The prime number theorem, established by Hadamard and de la Vallée Poussin independently in 1896, asserts that the density of primes in the positive integers is asymptotic to 1/ln x. Whereas their proofs made serious use of the methods of complex analysis, elementary proofs were provided by Selberg and Erdos in 1948. We describe a formally verified version of Selberg's proof, obtained using the Isabelle proof assistant.

1.1 Some examples of rule induction on permutations . . . . . . . 6 1.2 Ways of making new permutations . . . . . . . . . . . . . . . 7 1.3 Further results . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Removing elements . . . . . . . . . . (...) . . . . . . . . . . . . . . 8.. (shrink)

The concept of minimal risk has been used to regulate and limit participation by adolescents in clinical trials. It can be understood as setting an absolute standard of what risks are considered minimal or it can be interpreted as relative to the actual risks faced by members of the host community for the trial. While commentators have almost universally opposed a relative interpretation of the environmental risks faced by potential adolescent trial participants, we argue that the ethical concerns against the (...) relative standard may not be as convincing as these commentators believe. Our aim is to present the case for a relative standard of environmental risk in order to open a debate on this subject. We conclude by discussing how a relative standard of environmental risk could be defended in the specific case of an HIV vaccine trial among adolescents in South Africa. (shrink)

The American Journal of Bioethics, Volume 11, Issue 6, Page W1-W3, June 2011.

A challenge of performing research in the paediatric emergency and acute care setting is obtaining valid prospective informed consent from parents. The ethical issues are complex, and it is important to consider the perspective of participants, health care workers and researchers on research without prospective informed consent while planning this type of research. We performed a systematic review according to PRISMA guidelines, of empirical evidence relating to the process, experiences and acceptability of alternatives to prospective informed consent, in the paediatric (...) emergency or acute care setting. Major medical databases and grey sources were searched and results were screened and assessed against eligibility criteria by 2 authors, and full text articles of relevant studies obtained. Data were extracted onto data collection forms and imported into data management software for analysis. Thirteen studies were included in the review consisting of nine full text articles and four abstracts. Given the heterogeneity of the methods, results could not be quantitatively combined for meta-analysis, and qualitative results are presented in narrative form, according to themes identified from the data. Major themes include capacity of parents to provide informed consent, feasibility of informed consent, support for alternatives to informed consent, process issues, modified consent process, child death, and community consultation. Our review demonstrated that children, their families, and health care staff recognise the requirement for research without prior consent, and are generally supportive of enrolling children in such research with the provisions of limiting risk, and informing parents as soon as possible. Australian data and perspectives of children are lacking and represent important knowledge gaps. (shrink)

Task shifting is increasingly used to address human resource shortages impacting HIV service delivery in low- and middle-income countries. By shifting basic tasks from higher- to lower-trained cadres, such as Community Health Workers, task shifting can reduce overhead costs, improve community outreach, and provide efficient scale-up of essential treatments like antiretroviral therapies. Although there is rich evidence outlining positive outcomes that CHWs bring into HIV programs, important questions remain over their place in service delivery. These challenges often reflect concerns over (...) whether CHWs can mitigate HIV through a means that does not overlook the ethical and practical constraints that undergird their work. Ethical and practical guidance thus needs to become the cornerstone of CHW deployment. This paper analyzes such challenges through the lens of Ethical Principlism. We examined papers identifying substantive and ethical challenges impacting CHWs as they provide HIV services in low- and middle-income contexts. To do this, we analyzed papers written in English and published from year 2000 or later. These articles were identified using MEDLINE, Cochrane Database of Systematic Reviews, and Google Scholar databases. In total, 465 articles were identified, 78 of which met our inclusion criteria. Article reference lists and grey literature were also examined. CHWs experience specific challenges while carrying out their duties, such as conducting emotionally- and physically-demanding tasks with often inadequate training, supervision and compensation. CHWs have also been poorly integrated into health systems, which not only impacts quality of care, but can hinder their prospects for promotion and lead to CHW disempowerment. As we argue, these challenges can be addressed if a set of ethical principles is prioritized, which specifically entail the principles of respect for persons, justice, beneficence, proportionality and cultural humility. CHWs play a crucial role in HIV service delivery, yet the ethical challenges that can accompany their work cannot be overlooked. By prioritizing ethical principles, policymakers and program implementers can better ensure that CHWs are combatting HIV through a means that does not exploit or take their critical role within service delivery for granted. (shrink)

The field of cognitive modeling has progressed beyond modeling cognition in the context of simple laboratory tasks and begun to attack the problem of modeling it in more complex, realistic environments, such as those studied by researchers in the field of human factors. The problems that the cognitive modeling community is tackling focus on modeling certain problems of communication and control that arise when integrating with the external environment factors such as implicit and explicit knowledge, emotion, cognition, and the cognitive (...) system. These problems must be solved in order to produce integrated cognitive models of moderately complex tasks. Architectures of cognition in these tasks focus on the control of a central system, which includes control of the central processor itself, initiation of functional processes, such as visual search and memory retrieval, and harvesting the results of these functional processes. Because the control of the central system is conceptually different from the internal control required by individual functional processes, a complete architecture of cognition must incorporate two types of theories of control: Type 1 theories of the structure, functionality, and operation of the controller, and type 2 theories of the internal control of functional processes, including how and what they communicate to the controller. This book presents the current state of the art for both types of theories, as well as contrasts among current approaches to human-performance models. It will be an important resource for professional and student researchers in cognitive science, cognitive-engineering, and human-factors.Contributors: Kevin A. Gluck, Jerry T. Ball, Michael A. Krusmark, Richard W. Pew, Chris R. Sims, Vladislav D. Veksler, John R. Anderson, Ron Sun, Nicholas L. Cassimatis, Randy J. Brou, Andrew D. Egerton, Stephanie M. Doane, Christopher W. Myers, Hansjorg Neth, Jeremy M Wolfe, Marc Pomplun, Ronald A. Rensink, Hansjorg Neth, Chris R. Sims, Peter M. Todd, Lael J. Schooler, Wai-Tat Fu, Michael C. Mozer, Sachiko Kinoshita, Michael Shettel, Alex Kirlik, Vladislav D. Veksler, Michael J. Schoelles, Jerome R. Busemeyer, Eric Dimperio, Ryan K. Jessup, Jonathan Gratch, Stacy Marsella, Glenn Gunzelmann, Kevin A. Gluck, Scott Price, Hans P. A. Van Dongen, David F. Dinges, Frank E. Ritter, Andrew L. Reifers, Laura Cousino Klein, Michael J. Schoelles, Eva Hudlicka, Hansjorg Neth, Christopher W. Myers, Dana Ballard, Nathan Sprague, Laurence T. Maloney, Julia Trommershauser, Michael S. Landy, A. Hornof, Michael J. Schoelles, David Kieras, Dario D. Salvucci, Niels Taatgen, Erik M. Altmann, Richard A. Carlson, Andrew Howes, Richard L. Lewis, Alonso Vera, Richard P. Cooper, and Michael D. Byrne. (shrink)

Author Jeremy Waldron has thoroughly revised thirteen of his most recent essays in order to offer a comprehensive critique of the idea of the judicial review of legislation. He argues that a belief in rights is not the same as a commitment to a Bill of Rights. This book presents legislation by a representative assembly as a form of law making which is especially apt for a society whose members disagree with one another about fundamental issues of principle.

Evidentialism is the thesis that epistemic justification for belief supervenes on evidential support. However, we claim there are cases in which, even though two subjects have the same evidential support for a proposition, only one of them is justified. What make the difference are pragmatic factors, factors having to do with our cares and concerns. Our argument against evidentialism is not based on intuitions about particular cases. Rather, we aim to provide a theoretical basis for rejecting evidentialism by defending a (...) “pragmatic” necessary condition on epistemic justification. We argue for the following necessary condition for justification: S is justified in believing that p only if S is rational to prefer (and, hence, act) as if p. In light of this necessary condition, the price of evidentialism is skepticism, or something close to it. (shrink)

The new critical edition of the works and correspondence of Jeremy Bentham (1748-1832) is being prepared and published under the supervision of the Bentham Committee of University College London. In spite of his importance as jurist, philosopher, and social scientist, and leader of theUtilitarian reformers, the only previous edition of his works was a poorly edited and incomplete one brought out within a decade or so of his death. Eight volumes of the new Collected Works, five of correspondence, and (...) three of writings on jurisprudence, appeared between 1968 and 1981, published bythe Athlone Press. Further volumes in the series since then are published by Oxford University Press. The overall plan and principles of the edition are set out in the General Preface to The Correspondence of Jeremy Bentham, vol. 1, which was the first volume of the Collected Works to bepublished.An Introduction to the Principles of Morals and Legislation, Jeremy Bentham's best-known work, is a classic text in modern philosophy and jurisprudence. First published in 1789, it contains the important statement of the foundations of utilitarian philosophy and a pioneering study of crime andpunishment, both of which remain at the heart of contemporary debates in moral and political philosophy, economics, and legal theory. Printed here in full is the definitive edition, edited by the distinguished scholars J. H. Burns and H. L. A. Hart. An introductory essay by Hart, first published in1982 and a widely acknowledged classic in its own right, is reprinted here. It contains an important analysis of Bentham's principle of utility, theory of action, and an account of the relationship between law and morality.A new introduction by the leading Bentham scholar F. Rosen, specially written for this Clarendon Paperback edition, provides students with a helpful survey of Bentham's main ideas and an extensive bibliographical study of recent critical work on Bentham. Professor Rosen's essay also contains a newanalysis of the principle of utility in Bentham's philosophy which is compared with its use in Hume and J. S. Mill. (shrink)

Proponents of the rule of law argue about whether that ideal should be conceived formalistically or in terms of substantive values. Formalistically, the rule of law is associated with principles like generality, clarity, prospectivity, consistency, etc. Substantively, it is associated with market values, with constitutional rights, and with freedom and human dignity. In this paper, I argue for a third layer of complexity: the procedural aspect of the rule of law; the aspects of rule-of-law requirements that have to do with (...) "natural Justice" or "procedural due process." These I believe have been neglected in the jurisprudential literature devoted specifically to the idea of the rule of law and they deserve much greater emphasis. Moreover procedural values go beyond elementary principles like the guarantee of an unbiased tribunal or the opportunity to present and confront evidence. They include the right to argue in a court about what the law is and what its bearing should be on one's situation. The provision that law makes for argument is necessarily unsettling, and so this emphasis on the procedural aspect highlights the point predictability should not be regarded as the be-all and end-all of the rule of law. (shrink)

This volume collects two lectures by Jeremy Waldron that were originally given as Berkeley Tanner Lectures along with responses to the lectures from Wai Chee Dimock, Don Herzog, and Michael Rosen; a reply to the responses by Waldron; and an introduction by Meir Dan-Cohen.

It is often argued that certain metaphysical complications surrounding the phenomenon of monozygotic twinning force us to conclude that, prior to the point at which twinning is no longer possible, the zygote or early embryo cannot be considered an individual human organism. In this essay, I argue, on the contrary, that there are in fact several ways of making sense of monozygotic twinning that uphold the humanity of the original zygote, but also that there is no easy answer to what (...) happens when the human zygote twins. All of the options available carry with them one or more surprising, alarming, or otherwise counterintuitive implications. All things considered, I conclude that the “budding option,” according to which the original human organism present before twinning carries on as one of the resulting embryos but not the other, is the most plausible explanation of what happens when a human zygote twins. (shrink)

On the ethics of extending human life: healthy people have a right to carry on livingHumanity has long demonstrated a paradoxical ambivalence concerning the extension of a healthy human lifespan. Modest health extension has been universally sought, whereas extreme health extension has been regarded as a snare and delusion—a dream beyond all others at first blush, but actually something we are better off without. The prevailing pace of biotechnological progress is bringing ever closer the day when humanity will be able (...) to act on the latter view by rejecting a clear and present opportunity for much longer healthy lives. Indeed, some biogerontologists contend that that day has already arrived, to the extent that our hesitation in embarking on a vigorous “war on ageing” is already delaying the point at which a cure for ageing will be developed. Here I consider whether our present caution concerning the wisdom of truly curing ageing is likely to survive the increased scrutiny that it will receive in coming years as a result of these technical advances. I conclude that it will not, because of its irreconcilability with values that are more deeply held by the large majority of humanity than any values that argue against the quest for a cure. I further conclude that all the major current reasons given for not curing ageing are mere crutches to help us cope with the immutability of ageing that we have been brought up to accept. Our failure to set aside such irrationality is already shortening potential longevity—quite probably of those already alive today—to a staggering degree. Once we realise this, our determination to consign human ageing to history will be second …. (shrink)

Political theorist Jeremy Waldron makes a bracing case against identifying rule of law with predictability. Seeing the rule of law as just one value to which democracies aspire, he embraces thoughtfulness rather than rote rule-following, flexibility even at the cost of vagueness, and emphasizing procedure and argument over predictable outcomes.

Biography of the French philosopher, Christian mystic, and social activist Simone Weil (1909-1943). Unrevised and unpublished proofs.

Participants compared the mental capacities of various human and nonhuman characters via online surveys. Factor analysis revealed two dimensions of mind perception, Experience and Agency. The dimensions predicted different moral judgments but were both related to valuing of mind.