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.

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)

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.

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 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.

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 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 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.

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

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)

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.

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)

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.

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)

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)

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)

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

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)

We study the relationship between a computably enumerable real and its presentations. A set A presents a computably enumerable real α if A is a computably enumerable prefix-free set of strings such that equation image. Note that equation image is precisely the measure of the set of reals that have a string in A as an initial segment. So we will simply abbreviate equation image by μ. It is known that whenever A so presents α then A ≤wttα, where ≤wtt (...) denotes weak truth table reducibility, and that the wtt-degrees of presentations form an ideal ℐ in the computably enumerable wtt-degrees. We prove that any such ideal is equation image, and conversely that if ℐ is any nonempty equation image ideal in the computably enumerable wtt-degrees then there is a computable enumerable real α such that ℐ = ℐ. We also prove a kind of Rice Theorem for these ideals, namely that if the index set of such a equation image ideal is not empty or equal to ω then it is equation image-complete. (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)

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)

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)

The COVID-19 lockdown has significantly disrupted the higher education environment within the Netherlands and led to changes in available study-related resources and study demands of students. These changes in study resources and study demands, the uncertainty and confusion about educational activities, the developing fear and anxiety about the disease, and the implementation of the COVID-19 lockdown measures may have a significant impact on the mental health of students. As such, this study aimed to investigate the trajectory patterns, rate of change, (...) and longitudinal associations between study resources–demands and mental health of 141 university students from the Netherlands before and during the COVID-19 lockdown. The present study employed a longitudinal design and a piecewise latent growth modeling strategy to investigate the changes in study resources and mental health over a 3 month period. The results showed that moderate levels of student resources significantly decreased before, followed by a substantial rate of increase during, lockdown. In contrast, study demands and mental health were reported to be moderate and stable throughout the study. Finally, the growth trajectories of study resources–demands and mental health were only associated before the lockdown procedures were implemented. Despite growing concerns relating to the negative psychological impact of COVID-19 on students, our study shows that the mental health during the initial COVID-19 lockdown remained relatively unchanged. (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)

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)

Cognitive Science, Volume 46, Issue 9, September 2022.

This article offers a synthesis of and conclusion to the contributions included in the Special Issue 'Rethinking the European Social Market Economy'. Based on different understandings of citizenship in the European Union and the roles of the EU and its member states in providing social protection arrangements, it develops a typology of four models of the EU's role in social protection. It then discusses the contributions to this Special Issue in light of this typology and draws a number of overarching (...) conclusions. (shrink)

Human decisions are increasingly supported by decision support systems (DSS). Humans are required to remain “on the loop,” by monitoring and approving/rejecting machine recommendations. However, use of DSS can lead to overreliance on machines, reducing human oversight. This paper proposes “reflection machines” (RM) to increase meaningful human control. An RM provides a medical expert not with suggestions for a decision, but with questions that stimulate reflection about decisions. It can refer to data points or suggest counterarguments that are less compatible (...) with the planned decision. RMs think against the proposed decision in order to increase human resistance against automation complacency. Building on preliminary research, this paper will (1) make a case for deriving a set of design requirements for RMs from EU regulations, (2) suggest a way how RMs could support decision-making, (3) describe the possibility of how a prototype of an RM could apply to the medical domain of chronic low back pain, and (4) highlight the importance of exploring an RM’s functionality and the experiences of users working with it. (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.

The aim of this study was to investigate how job crafting, work engagement, and workaholism were related in public sector organizations. The participants were civil servants from three Finnish public organizations, representing different professions, such as school personnel, secretaries, directors, parking attendants, and ICT specialists. We duly operationalized job crafting, work engagement, and workaholism by using the Job Crafting Scale, the UWES-9, and the Work Addiction Risk Test. The current study focused on the Finnish public sector, since work engagement is (...) recognized at the governmental level and has been shown to be strongly and positively associated with economic activity and productivity, while workaholism is associated with poor wellbeing. We analyzed the data by using structural equation modeling and found that three job crafting dimensions were strongly intertwined with one another. These dimensions were increasing structural job resources, increasing social job resources, and increasing challenging job demands. In the structural model, dimension “increasing structural job resources” was positively related to work engagement, whereas dimension “decreasing hindering job demands” was negatively associated with workaholism. This study highlighted the relevance of employees learning to balance their job resources and demands. We recommend that, in the public sector, employees be systematically encouraged to practice job crafting behavior by enabling them to increase structural job resources. These results are of high relevance, considering the heavy workload of public sector employees during the COVID-19 pandemic. (shrink)

The Problem of Perception offers two arguments against direct realism--one concerning illusion, and one concerning hallucination--that no current theory of ...