This article presents the Arabic text of al-Q's short geometric treatise, The Book of the centres of the tangent circles on lines, by the method of analysis, with translation and a mathematical commentary. In this treatise al-Q solves by analysis an ordered set of eight problems where the goal is to locate, on a given line, the centre of a circle which is tangent to two given elements, which may be points, straight lines or circles. For example, (...) in the first problem he wanted to find the centre of a circle which contains two given points. In fact, al-Q establishes the locus of the solutions, and this locus can be a straight line or a conic. The treatise is reminiscent of one of the purposes of al-Q's work on the perfect compass, namely to assign to the conics the status of regular lines. (shrink)

Do there exist real numbers d with d2 = 0? The question is formulated provocatively, to stress a formalist view about existence: existence is consistency, or better, coherence.Also, the provocation is meant to challenge the monopoly which the number system, invented by Dedekind et al., is claiming for itself as THE model of the geometric line. The Dedekind approach may be termed “arithmetization of geometry”.We know that one may construct a number system out of synthetic geometry, as Euclid and (...) followers did : “geometrization of arithmetic”..Starting from the geometric side, nilpotent elements are somewhat reasonable, although Euclid excluded them. The sophist Protagoras presented a picture of a circle and a tangent line; the apparent little line segment D which tangent and circle have in common, are, by Pythagoras' Theorem, precisely the points, whose abscissae d have d2 = 0. Protagoras wanted to use this argument for destructive reasons: to refute the science of geometry.A couple of millenia later, the Danish geometer Hjelmslev revived the Protagoras picture. His aim was more positive: he wanted to describe Nature as it was. According to him, the Real Line, the Line of Sensual Reality, had many nilpotent infinitesimals, which we can see with our naked eyes. (shrink)

The derivative is a basic concept of differential calculus. However, if we calculate the derivative as change in distance over change in time, the result at any instant is 0/0, which seems meaningless. Hence, Newton and Leibniz used the limit to determine the derivative. Their method is valid in practice, but it is not easy to intuitively accept. Thus, this article describes the novel method of differential calculus based on the double contradiction, which is easier to accept intuitively. Next, the (...) geometrical meaning of the double contradiction is considered as follows. A tangent at a point on a convex curve is iterated. Then, the slope of the tangent at the point is sandwiched by two kinds of lines. The first kind of line crosses the curve at the original point and a point to the right of it. The second kind of line crosses the curve at the original point and a point to the left of it. Then, the double contradiction can be applied, and the slope of the tangent is determined as a single value. Finally, the meaning of this method for the foundation of mathematics is considered. We reflect on Dehaene’s notion that the foundation of mathematics is based on the intuitions, which evolve independently. Hence, there may be gaps between intuitions. In fact, the Ancient Greeks identified inconsistency between arithmetic and geometry. However, Eudoxus developed the theory of proportion, which is equivalent to the Dedekind Cut. This allows the iteration of an irrational number by rational numbers as precisely as desired. Simultaneously, we can define the irrational number by the double contradiction, although its existence is not guaranteed. Further, an area of a curved figure is iterated and defined by rectilinear figures using the double contradiction. (shrink)

In this paper, we give a thorough account of Brianchon and Poncelet’s joint memoir on equilateral hyperbolas subject to four given conditions, focusing on the most significant theorems expounded therein, and the determination of the “nine-point circle”. We also discuss about the origin of this very rare example of collaborative work for the time, and the general challenge of finding the nature of the loci described by the centres of the conic sections required to pass through m points and to (...) be tangent to n straight lines given in position, m + n = 4, which was posed at the end of their work. In the case m = 4, i.e. when the conic sections have to pass through the vertices of a quadrilateral, the locus of centres is another conic section passing through the intersection points of the opposite sides and the two diagonals of the quadrilateral, respectively, and, as Gergonne showed analytically shortly after, through other significant points connected with the quadrilateral; this curve was later given the name of the “nine-point conic”, being a natural generalization of the above mentioned circle. (shrink)

In this article, we assess the heuristic power of Greek geometrical analysis by trying to reconstruct some analyses of extant propositions of which only the demonstration is found in the text. We have reconstructed the analysis of the trisection of an angle, the property of the tangent to the parabola, to the hyperbola/ellipse, and to the spiral line. In all of these cases, the results and the demonstrations can be found by the analysis alone, without arguments by analogy (...) with other figures or kinematic considerations. We have thus concluded that analysis is a much more powerful tool than is usually assumed to be. We have also examined a part of Apollonius’ Cutting off of a ratio and confirmed that the number of possible cases to be distinguished in analysis tended to increase because the geometric objects and the magnitudes related to them were always considered in the geometric arrangement in which they appear. We suggest that the absence of an algebraic approach that would have detached the magnitudes from their geometrical context may have been one of the major obstacles to further development of Greek geometry. (shrink)

Summary The conical sundial from the museum Thyrrheion is found to be designed with cardinal parametersgeographical latitude ϕ = arc tan(3/5) = 30°57′50″half cone angle α = arc tan(4/9) = 23°57′45″radius at equinox r0 = 4 unciae = 98.7mm (pes monetalis)position of the cone tip h = 18 unciae = 444.3 mmThe half cone angle is equal to the angle of the ecliptic which leads to the special case of a conical sundial with the associated sphere being tangent at (...) the day line of the winter solstice. The ratio of sides in the generating triangle 4:9 may thus be interpreted as an approximation for the angle of ecliptic.The place of finding (operation) is 10° North of the intended latitude (design). The error of the sundial's indications due to the displacement are analyzed. (shrink)

Abstract.As an undergraduate at Cambridge, Newton entered into his ‘Waste Book’ an assumption that we have named the Equivalence Assumption (The Younger): ‘‘ If a body move progressively in some crooked line [about a center of motion]..., [then this] crooked line may bee conceived to consist of an infinite number of streight lines. Or else in any point of the croked line the motion may bee conceived to be on in the tangent.’’ In this assumption, Newton (...) somewhat imprecisely describes two mathematical models, a ‘‘polygonal limit model’’ and a ‘‘tangent deflected model,’’ for ‘‘one-body motion,’’ that is, for the motion of a ‘‘body in orbit about a fixed center,’’ and then claims that these two models are equivalent. In the first part of this paper, we study the Principia to determine how the elder Newton would more carefully describe the polygonal limit and tangent deflected models. From these more careful descriptions, we then create Equivalence Assumption (The Elder), a precise interpretation of Equivalence Assumption (The Younger) as it might have been restated by Newton, after say 1687. We then review certain portions of the Waste Book and the Principia to make the case that, although Newton never restates nor even alludes to the Equivalence Assumption after his youthful Waste Book entry, still the polygonal limit and tangent deflected models, as well as an unspoken belief in their equivalence, infuse Newton’s work on orbital motion. In particular, we show that the persuasiveness of the argument for the Area Property in Proposition 1 of the Principia depends crucially on the validity of Equivalence Assumption (The Elder). After this case is made, we present the mathematical analysis required to establish the validity of the Equivalence Assumption (The Elder). Finally, to illustrate the fundamental nature of the resulting theorem, the Equivalence Theorem as we call it, we present three significant applications: we use the Equivalence Theorem first to clarify and resolve questions related to Leibniz’s ‘‘polygonal model’’ of one-body motion; then to repair Newton’s argument for the Area Property in Proposition 1; and finally to clarify and resolve questions related to the transition from impulsive to continuous forces in ‘‘De motu’’ and the Principia. (shrink)

Conversation, talk, the communicative process, can be compared to the symphonic play of a piece of music. There is an orchestra, the musicians, whose tones and notes must flow, complement and harmonize with one another. There is a main theme. As the music builds variations on the theme are played, and new themes and subthemes are introduced. The basinett responds to the strings, the bass emphasizes the mood of the violin, while the french horn adds a new melody. The subtlety (...) and evenness of flow, the seeming simplicity of the piece, the rich interleaving of subdevelopments, variations, tangents, and recapitulations, are what make a piece of music great.Coherent communication is much the same. It looks easy. It flows. It seems effortless. In reality, of course, it is rich and complex, in both form and content. As in music, conversants may begin a conversation slowly, tentatively, with some simple (or complex) topic in mind. Slowly the momentum builds, the connections surface, and the themes become defined. As in music, these themes are then elaborated upon in various ways. Topic elaborations often spawn their own variations. New themes and subthemes are introduced. All the while, as in music, original themes reappear and are interwoven with the new ones. The twists and turns of the conversation seem to occur effortlessly.In music, there is usually one composer in control of which instrument plays next; one composer who is in charge of what the instrument will say. There is a single coordinator of theme introductions, developments, variations, and interweavings. The composition is done off-line and usually involves editing and re-editing for flaws. In discourse, however, we have on-line development with multiple parties responsible for flow coordination. All parties have to organize their own turns, themes, and variations, in addition to their being able to integrate these items into co-conversants'.In their book, “Understanding Computers and Cognition,” Winograd and Flores (1987) cite the following from Gadamer (Winograd and Flores, 1987, p. 32):It is not so much our judgments as it is our prejudices that constitute our being ... the historicity of our existence entails that prejudices, in the literal sense of the word, constitute the initial directedness of our whole ability to experience. Prejudices are biases of our openness to the world. They are simply conditions whereby we experience something — whereby what we encounter says something to us. (Gadamer, Philosophical Hermeneutics, 1976, p. 9). (shrink)

Introduction Conatus is a specific concept within Descartes’s physics. In particular, it assumes a crucial importance in the purely mechanistic description of the nature of light – an issue that Des- cartes considered one of the most crucial challenges, and major achievements, of his natural phil- osophy. According to Descartes’s cosmology, the universe – understood as a material continuum in which there is no vacuum – is composed of a number of separate yet interconnected vortices. Each of these vortices consists (...) in a set of bands rotating around their centres. The bands are com- posed of corpuscles of the three elements, each distinguished on the basis of their different shapes and sizes. The small globules of the second element, although impeded by the other parts of heaven, strive to move away from the centre of the vortex around which they revolve, thus exerting a certain force against the surrounding bodies. This striving or conatus, though a mere force rather than a genuine motion, is transmitted instan- taneously and along straight lines from body to body. According to Descartes, then, the nature of light consists in this striving alone. This account must be understood as strictly connected to the fundamental laws that regulate the Cartesian world. It is particularly important to recall that for Descartes the centrifugal force exerted by a rotating body is understood to be a consequence of the intrinsic rectilinearity of every motion. As the second of the three Laws of Nature set forth in Book II of the Principles of Philosophy establishes, “all motion is in itself rectilinear; and hence any body moving in a circle tends to move away from the centre of the circle which it describes as proved by the fact that a stone rotating in a sling tends to move centrifugally along the tangent of each point described by a circle.1 Similarly, each of the globules of the second element “strives to recede with a great force from the centre of the vortex in which it rotates; it is in fact prevented by the other globules placed all around, not differently than a stone in a sling”. Within this framework, as I show later, conatus occurs when a body’s intrinsic tendency to rectilinear motion is impeded by an external constraint. As Stephen Gaukroger notes, the use of the term conatus in the Principles – like “vis” and “ action ” – shows that Descartes “cannot avoid dynamic terminology”, despite his declared intent “to construe motion in a purely kinematic way”. Indeed, Gaukroger observes that the notions of force action and striving are systematically employed in the Principles – appearing 290, 59 and 8 times, respectively. Also noteworthy, conatus was – together with the more familiar concepts of actio and vis – a significant element of the conceptual apparatus of Scholastic natural philosophy. As will be seen later – and this is the first goal of this paper – here the concept of conatus had a very specific function. Indeed, it was a central part of the Aristotelian- Scholastic account of gravitation. Conatus was used to refer to the striving of a body to move towards its natural place – especially in cases where its natural motion was hindered or impeded by an external mover. This specific use of the concept of conatus can be found in texts on natural philosophy from the end of the sixteenth through the late seventeenth century. Notably, it occurs in some of the late -Scho- lastic texts which held special significance for Descartes’s thought. Therefore, Descartes introduces conatus in a context in which this concept already had a very specific meaning, and one of which he was very probably aware. The possible relations between these two apparently very different con- cepts have therefore to be scrutinized. I thereby propose to undertake a comparison between the Scho- lastic and the Cartesian conceptions of conatus. I hope to show that certain traits of the former are indeed echoed by the latter, although adapted to the much changed physical paradigm of Cartesian physics. In fact, Descartes’s conatus, though sharing some important similarities with the old one, underwent significant transformations in terms of both its meaning and its application. However, I hope to show that these concepts are both used to describe the behaviour of bodies in relation to their intrinsic motive tendency, and in particular when this tendency is impeded or prevented. Such a reconstruction offers two main areas of interest. On an immediate level, it furthers the general efforts of scholars over the past decades to reconstruct the full extent of the relations between Descartes’s thought and Scholastic philosophy. However, there is another significant reason for taking an interest in the ties between the Scholastic and the Cartesian conceptions of conatus. Indeed, the Cartesian conatus must be seen as crucial to a proper understanding of the broader, diverse conceptualization that this idea enjoyed in the thought of many of the most important philosophers of the early modern period, namely Spinoza, Hobbes and Leibniz. In particular, Spinoza, were directly influenced by Descartes in their unique formulations of conatus. Thus a reconstruction of the context in which Descartes formulated his conatus and of its relations to a pre-existing Scholastic conception will enable us to better reconstruct the history of this idea in the early modern period. The paper is structured as follows: in the first part, I provide a thorough review of the Scho- lastic employment of the concept conatus – both its meaning and the extent of its usage. I then show that it occurs in some of the most prominent Cartesian sources. Finally, I shall provide an account of Descartes’s theory of circular motion and conatus with the specific aim of empha- sizing the elements of both continuity and discontinuity that justify the claim that Descartes’s con- ception of conatus is reminiscent of the Scholastic one. (shrink)

This paper deals with the very different attitudes that Descartes and Pascal had to the cycloid—the curve traced by the motion of a point on the periphery of a circle as the circle rolls across a right line. Descartes insisted that such a curve was merely mechanical and not truly geometric, and so was of no real mathematical interest. He nevertheless responded to enquiries from Mersenne, who posed the problems of determining its area and constructing its tangent. Pascal, (...) in contrast, saw the cycloid as a paradigm of geometric intelligibility, and he made it the focus of a series of challenge problems he posed to the mathematical world in 1658. After dealing with some of the history of the cycloid , I trace this difference in attitude to an underlying difference in the mathematical epistemologies of Descartes and Pascal. For Descartes, the truly geometric is that which can be expressed in terms of finite ratios between right lines, which in turn are expressible as closed polynomial equations. As Descartes pointed out, this means that ratios between straight and curved lines are not geometrically admissible, and curves that require them must be banished from geometry. Pascal, in contrast, thought that the scope of geometry included curves such as the cycloid, which are to be studied by employing infinitesimal methods and ratios between curved and straight lines. (shrink)

Este escrito traz uma abordagem sobre a visão de alguns estudantes do ensino fundamental II e do ensino médio de escolas públicas do interior da Bahia, sobre como pensam as suas atuais situações educacionais em meio à pandemia causada pela COVID-19, motivo o qual as aulas presencias foram totalmente suspensas. Sobre o prisma das (im)possibilidades do acesso às TICs pelos estudantes, observamos o possível alargamento das suas autonomias educacionais, bem como impulsionamento de suas posturas critica reflexivas e, a partir destas, (...) a busca pelo empreendimento de suas próprias aprendizagens escolares. Buscamos externar as dificuldades de aprendizado em tempos pandêmicos; as exclusões digitais, cujas discrepâncias tornaram-se mais evidentes mediante a crise ocasionada pelo coronavírus. A partir de abordagem qualitativa e atividade de escuta dos sujeitos colaboradores em seus lugares e contextos, utilizando o instrumento entrevistas on line, buscamos dialogar com alguns autores como (Lemos, 2015); (Nicolaci–da-Costa, 2009); (Lévy 1999); (Silva, 2011); (Freire, 2006); (Amiél, 2018) e com os estudantes, jovens e adolescentes colaboradores buscando traçar uma imagem da realidade tangente a partir da visão destes sujeitos. Palavras -chave: Escola pública. Pandemia. Estudantes. Exclusão digital. Autonomia. (shrink)

We consider a uniform r-bundle E on a complex rational homogeneous space X and show that if E is poly-uniform with respect to all the special families of lines and the rank r is less than or equal to some number that depends only on X, then E is either a direct sum of line bundles or unstable with respect to some numerical class of a line. So we partially answer a problem posted by Muñoz et al.. In (...) particular, if X is a generalized Grassmannian \ and the rank r is less than or equal to some number that depends only on X, then E splits as a direct sum of line bundles. So we improve the main theorem of Muñoz et al. 664:141–162, 2012, Theorem 3.1) when X is a generalized Grassmannian. Moreover, by calculating the relative tangent bundles between two rational homogeneous spaces, we give explicit bounds for the generalized Grauert–Mülich–Barth theorem on rational homogeneous spaces. (shrink)

The kinematic aspects of the rocket-borne clock experiment by Vessot and Levine are analyzed with the revised Robertson's test theory of special relativity (Found. Phys. 14, 625 (1984)). Besides the expected time-dilation, it is found that the intermediate steps of this experiment yield in principle Michelson-Morley type information (a relation between longitudinal and transverse length contractions) in the third order of the velocities involved, but no relativity-of-simultaneity related effects.The flat space-time test theory induces a family of “spherically symmetric” line (...) elements that become the Schwarzschild line element in the relativistic case and also in theabinito rest frame of the theory. These line elements represent the same space-time manifold, but pertain in a one-to-one correspondence to the different flat space-time coordinate transformations of the test theory. The conserved energy is related to the family of local energies in the tangent plane. No deviations from the orthodoxy appear at the pertinent levels of approximation. Hence the unexplained residuals of the Vessot-Levine experiment are not due in obvious ways to kinematic and gravitational frequency shifts caused by deviations of the “real” coordinate transformations from the Lorentz transformations. (shrink)

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)

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)

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.

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).

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)

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)

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)

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)

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)

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)

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)

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)

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)

This special issue aims to help bridge this gap: it provides a flavour of how philosophical translation in particular was conceived in Renaissance Europe. It is also meant to help stimulate a debate concerning the viewpoint of Renaissance practitioners of the art of «interpretation»: when working from Latin or Greek, did they see the activities of translation and vernacularization, for instance, as identical? Did they conceive of “vertical” and “horizontal” translations as separate, according to an influential distinction outlined by Gianfranco (...) Folena? Did they adopt a broadly similar approach to translation, regardless of whether they were dealing with literary, scientific, or religious texts? Did they think of translations as clearly separate from other forms of interpretation, such as paraphrases or other renderings? (shrink)

This special issue aims to help bridge this gap: it provides a flavour of how philosophical translation in particular was conceived in Renaissance Europe. It is also meant to help stimulate a debate concerning the viewpoint of Renaissance practitioners of the art of «interpretation»: when working from Latin or Greek, did they see the activities of translation and vernacularization, for instance, as identical? Did they conceive of “vertical” and “horizontal” translations as separate, according to an influential distinction outlined by Gianfranco (...) Folena? Did they adopt a broadly similar approach to translation, regardless of whether they were dealing with literary, scientific, or religious texts? Did they think of translations as clearly separate from other forms of interpretation, such as paraphrases or other renderings? (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)

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)

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)

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)

This qualitative study examined hospital nurses’ methods in handling meal and nutrition care during inpatient time, with an underlying focus on undernourished older adult. Observations and interviews were used to document nurses’ methods through the span of a transition (defined by an entry, passage, and exit). The study finds inconsistencies in care methods due to institutional processes restricting both mealtime care and nutritional logging of information throughout hospitalization. It is concluded that the consequences of these inconsistencies must be recognized and (...) that new approaches to meals and nutritional care should be introduced in order to provide greater flexibility. Based on the assumption that mobilizing patient resources is pivotal for meal and nutritional care, it is argued that it may be important to mobilize patient resources during mealtime and in nutritional logging of information in order to increase the visibility of meal and nutritional care in patient transitions within the institution and across settings. Both nurses’ methods and institutions developmental initiatives regarding meal and nutritional care need to accommodate the differences between what in this paper is defined as social‐bodily care and text‐based care. This could be met through care methods that take place with, more than for the patient. (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)

This volume challenges readers to think about what music means in contemporary society, and how music education can remain culturally relevant in the new millennium. A collection of thought-provoking philosophical perspectives on music education. Explores the changing ways in which music is being produced, disseminated and received. Considers how current phenomena such as the commoditization of music, the use of new technologies, and access to hybrid music forms, relate to music education. Covers themes such as pragmatism, performativity, cultural identity, emotion, (...) autonomy and globalization. Asks how music teaching and learning can remain culturally relevant. (shrink)