This paper puts forward a new account of rigorous mathematical proof and its epistemology. One novel feature is a focus on how the skill of reading and writing valid proofs is learnt, as a way of understanding what validity itself amounts to. The account is used to address two current questions in the literature: that of how mathematicians are so good at resolving disputes about validity, and that of whether rigorous proofs are necessarily formalizable.

This paper sketches an account of the standard of acceptable proof in mathematics—rigour—arguing that the key requirement of rigour in mathematics is that nontrivial inferences be provable in greater detail. This account is contrasted with a recent perspective put forward by De Toffoli and Giardino, who base their claims on a case study of an argument from knot theory. I argue that De Toffoli and Giardino’s conclusions are not supported by the case study they present, which instead is a very (...) good illustration of the kind of view of proof defended here. (shrink)

Although Peano arithmetic is necessarily incomplete, Isaacson argued that it is in a sense conceptually complete: proving a statement of the language of PA that is independent of PA will require conceptual resources beyond those needed to understand PA. This paper gives a test of Isaacon’s thesis. Understanding PA requires understanding the functions of addition and multiplication. It is argued that grasping these primitive recursive functions involves grasping the double ancestral, a generalized version of the ancestral operator. Thus, we can (...) test Isaacon’s thesis by seeing whether when we phrase arithmetic in a context with the double ancestral operator, the result is conservative over PA. This is a stronger version of the test given by Smith, who argued that understanding the predicate “natural number” requires understanding the ancestral operator, but did not investigate what is required to understand the arithmetic functions. (shrink)

The initial motivating question for this thesis is what the standard of rigour in modern mathematics amounts to: what makes a proof rigorous, or fail to be rigorous? How is this judged? A new account of rigour is put forward, aiming to go some way to answering these questions. Some benefits of the norm of rigour on this account are discussed. The account is contrasted with other remarks that have been made about mathematical proof and its workings, and is tested (...) and illustrated by considering a case study discussed in the literature. On the view put forward here one can obtain a manner of informal, rigorous mathematics founded on any of a variety of proof systems. The latter part of the thesis is concerned with the question of how we should decide which of these competing proof systems we should base our mathematics on: i.e., the question of which proof system we should take as a foundation for our mathematics. A novel answer to this question is proposed, in which the key property we should require of a proof system is that for as many different kinds of structures as possible, when the proof system allows a generalization about that kind of structure to be proved, the generalization actually holds of all real examples of that kind of structure which exist. This is the requirement of soundness of the proof system. It is argued that the best way to establish the soundness of a proof system may be by giving an interpretation of its axioms on which they are established as true. As preparation for this discussion, the thesis first investigates the logical and conceptual basis of various arithmetic concepts, with the results obtained used in the final discussion of soundness. (shrink)

This paper gives a semantics for schematic logic, proving soundness and completeness. The argument for soundness is carried out in ontologically innocent fashion, relying only on the existence of formulae which are actually written down in the course of a derivation in the logic. This makes the logic available to a nominalist, even a nominalist who does not wish to rely on modal notions, and who accepts the possibility that the universe may in fact be finite.

On 8 October 2020, the British Medical Association published the results of its survey of BMA members on physician-assisted dying. With 28 986 respondents, this was one of the largest surveys of medical opinion on this topic ever carried out. This represents 19.35% of those who received an invitation to participate and the respondents were broadly representative of the BMA’s overall membership. The BMA was clear throughout this process that the results of the survey would not determine its policy. Its (...) current policy of opposition to all forms of physician-assisted dying would remain unless and until the Representative Body, which makes BMA policy, decided otherwise. The survey results would, however, inform a future debate on policy, currently scheduled to take place in June 2021. When asked what the BMA’s position should be on whether there should be a change in the law to allow doctors to prescribe drugs for an eligible patient to self-administer to end their own life, 40% said the BMA should be supportive, 33% opposed, 21% thought the BMA should be neutral and 6% were undecided. In relation to their own personal views, 50% were supportive, 39% opposed and 11% undecided. When asked whether they would be willing to participate in some way in the process, if it were to be legalised, 36% said yes, 45% said no and 19% were undecided. The same three questions were asked about a change in the law to allow doctors to administer drugs to end the life of an eligible patient. In response, 40% thought the BMA should oppose such a change, 30% thought the BMA should be supportive and 23% thought the BMA should be neutral; 7% of members responding were undecided on this question. In …. (shrink)

During the first UK wave of the pandemic, there were two areas of immediate ethical concern for the medical profession. The first was the possibility that life-saving resources could be overwhelmed. Early reports from hospitals in the Italian city of Bergamo suggested that ventilatory support might need rationing and emergency ‘battlefield’ triage was a real possibility.1 In the UK, several professional bodies, including the British Medical Association and the Royal College of Physicians rapidly developed guidance for doctors should triage become (...) a reality.2 The second issue was the acute shortage of personal protective equipment. Where doctors were unable to protect their patients – and themselves – from the risk of COVID-19, ethical challenges emerged. Ordinarily, doctors and patients do not present risks of significant harm to each other. To shift to a position where every patient – and every health professional – could potentially be a threat presented serious clinical and ethical challenges. To treat with inadequate PPE, so options for mitigating harms are radically reduced, deepens the challenges. Among the questions the BMA wrestled with was the extent of doctors’ duties to treat infected or potentially infected patients in the absence of effective PPE. The BMA was clear that despite obligations to treat, medicine is not a self-sacrificing profession: there were limits to the risk doctors could be required to expose themselves to.3 These issues no longer seem so pressing. In the UK at least, there is adequate PPE and with the second steep wave behind us, and significant numbers vaccinated, it is less likely that triage will be required in the UK. But as those concerns have receded so other ethical questions have arisen. Among them is a cluster of issues associated with what might be called COVID-19’s indirect harms. Understandably, in response to …. (shrink)

In parts of the world, discussion regarding COVID-19 has shifted towards endemicity, and questions of living with, rather than directly battling, the virus. As a result, ethical questions are being refocussed. The imperative is beginning to shift towards what we can learn from the pandemic, and how we can better prepare for future global outbreaks. Among the questions that need to be addressed is what Covid-29 has taught us about how research can be conducted ethically during major global public health (...) emergencies. It is widely accepted that research has an essential role to play in improving the effectiveness of health interventions in major public health crises.1 Even before COVID-19, a special series published in The Lancet highlighted the critical role of research in humanitarian crises, and lamented the paucity of good data on the effectiveness of health interventions in these particularly demanding contexts.2 The impact of expedited vaccine research on the mortality, morbidity and global disruption of the COVID-19 pandemic would be difficult to exaggerate. But it is clear that one important driver of vaccine hesitancy was public concern about the speed with which research into the vaccines was undertaken and hence the reliability of the data concerning their safety.3 Although for understandable reasons, the focus of attention on ethical research during the COVID-19 pandemic has been on vaccines and anti-virals, research in public health emergencies involves a wide range of activities designed to generate evidence, including social science research – which can be particularly critical in understanding barriers to vaccine uptake for example – along with epidemiological studies and health systems research. One widely acknowledged area of ethical tension concerning research in public health emergencies is between the need for rapid ethical review, and the strong moral requirement …. (shrink)

An Amnesty International briefing, published in July 2020, highlights the grave risks health workers are facing globally, particularly in the face of the COVID-19 pandemic.1 The report uses data from 63 countries across the world from January to June 2020 and is rich with examples. While recognising that information about the pandemic is constantly evolving, and each country is in a separate phase of the outbreak, Amnesty International draws attention to several troubling trends. By virtue of the role undertaken by (...) health workers, they face a greater exposure to COVID-19, which has contributed to many of the concerns they now deal with. The briefing notes the evidence of the higher death rate from health workers compared with the general population in countries ranging from Denmark to Argentina, while also pointing out the significantly higher death rate in BAME health workers raised by the BMA in the UK.2 PPE shortages had been reported in nearly all of the 63 countries analysed. Many health workers globally stated that they had to buy their own PPE and others described cases of ‘improvisation’, when suitable PPE was not available, such as using bin bags or raincoats. Furthermore, health workers in several countries had experienced increases in workload with formal measures to extend health workers’ contracted hours passed in some countries as well as further changes to their terms and conditions of service. There were also reports of increased mental stress, particularly from those working in ICUs; the increased work and stress is not being matched with suitable compensation or remuneration. Despite many countries passing special benefits for health workers, it was commonly stated that these benefits had not been received yet or that they did not apply to all health workers, with cleaners and other lower-paid yet vital roles excluded. Deeply concerning …. (shrink)

At the time of writing the COVID-19 pandemic was entering its ninth month, with nearly 800 000 recorded fatalities and 22 million infections in 188 countries and territories.1 In previous ethics briefings2 we raised concerns about the possibility that demand for life-sustaining treatment would overwhelm supply, with a consequent requirement for health professionals to make challenging triage decisions. Fortunately, to date, these have largely not been realised, although there is a possibility that countries in which containment measures have been less-successful, (...) such as South Africa, may still be required to triage.3 Despite the successful ‘flattening of the curve’ in many countries, there is a wide consensus that we remain firmly within the pandemic. Enormous practical challenges remain. It is unclear whether the pandemic will ultimately take the form of two or more successive waves, or whether the patchwork of global responses will lead to a sustained slow ‘burn’ with sporadic flare-ups.4 Areas of uncertainty include whether infection confers some immunity, how long any such immunity might last, whether effective vaccines can be developed and if seasonal temperature fluctuations alter the spread of the virus. The pandemic will also be fundamentally shaped by the decisions that governments make and the extent to which their diktats are complied with by citizens. With the – possibly temporary – retreat of urgent clinical ethics issues, such as triage, opportunities have arisen to reflect on some of the ethical questions that underlie and structure the demanding policy decisions that governments are wrestling with. One of the early questions was how to balance the complex constellation of costs and benefits associated with lockdown. Countries that …. (shrink)

In December, the National Data Guardian 1 for health and care in England, Dame Fiona Caldicott, published the outcomes of a public consultation about the Caldicott Principles and the role of Caldicott Guardians.1 The Caldicott Principles are good practice guidelines which have been used by health and social care organisations in the UK since 1997 to ensure that people’s data are kept safe and used in an ethical way.2 The role of the Caldicott Guardian is well-established in the UK. Caldicott (...) Guardians are senior people which support the upholding of the Caldicott Principles within organisations. In response to views expressed during the consultation the NDG has added an eighth Caldicott Principle to the existing seven and will use her statutory powers to issue guidance about the appointment of Caldicott Guardians for health and adult social care organisations. The new eighth Caldicott Principle is: ‘Inform patients and service users about how their confidential information is used’. It provides that: > A range of steps should be taken to ensure no surprises for patients and service users, so they can have clear expectations about how and why their confidential information is used, and what choices they have about this. These steps will vary depending on the use: as a minimum, this should include providing accessible, relevant and appropriate information - in some cases, greater engagement will be required. The NDG explains that the introduction of the new principle was prompted by consideration of the role that the legal concept of ‘reasonable expectations’ should play in shaping the circumstances under which health and care data may be legitimately shared. The NDG does not envisage that this principle will establish reasonable expectations as a legal basis in its own right …. (shrink)

As the COVID-19 vaccine roll out continues apace, in the higher-income countries at least, concerns remain about the level of vaccine coverage in some health and social care settings. Although most countries have seen a relatively high uptake of vaccination against COVID-19 among staff, there continue to be some pockets of hesitancy. The risk of outbreaks in settings with potentially very vulnerable patients has led some governments across Europe to consider, or to introduce, measures compelling healthcare staff to be vaccinated. (...) The justifiability of mandating the vaccination of healthcare professionals is a longstanding question but it has come to the fore in recent months following a resurgence of cases of COVID-19 and the prevalence of the more transmissible Delta variant. In deciding whether the introduction of a mandate is appropriate, states have to balance a range of ethical and practical considerations. A voluntary approach, backed up with education, respects healthcare workers’ autonomy to make private healthcare decisions, which is valued highly in liberal democracies. However, healthcare professionals also have an obligation to ensure that they do not present a risk of harm to their patients. Similarly, healthcare providers have a responsibility to take appropriate steps to minimise the risk of infection. Alongside balancing these rights and responsibilities, governments must also consider the potential consequences and risks of enforcing vaccine uptake. For example, there are concerns that a coercive approach could deepen mistrust and resentment among people who are genuinely fearful or hesitant. Moreover, a large number of refusals and the subsequent imposition of sanctions, such as suspension or redeployment, could affect the ability of providers to staff necessary services. In the UK, Wales, Northern Ireland and Scotland have all ruled out the introduction of compulsory vaccination. However, in July, the English Parliament voted through …. (shrink)

### Challenge to the abortion act 1967 dismissed In September, the High Court dismissed a judicial review of the Abortion Act 1967 that sought a judgement of incompatibility with the European Convention on Human Rights.1 The case focused on a clause in the Act which permits abortion in England, Scotland and Wales after 24 weeks if there is a substantial risk that, if the child were born, it would suffer from ‘such physical or mental abnormalities as to be seriously handicapped’. (...) The case was brought by three parties: Heidi Crowter, a 24 year old woman living independently with Downs Syndrome and a campaigner for disability rights; a 2 year old boy with DS; and his mother who, when pregnant with him, felt pressure to terminate the pregnancy. The claimants sought a declaration that the clause was incompatible with the right to life; freedom from torture, inhuman or degrading treatment; right to private and family life; and protection from discrimination. Further to this it was also argued that the Act does not permit abortion on the basis that an unborn child has been diagnosed with a non-fatal fetal disability such as DS and that such abortions should not be funded by the state. In dismissing the claim, the judges focused on the ‘margin of appreciation’ that the European law allows domestic states on this issue and the fact that a foetus has never been deemed to have personhood status under the ECHR. The judges noted the ability to provide for a disabled child would vary significantly and that some conditions would only be found late in a pregnancy, after 24 weeks. Stating that the case by its nature did not permit the Court to hear from other perspectives, including women who may be affected by any change to the law and further criminalisation of abortion, the judges emphasised …. (shrink)

In a recent judgment1 the Court of Protection was highly critical of health professionals for continuing to provide clinically-assisted nutrition and hydration in the face of disagreement about the patient’s best interests, without seeking to resolve the issue. This hearing had been set up specifically to consider whether GU’s dignity had been properly protected, and if not why not, given concerns raised by the Official Solicitor about what she considered to be “a complete abrogation of responsibility to consider properly or (...) at all, and to determine whether it was in GU’s best interests and therefore lawful to continue to give him an invasive medical treatment, CANH.” In April 2014, at 63 years old and living in Thailand, GU sustained severe injuries after suffering from an electrocution accident. He sustained a cardiorespiratory arrest with a significant delay before cardiopulmonary resuscitation was started and was unconscious and unresponsive. In September 2014 he was transferred to the UK. In August 2018, GU’s brother made a request for a best interests decision concerning the continuation of CANH. The family met to discuss this and all except GU’s son, agreed that continuing CANH was not in GU’s best interests. In view of the fact that there was not unanimity among the family, a decision was made that CANH should continue. Commenting on this decision, Mr Justice Hayden said ‘the apparent assumption that in the face of family disagreement ‘ therefore will continue to be cared for by nursing staff ” is a troubling non sequitur’ and stressed that ‘family dissent to a medical consensus should never stand in the way of an incapacitated patients’ best interests being properly identified’. He also made clear that the responsibility for ensuring that a best interests assessment is undertaken rests with the …. (shrink)

Restrictive border protection policies directed toward managing the flow of refugees coming into neoliberal democracies (and out of failing nation-states) are a defining feature of contemporary politics. In this book, Verónica Tello analyses how contemporary artists-such as Tania Bruguera, Isaac Julien, Rosemary Laing, Dinh Q. Lé, Dierk Schmidt, Hito Steyerl, Lyndell Brown and Charles Green-negotiate their diverse subject positions while addressing and taking part in the production of images associated with refugee experiences and histories. Tello argues that their practices, (...) which manifest across a range of contexts including Cuba, the United States, Australia and Europe, represent an emergent, global paradigm of contemporary art, 'counter-memorial aesthetics'. Counter-Memorial Aesthetics, Tello argues, is characterized by its conjunction of heterogeneous signifiers and voices of many times and places, generating an experimental, non-teleological approach to the construction of contemporary history, which also takes into account the complex, disorienting spatial affects of globalization. Spanning performance art, experimental 'history painting', aftermath photography and video installation, counter-memorial aesthetics bring to the fore, Tello argues, how contemporary refugee flows and related traumatic events critically challenge and conflict with many existing, tired if not also stubborn notions of national identity, borders, history and memory. Building on the writings of such thinkers as Michel Foucault and Jacques Rancière, this book offers a useful concept of 'counter-memory' for the twenty-first century. It shows how counter-memorial aesthetics is not only central to the nexus of contemporary art and refugee histories but also how it can offer a way of being critically present with many other, often interrelated, global crises in the contemporary era. (shrink)

In June 2021, the BMA published its report on moral distress and moral injury in UK doctors.1 The report includes definitions of the terms ‘moral distress’ and ‘moral injury’ as well as a summary of how the concepts have developed over time. There is also an analysis of the BMA’s pan-profession survey of moral distress and moral injury of doctors in the UK, the first of its kind. The impact of COVID-19 and recommendations for tackling moral distress also feature. Many (...) may be unfamiliar with the concepts of ‘moral distress’ and ‘moral injury’. These terms are relatively new, and debate is ongoing in academic circles on the best way to understand them.2 Some use the terms interchangeably. The BMA defines moral distress as the psychological unease generated where professionals identify an ethically correct action to take but are constrained in their ability to take that action. Even without an understanding of the morally correct action, moral distress can arise from the sense of a moral transgression. More simply, it is the feeling of unease stemming from situations where institutionally required behaviour does not align with moral principles. This can be as a result of a lack of power or agency, or structural limitations, such as insufficient staff, resources, training or time. The individual suffering from moral distress need not be the one who has acted or failed to act; moral distress can be caused by witnessing moral transgressions by others. Moral injury can arise where sustained moral distress leads to impaired function or longer-term psychological harm. Moral injury can produce profound guilt and shame, and in some cases also a sense of betrayal, anger and profound ‘moral disorientation’. It has also been linked to severe mental health issues. There is increasing recognition across the UK of the problem …. (shrink)

This chapter explores how what is dismissed as “trans activism” is often public philosophy. It considers how so‐called “public philosophy” on trans issues often does a substantially worse job of living up to the name. The chapter discusses how the dichotomy between “trans activism” and “public philosophy” provides a pretext for marginalizing trans voices. To draw on Black feminist philosophical thought, lived experience is a criterion for knowledge of the needs of marginalized people. Like other marginalized communities, trans communities have (...) encountered many areas in which hermeneutical liberation is needed. Public philosophy as trans activism is often systemically and systematically ignored or willfully misinterpreted as being biased and motivated by self‐interest, whereas anti‐trans (public) philosophy is seen as asking the important questions. (shrink)

Algorithms wield increasing control over our lives—over which jobs we get, whether we're granted loans, what information we're exposed to online, and so on. Algorithms can, and often do, wield their power in a biased way, and much work has been devoted to algorithmic bias. In contrast, algorithmic neutrality has gone largely neglected. I investigate three questions about algorithmic neutrality: What is it? Is it possible? And when we have it in mind, what can we learn about algorithmic bias?

Fallibilists claim that one can know a proposition on the basis of evidence that supports it even if the evidence doesn't guarantee its truth. Jessica Brown offers a compelling defence of this view against infallibilists, who claim that it is contradictory to claim to know and yet to admit the possibility of error.

According to the Desiderative Lockean Thesis, there are necessary and sufficient conditions, stated in the terms of decision theory, for when one is truly said to want. What one is truly said to want, it turns out, varies remarkably by context—and to an underappreciated degree. To explain this context-sensitivity—and closure properties of wanting—I advance a Desiderative Lockean view that is distinctive in having two context-sensitive parameters.

La 4e de couverture indique : "Du Mutterrecht, l'oeuvre majeure de Bachofen, Walter Benjamin écrivait qu'il s'agissait d'une « prophétie scientifique ». De prime abord, il s'agit là d'une étrange définition pour un ouvrage qui, loin de se tourner vers l'avenir et d'en délinéer les formes, explore les confins du passé pour esquisser, par le biais de l'étude des mythes, le contour de l'origine de nos sociétés. La pensée de Bachofen est prophétique car révolutionnaire, et par là même porteuse de (...) fruits pour l'avenir. Il a en effet avancé une thèse bouleversante : les premières sociétés humaines auraient été régies par un droit maternel, l'organisation patriarcale n'étant qu'une forme plus avancée, certes, mais plus tardive de l'évolution spirituelle et sociale de l'humanité. Sa pensée permet ainsi de réfléchir à la prégnance de l'opposition masculin/féminin, maternel/paternel dans les fondements mêmes de nos sociétés, mais aussi de considérer l'importance que la notion d'origine, et la représentation, pour erronée qu'elle soit, qui en est faite, revêt pour la construction et le maintien de la société et de ses structures. C'est bien là une réflexion avec laquelle, aux dires de Bachofen lui-même, « on n'est pas prêt d'en finir ».". (shrink)

You want to see the concert, but don’t want to take a long drive (even though the concert is far away). Such *strongly conflicting desire ascriptions* are, I show, wrongly predicted incompatible by standard semantics. I then object to possible solutions, and give my own, based on *some-things-considered desire*. Considering the fun of the concert, but ignoring the drive, you want to see the concert; considering the boredom of the drive, but ignoring the concert, you don’t want to take the (...) drive. (shrink)

In this paper, we examine the scientific, legal, and ethical foundations for inclusion of transgender women athletes in competitive sport, drawing on IOC principles and relevant Court of Arbitration for Sport decisions. We argue that the inclusion of trans athletes in competition commensurate with their legal gender is the most consistent position with these principles of fair and equitable sport. Biological restrictions, such as endogenous testosterone limits, are not consistent with IOC and CAS principles. We explore the implications for recognizing (...) that endogenous testosterone values are a ‘natural physical trait’ and that excluding legally recognized women for high endogenous testosterone values constitutes discrimination on the basis of a natural physical trait. We suggest that the justificatory burden for such prima facie discrimination is unlikely to be met. Thus, in place of a limit on endogenous testosterone for women, we argue that ‘legally recognized gender’ is most fully in line with IOC and CAS principles. (shrink)

The doctor-patient relationship -- Consent, choice, and refusal : adults with capacity -- Treating adults who lack capacity -- Children and young people -- Confidentiality -- Health records -- Contraception, abortion, and birth -- Assisted reproduction -- Genetics -- Caring for patients at the end of life -- Euthanasia and physician assisted suicide -- Responsibilities after a patient's death -- Prescribing and administering medication -- Research and innovative treatment -- Emergency situations -- Doctors with dual obligations -- Providing treatment and (...) care in detention settings -- Education and training -- Teamwork, referral, delegation, and shared care -- Public health dimensions of medical practice -- Reducing risk, clinical error, and poor performance. (shrink)

At the outset of an ethnographic inquiry, we navigated national and international resources to search for theoretical and practical guidance on obtaining parents and children’s informed consent/assent. While much theoretical guidance debating ethical issues to children’s participation in research was found, a paucity of published papers offering practical guidance on assent processes and/or visual representations of child assent forms and information sheets was discovered. The purpose of this article is to describe our experiences, both theoretically and practically, of negotiating the (...) process of obtaining informed consent and assent with parents and children for a non-therapeutic qualitative research study. We hope this article instigates a platform for others to explicate their experience and contributes to the construction of a coherent body of knowledge which will clearly delineate important elements that must be considered when negotiating children’s agreement to participate in research. (shrink)

Offers a historical-cultural context for the ethos of service in libraries and critically examines this professional value as it intersects with gender, sexuality, race and ethnicity, class, and (dis)ability"--Provided by publisher.

This article aims to reconstruct the essential lines of Kant’s theory of meaning as it appears in critical Kantian philosophy. More particularly, an originality of the Kantian theory of meaning is highlighted, namely the distinction that this theory introduces between two modalities of meaning, namely a theoretical modality and a practical, that is to say a moral modality.