The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is (...) Heisenberg's `quantum-theoretical Umdeutung (reinterpretation) of classical observables', which lies at the basis of quantization theory. Similarly, Bohr's correspondence principle (in somewhat revised form) and Schroedinger's wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), in the limit N goes to infinity of a large system with $N$ degrees of freedom (at fixed h), and through decoherence and consistent histories. The first limit is closely related to modern quantization theory and microlocal analysis, whereas the second involves methods of C*-algebras and the concepts of superselection sectors and macroscopic observables. In these limits, the classical world does not emerge as a sharply defined objective reality, but rather as an approximate appearance relative to certain ``classical" states and observables. Decoherence subsequently clarifies the role of such states, in that they are ``einselected", i.e. robust against coupling to the environment. Furthermore, the nature of classical observables is elucidated by the fact that they typically define (approximately) consistent sets of histories. This combination of ideas and techniques does not quite resolve the measurement problem, but it does make the point that classicality results from the elimination of certain states and observables from quantum theory. Thus the classical world is not created by observation (as Heisenberg once claimed), but rather by the lack of it. (shrink)

Beginning with Anderson, spontaneous symmetry breaking in infinite quantum systems is often put forward as an example of emergence in physics, since in theory no finite system should display it. Even the correspondence between theory and reality is at stake here, since numerous real materials show ssb in their ground states, although they are finite. Thus against what is sometimes called ‘Earman's Principle’, a genuine physical effect seems theoretically recovered only in some idealisation, disappearing as soon as the idealisation is (...) removed.We review the well-known arguments that no finite system can exhibit ssb, using the formalism of algebraic quantum theory in order to control the thermodynamic limit and unify the description of finite- and infinite-volume systems. Using the striking mathematical analogy between the thermodynamic limit and the classical limit, we show that a similar situation obtains in quantum mechanics versus classical mechanics.This discrepancy between formalism and reality is quite similar to the measurement problem, and hence we address it in the same way, adapting an argument of the Landsman and Reuvers that was originally intended to explain the collapse of the wave-function within conventional quantum mechanics. Namely, exponential sensitivity to perturbations of the dynamics as the system size increases causes symmetry breaking already in finite but very large quantum systems. This provides continuity between finite- and infinite-volume descriptions of quantum systems featuring ssb and hence restores Earman's Principle. (shrink)

Bijdragen aan een congres waarin de integriteit van juridische professionals bediscussieerd wordt.

Einstein's philosophy of physics (as clarified by Fine, Howard, and Held) was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed objectification, and thereby "physical thought" and "physical laws", to be impossible. Bohr's philosophy (as elucidated by Hooker, Scheibe, Folse, Howard, Held, and others), on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio's Theorem in algebraic (...) quantum theory that - within an appropriate class of physical theories - suitable mathematical translations of the doctrines of Bohr and Einstein are equivalent. Thus - upon our specific formalization - quantum mechanics accommodates Einstein's Trennungsprinzip if and only if it is interpreted a la Bohr through classical physics. Unfortunately, the protagonists themselves failed to discuss their differences in this constructive way, since their debate was dominated by Einstein's ingenious but ultimately flawed attempts to establish the "incompleteness" of quantum mechanics. This aspect of their debate may still be understood and appreciated, however, as reflecting a much deeper and insurmountable disagreement between Bohr and Einstein about the knowability of Nature. Using the theological controversy on the knowability of God as a analogy, we can say that Einstein was a Spinozist, whereas Bohr could be said to be on the side of Maimonides. Thus Einstein's off-the-cuff characterization of Bohr as a 'Talmudic philosopher' was spot-on. (shrink)

Einstein's philosophy of physics was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed objectification, and thereby "physical thought" and "physical laws", to be impossible. Bohr's philosophy, on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio's Theorem in algebraic quantum theory that - within an appropriate class of physical theories - suitable mathematical translations of the (...) doctrines of Bohr and Einstein are equivalent. Thus - upon our specific formalization - quantum mechanics accommodates Einstein's Trennungsprinzip if and only if it is interpreted a la Bohr through classical physics. Unfortunately, the protagonists themselves failed to discuss their differences in this constructive way, since their debate was dominated by Einstein's ingenious but ultimately flawed attempts to establish the "incompleteness" of quantum mechanics. This aspect of their debate may still be understood and appreciated, however, as reflecting a much deeper and insurmountable disagreement between Bohr and Einstein about the knowability of Nature. Using the theological controversy on the knowability of God as a analogy, we can say that Einstein was a Spinozist, whereas Bohr could be said to be on the side of Maimonides. Thus Einstein's off-the-cuff characterization of Bohr as a 'Talmudic philosopher' was spot-on. (shrink)

A Dutch 'folk theorem' holds that 'from exchange it comes to tears'. This seems to contradict the basic idea found in economics that exchange and trade can make both sides better off. We show that the 'folk theorem' has a better theoretical foundation than sometimes thought, as it is vindicated by the equilibrium of an exchange game with two-sided asymmetric information. We, then, explain the practical value of such 'folk wisdom' in the real world by showing why players might be (...) unlikely to learn such an equilibrium strategy. (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)

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)

This article investigates the naturalisation of the Bible. Three voices are of special importance in the narrative presented in this article; they are Aristotle, Rene Descartes and Baruc Spinoza. This article will investigate the scientific method and metaphysics espoused by each of the three scholars, thereby highlighting changes in scientific method and metaphysics that lead to the naturalisation of the Bible. Firstly, Aristotle pioneered a scientific method that would dominate for centuries, as well as a highly influential metaphysics. Secondly, Descartes, (...) witnessing the horrors of the Thirty Years War and seeing first-hand the new discoveries that brought about the scientific revolution, reacted against Aristotle’s metaphysics. Ironically he then used Aristotle’s scientific method to provide a foundation for the new science resulting in Descartes’s famous dualism. Thirdly, Spinoza, equally horrified by the amount of religious violence of his time, reacts against Descartes’s dualism, providing scholars with a monist metaphysics that would contribute greatly to the naturalisation of the Bible. This article will be relevant to theologians who wish to engage more fully with contemporary Western culture. (shrink)

Theologians are used to pointing the finger at European continental postmodernism when dealing with modern relativism. This article addresses a problem that is seldom highlighted within theology: modern relativism is the result of a series of epistemological discussions that took place during the early Enlightenment between scholars such as Rene Descartes, John Locke and Immanuel Kant. They were reacting, in part, to Aristotle’s metaphysics and logic. When the whole picture unravels, one immediately sees that modern relativism is deeply ingrained in (...) Western thought. In other words, modern relativism will not gather dust after the demise of postmodernism. To the contrary, this article would argue that modern relativism will continue to pose serious challenges to reformed churches in future. Pastors who want to engage with Western audiences will benefit from being made aware of this. Hopefully this will encourage theologians to re-evaluate the relevancy of reformed theological constructs in societies that are deeply steeped in relativist thought. (shrink)

We clarify the role of the Born rule in the Copenhagen Interpretation of quantum mechanics by deriving it from Bohr's doctrine of classical concepts, translated into the following mathematical statement: a quantum system described by a noncommutative C*-algebra of observables is empirically accessible only through associated commutative C*-algebras. The Born probabilities emerge as the relative frequencies of outcomes in long runs of measurements on a quantum system; it is not necessary to adopt the frequency interpretation of single-case probabilities (which will (...) be the subject of a sequel paper). Our derivation of the Born rule uses ideas from a program begun by Finkelstein (1965) and Hartle (1968), intending to remove the Born rule as a separate postulate of quantum mechanics. Mathematically speaking, our approach refines previous elaborations of this program - notably the one due to Farhi, Goldstone, and Gutmann (1989) as completed by Van Wesep (2006) - in replacing infinite tensor products of Hilbert spaces by continuous fields of C*-algebras. In combination with our interpretational context, this technical improvement circumvents valid criticisms that earlier derivations of the Born rule have provoked, especially to the effect that such derivations were mathematically flawed as well as circular. Furthermore, instead of relying on the controversial eigenvector-eigenvalue link in quantum theory, our derivation just assumes that pure states in classical physics have the usual interpretation as truthmakers that assign sharp values to observables. (shrink)

We model three examples of beliefs that agents may have about other agents' beliefs, and provide motivation for this conceptualization from the theory of mind literature. We assume a modal logical framework for modelling degrees of belief by partially ordered preference relations. In this setting, we describe that agents believe that other agents do not distinguish among their beliefs ('no preferences'), that agents believe that the beliefs of other agents are in part as their own ('my preferences'), and the special (...) case that agents believe that the beliefs of other agents are exactly as their own ('preference refinement'). This multi-agent belief interaction is frame characterizable. We provide examples for introspective agents. We investigate which of these forms of belief interaction are preserved under three common forms of belief revision. (shrink)

Axiom weakening is a novel technique that allows for fine-grained repair of inconsistent ontologies. In a multi-agent setting, integrating ontologies corresponding to multiple agents may lead to inconsistencies. Such inconsistencies can be resolved after the integrated ontology has been built, or their generation can be prevented during ontology generation. We implement and compare these two approaches. First, we study how to repair an inconsistent ontology resulting from a voting-based aggregation of views of heterogeneous agents. Second, we prevent the generation of (...) inconsistencies by letting the agents engage in a turn-based rational protocol about the axioms to be added to the integrated ontology. We instantiate the two approaches using real-world ontologies and compare them by measuring the levels of satisfaction of the agents w.r.t. the ontology obtained by the two procedures. (shrink)

We introduce and explore the notion of duality for entailment relations induced by preference orderings on states. We discuss the relationship between these preferential entailment relations from the perspectives of Boolean algebra, inference rules, and modal axiomatisation. Interpreting the preference relations as accessibility relations establishes modular Gödel-Löb logic as a suitable modal framework for rational preferential reasoning.

Globally, universities make use of peer physical examination in health professions students’ teaching of physical examination skills. PPE has many educational benefits, such as teaching normal anatomy and function, development of compassion and empathy, to feel what it is like to be examined from a patient’s perspective, improvement of communication skills, correcting errors in technique and improve confidence. The benefits for patients include protection from repeated examinations by unskilled students. The aim of the study was to investigate health sciences students’ (...) perceptions of the ethical aspects of PPE. A qualitative investigation, which included two focus group interviews with students and one with lecturers, was used for data collection. Most students and lecturers regarded PPE as beneficial, as it provides a safe environment for students in the health sciences to improve their clinical competence and confidence, without fear of embarrassment or failure. Students stated that PPE promoted the development of empathy with and respect for their patients. It was suggested that in a culturally diverse society, guidelines specifically related to religious customs and convictions should be provided to give students an indication of appropriate and acceptable behaviour towards fellow students when practising PPE. The use of PPE in the training of students in the health professions should support the ethical principles of Beauchamp and Childress, namely beneficence, non-maleficence, autonomy and justice/fairness. (shrink)

Although AGM theory contraction (Alchourrón et al., 1985; Alchourrón and Makinson, 1985) occupies a central position in the literature on belief change, there is one aspect about it that has created a fair amount of controversy. It involves the inclusion of the postulate known as Recovery. As a result, a number of alternatives to AGM theory contraction have been proposed that do not always satisfy the Recovery postulate (Levi, 1991, 1998; Hansson and Olsson, 1995; Fermé, 1998; Fermé and Rodriguez, 1998; (...) Rott and Pagnucco, 1999). In this paper we present a new addition, systematic withdrawal, to the family of withdrawal operations, as they have become known. We define systematic withdrawal semantically, in terms of a set of preorders, and show that it can be characterised by a set of postulates. In a comparison of withdrawal operations we show that AGM contraction, systematic withdrawal and the severe withdrawal of Rott and Pagnucco (1999) are intimately connected by virtue of their definition in terms of sets of preorders. In a future paper it will be shown that this connection can be extended to include the epistemic entrenchment orderings of Gärdenfors (1988) and Gärdenfors and Makinson (1988) and the refined entrenchment orderings of Meyer et al. (2000). (shrink)

Epistemic entrenchment, as presented by Gärdenfors and Makinson (1988) and Gärdenfors (1988), is a formalisation of the intuition that, when forced to choose between two beliefs, an agent will giveup the less entrenched one. While their formalisation satisfactorilycaptures the intuitive notion of the entrenchment of beliefs in a number ofaspects, the requirement that all wffs be comparable has drawn criticismfrom various quarters. We define a set of refined versions of theirentrenchment orderings that are not subject to the same criticism, andinvestigate (...) the relationship between the refined entrenched orderings,the entrenchment orderings of Gärdenfors and Makinson, and AGM theorycontraction (Alchourrón et al., 1985). To conclude, we compare refinedentrenchment with two related approaches to epistemic entrenchment. (shrink)

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hubert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families (...) of projections indexed by a partially ordered set C(A) of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that C(A) consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Hey ting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n x n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski-Mulvey) of the "Bohrification" A̱ of A, which is a commutative Rickart C*-algebra in the topos of functors from C(A) to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns-Lakser completions. Finally, we establish a connection between probability measures on the lattice of projections on a Hubert space H and probability valuations on the internal Gelfand spectrum of A̱ for A = B(H). (shrink)

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families (...) of projections indexed by a partially ordered set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}(A)}$$\end{document} of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}(A)}$$\end{document} consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Heyting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n × n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski–Mulvey) of the “Bohrification” \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\underline A}$$\end{document} of A, which is a commutative Rickart C*-algebra in the topos of functors from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}A}$$\end{document} to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns–Lakser completions. Finally, we establish a connection between probability measures on the lattice of projections on a Hilbert space H and probability valuations on the internal Gelfand spectrum of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\underline A}$$\end{document} for A = B(H). (shrink)

We model three examples of beliefs that agents may have about other agents’ beliefs, and provide motivation for this conceptualization from the theory of mind literature. We assume a modal logical framework for modelling degrees of belief by partially ordered preference relations. In this setting, we describe that agents believe that other agents do not distinguish among their beliefs (‘no preferences’), that agents believe that the beliefs of other agents are in part as their own (‘my preferences’), and the special (...) case that agents believe that the beliefs of other agents are exactly as their own (‘preference refinement’). This multi-agent belief interaction is frame characterizable. We provide examples for introspective agents. We investigate which of these forms of belief interaction are preserved under three common forms of belief revision. (shrink)

The Dutch philosopher of religion Hent de Vries has explored and complicated the boundaries between religion and modern thought in order to create the space for an innovative “minimal theology.” This article reconstructs de Vries's interpretation of the changes in Theodor W. Adorno's thought between Dialectic of Enlightenment and Negative Dialectics in order to demonstrate its fecundity for a philosophical account of otherness. It also examines and defends de Vries's own rhetorical mode of reading texts as an exemplary approach to (...) philosophical dialogue. Finally, however, the essay challenges de Vries's privileging of the religious as the site of ethical relationality and his intentional bracketing of Adorno's critical social theory. (shrink)

The Netherdutch Reformed Church of Africa (NRCA) did not escape this existential crisis of conflict. It manifests in various ways resulting in the bleeding of congregations, the exodus of congregants and the closure of congregations, as many congregants that declare themselves as members of the Church do not attend worship services or participate in the Holy Communion and exit the church. The study was conducted in the NRCA to determine the effect and response formation of observed conflict by ministers in (...) their respective congregations. The results of the study indicate that pastors and/or ministers do suffer emotional trauma because of the conflict in the congregation which, according to their own statements results in a loss of role performance. We provide an overview of the problem statement and methodology of the study. We discuss an abbreviated, theoretical perspective on conflict as a social phenomenon. We present the findings of our study and conclude with an abbreviated process to equip pastors with the necessary emotional maturity and self-management.Contribution: This study uncovers emotional trauma experienced by ministers, affecting their role performance. We offer a succinct problem statement, research methodology, and propose a scientifically informed process to enhance ministers’ emotional resilience within the NRCA. (shrink)

The chapters in this book offer an in-depth and profound overview of Hegel’s daring, many-faceted philosophical interpretations of the multifarious and dialectically interrelated, historical religions, including the Islam and the ‘revealed’ religion of Christianity.

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