This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is (...) of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures. (shrink)

The techniques of natural duality theory are applied to certain finitely generated varieties of Heyting algebras to obtain optimal dualities for these varieties, and thereby to address algebraic questions about them. In particular, a complete characterisation is given of the endodualisable finite subdirectly irreducible Heyting algebras. The procedures involved rely heavily on Priestley duality for Heyting algebras.

To describe the content of practice guidelines on euthanasia and assisted suicide (EAS) and to compare differences between settings and guidelines developed before or after enactment of the euthanasia law in 2002 by means of a content analysis. Most guidelines stated that the attending physician is responsible for the decision to grant or refuse an EAS request. Due care criteria were described in the majority of guidelines, but aspects relevant for assessing these criteria were not always described. Half of the (...) guidelines described the role of the nurse in the performance of euthanasia. Compared with hospital guidelines, nursing home guidelines were more often stricter than the law in excluding patients with dementia (30% vs 4%) and incompetent patients (25% vs 4%). As from 2002, the guidelines were less strict in categorically excluding patients groups (32% vs 64%) and in particular incompetent patients (10% vs 29%). Healthcare institutions should accurately state the boundaries of the law, also when they prefer to set stricter boundaries for their own institution. Only then can guidelines provide adequate support for physicians and nurses in the difficult EAS decision-making process. (shrink)

Theories of beauty are often divided into the objective and the subjective. I am doubtful whether a rigid distinction between the two can be maintained. It is difficult for an objective theory to assert that the impression of beauty is received quite passively, without any reaction or co-operation on the part of the subject, which is likely to be similar in the various cases.

Both syntactic and semantic solutions are given for the entailment problem of duality theory. The test algebra theorem provides both a syntactic solution to the entailment problem in terms of primitive positive formulae and a new derivation of the corresponding result in clone theory, viz. the syntactic description of $\operatorname{Inv(Pol}(R))$ for a given set R of finitary relations on a finite set. The semantic solution to the entailment problem follows from the syntactic one, or can be given in the form (...) of an algorithm. It shows, in the special case of a purely relational type, that duality-theoretic entailment is describable in terms of five constructs, namely trivial relations, intersection, repetition removal, product, and retractive projection. All except the last are concrete, in the sense that they are described by a quantifier-free formula. It is proved that if the finite algebra $\underline{M}$ generates a congruence-distributive variety and all subalgebras of $\underline{M}$ are subdirectly irreducible, then concrete constructs suffice to describe entailment. The concept of entailment appropriate to strong dualities is also introduced, and described in terms of coordinate projections, restriction of domains, and composition of partial functions. (shrink)

The paper investigates completions in the context of finitely generated lattice-based varieties of algebras. In particular the structure of canonical extensions in such a variety $${\mathcal {A}}$$ is explored, and the role of the natural extension in providing a realisation of the canonical extension is discussed. The completions considered are Boolean topological algebras with respect to the interval topology, and consequences of this feature for their structure are revealed. In addition, we call on recent results from duality theory to show (...) that topological and discrete dualities for $${\mathcal {A}}$$ exist in partnership. (shrink)

This paper studies in detail about the early years of José Gaos (1900- 1969) and his education in philosophy and literature. Therefore, we know that their studies (academic or not) were not purely “philosophical” in 1915. Literature and philosophy played in Gaos an equally important role. The first real encounter with philosophy happens before he comes to Valencia in 1915; but in this year Gaos also receives a strong education, in aesthetic and literary, through press and philosophical journals, and especially (...) within the group formed with Max Aub, José Medina Echeverría and his brother Carlos Gaos. (shrink)

Background: Older, frail patients with multimorbidity are at an especially high risk for disease severity and death from COVID-19. The social restrictions proved challenging for the residents, their relatives, and the care staff. While these restrictions clearly impacted daily life in Norwegian nursing homes, knowledge about how the pandemic influenced nursing practice is sparse. Aim: The aim of the study was to illuminate ethical difficult situations experienced by Norwegian nurses working in nursing homes during the COVID-19 pandemic. Research design and (...) participants: The research design involved semistructured individual interviews conducted with 15 nurses working in 8 nursing homes in 3 health regions in Norway, within both urban and rural areas. Ethical considerations: Oral and written information about the study was provided before the participants gave their written consent. The transcribed interviews were de-identified. The study was approved by the Norwegian Centre for Research Data. Findings: Four ethical difficult situations were identified: (a) turning the nursing home into a prison; (b) using medication to maintain peace and order; (c) being left alone with the responsibility; and (d) s. impact on decision-making. Conclusions: The nurses’ ethical challenges were intertwined with external factors, such as national and local guidelines, and the nurses’ own internalized factors, which were connected to their subjective professionality. This duality inflicted emotional distress and gave nurses few opportunities to perform nursing in a professionally sound and safe manner. (shrink)

In recent years, the genetic testing and selection of IVF embryos, known as preimplantation genetic testing (PGT), has gained much traction in clinical assisted reproduction for preventing transmission of genetic defects. However, a more recent ethically and morally controversial development in PGT is its possible use in selecting IVF embryos for optimal intelligence quotient (IQ) and other non–disease-related socially desirable traits, such as tallness, fair complexion, athletic ability, and eye and hair colour, based on polygenic risk scores (PRS), in what (...) is referred to as PGT-P. Artificial intelligence (AI) and machine learning–based analysis of big data sets collated from genome sequencing of specific human ethnic populations can be used to estimate an individual embryo’s likelihood of developing such multifactorial traits by analysing the combination of specific genetic variants within its genome. Superficially, this technique appears compliant with Islamic principles and ethics. Because there is no modification of the human genome, there is no tampering with Allah’s creation (_taghyīr khalq Allah_). Nevertheless, a more critical analysis based on the five maxims of Islamic jurisprudence (_qawa'id fiqhiyyah_) that are often utilized in discourses on Islamic bioethics, namely _qaṣd_ (intention), _yaqın̄_ (certainty), _ḍarar_ (injury), _ḍarūra_ (necessity), and _`urf_ (custom), would instead reveal some major ethical and moral flaws of this new medical technology in the selection of non–disease-related socially desirable traits, and its non-compliance with the spirit and essence of Islamic law (shariah). Muslim scholars, jurists, doctors, and biomedical scientists should debate this further and issue a fatwa on this new medical technology platform. (shrink)

Annotation A scholarly edition of a work by Adam Smith. The edition presents an authoritative text, together with an introduction, commentary notes, and scholarly apparatus.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Rabindranath Tagore is remembered today chiefly as a poet, and his fame as a poet has often eclipsed his great contributions to other fields of literature and life — especially education. Tagore pondered deeply on the fundamental problems of education — aims, curriculum, method, discipline, values and medium — and wrote and experimented on them freely and extensively. Tagore is perhaps the only literary genius in contemporary history who devoted a major part of his life to thinking about education and (...) creating an educational institution of international significance. Also, the institution he created at Santiniketan proved to be the most global and sustainable among the progressive educational institutions launched by individual thinkers such as Froebel and Russell. This edition revives a classic work, the first comprehensive, full-length account of Tagore’s educational thought and activity, commemorating his 150th birth anniversary. It presents a detailed chronological survey of Tagore’s educational writings and institutional activities in the perspective of his life and thought in general. The book also contains a detailed review and critical discussion on almost all major aspects of his educational work. Through an overall evaluation of Tagore’s unique contribution to education and his message to the world, it seeks to correct some common misconceptions that have existed from time to time about Santiniketan and Visva-Bharati. The book will help form a more complete view of Tagore’s life and work, filling as it does the gaps and voids in the literature that has grown around him, and reinforcing its relevance today. It will be of value to educationists, teachers, policymakers, those interested in modern Indian history and philosophy of education._ _. (shrink)

Background: Discussing treatment risks has become increasingly important in medical communication. Still, despite regulations, physicians must decide how much and what kind of information to present. Objective: To investigate patients’ preference for information about a small risk of a complication of colonoscopy, and whether medical and personal factors contribute to such preference. To propose a disclosure policy related to our results. Design: Vignettes study. Setting: Department of Gastroenterology, Academic Medical Centre, the Netherlands. Patients: 810 consecutive colonoscopy patients. Intervention: A home-sent (...) questionnaire containing three vignettes. Vignettes varied in the indication for colonoscopy, complication severity and level of risk. Patients were invited to indicate their wish to be informed and the importance of such information. In addition, sociodemograhic, illness-related and psychological characteristics were assessed. Main outcome measurements: Wish to be informed and importance of information. Results: Of 810 questionnaires, 68% were returned. Patients generally wished to be informed about low-risk complications, regardless of the indication for colonoscopy or the severity of the complication. The level of risk did matter, though (OR = 2.48, SE = 0.28, p = 0.001). The information was considered less important if done for population screening purposes or diagnosis of colon cancer, if the complication was less severe (bleeding) and if the risk was smaller (0.01% and 0.1%). Patients’ information preference was also related to age, mood and coping style. Limitations: Difficulty of vignettes. Conclusions: Patients generally wish to be informed about all possible risks. However, this might become uninformative. A stepwise approach is suggested. (shrink)