We study the connection between factors of the Medvedev lattice and constructive logic. The algebraic properties of these factors determine logics lying in between intuitionistic propositional logic and the logic of the weak law of the excluded middle (also known as De Morgan, or Jankov, logic). We discuss the relation between the weak law of the excluded middle and the algebraic notion of join-reducibility. Finally we discuss autoreducible degrees.

This book is the first part of a comprehensive study of Wittgenstein's conception of language description. Describing language was no pastime occupation for the philosopher. It was hard work and it meant struggle. It made for a philosophy that required Wittgenstein's full attention and half his life. His approach had always been working on himself, on how he saw things. The central claim of this book is that nothing will come of our exegetical efforts to see what Wittgenstein's later philosophy (...) amounts to if his work on describing language is not given the place and concern it deserves. The book shows what his philosophy might begin to look like in the light of critical questions around his interest to see the end of the day with descriptions, and these things only. (shrink)

We investigate the structure of the Medvedev lattice as a partial order. We prove that every interval in the lattice is either finite, in which case it is isomorphic to a finite Boolean algebra, or contains an antichain of size $2^{2^{\aleph }0}$ , the size of the lattice itself. We also prove that it is consistent with ZFC that the lattice has chains of size $2^{2^{\aleph }0}$ , and in fact these big chains occur in every infinite interval. We also (...) study embeddings of lattices and algebras. We show that large Boolean algebras can be embedded into the Medvedev lattice as upper semilattices, but that a Boolean algebra can be embedded as a lattice only if it is countable. Finally we discuss which of these results hold for the closely related Muchnik lattice. (shrink)

ABSTRACT In the work of Ernesto Laclau, populism is treated as a hegemonic challenge. Hegemony describes the usurpation of the image of society as a totality by a particular and underdetermined social imaginary. Seen through the lens of what Johann P. Arnason terms “post-transcendental phenomenology”, this concerns the way in which a society sees and experiences both itself and the world it inhabits. This article suggests that hegemonic social imaginaries are built into a society’s public spaces, and are in turn (...) experienced by citizens moving through these spaces, meaning that the built environment is central to the development of populist imaginaries. The article discusses how the neoliberal city exemplifies the way social imaginaries are inscribed into the physical landscape by highlighting three moments in the city; the institution of a certain imaginary as dominant; its sedimentation within the urban fabric over time; and finally, the re-activation of the original moment of institution, which opens up the possibility for new beginnings to overwrite the imaginaries encoded in the city. These three moments describe how physical, built spaces make concrete the power relations and horizons of possibility of the hegemonic imaginary—making possible and encouraging certain ways of being while discouraging (and hiding) others. This hegemonic logic of occupying a public space in the name of a particular subset of the population is a not only parallel to the form of populist politics, but populist sentiment is—at least in part—provoked by the experiences of inhabiting these spaces. (shrink)

We prove that there are uncountably many sets that are low for the class of Schnorr random reals. We give a purely recursion theoretic characterization of these sets and show that they all have Turing degree incomparable to 0'. This contrasts with a result of Kučera and Terwijn [5] on sets that are low for the class of Martin-Löf random reals.

In this study, we examine the influence of senior leadership on firms’ corporate social responsibility. We integrate upper echelons research that has investigated either the influence of the CEO or the top management team on CSR. We contend that functional experience complementarity between CEOs and TMTs in formulating and implementing CSR strategy may underlie differentiated strategies in CSR. We find that when CEOs who have predominant experience in output functions are complemented by TMTs with a lower proportion of members who (...) have experience in output functions, there is a pronounced effect on the community, product, and diversity dimensions of CSR. In turn, when output-oriented CEOs are complemented by output-oriented TMTs, we observe an effect on the employee relations dimension of CSR. Interestingly, we find no influence of CEO-TMT complementarity on the environment dimension of CSR. In general, our empirical results support the relevance of the interaction between CEOs and their TMTs in defining their firms’ CSR profile. (shrink)

Name der Zeitschrift: Wittgenstein-Studien Jahrgang: 5 Heft: 1 Seiten: 57-88.

Simpson introduced the lattice of Π0 1 classes under Medvedev reducibility. Questions regarding completeness in are related to questions about measure and randomness. We present a solution to a question of Simpson about Medvedev degrees of Π0 1 classes of positive measure that was independently solved by Simpson and Slaman. We then proceed to discuss connections to constructive logic. In particular we show that the dual of does not allow an implication operator (i.e. that is not a Heyting algebra). We (...) also discuss properties of the class of PA-complete sets that are relevant in this context. (shrink)

In this study, we examine the influence of senior leadership on firms’ corporate social responsibility. We integrate upper echelons research that has investigated either the influence of the CEO or the top management team on CSR. We contend that functional experience complementarity between CEOs and TMTs in formulating and implementing CSR strategy may underlie differentiated strategies in CSR. We find that when CEOs who have predominant experience in output functions are complemented by TMTs with a lower proportion of members who (...) have experience in output functions, there is a pronounced effect on the community, product, and diversity dimensions of CSR. In turn, when output-oriented CEOs are complemented by output-oriented TMTs, we observe an effect on the employee relations dimension of CSR. Interestingly, we find no influence of CEO-TMT complementarity on the environment dimension of CSR. In general, our empirical results support the relevance of the interaction between CEOs and their TMTs in defining their firms’ CSR profile. (shrink)

Model transfer refers to the observation that particular model structures are used across multiple distinct scientific domains. This paper puts forward an account to explain the inter-domain transfer of model structures. Central in the account is the role of validation criteria in determining whether a model is considered to be useful by practitioners. Validation criteria are points of reference to which model correctness for a particular purpose is assessed. I argue that validation criteria can be categorized as being mathematical, theoretical (...) or phenomenological in nature. Model transfer is explained by overlap in validation criteria between scientific domains. Particular emphasis is placed on overlap between phenomenological criteria. Overlap in phenomenological criteria can be explained through the notion of universal patterns. Universal patterns are abstract structures that can be made to refer to multiple distinct phenomena when coupled with phenomena-specific empirical content. I present the case study of the Yule Process, in which universal patterns play a crucial role in explaining model transfer. This paper provides an account of model transfer that stays close to modelling practice and expands existing accounts by introducing the notion of universal patterns. (shrink)

For every partial combinatory algebra, we define a hierarchy of extensionality relations using ordinals. We investigate the closure ordinals of pca’s, i.e., the smallest ordinals where these relations become equal. We show that the closure ordinal of Kleene’s first model is ${\omega _1^{\textit {CK}}}$ and that the closure ordinal of Kleene’s second model is $\omega _1$. We calculate the exact complexities of the extensionality relations in Kleene’s first model, showing that they exhaust the hyperarithmetical hierarchy. We also discuss embeddings of (...) pca’s. (shrink)

In the context of his theory of numberings, Ershov showed that Kleene's recursion theorem holds for any precomplete numbering. We discuss various generalizations of this result. Among other things, we show that Arslanov's completeness criterion also holds for every precomplete numbering, and we discuss the relation with Visser's ADN theorem, as well as the uniformity or nonuniformity of the various fixed point theorems. Finally, we base numberings on partial combinatory algebras and prove a generalization of Ershov's theorem in this context.

We define a variant of the standard Kripke semantics for intuitionistic logic, motivated by the connection between constructive logic and the Medvedev lattice. We show that while the new semantics is still complete, it gives a simple and direct correspondence between Kripke models and algebraic structures such as factors of the Medvedev lattice.

While parents have long received guidance on how to raise children, a relatively new element of this involves explicit references to infant brain development, drawing on brain scans and neuroscientific knowledge. Sometimes called ‘brain-based parenting’, this has been criticised from within sociological and policy circles alike. However, the engagement of parents themselves with neuroscientific concepts is far less researched. Drawing on 22 interviews with parents/carers of children living in Scotland, this article examines how they account for their use of concepts (...) and understandings relating to neuroscience. Three normative tropes were salient: information about children’s processing speed, evidence about deprived Romanian orphans in the 1990s, and ideas relating to whether or not children should ‘self-settle’ when falling asleep. We interrogate how parents reflexively weigh and judge such understandings and ideas. In some cases, neuroscientific knowledge was enrolled by parents in ways that supported biologically reductionist models of childhood agency. This reductionism commonly had generative effects, enjoining new care practices and producing particular parent and infant subjectivities. Notably, parents do not uncritically adopt or accept neurobiological and/or psychological knowledge; rather, they reflect on whether and when it is applicable to and relevant for raising their children. Thus, our respondents draw on everyday epistemologies of parenting to negotiate brain-based understandings of infant development and behaviour, and invest meaning in these in ways that cannot be fully anticipated within straightforward celebrations or critiques of the content of parenting programmes drawing on neuropsychological ideas. (shrink)

We investigate the initial segments of the Medvedev lattice as Brouwer algebras, and study the propositional logics connected to them.

A positive answer to a question of M. van Lambalgen and D. Zambella whether there exist nonrecursive sets that are low for the class of random sets is obtained. Here a set A is low for the class RAND of random sets if RAND = RAND A.

We develop arithmetical measure theory along the lines of Lutz [10]. This yields the same notion of measure 0 set as considered before by Martin-Löf, Schnorr, and others. We prove that the class of sets constructible by r.e.-constructors, a direct analogue of the classes Lutz devised his resource bounded measures for in [10], is not equal to RE, the class of r.e. sets, and we locate this class exactly in terms of the common recursion-theoretic reducibilities below K. We note that (...) the class of sets that bounded truth-table reduce to K has r.e.-measure 0, and show that this cannot be improved to truth-table. For Δ2-measure the borderline between measure zero and measure nonzero lies between weak truth-table reducibility and Turing reducibility to K. It follows that there exists a Martin-Löf random set that is tt-reducible to K, and that no such set is btt-reducible to K. In fact, by a result of Kautz, a much more general result holds. (shrink)

We prove a number of elementary facts about computability in partial combinatory algebras. We disprove a suggestion made by Kreisel about using Friedberg numberings to construct extensional pca’s. We then discuss separability and elements without total extensions. We relate this to Ershov’s notion of precompleteness, and we show that precomplete numberings are not 1–1 in general.

We discuss the effectivity of Arslanov’s completeness criterion. In particular, we show that a parameterized version, similar to the recursion theorem with parameters, fails. We also discuss the effectivity of another extension of the recursion theorem, namely Visser’s ADN theorem, as well as that of a joint generalization of the ADN theorem and Arslanov’s completeness criterion.

Partial combinatory algebras (pcas) are algebraic structures that serve as generalized models of computation. In this article, we study embeddings of pcas. In particular, we systematize the embeddings between relativizations of Kleene’s models, of van Oosten’s sequential computation model, and of Scott’s graph model, showing that an embedding between two relativized models exists if and only if there exists a particular reduction between the oracles. We obtain a similar result for the lambda calculus, showing in particular that it cannot be (...) embedded in Kleene’s first model. (shrink)

The Overview Effect is the commonly reported experience of astronauts viewing planet Earth from space, and the subsequent reflection on, and processing of this experience. The Overview Effect is associated with feelings of awe, self-transcendence, and a change of perspective and identity that manifest themselves in taking steps towards protecting the fragile ecosystem. In the current study, we investigated whether the Overview Effect can be obtained in school children when simulated using virtual reality and whether the effect has a positive (...) impact on learning gains. Using questionnaires and attention data in an existing simulation environment used in the school system, we showed that the virtual reality simulation elicits an Overview Effect experience. Moreover, the experience yields learning gains in the domain of astrophysics. These findings are in line with past evidence regarding the positive impact of awe on learning and can be used to support further investigations of the relation between the Overview Effect and behavioral changes, specifically for educational purposes. (shrink)

Religion in education in South Africa and the Netherlands: A comparative study. The aim of this article is the reconstruction and comparison of the historical evolution of the place and role of religion in education in South Africa and in the Netherlands. The article commences with an overview of the historical evolution of the place and role of religion in education, up to the present, and a discussion of the dissatisfaction and objections which could be and which have been levelled (...) against the current situation. The Netherlands has followed a more accommodating policy and practice regarding religious beliefs and diversity than the international norm. While South Africa can learn much from the Dutch approach to the problem of religion in education, this approach has also been challenged in recent times. In both systems, controversy about the accommodation of religion in education has given rise to tension between the notions of freedom, tolerance and accommodation, on the one hand, and the acknowledgement of human rights and the need for social cohesion on the other. Other considerations to be taken into account in this regard are the downsides of providing a partisan, confessional type of education that could hinder learners in maintaining themselves in the outside world. The trend in modern society is towards individualised belief systems, not collective ones. And the warning to be heeded is that the line between education and indoctrination is thin. The current Dutch model, despite the problems that it currently encounters, could provide direction in respect of all these issues. Contribution: The article concludes with an educational-philosophical perspective regarding the question as to how educationists and educators could guide learners to a state where they can independently decide about their personal religious orientation, given the fact that they are now living in a time when relativism prevails, also in terms of religion and faith. (shrink)

We study the model-theoretic aspects of a probability logic suited for talking about measure spaces. This nonclassical logic has a model theory rather different from that of classical predicate logic. In general, not every satisfiable set of sentences has a countable model, but we show that one can always build a model on the unit interval. Also, the probability logic under consideration is not compact. However, using ultraproducts we can prove a compactness theorem for a certain class of weak models.

We study a class of formulas generalizing the weak law of the excluded middle and provide a characterization of these formulas in terms of Kripke frames and Brouwer algebras. We use these formulas to separate logics corresponding to factors of the Medvedev lattice.

Optimism has reigned supreme for a long time regarding the potential of education (schooling) to address the many societal ailments that humankind has had to deal with. The outbreak of the COVID-19 pandemic in March 2020 shifted all such aspirations to the back-burner. Now, after just more than a year after the initial outbreak of the pandemic, the question can be raised whether those who managed the pandemic in the educational context followed the correct policies and instituted the correct (ethical, (...) moral) measures in combatting the pandemic. This comparison between the situation in the Netherlands and South Africa reveals that although the role-players in both countries had a good understanding of the situation and of their duties in such conditions, they tended to treat education as just another facet of society, thereby demonstrating a lack of empathy with the unique demands of education (schooling). CONTRIBUTION: In this article, the authors investigate the governance performance of two different countries during the first year of the COVID-19 pandemic concerning education and judge that performance based on a Biblically driven ethical-moral-pedagogical framework. (shrink)

Optimism has reigned supreme for a long time regarding the potential of education (schooling) to address the many societal ailments that humankind has had to deal with. The outbreak of the COVID-19 pandemic in March 2020 shifted all such aspirations to the back-burner. Now, after just more than a year after the initial outbreak of the pandemic, the question can be raised whether those who managed the pandemic in the educational context followed the correct policies and instituted the correct (ethical, (...) moral) measures in combatting the pandemic. This comparison between the situation in the Netherlands and South Africa reveals that although the role-players in both countries had a good understanding of the situation and of their duties in such conditions, they tended to treat education as just another facet of society, thereby demonstrating a lack of empathy with the unique demands of education (schooling). CONTRIBUTION: In this article, the authors investigate the governance performance of two different countries during the first year of the COVID-19 pandemic concerning education and judge that performance based on a Biblically driven ethical-moral-pedagogical framework. (shrink)

The South African-Dutch research group responsible for this article started its activities in 2012 by looking at religious tolerance as a means of addressing the tendency for religious intolerance, extremism and fundamentalism. While tolerance seemed to be a promising way to counter religious intolerable behaviour, some shortcomings also became apparent. For example, the concept of tolerance includes an aspect of passivity towards others who adhere to another religion. The concept also does not appear to be able to respond to attitudes (...) and values such as respect, human rights and diversity. Accurate investigation of this problem, both conceptually and empirically, led to the understanding that hospitality is a concept that embodies more active adaptation to those who are different. Hospitality, therefore, seems to be a more promising concept than tolerance for reducing religious tension between individuals and groups. The inner contradiction discovered by Derrida in the notion of hospitality does not detract from the concept of being defined from a Biblical point of view. Hospitality can also be taught to young people. Although there are no formal provisions for hospitality in the national curricula, an analysis of the Dutch and South African national curricula shows that there is room for hospitality education. (shrink)

Media reporting of science has consequences for public debates on the ethics of research. Accordingly, it is crucial to understand how the sciences of the brain and the mind are covered in the media, and how coverage is received and negotiated. The authors report here their sociological findings from a case study of media coverage and associated reader comments of an article from Annals of Neurology. The media attention attracted by the article was high for cognitive science; further, as associates/members (...) of the Centre where it was produced, the authors of the research reported here had rare insight into how the scientists responsible for the Annals of Neurology article interacted with the media. The data corpus included 37 news items and 228 readers’ comments, examined via qualitative thematic analysis. Media coverage of the article was largely accurate, without merely copying the press release. Analysis of reader comments showed these to be an important resource for considering issues of import to neuroethics scholars, as well as to scientists themselves. In particular, the findings demonstrate how personal experiences were vital in shaping readers’ accounts of their agreements with the scientific article. Furthermore, the data show how scientific research can catalyse political discussions in ways likely unanticipated by scientists. The analysis indicates the importance of dialogue between journalists, laboratory scientists and social scientists in order to support the communication of the messages researchers intend. (shrink)

Can heroin addicts give consent to research on trials in which heroin is prescribed to them? Analyses of addicts and informed consent have been objects of debate in several articles. Informed consent requires the agent not only to be competent but also to give consent voluntarily. This has been questioned because of alleged features of heroin addiction. Until recently the discussion has focused on heroin addicts' desires for heroin, whether these are irresistible and thus pose a problem for giving consent. (...) Still, in light of empirical evidence, there seems to be a consensus more or less that the problem is not whether the addicts can resist their desire for heroin. A recent article concentrates specifically on heroin addicts' false assumptions of options and voluntariness. We argue that the prevailing framing of the options in this discussion in terms of heroin and access to it is problematic. The way in which the options are typically laid out suggests an assumption that participation in the research is allegedly based on the addicts' views on using the drug. We argue that this way of presenting the options is, first, a mismatch to the studies carried out and, second, symptomatic of potential misconceptions about heroin addiction and addicts. Furthermore, we also suggest that the account of voluntariness needs to be realistic in order for subjects to be able to give consent voluntarily in actual situations, and for medical research to carry out studies on improving outcomes in addiction treatment in an ethical way. (shrink)

Can the straight line be analysed mathematically such that it does not fall apart into a set of discrete points, as is usually done but through which its fundamental continuity is lost? And are there objects of pure mathematics that can change through time? Mathematician and philosopher L.E.J. Brouwer argued that the two questions are closely related and that the answer to both is "yes''. To this end he introduced a new kind of object into mathematics, the choice sequence. But (...) other mathematicians and philosophers have been voicing objections to choice sequences from the start. This book aims to provide a sound philosophical basis for Brouwer's choice sequences by subjecting them to a phenomenological critique in the style of the later Husserl. (shrink)

We report on some recent work centered on attempts to understand when one set is more random than another. We look at various methods of calibration by initial segment complexity, such as those introduced by Solovay [125], Downey, Hirschfeldt, and Nies [39], Downey, Hirschfeldt, and LaForte [36], and Downey [31]; as well as other methods such as lowness notions of Kučera and Terwijn [71], Terwijn and Zambella [133], Nies [101, 100], and Downey, Griffiths, and Reid [34]; higher level randomness notions (...) going back to the work of Kurtz [73], Kautz [61], and Solovay [125]; and other calibrations of randomness based on definitions along the lines of Schnorr [117].These notions have complex interrelationships, and connections to classical notions from computability theory such as relative computability and enumerability. Computability figures in obvious ways in definitions of effective randomness, but there are also applications of notions related to randomness in computability theory. For instance, an exciting by-product of the program we describe is a more-or-less naturalrequirement-freesolution to Post's Problem, much along the lines of the Dekker deficiency set. (shrink)

In our previous article on the question whether heroin addicts are able to give informed consent voluntarily to research on heroin-assisted treatment, we criticized the ongoing bioethical discussion of a flawed conceptualization of heroin addicts' options. As a participant in this discussion, Edmund Henden defends the conceptualization as sufficient for determining whether heroin addicts are able to give informed consent to the research on heroin-assisted treatment voluntarily. This discussion on research on heroin-assisted treatment seems to go astray in several respects. (...) In his reply to our article Henden maintains some of the biases, such as the necessity of abstinence in recovery, that seem to prevail in addiction research on a more general level as well. These biases run the danger of having implausible ethical implications on stakeholders in addiction research and treatment. In our reply to him, we will further clarify and discuss the importance of describing the relevant issues in plausible terms that do justice to the realities of the cases of informed consent in research on heroin-assisted treatment and also raise a wider issue of the ethics of wording as well as of the narrow scope, or ‘tunnel vision’, in addiction research as currently conducted. (shrink)

This article was derived from my doctoral thesis, ‘Post-apartheid racism among Afrikaans speaking urban adolescents: A narrative-pastoral reflection’. The impetus for this study was the seemingly increasing occurrences of racism amongst post-apartheid Afrikaans-speaking urban adolescents in South Africa by taking a narrative practical theological perspective on the matter to help build meaningful cross-cultural dialogue. This study explored the level of dialogue of the participants using a postfoundational paradigm. Two questions guided the investigation: How deeply embedded are objectifying of cross-cultural relationships? (...) How can we instigate honest dialogue aiding us in being more aware of our biases to embrace diversity and going forward as a unity in diversity? This study was conducted in 2016 amongst white Afrikaans-speaking urban adolescents living in Pretoria-East, South Africa. I had four group conversations with my co-researchers, with six to eight adolescents per group. I made use of certain empirical research methods, such as narrative interviewing and group discussions. From an epistemological perspective, a postfoundational, social constructionist perspective, including an auto-ethnographical approach, was followed. The research indicated that Afrikaner adolescents could live life unquestioned from a position of power and objectivity that was culturally inherited. It was found that by objectifying relationships, diverse engagement becomes almost impossible. Consequently, this article advocates for a dialogical approach towards building relationships in a context where people feel vulnerable and shameful, have fears, but also gain trust to contribute to meaningful dialogue with ‘others’. (shrink)

This contribution offers an introduction to the Special Issue 'Rethinking the European Social Market Economy'. It places the Special Issue against the background of the debate on free markets versus social protection in the European Union and the inclusion of the notion of 'social market economy' in the Treaty on European Union. It sketches the meaning and development of the social market economy concept, and introduces the key questions underlying this Special Issue and the contributions included in it.

If is a random sequence, then the sequence is clearly not random; however, seems to be “about half random”. L. Staiger [Kolmogorov complexity and Hausdorff dimension, Inform. and Comput. 103 159–194 and A tight upper bound on Kolmogorov complexity and uniformly optimal prediction, Theory Comput. Syst. 31 215–229] and K. Tadaki [A generalisation of Chaitin’s halting probability Ω and halting self-similar sets, Hokkaido Math. J. 31 219–253] have studied the degree of randomness of sequences or reals by measuring their “degree (...) of compression”. This line of study leads to various definitions of partial randomness. In this paper we explore some relations between these definitions. Among other results we obtain a characterisation of Σ1-dimension in terms of strong Martin-Löf ε-tests , and we show that ε-randomness for ε is different than the classical 1-randomness. (shrink)

BackgroundThe COVID-19 pandemic has created ethical challenges for intensive care unit (ICU) professionals, potentially causing moral distress. This study explored the levels and causes of moral distress and the ethical climate in Dutch ICUs during COVID-19.MethodsAn extended version of the Measurement of Moral Distress for Healthcare Professionals (MMD-HP) and Ethical Decision Making Climate Questionnaire (EDMCQ) were online distributed among all 84 ICUs. Moral distress scores in nurses and intensivists were compared with the historical control group one year before COVID-19. ResultsThree (...) hundred forty-five nurses (70.7%), 40 intensivists (8.2%), and 103 supporting staff (21.1%) completed the survey. Moral distress levels were higher for nurses than supporting staff. Moral distress levels in intensivists did not differ significantly from those of nurses and supporting staff. “Inadequate emotional support for patients and their families” was the highest-ranked cause of moral distress for all groups of professionals. Of all factors, all professions rated the ethical climate most positively regarding the culture of mutual respect, ethical awareness and support. “Culture of not avoiding end-of-life-decisions” and “Self-reflective and empowering leadership” received the lowest mean scores. Moral distress scores during COVID-19 were significantly lower for ICU nurses (p < 0.001) and intensivists (p < 0.05) compared to one year prior.ConclusionLevels and causes of moral distress vary between ICU professionals and differ from the historical control group. Targeted interventions that address moral distress during a crisis are desirable to improve the mental health and retention of ICU professionals and the quality of patient care. (shrink)