, is determined by the social conditions of the moment. [Y: think about this when I give the meanings of sirhak]\n(64-65) …every historical research supposes that the inquiry has a direction at the very first step. In the beginning, there must be the guiding spirit. Mere passive observation, even supposing such a thing were possible, has never contributed anything productive to any science. \n(71) Every historical book worthy of the name oought to include a chapter, or if one prefers, a series of paragraphs inserted at turning points in the development, which might almost entitled: “How can I know what I am about to say?” I am persuaded that even the lay reader would experience an actual intellectual pleasure in examining these “confessions.”. (shrink)

It is shown that there exists a low2 Harrington non-splitting base-that is, a low2 computably enumerable (c.e.) degree a such that for any c.e. degrees x, y, if $0' = x \vee y$ , then either $0' = x \vee a$ or $0' = y \vee a$ . Contrary to prior expectations, the standard Harrington non-splitting construction is incompatible with the $low_{2}-ness$ requirements to be satisfied, and the proof given involves new techniques with potentially wider application.

Numerous studies have examined technological advances and their effects on industry, urbanization, social and economic shifts in power and expertise. Action into Nature assesses technology as the constitutional or political essence of the contemporary world.

Consciousness and Politics begins with an analysis of the problem of the historicity of truth as it was formulated shortly before Voegelin abandoned his eight-volume History of Political Ideas. The analysis then follows a more or less chronological path, discussing the arguments developed in The New Science of Politics, Voegelin's most famous book, the differentiation of consciousness and the problems of myth and nature as presented in the early volumes of Order and History. Starting in the 1960s, Voegelin began a (...) lengthy argument in several volumes that resumed his concern with the philosophy of consciousness, which he had outlined in his early writings, and its connection to what we conventionally call philosophy of history. Voegelin's late and often difficult essays, lectures, and the final volume of Order and History, many scholars have noticed, emphasize the meditative origins of his political science and, more broadly, of philosophy. The concluding chapters analyze this subject-matter and a perennial question that so many of Voegelin's readers have raised: what is the relation of his political science or philosophy to Christianity? (shrink)

Comparative Political Philosophy: Studies Under the Upas Tree examines four major traditions of political philosophy and discusses similarities in their key ideas and assumptions. An intellectually daring enterprise, this fascinating volume focuses on key texts from Chinese, Indian, Western and Islamic political philosophy.