Through an in-depth analysis of the notes that Leibniz made while reading Pascal’s manuscript treatise on conic sections, we aim to show the real extension of what he called “hexagrammum mysticum”, and to highlight the main results he achieved in this field, as well as proposing plausible proofs of them according to the methods he seems to have developed.

In 1813, J.-V. Poncelet discovered that if there exists a polygon of n-sides, which is inscribed in a given conic and circumscribed about another conic, then infinitely many such polygons exist. This theorem became known as Poncelet’s porism, and the related polygons were called Poncelet’s polygons. In this article, we trace the history of the research about the existence of such polygons, from the “prehistorical” work of W. Chapple, of the middle of the eighteenth century, to the modern approach of (...) P. Griffiths in the late 1970s, and beyond. For reasons of space, the article has been divided into two parts, the second of which will appear in the next issue of this journal. (shrink)

In this paper we discuss in some depth the main theorems pertaining to Carnot’s theory of transversals, their initial reception by Servois, and the applications that Brianchon made of them to the theory of conic sections. The contributions of these authors brought the long-forgotten theorems of Desargues and Pascal fully to light, renewed the interest in synthetic geometry in France, and prepared the ground from which projective geometry later developed.

Published here, and discussed, are some manuscripts and a letter of Sophie Germain concerning her work on Fermat’s Last theorem. These autographs, held at Bibliothèque Nationale of Paris, at the Moreniana Library of Florence and at the University Library of Göttingen, contribute to a substantial revaluation of her work on this subject.

This is an attempt to explain Kepler’s invention of the first “non-cone-based” system of conics, and to put it into a historical perspective.

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 paper, we try to understand what considerations and possible sources of inspiration Desargues used to formulate his concepts of involution and transversal, and to state the related theorems that are at the basis of his Brouillon project. To this end, we trace some clues which are found scattered throughout his works, we connect them together in the light of his experience and knowledge in the field of perspective, and we investigate what were his motivations within Mersenne’s academy. As (...) a result of our research, we can safely say that were his great geometrical insight and his projective vision of space which, guided by some classical theorems, led him to these completely new concepts in the panorama of the geometry of that time that were destined to remain misunderstood for about two centuries. (shrink)

The first part of the article appeared in the previous issue of this journal. It deals with the history of the research on Poncelet’s porism, and related subjects, which were developed from the middle of the eighteenth century until the end of the nineteenth century. In this second part, we take the research developed in the twentieth century. We also offer a comparison of the main works on the subject, and we draw some conclusions.

To solve the direct problem of central forces when the trajectory is an ellipse and the force is directed to its centre, Newton made use of the famous Lemma 12 (Principia, I, sect. II) that was later recognized equivalent to proposition 31 of book VII of Apollonius’s Conics. In this paper, in which we look for Newton’s possible sources for Lemma 12, we compare Apollonius’s original proof, as edited by Borelli, with those of other authors, including that given by Newton (...) himself. Moreover, after having retraced its editorial history, we evaluate the dissemination of Borelli's edition of books V-VII of Apollonius’s Conics before the printing of the Principia. (shrink)

In this paper, we describe the genesis of Boscovich’s Sectionum Conicarum Elementa and discuss the motivations which led him to write this work. Moreover, by analysing the structure of this treatise in some depth, we show how he developed the completely new idea of “eccentric circle” and derived the whole theory of conic sections by starting from it. We also comment on the reception of this treatise in Italy, and abroad, especially in England, where—since the late eighteenth century—several authors found (...) inspiration in Boscovich’s work to write their treatises on conic sections. (shrink)

This paper publishes the correspondence between S. Germain and C.F. Gauss. The mathematical notes enclosed in her letters are published for the first time. These notes, in which she submitted some of her results, proofs and conjectures to Gauss for his evaluation, were inspired by her study of the Disquisitiones Arithmeticae. The interpretation of these mathematical notes not only shows how deeply she went into Gauss’s treatise and mastered it long before any other mathematician, but also, more importantly, shows that (...) she obtained interesting results in the theory of power residues that have never previously been attributed to her. (shrink)

According to the actualist view, what is essential to the truth conditions of a future-tensed sentence ‘it will be the case that ϕ’ is reference to the unique course of events that will become actual. On the other hand, the modal view has it that the truth conditions of such a sentence require that the truth of ϕ be already “settled” at the time of utterance, where “being settled at time t” is defined by universal quantification over a domain of (...) courses of events, the futures compatible with what has happened up to time t. On the proposal we discuss in this paper, the actualist view and the modal view are seen as two related attitudes that speakers can have when they evaluate future-tensed sentences, and the corresponding interpretations undergo a unified semantic treatment based on a contextual notion of settledness. A central feature of our approach is a dynamic view of contexts of utterance, whereby the world of the utterance is not fixed once and for all, as different worlds, by the passing of time, can play this role in turn. Finally, one major goal of the paper is to show how the unified analysis we propose accounts for a particularly interesting interpretation of future-tensed sentences, often referred to as ‘epistemic reading’. (shrink)

In this paper, we describe the genesis of Boscovich’s Sectionum Conicarum Elementa and discuss the motivations which led him to write this work. Moreover, by analysing the structure of this treatise in some depth, we show how he developed the completely new idea of “eccentric circle” and derived the whole theory of conic sections by starting from it. We also comment on the reception of this treatise in Italy, and abroad, especially in England, where—since the late eighteenth century—several authors found (...) inspiration in Boscovich’s work to write their treatises on conic sections. (shrink)

Business Ethics: A European Review, EarlyView.

The study here is a qualitative research based on multiple case studies of banking service providers to analyze the role of corporate social responsibility (CSR) in the definition of the corporate identity of these kinds of organizations. The results show that, although companies increasingly integrate CSR into their business strategies, there are some aspects of its management such as its communication or the measurement of its results that detract from its success. These results have important implications for those managers pursuing (...) an effective management of CSR policies and strategies in their organizations, especially as the information comes from 6 of the biggest and most important banking institutions in a European country, with a declared assets (loans) volume which represents 62.75% of the total assets in the national banking industry, and thus largely representing the possible heterogeneity of the market in terms of company size, location, legal status, and management styles. (shrink)

The authors describe the intensity and orientation of the corporate social responsibility reporting in four Spanish industries and explore the relationship that exists between both concepts and an independent measurement of reputation for CSR. The results demonstrate that the CSR reporting is especially relevant and useful in the finance industry. Finance companies report significantly more CSR information than most industries in Spain, and this reporting is more closely linked to their CSRR than the CSR reporting of basic, consumer goods and (...) services industries. (shrink)

Because previous scholars have offered few comprehensive models to understand the benefits of corporate social responsibility image in terms of customer behaviour, the authors of this paper propose a hierarchy of effects model to study how customer perceptions of the social responsibility of companies influence customer affective and conative responses in a service context. The authors test a structural equation model using information collected directly from 1,124 customers of banking services in Spain. The findings demonstrate that corporate social responsibility image (...) influences customer identification with the company, the emotions evoked by the company and satisfaction positively. Identification also influences the emotions generated by the service performance and customer satisfaction determines loyalty behaviour. The findings have significant implications for service managers because they demonstrate that there are two paths to explain the satisfaction and loyalty of service customers. The first path is composed of the beliefs and emotions generated by the company at the institutional level. The second path is composed of the thoughts, attitudes, emotions and feelings generated by the company’s services. (shrink)

Although research on the corporate social responsibility (CSR) dimension of corporate image has notably increased in recent years, the definition and measurement of the concept for academic purposes still concern researchers. In this article, literature regarding the measurement of CSR image from a customer viewpoint is revised and areas of improvement are identified. A multistage method is implemented to develop and to validate a reliable scale based on stakeholder theory. Results demonstrate the reliability and validity of this new scale for (...) measuring customer perceptions regarding the CSR performance of their service providers. With regard to this, CSR includes corporate responsibilities towards customers, shareholders, employees and society. The scale is consistent among diverse customer cohorts with different gender, age and level of education. Furthermore, results also confirm the applicability of this new scale to structural equation modelling. (shrink)

Does the Ship of Theseus present a genuine puzzle about persistence due to conflicting intuitions based on “continuity of form” and “continuity of matter” pulling in opposite directions? Philosophers are divided. Some claim that it presents a genuine puzzle but disagree over whether there is a solution. Others claim that there is no puzzle at all since the case has an obvious solution. To assess these proposals, we conducted a cross-cultural study involving nearly 3,000 people across twenty-two countries, speaking eighteen (...) different languages. Our results speak against the proposal that there is no puzzle at all and against the proposal that there is a puzzle but one that has no solution. Our results suggest that there are two criteria—“continuity of form” and “continuity of matter”— that constitute our concept of persistence and these two criteria receive different weightings in settling matters concerning persistence. (shrink)

This book looks at the ways in which conditionals, an integral part of philosophy and logic, can be of practical use in computer programming. It analyzes the different types of conditionals, including their applications and potential problems. Other topics include defeasible logics, the Ramsey test, and a unified view of consequence relation and belief revision. Its implications will be of interest to researchers in logic, philosophy, and computer science, particularly artificial intelligence.

Internationally recognized logicians present current thinking on the understanding of the role of deduction in human reasoning.

This paper provides several examples of how modal logic can be used in studying the XML document navigation language XPath. More specifically, we derive complete axiomatizations, computational complexity and expressive power results for XPath fragments from known results for corresponding logics. A secondary aim of the paper is to introduce XPath in a way that makes it accessible to an audience of modal logicians.

Since at least Hume and Kant, philosophers working on the nature of aesthetic judgment have generally agreed that common sense does not treat aesthetic judgments in the same way as typical expressions of subjective preferences—rather, it endows them with intersubjective validity, the property of being right or wrong regardless of disagreement. Moreover, this apparent intersubjective validity has been taken to constitute one of the main explananda for philosophical accounts of aesthetic judgment. But is it really the case that most people (...) spontaneously treat aesthetic judgments as having intersubjective validity? In this paper, we report the results of a cross‐cultural study with over 2,000 respondents spanning 19 countries. Despite significant geographical variations, these results suggest that most people do not treat their own aesthetic judgments as having intersubjective validity. We conclude by discussing the implications of our findings for theories of aesthetic judgment and the purpose of aesthetics in general. (shrink)

Recently, organizational identity is being given more attention than ever before in the business world. This notion has grown substantially in importance in the hospitality industry. Facing increased competition, hospitality companies are driven to project a positive image to their stakeholders. Therefore, these organizations have begun to develop new organizational identity programs as part of their strategies to achieve their desired identities. This study analyzes the role of corporate social responsibility in the definition of the Organizational Identity of these organizations, (...) employing a qualitative research methodology based on an illustrative case study. Particularly, the authors analyze the case of Meliá Hotels International, a leading hotel company in Spain with a presence in 27 countries. The findings indicate that the company has formally integrated CSR into its strategy to align its actual identity with its desired and conceived identity in view of the critics in its local community. Moreover, the interest of the firm toward its stakeholders suggests that the company understands its conceived identity as an important link in understanding its organizational identity. This paper demonstrates that firm’s organizational identity is a set of several elements. When analyzing Meliá Hotels International’s identity, we see that the firm defines this concept as that which is most central, enduring, and distinctive about the organization. In this sense, the company appears to follow the vision-driven approach by referring to the organizational mission and vision statements, organizational philosophy, and core values as the basis of organizational identity. (shrink)

Philosophers have long debated whether, if determinism is true, we should hold people morally responsible for their actions since in a deterministic universe, people are arguably not the ultimate source of their actions nor could they have done otherwise if initial conditions and the laws of nature are held fixed. To reveal how non-philosophers ordinarily reason about the conditions for free will, we conducted a cross-cultural and cross-linguistic survey (N = 5,268) spanning twenty countries and sixteen languages. Overall, participants tended (...) to ascribe moral responsibility whether the perpetrator lacked sourcehood or alternate possibilities. However, for American, European, and Middle Eastern participants, being the ultimate source of one’s actions promoted perceptions of free will and control as well as ascriptions of blame and punishment. By contrast, being the source of one’s actions was not particularly salient to Asian participants. Finally, across cultures, participants exhibiting greater cognitive reflection were more likely to view free will as incompatible with causal determinism. We discuss these findings in light of documented cultural differences in the tendency toward dispositional versus situational attributions. (shrink)

In the remainder of this article, we will disarm an important motivation for epistemic contextualism and interest-relative invariantism. We will accomplish this by presenting a stringent test of whether there is a stakes effect on ordinary knowledge ascription. Having shown that, even on a stringent way of testing, stakes fail to impact ordinary knowledge ascription, we will conclude that we should take another look at classical invariantism. Here is how we will proceed. Section 1 lays out some limitations of previous (...) research on stakes. Section 2 presents our study and concludes that there is little evidence for a substantial stakes effect. Section 3 responds to objections. The conclusion clears the way for classical invariantism. (shrink)

El presente artículo plantea, partiendo de las vivencias de padres oyentes ante la llegada de un hijo sordo a partir de sus narraciones y experiencias de vida, por un lado, la comprensión de las etapas por las que atraviesan desde el momento en que se sospecha la existencia de la discapacidad de su hijo, hasta el momento en que es confirmada y asumida; por otro lado, describir los cambios que se producen al interior de la dinámica familiar ante la llegada (...) de un hijo en situación de discapacidad auditiva. (shrink)

El objetivo del artículo es analizar la percepción que tienen los estudiantes de contaduría pública sobre pruebas estandarizadas del Estado, antes de su titulación, permitirá a su vez establecer si dicha percepción influye en el desempeño.Se utiliza la metodología mixta con una perspectiva de tipo descriptiva, que se basó en una revisión documental sobre modelos de evaluación, diseñando un instrumento con una muestra de 99 participantes de último grado.Se concluye una reducción en puntajes frente a competencias genéricas; comprensión lectora, matemáticas (...) e inglés, lo cual busca una mejora continua desde el punto de vista investigativo y formativo. (shrink)

This article examines whether people share the Gettier intuition (viz. that someone who has a true justified belief that p may nonetheless fail to know that p) in 24 sites, located in 23 countries (counting Hong Kong as a distinct country) and across 17 languages. We also consider the possible influence of gender and personality on this intuition with a very large sample size. Finally, we examine whether the Gettier intuition varies across people as a function of their disposition to (...) engage in “reflective” thinking. (shrink)

As systems based on opaque Artificial Intelligence (AI) continue to flourish in diverse real-world applications, understanding these black box models has become paramount. In response, Explainable AI (XAI) has emerged as a field of research with practical and ethical benefits across various domains. This paper not only highlights the advancements in XAI and its application in real-world scenarios but also addresses the ongoing challenges within XAI, emphasizing the need for broader perspectives and collaborative efforts. We bring together experts from diverse (...) fields to identify open problems, striving to synchronize research agendas and accelerate XAI in practical applications. By fostering collaborative discussion and interdisciplinary cooperation, we aim to propel XAI forward, contributing to its continued success. Our goal is to put forward a comprehensive proposal for advancing XAI. To achieve this goal, we present a manifesto of 27 open problems categorized into nine categories. These challenges encapsulate the complexities and nuances of XAI and offer a road map for future research. For each problem, we provide promising research directions in the hope of harnessing the collective intelligence of interested stakeholders. (shrink)

Is behavioral integration a necessary feature of belief in folk psychology? Our data from over 5,000 people across 26 samples, spanning 22 countries suggests that it is not. Given the surprising cross-cultural robustness of our findings, we argue that the types of evidence for the ascription of a belief are, at least in some circumstances, lexicographically ordered: assertions are first taken into account, and when an agent sincerely asserts that p, nonlinguistic behavioral evidence is disregarded. In light of this, we (...) take ourselves to have discovered a universal principle governing the ascription of beliefs in folk psychology. (shrink)

This volume has 41 chapters written to honor the 100th birthday of Mario Bunge. It celebrates the work of this influential Argentine/Canadian physicist and philosopher. Contributions show the value of Bunge’s science-informed philosophy and his systematic approach to philosophical problems. The chapters explore the exceptionally wide spectrum of Bunge’s contributions to: metaphysics, methodology and philosophy of science, philosophy of mathematics, philosophy of physics, philosophy of psychology, philosophy of social science, philosophy of biology, philosophy of technology, moral philosophy, social and political (...) philosophy, medical philosophy, and education. The contributors include scholars from 16 countries. Bunge combines ontological realism with epistemological fallibilism. He believes that science provides the best and most warranted knowledge of the natural and social world, and that such knowledge is the only sound basis for moral decision making and social and political reform. Bunge argues for the unity of knowledge. In his eyes, science and philosophy constitute a fruitful and necessary partnership. Readers will discover the wisdom of this approach and will gain insight into the utility of cross-disciplinary scholarship. This anthology will appeal to researchers, students, and teachers in philosophy of science, social science, and liberal education programmes. 1. Introduction Section I. An Academic Vocation Section II. Philosophy Section III. Physics and Philosophy of Physics Section IV. Cognitive Science and Philosophy of Mind Section V. Sociology and Social Theory Section VI. Ethics and Political Philosophy Section VII. Biology and Philosophy of Biology Section VIII. Mathematics Section IX. Education Section X. Varia Section XI. Bibliography. (shrink)