Part II Central and Eastern Europe -- Mikhail Bakhtin: Direct and Indirect Reception of Kierkegaard in Works of the Russian Thinker -- Péter Esterházy: Semi-Serious -- Witold Gombrowicz: The Struggle for the Authentic Self -- Ivan Klíma: "To Save My Inner World"--Péter Nádas: Books and Memories -- Pinhas Sadeh: The Poet as "the Single Individual" -- Index of Persons -- Index of Subjects.

In lieu of an abstract, here is a brief excerpt of the content:Subjective Experiences of Tourette SyndromeBeyond the Premonitory UrgeThe authors report no conflicts of interest.There is an evolving recognition in healthcare that the patient's subjective experience needs to be privileged both in understanding clinical phenomena and also ensuring the salience of outcomes used to evaluate the impact of treatment interventions. This is reflected in the expansion of patient-reported outcome measures to capture a person's perception of their own health, and (...) the increasing requirement of involving people with lived experience in the co-design of research studies (National Health and Medical Research Council, 2016) and care improvement initiatives. In mental health it has been long understood that observable behavioral phenomena can only partially inform clinical understanding of the experience of the patient living with the condition. However, capturing the patient's subjective experience faithfully remains a challenge.Tourette syndrome (TS) is a complex condition in which there are clearly observable behavioral phenomena (vocal and motor tics, compulsive and socially inappropriate behaviors), but also a broad and varied range of subjective phenomena reported by different individuals. These may include sensory phenomena such as the premonitory sensory urge preceding a tic, compulsions to touch things a certain number of times or do something repeatedly until it feels "just right," or bothersome intrusive thoughts or images. To further complicate the picture most patients with TS have one or more co-occurring conditions such as attention deficit hyperactivity disorder, obsessive-compulsive disorder, and anxiety, which may actually cause a greater burden of dysfunction and distress than the Tourette symptoms.In their paper, Curtis-Wendlandt et al. (2024) challenge the dependence of current psychiatric diagnostic criteria (e.g., the Diagnostic and Statistical Manual of Mental Disorders, 5th edition) on observable tics, and propose a broader and more dimensional approach to nosology which incorporates sensory, cognitive and affective phenomena. [End Page 47] Data from interviews they conducted identified that premonitory phenomena and urge experiences in tic disorders are more complex and diverse than what is currently reflected in the literature and clinical scales. They also interviewed participants who reported "no urges" or "no premonitory sensations." They commented that the literature generally treats reports of urge absences at face value, and does not address the likelihood that such reports may be ambiguous or problematic. Overall, they concluded that their research suggests that premonitory urges in TS are a complex and diverse phenomenon that requires further study. This reflects with our clinical experience in working with TS patients. Although a large proportion of older patients describe sensory-based premonitory urges, descriptions are not homogenous, with many describing other experiences preceding their tics.When evaluating a patient's response to an intervention (either behavioral or pharmacological) clinicians incorporate a range of information. This includes the severity of their tics (number, type, frequency, intensity, and associated impairment), as well as their mood, participation and performance in study, work, and social activities, and overall quality of life. Standard clinical practice would not typically include assessment of some of the subjective experiences which precede tics. If it was accepted that these subjective phenomena are indeed salient to the patient's well-being, then a challenge would be how to consistently and reliably capture these feelings to operationalize a comprehensive patient-centered assessment.The primary evidence-based treatment for tic disorders, comprehensive behavioral intervention for tics (CBIT), involves training to increase the awareness of premonitory urges (Woods et al., 2008). Furthermore, successful 'blocking' of tics during the course of CBIT requires the patient to be aware of premonitory urges. Clinicians having a better understanding of the complexity and diversity of experiences which precede tics, as well as using open-ended questioning styles, may assist with improving CBIT outcomes. [End Page 48]Related ArticlesFeature Article: Dimensions, Not Types: On the Phenomenology of Premonitory Urges in Tourette SyndromeCommentary: Priming and Narrative Habits in the Phenomenological Interview: Reflections on a Study of Tourette SyndromeCommentary: Subjective Experiences of Tourette Syndrome: Beyond the Premonitory UrgeResponse: Phenomenological Interviews and Tourette’sDaryl EfronThe Royal Children's Hospital MelbourneIvan MathiesonThe Laneway ClinicDaryl Efron Daryl Efron is a Consultant Pediatrician, Royal Children's Hospital Senior Research Fellow, Murdoch... (shrink)

We present a study of the linguistic output of the German-speaking writer Robert Walser using Natural Language Processing (NLP). We curated a corpus comprising texts written by Walser during periods of sound health, and writings from the year before his hospitalization, and writings from the first year of his stay in a psychiatric clinic, all likely attributed to schizophrenia. Within this corpus, we identified and analyzed a total of 20 linguistic markers encompassing established metrics for lexical diversity, semantic similarity, and (...) syntactic complexity. Additionally, we explored lesser-known markers such as lexical innovation, concreteness, and imageability. Notably, we introduced two additional markers for phonological similarity for the first time within this context. Our findings reveal significant temporal dynamics in these markers closely associated with Walser’s contemporaneous diagnosis of schizophrenia. Furthermore, we investigated the relationship between these markers, leveraging them for classification of the schizophrenic episode. (shrink)

This paper explores the effects of incidental guilt on Socially Responsible Investment (SRI) decisions of retail investors. Do investors who feel guilty invest more in SRIs to clear their conscience? Are guilty investors willing to sacrifice returns to restore their moral selves? Using survey data from an online quasi-experiment among a sample of US retail investors, we find that individuals who experience incidental guilt are willing to invest more in SRI funds than those in a neutral state. We show that (...) this effect, albeit moderate in magnitude, cannot be explained solely by differences in retail investors’ moral reasoning, attitudes towards social responsibility, risk tolerance and demographic factors. When presented with a trade-off between sustainability, risk and return characteristics of the funds, guilty investors are more willing to sacrifice returns for greater sustainability than non-guilty participants. Our research provides new evidence of the effect that incidental guilt has on the sustainable investing decisions of retail investors. (shrink)

The existing scholarship has developed six main explanations to account for the success of the Chinese Revolution, which has been anomalous for major paradigms derived from cross-national comparisons. Methodologically, we use a social geographical approach to test these existing explanations systematically by constructing and analyzing a unique dataset of Communist growth in 93 counties in the three most contested provinces during its most pivotal period of ascendence. Theoretically, we advance and test an alternative perspective, based on the groundwork of Tocqueville (...) and Fei Xiaotong, that integrates the state-centric theory, elite theory, and cultural analysis. Our perspective emphasizes the interplay between state centralization and local elite structure, which leads to intensified state extraction and local elite fracturing, thus creating favorable conditions for revolution. The quantitative analysis strongly supports the importance of the Japanese invasion but provides limited support for many other conventional explanations. The analysis largely confirms the Tocqueville-Fei perspective on state centralization, elite fracturing, cultural change, and revolution. The findings are buttressed by a detailed case study of Lianshui County. The study unveils a common structural challenge that a modernizing state faces in an agrarian status society, to recreate its political legitimacy while disrupting local elite structure. It also sheds historical light on the evolution of state-society relationship through the Chinese Revolution. (shrink)

As result of the ongoing doctoral research, this paper composes the Communication delivered at the First National Post-Graduate Meeting in Philosophy of the University of Brasilia. The thesis relates to the real political action arising from liberty and immanent power. Structured in two moments of the Gramscian thought, that is: a) the juvenile phase (1914-1919), correspondent to the initial period of political engagement towards adherence to the Turin labor movement; and b) the analysis of the 48th § of Volume 3 (...) Prison Notebooks (Q 3, 48, 197) about the real political action. The whole problematic of the research relies in the investigation about Gramscian philosophical demands of the real political action that distinguishes it from the utopian idealism. In this sense, which are Gramscian´s contributions towards the Philosophy of praxis? The research indicates that the praxis requires a critical consciousness – passed through intellectual action in the formation of the people –, since the historical conditions are already given. (shrink)

An increase in the scale of modern science is associated with the proliferation of a new kind of research formation: collaborations involving teams of researchers from several organizations. Historical and sociological studies indicate substantial variation in such formations, but no general classification scheme exists. The authors provide the outline of a scheme through a systematic analysis of multi-institutional collaborations that span a variety of fields in physical science. First, general dimensions of scientific collaborations were identified through a qualitative, historical analysis (...) of collaborations in high energy physics, space science, and geophysics. Next, the authors used informants in five new areas to collect systematic information on twenty-three recent collaborations. Finally, cluster analysis was employed to develop a variety of classification schemes and examine their relationships with outcome dimensions. Results show that a classification based on a broad conception of technological practice is superior to others in its ability to predict perceived success, trust, stress, conflict, and documentary routines. (shrink)

The Earth is facing pressing societal grand challenges that require urgent managerial action. Responsible management learning has emerged as a discipline to prepare managers to act as responsible leaders that can effectively address such pressing challenges. This article aims to extend current knowledge on RML in the domain of corporate sustainability through the application of threshold concepts, novel ideas which provide a doorway to new knowledge and transform a learner’s mindset. Specifically, after conducting a systematic review of the management literature, (...) we identify 33 CS threshold concepts that are useful for mainstream managers and practitioners in their RML process. We group them into six CS threshold concept themes that can help managers understand the complexities and interconnectedness that characterize CS. Finally, we map CS threshold concepts with key competences for effective RML. Therefore, our contribution relies on translating existing CS theoretical frameworks into transformative, specific, understandable and applicable pieces of knowledge that might help mainstream managers to embed CS principles in their daily management practices. (shrink)

The Earth is facing pressing societal grand challenges that require urgent managerial action. Responsible management learning has emerged as a discipline to prepare managers to act as responsible leaders that can effectively address such pressing challenges. This article aims to extend current knowledge on RML in the domain of corporate sustainability through the application of threshold concepts, novel ideas which provide a doorway to new knowledge and transform a learner’s mindset. Specifically, after conducting a systematic review of the management literature, (...) we identify 33 CS threshold concepts that are useful for mainstream managers and practitioners in their RML process. We group them into six CS threshold concept themes that can help managers understand the complexities and interconnectedness that characterize CS. Finally, we map CS threshold concepts with key competences for effective RML. Therefore, our contribution relies on translating existing CS theoretical frameworks into transformative, specific, understandable and applicable pieces of knowledge that might help mainstream managers to embed CS principles in their daily management practices. (shrink)

Voluntary sustainability standards that establish global rules for firms’ environmental and/or social conduct and allow for verification of firm compliance via third-party certification hold the promise to govern firms’ sustainability conduct in a globalizing world economy. However, the recent proliferation of competing and overlapping global sustainability standards that have been developed by various stakeholders with different agendas, creates uncertainties for firms that likely reduce their propensity to adopt any standard. Without widespread adoption these standards cannot effectively govern firm conduct and (...) in contrast create barriers for firms’ access to export markets. We suggest that the uncertainties associated with competing standards and the effect of these uncertainties on standard certification decisions are especially large for firms in emerging economies because these firms lack access to information about current and future standards and the resources to obtain certifications to multiple standards. We theoretically propose and empirically identify three distinct sources of sustainability standard uncertainty: diversity of customer requirements, dynamism of customer requirements, and the unpredictability of the future evolution of standard and propose that each of these sources reduces firms’ propensity to obtain certification to any standard. Our empirical results based on certifications to food safety standards by a sample of 97 Mexican food exporting firms confirm that three distinct sources of sustainability standard uncertainty exist and that all of them negatively impact certification. We discuss ethical implications and offer recommendations for both suppliers as well as standard setting organizations. (shrink)

Paraorthomodular posets are bounded partially ordered sets with an antitone involution induced by quantum structures arising from the logico-algebraic approach to quantum mechanics. The aim of the present work is starting a systematic inquiry into paraorthomodular posets theory both from algebraic and order-theoretic perspectives. On the one hand, we show that paraorthomodular posets are amenable of an algebraic treatment by means of a smooth representation in terms of bounded directoids with antitone involution. On the other, we investigate their order-theoretical features (...) in terms of forbidden configurations. Moreover, sufficient and necessary conditions characterizing bounded posets with an antitone involution whose Dedekind–MacNeille completion is paraorthomodular are provided. (shrink)

The article reveals the essential features and conditions of the long-term process of development of competitive innovation economy - knowledge economy on the example of Ukraine, where the dialogue of late postmodernism and early post-industrialism create special regional conditions. The article characterizes education as not just a form of social consciousness and practice, but as a social and cultural engine and simultaneously marker of civilization development level; considers higher education system from the point of view of society request to form (...) specialists of high qualification level and as a result powerful factor of regional economic growth; offers the directions of Ukraine higher education reforming, which still has signs of late postmodernism. The authors of this article have proved that the synergy of the economic and educational-scientific spheres is capable of changing the global laws of society's existence and returning the course of history to a truly humanistic, technological and divinely attentive course. The development of innovative activities, the introduction of new technologies, which in the long term to overcome the negative trends, primarily related to the need for structural reform of the educational sector in Ukraine and other regions, which are attractors of world change. In particular, cardinal changes require higher education as the most important resource potential that determines the direction of sustainable economic development. (shrink)

This chapter contains sections titled: Respecting Sacred Objects: Some Difficulties Alternative Grounds for Respect: The Historical and Aesthetic Properties of an Object.

Višestoljetni model Crkve kao zajednice laika i klerika koji ju inspiriraju i vode, ulazi u funkcionalnu krizu. U doba revolucija i liberalizma laici se nalaze u novim, često oprečnim ulogama: vjernika odanih Crkvi i građana lojalnih sekularnom društvu. Tražeći izlaz iz krize, Crkva se oslanja na sposobnost demokratskog djelovanja laika koji svojim društvenim nastupom promiču kršćanske vrijednosti, ali se i bore za politička prava Crkve. Uz političke stranke katoličke inspiracije posebnu ulogu ima organizirani katolički laikat, kulturno i moralno oblikujući laičke (...) staleže. Pretpovijest nastanka katoličkoga laičkog pokreta (Katoličke akcije) daje uvide u složenost društava druge polovice XIX. i početka XX. st., ali i zavidnu razinu inventivnosti i laika i hijerarhije u aktiviranju laika, što će postati epohalni uspjeh Crkve XX. stoljeća. (shrink)

In this thesis, I propose and defend a theory according to which committing oneself to knowing the proposition expressed counts as an assertion of that proposition. A consequence of this view is the knowledge account of assertion, according to which one asserts that p correctly only if one knows that p. In support of this approach, I offer a strategy of identifying an assertion’s “normative consequences”, types of act that normally take place as a result of one’s making an assertion (...) incorrectly. I outline two such phenomena: retraction and disavowal of knowledge. In continuation, I put the theory to test and critically examine four sets of objections against it, arguing that it can convincingly defuse them. Finally, I discuss two related issues: I maintain that by performing “aesthetic assertions” one also normally performs a non-assertoric speech act of recommendation, and argue for the possibility of “non-linguistic assertions”, whose content is expressed by gestures in appropriate contexts. (shrink)

I discuss the role of beauty in physics. Physicists are sometimes described as platonists for their conviction that the fundamental laws are elegant and aesthetic arguments represent an important epistemic tool. After a review of the ideas of Plato and some of the leading figures of modern physics, which suggest that this is indeed the case, I present a list of current aesthetic criteria. I focus on symmetry and unity and demonstrate their increasing relevance in an array of experimentally verified (...) theories. I also deal with an open issue of naturalness as the third criterion. The laws of nature appear increasingly beautiful as we uncover them, and it is important to see if the trend continues in the future. (shrink)

As Classical Propositional Logic finds its algebraic counterpart in Boolean algebras, the logic of Quantum Mechanics, as outlined within G. Birkhoff and J. von Neumann’s approach to Quantum Theory (Birkhoff and von Neumann in Ann Math 37:823–843, 1936) [see also (Husimi in I Proc Phys-Math Soc Japan 19:766–789, 1937)] finds its algebraic alter ego in orthomodular lattices. However, this logic does not incorporate time dimension although it is apparent that the propositions occurring in the logic of Quantum Mechanics are depending (...) on time. The aim of the present paper is to show that tense operators can be introduced in every logic based on a complete lattice, in particular in the logic of quantum mechanics based on a complete orthomodular lattice. If the time set is given together with a preference relation, we introduce tense operators in a purely algebraic way. We derive several important properties of such operators, in particular we show that they form dynamic pairs and, altogether, a dynamic algebra. We investigate connections of these operators with logical connectives conjunction and implication derived from Sasaki projections in an orthomodular lattice. Then we solve the converse problem, namely to find for given time set and given tense operators a time preference relation in order that the resulting time frame induces the given operators. We show that the given operators can be obtained as restrictions of operators induced by a suitable extended time frame. (shrink)

The research deals with the issue of genre hybridization in the novel “Silence – Chronicle of a Killer” written by a contemporary Austrian writer Thomas Raab. An examination of the novel's composition and structure, as a text in motion, has been accomplished in the article. The novel “Silence” is an excellent illustration of how the genre of adventure has been adapted to include elements of science fiction. This novel is a love tale, a rural life saga, a formation narrative, and (...) a psychological thriller all in one. As a fictionalized account of the life of a serial murderer with hypersensitive hearing who became a legend for his mental torment and suffering, it serves both as a biography and a thriller. Novelist Raab uses elements from classic horror novels like Frankenstein, German romantics, in particular, G. Kleist, the tale of Casper Hauser, and detective novels like Friedrich Durrenmatt's "Promise" to tell the story of Casper Hauser's disappearance in his book. A new aesthetic experience may be formed at various degrees of identification ranging from naive perception to higher levels of literary reception. Concentration is required for poetic and philosophical substance. Michel Focalut's nomadism, marginality, and authoritarian power rhetoric have been discussed in this article. The novel's ultimate content has been disclosed as the aphesis torment, emotional sublimation, as the birth of an artwork and, at the same time, death of the author, who exposes discourses, accountable for creating texts that are allocated to him. (shrink)

In this article, I want to show that the concept “rationality”, which is important for the French school of epistemology of science, has a dual content and is not very successful. This is the main point of my polemic with Tatyana Sokolova. On the one hand, there seems to be general rationality in it, understood as a preference (in the broad sense) for benefits over costs. Benefits include true knowledge. On the other hand, there is a historical socio-cultural context in (...) which scientific knowledge arises and in which the parameters of practice are determined, which serves as the final instance for testing knowledge. At the same time, there are many such contexts in society, which I call human interfaces. The world, for its part, offers many of its interfaces as collections of interaction tools. When some interface of a person and some interface of the world assimilate each other, knowledge arises, that is confirmed by practice. It can be considered rational. But with a change in the sociocultural context, the human interface also changes, so that a search for new assimilation takes place. It is carried out by science. I agree with Tatyana Sokolova’s characterization of the progress of science, but I suggest at least differentiating the levels of rationality. One operates in the historical sociocultural locus, the other ensures the change of such loci and the adaptation of knowledge to them. I consider the progress of science to be an evaluative characteristic; no objectively recorded phenomenon corresponds to it. The disciplinary distinction of science is derived from the concepts of “object” and “method”, which have a performative content. (shrink)

I connect the idea of an existential turn in philosophical science, presented by Ilya Kasavin and Vladimir Porus in their recent article, with the problem of rationality and culture crisis, as well as the opposition of profession and vocation in Max Weber’s famous speech on politics. I offer an analysis of the structure of vocation to politics and to science as affects of a special kind. To do this, I draw on Jacques Lacan’s analysis of hysteria. My conclusions are that (...) the structure of a target affect coincides to that of hysteria. This means that scientist tries to show that the truth exists, seeks to force other people to recognize this fact and submit to science as an only acceptable form of worldview. Until this can be done, the scientist gives his relationship to the community the character of service to the highest entity. At the same time, he waits for the inversion of this service, i.e. a transition to power through acknowledgement. It should be noted that scientific research is never limited by the science itself, no matter how dangerous it may be. The existential choice in science is a choice between the pursuit of truth in natural sciences and exact sciences and maintaining the sustainability of culture in social and humanitarian knowledge. The latter, contrary to Weber, is always intertwined with politics. The first is not political, but affective. This allows me to see the definition of the vocation to the science that Kasavin gives in a new way. At the center of the “cognitive-existential mood” in the search for truth, affect dominates, the engine of which is hysteria, and in its basic attitudes truth and the scientist are opposed to the plausible and the profane. (shrink)

Contrairement à la philosophie théorique, où la raison vise à la contemplation désintéressée, la philosophie pratique vise à l'action bonne ; et celle-ci est éthique ou politique, selon qu'elle a pour objet le bien de l'individu ou le bien de la cité. Les deux traités classiques qui, dans ce double domaine pratique, livrent la pensée définitive d'Aristote, sont l'Ethique nicomachéenne et la Politique. Ils font ici l'objet d'une étude historique et analytique. Mais il paraît indispensable aussi de soumettre à un (...) examen les trois autres traités d'Aristote qui ont préparé l'Ethique nicomachéenne : la Grande éthique, l'Ethique eudémienne et la Rhétorique. En particulier, le premier d'entre eux, qui a été systématiquement rejeté ou négligé par les spécialistes, a de bonnes chances d'être d'Aristote lui-même et ne peut être sous-estimé dans un travail consacré à la genèse et à l'épanouissement de sa philosophie pratique. (shrink)

RESUMEN Los zapatos nos sirven y nos acompañan, testimonian diferentes verdades, dependiendo de su utilidad y su dueño. Pueden ser de vagabundos o de prisioneros, de militares, artistas o campesinos, de adultos o de niños, de asesinos o de asesinados. Muchos guardan un misterio, todos tienen una historia. El arte los ha acogido desde sus comienzos, vinculándolos a diferentes sucesos, como en las obras de Vincent Van Gogh, Can Togay y Gyula Pauer. A partir del trabajo de estos artistas se (...) busca vincular el vacío y el horror en el arte con el tema de la verdad, entendida como alétheia o desocultación, rememoración y acontecimiento, e indagar por la historia que se oculta tras ciertas obras artísticas. ABSTRACT Shoes are not only useful; they are also our constant companions, and, as such, they attest to different truths, depending on their utility and their owner. They can belong to vagabonds or prisoners, to soldiers, artists, or peasants, to adults or children, to murderers or victims Many conceal a mystery, and they all have a history. Since its beginnings, art has included them and linked them to diverse events, as is the case in the works of Vincent Van Gogh, Can Togay, and Gyula Pauer. On the basis of the work of these artists, the article connects emptiness and horror in art with truth, understood as alétheia or unconcealment, remembrance, and event, and inquires into the hidden story of certain artworks. (shrink)

Los zapatos nos sirven y nos acompañan, testimonian diferentes verdades, dependiendo de su utilidad y su dueño. Pueden ser de vagabundos o de prisioneros, de militares, artistas o campesinos, de adultos o de niños, de asesinos o de asesinados. Muchos guardan un misterio, todos tienen una historia. El arte los ha acogido desde sus comienzos, vinculándolos a diferentes sucesos, como en las obras de Vincent Van Gogh, Can Togay y Gyula Pauer. A partir del trabajo de estos artistas se busca (...) vincular el vacío y el horror en el arte con el tema de la verdad, entendida como alétheia o desocultación, rememoración y acontecimiento, e indagar por la historia que se oculta tras ciertas obras artísticas. (shrink)

The paper analyses John Stuart Mill’s harm principle and its proper application in the process of drafting and evaluating laws, political decisions, and measures used to prevent the spread of contagious diseases. By interpreting Mill as an epistemic democrat and an epistemic liberal, the paper focuses on Mill’s thoughts regarding the decision-making procedures appropriate for legislation in a pandemic. Additionally, it discusses the proper division of epistemic and political labor, one of the most important mechanisms Mill uses to filter the (...) public will, and demonstrates how Mill’s arguments can help us balance between epistemic and moral virtues, i.e. between democratic and expert-oriented decision-making. (shrink)

Cosa accade se filosofi del presente e del passato, personaggi di finzione e romanzieri di fantascienza si mettono a dialogare su alcuni dei temi fondamentali del mondo sociale? La discussione sulla natura della realtà documentale origina un caleidoscopico divertissement incentrato sulla disamina della supposta irrealtà degli oggetti videoludici.

Religious Remembrance. Professor Valentin Vandishev.

Clearly a Late Antiquity’s phenomenon, the Neoplatonism represented to the ancient men the last bastion of its old traditions, the religion of their ancestors and classical culture. Especially the neoplatonic philosophy of Plotinus, that had engendred precepts which, by its meanings, resounded through the last voices of paganism and survived the Middle Ages into the scholastic philosopy. Although the ideas of Plotinus achieved such later importance, it were the main problem conceiving the conflicts between the philosophers Porphyry and Iamblichus. That (...) will be the starting point of this paper, which analyzes the layers of Neoplatonism throught its historical context. (shrink)

In the 1870s, Carl Neumann proposed the so-called method of the arithmetic mean for solving the Dirichlet problem on convex domains. Neumann’s approach was considered at the time to be a reliable existence proof, following Weierstrass’s criticism of the Dirichlet principle. However, in 1937 H. Lebesgue pointed out a serious gap in Neumann’s proof. Curiously, the erroneous argument once again involved confusion between the notions of infimum and minimum. The objective of this paper is to show that Lebesgue’s sharp criticism (...) of Neumann’s proof was only partially justified. (shrink)

A Kleene lattice is a distributive lattice equipped with an antitone involution and satisfying the so-called normality condition. These lattices were introduced by J. A. Kalman. We extended this concept also for posets with an antitone involution. In our recent paper (Chajda, Länger and Paseka, in: Proceeding of 2022 IEEE 52th International Symposium on Multiple-Valued Logic, Springer, 2022), we showed how to construct such Kleene lattices or Kleene posets from a given distributive lattice or poset and a fixed element of (...) this lattice or poset by using the so-called twist product construction, respectively. We extend this construction of Kleene lattices and Kleene posets by considering a fixed subset instead of a fixed element. Moreover, we show that in some cases, this generating poset can be embedded into the resulting Kleene poset. We investigate the question when a Kleene poset can be represented by a Kleene poset obtained by the mentioned construction. We show that a direct product of representable Kleene posets is again representable and hence a direct product of finite chains is representable. This does not hold in general for subdirect products, but we show some examples where it holds. We present large classes of representable and non-representable Kleene posets. Finally, we investigate two kinds of extensions of a distributive poset $${\textbf{A}}$$ A, namely its Dedekind-MacNeille completion $${{\,\mathrm{\textbf{DM}}\,}}({\textbf{A}})$$ DM ( A ) and a completion $$G({\textbf{A}})$$ G ( A ) which coincides with $${{\,\mathrm{\textbf{DM}}\,}}({\textbf{A}})$$ DM ( A ) provided $${\textbf{A}}$$ A is finite. In particular we prove that if $${\textbf{A}}$$ A is a Kleene poset then its extension $$G({\textbf{A}})$$ G ( A ) is also a Kleene lattice. If the subset X of principal order ideals of $${\textbf{A}}$$ A is involution-closed and doubly dense in $$G({\textbf{A}})$$ G ( A ) then it generates $$G({\textbf{A}})$$ G ( A ) and it is isomorphic to $${\textbf{A}}$$ A itself. (shrink)