The multiverse hypothesis is growing in popularity among theistic philosophers because some view it as the preferable way to solve certain difficulties presented by theistic belief. In this paper, I am concerned specifically with its application to Rowe’s problem of no best world, which suggests that God’s existence is impossible given the fact that the world God actualizes must be unsurpassable, yet for any given possible world, there is one greater. I will argue that, as a solution to the (...) problem of no best world, the multiverse hypothesis fails. To defend my thesis, I will first define the multiverse hypothesis and articulate the problem of no best world and how the multiverse hypothesis is thought to solve it. I will then show that the solution fails by articulating two problems that have been mentioned, but not developed, in the literature—what I call the problem of no highest standard and the problem of multiverse cardinality. In each case, after articulating the problem, I will offer possible responses to the problem and show why those responses are inadequate. (shrink)

Cardinal Mercier’s Manual of Modern Scholastic Philosophy is a standard work, prepared at the Higher Institute of Philosophy, Louvain, mainly for the use of clerical students in Catholic Seminaries. Though undoubtedly elementary, it contains a clear, simple, and methodological exposition of the principles and problems of every department of philosophy, and its appeal is not to any particular class, but broadly human and universal. Volume I includes a general introduction to philosophy and sections on cosmology, psychology, criteriology, and metaphysics or (...) ontology. (shrink)

Karol Wojtyła found phenomenology very helpful for the analysis of concrete human experience and for overcoming the ethical formalism ofKant. Phenomenology, he believed, could also enrich classical Thomism by exploring the lived experience of freedom, interiority, and self-governance. But phenomenology, in his opinion, needed to be supplemented by metaphysics in order to ground experiences such as the sense of duty in the real order. He criticized much modern philosophy for abandoning metaphysics and thus neglecting the sapiential dimension. Since his career (...) as a professor was very short, he did not have time to complete his project of a personalist Thomism in which phenomenology and metaphysics would be harmoniously combined. (shrink)

'ground-breaking anthology... wide array of perspectives on WW1, from both sides of the fighting' -B. Adler, Choice 'a very fine anthology' -Times Literary SupplementThe First World War inspired a huge outpouring of writing that, until recently, was thought to be almost the exclusive preserve of men. Yet the war also acted as a catalyst which enabled women writers to find a literary and political voice. This anthology bears witness to the great variety and scope of women's writing about the war. (...) Covering the years 1914-1930, the book brings together little-known writing from across the world, drawing on a wide spectrum of genres from letters and diary entries to essays, novels, and short stories. Among the celebrated writers featured in this anthology are: Radclyffe Hall, Sylvia Pankhurst, Maud Gonne, Rebecca West, May Sinclair, Olive Schreiner, Colette, Vera Brittain, Gertrude Stein, Katherine Mansfield, HD, and Virginia Woolf. (shrink)

Cardinal Mercier's A Manual of Modern Scholastic Philosophy is a standard work, prepared at the Higher Institute of Philosophy, Louvain, mainly for the use of clerical students in Catholic seminaries. Though undoubtedly elementary, it contains a clear, simple, and methodological exposition of the principles and problems of every department of philosophy, and its appeal is not to any particular class, but broadly human and universal. Volume I includes a general introduction to philosophy and sections on cosmology, psychology, criteriology, and metaphysics (...) or ontology. Volume II contains sections on natural theology, logic, ethics, and outlines of the history of philosophy. (shrink)

The proposed heavy dependence on Pavlovian conditioning to account for social behavior confounds phylogenically and ontogenically selected behavior patterns and ignores the extension of the principle of selection by consequences from biological to learning theory. Instead of acknowledging operant relations, Domjan et al. construct vaguely specified mechanisms based upon anticipatory cost-benefit considerations that are not supported by the Pavlovian conditioning literature.

Cardinal Mercier’s Manual of Modern Scholastic Philosophy is a standard work, prepared at the Higher Institute of Philosophy, Louvain, mainly for the use of clerical students in Catholic Seminaries. Though undoubtedly elementary, it contains a clear, simple, and methodological exposition of the principles and problems of every department of philosophy, and its appeal is not to any particular class, but broadly human and universal. Volume II contains sections on natural theology, logic, ethics and outlines of the history of philosophy.

Rousseau’s political project consists in ensuring that the citizens of the social contract, in uniting with each other, preserve their ability to self-legislate, or be autonomous. For this to work, however, members of the social contract would need to feel intrinsically linked to the political whole. This essay investigates what that feeling might be and how it can be grown. I argue that Rousseau develops a model of the energy or character of the being capable of autonomy, capable of experiencing (...) themselves as part of the whole. That energy is a pathos of vigour, a strong sentiment and way of being that I develop from Rousseau’s educational precepts in Émile, which makes the citizen feel free and robust in dependence and boundedness. Autonomy, then, comes from the active exercise of oneself, physically and mentally, in an environment bounded by things, and this results in a sentiment of vigour, a vitality that produces confidence and poise, which then entices further activity. (shrink)

Levada, William Cardinal; Ladaria, Luis F The supreme law of the Church is the salvation of souls. As such, throughout its history, the Church has always found the pastoral and juridical means to care for the good of the faithful. With the Apostolic Construction Anglicanorum coetibus, promulgated on 4 November 2009, the Holy Father, Pope Benedict XVI, provided for the establishment of Personal Ordinariates through which Anglican faithful may enter, even in a corporate manner, into full communion with the Catholic (...) Church. On that same date, the Congregation for the Doctrine of the Faith published Complementary Norms relating to such Ordinariates. In conformity with what is established in Art, I and 1 and 2 of the Apostolic Coinstitution Anglicanorum coetibus, having received requests from a considerable number of Anglican faithful, and having consulted with the Australian Catholic Bishops Conference, the Congregation for the Doctrine of the Faith. (shrink)

This paper concerns late 1920 s attempts to construct unitary theories of gravity and electromagnetism. A first attempt using a non-standard connection—with torsion and zero-curvature—was carried out by Albert Einstein in a number of publications that appeared between 1928 and 1931. In 1929, Tullio Levi-Civita discussed Einstein’s geometric structure and deduced a new system of differential equations in a Riemannian manifold endowed with what is nowadays known as Levi-Civita connection. He attained an important result: Maxwell’s electromagnetic equations and the gravitational (...) equations were obtained exactly, while Einstein had deduced them only as a first order approximation. A main feature of Levi-Civita’s theory is the essential use of the Ricci’s rotation coefficients, introduced by Gregorio Ricci Curbastro many years before. We trace the history of Ricci’s coefficients that are still used today, and highlight their geometric and mechanical meaning. (shrink)

Real-life stories from teachers who share their passion for shaping the lives of young people today.

Le terme 'sacrement' a été attribué à l'Église par Vatican II qui en avait retrouvé la signification grâce au récent renouveau de la patristique. Le 'mystère' spécifie traditionnellement tout sacrement. Le mystère fondateur de l'Église-communion en Christ invite aussi à interpréter son essence sans la réduire à n'être qu'une des voies possibles du salut, mais sans lui réserver non plus une exclusivité d'ordre 'physique'. L'Église est structurée selon sa mission de sainteté, sa finalité étant le salut du monde.

In this paper we engage in a conversation speaking from three different perspectives and discuss the ways literature and our personal life experiences can inform policy and practice in relation to the concepts of well-being, education, and culture. We gathered around a metaphorical kitchen table, bringing to it our life experiences, as well as the literature that informed our individual research programs (positive psychology, Indigenous world view, and narrative inquiry) and we began to unpack the questions: “What role does culture (...) play in understanding and educating for well-being and why should an education system be concerned about it?”. (shrink)

Thus emerges the paradox of All Israel's destiny. Some of the children of Israel gathered in a state like all others—no more and no less and this is legitimate and necessary. This state was founded by the children of the People whom God called not to be like the others, but, rather for the others, because of His design for universal salvation. What is true for the people who have settled in this state which was recreated for the Jews, is (...) true for the members, of the Jewish people who are dispersed throughout the Diaspora as citizens of various countries. But this vocation to testify is in the hands of God, and not in the power of man. The destiny of Israel is that its destiny overtakes it over and over. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy of Music Education Review 12.1 (2004) 89-93 [Access article in PDF] Richard Shusterman, Performing Live: Aesthetic Alternatives for the Ends of Art (New York: Cornell University Press, 2000) Performing Live can be ascribed to post-modern American pragmatism in its widest expression. The author's intention is to revalue aesthetic experience, as well as to expand its realm to the extent where such experience also encompasses areas alien to traditional (...) aesthetics (for example, popular art or the somatic arts of self-improvement), reaching "the art of living" and reclaiming life itself as performance.After the introduction, titled "Aesthetic Renewal for the Ends of Art: An Overture," the text is organized in two main parts: "Aesthetic Experience and Popular Art" and "Soma, Self, and Society." Along with its ambitious title, the book's organization and structure promise a consistency of approach and narrative that somewhat dissolves during the reading. Shusterman recognizes that the stylistic problems that arise from a compilation of articles spanning ten years, mixing newly written and revised articles, but appeals to the reader's appreciation of the "quality of the mix" (11). Despite this feature, he is a lucid and thoughtful communicator and his writing style is excellent.In order to propose new or revitalized alternatives for the ends of art, Shusterman [End Page 89] explores the crisis in traditional visions of art, pointing to the compartmentalization and lack of credibility in current artistic thought and practice. Hegel, Walter Benjamin, Gianni Vattimo, and Arthur Danto provide him with the philosophical arguments accounting for the modern "exhaustion" of art. He supports a dialectical approach, both naturalistic and historicist, and builds a solid case for the possibility of alternatives in aesthetic thought and experience. He proposes two alternatives in his introduction: The two most prominent sites for today's aesthetic alternatives are clearly the mass-media popular arts and the complex cluster of disciplines devoted to bodily beauty and the art of living as expressed in today's preoccupation with aesthetic lifestyles. (7) It is unclear why these alternatives are "clearly" "the two most prominent." The author does not build a case for this assumption or for the "newness" of these alternatives. The "compilation style" mentioned above and this lack of justification for one of the most original elements in the book make this text often read as a philosophical drafting board. Keeping these characteristics in mind and also critically pondering the degrees of success in the enterprise, the reader must give Shusterman credit for taking risks while suggesting concrete examples for an experiential, holistic philosophy. In this sense, he mentions (in a different context) that "all of us [are caught] between conceptual history and futuristic speculation" (145), and he takes to heart this situation and its challenges.The first chapter in Performing Live aims to redeem or revalue the concept of aesthetic experience. For Shusterman, the loss of "felt experience" in art makes the interest in this concept utterly relevant for art's survival. He traces the lineage of this aesthetic philosophy to John Dewey, Monroe Beardsley, Nelson Goodman, and Arthur Danto. Besides focusing on these authors, his analysis revisits some of the main currents of thought in Western philosophy on the topic (for example, Plato, Hume, Kant, Dickie, Adorno, Benjamin, Gadamer). He concludes that a pragmatic approach to aesthetics, applying the concept of aesthetic experience directionally (as a means towards the actual experience rather than as a definable concept), can provide new paths for revitalizing art. Throughout the text this concept is also used expansively. The post-modern justification of the proposed aesthetics, by allowing the extension of aesthetic experience to embrace "the art of living," can leave the reader wondering if Shusterman has not simply turned Kierkegaard's existentialist stages to self-realization upside down.The second chapter is an open defense of popular art, carried out by contesting the main complaints found in current art criticism. Shusterman's defense is not directed to the products of popular art, but against the claim that popular art is aesthetically "worthless." His definition of "popular art... (shrink)

Quelles politiques linguistiques vont le mieux permettre de mettre en valeur les avantages du bilinguisme et l'apprentissage des langues tout en favorisant la pérennité des langues minoritaires à l'ère de la mondialisation? Cet article tente de répondre à la question en basant son propos sur l'exemple des politiques d'aménagement linguistique du Canada et du Québec. Il montre que la mondialisation linguistique exerce une pression supplémentaire sur un équilibre déjà fragile entre les francophones et les anglophones au Canada et il suggère (...) de réviser les principes actuels afin d'assurer la pérennité du français, notamment au Québec.What language policies will best help highlight the benefits of bilingualism and language learning while promoting the sustainability of minority languages ​​in the era of globalization? This article attempts to answer the question, basing his remarks on the example of language planning policies of Canada and Quebec. It shows that linguistic globalization puts additional pressure on already fragile balance between Francophones and Anglophones in Canada and suggested revising the current principles in order to ensure the sustainability of the French, especially in Quebec. (shrink)

In Balcony in the Forest, Julien Gracq composes a soundscape in four dimensions: he establishes an undulating background by involving spatial events; he forms temporal figures by involving material affects—spatial events and material affects extracted from depths before being enveloped by a resonant place. Each of the four dimensions has a particular relationship to the sounds of power and the power of sound, and it is up to the reader to decide whether the soundscape composed in and by the writing (...) makes this double... (shrink)

Nicholas of Cusa (1401-1464), a student of canon law who became a Catholic cardinal, was widely considered the most important original philosopher of the Renaissance. He wrote principally on theology, philosophy, and church politics. This volume makes most of Nicholas's other writings on Church and reform available in English for the first time.

The March 2002 symposium Human Dignity and Reproductive Technology brought together philosophers, theologians, scientists, lawyers, and scholars from across the United States. The essays of this book are the contributions of the symposium's participants.

The essays in this volume were written when John Henry Newman was a Fellow of Oriel College, Oxford. He wrote the first, on biblical miracles "The Miracles of Scripture," in 1825-26, as a relatively young man; the other, "The Miracles of Early Ecclesiastical History," was written in 1842-43. A comparison of the two essays displays a shift in Newman's theological stances. In the earlier essay, Newman argues in accordance with the theology of evidence of his time, maintaining that the age (...) of miracles was limited to those recorded in the Old Testament scriptures and in the Gospels and Acts. He asserts that biblical miracles served to demonstrate the divine inspiration of biblical revelation and to attest to the divinity of Christ. However, with the end of the apostolic age, the age of miracles came to an end; miracles reported from the early ages of the Church Newman dismissed as suspicious and possibly fraudulent. With this view, Newman entered into an ongoing debate between the skepticism of Hume and Paine and its continuation in the utilitarianism of Bentham, on the one hand, and the views of Christian apologists rebutting Hume's arguments, on the other. In "The Miracles of Early Ecclesiastical History," Newman can be seen as coming closer to accepting the doctrines of the Catholic Church. He rejects the stance he took in "The Miracles of Scripture," now arguing for a continuity of sacred history between the biblical and ecclesiastical periods. He had clearly abandoned the position of "evidence theologians" that miracles ended after the time of the Apostles. Newman's movement between the writing of the two essays is essentially a growing into a deeper awareness of the Church as a divine society in whose life miracles and supernatural gifts were to be expected. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy of Music Education Review 12.1 (2004) 89-93 [Access article in PDF] Richard Shusterman, Performing Live: Aesthetic Alternatives for the Ends of Art (New York: Cornell University Press, 2000) Performing Live can be ascribed to post-modern American pragmatism in its widest expression. The author's intention is to revalue aesthetic experience, as well as to expand its realm to the extent where such experience also encompasses areas alien to traditional (...) aesthetics (for example, popular art or the somatic arts of self-improvement), reaching "the art of living" and reclaiming life itself as performance.After the introduction, titled "Aesthetic Renewal for the Ends of Art: An Overture," the text is organized in two main parts: "Aesthetic Experience and Popular Art" and "Soma, Self, and Society." Along with its ambitious title, the book's organization and structure promise a consistency of approach and narrative that somewhat dissolves during the reading. Shusterman recognizes that the stylistic problems that arise from a compilation of articles spanning ten years, mixing newly written and revised articles, but appeals to the reader's appreciation of the "quality of the mix" (11). Despite this feature, he is a lucid and thoughtful communicator and his writing style is excellent.In order to propose new or revitalized alternatives for the ends of art, Shusterman [End Page 89] explores the crisis in traditional visions of art, pointing to the compartmentalization and lack of credibility in current artistic thought and practice. Hegel, Walter Benjamin, Gianni Vattimo, and Arthur Danto provide him with the philosophical arguments accounting for the modern "exhaustion" of art. He supports a dialectical approach, both naturalistic and historicist, and builds a solid case for the possibility of alternatives in aesthetic thought and experience. He proposes two alternatives in his introduction: The two most prominent sites for today's aesthetic alternatives are clearly the mass-media popular arts and the complex cluster of disciplines devoted to bodily beauty and the art of living as expressed in today's preoccupation with aesthetic lifestyles. (7) It is unclear why these alternatives are "clearly" "the two most prominent." The author does not build a case for this assumption or for the "newness" of these alternatives. The "compilation style" mentioned above and this lack of justification for one of the most original elements in the book make this text often read as a philosophical drafting board. Keeping these characteristics in mind and also critically pondering the degrees of success in the enterprise, the reader must give Shusterman credit for taking risks while suggesting concrete examples for an experiential, holistic philosophy. In this sense, he mentions (in a different context) that "all of us [are caught] between conceptual history and futuristic speculation" (145), and he takes to heart this situation and its challenges.The first chapter in Performing Live aims to redeem or revalue the concept of aesthetic experience. For Shusterman, the loss of "felt experience" in art makes the interest in this concept utterly relevant for art's survival. He traces the lineage of this aesthetic philosophy to John Dewey, Monroe Beardsley, Nelson Goodman, and Arthur Danto. Besides focusing on these authors, his analysis revisits some of the main currents of thought in Western philosophy on the topic (for example, Plato, Hume, Kant, Dickie, Adorno, Benjamin, Gadamer). He concludes that a pragmatic approach to aesthetics, applying the concept of aesthetic experience directionally (as a means towards the actual experience rather than as a definable concept), can provide new paths for revitalizing art. Throughout the text this concept is also used expansively. The post-modern justification of the proposed aesthetics, by allowing the extension of aesthetic experience to embrace "the art of living," can leave the reader wondering if Shusterman has not simply turned Kierkegaard's existentialist stages to self-realization upside down.The second chapter is an open defense of popular art, carried out by contesting the main complaints found in current art criticism. Shusterman's defense is not directed to the products of popular art, but against the claim that popular art is aesthetically "worthless." His definition of "popular art... (shrink)

Issues surrounding transsexualism, especially when surgical operations have been performed to achieve the desired sex, can create serious problems for canon law. After an examination of how sex is determined, the author provides a clear explanation of transsexualism and then differentiates it from hermaphroditism, homosexuality, and transvestitism. Transsexualism’s effect on the liciety of marriage is analyzed, followed by an exploration of considerations regarding transsexualism and Holy Orders. Finally, transsexualism and the vowed religious life are examined. The author encourages those faced (...) with such situations to pursue solutions that preserve, as well as possible, the good of the patient and their community, as well as the Church. National Catholic Bioethics Quarterly 14.1 : 105–118. (shrink)

The present article, which was originally the keynote presentation on August 12, 2004, at the annual conference of the Venerable John Henry Newman Association at Mundelein, Illinois, traces the stages of Newman’s view of the hierarchy from the time of his involvement in the Oxford Movement to his post-conciliar reflections about the teaching of the First Vatican Council.Newman’s theology of the hierarchy, which cannot be understood apart from the controversies which engaged him, is, from a present-day perspective, both “stimulating and (...) problematic.”. (shrink)

Cardinal Etchegaray argues here that the dialogue between church and state, with both parties rooted in sometimes conflicting absolute claims and values, has become more recently a wider-ranging dialogue between the church and a pluralist, relativist liberal society. The very definition of “liberal society” is open to argument, and the church may find elements to commend or oppose in any given definition. Since the nineteenth century the church has often found itself in opposition to various ideas of “liberty,” especially those (...) that represent an idolatry of absolute rights that push aside Christian spiritual and moral concerns. Now that liberalism has become the pervasive model for society, the church finds it may more easily express its critique, with the aim of making society more conducive to allowing people to become fully human. Indeed, the church provides a necessary check on the excesses of liberal society, particularly those of capitalism and democratic populism. Its essential point is the transcendent dimension of the human person—our connection with the divine. The pursuit of economic and political ends needs to be governed by a concern for the ethical, itself founded on the divine. Liberal society will only live up to its own highest aspirations through promoting self-mastery and an awareness that humanity’s freedom is ultimately found only in God. (shrink)

This article, originally the concluding chapter of Cardinal Dulles’ recent book on Newman’s theology, provides an insightful discussion of Newman’s relevance for today by comparing his theological thought with a series of themes that were subsequently treated by the Second Vatican Council (1962-65): from revelation and faith, scripture and tradition, and the development of doctrine, to questions of ecclesiology, especially infallibility, the role of the laity, and social-political issues.“After nearly two centuries, the writings of Newman continue to have a very (...) modern ring,” Dulles writes. (shrink)

The aim of this work was to compare experimental investigations on effects of lidocaine, calcium and, BRL 34915 on reentries to simulated data obtained by use of a model of propagation based on the Huygens' constriction method already described in previous works. Calcium and lidocaine effects are investigated on anisotropic conduction conditions. In both cases, reduction in conduction velocities are observed. In lidocaine case, a refractory area is located along the longitudinal axis. In agreement with experimental electrical mapping, the simulations (...) show that the stabilization of reentrant excitation is mainly due to the existence of this refractory area around which the reentrant circuit can develop. The experimental study shows that BRL 34915 has both arrhythmogenic and antiarrhythmic effects. A detailed electrophysiological analysis has shown that drug infusion act on normal cardiac cells by decreasing the relative and absolute refractory period. BRL 34915 action is simulated by a decrease in the refractory period showing that the time frequency of the reentrant activity is increased and that the spatial size where the reentry is developing is becoming smaller. These two effects are arrhythmogenic, the simulated data being so in good agreement with the experimental ones. (shrink)

Résumé : Cet article s’inscrit dans le cadre d’un programme de recherche portant sur les liens entre les missions d’instruction et de socialisation de l’école québécoise à travers l’enseignement de diverses matières scolaires. Les premiers résultats de la recherche ont montré que pour les enseignants, la construction de l’identité de l’élève a beaucoup plus d’importance que la construction de l’identité collective. Cependant, le processus de subjectivation identifié ne signifie pas pour autant qu’il n’y ait plus aucune transmission ou production de (...) « valeurs » ou de « références » communes dans l’enseignement des différentes matières. Par exemple, dans l’enseignement de l’histoire et éducation à la citoyenneté, la construction de l’identité individuelle et celle de l’identité collective sont en continuelle tension. Cependant, l’identité collective ne passe plus tant par le canal d’une mémoire identitaire ou d’un récit national que par la promotion d’une modernité articulée au pluralisme, à la critique, à la rationalité intersubjective et, paradoxalement, à la subjectivation précédemment évoquée. L’article portera donc particulièrement sur cette tendance observée au sein de l’enseignement du cours d’histoire et éducation à la citoyenneté. Abstract : This paper is part of a research program about the links between the missions of instruction and socialization of the Quebec school by the teaching of different school subjects. The first results of this research showed that for teachers, the construction of the identity of the student is much more important than the construction of collective identity. However, the process of subjectivation identified not mean that there is no more transmission or production of «values» or «references» common in teaching different school subjects. For example, in the teaching of history and citizenship education, construction of individual identity and the collective identity are in constant tension. However, the collective identity does not pass anymore by the way of a memory or a national story, but by the promotion of modernity articulated with pluralism, criticism, intersubjective rationality and, paradoxically, the subjectivation previously mentioned. This paper will therefore especially on this trend in the teaching of the course of history and citizenship education. (shrink)

Résumé : L’actuel programme d’« Histoire et éducation à la citoyenneté » pour le 2e cycle du secondaire, portant sur l’histoire du Québec, a suscité depuis 2006 de nombreux commentaires dans les milieux intellectuels en raison de son contenu. Certains affirment que la transmission des grands événements historiques qui structurent la mémoire collective ou nationale y est inexistante, d’autres soutiennent qu’il doit favoriser le développement des compétences critiques et citoyennes, donc, l’autonomie de l’élève face à la mémoire collective ou nationale. (...) Quelle position les enseignants du secondaire occupent-ils dans ce débat ? Il est possible de le découvrir par l’entremise de la perception qu’ils se font du programme et de ses trois compétences. Abstract: The current program «History and Citizenship Education» for the second cycle of secondary education, on the Quebec history, raised many comments in intellectual circles because of its content since 2006. Some argue that the transmission of major historical events that shape the collective or national memory is non-existent, others argue that it should promote the development of critical thinking and citizenship skills, thus the autonomy of the student facing the memory collective or national. What position secondary teachers do they have in this debate? It’s findable out through the teachers perceptions about program and its three skills. (shrink)

The purpose of this valuable book is to consider recent cultural trends in bioethics from a Catholic perspective. Bioethics is intended for a lay audience interested in understanding bioethical issues from a Catholic perspective.

This volume explores how Catholicism began and continues to open its doors to the wider world and to other confessions in embracing ecumenism, thanks to the vision and legacy of the Second Vatican Council. It explores such themes as the twentieth century context preceding the council; parallels between Vatican II and previous councils; its distinctively pastoral character; the legacy of the council in relation to issues such as church-world dynamics, as well as to ethics, social justice, economic activity. Several chapters (...) discuss the role of women in the church before, during, and since the council. Others discern inculturation in relation to Vatican II. The book also contains a wide and original range of ecumenical considerations of the council, including by and in relation to Free Church, Reformed, Orthodox, and Anglican perspectives. Finally, it considers the Council’s ongoing promise and remaining challenges with regard to ecumenical issues, including a groundbreaking essay on the future of ecumenical dialogue by Cardinal Walter Kasper. (shrink)

Resumen: Este artículo presenta un acercamiento al cuento “El Aleph” de Jorge Luis Borges a partir del tema de los universos paralelos desde dos perspectivas, el concepto matemático de transinfinito y la observación de lo cotidiano. Siguiendo la jerarquía del multiverso de Max Tegmark, se propone extender su contenido filosófico definiendo cómo “El Aleph” argumenta la idea de multiverso. Por un lado, el cuento de Borges es capaz de reflejar el estado espacio-temporal abigarrado de otros universos simultáneos que coexisten con (...) el propio y, por otro lado, puede comprimir toda esa complejidad en su mínima representación, el punto. Este colapso de lo complejo a lo simple en el cuento de Borges demuestra que la percepción de otras realidades, de otros universos, yace en la aparente insignificancia de lo cotidiano.: This article presents an approach to the short story “The Aleph” by Jorge Luis Borges based on the parallel universes subject from two perspectives, the mathematical concept of transfinite, and the everyday life observation. Following Max Tegmark’s hierarchy of the multiverse, it is set out to extend its philosophical content by defining how “The Aleph” argues the idea of the multiverse. On the one hand, this short story is capable of reflecting the motley spatio-temporal state of other simultaneous coexisting universes and, on the other hand, it can compress all its complexity into the simplest figure for its representation, the point. This collapse from the complex to the simple in Borges’ short story shows that the perception of other realities, of other universes, lies in the apparent insignificance of the everyday life. (shrink)

In the Zermelo–Fraenkel set theory (ZF), |$|\textrm {fin}(A)|<2^{|A|}\leq |\textrm {Part}(A)|$| for any infinite set |$A$|⁠, where |$\textrm {fin}(A)$| is the set of finite subsets of |$A$|⁠, |$2^{|A|}$| is the cardinality of the power set of |$A$| and |$\textrm {Part}(A)$| is the set of partitions of |$A$|⁠. In this paper, we show in ZF that |$|\textrm {fin}(A)|<|\textrm {Part}_{\textrm {fin}}(A)|$| for any set |$A$| with |$|A|\geq 5$|⁠, where |$\textrm {Part}_{\textrm {fin}}(A)$| is the set of partitions of |$A$| whose members are finite. (...) We also show that, without the Axiom of Choice, any relationship between |$|\textrm {Part}_{\textrm {fin}}(A)|$| and |$2^{|A|}$| for an arbitrary infinite set |$A$| cannot be concluded. (shrink)

We write and for the cardinalities of the set of finite sequences and the set of finite subsets, respectively, of a set which is of cardinality. With the axiom of choice (), for every infinite cardinal but, without, any relationship between and for an arbitrary infinite cardinal cannot be proved. In this paper, we give conditions that make and comparable for an infinite cardinal. Among our results, we show that, if we assume the axiom of choice for sets of (...) finite sets, then for every Dedekind‐infinite cardinal and the condition that is Dedekind‐infinite cannot be weakened to weakly Dedekind‐infinite. (shrink)