This essay traces the history of early molecular dynamics simulations, specifically exploring the development of SHAKE, a constraint-based technique devised in 1976 by Jean-Paul Ryckaert, Giovanni Ciccotti and the late Herman Berendsen at CECAM (Centre Européen de Calcul Atomique et Moléculaire). The work of the three scientists proved to be instrumental in giving impetus to the MD simulation of complex polymer systems and it currently underpins the work of thousands of researchers worldwide who are engaged in computational physics, (...) chemistry and biology. Despite its impact and its role in bringing different scientific fields together, accurate historical studies on the birth of SHAKE are virtually absent. By collecting and elaborating on the accounts of Ryckaert and Ciccotti, this essay aims to fill this gap, while also commenting on the conceptual and computational difficulties faced by its developers. (shrink)

In this paper I will argue for a plausible account for moral luck in the Ruist tradition. In part one I will offer a preliminary framework for moral luck to establish an intersection between Ruist virtue ethics and its counterparts outside of Ruism. I will situate the term moral luck in a Ruist context. Although the term moral luck does not appear in The Mengzi the concept was known to Master Meng and is useful for comparison with its foreign counterparts. (...) In part two, guided by Thomas Nagle’s four categories for moral luck, I show where Ruist moral luck can be found in The Mengzi. I conclude by highlighting the contributions that Ruism offers to the broader moral luck discussion. (shrink)

This is the first book to provide a coherent overview over the ethical implications of AI-related technologies in medicine. It explores how these technologies transform practices, relationships, and environments in the clinical field. It provides an introduction into ethical issues such as data security and privacy protection, bias and algorithmic fairness, trust and transparency, challenges to the doctor-patient relationship, and new perspectives for informed consent. The book focuses on the transformative impact that technology is having on medicine, and discusses several (...) strategies for dealing with the resulting challenges. It also introduces innovative methods of ethics research for addressing existing desiderata and future challenges. This book is written to inform health care professionals, policy-makers, and researchers in medicine, health sciences, nursing science, social sciences, and ethics, but may also function as a primary textbook for graduate as well as undergraduate university courses. (shrink)

This paper defends the view that one's own mental states are metaphysically privileged vis-à-vis the mental states of others, even if only subjectively so. This is an instance of a more general view called Subjectivism, according to which reality is only subjectively the way it is. After characterizing Subjectivism in analogy to two relatively familiar views in the metaphysics of modality and time, I compare the Subjectivist View of the Mental with Egocentric Presentism, a version of Subjectivism recently advocated by (...) Caspar Hare. I argue that the Subjectivist View of the Mental goes a considerable way towards solving certain long-standing philosophical puzzles having to do with the unity of consciousness, the contents of self-awareness and the intransmissibility of experiential knowledge through testimony. (shrink)

Within the technical frame supplied by the algebraic variety of diagonalizable algebras, defined by R. Magari in [2], we prove the following: Let T be any first-order theory with a predicate Pr satisfying the canonical derivability conditions, including Löb's property. Then any formula in T built up from the propositional variables $q,p_{1},...,p_{n}$ , using logical connectives and the predicate Pr, has the same "fixed-points" relative to q (that is, formulas $\psi (p_{1},...,p_{n})$ for which for all $p_{1},...,p_{n}\vdash _{T}\phi (\psi (p_{1},...,p_{n}),p_{1},...,p_{n})\leftrightarrow \psi (...) (p_{1},...,p_{n})$ ) of a formula $\phi ^{\ast}$ of the same kind, obtained from φ in an effective way. Moreover, such $\phi ^{\ast}$ is provably equivalent to the formula obtained from φ substituting with $\phi ^{\ast}$ itself all the occurrences of q which are under Pr. In the particular case where q is always under Pr in φ, $\phi ^{\ast}$ is the unique (up to provable equivalence) "fixed-point" of φ. Since this result is proved only assuming Pr to be canonical, it can be deduced that Löb's property is, in a sense, equivalent to Gödel's diagonalization lemma. All the results are proved more generally in the intuitionistic case. (shrink)

Epistemic reliabilism holds that a belief is justified if and only if it is produced by a reliable or truth-conducive process. I argue that reliabilism offers an epistemology for bounded rationality. This latter concept refers to normative and descriptive accounts of real-world reasoning instead of some ideal reasoning. However, as initially formulated, reliabilism involves an absolute, context-independent assessment of rationality that does not do justice to the fact that several processes are reliable in some reasoning environments but not in others, (...) as is widely reported in the cognitive sciences literature. I consider possible solutions to this problem. Resorting to ‘normality reliabilism’, a variant of the theory, is one; but I find it insufficient. Therefore, in addition, I propose to relativise the reliability assessment to reasoning environments. This novel version of reliabilism fits bounded rationality better than the original one does. (shrink)

This paper offers a conceptual framework which (re)integrates goal-directed control, motivational processes, and executive functions, and suggests a developmentalpathway from situated action to higher level cognition. We first illustrate a basic computational (control-theoretic) model of goal-directed action that makes use of internalmodeling. We then show that by adding the problem of selection among multiple actionalternatives motivation enters the scene, and that the basic mechanisms of executivefunctions such as inhibition, the monitoring of progresses, and working memory, arerequired for this system to (...) work. Further, we elaborate on the idea that the off-line re-enactment of anticipatory mechanisms used for action control gives rise to (embodied)mental simulations, and propose that thinking consists essentially in controlling mental simulations rather than directly controlling behavior and perceptions. We concludeby sketching an evolutionary perspective of this process, proposing that anticipationleveraged cognition, and by highlighting specific predictions of our model. (shrink)

Much of the recent philosophical debate on causation and causal explanation in the biological and biomedical sciences has focused on the notion of mechanism. Mechanisms, their nature and epistemic roles have been tackled by a range of so-called neo-mechanistic theories, and widely discussed. Without denying the merits of this approach, our paper aims to show how lately it has failed to give proper credit to processes, which are central to the field, especially of contemporary molecular biology. Processes can be summed (...) up in the notion of ‘pathway’, which is far from being just equivalent to that of ‘mechanism’ and has a profound epistemological and explanatory relevance. It is argued that an adequate consideration of pathways impels some rethinking of scientific explanation in molecular biology, namely its functional and contextual features. A number of examples are given to suggest that the focus of philosophical attention in this disciplinary field should shift from the notion of mechanism to the notion of pathway. (shrink)

Humanity’s self-ordained mandate to subdue and dominate nature is part of the cognitive foundation of the modern world—a perspective that remains deeply ingrained in science and technology. Marine biology has not been immune to this anthropocentric bias. But this needs to change, and the gaps between basic scientific disciplines and the global conservation imperatives of our time need to be bridged. In the face of a looming ecological and climate crisis, marine biologists must upgrade their values and professional standards and (...) help foster the radical transformation needed to avert a climate and ecological breakdown. To prevent some of the damage, they must cross the imaginary line that separates science from science-based activism and consciously pursue the health and durability of human and natural communities. To this end, they can (1) develop compelling narratives that engage human society, with emphasis on care for the wild living world; (2) move beyond marine conservation on paper and avoid self-serving complaisance; (3) advocate constructive changes in market and human behaviour, not only by documenting damage but also by clarifying how the extraction, production and consumption system can be steered away from practices that harm nature; (4) push for systemic change in politics through individual and collective efforts, supporting environmental activism and those who demand biosphere-saving policies; and (5) endorse a more ecocentric and holistic world vision, relinquishing contempt for spiritual wisdom and liaising with (or at least not dismissing) spiritual traditions that encourage equality, self-restraint and environmental sustainability. (shrink)

Richard Owen has been condemned by Darwinians as an anti-evolutionist and an essentialist. In recent years he has been the object of a revisionist analysis intended to uncover evolutionary elements in his scientific enterprise. In this paper I will examine Owen's evolutionary hypothesis and its connections with von Baer's idea of divergent development. To give appropriate importance to Owen's evolutionism is the first condition to develop an up-to-date understanding of his scientific enterprise, that is to disentagle Owen's contribution to the (...) modernization of typology and morphology. I will argue that Owen's Platonic essentialism is rhetorical and incongruous. On the contrary, an interpretation of the archetype based on Aristotle's biological works makes possible a new conception of type, based on a homeostatic mechanism of stability. The renewal of morphology hinges on homological correspondences and a homeostatic process is also the origin of serial and special homology. I will argue that special homology shows an evolutionary orientation insofar as it is a typically inter-specific character while serial homology is determined through an elementary usage of the categories of developmental morphology. (shrink)

This paper proposes to model legal reasoning asdialectical theory-constructiondirected by teleology. Precedents are viewed asevidence to be explained throughtheories. So, given a background of factors andvalues, the parties in a case canbuild their theories by using a set of operators,which are called theory constructors.The objective of each party is to provide theoriesthat both explain the evidence (theprecedents) and support the decision wished by thatparty. This leads to theory-basedargumentation, i.e., a dialectical exchange ofcompeting theories, which support opposedoutcomes by explaining the same (...) evidence and appealingto the same values. The winneris the party that can reply with a more coherent theoryto all theories of its adversary. (shrink)

Research in the field of management has increasingly focused on strategies and tools related to corporate sustainability. Of the tools examined, codes of ethics have been found to play a primary role. Many studies have investigated the content of such codes, as well as their capacity to condition the behaviour of people within organizations. However, few studies have considered the intrinsic quality of codes of ethics. This study aims to investigate the impact that specific factors—firm size, degree of internationalization and (...) industry effect—can have on the quality of codes of ethics. Based on a sample of 248 listed Italian companies, the results of the empirical analysis show that the quality standard is particularly high in larger companies and in those firms operating in industries in which relationships established with critical stakeholders—and disclosure to those stakeholders—play a crucial role. These results have interesting implications for both researchers and practitioners. (shrink)

Definition of the problem Biomedical research based on big data offers immense benefits. Large multisite research that integrates large amounts of personal health data, especially genomic and genetic data, might contribute to a more personalized medicine. This type of research requires the transfer and storage of highly sensitive data, which raises the question of how to protect data subjects against data harm, such as privacy breach, disempowerment, disenfranchisement, and exploitation. As a result, there is a trade-off between reaping the benefits (...) of big-data-based biomedical research and protecting data subjects’ right to informational privacy. Arguments Blockchain technologies are often discussed as a technical fix for the abovementioned trade-off due to their specific features, namely data provenance, decentralization, immutability, and access and governance system. However, implementing blockchain technologies in biomedical research also raises questions regarding consent, legal frameworks, and workflow integration. Hence, accompanying measures, which I call enablers, are necessary to unleash the potential of blockchain technologies. These enablers are innovative models of consent, data ownership models, and regulatory models. Conclusion Blockchain technologies as a technical fix alone is insufficient to resolve the aforementioned trade-off. Combining this technical fix with the enablers outlined above might be the best way to perform biomedical research based on big data and at the same time protect the informational privacy of data subjects. (shrink)

Why is interaction so simple? This article presents a theory of interaction based on the use of shared representations as “coordination tools” (e.g., roundabouts that facilitate coordination of drivers). By aligning their representations (intentionally or unintentionally), interacting agents help one another to solve interaction problems in that they remain predictable, and offer cues for action selection and goal monitoring. We illustrate how this strategy works in a joint task (building together a tower of bricks) and discuss its requirements from a (...) computational viewpoint. (shrink)

The paper focuses on the role of relativistic ideas in Wittgenstein’s philosophy. In particular, it focuses on On Certainty (1969), where in (305), Wittgenstein explicitly invokes Einstein’s theory of relativity: “Here once more there is needed a step like the one taken in relativity theory.” The aim of the paper is to establish a connection between Wittgenstein and Einstein that is both theoretically and exegetically sound. In particular, the paper argues that Wittgenstein’s reaction to scepticism closely resembles Einstein’s reaction to (...) the ether. (shrink)

This paper examines the effectiveness of the use of executive compensation linked to Corporate Social Responsibility (CSR) goals across US firms. Empirical analysis of a cross-industry sample of 746 listed companies for the period 2002–2013 showed that the use of CSR-linked compensation contracts for Named Executive Officers (NEOs) promotes CSR performance. More specifically, we found that linking NEOs’ compensation to CSR goals produces positive effects in the 3rd year after adoption. As firms accumulate experience and learn how to use the (...) system over the following eight periods, CSR performance increases monotonically. Furthermore, experience accumulated over time affects the different specifications of CSR performance asymmetrically, by reducing both environmental and social CSR concerns and increasing only environmental CSR strengths. Interestingly, we also found that the simultaneous use of other CSR-focused governance systems moderates the effect of a firm’s accumulated experience in using CSR-linked executive compensation on CSR performance: the existence of a CSR committee at the board level and the public release of a CSR report are likely to have a positive moderating effect, while the purchase of a CSR audit has no moderating effect. (shrink)

Pretopologies were introduced in [S], and there shown to give a complete semantics for a propositional sequent calculus BL, here called basic linear logic, as well as for its extensions by structural rules,ex falso quodlibetor double negation. Immediately after Logic Colloquium '88, a conversation with Per Martin-Löf helped me to see how the pretopology semantics should be extended to predicate logic; the result now is a simple and fully constructive completeness proof for first order BL and virtually all its extensions, (...) including the usual, or structured, intuitionistic and classical logic. Such a proof clearly illustrates the fact that stronger set-theoretic principles and classical metalogic are necessary only when completeness is sought with respect to a special class of models, such as the usual two-valued models.To make the paper self-contained, I briefly review in §1 the definition of pretopologies; §2 deals with syntax and §3 with semantics. The completeness proof in §4, though similar in structure, is sensibly simpler than that in [S], and this is why it is given in detail. In §5 it is shown how little is needed to obtain completeness for extensions of BL in the same language. Finally, in §6 connections with proofs with respect to more traditional semantics are briefly investigated, and some open problems are put forward. (shrink)

Reale's monumental work establishes the exact dimensions of Aristotle's concept of first philosophy and proves the profound unity of concept that exists in Aristotle's Metaphysics.

In 1685, during the heyday of Scottish Cartesianism, regent Robert Lidderdale from Edinburgh University declared Cartesianism the best philosophy in support of the Reformed faith. It is commonplace that Descartes was ostracised by the Reformed, and his role in pre-Enlightenment Scottish philosophy is not yet fully acknowledged. This paper offers an introduction to Scottish Cartesianism, and argues that the philosophers of the Scottish universities warmed up to Cartesianism because they saw it as a newer, better version of their own traditional (...) Reformed scholasticism, chiefly in metaphysics and natural philosophy. (shrink)

The recent outbreak of the SARS-CoV-2 coronavirus is posing many different challenges to local communities, directly affected by the pandemic, and to the global community, trying to find how to respond to this threat in a larger scale. The history of the Eyam Plague, read in light of Ross Upshur’s Four Principles for the Justification of Public Health Intervention, and of the Siracusa Principles on the Limitation and Derogation Provisions in the International Covenant on Civil and Political Rights, could provide (...) useful guidance in navigating the complex ethical issues that arise when quarantine measures need to be put in place. (shrink)

In der Reihe werden herausragende monographische Untersuchungen und Sammelbände zu allen Aspekten der Philosophie Kants veröffentlicht, ebenso zum systematischen Verhältnis seiner Philosophie zu anderen philosophischen Ansätzen in Geschichte und Gegenwart. Veröffentlicht werden Studien, die einen innovativen Charakter haben und ausdrückliche Desiderate der Forschung erfüllen. Die Publikationen repräsentieren den aktuellsten Stand der Forschung.

Born from the combination of two projects--a presentation of the important essays from the Critical Journal of Schelling and Hegel that were still untranslated and an anthology of excerpts from the works of the generation of German thinkers ...

A radical reform of the agri-food biotech regulation in the EU is considered in many quarters as a pressing necessity. Indeed, two important decisions on the legal status of the so-called New Breeding Techniques are expected shortly. In order to clarify some basic aspects of the complex scenario, after a brief introduction regarding the “GMO” fallacy, we offer our point of view on the following facets: A faulty approach is frequent in the discussion of the agri-food regulation; NBTs, genome editing (...) may lead to the disappearance of the “GMO” meme; Beyond health and safety issues: socio-economic considerations; Sustainability: the comprehensive, meaningful starting point of a positive reform; The theoretical and legal basis for the reform are already contained in the EU’s general guidelines to legislation. (shrink)

This article introduces Designing for Care (D4C), a distinctive approach to project management and technological design informed by Care Ethics. We propose to conceptualize “care” as both the foundational value of D4C and as its guiding mid-level principle. As a value, care provides moral grounding. As a principle, it equips D4C with moral guidance to enact a caring process. The latter is made of a set of concrete, and often recursive, caring practices. One of the key assumption of D4C is (...) a relational ontology of individual and group identities, which fosters the actualization of caring practices as essentially relational and (often) reciprocal. Moreover, D4C adopts the “ecological turn” in CE and stresses the ecological situatedness and impact of concrete projects, envisioning an extension of caring from intra-species to inter-species relations. We argue that care and caring can influence directly some of the phases and practices within the management of (energy) projects and the design of sociotechnical (energy) artefacts and systems. When issues related to “value change” emerge as problematic (e.g., values trade-offs, conflicts), the mid-level guiding principle of care helps evaluate and prioritize different values at stake within specific projects. Although there may be several actors and stakeholders involved in project management and technological design, here we will focus on the professionals in charge of imagining, designing, and carrying out these processes (i.e., project managers, designers, engineers). We suggest that adopting D4C would improve their ability to capture and assess stakeholders’ values, critically reflect on and evaluate their own values, and judge which values prioritize. Although D4C may be adaptable to different fields and design contexts, we recommend its use especially within small and medium-scale (energy) projects. To show the benefits of adopting it, we envisage the application of D4C within the project management and the technological design of a community battery. The adoption of D4C can have multiple positive effects: transforming the mentality and practice of managing a project and designing technologies; enhancing caring relationships between managers, designers, and users as well as among users; achieving better communication, more inclusive participation, and more just decision-making. This is an initial attempt to articulate the structure and the procedural character of D4C. The application of D4C in a concrete project is needed to assess its actual impact, benefits, and limitations. (shrink)

This article argues that Robert Alexy's influential theory of balancing is affected by a contradiction that makes it unfeasible as an instrument by which to explain some aspects of law and legal reasoning it aims to clarify. In particular, I will show that one of the premises of Alexy's theory of balancing is incompatible with its conclusion. Alexy's theory is based upon a sharp distinction between rules and principles. However, as my analysis will demonstrate, its conclusion implies that it is (...) impossible to distinguish between rules and principles. This is because the so‐called weight formula and the law of colliding principles (i.e., the two main notions used by Alexy to explain balancing) cancel out any difference between these two types of norms. (shrink)

We give a self-contained geometric proof of the completeness theorem for the infinite-valued sentential calculus of Łukasiewicz.

Digital technologies have become a crucial factor in nursing. Given the fact that many tasks could also be done by robots or AI systems, the place for the nurse in this scenario is unclear. In what way and to what extent will the implementation of ever more sophisticated technology affect nursing practice? It is the aim of this paper to analyse the potential challenges of nursing practice in the digital age. The analysis is conducted through the lens of new materialism, (...) a set of theoretical models that understand the relationship between humans and technology as dynamic and performative. According to this view, there is no prefixed essence of technology. Rather, the meaning of technology is enacted in concrete practice. The analysis shows that in past debates on technology use in nursing, the nurses’ role has been defined as guardians of humanity, defending the patient against the dehumanizing effects of technology. This role has been transferred to the digital age, where it is the duty of nurses to cushion the negative effects of digital technology. As an alternative to this outdated role, nurses should be included in processes of technology design and policymaking. Enabling nursing professionals to shape the circumstances of a digitally enhanced holistic practice may empower their status within the healthcare system and also benefit the patient by contributing to a more person‐centred care. (shrink)

I shall compare two views of legal concepts: as nodes in inferential nets and as categories in an ontology (a conceptual architecture). Firstly, I shall introduce the inferential approach, consider its implications, and distinguish the mere possession of an inferentially defined concept from the belief in the concept’s applicability, which also involves the acceptance of the concept’s constitutive inferences. For making this distinction, the inferential and eliminative analysis of legal concepts proposed by Alf Ross will be connected to the views (...) on theoretical concepts in science advanced by Frank Ramsey and Rudolf Carnap. Consequently, the mere comprehension of a legal concept will be distinguished from the application of the concept to a particular legal system, since application presupposes a doctrinal commitment, namely, the belief that the inferences constituting the concept hold in that system. Then, I shall consider how concepts can be characterised by defining the corresponding terms and placing them within an ontology. Finally, I shall argue that there is a tension between the inferential and the ontological approach, but that both need to be taken into account, to capture the meaning and the cognitive function of legal concepts. (shrink)

The coronavirus COVID-19 pandemic is an unprecedented health crisis. Many governments around the world have responded by implementing lockdown measures of various degrees of intensity. To be effective, these measures must rely on citizens’ cooperation. In the present study, we drew samples from the United States (N= 597), Italy (N= 606), and South Korea (N= 693) and examined predictors of compliance with social distancing and intentions to report the infection to both authorities and acquaintances. Data were collected between April 6th (...) and 8th 2020. We investigated the role of cultural orientations of horizontal and vertical individualism and collectivism, self-conscious emotions of shame and guilt related to the infection and trust in the government’s action. Across all countries, vertical collectivism (VC) predicted stronger shame, whereas horizontal collectivism predicted stronger trust in the government. Only in the United States, VC was associated with stronger trust. Stronger feelings of shame predicted lower compliance and intentions to report the infection to both authorities and acquaintances. In contrast, guilt was associated with stronger intentions to report the infection to the authorities. Finally, trust was associated with stronger compliance and intentions to report the infection to the authorities. Unlike Italy and South Korea, the association between trust on compliance was not statistically significant in the United States, implications of the findings, and directions for future research are discussed. (shrink)

In this paper we propose an approach to vagueness characterised by two features. The first one is philosophical: we move along a Kantian path emphasizing the knowing subject’s conceptual apparatus. The second one is formal: to face vagueness, and our philosophical view on it, we propose to use topology and formal topology. We show that the Kantian and the topological features joined together allow us an atypical, but promising, way of considering vagueness.

Assuming a radical stance on embodied cognition, according to which the information ac- quired through basic cognitive processes is not contentful (Hutto and Myin, 2013), and as- suming that perception is a source of rationally grounded knowledge (Pritchard, 2012), a pluralistic account of perceptual knowledge is developed. The paper explains: (i) how the varieties of perceptual knowledge fall under the same broader category; (ii) how they are subject to the same kind of normative constraints; (iii) why there could not be (...) a conflict between the different varieties of perceptual knowledge; and (iv) why the traditional episte- mological inquiry is inclined to overestimate the role of propositional perceptual knowledge. (shrink)

AgeTech involves the use of emerging technologies to support the health, well-being and independent living of older adults. In this paper we focus on how AgeTech based on artificial intelligence (AI) may better support older adults to remain in their own living environment for longer, provide social connectedness, support wellbeing and mental health, and enable social participation. In order to assess and better understand the positive as well as negative outcomes of AI-based AgeTech, a critical analysis of ethical design, digital (...) equity, and policy pathways is required. A crucial question is how AI-based AgeTech may drive practical, equitable, and inclusive multilevel solutions to support healthy, active ageing. In our paper, we aim to show that a focus on equity is key for AI-based AgeTech if it is to realize its full potential. We propose that equity should not just be an extra benefit or minimum requirement, but the explicit aim of designing AI-based health tech. This means that social determinants that affect the use of or access to these technologies have to be addressed. We will explore how complexity management as a crucial element of AI-based AgeTech may potentially create and exacerbate social inequities by marginalising or ignoring social determinants. We identify bias, standardization, and access as main ethical issues in this context and subsequently, make recommendations as to how inequities that stem form AI-based AgeTech can be addressed. (shrink)

Starting from the formal expressions of the hydrodynamical (or “local”) quantities employed in the applications of Clifford algebras to quantum mechanics, we introduce—in terms of the ordinary tensorial language—a new definition for the field of a generic quantity. By translating from Clifford into tensor algebra, we also propose a new (nonrelativistic) velocity operator for a spin- ${\frac{1}{2}}$ particle. This operator appears as the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of a (...) second part associated with the so-called Zitterbewegung, which is the spin “internal” motion observed in the center-of-mass frame (CMF). This spin component of the velocity operator is nonzero not only in the Pauli theoretical framework, i.e., in the presence of external electromagnetic fields with a nonconstant spin function, but also in the Schrödinger case, when the wavefunction is a spin eigenstate. Thus, one gets even in the latter case a decomposition of the velocity field for the Madelung fluid into two distinct parts, which constitutes the nonrelativistic analogue of the Gordon decomposition for the Dirac current. Explicit calculations are presented for the velocity field in the particular cases of the hydrogen atom, of a spherical well potential, and of an electron in a uniform magnetic field. We find, furthermore, that the Zitterbewegung motion involves a velocity field which is solenoidal, and that the local angular velocity is parallel to the spin vector. In the presence of a nonuniform spin vector (Pauli case) we have, besides the component of the local velocity normal to the spin (present even in the Schrödinger theory), also a component which is parallel to the curl of the spin vector. (shrink)