We study the relationship between a computably enumerable real and its presentations. A set A presents a computably enumerable real α if A is a computably enumerable prefix-free set of strings such that equation image. Note that equation image is precisely the measure of the set of reals that have a string in A as an initial segment. So we will simply abbreviate equation image by μ. It is known that whenever A so presents α then A ≤wttα, where ≤wtt (...) denotes weak truth table reducibility, and that the wtt-degrees of presentations form an ideal ℐ in the computably enumerable wtt-degrees. We prove that any such ideal is equation image, and conversely that if ℐ is any nonempty equation image ideal in the computably enumerable wtt-degrees then there is a computable enumerable real α such that ℐ = ℐ. We also prove a kind of Rice Theorem for these ideals, namely that if the index set of such a equation image ideal is not empty or equal to ω then it is equation image-complete. (shrink)

If is a random sequence, then the sequence is clearly not random; however, seems to be “about half random”. L. Staiger [Kolmogorov complexity and Hausdorff dimension, Inform. and Comput. 103 159–194 and A tight upper bound on Kolmogorov complexity and uniformly optimal prediction, Theory Comput. Syst. 31 215–229] and K. Tadaki [A generalisation of Chaitin’s halting probability Ω and halting self-similar sets, Hokkaido Math. J. 31 219–253] have studied the degree of randomness of sequences or reals by measuring their “degree (...) of compression”. This line of study leads to various definitions of partial randomness. In this paper we explore some relations between these definitions. Among other results we obtain a characterisation of Σ1-dimension in terms of strong Martin-Löf ε-tests , and we show that ε-randomness for ε is different than the classical 1-randomness. (shrink)

In the context of his theory of numberings, Ershov showed that Kleene's recursion theorem holds for any precomplete numbering. We discuss various generalizations of this result. Among other things, we show that Arslanov's completeness criterion also holds for every precomplete numbering, and we discuss the relation with Visser's ADN theorem, as well as the uniformity or nonuniformity of the various fixed point theorems. Finally, we base numberings on partial combinatory algebras and prove a generalization of Ershov's theorem in this context.

We discuss the effectivity of Arslanov’s completeness criterion. In particular, we show that a parameterized version, similar to the recursion theorem with parameters, fails. We also discuss the effectivity of another extension of the recursion theorem, namely Visser’s ADN theorem, as well as that of a joint generalization of the ADN theorem and Arslanov’s completeness criterion.

We compare various notions of algorithmic randomness. First we consider relativized randomness. A set is n-random if it is Martin-Löf random relative to ∅. We show that a set is 2-random if and only if there is a constant c such that infinitely many initial segments x of the set are c-incompressible: C ≥ |x|-c. The ‘only if' direction was obtained independently by Joseph Miller. This characterization can be extended to the case of time-bounded C-complexity. Next we prove some results (...) on lowness. Among other things, we characterize the 2-random sets as those 1-random sets that are low for Chaitin's Ω. Also, 2-random sets form minimal pairs with 2-generic sets. The r.e. low for Ω sets coincide with the r.e. K-trivial ones. Finally we show that the notions of Martin-Löf randomness, recursive randomness, and Schnorr randomness can be separated in every high degree while the same notions coincide in every non-high degree. We make some remarks about hyperimmune-free and PA-complete degrees. (shrink)

We prove a number of elementary facts about computability in partial combinatory algebras. We disprove a suggestion made by Kreisel about using Friedberg numberings to construct extensional pca’s. We then discuss separability and elements without total extensions. We relate this to Ershov’s notion of precompleteness, and we show that precomplete numberings are not 1–1 in general.

Partial combinatory algebras (pcas) are algebraic structures that serve as generalized models of computation. In this article, we study embeddings of pcas. In particular, we systematize the embeddings between relativizations of Kleene’s models, of van Oosten’s sequential computation model, and of Scott’s graph model, showing that an embedding between two relativized models exists if and only if there exists a particular reduction between the oracles. We obtain a similar result for the lambda calculus, showing in particular that it cannot be (...) embedded in Kleene’s first model. (shrink)

For every partial combinatory algebra, we define a hierarchy of extensionality relations using ordinals. We investigate the closure ordinals of pca’s, i.e., the smallest ordinals where these relations become equal. We show that the closure ordinal of Kleene’s first model is ${\omega _1^{\textit {CK}}}$ and that the closure ordinal of Kleene’s second model is $\omega _1$. We calculate the exact complexities of the extensionality relations in Kleene’s first model, showing that they exhaust the hyperarithmetical hierarchy. We also discuss embeddings of (...) pca’s. (shrink)

We report on some recent work centered on attempts to understand when one set is more random than another. We look at various methods of calibration by initial segment complexity, such as those introduced by Solovay [125], Downey, Hirschfeldt, and Nies [39], Downey, Hirschfeldt, and LaForte [36], and Downey [31]; as well as other methods such as lowness notions of Kučera and Terwijn [71], Terwijn and Zambella [133], Nies [101, 100], and Downey, Griffiths, and Reid [34]; higher level (...) randomness notions going back to the work of Kurtz [73], Kautz [61], and Solovay [125]; and other calibrations of randomness based on definitions along the lines of Schnorr [117].These notions have complex interrelationships, and connections to classical notions from computability theory such as relative computability and enumerability. Computability figures in obvious ways in definitions of effective randomness, but there are also applications of notions related to randomness in computability theory. For instance, an exciting by-product of the program we describe is a more-or-less naturalrequirement-freesolution to Post's Problem, much along the lines of the Dekker deficiency set. (shrink)

We study reals with infinitely many incompressible prefixes. Call $A \in 2^{\omega}$ Kolmogorot random if $(\exists^{\infty}n) C(A \upharpoonright n) \textgreater n - \mathcal{O}(1)$ , where C denotes plain Kolmogorov complexity. This property was suggested by Loveland and studied by $Martin-L\ddot{0}f$ , Schnorr and Solovay. We prove that 2-random reals are Kolmogorov random. Together with the converse-proved by Nies. Stephan and Terwijn [11]-this provides a natural characterization of 2-randomness in terms of plain complexity. We finish with a related characterization of (...) 2-randomness. (shrink)

S. A. Lloyd proposes a radically new interpretation of Hobbes's Leviathan that shows transcendent interests - interests that override the fear of death - to be crucial to both Hobbes's analysis of social disorder and his proposed remedy to it. Most previous commentators in the analytic philosophical tradition have argued that Hobbes thought that credible threats of physical force could be sufficient to deter people from political insurrection. Professor Lloyd convincingly shows that because Hobbes took the transcendence of religious and (...) moral interests seriously, he never believed that mere physical force could ensure social order. Lloyd's interpretation demonstrates the ineliminability of that half of Leviathan devoted to religion, and attributes to Hobbes a much more plausible conception of human nature than the narrow psychological egoism traditionally attributed to Hobbes. (shrink)

Originally published in 1944, this book was originally intended as a continuation of the 1943 publication Nautical Mathematics, which is also reissued in this series. In it, the principles set out in Nautical Mathematics are given practical applications, and the text is supplied with exercises to test and clarify the lessons. This book will be of value to anyone with an interest in the history of education in the forces during WWII.

Работа предназначена для ученых и специалистов, преподавателей, аспирантов, слушателей, студентов, а также всех интересующихся рассматриваемой темой.

Implementation of the Peace Program propounded by the Twenty-Fourth Congress of the CPSU is substantially furthered by the struggle against bourgeois ideology in a field directly related to interpretation of the principal problems of contemporary foreign policy - the field of the theory of international relations. Naturally, the success of this struggle depends in large degree on the depth and care with which one analyzes the conditions and tendencies characteristic of bourgeois studies of international politics.

In this book, S. A. Lloyd provides a radical interpretation of Hobbes' laws of nature, revealing them to be not egoistic precepts of personal prudence but rather moral instructions for obtaining the common good. This account of Hobbes' moral philosophy stands in contrast to both divine command and rational choice interpretations. Drawing from the core notion of reciprocity, Lloyd explains Hobbes' system of 'cases in the law of nature' and situates Hobbes' moral philosophy in the broader context of his political (...) philosophy and views on religion. Offering ingenious new arguments, Lloyd defends a reciprocity interpretation of the laws of nature through which humanity's common good is secured. (shrink)

Next SectionBackground: Physicians face ethical difficulties daily, yet they seek ethics consultation infrequently. To date, no systematic data have been collected on the strategies they use to resolve such difficulties when they do so without the help of ethics consultation. Thus, our understanding of ethical decision making in day to day medical practice is poor. We report findings from the qualitative analysis of 310 ethically difficult situations described to us by physicians who encountered them in their practice. When facing such (...) situations, the physicians sought to avoid conflict, obtain assistance, and protect the integrity of their conscience and reputation, as well as the integrity of the group of people who participated in the decisions. These goals could conflict with each other, or with ethical goals, in problematic ways. Being aware of these potentially conflicting goals may help physicians to resolve ethical difficulties more effectively. This awareness should also contribute to informing the practice of ethics consultation. Objective: To identify strategies used by physicians in dealing with ethical difficulties in their practice. Design, setting, and participants: National survey of internists, oncologists, and intensive care specialists by computer assisted telephone interviews (n = 344, response rate = 64%). As part of this survey, we asked physicians to tell us about a recent ethical dilemma they had encountered in their medical practice. Transcripts of their open-ended responses were analysed using coding and analytical elements of the grounded theory approach. Main measurements: Strategies and approaches reported by respondents as part of their account of a recent ethical difficulty they had encountered in their practice. Results: When faced with ethical difficulties, the physicians avoided conflict and looked for assistance, which contributed to protecting, or attempting to protect, the integrity of their conscience and reputation, as well as the integrity of the group of people who participated in the decisions. These efforts sometimes reinforced ethical goals, such as following patients’ wishes or their best interests, but they sometimes competed with them. The goals of avoiding conflict, obtaining assistance, and protecting the respondent’s integrity and that of the group of decision makers could also compete with each other. Conclusion: In resolving ethical difficulties in medical practice, internists entertained competing goals that they did not always successfully achieve. Additionally, the means employed were not always the most likely to achieve those aims. Understanding these aspects of ethical decision making in medical practice is important both for physicians themselves as they struggle with ethical difficulties and for the ethics consultants who wish to help them in this process. (shrink)

Background: Ethics support services are growing in Europe to help doctors in dealing with ethical difficulties. Currently, insufficient attention has been focused on the experiences of doctors who have faced ethical difficulties in these countries to provide an evidence base for the development of these services.Methods: A survey instrument was adapted to explore the types of ethical dilemma faced by European doctors, how they ranked the difficulty of these dilemmas, their satisfaction with the resolution of a recent ethically difficult case (...) and the types of help they would consider useful. The questionnaire was translated and given to general internists in Norway, Switzerland, Italy and the UK.Results: Survey respondents ranged in age from 28 to 82 years, and averaged 25 years in practice. Only a minority reported having access to ethics consultation in individual cases. The ethical difficulties most often reported as being encountered were uncertain or impaired decision-making capacity , disagreement among caregivers and limitation of treatment at the end of life . The frequency of most ethical difficulties varied among countries, as did the type of issue considered most difficult. The types of help most often identified as potentially useful were professional reassurance about the decision being correct , someone capable of providing specific advice , help in weighing outcomes and clarification of the issues . Few of the types of help expected to be useful varied among countries.Conclusion: Cultural differences may indeed influence how doctors perceive ethical difficulties. The type of help needed, however, did not vary markedly. The general structure of ethics support services would not have to be radically altered to suit cultural variations among the surveyed countries. (shrink)

Environmentalist philosophers often paint a holistic picture, stressing such things as the continuity of humanity with wider nature and our membership of the 'natural community' . The implication seems to be that a non-anthropocentric philosophy requires that we strongly identify ourselves with nature and therefore that we downplay any human/non-human distinction. An alternative view, I think more interesting and plausible, stresses the distinction between humanity and a nature valued precisely for its otherness. In this article I discuss some of its (...) main elements, and some of the difficulties involved with keeping nature's otherness in focus. Firstly (in sections 1-5), I try to clarify what I take to be the otherness-based position by distinguishing it from the apparently similar views of John Passmore, Robert Elliott and Keekok Lee, and some opposed holistic views, especially of J. Baird Callicott. Then, in the second half of the article (sections 6-7), I argue that if nature is valued in virtue of its otherness, this value is best thought of as an extrinsic, final and objective good, where 'objectivity' is a 'method of understanding', in Thomas Nagel's sense. Although I give some reasons for preferring an otherness account to certain alternative positions, I make no overall attempt to 'prove' that nature is valuable for its otherness. My aim is to show that, if it is, then this seems the best way to understand that value. (shrink)

In this book, S. A. Lloyd offers a radically new interpretation of Hobbes's laws of nature, revealing them to be not egoistic precepts of personal prudence but rather moral instructions for obtaining the common good.

Background: In 2014, companies began covering the costs of egg freezing for their employees. The adoption of this benefit was highly contentious. Some argued that it offered women more reproductive...

In On the Edge of Anarchy, A. John Simmons simultaneously pursues two distinguishable ends: to defend an interpretation of Locke as a “pure consent” theorist the essence of whose theory is that only actual voluntary individual consent can ground political obligations and authority, and to defend pure consent theory as the best theory of political obligation. Both ends are pursued under the heading of justifying “Lockean” consent theory, and the arguments for them overlap considerably because most of Simmons’s defense of (...) his interpretation of Locke’s theory depends on his arguments that the position he attributes to Locke is, for independent philosophical reasons, the most defensible version of “voluntaristic” theory. Two of the very interesting, and surprising, inferences Simmons defends in this book are that believing ourselves to be naturally free from political obligation implies that most existing states are illegitimate, and that Locke was committed to the view that “political drudgery,” a condition in which all of our rights are alienated to the government, although imprudent, is not morally impermissible. (shrink)

Collection of 10 Jaina philosophical tracts.

As support for clinical ethics committees in the UK grows, care must be taken to define their function, membership and method of working and the status of their decisions.The modern practice of medicine raises a plethora of complex issues—medical, ethical and legal. Doctors and other healthcare professionals increasingly must try to resolve these and may sometimes have to do so in the face of contrary opinion expressed by patients and/or their surrogates. While clearly qualified in the medical arena, and although (...) there is now more ethics teaching in the medical curriculum, healthcare professionals are seldom qualified to adjudicate on ethical or legal matters, or even, perhaps, to recognise them when they arise. Yet, as Doyal says, “clinical life must go on and moral and legal indeterminacy within medicine cries out for practical resolution.”1 Meanwhile, the expectations of patients and their families—and, indeed, of wider society—are that decisions about patient care, resources and therapeutic regimes should be soundly based on appropriate ethicolegal, as well as scientific, principle.Recognition of these additional burdens on healthcare professionals has generated some interest in the provision of ethics consultation. In the USA this has been undertaken by a variety of tribunals and individuals. Hospital ethics committees and ethics consultants feature in many US hospitals and perform a variety of roles. In Europe, a number of countries have also established clinical ethics committees and they are becoming more common in the UK—primarily in England and Wales for the moment. Whereas, however, “[i]n North America, CECs have … become an integral part of the organisational infrastructure of hospitals ...”,1 in the United Kingdom they remain essentially ad hoc bodies, generated for a variety of reasons and with different goals, structures, membership, methods of working and functions. The initial impetus for the …. (shrink)

Next SectionThis article argues against two dominant accounts of the nature of nostalgia. These views assume that nostalgia depends, in some way, on comparing a present situation with a past one. However, neither does justice to the full range of recognizably nostalgic experiences available to us – in particular, ‘Proustian’ nostalgia directed at involuntary autobiographical memories. Therefore, the accounts in question fail. I conclude by considering an evaluative puzzle raised by Proustian nostalgia when it is directed at memories that the (...) nostalgist herself regards as non-veridical. (shrink)

In an international survey of rationing we have found that European physicians encounter scarcity-related ethical difficulties, and are dissatified with the resolution of many of these cases. Here we further examine survey results to explore whether ethics support services would be potentially useful in addressing scarcity related ethical dilemmas. Results indicate that while the type of help offered by ethics support services was considered helpful by physicians, they rarely referred difficulties regarding scarcity to ethics consultation. We propose that ethics consultants (...) could assist physicians by making the process less difficult, and by contributing to decisions being more ethically justifiable. Expertise in bringing considerations of justice to bear on real cases could also be useful in recognising an unjust limit, as opposed to a merely frustrating limit. Though these situations are unlikely to be among the most frequently referred to ethics support services, ethics consultants should be prepared to address them. (shrink)

This chapter suggests that the state of nature is a continuum notion that lies in a segment along a larger continuum of the scope of private judgment, as does the continuum notion of civil authority. Jean Hampton saw Thomas Hobbes's state of nature as a “presocietal” condition of “isolated asocial individuals,” “stripped of their social connections.” There is plentiful evidence against Hampton's interpretation of the state of nature as an “asocial” condition in Hobbes's insistence across all his political writings that (...) men care deeply about their relative social standing and reputations, and that this is a major source of conflict in a state of nature. A potentially more promising way of understanding the state of nature is as a lawless condition. Societies exhibiting a high degree of consensus among private judgments may be able to tolerate incomplete removal from the mere state of nature, without threat to their stability. (shrink)