An Abelian group G is strongly λ -free iff G is L ∞, λ -equivalent to a free Abelian group iff the isomorphism player has a winning strategy in an Ehrenfeucht–Fraı̈ssé game of length ω between G and a free Abelian group. We study possible longer Ehrenfeucht–Fraı̈ssé games between a nonfree group and a free Abelian group. A group G is called ε -game-free if the isomorphism player has a winning strategy in an Ehrenfeucht–Fraı̈ssé (...) game of length ε between G and a free Abelian group. We prove in ZFC existence of nonfree ε -game-free groups for many successors of regular cardinals. We also show that the length of the game obtained is very close to the optimal length provable in ZFC alone. On the other hand, assuming existence of a Mahlo cardinal, we sketch a proof that it is consistent to have a very highly game-free still nonfree group. First we present an introduction to basic constructions and then we introduce some results concerning the standard tools for building more complicated groups, namely transversals and λ -systems. It follows that all the constructions generalize to algebras in a fixed variety satisfying the strong construction principle. (shrink)

We investigate under what conditions a given set of collective judgments can arise from a specific voting procedure. In order to answer this question, we introduce a language similar to modal logic for reasoning about judgment aggregation procedures. In this language, the formula expresses that is collectively accepted, or that is a group judgment based on voting. Different judgment aggregation procedures may be underlying the group decision making. Here we investigate majority voting, where holds if a majority of (...) individuals accepts, consensus voting, where holds if all individuals accept, and dictatorship. We provide complete axiomatizations for judgment sets arising from all three aggregation procedures. (shrink)

Conspiracy Theories The term “conspiracy theory” refers to a theory or explanation that features a conspiracy among a group of agents as a central ingredient. Popular examples are the theory that the first moon landing was a hoax staged by NASA, or the theory that the 9/11 attacks on the World Trade Center were not … Continue reading Conspiracy Theories →.

Employers must determine the types of health care plans to offer and also set employee premiums for each plan provided. Depending on the structure of the employee share of premiums across different health insurance plans, the incentives to choose one plan over another are altered. If employees know premiums do not fully reflect the risk differences among workers, such pricing can give rise to a so-called “death spiral” due to adverse selection. This paper uses longitudinal information from a natural experiment (...) in the management of health benefits for a large employer to explore the impact of moving from a fixed-dollar contribution policy to a partially risk-adjusted employer contribution policy. Our results show that implementing a significant risk adjustment had no discernable effect on adverse selection against the most generous indemnity insurance policy. This stands in stark contrast to previous studies, which have tended to estimate large impacts attributed to selection when employers move to a fixed-dollar policy from one with some risk adjustment. Further analysis suggests that previous studies, which appeared to detect plans in the throes of a death spiral, may instead have been reflecting an inexorable movement away from a non-preferred product, one that would have been inefficient for nearly all workers even in the absence of adverse selection. (shrink)

Philosophy & Social Criticism, Volume 48, Issue 3, Page 437-456, March 2022. Societal polarization has given rise to opposing groups that fight each other as enemies and that have very different ideas about what should be done and about what is the case. This article investigates what tools there are in the philosophy of Martin Buber to address this societal polarization. Buber’s notion of community, the relationship between means and ends, his opposition to the political principle, the notion of an (...) I-Thou dialogue and his conception of truth are presented as relevant for overcoming societal polarization. The article also presents the case of Daryl Davis as manifesting some of these Buberian principles. (shrink)

We strengthen nonstructure theorems for almost free Abelian groups by studying long Ehrenfeucht–Fraı̈ssé games between a fixed group of cardinality λ and a free Abelian group. A group is called ε -game-free if the isomorphism player has a winning strategy in the game of length ε ∈ λ . We prove for a large set of successor cardinals λ = μ + the existence of nonfree -game-free groups of cardinality λ . We concentrate on successors of singular (...) cardinals. (shrink)

The limitations of rational models of ethical decision making and the importance of nurses’ human involvement as moral agents is increasingly being emphasized in the nursing literature. However, little is known about how nurses involve themselves in ethical decision making and action or about educational processes that support such practice. A recent study that examined the meaning and enactment of ethical nursing practice for three groups of nurses (nurses in direct care positions, student nurses, and nurses in advanced practice positions) (...) highlighted that humanly involved ethical nursing practice is also simultaneously a personal process and a socially mediated one. Of particular significance was the way in which differing role expectations and contexts shaped the nurses’ ethical practice. The study findings pointed to types of educative experiences that may help nurses to develop the knowledge and ability to live in and navigate their way through the complex, ambiguous and shifting terrain of ethical nursing practice. (shrink)

Suppose λ is a singular cardinal of uncountable cofinality κ. For a model M of cardinality λ, let No (M) denote the number of isomorphism types of models N of cardinality λ which are L ∞λ - equivalent to M. In [7] Shelah considered inverse κ- systems A of abelian groups and their certain kind of quotient limits Gr(A)/ Fact(A). In particular Shelah proved in [7, Fact 3.10] that for every cardinal μ there exists an inverse κ-system A such that (...) A consists of abelian groups having cardinality at most μ κ and card(Gr(A)/Fact(A)) = μ. Later in [8, Theorem 3.3] Shelah showed a strict connection between inverse κ-systems and possible values of No (under the assumption that $\theta^\kappa for every $\theta ): if A is an inverse κ- system of abelian groups having cardinality $\theta^\kappa for every $\theta ): for every nonzero $\mu or μ = λ κ there is a model M μ of cardinality λ with No(M μ ) = μ. In this paper we show: for every nonzero μ ≤ λ κ there is an inverse κ-system A of abelian groups having cardinality $2^\kappa and $\theta^{ for all $\theta when $\mu > \lambda$ ), with the obvious new consequence concerning the possible value of No. Specifically, the case No(M) = λ is possible when $\theta^\kappa for every $\theta. (shrink)

This study aimed to determine the extent to which the principles of privacy and equality were observed during diagnostic genetic testing according to views held by patients or child patients' parents (n = 106) and by staff (n = 162) from three Finnish university hospitals. The data were collected through a structured questionnaire and analysed using the SAS 8.1 statistical software. In general, the two principles were observed relatively satisfactorily in clinical practice. According to patients/parents, equality in the post-analytic phase (...) and, according to staff, privacy in the pre-analytic phase, involved the greatest ethical problems. The two groups differed in their views concerning pre-analytic privacy. Although there were no major problems regarding the two principles, the differences between the testing phases require further clarification. To enhance privacy protection and equality, professionals need to be given more genetics/ethics training, and patients individual counselling by genetics units staff, giving more consideration to patients' world-view, the purpose of the test and the test result. (shrink)

The modern state of the Pauli exclusion principle studies is discussed. The Pauli exclusion principle can be considered from two viewpoints. On the one hand, it asserts that particles with half-integer spin (fermions) are described by antisymmetric wave functions, and particles with integer spin (bosons) are described by symmetric wave functions. This is a so-called spin-statistics connection. The reasons why the spin-statistics connection exists are still unknown, see discussion in text. On the other hand, according to the (...) class='Hi'>Pauli exclusion principle, the permutation symmetry of the total wave functions can be only of two types: symmetric or antisymmetric, all other types of permutation symmetry are forbidden; although the solutions of the Schrödinger equation may belong to any representation of the permutation group, including the multi-dimensional ones. It is demonstrated that the proofs of the Pauli exclusion principle in some textbooks on quantum mechanics are incorrect and, in general, the indistinguishability principle is insensitive to the permutation symmetry of the wave function and cannot be used as a criterion for the verification of the Pauli exclusion principle. Heuristic arguments are given in favor that the existence in nature only the one-dimensional permutation representations (symmetric and antisymmetric) are not accidental. As follows from the analysis of possible scenarios, the permission of multi-dimensional representations of the permutation group leads to contradictions with the concept of particle identity and their independence. Thus, the prohibition of the degenerate permutation states by the Pauli exclusion principle follows from the general physical assumptions underlying quantum theory. (shrink)

Une épistémologie phénoménologique est nécessairement intéressée aux points de contact et de passage entre problèmes scientifiques et problèmes philosophiques. Il est instructif, dans cette perspective, de revenir sur un moment historiquement décisif, mais éminemment équivoque, encore porteur de prolongements et de retournements dont nous n’avons peut-être pas encore pris toute la mesure : l’énoncé du principe de Pauli. Le statut logique de cet énoncé est lui-même ambigu : règle technique, semi-empirique, postulat, principe ou théorème, etc. Pour le meilleur et (...) le pire, ce principe se trouve accouplé dès l’origine au problème de l’individuation en physique. Nous proposons de revenir sur quelques traits philosophiquement saillants des interprétations que Weyl et de Broglie proposent dudit « principe d’exclusion Pauli » (ou PEP). L’un et l’autre y voient l’occasion d’un approfondissement du principe d’individuation prévalant jusqu’alors dans la physique classique : l’espace. Weyl associe le PEP au principe leibnizien des indiscernables et tente de modéliser l’espace en jeu au moyen de la théorie des groupes. Les changements de position de Pauli lui-même à ce propos ne sont pas moins instructifs. La position de De Broglie sur ce principe est un marqueur de sa trajectoire : de la théorie audacieuse, et, équivoque, de « l’onde-pilote », jusqu’à celle dite de la « double solution », en passant par la période de rétractation consécutive au congrès de Solvay de 1927. Ce qui persiste d’un bout à l’autre, c’est un partage entre espace « réel » empirique et espace de configuration mathématique imaginaire. Chez l’un et l’autre, cette interprétation est ainsi indissociable d’un nouveau partage du subjectif et de l’objectif et d’une réflexion critique sur le principe traditionnel d’individuation qu’est l’espace (ou le temps physique) au profit d’une articulation toujours plus subtile et complexe entre l’espace de la phénoménalisation (de l’observation) et les « espaces » de la modélisation mathématique, en particulier les espaces des états possibles décrits dans le formalisme de la statistique quantique. (shrink)

Verbs and nouns gear θ-dependencies, Case, agreement, or construal relations. Building on Chomsky’s 1974 decomposition of such categories into ±N, ±V features, by translating said features into ±1, ±i scalars that allow for the construction of a vector space, this paper studies the possibility of organizing said features into 2 × 2 square matrices. In the system proposed to explore “head-complement” relations, operating on nouns yields a measurable/observable (Hermitian matrix), which in turn limits other potential combinations with abstract lexical categories. (...) Functional/grammatical categories in the system deploy the same features, albeit organized differently in the matrix diagonal and off-diagonal. The algebraic result is a group with well-defined mathematical properties, which properly includes the Pauli group of standard use in quantum computation. In the system, the presumed difference between categories and interactions—here, in a context of the head-complement sort—reduces to whether the magnitude of the matrix eigenvalue is 1 or not, in the latter instance inducing asymmetric interactions. (shrink)

We investigate a series of logics that allow to reason about agents' actions, abilities, and their knowledge about actions and abilities. These logics include Pauly's Coalition Logic CL, Alternating-time Temporal Logic ATL, the logic of ‘seeing-to-it-that' (STIT), and epistemic extensions thereof. While complete axiomatizations of CL and ATL exist, only the fragment of the STIT language without temporal operators and without groups has been axiomatized by Xu (called Ldm). We start by recalling a simplification of the Ldm that has been (...) proposed in previous work, together with an alternative semantics in terms of standard Kripke models. We extend that semantics to groups via a principle of superadditivity, and give a sound and complete axiomatization that we call Ldm G. We then add a temporal ‘next' operator to Ldm G, and again give a sound and complete axiomatization. We show that Ldm G subsumes coalition logic CL. Finally, we extend these logics with standard S5 knowledge operators. This enables us to express that agents see to something under uncertainty about the present state or uncertainty about which action is being taken. We focus on the epistemic extension of X-Ldm G, noted E-X-Ldm G. In accordance with established terminology in the planning community, we call this extension of X-Ldm G the conformant X-Ldm G. The conformant X-Ldm G enables us to express that agents are able to perform a uniform strategy. We conclude that in that respect, our epistemic extension of X-Ldm G is better suited than epistemic extensions of ATL. (shrink)

The automorphism groups of scalar products of spinors are determined. Spinors are considered as elements of minimal left ideals of Clifford algebras on quadratic modules, e.g., on orthogonal spaces. Orthogonal spaces of any dimension and arbitrary signature are discussed. For example, the automorphism groups of scalar products of Pauli spinors and Dirac spinors are, respectively, isomorphic to the matrix groups U(2) and U(2, 2). It is found that there are, in general, 32 different types or similarity classes of such (...) automorphism groups, if one considers real orthogonal spaces of arbitrary dimension and arbitrary signature. On a more abstract level this means that the Brauer-Wall group of the real field R, consisting of graded central simple algebras over R, can be extended from the cyclic group of 8 elements to an abelian group with32 elements. This extended Brauer-Wall group is seen to be isomorphic with the group (Z 8 × Z 8 )/Z 2 and it consists of real Clifford algebras with antiinvolutions. Moreover, the subgroup determined by the antiinvolution is isomorphic to the automorphism group of scalar products of spinors. (shrink)

This contribution explores Wolfgang Pauli's idea that mind and matter are complementary aspects of the same reality. We adopt the working hypothesis that there is an undivided timeless primordial reality (the primordial 'one world'). Breaking its symmetry, we obtain a contextual description of the holistic reality in terms of two categorically different domains, one tensed and the other tenseless. The tensed domain includes, in addition to tensed time, nonmaterial processes and mental events. The tenseless domain refers to matter and (...) physical energy. This concept implies that mind cannot be reduced to matter, and that matter cannot be reduced to mind. The non-Boolean logical framework of modern quantum theory is general enough to implement this idea. Time is not taken to be an a priori concept, but an archetypal acausal order is assumed which can be represented by a one-parameter group of automorphisms, generating a time operator which parametrizes all processes, whether material or nonmaterial. The time-reversal symmetry is broken in the nonmaterial domain, resulting in a universal direction of time for the material domain as well. (shrink)

We give a derivation of exclusion principles for the elementary particles of the standard model, using simple mathematical principles arising from a set theory of identical particles. We apply the theory of permutation group actions, stating some theorems which are proven elsewhere, and interpreting the results as a heuristic derivation of Pauli's Exclusion Principle (PEP) which dictates the formation of elements in the periodic table and the stability of matter, and also a derivation of quark confinement. We arrive (...) at these properties by using a symmetry property of collections of the particles themselves as compared for example to the symmetry property of their wave function under interchange of two particles. (shrink)

We apply the Galilean covariant formulation of quantum dynamics to derive the phase-space representation of the Pauli–Schrödinger equation for the density matrix of spin-1/2 particles in the presence of an electromagnetic field. The Liouville operator for the particle with spin follows from using the Wigner–Moyal transformation and a suitable Clifford algebra constructed on the phase space of a (4 + 1)-dimensional space–time with Galilean geometry. Connections with the algebraic formalism of thermofield dynamics are also investigated.

The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary (...) particle, neutrino, on the ground of energy conservation in quantum mechanics, afterwards confirmed experimentally. Bohr recognized his defeat and Pauli’s truth: the paradigm of elementary particles (furthermore underlying the Standard model) dominates nowadays. However, the reason of energy conservation in quantum mechanics is quite different from that in classical mechanics (the Lie group of all translations in time). Even more, if the reason was the latter, Bohr, Cramers, and Slatters’s argument would be valid. The link between the “conservation of energy conservation” and the problem of hidden variables is the following: the former is equivalent to their absence. The same can be verified historically by the unification of Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics in the contemporary quantum mechanics by means of the separable complex Hilbert space. The Heisenberg version relies on the vector interpretation of Hilbert space, and the Schrödinger one, on the wave-function interpretation. However the both are equivalent to each other only under the additional condition that a certain well-ordering is equivalent to the corresponding ordinal number (as in Neumann’s definition of “ordinal number”). The same condition interpreted in the proper terms of quantum mechanics means its “unitarity”, therefore the “conservation of energy conservation”. In other words, the “conservation of energy conservation” is postulated in the foundations of quantum mechanics by means of the concept of the separable complex Hilbert space, which furthermore is equivalent to postulating the absence of hidden variables in quantum mechanics (directly deducible from the properties of that Hilbert space). Further, the lesson of that unification (of Heisenberg’s approach and Schrödinger’s version) can be directly interpreted in terms of the unification of general relativity and quantum mechanics in the cherished “quantum gravity” as well as a “manual” of how one can do this considering them as isomorphic to each other in a new mathematical structure corresponding to quantum information. Even more, the condition of the unification is analogical to that in the historical precedent of the unifying mathematical structure (namely the separable complex Hilbert space of quantum mechanics) and consists in the class of equivalence of any smooth deformations of the pseudo-Riemannian space of general relativity: each element of that class is a wave function and vice versa as well. Thus, quantum mechanics can be considered as a “thermodynamic version” of general relativity, after which the universe is observed as if “outside” (similarly to a phenomenological thermodynamic system observable only “outside” as a whole). The statistical approach to that “phenomenological thermodynamics” of quantum mechanics implies Gibbs classes of equivalence of all states of the universe, furthermore re-presentable in Boltzmann’s manner implying general relativity properly … The meta-lesson is that the historical lesson can serve for future discoveries. (shrink)

We consider the global structure of momentum space Π3, 1 in a field theory which is covariant with respect to the action of global conformal group G. We show that Π3, 1 is a homogeneous space for G which coincides with (S3×S1)/Z2 compact space. The radius of momentum space determines the natural invariant ultraviolet cutoff which may take the form of a Pauli-Vilars form factor in perturbation theory. We demonstrate in the case of the massless λφ4 theory how (...) the conventional ultraviolet divergences which appear in the flat momentum space are regularized in Π3, 1 global momentum space. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Plotinus and the Parmenz'des B. DARRELL JACKSON IN 1928 E. R. DODDSARGUED that the first two hypotheses of Plato's Parmenides are the primary source of Plotinus' doctrines of the One and of Nous. I Dodds' main evidence was a list of parallels between the Parmenides and the Enneads? He argued further that the Neoplatonic interpretation of the Parmenides as positive metaphysics was neo-Pythagorean in origin. Several Plotinus scholars have (...) accepted and extended Dodds' view of the importance of the Parmenides for Plotinus. This group includes ]~mile Br6hier, ~ A. H. Armstrong, 4 Hans-Rudolf Schwyzer, 5 and Paul Henry. n But Dodds' position is by no means universally accepted. Elmer O'Brien has recently argued that the Plotinian One was derived ultimately from Philo and mediated to Plotinus through Albinus and Numenius. 7 He says that Dodds' case, though good, is not convincing. It. A. Wolfson has been the great advocate of the Philonic origin of Plotinus' views. According to Wolfson, the doctrines attributed by Plotinus to Plato are not Plato's but mainly Philo's. 8 Others see Plotinus in varying degrees of dependence upon Plato. Philip Merlan holds that Plotinus is more in debt to the immediate successors of Plato and to Aristotle's interpretation of Plato than to the Platonic writings themselves. 9 C. J. de Vogel sees Plotinus as dependent upon Plato for a hierarchy of being which was accepted and elaborated by various middle Platonists and Gnostics. 1~According to de Vogel, the Parmenides wus not importan% in this hierarchy tradition, n In this article I shall re-examine Dodds' position. I believe the case for Plotinus' dependence upon the Parmenides can be strengthened. I shall try to do this by examining the systematic relation of Plotinus' thought to the Parmenides. Dodds x"The Parmenides of Plato and the Origin of the Neoplatonic 'One'," The Classical Quarterly, XXII (1928), 129-142. 2Ibid., 132 f. *In the introductions to Enneads V.3 (esp. pp. 43 f., 46 f.), V.5 (pp. 87 ft.), VI.4-5 (pp. 161163,165-168),and VI.7 (pp. 49, 60) in his Bud~ edition and translation of the Enneads (Paris, 1931-38). 4The Architecture of the Intelligible Universe in the Philosophy of Plotinus (Cambridge, at the University Press: 1940), pp. 14-28. In his article "Plotinos", Vol. 21, pt. 1 of Paulys Real-Encyclopgdie der Klassischen Altertumswissenschaft, 1951, cols. 552-554. eIntroduction to the second edition of Stephen MacKenna's translation of the Ennead.~ (New York: Pantheon Books Inc., n. d.), pp. xli-xliv. Elmer O'Brien (ed. and trans.), The Essential Plotinus (New York: Mentor, 1964),p. 15. 8"Albinus and Plotinus on Divine Attributes," Harvard Theological Review, XXXXV (1952), 115. 9From Platonism to Neoplatonism (2n ed. rev.; The Hague: Martinus Nijhoff, 1960). 10"On the Neoplatonic Character of Platonism and the Platonic Character of Neoplatonism," Mind, LXIII (1953), 43-64. 11Ibid., 58. [3]5] 316 HISTORY OF PHILOSOPHY considered only parallel terminology. I shall in addition look at parallel argumentation and conclusions. Furthermore, since Dodds accounts only for Plotinus' first two hypostases, I shall consider the relation of the third hypostasis (soul) to the Parmenides. My primary interest is not the source of Plotinus' interpretation of the Parmenides but the way he carries that interpretation out. TM The former issue has often been focal in the literature on this subject. ~8It is certain thay many of the ideas used by Plotinus were already in circulation. But it is equally certain that in his combination of these ideas of a hierarchy, of transcendence, etc., Plotinus is original. I shall argue that this originality of combination is largely determined by an interpretation of the Parmenides. I should add that I am not concerned with whether Plotinus' interpretation is correct. ~4 In the following pages I shall attempt to show three things: (1) how Plotinus explicitly interprets the Parmenides, (2) to what extent he draws upon the language of the Parmenides, and (3) to what extent Plotinus' system may be understood by its relation to the Parmenides. I. Plotinus' Interpretation of the Parmenides The obvious place to begin an analysis of Plotinus' relation to the Parmenides is Enneads V... (shrink)

In 1932, Wolfgang Pauli was a world-renowned physicist and had already done the work that would win him the 1945 Nobel Prize. He was also in pain. His mother had poisoned herself after his father's involvement in an affair. Emerging from a brief marriage with a cabaret performer, Pauli drank heavily, quarreled frequently and sometimes publicly, and was disturbed by powerful dreams. He turned for help to C. G. Jung, setting a standing appointment for Mondays at noon. Thus (...) bloomed an extraordinary intellectual conjunction not just between a physicist and a psychologist but between physics and psychology. Eighty letters, written over twenty-six years, record that friendship. This artful translation presents them in English for the first time. Though Jung never analyzed Pauli formally, he interpreted more than 400 of his dreams--work that bore fruit later in Psychology and Alchemy and The Analysis of Dreams. As their acquaintance developed, Jung and Pauli exchanged views on the content of their work and the ideas of the day. They discussed the nature of dreams and their relation to reality, finding surprising common ground between depth psychology and quantum physics. Their collaboration resulted in the combined publication of Jung's treatise on synchronicity and Pauli's essay on archetypal ideas influencing Kepler's writings in The Interpretation of Nature and the Psyche. Over time, their correspondence shaped and reshaped their understanding of the principle they called synchronicity, a term Jung had suggested earlier. Through the association of these two pioneering thinkers, developments in physics profoundly influenced the evolution of Jungian psychology. And many of Jung's abiding themes shaped how Pauli--and, through him, other physicists--understood the physical world. Of clear appeal to historians of science and anyone investigating the life and work of Pauli or Jung, this portrait of an incredible friendship will also draw readers interested in human creativity as well as those who merely like to be present when great minds meet. (shrink)

The empirical rule that systems of identical particles always obey either Bose or Fermi statistics is customarily imposed on the theory by adding it to the axioms of nonrelativistic quantum mechanics, with the result that other statistical behaviors are excluded a priori. A more general approach is to ask what other many-particle statistics are consistent with the indistinguishability of identical particles. This strategy offers a way to discuss possible violations of the Pauli Exclusion Principle, and it leads to some (...) interesting issues related to preparation of states and a superselection rule arising from invariance under the permutation group. (shrink)

In this paper, we report on a new approach to relativistic quantum theory. The classical theory is derived from a new implementation of the first two postulates of Einstein, which fixes the proper-time of the physical system of interest for all observers. This approach leads to a new group that we call the proper-time group. We then construct a canonical contact transformation on extended phase space to identify the canonical Hamiltonian associated with the proper-time variable. On quantization we (...) get a new relativistic wave equation for spin 1/2 particles that generalizes the Dirac theory. The Hamiltonian is positive definite so we naturally interpret antiparticles as particles with their proper-time reversed. We show that for the hydrogen atom problem, we get the same fine structure separation. When the proton spin magnetic moment is taken into account, we get the standard hyperfine splitting terms of the Pauli approximation and two additional terms. The first term is small in p-states. It diverges in s-states, and provides more than enough to account for the Lamb-shift when the proton radius is used as a cut off. The last term promises to provide a correction to the hyperfine splitting term. Although incomplete, the general approach offers hope of completely accounting for the hydrogen spectrum as an eigenvalue problem. (shrink)

The article is devoted to context specific of folk songs from the collection “Songs of people of Galicia” by polish folklorist Z. Pauli. General and subjective problems and issues of Ukrainian society in 17th and 18th centuries were revealed. Song’s lyrics were analyzed and actual problems of baroque Ukrainian’s life were highlighted. Each of these problems and issues has it’s specific worldview expression. This worldview response to society and subjective problems of Baroque was presented in folk songs. Thus, the (...) problems of Ukrainian community and personal issues was considered in terms of worldview specific. So, in our point of view the main problems of Ukrainian Baroque society were “cossachyna” and conscription. Attitude of ordinary people to cossacks, their life and role in the state’s fate presented in historical songs, epic songs and Cossack songs. Context of these songs from Z. Pauli collection showed us some important worldview responses to the Cossacks. As a response to the historical events of the seventeenth and eighteenth centuries formed the cult of the warrior’s force. So the main virtues were agility and courage of the warrior. “Cossack glory” was one of the main values in the mass perception of Ukrainians. And was defeating during the battle was the most threat in terms of the relatives of warrior. In the song’s lyrics of 18th century the theme of soldier’s military duty hade wide spreading. Many families had to say good bye to their close relatives. That’s why the frequently motives of soldier songs are farewell, anguish and sorrow. Social problems such as insecurity, orphanhood and gender imbalance, caused by man’s military service, became a relevant for ordinary citizens. Personal existential problems presented in lyric songs and ballads. Widespread subjective problems such as freedom of someone own choice, choice contrary to the social or family opinion, contradictory feelings, emotions and actions outlined in folk-song’s lyrics. Frequently such song’s lyrics expressed metaphysical meditations about loneliness, person’s place in the world, happiness and desire to be happy, the influence of fate on human life etc. This group of songs present a typical Baroque pessimism. So, us our research showed ancient folk songs are real rich source for understanding worldview of our ancestors. (shrink)

In this paper, we use the differential forms of three-dimensional Euclidean space to realize a Clifford algebra which is isomorphic to the algebra of the Pauli matrices or the complex quaternions. This is an associative vector-antisymmetric tensor algebra with division: We provide the algebraic inverse of an eight-component spinor field which is the sum of a scalar + vector + pseudovector + pseudoscalar. A surface of singularities is defined naturally by the inverse of an eight-component spinor and corresponds to (...) a generalized Minkowski “double” light cone in the parameter space. A general description of finite spatial rotations, which utilizes the Baker-Campbell-Hausdorff formula, generalizes the usual infinitesimal treatments of the rotation group. We derive an explicit expression for the angle corresponding to two successive finite rotations in any direction. We also discuss Lorentz transformations and duality rotations of the electromagnetic field and exhibit a relationship between the algebraic inverse and a duality rotated field. Using a combined transformation, one can always transform an arbitrary electromagnetic field (E≠0) into a pure electric field, but never into a pure magnetic field. (shrink)

The traditional standard theory of quantum mechanics is unable to solve the spin–statistics problem, i.e. to justify the utterly important “Pauli Exclusion Principle” but by the adoption of the complex standard relativistic quantum field theory. In a recent paper :858–873, 2015) we presented a proof of the spin–statistics problem in the nonrelativistic approximation on the basis of the “Conformal Quantum Geometrodynamics”. In the present paper, by the same theory the proof of the spin–statistics theorem is extended to the relativistic (...) domain in the general scenario of curved spacetime. The relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. No relativistic quantum field operators are used and the particle exchange properties are drawn from the conservation of the intrinsic helicity of elementary particles. It is therefore this property, not considered in the standard quantum mechanics, which determines the correct spin–statistics connection observed in Nature :858–873, 2015). The present proof of the spin–statistics theorem is simpler than the one presented in Santamato and De Martini :858–873, 2015), because it is based on symmetry group considerations only, without having recourse to frames attached to the particles. Second quantization and anticommuting operators are not necessary. (shrink)

We introduce a new structure, the critical multi-cubic lattice. Notably the critical multi-cubic lattice is the first true generalization of the cubic lattice to higher dimensional spaces. We then introduce the notion of a homomorphism in the category of critical multi-cubic lattices, compute its automorphism group, and construct a Hilbert space over which we represent the group. With this unitary representation, we re-derive the generalized Pauli matrices common in quantum computation while also defining an algebraic framework for (...) an infinite system of qudits. We also briefly explore the critical multi-cubic lattice as a novel implication algebra serving as a logical framework for qudit gates. (shrink)

Der hier erstmals ver]ffentlichte Briefwechsel zwischen dem Psychiater C.G. Jung und dem Nobelpreistr{ger der Physik Wolfgang Pauli ist ein geistesgeschichtliches Dokument ersten Ranges. Ein privates Schicksal hat sie zusammengef}hrt, und daraus ist ein vorwissenschaftlicher Dialog erwachsen, in dem versucht wird, naturwissenschaftliches und psychologischesDenken zu vereinheitlichen. Die Briefe verdeutlichen, da~ es weder f}r den Psychologen zul{ssig ist, die methodischen Einsichten der Physik, noch f}r den Physiker, die Erfahrungen im Umgang mit dem Psychischenzu vernachl{ssigen.

Both editors have long been known for their work on Plotinus. Schwyzer has published important articles on the MSS A, V, and D, on the Pseudo-Aristotelian Theology and its relation to Porphyry's edition of the Enneads, on Plotinus' interpretation of Timaeus 35 A, and on the relation of Plotinus' triad of hypostases to his interpretation of Parmenides 139-145 ; and he is the author of the new article on Plotinus in the Pauly-Wissowa Realencyclopädie. Ever since 1933 Henry has been publishing (...) a series of books and articles dealing with the text of Plotinus, its constitution, influence, and transmission. Of these works three books are especially important, since they were meant to constitute a critical introduction to the edition of the Enneads. The first of these, Recherches sur la Préparation Évangélique d'Eusèbe et l'Édition Perdue des Oeuvres de Plotin Publiée par Eustochius, undertakes to establish the fidelity of Porphyry, the first editor of the Enneads, to the autographs of Plotinus from which he made his recension. The second, Études Plotiniennes I: Les États du Texte de Plotin, a detailed study of the indirect tradition, reinforces this conclusion and establishes the authority of the archetype of the direct tradition. That archetype, Henry concludes, was as faithful to the recension of Porphyry as Porphyry was to the original written by Plotinus, and the indirect tradition is rather a guarantee of the faithfulness of the Porphyrian edition reproduced by the archetype than a source of corrections for the text of our MSS. The third volume, Études Plotiniennes II: Les Manuscrits des Ennéades, an exhaustive study of the character and history of the extant MSS, has for its purpose the determination of the necessary and sufficient evidence for the reconstitution of the archetype, the common ancestor of all the MSS of the direct tradition. No attempt is made to establish a stemma leading from the original to the extant MSS. Henry is here concerned rather to identify in the mass of material all the representative elements of the direct tradition and so to establish the apparatus of the critical edition on a basis broad enough to be forever independent of any hypothesis concerning the ultimate relations of the families represented by the extant MSS. In four chapters he studies the MSS of groups w, x, y, z respectively, in a fifth the MSS which Perna used for the editio princeps, and in two Appendices four lost MSS of which some record remains and the fragment of Eusebius in Vaticanus Rossianus 986. The volume is equipped with a detailed inventory of the MSS, a table of water, marks, and an index of proper names. One of the most important results of this study of Henry's is the identification of the MSS derivative from A, several of which had been used as independent witnesses to the arche- typal text but which Henry has shown to have no textual authority whatever. The results of this volume, however, are to be corrected in the light of three pages of "Corrections et Compléments" at the end of the second edition, which save for this list is an exact reimpression of the first. In 1946 Henry and Schwyzer began their collaboration in the preparation of the critical edition, and their study of the variants led them to certain conclusions different from those that Henry had printed in Les Manuscrits. In particular, they decided that D, which Henry had, though with some hesitation, treated as a member of family y, does not belong to y or to any other of the recognized groups of MSS but constitutes a family of its own; and they distinguished in the hand which Henry had hitherto called A1 and Schwyzer A2 two separate hands: one, hereafter to be called A1, which they believe to be that of the scribe of A himself correcting his MS from a source different from any extant MS and different also from the sub-archetypes of these MSS, so that the readings of A1 must represent a separate family or another archetype ; and a second, hereafter to be called A2, the corrections of which appear to be conjectures and so to have no authority for the text. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 34.2 (2001) 177-178 [Access article in PDF] Book Review Quantum Dialogue: The Making of a Revolution Quantum Dialogue: The Making of a Revolution. Mara Beller. Chicago: U of Chicago P, 1999. Pp. xv + 365. $35.00 cloth. This book presents a critical discussion of the development of quantum physics in the early part of the second quarter of the twentieth century. The opening statement of the (...) first chapter, a quotation attributed to Werner Heisenberg--"Science is rooted in conversations"--sets the tone for the whole book.The book is divided into two parts: "Dialogical Emergence" and "Rhetorical Consolidation." An introductory chapter, "Novelty and Dogma," outlines what is new for quantum theory as compared with what is already accepted in physics. Another six chapters build upon the various relationships between the people and ideas that led ultimately to the acceptance of a number of principles to explain a large variety of physical phenomena at the atomic level. The next six chapters generally show how a vocal group of scientists put forward the "Copenhagen Interpretation"; these scientists used the rhetorical skills of Niels Bohr and often unjustly criticized other views significant to the development of quantum mechanics. The final two chapters relate to later philosophical and historical implications of the development of quantum theory as discussed by the scientists themselves, as well as philosophers and historians of science, including the author.Mara Beller carries out a rather unique discussion of the scientific ideas and the social relationships among the scientists. She has carefully studied many of the original letters between the leading scientists at the time--Niels Bohr, Max Born, Paul Dirac, Albert Einstein, Werner Heisenberg, Wolfgang Pauli, Erwin Schrodinger--and numerous others who were not so well known. In particular, she discusses how these scientists influenced each other. A prime example is carefully developed in the early chapters of the book, where Beller discusses Heisenberg's work on matrix mechanics. After Heisenberg learned of Schrodinger's wave mechanics, he strongly denied the use of this rival method. As a result of discussions with [End Page 177] Bohr, Pauli, and others, however, many elements of wave mechanics began to appear in matrix mechanics in somewhat hidden forms. As quantum theory evolved in the following years, aspects of both wave mechanics and matrix mechanics came together in complementarity, due largely to the influence of Bohr. Yet, Beller questions, in the second part of the book, whether much of the process of assimilation by Bohr was one sided, so that the Copenhagen interpretation always came out the stronger.This book has scientific merit for both students and professionals in the physical sciences. During the intervening three quarters of a century since the founding years of quantum mechanics, many fundamental ideas have come to be accepted as basic concepts in chemistry, physics, material science, and related fields in engineering. In fact, the acceptance of the usefulness of quantum mechanics is so strong that many of ideas are seen as an integral part of the field itself, to the point that the proceeding concepts in early quantum theory are often neglected. This situation is rather unfortunate. It arises in part from the contemporary educational system, in which only the most immediate examples relevant to a particular field are used. The discussions in this book bring forward a completely different side of the development of quantum theory, which in many ways continues right up to the present. Here, the philosophical and social sides are stressed over the practical applications. Above and beyond this strength, the presentation could be understood by many people outside the physical sciences even though many of the scientific objectives may not be so very apparent. Quantum Dialogue is recommended to all readers who have an interest in the issues that arose during the early years of quantum theory's development. David E. Miller Department of Physics The Pennsylvania State University... (shrink)

In the range of his intellectual interests and the profundity of his mathematical thought Hermann Weyl towered above his contemporaries, many of whom viewed him with awe. This volume, the most ambitious study to date of Weyl's singular contributions to mathematics, physics, and philosophy, looks at the man and his work from a variety of perspectives, though its gaze remains fairly steadily fixed on Weyl the geometer and space‐time theorist. Structurally, the book falls into two parts, described in the general (...) introduction by the editor: Part 1 contains four essays on particular aspects of Weyl's work, highlighting ideas he developed in various editions of his classic Raum‐Zeit‐Materie. Part 2 presents a lengthy study by Robert Coleman and Herbert Korté covering nearly the whole gamut of Weyl's mathematical research, an impressive feat. Both in the introduction as well as in footnotes to the articles Erhard Scholz's editorial voice chimes in discreetly, helping tie all five studies together.Coleman and Korté begin chronologically with Weyl's early work in analysis and the modern theory of Riemann surfaces before turning to differential geometry, unified field theory, and the space problem, a topic they use as a springboard for a discussion of their own recent work on the foundations of space‐time. They then take up Weyl's shift to group representation theory and its applications to quantum mechanics, ending with his much earlier research on the structure of the continuum. All of these topics are well handled, but the authors' own agendas coupled with their penchant for overlooking chronology in order to package Weyl's work into neat little bundles leave one feeling rather stranded and far removed from the sources of Weyl's inspiration. Moreover, the narrative style makes this part of the volume read like a technical appendix, albeit a most informative one. Readers who tackle Scholz's far more contextualized essay will be amply rewarded by comparing his views with the opinions set forth by Coleman and Korté in Part 2.Scholz gives a masterful account of Weyl's intellectual journeys from 1917 to 1925 in a study that serves as a fulcrum for the entire volume. Drawing on a number of recently published studies, including his own, on the interplay between mathematics and physics inspired by Einstein's theory of general relativity, Scholz describes how Weyl responded to this challenge by developing a truly infinitesimal space‐time geometry that generalized classical Riemannian geometry. Although unconvinced by Einstein's critique of his unified field theory, Weyl shifted his focus from this realm to the classical space problem, analyzed earlier with more primitive techniques by Hermann Helmholtz and Sophus Lie. In this connection, it should be mentioned that Thomas Hawkins has given a probing analysis of Weyl's related work on the representation of Lie groups in his tour‐de‐force work, Emergence of the Theory of Lie Groups . Scholz argues that Weyl's struggle to tame his modernized version of the space problem stemmed from a deep‐seated belief in his geometrical ideas, which in turn were nourished by philosophical musings. By demonstrating the closely related conceptual links that motivated Weyl's research in infinitesimal geometry, space‐time physics, and the foundations of mathematics, Scholz nicely illuminates the underlying fabric of epistemological concerns that occupied Weyl's attention during this fertile period.The three remaining essays in Part 1 focus on other aspects of Weyl's work in mathematical physics and cosmology. Skuli Sigurdsson's “Journeys in Spacetime” offers a broad interpretation of Weyl's career, one that emphasizes Weyl's sensitivity to cultural tensions as reflected in his philosophical roots, which combined phenomenology with facets of German idealism. Shaken by the annihilation of cultural values in Nazi Germany, Weyl became deeply aware of the gulf that separated his earlier life in Göttingen and Zurich from the one he took up at Princeton's Institute for Advanced Study in 1933. He tried to adapt, but felt out of place in an Anglo‐American scientific culture openly hostile toward metaphysics and speculative philosophy. Sigurdsson stresses these tensions, contrasting the introspective, creative individual against the backdrop of the collective in the age of the machine, but without spelling out which collective were most important for him. Wolfgang Pauli thought he knew and, like Einstein before him, he had no compunction about bluntly telling Weyl he was a mathematician, not a physicist.Pauli's opinions notwithstanding, Weyl did far more than just dabble around the mathematical edges of the new physics. If Coleman and Korté perhaps press their case for his visionary accomplishments too far, Norbert Straumann's essay “Ursprünge der Eichtheorien” suggests why Weyl's reputation among physicists has risen steadily ever since the advent of Yang‐Mills theory in the 1950s. In the course of describing Weyl's adaptation of his gauge transformation formalism to Dirac's electron theory, Straumann sheds considerable light on Pauli's role as self‐appointed watchman guarding the disciplinary boundary that separated theoretical physics from physical mathematics . He further suggests that disciplinary jealousy was a major reason why Pauli dismissed Weyl's two‐component formalism for spinors out of hand.In the realm of cosmology, on the other hand, Weyl's work has long since passed into the dustbins of history, as Hubert Goenner remarks in recounting a fascinating chapter in the infancy of space‐time physics. While doing so, Goenner shows how initially Weyl almost slavishly adopted what Einstein called Mach's principle, which asserts that the metric structure of space‐time is solely determined by the distribution of matter in the universe. This notion was quickly challenged by Willem De Sitter, who showed that Einstein's matter‐free field equations admitted a global solution with non‐zero constant curvature. Both Einstein and Weyl tried to argue that invisible masses must be present just over the “spatial horizon” of De Sitter's world in order to account for its curvature. Goenner meticulously analyzes the physical and mathematical issues at stake in this debate, stressing how Weyl gradually moved away from a strong physical interpretation to one in which mathematics models rather than physics models simply reveal natural phenomena. He argues further that Weyl's cosmological principle arose as the final expression of his search for a deeper physical meaning.Given the quality of these essays, it is regrettable that this book contains so little about Weyl's professional career, a weakness the editor could have redressed at least partially in his general introduction. This omission is all the more unfortunate given the dearth of readily accessible information about Weyl's life available elsewhere. For however mundane his outward existence may have been, the reader cannot be expected to appreciate the interplay between the world Weyl knew and his creative responses to it without fairly detailed knowledge of his biography. Shorn from these contexts, it becomes difficult to form a flesh‐and‐blood image of Weyl beyond the cliché‐ridden stereotype that sees him as a “heroic thinker in the grand German tradition.” While none of the authors falls into this trap, the collective impression they leave suggests a most enigmatic figure. Either Weyl the man tends to get lost in the shadows of his collected scientific output or he appears as a mystic loner, an outcast who abhorred the machine age in which he lived. Closer attention to the people in his life would no doubt produce a very different picture of the man and his interests. This major lacuna notwithstanding, the present volume will surely remain an indispensable resource for any future investigations of Weyl's staggering intellectual achievements. (shrink)

Logical puzzles like the doctrinal paradox raise the problem of how to aggregate individual judgements into a collective judgement, or alternatively, how to merge collectively inconsistent knowledge bases. In this paper, we view judgement aggregation as a function on propositional logic valuations, and we investigate how logic constrains judgement aggregation. In particular, we show that there is no non-dictatorial decision method for aggregating sets of judgements in a logically consistent way if the decision method is local, i.e., only depends on (...) the individual judgements on the proposition under consideration. (shrink)

Moral distress is a phenomenon of increasing concern in nursing practice, education and research. Previous research has suggested that moral distress is associated with perceptions of ethical climate, which has implications for nursing practice and patient outcomes. In this study, a randomly selected sample of registered nurses was surveyed using Corley’s Moral Distress Scale and Olson’s Hospital Ethical Climate Survey (HECS). The registered nurses reported moderate levels of moral distress intensity. Moral distress intensity and frequency were found to be inversely (...) correlated with perceptions of ethical climate. Each of the HECS factors (peers, patients, managers, hospitals and physicians) was found to be significantly correlated with moral distress. Based on these findings, we highlight insights for practice and future research that are needed to enhance the development of strategies aimed at improving the ethical climate of nurses’ workplaces for the benefit of both nurses and patients. (shrink)

Nobel Laureate's brilliant early treatise on Einstein's theory consists of his original 1921 text plus retrospective comments 35 years later.

This ground-breaking book brings together researchers from a wide range of disciplines to discuss the control and coordination of processes involved in perceptually guided actions. The research area of motor control has become an increasingly multidisciplinary undertaking. Understanding the acquisition and performance of voluntary movements in biological and artificial systems requires the integration of knowledge from a variety of disciplines from neurophysiology to biomechanics.

Logical puzzles like the doctrinal paradox raise the problem of how to aggregate individual judgements into a collective judgement, or alternatively, how to merge collectively inconsistent knowledge bases. In this paper, we view judgement aggregation as a function on propositional logic valuations, and we investigate how logic constrains judgement aggregation. In particular, we show that there is no non-dictatorial decision method for aggregating sets of judgements in a logically consistent way if the decision method is local, i.e., only depends on (...) the individual judgements on the proposition under consideration. (shrink)

BackgroundThe theory and practice of ethics consultations (ECs) in health care are still characterized by many controversies, including, for example, the practice of giving recommendations. These controversies are complicated by an astonishing lack of evidence in the whole field. It is not clear how often a recommendation is issued in ethics consultations and when and why this step is taken. Especially in a facilitation model in which giving recommendations is optional, more data would be helpful to evaluate daily practice, ensure (...) that this practice is in line with the overarching goals of this approach and support the development of standards.MethodsWe analyzed all consultations requested from an EC service working under a facilitation approach at a maximum-care university hospital in Germany over a period of more than 10 years. Our aim was to better understand why—and under what circumstances—some consultation requests result in a recommendation, whereas others can be sufficiently addressed solely by facilitated meetings. We especially wanted to know when and why clients felt the need for clear advice from the EC service while in other cases they did not. We compared ethics consultations in terms of the differences between cases with and without recommendations issued by the ethics consultants using χ2 difference tests and Welch’s t-test.ResultsA total of 243 ECs were carried out between September 2008 and December 2019. In approximately half of the cases, a recommendation was given. All recommendations were issued upon the request of clients. When physicians asked for an EC, the consultation was significantly more likely to result in a recommendation than when the EC was requested by any other party. ECs in cases on wards with ethics rounds resulted in comparably fewer recommendations than those in wards without ethics rounds. When interpersonal conflicts were part of the problem or relatives were present in the meeting, clients less frequently asked for a recommendation.ConclusionFrom the client’s point of view, there does not seem to be only one “right” way to provide ethics consultations, but rather several. While facilitated meetings are obviously appreciated by clients, there also seem to be situations in which a recommendation is desired (especially by physicians). Further empirical and theoretical research is needed to validate our single-center results and re-evaluate the role of recommendations in ethics consultations. (shrink)

Multinational corporations are operating in complex business environments. They are confronted with contradictory institutional demands that often represent mutually incompatible expectations of various audiences. Managing these demands poses new organizational challenges for the corporation. Conducting an empirical case study at the sportswear manufacturer Puma, we explore how multinational corporations respond to institutional complexity and what legitimacy strategies they employ to maintain their license to operate. We draw on the literature on institutional theory, contingency theory, and organizational paradoxes. The results of (...) our qualitative longitudinal study show that managing corporate legitimacy is a dynamic process in which corporations adapt organizational capacities, structures, and procedures. (shrink)

Game Logic is a modal logic which extends Propositional Dynamic Logic by generalising its semantics and adding a new operator to the language. The logic can be used to reason about determined 2-player games. We present an overview of meta-theoretic results regarding this logic, also covering the algebraic version of the logic known as Game Algebra.

Continuous reducibilities are a proven tool in Computable Analysis, and have applications in other fields such as Constructive Mathematics or Reverse Mathematics. We study the order-theoretic properties of several variants of the two most important definitions, and especially introduce suprema for them. The suprema are shown to commutate with several characteristic numbers.

Axiomatic characterization results in social choice theory are usually compared either regarding the normative plausibility or regarding the logical strength of the axioms involved. Here, instead, we propose to compare axiomatizations according to the language used for expressing the axioms. In order to carry out such a comparison, we suggest a formalist approach to axiomatization results which uses a restricted formal logical language to express axioms. Axiomatic characterization results in social choice theory then turn into definability results of formal logic. (...) The advantages of this approach include the possibility of non-axiomatizability results, a distinction between absolute and relative axiomatizations, and the possibility to ask how rich a language needs to be to express certain axioms. We argue for formal minimalism, i.e., for favoring axiomatizations in the weakest language possible. (shrink)