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)

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)

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.

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.

Transition education is a major challenge to be taken up. It is not simply a question of teaching a person a specific area of ​​knowledge – in this case ecological and societal questions – but rather recognizing that individuals are built by their reflections, with their feelings and according to their experiences. None of these dimensions should be left aside if we want to promote the full development of each individual. In this sense it seems important to us to explain (...) the values ​​that underlie our educational offer and the goals pursued by transition education, as well as its founding roots. This chapter thus starts by presenting the pillars for head-heart-body learning, namely a pedagogy that is relational and transformational, integrative and holistic, inter- and transdisciplinary, rooted and open. Secondly, we structure the pedagogy of the transition around six major areas of questioning, corresponding to the six gates of the FORTES approach. Eventually, drawing on the competency-based approach we present the six main transversal skills to be acquired. (shrink)

Implementing a head-heart-body pedagogy in higher education institutions needs the mobilization of all the actors currently involved in education, to identify those who are absent today and surpass the logic that feeds on silo effects in order to support actors towards sustainable educational actions. By transforming campuses and courses, the university can thus become a learning organization where everything is about learning not only for students, but also for all actors in the university community. This chapter mentions first students, who (...) are the direct beneficiaries of education as well as the future actors of the transition. Secondly, it calls upon teacher-researchers to incarnate the multifaceted role of mentors, which far beyond the transmission of knowledge involves accompanying the students in a holistic transformation. Third, it turns towards pedagogical support services, whose diverse disciplines and skills are essential to develop the pedagogical methods required for transition education. Finally, the chapter underlies the role of public authorities to systematize good practices, to allow bottom-up incentives to grow, to put in place the necessary conditions and resources as well as to engage the whole of society. (shrink)

Objectives To conduct an independent evaluation of the first phase of the Health Foundation’s Safer Patients Initiative (SPI), and to identify the net additional effect of SPI and any differences in changes in participating and non-participating NHS hospitals. Design Mixed method evaluation involving five substudies, before and after design. Setting NHS hospitals in the United Kingdom. Participants Four hospitals (one in each country in the UK) participating in the first phase of the SPI (SPI1); 18 control hospitals. Intervention The SPI1 (...) was a compound (multi-component) organisational intervention delivered over 18 months that focused on improving the reliability of specific frontline care processes in designated clinical specialties and promoting organisational and cultural change. Results Senior staff members were knowledgeable and enthusiastic about SPI1. There was a small (0.08 points on a 5 point scale) but significant (P<0.01) effect in favour of the SPI1 hospitals in one of 11 dimensions of the staff questionnaire (organisational climate). Qualitative evidence showed only modest penetration of SPI1 at medical ward level. Although SPI1 was designed to engage staff from the bottom up, it did not usually feel like this to those working on the wards, and questions about legitimacy of some aspects of SPI1 were raised. Of the five components to identify patients at risk of deterioration—monitoring of vital signs (14 items); routine tests (three items); evidence based standards specific to certain diseases (three items); prescribing errors (multiple items from the British National Formulary); and medical history taking (11 items)—there was little net difference between control and SPI1 hospitals, except in relation to quality of monitoring of acute medical patients, which improved on average over time across all hospitals. Recording of respiratory rate increased to a greater degree in SPI1 than in control hospitals; in the second six hours after admission recording increased from 40% (93) to 69% (165) in control hospitals and from 37% (141) to 78% (296) in SPI1 hospitals (odds ratio for “difference in difference” 2.1, 99% confidence interval 1.0 to 4.3; P=0.008). Use of a formal scoring system for patients with pneumonia also increased over time (from 2% (102) to 23% (111) in control hospitals and from 2% (170) to 9% (189) in SPI1 hospitals), which favoured controls and was not significant (0.3, 0.02 to 3.4; P=0.173). There were no improvements in the proportion of prescription errors and no effects that could be attributed to SPI1 in non-targeted generic areas (such as enhanced safety culture). On some measures, the lack of effect could be because compliance was already high at baseline (such as use of steroids in over 85% of cases where indicated), but even when there was more room for improvement (such as in quality of medical history taking), there was no significant additional net effect of SPI1. There were no changes over time or between control and SPI1 hospitals in errors or rates of adverse events in patients in medical wards. Mortality increased from 11% (27) to 16% (39) among controls and decreased from 17% (63) to 13% (49) among SPI1 hospitals, but the risk adjusted difference was not significant (0.5, 0.2 to 1.4; P=0.085). Poor care was a contributing factor in four of the 178 deaths identified by review of case notes. The survey of patients showed no significant differences apart from an increase in perception of cleanliness in favour of SPI1 hospitals. Conclusions The introduction of SPI1 was associated with improvements in one of the types of clinical process studied (monitoring of vital signs) and one measure of staff perceptions of organisational climate. There was no additional effect of SPI1 on other targeted issues nor on other measures of generic organisational strengthening. (shrink)

There is a strong need to connect agricultural research to social movements and community-based food system reform efforts. Participatory research methods are a powerful tool, increasingly used to give voice to communities overlooked by academia or marginalized in the broader food system. Plant breeding, as a field of research and practice, is uniquely well-suited to participatory project designs, since the basic process of observing and selecting plants for desirable traits is accessible to participants without formal plant breeding training. The challenge (...) for plant breeders engaged in participatory research is to consider not only how their work incorporates farmer input in developing new varieties, but also how it interacts with broader questions of food sovereignty, food justice, diversity and democratization in the food system. This article examines these issues in the context of the Seed to Kitchen Collaborative, a participatory variety evaluation and breeding project at the University of Wisconsin-Madison. (shrink)

To meet the ecological challenge, higher education must face many challenges: the educational offer, which is currently limited in many aspects, must evolve by renewing its methods while adapting its content. An “ecological awakening” is necessary to stimulate student awareness and action. This awakening is already present in some establishments which have transformed their educational model as well as their training in order to integrate and incarnate a more holistic vision of the world. These examples are all sources of inspiration (...) that can serve as a basis for reflection to modify university courses in depth. This chapter outlines first the shortcomings of the current educational model – in terms of content and methods – drawing on the authors’ insights, mostly from France. Then, the chapter turns towards recent evolutions, be it structural or transient, as well as incentives at various levels that could contribute to a transition of higher education. (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.

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...

This introduction draws on Charles Dickens’ analysis of schooling in England during the industrial revolution to highlight the connection bethween the Anthropocene epoch we currently live in and education. While we outline points for critique, we are far from making a simple judgment. In reaction, we present the Great Transition Handbook with its systemic approach based on six gates, and we call on pedagogy to be more holistic in order to integrate all dimensions of humanity. We also clarify our understanding (...) of the Great Transition, as a process interweaving both social and ecological concerns. (shrink)

Some universities have set up courses relating to the systemic integration of ecological and social issues into their curricula. We are presenting two types of initiatives here: first, those that come directly from universities or higher education institutions, such as the University of Lausanne; secondly, those which emanate from small organizations created to constitute a higher education transition laboratory, linked to a university institution, as is the case of Schumacher College (United Kingdom) linked to the University of Plymouth or the (...) Sustainability Institute (South Africa) attached to Stellenbosch University. (shrink)

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.

In this chapter we identify seven transversal principles which guide our pedagogical approach, and which are today widely shared by teachers. These principles also seem to us to be consistent with research in neuroscience, in particular that of Stanislas “Dehaene, Stanislas. Apprendre! les talents du cerveau, le défi des machines. Odile Jacob, Paris, (2018)” and his four pillars of learning – attention, active engagement, error and surprise signals and the consolidation of acquired knowledge – or those of Antonio “Damasio, Antonio (...) R. L’erreur de Descartes: la raison des émotions. Odile Jacob, Paris, (1995)” on the fundamental role of emotions in supporting learning. The principles advocated are: solicitation of curiosity and commitment; learning through sensitive experiences; connection of knowledge, emotions and values; reappropriation of assessment methods; multifaceted posture of the teacher; politicization of education; self-awareness and striving for common good.The principles highlighted in this section represent the major levers to be operated in order to provide students with truly transformative learning. Tools and examples of real-life implementation of these principles will be detailed in the second part of this book. (shrink)

Teachers may be skeptical about the possibility of implementing transition pedagogy, as outlined in the first part of this book, given the current context of higher education. Here we synthetize therefore the pedagogical tools that we have identified in the courses offered by establishments that have practiced a transition pedagogy for a long time, as well as those being used at the Campus de la Transition since 2018. We also draw on interviews with experts and practitioners, psychologists, teachers and explorers (...) of new practices. (Interviews with Chrysoline Brabant – clinical psychologist and certified coach, Mark Swilling – founder of the Sustainability Institute, Jacques Tardif – professor at the University of Sherbrooke and specialist in university pedagogy, Laurent Van Ditzhuyzen – co-founder of the Université du Nous, Thibault Griessinger – PhD in cognitive sciences and founder of Acte Lab, Hubert Trapet and Valérie Fayard – Emmaüs France CEO and vice-chair). The chapter starts with the lightest tools, which can be set up quite easily in a classroom, moving towards the most ambitious, and resulting in a coherent picture of the higher establishment in service of the Great Transition teachings. (shrink)

We re-express our theorem on the strong-normalisation of display calculi as a theorem about the well-foundedness of a certain ordering on first-order terms, thereby allowing us to prove the termination of systems of rewrite rules. We first show how to use our theorem to prove the well-foundedness of the lexicographic ordering, the multiset ordering and the recursive path ordering. Next, we give examples of systems of rewrite rules which cannot be handled by these methods but which can be handled by (...) ours. Finally, we show that our method can also prove the termination of the Knuth-Bendix ordering and of dependency pairs. Keywords: rewriting, termination, well-founded ordering, recursive path ordering.. (shrink)

We compare several methods of implementing the display (sequent) calculus RA for relation algebra in the logical frameworks Isabelle and Twelf. We aim for an implementation enabling us to formalise within the logical framework proof-theoretic results such as the cut-elimination theorem for RA and any associated increase in proof length. We discuss issues arising from this requirement.

We use a deep embedding of the display calculus for relation algebras ÆRA in the logical framework Isabelle /HOL to formalise a machine-checked proof of cut-admissibility for ÆRA. Unlike other “implementations”, we explicitly formalise the structural induction in Isabelle /HOL and believe this to be the first full formalisation of cutadmissibility in the presence of explicit structural rules.

Nationalism was a driving, moving spirit in the nineteenth-century Germany of Friedrich Schleiermacher. Jerry F. Dawson, through his thoughtful and well-wrought study of Friedrich Schleiermacher, provides an insight into contemporary nationalistic movements and the people who have a part in them. Schleiermacher, a prominent theologian and educator, was also a leading contributor to the tide of nationalism which swept Germany during the Napoleonic era. Dawson does not present Schleiermacher as an archetype for nationalists, but rather as an example of one (...) man who was willing to sacrifice everything for the good of the nation. Examining the influence of Pietism, rationalism, and romanticism on Schleiermacher, the author explains the origins of his subject's nationalistic activities and traces the evolution of his patriotic point of view. Dawson depicts the development of Schleiermacher's patriotism from Prussian particularism to German nationalism—an allegiance to an idealized Germany unified in religion, language, folkways. He describes the diverse approaches utilized by Schleiermacher to achieve a patriotic awakening among his countrymen: "…he preached nationalistic sermons; he delivered scholarly lectures; he repeatedly risked his life on dangerous missions which would help free Germany from France; he used his journalistic talents to try to stimulate the national consciousness of the German people; and he even served in the government of Prussia in an attempt to reconstruct the educational system so that nationalism might be advanced.". (shrink)

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

The Heythrop Journal, Volume 63, Issue 1, Page 35-48, January 2022.

We describe how we used the interactive theorem prover Isabelle to formalise and check the laws of the Timed Interval Calculus (TIC). We also describe some important corrections to, clarifications of, and flaws in these laws, found as a result of our work.

In this article, I demonstrate that Friedrich Nietzsche offers us a unique form of hermeneutic critique. In particular, I contend that when reading Nietzsche’s perspectivism and will to power in light of each other, they provide us with the tools to overcome habits of interpretation through the concepts of genealogy and creative hermeneutics. I show this in three sections. In section one, I introduce Nietzsche’s perspectivism and situate it within his concept of the will to power. In doing so, I (...) demonstrate that interpretations exist amidst a complex field of agonistic, reciprocal relations in life’s constant production of meaning. In section two, I then analyze how certain interpretations sediment into habits, forming harmful blind spots in interpretive activity. Such habits, Nietzsche shows, when privileged as prima facie ‘True’ and left uncontested exclude different ways of interpreting and existing, stagnating the production of meaning and denying the agonistic conditions of life. In the final section, I argue that Nietzsche critiques such habits in the two directions of genealogy and creative hermeneutics. Through the backward approach of genealogy, Nietzsche problematizes the habit, excavates its lowly origin, and deconstructs its supposed universality. Through the forward approach of creative hermeneutics, he overcomes and reinterprets them out of their origins, experiments with difference and multiplicity, and engages in an ongoing critique to open up new perspectives. (shrink)

Native women residing in the Subarctic and Arctic are currently struggling for the right to decide whether they will be hospitalized or have a midwife present for the birth of their children. The argument presented in this review paper outlines the cultural and clinical factors in favour of recognizing and legalizing traditional midwifery in the North and critically examines the statistical and safety concerns raised by those arguing against giving Northern Native women an alternative to evacuation from their home communities.