Religious beliefs are often singled out for special treatment in secular liberal societies. Yet if a legal exemption is granted for a belief with a religious foundation, the question arises whether a similar, non‐religious moral belief must also be granted an exemption. I argue that common reasons for favoring religious over non‐religious beliefs fail to provide a convincing moral case for drawing a distinction of this nature. I focus on arguments concerning the role of religious beliefs in constituting an individual's (...) identity and the transcendental nature of religion, which lead me to consider in the final section the role of choice in religious belief. (shrink)

This book is a collection of fictionalized case studies of everyday ethical dilemmas and challenges, encountered in the process of conducting global health research in places where the effects of political and economic inequality are particularly evident. It is a training tool to fill the gap between research ethics guidelines and their implementation "on the ground." The cases focus on "relational" ethics: ethical actions and ideas that continuously emerge through relations with others, rather than being determined by bioethics regulation. They (...) are based on stories and experiences collected by a group of social anthropologists who have worked with leading transnational medical research organizations across Africa in the past decade. Accompanied by guidelines, discussion questions and selected further readings, the book provides a flexible resource for training and self-study for people engaged in health research with, universities, international collaborative sites and NGOs and for everyone interested in the realities of global health research today.". (shrink)

In this paper, we explore a new perspective on digital humanism, emphasizing the centrality of multi-stakeholder dialogues and a bottom-up approach to surfacing stakeholder values. This approach starkly contrasts with existing frameworks, such as the Vienna Manifesto's top-down digital humanism, which hinges on pre-established first principles. Our approach provides a more flexible, inclusive framework that captures a broader spectrum of ethical considerations, particularly those pertinent to the digital realm. We apply our model to two case studies, comparing the insights generated (...) with those derived from a utilitarian perspective and the Vienna Manifesto's approach. The findings underscore the enhanced effectiveness of our approach in revealing additional, often overlooked stakeholder values, not typically encapsulated by traditional top-down methodologies. Furthermore, this paper positions our digital humanism approach as a powerful tool for framing ethics-by-design, by promoting a narrative that empowers and centralizes stakeholders. As a result, it paves the way for more nuanced, comprehensive ethical considerations in the design and implementation of digital technologies, thereby enriching the existing literature on digital ethics and setting a promising agenda for future research. (shrink)

Quelle conviction précède ce livre? Celle de l'ordre des raisons d'une pensée qui se prolonge et s'outrepasse par l'ordre du dialogue. Dans cet ouvrage, la pensée ne s'expose pas seule, elle vient en seconde position comme réponse à la lecture que des théologiens et des philosophes ont effectuée face à l'oeuvre d'Yves Charles Zarka. Chapitre après chapitre, les lecteurs entendront aussi bien les interpellations d'autres lecteurs que les réponses, réflexions et ouvertures de l'auteur lui-même dans un récit autobiographique, récit fort (...) et sans détours qui invite à prendre part à cette conversation et qui permet d'entrer dans les structures argumentatives et le parcours historique de notre auteur. Maintenant, c'est à vous, lecteurs, de penser le politique et ce qui lui échappe. (shrink)

A central diagnostic and anecdotal feature ofautismis difficulty with socialcommunication. We take the position that communication is a two-way,intersubjectivephenomenon—as described by thedouble empathy problem—and offer uprelevance theory(a cognitive account of utterance interpretation) as a means of explaining such communication difficulties. Based on a set of proposed heuristics for successful and rapid interpretation of intended meaning, relevance theory positions communication as contingent on shared—and, importantly,mutuallyrecognized—“relevance.” Given that autistic and non-autistic people may have sometimes markedly different embodied experiences of the world, we (...) argue that what is most salient to each interlocutor may be mismatched. Relevance theory would predict that where this salient information is not (mutually) recognized or adjusted for, mutual understanding may be more effortful to achieve. This paper presents the findings from a small-scale, linguistic ethnographic study of autistic communication featuring eight core autistic participants. Each core autistic participant engaged in three naturalistic conversations around the topic of loneliness with: (1) a familiar, chosen conversation partner; (2) a non-autistic stranger and (3) an autistic stranger. Relevance theory is utilized as a frame for the linguistic analysis of the interactions. Mutual understanding was unexpectedly high across all types of conversation pairings. In conversations involving two autistic participants, flow, rapport and intersubjective attunement were significantly increased and in three instances, autistic interlocutors appeared to experience improvements in their individual communicative competence contrasted with their other conversations. The findings have the potential to guide future thinking about how, in practical terms, communication between autistic and non-autistic people in both personal and public settings might be improved. (shrink)

Artificial Intelligence-as-a-Service empowers individuals and organisations to access AI on-demand, in either tailored or ‘off-the-shelf’ forms. However, institutional separation between development, training and deployment can lead to critical opacities, such as obscuring the level of human effort necessary to produce and train AI services. Information about how, where, and for whom AI services have been produced are valuable secrets, which vendors strategically disclose to clients depending on commercial interests. This article provides a critical analysis of how AIaaS vendors manipulate the (...) visibility of human labour in AI production based on whether the vendor relies on paid or unpaid labour to fill interstitial gaps. Where vendors are able to occlude human labour in the organisational ‘backstage,’ such as in data preparation, validation or impersonation, they do so regularly, further contributing to ongoing techno-utopian narratives of AI hype. Yet, when vendors must co-produce the AI service with the client, such as through localised AI training, they must ‘lift the curtain’, resulting in a paradoxical situation of needing to both perpetuate dominant AI hype narratives while emphasising AI’s mundane limitations. (shrink)

BackgroundUnderstanding sex and gender in health research can improve the quality of scholarship and enhance health outcomes. Funding agencies and academic journals are two key gatekeepers of knowledge production and dissemination, including whether and how sex/gender is incorporated into health research. Though attention has been paid to key issues and practices in accounting for sex/gender in health funding agencies and academic journals, to date, there has been no systematic analysis documenting whether and how agencies and journals require attention to sex/gender, (...) what conceptual explanations and practical guidance are given for such inclusion, and whether existing practices reflect the reality that sex/gender cannot be separated from other axes of inequality.MethodsOur research systematically examines official statements about sex/gender inclusion from 45 national-level funding agencies that fund health research across 36 countries (covering the regions of the EU and associated countries, North America, and Australia) and from ten top-ranking general health (the top five in “science” and the top five in “social science”) and ten sex- and/or gender-related health journals. We explore the extent to which agencies and journals require inclusion of sex/gender considerations and to what extent existing strategies reflect state of the art understandings of sex/gender, including intersectional perspectives.ResultsThe research highlights the following: (a) there is no consistency in whether sex/gender are mentioned in funding and publishing guidelines; (b) there is wide variation in how sex/gender are conceptualized and how researchers are asked to address the inclusion/exclusion of sex/gender in research; (c) funding agencies tend to prioritize male/female equality in research teams and funding outcomes over considerations of sex/gender in research content and knowledge production; and (d) with very few exceptions, agency and journal criteria fail to recognize the complexity of sex/gender, including the intersection of sex/gender with other key factors that shape health.ConclusionsThe conceptualization and integration of sex/gender needs to better capture the interacting and complex factors that shape health—an imperative that can be informed by an intersectional approach. This can strengthen current efforts to advance scientific excellence in the production and reporting of research. We provide recommendations and supporting questions to strengthen consideration of sex/gender in policies and practices of health journals and funding agencies. (shrink)

La "Conversa de la Propiedad Ackermann" (CAP) es la no demostrabilidad de proposiciones puramente no-necesitivas a partir de proposiciones necesitivas. En nuestro trabajo definimos las dos restricciones básicas de la lógica intuicionista mínima con la CAP.

In the cubist expression of the early twentieth century, thought begins to play a fundamental role in the creative process. The reason lies in the fact that it is a revolution of thought, even before an aesthetic revolution. It is the basic concept that changes, thanks to the reflection that, unknowingly or not, it takes its moves from the thought of men of the past, including Augustine, Plato, Aristotle, Descartes, but also Husserl, Hildebrand, Bergson. This is because every human expression (...) is the result of concepts studied and observed, deepened and challenged. The sculpture was, however, part of the great revolution in art history just as much as painting, due to the work of some artists including Picasso, Boccioni, Brancusi, Archipenko, Gaudier-Brzeska, Lipchitz, Nadelman and Duchamp-Villon.In the particular case of the cubist sculptors, the expressive solutions they adopt are consequent to a new way of implying the world and the intellectualistic phenomena that accompany its evolution. Keywords: Cubism; Phenomenology of Cubism; Cubist painting; Cubist sculpture. (shrink)

First published in 1990. Routledge is an imprint of Taylor & Francis, an informa company.

This article discusses the nature of copyright as a fundamental right. After studying the two faces of copyright, both economic and moral, I analyze whether copyright should be seen as part of the freedom of artistic and scientific creation (article 20.1.b Spanish Constitution) or as part of the general property right (article 33). Finally, I explore the possibility of applying these conclusions to other intellectual property rights (related rights, patents, trademarks, etc.). This discussion is not trivial. The weight of copyright (...) in case of conflict with other rights (such as privacy and freedom of speech) depends on the nature of copyright as a fundamental right or not. (shrink)

The letters of the learned and indomitable Lady Anne Bacon, mother of the philosopher Francis Bacon, are made accessible for the first time in this edition. Bringing together nearly two hundred letters, scattered in repositories throughout the world, her correspondence sheds fresh light not only on the activities of early modern elite women, but also on well-known Elizabethan figures, including her children, her privy councillor relatives, such as William Cecil, Lord Burghley, and controversial figures, including the Earl of Essex. Translations (...) of Lady Anne's frequent use of Latin, Greek and Hebrew reveal the impact of her humanist education on her correspondence and a substantial introductory chapter allows a detailed picture of Anne's life to emerge through her surviving letters. (shrink)

We are inhabitants of a culture that knows how to speak but not how to listen. Against a tradition that has endorsed the power of discourse, where warring monologues are mistaken for genuine dialogue, Gemma Corradi Fiumara examines and reveals the other side of language - listening.

First published in 1990. Routledge is an imprint of Taylor & Francis, an informa company.

In this paper, we explore the empirical phenomenon of large multinational corporations acquiring socially oriented enterprises, such as the Unilever–Ben & Jerry’s, and the L`Oréal-The Body Shop takeovers. When focusing on these cases, we argue that variance in organisational identity orientations, as the dominant logic of managers within the acquiring organisations, determines whether MNCs consider the transaction not only in financial terms, but also decide to adopt “social technology” in the form of CSR-related organisational practices from the acquired unit. We (...) argue that in turn based on a “match” with the organisational identity of the acquired unit, managers will opt to adopt CSR practices more fully or selectively, and in more substantial or symbolic ways. With these propositional arguments we not only aim to contribute to the literature on CSR adoption by MNCs, but we also set out to develop theory on the widespread but so far undocumented phenomenon of MNCs “buying CSR” by acquiring socially oriented enterprises. (shrink)

Realising the societal gains from publicly funded health and medical research requires a model for a reflexive evaluation precedent for the societal impact of research. This research explores UK Research Excellence Framework evaluators’ values and opinions and assessing societal impact, prior to the assessment taking place. Specifically, we discuss the characteristics of two different impact assessment extremes – the “quality-focused” evaluation and “societal impact-focused” evaluation. We show the wide range of evaluator views about impact, and that these views could be (...) conceptually reflected in a range of different positions along a conceptual evaluation scale. We describe the characteristics of these extremes in detail, and discuss the different beliefs evaluators had which could influence where they positioned themselves along the scale. These decisions, we argue, when considered together, form a dominant definition of societal impact that influences the direction of its evaluation by the panel. (shrink)

Migration is a phenomenon that is as old as humankind. Today, however, it is undergoing changes that are not only radically re-defining human geography but are also offering insights for theological reflection into the contemporary human condition. The shift in gender composition or the emergence of the so-called ‘feminisation of international migration’ is one of these. This paper scrutinises, from a theological perspective, the religious ways in which migrant women deal with the difficult and oppressive conditions that are born out (...) of migration. It draws heavily from the experience of Asian women migrants in general and Filipino women migrants in particular. It starts with a brief introduction that takes as its starting-point the case of Filipino women migrants to illustrate how faith is significantly woven in migrant women’s lives. Then it explores three concrete faith-based ways of surviving common to Asian migrant women namely courageous hope, creative resistance, and steadfast faith. The paper then ends with a brief conclusion. (shrink)

Immigration reform is a highly complex and multifaceted task with significant economic, political and religio-cultural repercussions thereby bringing tremendous ethical challenges and implications. This article explores the possible contribution of modern Catholic Social Teaching in addressing the ethical challenges of immigration reform, particularly in the United States, by examining key themes that could address critical issues in the current debate on immigration reform and arguing how an ethic of risk which, the author submits, runs through the key themes of Catholic (...) Social Teaching explored in this paper, could then serve as an approach in articulating how Christian discipleship could foreground citizenship in the context of immigration. (shrink)

Caritas in Veritate, the first social encylical of Benedict XVI, tackles the problems of global development and progress towards the common good of all peoples. Taking its cue from the encyclical’s discussion on migration as an ‘aspect of integral human development’ this article examines the experience of contemporary migrant women and the transnational family vis-à-vis Caritas in Veritate. The paper begins with an overview of Caritas in Veritate followed by a look at the effects of the global economy on women (...) and a discussion on the effects of transnationalism to women and their families, especially with women-away transnational families. The paper then explores the points of convergence and divergence between Caritas in Veritate and the experience of migrant women and the transnational family and ends with a brief conclusion. (shrink)

Despite ample evidence of the efficacy and effectiveness of evidence-based parenting programmes (EBPPs) within research-led environments, there is very little evidence of maintenance of effectiveness when programmes are delivered as part of regular service provision. The present study examined the effectiveness of EBPPs provided during a period of sustained service-led implementation in comparison to research-led effectiveness evaluation. Data from 3706 parents who received EBPPs during sustained implementation by services were compared to data from 1390 parents who had participated in an (...) earlier researcher-led effectiveness trial of a national roll-out of EBPPs in England. In both phases, parents completed measures of child behaviour problems, parenting style and parental mental well-being prior to starting parenting programmes (pre-test), at the end of the programmes (post) and at 12-months follow up. Results from Generalised Estimating Equations controlling for potential covariates indicated significant improvements in child behaviour problems during sustained implementation, similar to the effectiveness phase; significant improvements in parenting style which were larger than the effectiveness phase at 12-month follow up; and significant improvements in parental mental well- being. Our findings demonstrate effective maintenance of gains when EBPPs are provided as part of regular provision across a large sample of English parents. Successful long-term implementation should consider effectiveness of EBPPs across the population, given the large contextual changes that take place between researcher-led evaluations and service take-up. Our findings support the integration of EBPPs in public health approaches to addressing child behaviour problems and parent well-being. (shrink)

ABSTRACTA conditional is natural if it fulfils the three following conditions. It coincides with the classical conditional when restricted to the classical values T and F; it satisfies the Modus Ponens; and it is assigned a designated value whenever the value assigned to its antecedent is less than or equal to the value assigned to its consequent. The aim of this paper is to provide a ‘bivalent’ Belnap-Dunn semantics for all natural implicative expansions of Kleene's strong 3-valued matrix with two (...) designated elements. (shrink)

As is well known, the variable-sharing property (vsp) is, according to Anderson and Belnap, a necessary property of any relevant logic. In this paper, we shall consider two versions of the vsp, what we label the "weak vsp" (wvsp) and the "strong vsp" (svsp). In addition, the "no loose pieces property," a property related to the wvsp and the svsp, will be defined. Each one of these properties shall generally be characterized by means of a class of logical matrices. In (...) this way, any logic verified by an actual matrix in one of these classes has the property the class generally represents. Particular matrices (and so, logics) in each class are provided. (shrink)

Coexistence in schools inevitably carries a higher risk of conflicts among peers. This fact can be detrimental to the well-being and academic achievement of the students. In many developed countries, about 90% of the pupils in compulsory secondary education report witnessing assaults among peers. In this regard, recognizing, controlling and managing emotions is key to ensure a healthy and effective interaction with others. Negative emotions, such as anger, can trigger conflicts or even episodes of violence if not regulated properly. Interactive (...) tools, such as specialised software’s, have shown high rates of efficacy for the training of different kinds of competences like the regulation of emotions. The aim of the present work is to describe the Happy Emotional Education Program and its effects over a sample of secondary school students. This software focuses in the training of emotional competences of the students with the objective of solving conflicts in a more assertive way. The design employed in the present work was a quasiexperimental design with pretest and posttest with a control group. Results show that Happy Emotional Education Program contributes to the management of emotions and well-being in a significant way. Additionally, the constant use of this interactive tool enhances motivation and the learning process of students. Results also indicate the importance of assessing the effects of the program in the long term. This would enable researchers to further assess the effects of the program over those emotional competences that are more resistant to change given its stable nature. (shrink)

BackgroundSome people with progressive neurological diseases find they need additional support with eating and drinking at mealtimes, and may require artificial nutrition and hydration. Decisions concerning artificial nutrition and hydration at the end of life are ethically complex, particularly if the individual lacks decision-making capacity. Decisions may concern issues of life and death: weighing the potential for increasing morbidity and prolonging suffering, with potentially shortening life. When individuals lack decision-making capacity, the standard processes of obtaining informed consent for medical interventions (...) are disrupted. Increasingly multi-professional groups are being utilised to make difficult ethical decisions within healthcare. This paper reports upon a service evaluation which examined decision-making within a UK hospital Feeding Issues Multi-Professional Team.MethodsA three month observation of a hospital-based multi-professional team concerning feeding issues, and a one year examination of their records. The key research questions are: a) How are decisions made concerning artificial nutrition for individuals at risk of lacking decision-making capacity? b) What are the key decision-making factors that are balanced? c) Who is involved in the decision-making process?ResultsDecision-making was not a singular decision, but rather involved many different steps. Discussions involving relatives and other clinicians, often took place outside of meetings. Topics of discussion varied but the outcome relied upon balancing the information along four interdependent axes: Risks, burdens and benefits; Treatment goals; Normative ethical values; Interested parties.ConclusionsDecision-making was a dynamic ongoing process with many people involved. The multiple points of decision-making, and the number of people involved with the decision-making process, mean the question of ‘who decides’ cannot be fully answered. There is a potential for anonymity of multiple decision-makers to arise. Decisions in real world clinical practice may not fit precisely into a model of decision-making. The findings from this service evaluation illustrate that within multi-professional team decision-making; decisions may contain elements of both substituted and supported decision-making, and may be better represented as existing upon a continuum. (shrink)

There is little consensus on what artificial intelligence (AI) systems may or may not embrace. Although this may point to multiplicity of interpretations and backgrounds, a lack of conceptual clarity could thwart the development of common ground around the concept among researchers, practitioners and users of AI and pave the way for misinterpretation and abuse of the concept. This article argues that one of the effective ways to delineate the concept of AI is to compare and contrast it with human (...) intelligence. In doing so, the article broaches the unique capabilities of humans and AI in relation to one another (human and machine tacit knowledge), as well as two types of AI systems: one that goes beyond human intelligence and one that is necessarily and inherently tied to it. It finally highlights how humans and AI can augment their capabilities and intelligence through synergistic human–AI interactions (i.e., human-augmented AI and augmented human intelligence), resulting in hybrid intelligence, and concludes with a future-looking research agenda. (shrink)

In this article, I turn my attention to the figure of the ignorant master, Joseph Jacotot, that is depicted in The Ignorant Schoolmaster. Five Lessons in Intellectual Emancipation (1991). I will show that the voice of Jacotot can actually be read as a reaction against the progressive figure of the teacher which, following Rancière's view, can be seen as effecting a stultification. In some respects, however, Rancière's analysis of the pedagogical order no longer seems to be valid in today's partly (...) reconfigured, pedagogical order that depicts the teacher in terms of facilitation. Yet, the figure of the facilitator can be seen as effecting a stultification as well. Therefore, I will stress that Jacotot's voice is highly relevant today. The most important difference between the figure of the (old and current) figure of the stultifyer and that of the ignorant master is identified in their starting point. The stultifying master starts from the assumption of inequality. S/he transforms taught material (words, text, images, etc.) into objects of knowledge or resources for competence development that open the door to another world. The ignorant master (Jacotot) assumes equal intelligence and draws attention to a thing in common. According to Rancière, the ignorant master keeps the door closed and puts his/her students in the presence of a thing in common. (shrink)

Metaphor is much more than just a linguistic phenomena, argues Gemma Corradi Fiumara, it is in fact the key process by which we construct and develop our ability to understand the world and the people we share it with. Rationality as understood by philosophers has led to a disembodied view of ourselves in which interaction between life and language has been downplayed. By looking at the metaphoric process - in an interpersonal rather than a formal way - its importance (...) in allowing us access to new worlds of experience is revealed. The metaphoric potential in us all exposes us to the world and initiates our involvement in it. (shrink)

Feminist aesthetics can be characterized as a critical conceptual framework for analyzing the gender assumptions Western aesthetics, philosophy of the arts and the arts have had and their implications in the categories they have historically employed. It emerged as a result the influence feminism had in the study of gender bias in the artistic production and its reception. Works like Linda Nochlin’s Why Have There Been No Great Women Artists? (1971) and Laura Mulvey’s Visual Pleasure and Narrative Cinema (1975) were (...) fundamental for recognizing the exclusion of women from the history of the great visual artists and how the male gaze is a predominant kind of depiction that satisfies and is designed from a masculine and heterosexual point of view. -/- During the 1970s and 1980s it started the analysis of the male gaze in literature, film and visual arts, but also the women’s artistic production demanding its recognition. However, it was not until the 1990s that philosophical feminist aesthetics was first addressed as an important and necessary area of study with the special issues Feminism and aesthetics (Hein, Korsmeyer 1990) in “Hypatia: a journal of Feminist Philosophy”, and Feminism and traditional aesthetics (Brand, Korsmeyer 1990) in “The Journal of Aesthetics and Art Criticism”. And the first introductory book on the field, Gender and aesthetics: an introduction by Carolyn Korsmeyer (2004) was published during the first decade of the 2000s. -/- Although feminist aesthetics came later than feminist political philosophy, it appeared almost at the same time as feminist perspectives of other philosophical fields, such as epistemology and philosophy of science. Like other feminist approaches to different philosophical domains, there is not a unitary feminist perspective on aesthetics, however, despite the variety of approaches, all implicitly or explicitly demand the recognition of women in its sphere of influence, that is, philosophy and the arts. Nevertheless, contrary to other fields it does not only take contributions from analytic and continental feminism, but also from cultural theory, art history, comparative literature, film theory, psychoanalysis, just to name a few disciplines and theories. Feminist aesthetics’ literature covers a broad range of topics, but the most important are the feminist critique of philosophical aesthetics and the feminist philosophy and theory of the arts. (shrink)

In the modern age a specific lexicon has arisen to defend liberty and equality. This vocabulary has also been employed to defend misogynist positions and to justify the inequality between women and men. One clear example is Rousseau’s explanation of the sexual division of labour: women “naturally” decide to remain at home and look after the children while the men search for the resources necessary for the group. In this manner he intends to explain the relegation of women to the (...) private and domestic sphere. In the twentieth century this division entered in crisis due to the critical work of many feminist thinkers and groups. Among these Betty Friedan, Kate Millett and the Radicalesbians stand out. Their analyses put in question this division of spheres, their limits, their nature and their acceptance in society. Moreover they show the political scope and the power which underlies this division of labour, as well as the liberating possibilities resulting from the criticism of and the disobedience to the same. Betty Friedan denounces the social obstacles faced by women who wish to work outside the home and highlights the devastating consequences for the female psyche. Kate Millett puts in evidence the political system which oppresses women and how it colonises personal and intimate spaces. The Radicalesbians group underlines the freedom realised by woman-identified women. These feminists offer open and rich interpretations which are relevant in the present. (shrink)

This article provides a review of scholarly approaches to assessing the impact of certification standards for sustainability. While we observe that some theoretical advances have afforded a better understanding of the potential impacts of adopting such standards, we also find that progress has been constrained due to a strong emphasis on assessing impact via linear causal pathways. This linear focus on the net effects for single stakeholders, such as farmers and producers, local communities and ecosystems, falls short of adequately capturing (...) the broader impact of certifications across social and ecological dimensions. Inspired by theories on complex systems thinking, we present a framework based on a systems-based impact logic that better captures and assesses the impacts of certification standards within broader social-ecological systems. Our framework can be used as a heuristic to design impact-related studies and assess the impact of certification standards across disciplinary vantage points and empirical contexts. (shrink)

The logic E4 is related to Brady’s BN4 in a similar way to which Anderson and Belnap’s logic of entailment E is related to their logic of the relevant implication R. In ‘A companion to Brady’s 4-valued relevant logic: the 4-valued logic of entailment E4’, quoted in this paper, three alternatives to BN4 and another three to E4 are summarily introduced in a couple of pages as the only alternatives containing Routley and Meyer’s basic logic B, provided some conditions are (...) fulfilled. The aim of this note is to prove BN4 and its three alternatives are the same logic up to some point, since they are functionally equivalent to each other, as it is the case with E4 and its three alternatives, which are also functionally equivalent to each other; to some extent, E4 is superior to BN4, since the latter is functionally included in the former, but not conversely. (shrink)

A classical result by Słupecki states that a logic L is functionally complete for the 3-element set of truth-values THREE if, in addition to functionally including Łukasiewicz’s 3-valued logic Ł3, what he names the ‘$T$-function’ is definable in L. By leaning upon this classical result, we prove a general theorem for defining binary expansions of Kleene’s strong logic that are functionally complete for THREE.