A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic reviews of the relevant material are provided. Further chapters are devoted to the stability of invariant sets, bifurcation theory, chaotic dynamics and the transition to chaos. In the final two chapters the authors approach the subject from a measure-theoretical (...) point of view and compare results to those given for the geometrical or topological approach of the first eight chapters. Includes about one hundred exercises. A Windows-compatible software programme called DMC, provided free of charge through a website dedicated to the book, allows readers to perform numerical and graphical analysis of dynamical systems. Also available on the website are computer exercises and solutions to selected book exercises. See www.cambridge.org/economics/resources. (shrink)

Mathematicians often intentionally leave gaps in their proofs. Based on interviews with mathematicians about their refereeing practices, this paper examines the character of intentional gaps in published proofs. We observe that mathematicians’ refereeing practices limit the number of certain intentional gaps in published proofs. The results provide some new perspectives on the traditional philosophical questions of the nature of proof and of what grounds mathematical knowledge.

We present a taxonomy of errors in the scientific literature and an account of how the errors are distributed over the categories. We have developed the taxonomy by studying substantial errors in the scientific literature as described in retraction notices published in the journal Science over the past 35 years. We then examine how the sorts of errors that lead to retracted papers can be prevented and detected, considering the perspective of collaborating scientists, journal editors and referees, and readers of (...) the published articles. (shrink)

The authorship policies of scientific journals often assume that in order to be able to properly place credit and responsibility for the content of a collaborative paper we should be able to distinguish the contributions of the various individuals involved. Hence, many journals have introduced a requirement for author contribution statements aimed at making it easier to place credit and responsibility on individual scientists. We argue that from a purely descriptive point of view the practices of collaborating scientists are at (...) odds with the requirement for author contribution statements. We also argue that from a normative point of view the authorship policies may be unnecessary. Our arguments draw on an examination of 35 years of retraction notices in the journal Science. (shrink)

We present a case study of how mathematicians write for mathematicians. We have conducted interviews with two research mathematicians, the talented PhD student Adam and his experienced supervisor Thomas, about a research paper they wrote together. Over the course of 2 years, Adam and Thomas revised Adam’s very detailed first draft. At the beginning of this collaboration, Adam was very knowledgeable about the subject of the paper and had good presentational skills but, as a new PhD student, did not yet (...) have experience writing research papers for mathematicians. Thus, one main purpose of revising the paper was to make it take into account the intended audience. For this reason, the changes made to the initial draft and the authors’ purpose in making them provide a window for viewing how mathematicians write for mathematicians. We examined how their paper attracts the interest of the reader and prepares their proofs for validation by the reader. Among other findings, we found that their paper prepares the proofs for two types of validation that the reader can easily switch between. (shrink)

If we want to understand why mathematical knowledge is extraordinarily reliable, we need to consider both the nature of mathematical arguments and mathematical practice as a social practice. Mathematical knowledge is extraordinarily reliable because arguments in mathematics take the form of deductive mathematical proofs. Deductive mathematical proofs are surveyable in the sense that they can be checked step by step by different experts, and a purported proof is only accepted as a proof by the mathematical community once a number of (...) experts have checked the proof. Hence, the reliability of the body of mathematical knowledge is in part obtained through the surveyability of proofs and the social process of proof validation. This chapter reviews work relating to (1) the norm in the mathematical community of only counting as argument deductive mathematical proof, and (2) the norm of only counting as deductive mathematical proof an argument that has been confirmed to be a deductive mathematical proof by a number of experts. The chapter also presents cases of unusual mathematical proofs or arguments that challenge these norms. (shrink)

Mathematicians appear to have quite high standards for when they will rely on testimony. Many mathematicians require that a number of experts testify that they have checked the proof of a result p before they will rely on p in their own proofs without checking the proof of p. We examine why this is. We argue that for each expert who testifies that she has checked the proof of p and found no errors, the likelihood that the proof contains no (...) substantial errors increases because different experts will validate the proof in different ways depending on their background knowledge and individual preferences. If this is correct, there is much to be gained for a mathematician from requiring that a number of experts have checked the proof of p before she will rely on p in her own proofs without checking the proof of p. In this way a mathematician can protect her own work and the work of others from errors. Our argument thus provides an explanation for mathematicians’ attitude towards relying on testimony. (shrink)

The phenomenon of shared intention has received much attention in the philosophy of mind and action. Margaret Gilbert (1989, 2000c, 2014b) argues that a shared intention to do A consists in a joint commitment to intend to do A. But we need to know more about the nature of joint commitments to know what exactly this implies. While the persistence of joint commitments has received much attention in the literature, their impersistence has received very little attention. In this paper, we (...) shed light on the impersistence of joint commitments by showing how joint commitments can be dissolved by unexpected events. (shrink)

It has been a common belief among scientists, including mathematicians, that young scientists are especially good at bringing about scientific change. A number of studies suggest, however, that older scientists are not more resistant to change than young scientists are. It is nonetheless worth examining why a scientist’s or mathematician’s outsider status – due to age, educational background, or something else – can sometimes be effective in enabling scientific change. This paper focuses on the case of the solving of the (...) Four Color Problem by Wolfgang Haken and Kenneth Appel. Building on Donald MacKenzie’s paper ‘Slaying the kraken: The sociohistory of a mathematical proof’, I argue that Haken’s outsider status is central to understanding his success with the problem. On this basis, I offer an argument against Margaret Gilbert’s account of why a scientist’s outsider status can be effective in enabling scientific change. (shrink)

This paper investigates the relationships between organizational change and trust in management. It is argued that organizational change represents a critical episode for the production and destruction of trust in management. Although trust in management is seen as a semi stable psychological state, changes in organizations make trust issues salient and organizational members attend to and process trust relevant information resulting in a reassessment of their trust in management. The direction and magnitude of change in trust is dependent on a (...) set of change dimensions that reflect trust relevant experiences and information. We distinguish between dimensions related to trust relevant consequences of the change and trust relevant aspects of how the change process is performed. Empirical results indicate that increases in post change emotional stress and the use of referential accounts for justifying change are both negatively related to post change trust in management. The use of ideological accounts and participation were found to be positively related to post change trust in management, so was perceived decision quality. Findings also indicate that the effects of change on trust are negatively moderated by tenure. (shrink)

The authorship policies of scientific journals often assume that in order to be able to properly place credit and responsibility for the content of a collaborative paper we should be able to distinguish the contributions of the various individuals involved. Hence, many journals have introduced a requirement for author contribution statements aimed at making it easier to place credit and responsibility on individual scientists. We argue that from a purely descriptive point of view the practices of collaborating scientists are at (...) odds with the requirement for author contribution statements. We also argue that from a normative point of view the authorship policies may be unnecessary. Our arguments draw on an examination of 35 years of retraction notices in the journal Science. (shrink)

Peter Goldie’s account of grief as a narrative process that unfolds over time allow us to address the structure of self-understanding in the experience of loss. Taking up the Goldie’s idea that narrativity plays a crucial role in grief, I will argue that the experience of desynchronization and an altered relation to language disrupt even of our ability to compose narratives and to think narratively. Further, I will argue that Goldie’s account of grief as a narratively structured process focus on (...) the process having come to an end. By contrast, I will propose the idea that grief can be understood as an open-ended rehearsal of our capacity to be alone in the company of an absent other. This makes grief a relational activity that differs from composing narratives about one’s past and about one’s process of grieving. Thus, grief is not primarily a process of recollecting our past narratively; rather, it can be seen as a dedicational activity which involves a future-oriented and open-ended rehearsal of relatedness despite irrevocable absence. (shrink)

An action is typically carried out over time, unified by an intention that is known to the agent under some description. In some of our habitual doings, however, we are often not aware of what or why we do as we do. Not knowing this, we must ask what kind of agency is at stake in these habitual doings, if any. This paper aims to show how habitual doings can still be considered actions of a subject even while they involve (...) a sense of involuntariness and there is a temporal displacement in the self-understanding they afford. It turns out that in some forms of habitual agency, we do not have the relevant intentional description at hand when we are engaged in the process of doing what we so typically do; on the contrary, such a description can only be appropriated with effort and subsequent to the time of the action. I will focus on two approaches to habits, broadly construed; a phenomenological and an action theoretic one, and I will suggest that both approaches focus too narrowly on a synchronic relation between habitual action and self-understanding. I will suggest that we need a diachronic account of the potential for self-understanding required for agency that allows us to explain the experience of diminished control and alienation involved in certain of our habitual actions. The suggested perspective enables us to explain how some habits can be experienced as both momentarily involuntary and unconscious while at the same time they play a significant role for self-understanding. (shrink)

This study uses university commentaries on Aristotle's Nicomachean Ethics as a window onto changing ideals and practices of education and of humanist Aristotelianism in Renaissance Italy, particularly in Florence, Padua, Bologna, and Rome (including the Collegio Romano).

In phenomenology the body is often referred to as the lived body which makes the world familiar to me. In this paper, however, I discuss bodily self-consciousness in terms of self-distance. Self-distance is the suggestion that bodily self-consciousness consist in a reflective stance where you conceive of your body as a physical thing, an object in the world as well as the subject of bodily experiences. I argue that we are bodily self-conscious because we experience our own body in more (...) than one way and that these ways are not derivative of one another or hierarchically ordered. This latter claim conflicts with certain phenomenological readings of how the body is experienced, one of which I will refer to and discuss as the Familiarity Objection to my idea of self-distance. I end the paper with a discussion of why we need the conception of experienced objectification that is entailed in the notion of self-distance to account for both pathological and non-pathological bodily self-experiences. The notion of self-distance improves our understanding of how the body plays a central role in psychosis for the experience of distorted inter-subjective relations. (shrink)

In recent years, questions regarding the ontological status of the human have been raised with renewed interest and imagination within various fields of critical thought. In the face of biotechnological findings and increasingly advanced technologies that connect as well as disturb settled boundaries, whether geographical or bodily, not to mention philosophical questionings of traditional western humanism, the boundaries of the human subject have been contested. The human body, traditionally imagined as closed and autonomous, has been opened up to a world (...) of forces and agencies that are strange, other and often deeply disturbing when viewed from an anthropocentric standpoint. Rather than close down anxieties concerning such boundary transgressions and ontological uncertainties, scholars – not least within areas such as feminist, posthumanist and queer theory – have argued that here lie possibilities as well as an ethical urgency to rethink the human subject, its world(s) and its others. Indeed, what might it mean to view the world from positions that do not take the pure and autonomous human form as its starting point? And what ethical considerations does such a viewpoint demand of us? (shrink)

The visual attention (VA) span is defined as the amount of distinct visual elements which can be processed in parallel in a multi-element array. Both recent empirical data and theoretical accounts suggest that a VA span deficit might contribute to developmental dyslexia, independently of a phonological disorder. In this study, this hypothesis was assessed in two large samples of French and British dyslexic children whose performance was compared to that of chronological-age matched control children. Results of the French study show (...) that the VA span capacities account for a substantial amount of unique variance in reading, as do phonological skills. The British study replicates this finding and further reveals that the contribution of the VA span to reading performance remains even after controlling IQ, verbal fluency, vocabulary and single letter identification skills, in addition to phoneme awareness. In both studies, most dyslexic children exhibit a selective phonological or VA span disorder. Overall, these findings support a multi-factorial view of developmental dyslexia. In many cases, developmental reading disorders do not seem to be due to phonological disorders. We propose that a VA span deficit is a likely alternative underlying cognitive deficit in dyslexia. (shrink)

ABSTRACT In this comment, I argue that transformative experiences such as experiences of grief often imply a break in one's coherent, non-fictional and biographical narratives and practical identities. The nature of these breaks is of a certain kind, as they interrupt even the process of narration. To insist that the process of narration as well as the narratives themselves belong to one and the same process of adjustment in transformative experiences such as grief might overlook the importance of such breaks, (...) namely that the contain a moment of refusal and revolting against mourning. The tension involved in such breaks might not allow to be circumscribed into narratives nor do they fit into the process of narration as a destabilizing moment; the breaks insist on the incomprehensibility of each loss and they remain part of what it means to survive and to undergo transformative experiences. (shrink)

The aesthetic -- The ethical -- The no woman's land of Kierkegaardian exceptions -- The religious.

In what sense can bodily manifestations in psychopathology be conceived of as modes of speaking? In which ways can a patient be listened to and responded to? In this paper, we consider these questions in the framework both of phenomenology and psychoanalysis. On the one hand, a phenomenological approach helps considering the body as expressive, but, we argue, more refinement is needed, and in particular, expression ought to be differentiated from communication, in the aim of better capturing the phenomenon of (...) body language. On the other hand, a psychoanalytic approach helps considering the clinical strength of an encounter where the only vehicle is the speech one addresses another, but, we argue, this should not... (shrink)

This article explores variation in how immigrant Muslim women in Oslo, Norway, interpret and practice gender relations within the framework of Islam. Religion, family, and work are important sites for the formation, negotiation, and change of gender relations. The article therefore discusses the views and experiences of immigrant Muslim women concerning wife-husband relations and participation in the labor market. Four analytical types of views toward gender relations are introduced, and the variation in gender practices and views found among Muslim women (...) in Oslo is discussed in relation to these types. The analysis suggests that immigrant Muslim women use Islam as a flexible resource for interpreting gender relations. It also shows that while women generally uphold a religious ideal of complementary gender roles, their actual practice often contradicts with and contests this ideal. (shrink)

Although social justice is an integral component of medical professionalism, there is little discussion in medical education about how to teach it to future physicians. Using adult learning theory and the work of Brazilian educator Paulo Freire, medical educators can teach a socially-conscious professionalism through educational content and teaching strategies. Such teaching can model non-hierarchical relationships to learners, which can translate to their clinical interactions with patients. Freirian teaching can additionally foster professionalism in both teachers and learners by ensuring that (...) they are involved citizens in their local, national and international communities. (shrink)

La reflexion sur l'experience politique est au coeur de L'Esprit des lois. a l'instar de nombreux auteurs du XVIIIe siecle, Montesquieu s'interroge sur la perennite des Republiques animees par la vertu. L'essor de l'economie, dans les grands etats europeens, nuit a l'expression des vertus et - corrompt les moeurs pures -. Or en l'absence de devouement civique, les etats peuvent-ils fonder le lien social et garantir la liberte politique? La vertu patriotique, passion dominante des cites antiques, peut-elle devenir caduque sans (...) prejudice pour l'homme moderne? En revenant sur l'inscription de Montesquieu dans la tradition du liberalisme politique, cette etude explore les voies plurielles tracees par Montesquieu face au - mal politique - incarne dans le despotisme. Elle invite a approfondir la reflexion consacree au concept de societe civile.". (shrink)

A phenomenological insight in the debate on empathy is that it is possible to directly perceive other people’s emotions in their expressive bodily behaviour. Contrary to what is suggested by many phenomenologists, namely that this perceptual skill is immediately available if one has vision, this paper argues that the perceptual skill for empathy is acquired. Such a skill requires that we have undergone certain emotional experiences ourselves and that we have had the experience of seeing the world differently, which is (...) a form of pretence. By investigating how we retain knowledge of what is real while pretending, that is, how we anchor the experience of pretence in something that is not pretended, the paper argues that we split our experiential perspective into a double perspective, which differs from the cognitive act of understanding what a perspective is. With this notion in hand, we can return to the debate on empathy. It is argued that in order to have the capacity for direct empathic perception, one must have undergone experiences involving a double perspective. (shrink)

We are grateful to René Rosfort for his comment on our target paper Clinical Response to Bodily Symptoms in Psychopathology. Rosfort’s remarks lead us here to specify an important point which our initial proposal may have left too implicit. Within the realm of clinical practice in psychopathology, we argue that bodily manifestations can be offered an expressive space and that they can be listened to in the clinical encounter as being part of the patient’s speech whereby she, by way of (...) her bodily symptoms, addresses a demand to be attended to as a subject of communication. We detail the circumstances under which bodily manifestations may or may not be addressed to a person who is expected to respond, especially in a... (shrink)

Nurses have an important role in preventing and responding to child abuse and neglect. This paper reports on nurses' perceptions of how organisational systems and hierarchies shaped their capacity to respond to child abuse and neglect. This is one of four key themes identified through an inductive analysis of data from a broader qualitative study that explored nurses' perceptions and experiences of keeping children safe. The study was guided by social constructionist theory, and data were collected through in‐depth interviews with (...) nurses working with children in Australia (n = 21). Key findings showed that nurses experienced many challenges to responding to child abuse, including difficulties sharing information, fear of making mistakes and inflexible systems of care. This was underpinned by an organisational ‘rule‐centred’ culture of following policies at the expense of maintaining an explicit focus on children's needs. These findings demonstrate first the importance of creative and flexible thinking from individual professionals, so policies are enacted with a clear child focus. Second, they highlight the need for leadership to enact organisational and systemic cultural change that maintains a genuinely child‐centred approach. (shrink)

This essay considers the way and manner in which a musician and music educator approaches his or her work. It is suggested that anthropomorphic conceptions of music have endured in music education practice in the West. It is proposed that our view of the ‘processes’ of music making, music reception and music learning can be challenged and reconsidered. Heidegger's theory of art is used as a way of rethinking these processes, and of reconsidering our relational dimension with music. The unfolding (...) of music in music‐events occurs as people ‘work‐with’ music and interact with its dimensions in a way that is culturally and dialogically vibrant. Music education can thus become more responsive to changing ‘modes of beings’ in the moment. (shrink)

Trust has a great potential for furthering our understanding of organizational change and learning. This potential however remains largely untapped. It is argued that two reasons as for why this potential remains unrealized are: (i) A narrow conceptualization of change as implementation and (ii) an emphasis on direct and aggregated effects of individual trust to the exclusion of other effects. It is further suggested that our understanding of the effects of trust on organizational change, should benefit from including effects of (...) trust on the formulation stage. It should also benefit from exploring the structuring effects of trust in organizations. Throughout this chapter, ways to extend current research on trust in organizations are suggested. The chapter also provides examples of relevant contributions where available. In order to capture organizational effects of trust, it is suggested that trust should be studied over longer time intervals, and include several referents of trust, spanning both horizontal and vertical relationships in the organization. (shrink)

Sigmund Freud’s reflections on transience left him surprised that someone could revolt against the process of mourning. In Jonathan Lear’s interpretation of transience, the revolt is not simply a passing struggle of the mind, but a response to a difficulty of reality, that is, an existential struggle. Central to the experience of transience, according to Lear, is the disbelief in the existence of an afterlife. How might we understand the idea of an afterlife philosophically? I first consider three different philosophical (...) conceptions of the afterlife that—in different ways—underline the relation between collective memory and the process of mourning. These reflections make it clearer which aspects of the afterlife play a role in the existential struggle that Lear describes. However, a further analysis of the temporality at stake in the denial of an afterlife is needed. I therefore look at two psychoanalytic interpretations of the refusal to mourn. The first considers the refusal to mourn as a way to deny change. The second interpretation sees the refusal as a realisation of meaninglessness that prevents the flow of time. I end the paper by arguing that the afterlife can be understood as a practice of articulation, which allows a shared time to flow. Such a practice will commit us anew to a shared world in which we survive with the wounding difficulties of reality. (shrink)

Music education is a social act oriented around interactions between people in public spaces. These spaces provide opportunities for what Hannah Arendt calls natality, which we interpret as new and unexpected actions that arise in a shared space. Drawing from a range of ideas and experiences of Arendt, bell hooks, Joan Baez, Martha Nussbaum, and music education philosophers and practitioners, we argue that it is important for music educators to make room for this space by becoming more critically aware of (...) their emotions. Opening up to the unexpected in human interactions can at times be difficult and elicit fear. It also calls for a civic love. Cultivating this kind of love includes recognizing that our emotions and matters of the heart are instruments of power that can support or hinder others from becoming actors in their own right. As agents within music education, we can strive to realize this by developing a critical pedagogic consciousness and reflecting on the unexpected and emotional spaces of interaction. (shrink)

Like the human mind, the human body is the medium by which we represent ourselves, whether we are patients or healthcare providers. This paper concerns the significance of understanding the existential phenomenological side of a patient’s body within healthcare. To care for a patient’s body, one needs to be aware of how the body appears to itself, to others, and in a lager environmental reality. We think and feel and observe the world with our body, especially with the brain and (...) nervous system, but also with other dimensions of the body manifesting itself as a somatic tonus. The healthcare providers’ body does not only represent a profession, but also who they are as a person and what kind of environment they are affected by. The same applies to the patients' body. As a tool for experiencing, a tool inseparable from our very being, our physical body functions as a surface open to and in contact with the healthcare environment that surrounds it. In the modern healthcare regime, the human body is nearly always visible and under constant surveillance. In the environment of control and visibility bodies become psychologized and normalized to fit into sociocultural demands of economic adaption, social participation, and communication, which in certain situations seem hostile to the ideology of care, freedom, and humanity. We should realize that all our ethical concepts and norms, even the very notion of humanity that underwrites them, depend on social forms of life involving the ways we experience our bodies in different medical and sociocultural situations. (shrink)