The Foundations of Mathematics (Stewart and Tall) is a horse of a different color. The writing is excellent and there is actually some useful mathematics. I definitely like this book."--The Bulletin of Mathematics Books.

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large is intimately related to the infinitely small. Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon some version (...) of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals.In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectual exercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable. (shrink)

Dugald Stewart is usually thought of as the final major figure of the Scottish Enlightenment. But though his name is a recognisable one among intellectual historians, few would probably be able to...

In his testamentary letter to Auguste Chevalier, Évariste Galois states that, in modern terminology, the smallest simple group has order 60. No proof of this statement survives in his papers, and it has been suggested that a proof would have been impossible using the methods available at the time. We argue that this assertion is unduly pessimistic. Moreover, one fragmentary document, dismissed as a triviality and misunderstood, looks suspiciously like cryptic notes related to this result. We give an elementary proof (...) of Galois’s statement, explain why it is likely that he would have been aware of the methods involved, and discuss the potential relevance of the fragment. (shrink)

This article examines the English scholar James Cowles Prichard's attention to language and comparative philology within his wider project on the natural history of man. It reveals that linguistic evidence was among the most important elements for Prichard in his overarching scientific aim of investigating human physical diversity, and served as the evidential foundation for his ethnology. His work on Celtic comparative philology made him not only one of the earliest British adopters of German comparative grammar, but a comparative philologist (...) of European stature in his own right. More generally, linguistic evidence helped Prichard to keep his magnum opus, Researches into the Physical History of Mankind, as logically ordered as possible, and therefore to turn ethnology into a discipline with analytical aspirations on a global scale. (shrink)

Scholars of the nineteenth-century race sciences have tended to identify the period from c.1820– c.1850 as a phase of transition from philologically to physically focused study. In France, the physiologist William Frédéric Edwards is normally placed near the center of this transformation. A reconsideration of Edwards’ oeuvre in the context of his larger biography shows that it is impossible to see a clear-cut philological to physical “paradigm shift.” Although he has been remembered almost solely for his principle of the permanency (...) of physical “types,” Edwards was also committed to what he recognized as the new science of “ linguistique” and proposed a new branch of comparative philology based on pronunciation. Bearing Edwards’ attention to linguistics in mind, this article reconstructs his racial theories in their intellectual contexts and suggests that at a time of emergent disciplinary specialization, Edwards tried to hold discrete fields together and mold them into a new “natural history of man.”. (shrink)

BackgroundSocio-cultural perceptions surrounding death have profoundly changed since the 1950s with development of modern intensive care and progress in solid organ transplantation. Despite broad support for organ transplantation, many fundamental concepts and practices including brain death, organ donation after circulatory death, and some antemortem interventions to prepare for transplantation continue to be challenged. Attitudes toward the ethical issues surrounding death and organ donation may influence support for and participation in organ donation but differences between and among diverse populations have not (...) been studied.ObjectivesIn order to clarify attitudes toward brain death, organ donation after circulatory death and antemortem interventions in the context of organ donation, we conducted a scoping review of international English-language quantitative surveys in various populations.Study appraisalA search of literature up to October 2020 was performed, using multiple databases. After screening, 45 studies were found to meet pre-specified inclusion criteria.Results32 studies examined attitudes to brain death, predominantly in healthcare professionals. In most, around 75% of respondents accepted brain death as equivalent to death of the person. Less common perspectives included equating death with irreversible coma and willingness to undertake organ donation even if it caused death. 14 studies examined attitudes to organ donation following circulatory death. Around half of respondents in most studies accepted that death could be confidently diagnosed after only 5 min of cardiorespiratory arrest. The predominant reason was lack of confidence in doctors or diagnostic procedures. Only 6 studies examined attitudes towards antemortem interventions in prospective organ donors. Most respondents supported minimally invasive procedures and only where specific consent was obtained.ConclusionsOur review suggests a considerable proportion of people, including healthcare professionals, have doubts about the medical and ethical validity of modern determinations of death. The prognosis of brain injury was a more common concern in the context of organ donation decision-making than certainty of death. (shrink)

It describes and explains the patient-centered model examining and evaluating qualitative and quantitative research. It comprehensively covers the evolution and the six interactive components of the patient-centered clinical method, taking the reader through the relationships between the patient and doctor and the patient and clinician. All the editors are professors in the Department of Family Medicine at the University of Western Ontario, London, Canada.

The practice of biobank networking—where biobanks are linked together, and researchers share human tissue samples—is an increasingly common practice both domestically and internationally. The benefits from networking in this way are well established. However, there is a need for ethical oversight in the sharing of human tissue. Ethics committees will increasingly be called upon to approve the sharing of tissue and data with other researchers, often via biobanks, and little guidance currently exists for such committees. In this paper, we provide (...) a structured approach to the ethical review of on-sharing of data and tissue for research purposes. (shrink)

BackgroundBiobanks provide an important foundation for genomic and personalised medicine. In order to enhance their scientific power and scope, they are increasingly becoming part of national or international networks. Public trust is essential in fostering public engagement, encouraging donation to, and facilitating public funding for biobanks. Globalisation and networking of biobanking may challenge this trust.MethodsWe report the results of an Australian study examining public attitudes to the networking and globalisation of biobanks. The study used quantitative and qualitative methods in conjunction (...) with bioethical analysis in order to determine factors that may contribute to, and threaten, trust.ResultsOur results indicate a generally high level of trust in biobanks and in medical research more broadly. Key factors that can reduce perceived trustworthiness of biobanks are commercialisation and involvement in global networking.ConclusionsWe conclude that robust ethical oversight and governance standards can both promote trust in global biobanking and ensure that this trust is warranted. (shrink)

In recent years, there has been a rapid growth in the use of autologous stem cell-based interventions to treat a wide range of medical conditions, including those for which there is limited evidence of safety and efficacy. One justification for this growth in the use of unproven interventions is that clinicians should be free to innovate, as long as consumers are adequately informed about risks and benefits. In this essay, we systematically refute the strong claim that consumer and clinician autonomy (...) provide sufficient justification for clinical innovation with autologous stem cells. While we do not deny the importance of consumer and clinician autonomy, we argue that equal consideration needs to be given... (shrink)

We describe the case of an eighty‐four‐year‐old man with disseminated lung cancer who had been receiving palliative care in the hospital and was found by nursing staff unresponsive, with clinically obvious signs of death, including rigor mortis. Because there was no documentation to the contrary, the nurses commenced cardiopulmonary resuscitation and called a code blue, resulting in resuscitative efforts that continued for around twenty minutes. In discussion with the hospital ethicist, senior nurses justified these actions, mainly citing disciplinary and medicolegal (...) concerns. We argue that moral harms arise from CPR performed on a corpse and that legal concerns about failing to perform it are unfounded. We contend that such efforts are an unintended consequence of managerialist policies mandating do‐not‐resuscitate orders and advance care plans and of defensive practices that can value the interests of institutions and practitioners over those of patients. Health management teaching should include managerialism and its pitfalls, while clinician training should prioritize ethical reasoning and legal knowledge over defensive practice. (shrink)

In response to the COVID-19 pandemic, there has been a rapid growth in research focused on developing vaccines and therapies. In this context, the need for speed is taken for granted, and the scientific process has adapted to accommodate this. On the surface, attempts to speed up the research enterprise appear to be a good thing. It is, however, important to consider what, if anything, might be lost when biomedical innovation is sped up. In this article we use the case (...) of a study recently retracted from the Lancet to illustrate the potential risks and harms associated with speeding up science. We then argue that, with appropriate governance mechanisms in place, it should be quite possible to both speed up science and remain attentive to scientific quality and integrity. (shrink)

Ethics and Law for the Health Professions is a cross-disciplinary medico-legal book whose previouseditions have been widely used in the medical world. This new 3rd edition is fully revised with all ethics and law topics updated to reflect recent developments. New chapters include dealing specifically with children, health care and the environment, infectious diseases, public health, and ethics and chronic disease. All law sections have been extensively re-visited by Dr Cameron Stewart. Its special features are its focus on a (...) clinically relevant approach, and its recognition that health care professionals are often confronted by legal issues and ethical issues at the same time. Health professionals have to satisfy both, and their legal advisers need to be aware of the dilemmas this can present. This book is careful to distinguish between ethics and law. Its chapters take account of all the health professions, and their differing responsibilities, and cover a very wide range of the issues they face. (shrink)

In 2016, the Office of the State Coroner of New South Wales released its report into the death of an Australian woman, Sheila Drysdale, who had died from complications of an autologous stem cell procedure at a Sydney clinic. In this report, we argue that Mrs Drysdale's death was avoidable, and it was the result of a pernicious global problem of an industry exploiting regulatory systems to sell unproven and unjustified interventions with stem cells.

ABSTRACTAIan Rumfitt's new book presents a distinctive and intriguing philosophy of logic, one that ultimately settles on classical logic as the uniquely correct one–or at least rebuts some prominent arguments against classical logic. The purpose of this note is to evaluate Rumfitt's perspective by focusing on some themes that have occupied me for some time: the role and importance of model theory and, in particular, the place of counter-arguments in establishing invalidity, higher-order logic, and the logical pluralism/relativism articulated in my (...) own recent *Varieties of logic*. (shrink)

ABSTRACTIn reply to Linnebo, I defend my analysis of Tait's argument against the use of classical logic in set theory, and make some preliminary comments on Linnebo's new argument for the same conclusion. I then turn to Shapiro's discussion of intuitionistic analysis and of Smooth Infinitesimal Analysis. I contend that we can make sense of intuitionistic analysis, but only by attaching deviant meanings to the connectives. Whether anyone can make sense of SIA is open to doubt: doing so would involve (...) making sense of mathematical quantities whose relationship to zero and to one another is inherently indeterminate. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:An Enquiry Concerning the Principles of MoralsIan RossDavid Hume. An Enquiry Concerning the Principles of Morals. Tom L. Beauchamp, editor. The Clarendon Edition of the Works of David Hume. New York: Oxford University Press, 1998.An edition of Hume's philosophic writings on rigorous, modern bibliographic principles has long been a scholarly desideratum. Readers in the many fields in which Hume's thought and style have made a profound impression have (...) basically relied on the originals or derivatives of efforts of the Victorian era. One is Hume's Philosophical Works (4 v., London: Longmans, Green & Co., 1874-75), edited by the Oxford dons, T. H. Green and T. H. Grose. Well-known for his idealist philosophy and theory of liberalism, Green contributed introductions to the first and second volumes criticizing Hume from an anti-empirical standpoint. Grose offered a "History of [Hume's] Editions" as an introduction to the third volume, and claimed to have revised Hume's text throughout. This edition has the virtue of comprehensiveness, but is deficient in its offering of variant readings. Later there came from Oxford University Press editions of the Treatise of Human Nature (1888), deemed generally sound, and the two Enquiries (1894), marred by departures from Hume's text, prepared by a prominent civil servant, Sir Lawrence Amherst Selby-Bigge, whose chief contribution was to provide useful analytical indices. An attempt at achieving higher editorial standards was made by P. H. Nidditch, Professor of Philosophy in the University of Sheffield, in a "second" edition of Selby-Bigge's Treatise (1976) and a "third" edition of his text of the Enquiries (1975). Limits were imposed by Oxford University Press, apparently unwilling to make more then small changes in the existing pages. Nidditch announced (Enquiries, 1975, at p.348, n.2) that he had a "fresh" edition in preparation, but he did not live to complete this project.In the event, the challenge to produce a critical edition of Hume's philosophical, political, and literary writings was canvassed at early meetings of the Hume Society formed in 1973. Thereafter, in 1982, a team of general editors was formed by T. L. Beauchamp, D. F. Norton, and M. A. Stewart, determined to organize and finish the task in hand, and Oxford University Press finally conceded it was time to replace Selby-Bigge. With the appearance of Tom Beauchamp's "critical edition" of the second Enquiry (hereafter identified as EPM), published on 4 August 1999, but bearing the date 1998, the long wait for a reliable text, bibliographic apparatus, and ancillary scholarship, worthy of Hume, must be declared over.If we grant that it is appropriate to introduce the new Clarendon Edition of the Works of David Hume with the piece he deemed "best," it must also be asked why he made this judgment. Philosophers have generally held that his Treatise of Human Nature (1739-40) is the most profound and searching statement of his epistemological and moral thought, but its seeming lack of immediate success with readers made Hume dissatisfied with it. Such were his negative feelings, coupled with irritation at attacks on him focused on this "juvenile" work, that he partially repudiated the Treatise at the end of his life. He wrote an "Advertisement" to this effect, and it was inserted as a preface to the authoritative and posthumous 1777 edition of his Essays and Treatises. Here he stated he was "sensible of the error of going to the press too early, and he cast the whole [of [End Page 280] the Treatise] anew in the following pieces [including EPM], where some negligences in his former reasoning and more in the expression, are, he hopes, corrected" (EPM Intro., xii-xiii, n.4).On the evidence of Beauchamp's editorial labors, it would appear that EPM is Hume's "best" work in this sense. It represents the most thorough recasting of source material provided by the Treatise. Its essential moral principles and psychological insights about the passions are retained, but "readability and elegance" are achieved by pruning, simplifying, and compacting the Treatise's complex teaching, while adding a wealth of illustrative material drawn from Hume's mature reflection on his subject and... (shrink)

This paper employs Ian Hacking’s notion of interactive kinds to examine the recent construction of the kind, “depressed adolescent.” I examine first how adolescents themselves were constructed. I then trace how, in North America, we have moved in the past thirty-odd years from a situation of virtually no adolescent depression to the current situation where it is estimated that approximately one in four adolescents is depressed. I offer some reasons why we should be uncomfortable both with the exponential increases in (...) this kind and with the way in which depressed adolescents are being treated at present. In conclusion, I tentatively suggest some ways of proceeding in the future. (shrink)

This paper employs Ian Hacking’s notion of interactive kinds to examine the recent construction of the kind, “depressed adolescent.” I examine first how adolescents themselves were constructed. I then trace how, in North America, we have moved in the past thirty-odd years from a situation of virtually no adolescent depression to the current situation where it is estimated that approximately one in four adolescents is depressed. I offer some reasons why we should be uncomfortable both with the exponential increases in (...) this kind and with the way in which depressed adolescents are being treated at present. In conclusion, I tentatively suggest some ways of proceeding in the future. (shrink)