We investigate the “mathematical” strength of the theory I*2. In particular we prove the quadratic reciprocity law and Bertrand's postulate, using fragments of I*2 which employ some well-known number-theoretic functions.

We study the strength (over bounded induction) of axioms expressing particular cases of the Chinese Remainder Theorem with respect to the axiom ∀ x, y∃ z (z = xy).

. We provide an alternative proof of a theorem of P. Clote concerning end extensions of models of $\Sigma_n$ -induction, for $n \geq 2$.

We study problems of Clote and Paris, concerning the existence of end extensions of models of Σ n -collection. We continue the study of the notion of ‘Γ-fullness’, begun by Wilkie and Paris (Logic, Methodology and Philosophy of Science VIII (Moscow, 1987). Stud. Logic Found. Math., vol. 126, pp. 143–161. North- Holland, Amsterdam, 1989) and introduce and study a generalization of it, to be used in connection with the existence of Σ n -elementary end extensions (instead of plain end extensions). (...) We obtain (a) alternative proofs of results (Adamowicz in Fund. Math. 136, 133–145, 1990) and (Wilkie and Paris in Logic, Methodology and Philosophy of Science VIII (Moscow, 1987). Stud. Logic Found. Math., vol. 126, pp. 143–161. North-Holland, Amsterdam, 1989) related to the problem of Paris and (b) a partial solution to the problem of Clote. (shrink)

Analyse: Le penseur chinois Wang Chong (27-97?) fut souvent considéré comme un auteur hétérodoxe, voire anti-confucianiste, tant en Chine ancienne qu'au XXe siècle.

The relation between peace-oriented politics and theology will be discussed from a philosophical point of view by approaching the problem in five steps. In a first step, I will focus on logic as one of the most powerful and simultaneously misleading forces in our thinking. Utilising the results of this step will, secondly, enable a clarification of the misunderstanding implied in an idea such as eternal peace. Thirdly, the article will unveil the paradoxical character of violence inherent in the notion (...) of political power as well as the antinomy of war and peace. This will open the space for accepting second-best solutions. In so doing at least some of the problems implied in any philosophical contribution to a political theology of pacifism may be solved. (shrink)

A useful logic in which to specify normative system behaviour, deontic logic has a broad spectrum of possible applications within the field: from legal expert systems to natural language processing, database integrity to electronic contracting and the specification of fault-tolerant software.

The theory of evolution has provided an historical outlook for the science of biology and has demonstrated that all living organisms on earth are kin to one another - be this kinship distant or close - that they all have their origin in the simple protoplast, and that the living world is a continual, historical entity. Every branch of the science of biology is permeated with the idea of evolution, and each branch has made contributions to the theory of evolution. (...) The theory of evolution is like a strand of red thread running through the entire science of biology. (shrink)

When making decisions, governments can and should strive consciously to balance the demands of the present with the needs of future generations. Various advocates for greater governmental foresight have created new processes or institutions within existing systems of democratic government. These include long-range planning departments, futures commissions, impact statements on proposed legislation, environmental protection agencies, and formal technology assessment. But, much more remains to be done. Based on their extensive scholarly and practical experience, the contributors to this volume propose a (...) variety of techniques that will enable foresight to be effectively incorporated into governmental institutions and practices. (shrink)

Mongolian philosophy on governance aiming at reforming Mongolian society; transliterated from old Mongolian into Cyrillic.

译自: Philosophy and sociology of science: an introduction/Stewart Richards. -- 英国: Blackwell, 1983.

Actualmente, la reflexión sobre la imagen se centra mayoritariamente sobre su masiva presencia y su interminable reproducción. En este trabajo nos centraremos, a la inversa, en cómo las imágenes se destruyen masiva y sistemáticamente. Si el examen interdisciplinar es una prerrogativa fundamental en los estudios visuales, el volumen Striking Images, Iconoclasms Past and Present (Ashgate 2013), compilado por excelentes históricos y arqueólogos, ofrece a los filósofos un modelo importante de colaboración a la hora de pensar qué son las imágenes. El (...) propósito de este trabajo es presentar y discutir brevemente algunos aspectos originales de estos ensayos, enfatizando la importancia de los distintos modos y motivos por los que nuestros antepasados no solo han creado, sino también han destruido imágenes. Distinguiendo la iconoclasia del simple vandalismo, podemos descubrir una ambigüedad fundamental según la cual quien intenta preservar las imágenes, acaba con destruirlas y quien aparece como destros antepasados no solo han tructor, logra fertilizar nuevas concepciones y significados para su propia tradición figurativa. Quizás esta ambigüedad no sea algo que las imágenes sufren desde fuera, sino que sea algo connatural a la imagen misma. Y si es así, quien hoy estudia la vida de las imágenes, quizás podría encontrar un acceso privilegiado en esa a través una lógica paradójica que destaca como las imágenes mueren. PALABRAS CLAVESICONOCLASIA, ICONOFÍLIA, FILOSOFÍA Y TEORÍA DE LAS IMÁGENES, ESTUDIOS VISUALES.ABSTRACTContemporary thought on images focuses mostly on their massive presence and their endless reproduction. On the contrary, in this paper, I will focus on how images have been massively and systematically destroyed. If the interdisciplinary exam is a fundamental prerogative in visual studies, the volume Striking Images, Iconoclasms Past and Present (Ashgate 2013), compiled by excellent historians and archaeologists, could offer to philosophers an important frame of teamwork in thinking what the images are. The purpose of this paper is to present and discuss briefly some original aspects of these essays, by emphasizing the importance of means and reasons through which our ancestors have not only created, but also destroyed images. Once distinguished iconoclasm and mere vandalism, we could discover a fundamental ambiguity whereby any person who tries to preserve the images, finishes with wrecking them; while on the contrary somebody who appears as a destroyer, succeeds to fertilize new concepts and meanings for his/her own figurative tradition. Perhaps this ambiguity is not something that image suffers extrinsically, but something inherent to the image itself. And if it is so, he/she who wants to study the life of images, could perhaps find a privileged access to it, through a paradoxical logic that explains, instead, how images die.KEYWORDSICONOCLASM, ICONOPHILIA, PHILOSOPHY AND THEORY OF IMAGES, VISUAL STUDIES. (shrink)

Dos eventos, aparentemente distantes uno del otro y sin vínculos directos entre ellos, pero sin embargo estrictamente relacionados por un legado espiritual común, constituyen el tema de este trabajo. El primero, tuvo lugar en 1971, cuando una «capilla ecuménica» muy especial abrió sus puertas al público. Es conocida bajo el nombre de «Rothko Chapel», debido al proyecto general, realizado por el pintor Mark Rothko. Desde entonces, se ha convertido en una de las obras de arte más valiosas que representan la (...) estética religiosa contemporánea. Las pinturas negras de Rothko, la planta del edificio de «cruz griega» diseñado por el arquitecto Philip Johnson, el obelisco del artista Barnett Newman y la música compuesta para este ambiente por el compositor Morton Feldman, han reemplazado lo que tradicionalmente ha sido llamado «imago templi»; pero, contrariamente a toda tradición cristiana, representan nada (literalmente: no-thing). El segundo evento, tuvo lugar en 1795, cuando dos jóvenes amigos, Hegel y Schelling, estaban haciendo una especie de juramento bajo el signo de una Iglesia Invisible, actualizando un concepto ambiguo que, incluso arraigándose en las Sagradas Escrituras, ya había sido condenado por las iglesias oficiales por sus consecuencias heréticas. La relación entre estos dos eventos está dada por historiadores del arte moderno que han establecido que la pintura abstracta, desde un punto de vista formal, tiene sus raíces en la tradición romántica. Con este trabajo me gustaría contribuir al establecimiento de esta conexión, no solo por medios formales, sino también mostrando una actitud espiritual común hacia las imágenes. El cristianismo, esencialmente figurativo en su estética religiosa, siempre ha tenido que lidiar con la prohibición judía de la creación de imágenes. Esta dificultad ha sido trasferida a los debates contemporáneos en los que artistas con lecturas y educación clásicas, a menudo de origen judío pero activos en sociedades cristianas, intentan crear un nuevo tipo de arte, fuera de toda tradición y sin dogmas. Según mi sugerencia, Rothko Chapel debería considerarse como la realización de un equilibrio frágil en el que tanto el «aniconismo» como la «necesidad de imágenes» han superado su mutua unilateralidad, produciendo una etapa espiritual más elevada. Por lo tanto, tal capilla no sería un simple espacio donde todas las religiones podrían solo reunirse y dialogar, pero debería considerarse algo más sorprendente, es decir, una realización única de lo que lógicamente aparece como una pura contradicción: la realización de un Imago Templi para una Iglesia Invisible.Key words: Rothko; Hegel; Arte Abstracto; Idealismo; Iglesia Invisible. (shrink)

Two events, apparently distant one from the other and without any direct link between them, but nevertheless strictly connected by a common spiritual legacy, constitute the subject of this paper. The first one, took place in 1971, when a very special «ecumenical chapel» opened its doors to the public. It is known under the name of «Rothko Chapel», due to the general project, undertaken by the painter Mark Rothko. Since that time, it has become one of the most precious artworks (...) that represent the contemporary religious aesthetics. The black Rothko’s paintings, the Greek-cross building designed by the architect Philip Johnson, the Broken Obelisk of the artist Barnett Newman standing right out of the Chapel and the music composed for this ambient by the composer Morton Feldman, have replaced what traditionally has been called an «imago templi»; but contrary to all Christian tradition they represent (literally) no-thing. The second event, took place in 1795, when two young friends, Hegel and Schelling, were making a kind of oath under the sign of an Invisible Church, actualizing an ambiguous concept that, even if rooted in the Holy Scriptures, it had been condemned for its consequences as heretical. The relationship between these two events is given by contemporary art historians which have established that modern abstract painting, from a formal point of view, is rooted in the Romantic tradition. With this paper I would like to contribute to the establishment of this connection, not only by formal means, but by showing a common spiritual attitude towards images. Christianity, essentially figurative in its religious aesthetics, has always had to deal with the Jewish prohibition of image-making. This difficulty has been inherited to contemporary debates in which artist with classical readings and education, often of Jewish origins but active in Christian societies, try to create a new kind of art, above all traditions and free of dogmas. According to my suggestion, Rothko Chapel should be considered as the realization of a fragile balance in which both «aniconism» and «need of images» have simultaneously sublated their one-sidedness, producing a higher spiritual stage. Thus, such a chapel would not be a simple space where all religions could only meet and undertake a dialog, but should be considered as something more surprising: a unique realization of what logically appears as a pure contradiction: the realization of an Imago Templi for an Invisible Church. (shrink)

A very special kind of feast belongs to the Christian Orthodox tradition: there is a specific liturgical celebration of the Images in the so-called Sunday of Orthodoxy. While in many cultures images are employed in order to celebrate an historic event, this is the only feast in which, on the contrary, images are celebrated for themselves. Nonetheless, the role of images in Orthodoxy is not univocally and positively accepted. In fact, the title’s expression.the wolf as a shepherd. belongs to a (...) Desert Father and refers to the role of images in our mental life. This is not reported by a heretical iconoclastic document, but by the well-known Philokalia, a kind of handbook of Orthodox Aesthetics. This paper aims to present these two aspects in their paradoxical partnership. First, I will present some historical, symbolic and liturgical aspects of this feast. Thus, we should be able to understand better why many contemporary authors claimed that the origins of our visual culture can be traced in this Feast. However, if we comprehend the philosophical value of Byzantine icons, we realise that they have little to do with our contemporary images, no matter whether we mean artistic, religious or media images. We often talk about the.power of images., but just to blame them -as if they were autonomous entities- or to praise them, in a generalized aestheticization of contemporary life. Iconophobia and iconodoulia, I claim, are emerging as ontologically impoverished versions of the former Byzantine theoretical models. What falls into oblivion is the paradoxical status of the image as.appearance of the essence of Being. that demands as a condition of its own existence its self-sublation. These dialectics, conceptually inspired by the Hegelian logic, are fully present in Byzantine Aesthetics, where the feast is considered as a precarious image, held in memory of a future image-loss event known as eschaton. (shrink)

Designed to be used on its own or with its companion text, Ultimate Questions: Thinking About Philosophy 3e, this collection of readings covers the major topic areas in philosophy: Knowledge; Free Will; Personal Identity; Mind/Body; God; Ethics; and Political Philosophy. While focusing primarily on contemporary philosophy, it also includes many of the classic works essential to an introductory course.

This print textbook is available for students to rent for their classes. The Pearson print rental program provides students with affordable access to learning materials, so they come to class ready to succeed. For courses in Introductory Philosophy An active approach to philosophy While most introduction to philosophy courses focus on reading philosophical texts, Ultimate Questions: Thinking about Philosophy pushes students toward an active learning approach. The text is designed to instigate meaningful discussions between students and instructors, relying on more (...) than 100 "Food for Thought" exercises throughout. These exercises are based on the author's own experience engaging students in lecture environments and are designed to help students discover how well they understand philosophical concepts and how to apply them to real-life scenarios. The 4th Edition has been extensively updated with a new chapter, chapter expansions, and more. (shrink)