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)

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.

Public health decisions made by the state involve considerable disagreements on the course of actions, uncertainties, and compromises that arise from moral tensions between the demands of civil liberties and the goals of public health. With such complex decisions, it can be extremely difficult to arrive at and justify the best option. In this article, we propose an ethical decision-making framework based on the philosophy of Ubuntu and argue that in sub-Saharan African settings, this approach provides attractive alternative conventions of (...) moral decision-making and a useful language for understanding moral reasoning and ethics. Through its emphasis on humanity, compassion, and social responsibility, Ubuntu (“I am because we are”) has the potential to facilitate solutions to and avert conflicts between individual rights and public health. The use of Ubuntu shifts the moral reasoning and ethics of decision-making from a field of philosophy shaped by the global north, to the everyday values, decision-making, and consequent practices of people in much of Africa. Using examples of Ebola, pandemic influenza, and tuberculosis, we illustrate how Ubuntu can be applied to tackle conflicting ethical problems in public health and medicine. (shrink)

Prior to the productive encounters that can be staged between Emmanuel Levinas’sthought and cinema at the level of reception, Jean-Pierre and Luc Dardenne introducehis philosophy to their filmmaking at its moment of inception.1Luc Dardenne’s diary Audos de nos images documents their filmmaking from 1991 to 2005, and isinterspersed with brief but erudite references to Levinas’s work. While Levinasianthinking is one among many cited influences in this text, which also features quotationsfrom the writings of novelists, poets, and other philosophers, along with (...) detailedreferences to other filmmakers, his work is a signal point of inspiration and ethicalaspiration for their filmmaking. The Dardenne brothers seek permanently to unsettlereceived ideas of what cinema is. In this, their approach is bound up explicitly, but notexclusively, with the ethical underpinnings of Levinas’s thought. Levinas’s reformulationof ethics as first philosophy creates a fissure at the root of the philosophy of being. TheDardennes’ films, in turn, perform a Levinasian-inspired challenge to the being ofcinema. At its most extreme moments, to kill or not to kill is the key question that theircinema raises. This tacit rewriting of the interrogative opening to Hamlet’s infamous soliloquy, shifts attention away from a self-centered concern with being or non-being,and towards the survival of the other. The passage from being to non-being, whichwould involve the death of the subject, is displaced here by a preoccupation with killing,or failing to kill, someone else. This particular move from dying to killing lies at the heartof the Dardennes’ mortal ethics. (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.

In Selfless Cinema?, Sarah Cooper maps out the power relations of making, and viewing, documentaries in ethical terms. The ethics of filmmaking are often examined in largely legalistic terms, dominated by issues of consent, responsibility, and participantse(tm) or film-makerse(tm) rights, but Cooper approaches four representative French film-makers e" Jean Rouch, Chris Marker, Raymond Depardon, and Agns Varda e" in a far less juridical way, drawing on the ethical philosophy of Emmanuel Levinas. She argues that, in spite of Levinase(tm)s iconoclastic, anti-ocular (...) thinking, his concept of visage is richly applicable to film, and especially to documentary. (shrink)

Objective: To examine changes in patients’ desired control of the deep brain stimulator and perception of global life control throughout DBS.Methods: A consecutive cohort of 52 patients with Parkinson’s disease was recruited to participate in a prospective longitudinal study over three assessment points. Semi-structured interviews assessing participants’ desire for stimulation control and perception of global control were conducted at all three points. Qualitative data were coded using content analysis. Visual analog scales were embedded in the interviews to quantify participants’ perceptions (...) of control over time.Results: Participants reported significant increases in their perception of global control over time and significant declines in their desired control of the stimulation. These changes were unrelated to improvements in motor symptoms. Improvements in global control were negatively correlated with a decline in desired stimulation control. Qualitative data indicate that participants have changed, nuanced levels of desired control over their stimulators. Increased global life control following DBS may be attributed to increased control over PD symptoms, increased ability to engage in valued activities, and increased overall self-regulation, while other domains related to global control remained unaffected by DBS.Conclusions: There are few empirical data documenting patients’ desire for stimulation control throughout neuromodulation and how stimulation control is related to other aspects of control despite the growing application of neuromodulation devices to treat a variety of disorders. Our data highlight distinctions in different types of control and have implications for the development of patient-controlled neurostimulation devices. (shrink)

Emmanuel Levinas never wrote about cinema. To the uninitiated, this may appearsurprising, given that his life spanned the twentieth century, in which film emerged as amajor art form, and his work includes tantalising allusions to films and the cinematicmedium. Far from surprising, however, the liminal place that cinema occupies inLevinas’s thought is entirely understandable. Although his philosophy features manycultured references to literature and the other arts, and he discusses the work of suchwriters as Marcel Proust and Michel Leiris in some (...) detail, his early work is dismissive ofthe aesthetic dimension in ethical terms. More significantly still, his philosophy bears achallenging relation to questions of vision and the phenomenological world ofappearance, tending towards the anti-ocular and revealing an iconoclastic approach toimages. There is something provocative, then, in wanting to ask what Levinas’sphilosophy has to say about cinema, if we understand this realm as the location parexcellence of the moving image. Yet this is precisely the guiding question of this SpecialIssue, which is the first to bring together articles on the work of Levinas and the insightsthat his philosophy can offer to film studies. The collection features an internationalselection of contributors, and includes Levinas specialists as well as film scholars. Thereis no easy bond to be forged between this philosopher and film, and the possibility ofmaking this connection remains open to interrogation throughout some of the articles.But by taking Levinas to the cinema, while tracking the cinematic aspects of his thinking,all of the contributors address this hitherto occluded relation in generative ways, andeach creates a critical opening for future research in the field. (shrink)

Iris Murdoch was a philosopher and novelist who wrote extensively on the themes of love, goodness, religion, and morality. In this article, we explore her notion of ‘moral vision’; the idea that morality is not just about how we act and make choices, but how we see the world in a much broader sense.

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.

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 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)

Logicians and theoretical physicists will also benefit from this book.

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.

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

Although it is well accepted that working memory is intimately related to consciousness, little research has illuminated the liaison between the two phenomena. To investigate this under-explored nexus, we used an imagery monitoring task to investigate the subjective aspects of WM performance. Specifically, in two experiments, we examined the effects on consciousness of holding in mind information having a low versus high memory load, and holding memoranda in mind during the presentation of distractors . Higher rates of rehearsal occurred in (...) the high load and distractor conditions than in comparable control conditions. Examination of the temporal properties of the rehearsal-based imagery revealed that, across subjects, imagery events occurred evenly throughout the delay. We hope that future variants of this new imagery monitoring task will reveal additional insights about WM, consciousness, and action control. (shrink)

Burning fossil fuel in the North American continent contributes more to the CO2 global warming problem than in any other continent. The resulting climate changes are expected to alter food production. The overall changes in temperature, moisture, carbon dioxide, insect pests, plant pathogens, and weeds associated with global warming are projected to reduce food production in North America. However, in Africa, the projected slight rise in rainfall is encouraging, especially since Africa already suffers from severe shortages of rainfall. For all (...) regions, a reduction in fossil fuel burning is vital. Adoption of sound ecological resource management, especially soil and water conservation and the prevention of deforestation, is important. Together, these steps will benefit agriculture, the environment, farmers, and society as a whole. (shrink)

There is a moment in Peter Brosens and Jessica Woodworth’s Khadak (2006) when the image of a tree is rotated 180 degrees [...].

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.

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

We study the minimal enumeration degree problem in models of fragments of Peano arithmetic () and prove the following results: in any model M of Σ2 induction, there is a minimal enumeration degree if and only if M is a nonstandard model. Furthermore, any cut in such a model has minimal e-degree. By contrast, this phenomenon fails in the absence of Σ2 induction. In fact, whether every Σ2 cut has minimal e-degree is independent of the Σ2 bounding principle.

How does modern writing in French grapple with the present absence and absent presence of lost loved ones? How might it challenge and critique the relegation of certain deaths to the realm of the unmournable? What might this reveal about the role of the literary in the French and francophone world and shifting conceptions of the nation state? Essays from the Revolution to the present day explore these questions from a variety of perspectives, bringing out the ways in which mourning (...) blurs the boundaries between the personal and the historical, the aesthetic and the ethical, the self and the other, and ultimately reasserting its truly critical resonance as a concept. (shrink)

While educational settings may be envisioned as safe spaces that facilitate learning, foster creativity, and promote healthy development for youth, research has found that this is not always true for Black girls. Their negative experiences within educational settings are both gendered and racialized, often communicating broader societal perceptions of Black girls that ultimately shape their identity development. Utilizing semi-structured interviews with adolescent Black girls, the current investigation explored Black girls' educational experiences, their meaning making of Black girlhood, and the role (...) of parents in their positive development. By centering Black girls' voices, this study illuminated how Black girls negotiate their multiple marginalized identities and how their identities are shaped by their home and school environments. Findings revealed that Black girls are aware of the difficulties in navigating educational settings for Black girls, but this awareness was coupled with parental support that promoted positive gendered racial identities for Black girls in middle school and high school. This investigation advanced current knowledge of Black girls' identity development and highlighted the protective role of parental socialization. Future research directions and implications are also discussed. (shrink)