From ancient times to the present, the discovery and presentation of new proofs of previously established theorems has been a salient feature of mathematical practice. Why? What purposes are served by such endeavors? And how do mathematicians judge whether two proofs of the same theorem are essentially different? Consideration of such questions illuminates the roles that proofs play in the validation and communication of mathematical knowledge and raises issues that have yet to be resolved by mathematical logicians. The Appendix, in (...) which several proofs of the Fundamental Theorem of Arithmetic are compared, provides a miniature case study. (shrink)

This article provides an English translation of a historic discussion on the foundations of mathematics, during which Kurt GÖdel first announced his incompleteness theorem to the mathematical world. The text of the discussion is preceded by brief background remarks and commentary.

As initially envisioned, Gödel's Collected Works were to include transcriptions of material from his mathematical workbooks. In the end that material, as well as some other manuscript items from Gödel's Nachlass, had to be left out. This note describes some of the unpublished items in the Nachlass that are likely to attract the notice of scholars and surveys the extent of shorthand transcription efforts undertaken hitherto. Some examples of sources outside Gödel's Nachlass that may be of interest to Gödel scholars (...) are also indicated. (shrink)

Though regarded today as one of the most important results in logic, the compactness theorem was largely ignored until nearly two decades after its discovery. This paper describes the vicissitudes of its evolution and transformation during the period 1930-1970, with special attention to the roles of Kurt Gödel, A. I. Maltsev, Leon Henkin, Abraham Robinson, and Alfred Tarski.

In September of 2002, without fanfare, Ivor Grattan-Guinness retired from the faculty of Middlesex University. His scholarly activity, however, has continued unabated, his time now no longer fetter...

The word “euthanasia” is hopelessly overloaded with emotional connotations. It means so many things to many different people. The implications of euthanasia associated with the Second World War have often rendered the term unsuitable for discussions of a rational manner. As far as I am concerned, what happened in Germany under Hitler had nothing to do with the classic meaning of a gentle and easy death but was rather simply a policy of mass murder.

Despite recent advances in HIV prevention and treatment, high HIV incidence persists among people who inject drugs. Difficult legal and political environments and lack of services for PWID likely contribute to high HIV incidence. Some advocates question whether any HIV prevention research is ethically justified in settings where healthcare system fails to provide basic services to PWID and where implementation of research findings is fraught with political barriers. Ethical challenges in research with PWID include concern about whether research evidence will (...) be translated into practice; concerns that research might exacerbate background risks; and ethical challenges regarding the standard of HIV prevention in research. While these questions arise in other research settings, for research with PWID, these questions are especially controversial. This paper analyses four ethical questions in determining whether research could be ethically acceptable: Can researchers ensure that research does not add to the burden of social harms and poor health experienced by PWID? Should research be conducted in settings where it is uncertain whether research findings will be translated into practice? When best practices in prevention and care are not locally available, what standard of care and prevention is ethically appropriate? Does the conduct of research in settings with oppressive policies constitute complicity? We outline specific criteria to address these four ethical challenges. We also urge researchers to join the call to action for policy change to provide proven safe and effective HIV prevention and harm reduction interventions for PWID around the world. (shrink)

Despite recent advances in HIV prevention and treatment, high HIV incidence persists among people who inject drugs. Difficult legal and political environments and lack of services for PWID likely contribute to high HIV incidence. Some advocates question whether any HIV prevention research is ethically justified in settings where healthcare system fails to provide basic services to PWID and where implementation of research findings is fraught with political barriers. Ethical challenges in research with PWID include concern about whether research evidence will (...) be translated into practice; concerns that research might exacerbate background risks; and ethical challenges regarding the standard of HIV prevention in research. While these questions arise in other research settings, for research with PWID, these questions are especially controversial. This paper analyses four ethical questions in determining whether research could be ethically acceptable: Can researchers ensure that research does not add to the burden of social harms and poor health experienced by PWID? Should research be conducted in settings where it is uncertain whether research findings will be translated into practice? When best practices in prevention and care are not locally available, what standard of care and prevention is ethically appropriate? Does the conduct of research in settings with oppressive policies constitute complicity? We outline specific criteria to address these four ethical challenges. We also urge researchers to join the call to action for policy change to provide proven safe and effective HIV prevention and harm reduction interventions for PWID around the world. (shrink)

According to several commentators, Kurt Godel's incompleteness discoveries were assimilated promptly and almost without objection by his contemporaries - - a circumstance remarkable enough to call for explanation. Careful examination reveals, however, that there were doubters and critics, as well as defenders and rival claimants to priority. In particular, the reactions of Carnap, Bernays, Zermelo, Post, Finsler, and Russell, among others, are considered in detail. Documentary sources include unpublished correspondence from Godel's Nachlass.

If stem cell-based therapies are developed, we will likely confront a difficult problem of justice: for biological reasons alone, the new therapies might benefit only a limited range of patients. In fact, they might benefit primarily white Americans, thereby exacerbating long-standing differences in health and health care.

In crafting our paper on addressing the ethical challenges in HIV prevention research with people who inject drugs,1 we had hoped to stimulate further discussion and deliberation about the topic. We are pleased that three commentaries on our paper have begun this process.2 3 4 The commentaries rightly bring up important issues relating to community engagement and problems in translating research into practice in the fraught environments in which PWID face multiple risks. These risks include acquisition of HIV as well (...) as criminalisation, stigma and lack of access to needed healthcare, prevention and social services. We take this opportunity to respond to the excellent points raised by the commentators. All of the commentaries support our emphasis on robust community engagement with PWID and other stakeholders in designing and conducting HIV prevention research, but urge us to go farther. Wolfe highlights the difficulty of even engaging with community members in oppressive settings, where authorities severely restrict civil liberties of PWID so that even discussing issues related to drug use and enforcement may place individuals at risk. To overcome such limitations, he appropriately suggests interviewing confidentially those who have previously been detained in closed settings as part of the community engagement process. Similarly, Wolfe observes that critical issues can be overlooked with a narrow focus on study procedures if contextual factors before, during or after a study are ignored. For example, he cites the risk of overdose for study participants who have been abstinent during a study and subsequently resume injecting when the study concludes. These kinds of risks may not be obvious …. (shrink)

In crafting our paper on addressing the ethical challenges in HIV prevention research with people who inject drugs, 1 we had hoped to stimulate further discussion and deliberation about the topic. We are pleased that three commentaries on our paper have begun this process. 2 3 4 The commentaries rightly bring up important issues relating to community engagement and problems in translating research into practice in the fraught environments in which PWID face multiple risks. These risks include acquisition of HIV (...) as well as criminalisation, stigma and lack of access to needed healthcare, prevention and social services. We take this opportunity to respond to the excellent points raised by the commentators. All of the commentaries support our emphasis on robust community engagement with PWID and other stakeholders in designing and conducting HIV prevention research, but urge us to go farther. Wolfe highlights the... (shrink)

A colleague’s personal recollections of Jean van Heijenoort’s contributions to the editing of volumes I–III of Gödel’s Collected Works and of his interactions with the other editors.

The papers of Kurt Gödel were donated to the Institute for Advanced Study by his widow Adele shortly after his death in 1978. They were catalogued by the review.

History and Philosophy of Logic, Volume 0, Issue 0, Page 1-2, Ahead of Print.

It is with profound sadness that the editors note the passing on 12 December 2014 of Professor Ivor Grattan-Guinness. Born 23 June 1941, Ivor was the founding editor of History and Philosophy of Lo...

Summary Background Self-binding directives instruct clinicians to overrule treatment refusal during future severe episodes of illness. These directives are promoted as having potential to increase autonomy for individuals with severe episodic mental illness. Although lived experience is central to their creation, service users’ views on self-binding directives have not been investigated substantially. This study aimed to explore whether reasons for endorsement, ambivalence, or rejection given by service users with bipolar disorder can address concerns regarding self-binding directives, decision-making capacity, and human (...) rights. Methods This study used qualitative data from an internet-based survey distributed to the mailing list of the UK charity Bipolar UK, which contained multiple closed and open questions on advance decision-making in bipolar disorder. Quantitative analysis of a closed question about self-binding directives had already demonstrated endorsement amongst a very high proportion of participants with bipolar disorder who completed the survey. We conducted thematic analysis of responses from those participants who answered a subsequent open question about reasons for their view. Research was co-produced within a multi-disciplinary team, with clinical, legal, and ethical expertise, and lived experience of bipolar disorder. Ideas and methodologies associated with all these areas of expertise were used in the analysis of these reasons and to gain insight into the thoughts of individuals with bipolar disorder about self-binding directives and associated issues. Findings Between Oct 23 and Dec 5, 2017, 932 individuals with a self-reported clinical diagnosis of bipolar disorder completed the internet survey, with 565 (154 men; 400 women; 11 transgender or other) providing free text answers to the open question. A large majority of respondents endorsed self-binding directives, nearly all describing a determinate shift to types of distorted thinking and decision-making when unwell as their key justification. Responses indicating ambivalence were dominated by logistical concerns about the drafting and implementation of self-binding directives, while those who rejected self-binding directives also cited logistical concerns, validity of their thinking when unwell, and potential contravention of human rights. Interpretation This study is, to our knowledge, the first large study of reasons why mental health service users might endorse or reject the use of self-binding directives. The findings provide empirical support for introducing self-binding directives into mental health advance decision-making practice and policy and may help to address enduring ethical concerns surrounding possible implementation of the directive while a person retains decision-making capacity. The opinions expressed here in responses given by multiple service users with bipolar disorder challenge a prominent view within international disability rights debates that involuntary treatment and recognition of impaired mental capacity constitute inherent human rights violations. Funding The Wellcome Trust . (shrink)