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)

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.

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.

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.

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)

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)

The Major Sub-degree Problem of A. H. Lachlan (first posed in 1967) has become a long-standing open question concerning the structure of the computably enumerable (c.e.) degrees. Its solution has important implications for Turing definability and for the ongoing programme of fully characterising the theory of the c.e. Turing degrees. A c.e. degree a is a major subdegree of a c.e. degree b > a if for any c.e. degree x, ${{\bf 0' = b \lor x}}$ if and only if (...) ${{\bf 0' = a \lor x}}$ . In this paper, we show that every c.e. degree b ≠ 0 or 0′ has a major sub-degree, answering Lachlan’s question affirmatively. (shrink)

We show that every nonzero Δ20, e-degree bounds a minimal pair. On the other hand, there exist Σ20, e-degrees which bound no minimal pair.

In this paper we examine a class of pairs of recursively enumerable degrees, which is related to the Slaman-Soare Phenomenon.

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.

We show that for any computably enumerable set A and any equation image set L, if L is low and equation image, then there is a c.e. splitting equation image such that equation image. In Particular, if L is low and n-c.e., then equation image is n-c.e. and hence there is no low maximal n-c.e. degree.

Although Responsible Conduct of Research training is common in the sciences, the effectiveness of RCR training is open to question. Three key factors appear to be particularly important in ensuring the effectiveness of ethics education programs: educational efforts should be tied to day-to-day practices in the field, educational efforts should provide strategies for working through the ethical problems people are likely to encounter in day-to-day practice, and educational efforts should be embedded in a broader program of on-going career development efforts. (...) This article discusses a complex qualitative approach to RCR training development, based on a sensemaking model, which strives to address the afore-mentioned training concerns. Ethnographic observations and prior RCR training served the purpose of collecting information specific to a multi-disciplinary and multi-university research center with the goal of identifying metacognitive reasoning strategies that would facilitate ethical decision-making. The extensive qualitative analyses resulted in the identification of nine metacognitive reasoning strategies on which future RCR training will be developed. The implications of the findings for RCR training in the sciences are discussed. (shrink)

We prove that there exists a noncappable enumeration degree strictly below 0' e.

We give a corrected proof of an extension of the Robinson Splitting Theorem for the d. c. e. degrees.

Integrity is a critical determinant of the effectiveness of research organizations in terms of producing high quality research and educating the new generation of scientists. A number of responsible conduct of research (RCR) training programs have been developed to address this growing organizational concern. However, in spite of a significant body of research in ethics training, it is still unknown which approach has the highest potential to enhance researchers’ integrity. One of the approaches showing some promise in improving researchers’ integrity (...) has focused on the development of ethical decision-making skills. The current effort proposes a novel curriculum that focuses on broad metacognitive reasoning strategies researchers use when making sense of day-to-day social and professional practices that have ethical implications for the physical sciences and engineering. This sensemaking training has been implemented in a professional sample of scientists conducting research in electrical engineering, atmospheric and computer sciences at a large multi-cultural, multi-disciplinary, and multi-university research center. A pre-post design was used to assess training effectiveness using scenario-based ethical decision-making measures. The training resulted in enhanced ethical decision-making of researchers in relation to four ethical conduct areas, namely data management, study conduct, professional practices, and business practices. In addition, sensemaking training led to researchers’ preference for decisions involving the application of the broad metacognitive reasoning strategies. Individual trainee and training characteristics were used to explain the study findings. Broad implications of the findings for ethics training development, implementation, and evaluation in the sciences are discussed. (shrink)

ABSTRACT BACKGROUND: The objective of this study was to identify factors motivating women to take part in endometriosis research and to determine if these factors differ for women participating in clinical versus basic science studies. METHODS: A consecutive series of 24 women volunteering for participation in endometriosis‐related research were asked to indicate, in their own words, why they chose to volunteer. In addition, the women were asked to rate, on a scale of 0 to 10, sixteen potentially motivating factors. The (...) information was gathered in the form of an anonymous self‐administered questionnaire. RESULTS: Strong motivating factors (mean score >8) included potential benefit to other women's health, improvement to one's own condition, and participation in scientific advancement. Weak motivating factors (mean score <3) included financial compensation, making one's doctor happy, and use of ‘natural’ products. No difference was detected between clinical and basic science study participants. CONCLUSION: This study is the first study to specifically investigate the factors that motivate women to take part in endometriosis research. Understanding why women choose to take part in such research is important to the integrity of the informed consent process. The factors most strongly motivating women to participate in endometriosis research related to improving personal or public health; the weakest, to financial compensation and pleasing the doctor. (shrink)

Although Responsible Conduct of Research (RCR) training is common in the sciences, the effectiveness of RCR training is open to question. Three key factors appear to be particularly important in ensuring the effectiveness of ethics education programs: (1) educational efforts should be tied to day-to-day practices in the field, (2) educational efforts should provide strategies for working through the ethical problems people are likely to encounter in day-to-day practice, and (3) educational efforts should be embedded in a broader program of (...) on-going career development efforts. This article discusses a complex qualitative approach to RCR training development, based on a sensemaking model, which strives to address the afore-mentioned training concerns. Ethnographic observations and prior RCR training served the purpose of collecting information specific to a multi-disciplinary and multi-university research center with the goal of identifying metacognitive reasoning strategies that would facilitate ethical decision-making. The extensive qualitative analyses resulted in the identification of nine metacognitive reasoning strategies on which future RCR training will be developed. The implications of the findings for RCR training in the sciences are discussed. (shrink)

Introducing the sixth and final installment of the Common Knowledge symposium “Apology for Quietism,” Allen looks at the symposium retrospectively and concludes that it has mainly concerned “sage knowledge,” defined as foresight into the development of situations. The sagacious knower sees the disposition of things in an early, incipient form and knows how to intervene with nearly effortless and undetectable (quiet) effectiveness. Whatever the circumstance, the sage handles it with finesse, never doing too much but also never leaving anything undone (...) that must be accomplished. Quiet, when it is knowingly and effectively quiet (not pusillanimous or poor in spirit), is about what not to do, how not to approach a problem, what not to decide, what is not known, what will not work. Allen explains these principles in terms of traditional Chinese thought, Daoist and Confucian: wei we wei, or “doing-not-doing,” means effective inaction. What makes such wisdom possible is not mystical insight, he argues, but discipline in a certain kind of art. The sage has no need of reasons (let alone doctrines), only effectiveness; and he does not need truth or justice, only subtlety. The detachment of a quietist has little, if anything, to do with transcending perspectives. Detachment is good as a means to flexibility, and instead of transcending perspectives, a sage is skilled in the quiet art of never getting stuck in one. To be effectively quiet is not so much to be silent as to be inaudible, invisible; the sage “vanishes into things.”. (shrink)

Foucault is often thought to have a great deal to say about the history of madness and sexuality, but little in terms of a general analysis of government and the state.; This volume draws on Foucault's own research to challenge this view, demonstrating the central importance of his work for the study of contemporary politics.; It focuses on liberalism and neo- liberalism, questioning the conceptual opposition of freedom/constraint, state/market and public/private that inform liberal thought.

We develop an approach to the longstanding conjecture of Kierstead concerning the character of strongly nontrivial automorphisms of computable linear orderings. Our main result is that for any η-like computable linear ordering, such that has no interval of order type η, and such that the order type of is determined by a -limitwise monotonic maximal block function, there exists computable such that has no nontrivial automorphism.

Previous work demonstrates that music with more surprising chords tends to be perceived as more enjoyable than music with more conventional harmonic structures. In that work, harmonic surprise was computed based upon a static distribution of chords. This would assume that harmonic surprise is constant over time, and the effect of harmonic surprise on music preference is similarly static. In this study we assess that assumption and establish that the relationship between harmonic surprise and music preference is not constant as (...) time goes on. Analyses of harmonic surprise and preference from 1958 to 1991 showed increased harmonic surprise over time, and that this increase was significantly more pronounced in preferred songs. Separate analyses showed similar increases over the years from 2000 to 2019. As such, these findings provide evidence that the human perception of tonality is influenced by exposure. Baseline harmonic expectations that were developed through listening to the music of “yesterday” are violated in the music of “today,” leading to preference. Then, once the music of “today” provides the baseline expectations for the music of “tomorrow,” more pronounced violations—and with them, higher harmonic surprise values—become associated with preference formation. We call this phenomenon the “Inflationary-Surprise Hypothesis.” Support for this hypothesis could impact the understanding of how the perception of tonality, and other statistical regularities, are developed in the human brain. (shrink)

Part philosophical meditation, part cultural critique, The Body in Pain is a profoundly original study that has already stirred excitement in a wide range of intellectual circles. The book is an analysis of physical suffering and its relation to the numerous vacabularies and cultural forces--literary, political, philosophical, medical, religious--that confront it. Elaine Scarry bases her study on a wide range of sources: literature and art, medical case histories, documents on torture compiled by Amnesty International, legal transcripts of personal injury (...) trials, and military and strategic writings by such figures as Clausewitz, Churchill, Liddell Hart, and Kissinger, She weaves these into her discussion with an eloquence, humanity, and insight that recall the writings of Hannah Arendt and Jean-Paul Sartre. Scarry begins with the fact of pain's inexpressibility. Not only is physical pain enormously difficult to describe in words--confronted with it, Virginia Woolf once noted, "language runs dry"--it also actively destroys language, reducing sufferers in the most extreme instances to an inatriculate state of cries and moans. Scarry analyzes the political ramifications of deliberately inflicted pain, specifically in the cases of torture and warfare, and shows how to be fictive. From these actions of "unmaking" Scarry turns finally to the actions of "making"--the examples of artistic and cultural creation that work against pain and the debased uses that are made of it. Challenging and inventive, The Body in Pain is landmark work that promises to spark widespread debate. About the Author: Elaine Scarry is Associate Professor of English at the University of Pennsylvania. (shrink)

Despite the enormous influence of Michel Foucault in gender studies, social theory, and cultural studies, his work has been relatively neglected in the study of politics. Although he never published a book on the state, in the late 1970s Foucault examined the technologies of power used to regulate society and the ingenious recasting of power and agency that he saw as both consequence and condition of their operation. These twelve essays provide a critical introduction to Foucault's work on politics, exploring (...) its relevance to past and current thinking about liberal and neo-liberal forms of government. Moving away from the great texts of liberal political philosophy, this book looks closely at the technical means with which the ideals of liberal political rationalities have been put into practice in such areas as schools, welfare, and the insurance industry. This fresh approach to one of the seminal thinkers of the twentieth century is essential reading for anyone interested in social and cultural theory, sociology, and politics. (shrink)

Here we present what we believe is a novel account of what languages are, along with an axiomatically rich representation of languages and language-related data that is based on this account. We propose an account of languages as aggregates of dispositions distributed across aggregates of persons, and in doing so we address linguistic competences and the processes that realize them. This paves the way for representing additional types of language-related entities. Like demographic data of other sorts, data about languages may (...) be of use to researchers in a number of areas, including biomedical research. Data on the languages used in clinical encounters are typically included in medical records, and capture an important factor in patient-provider interactions. Like many types of patient and demographic data, data on a person’s preferred and primary languages are organized in different ways by different systems. This can be a barrier to data integration. We believe that a robust framework for representing language in general and preferred and primary language in particular – which has been lacking in ontologies thus far – can promote more successful integration of language-related data from disparate data sources. (shrink)

Foucault is often thought to have a great deal to say about the history of madness and sexuality, but little in terms of a general analysis of government and the state.; This volume draws on Foucault's own research to challenge this view, demonstrating the central importance of his work for the study of contemporary politics.; It focuses on liberalism and neo- liberalism, questioning the conceptual opposition of freedom/constraint, state/market and public/private that inform liberal thought.

Late in 1990, the Center for the Study of Ethics in the Professions at Illinois Institute of Technology (lIT) received a grant of more than $200,000 from the National Science Foundation to try a campus-wide approach to integrating professional ethics into its technical curriculum.! Enough has now been accomplished to draw some tentative conclusions. I am the grant's principal investigator. In this paper, I shall describe what we at lIT did, what we learned, and what others, especially philosophers, can learn (...) from us. We set out to develop an approach that others could profitably adopt. I believe that we succeeded. (shrink)

The Black Lives Matter movement marks a critical moment in the ebb and flow of racial progress. But as Camisha Russell points out, this moment might not last long. Prior high-water marks in...