We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...) Bos and Laugwitz seek to explore Eulerian methodology, practice, and procedures in a way more faithful to Euler’s own. Euler’s use of infinite integers and the associated infinite products are analyzed in the context of his infinite product decomposition for the sine function. Euler’s principle of cancellation is compared to the Leibnizian transcendental law of homogeneity. The Leibnizian law of continuity similarly finds echoes in Euler. We argue that Ferraro’s assumption that Euler worked with a classical notion of quantity is symptomatic of a post-Weierstrassian placement of Euler in the Archimedean track for the development of analysis, as well as a blurring of the distinction between the dual tracks noted by Bos. Interpreting Euler in an Archimedean conceptual framework obscures important aspects of Euler’s work. Such a framework is profitably replaced by a syntactically more versatile modern infinitesimal framework that provides better proxies for his inferential moves. (shrink)

The first half of the 17th century was a time of intellectual ferment when wars of natural philosophy were echoes of religious wars, as we illustrate by a case study of an apparently innocuous mathematical technique called adequality pioneered by the honorable judge Pierre de Fermat, its relation to indivisibles, as well as to other hocus-pocus. André Weil noted that simple applications of adequality involving polynomials can be treated purely algebraically but more general problems like the cycloid curve cannot be (...) so treated and involve additional tools–leading the mathematician Fermat potentially into troubled waters. Breger attacks Tannery for tampering with Fermat’s manuscript but it is Breger who tampers with Fermat’s procedure by moving all terms to the left-hand side so as to accord better with Breger’s own interpretation emphasizing the double root idea. We provide modern proxies for Fermat’s procedures in terms of relations of infinite proximity as well as the standard part function. (shrink)

Researchers and technologists involved in the development of weapon systems can take their work to such extremes as to cause unplanned injury or death to others and lasting damage to the environment, reviewed here. In some cases innocent human casualties and ecological harm may actually be programmed and achieved. An analysis is proffered, attributing blame, and indicating efforts to correct the situation. The ethics involved are “complexified”, moral boundaries are exceeded, and humanity is transgressed as it develops solutions to the (...) problem. The license to make mistakes becomes more limited with the passing of the years.. (shrink)

Weapons of both defense and offense have grown steadily in their effectiveness—especially since the industrial revolution. The mass destruction of humanity, by parts or in whole, became reality with the advent of toxic agents founded on chemistry and biology or nuclear weapons derived from physics. The military’s new non-combat roles, combined with a quest for non-lethal weapons, may change the picture in regard to conventional defense establishments but are unlikely to deter bellicose tyrants or the new terrorists from using the (...) unlimited potential of today’s and tomorrow’s arsenals. The author addresses the issues that are raised by this developing situation with the intent of seeking those ethics that will enable us to survive in a future and uncertain world. (shrink)

This book explores the thought of Jacques Derrida as it relates to the tradition of apophatic thought--negative theology and philosophy--in both Western and Eastern traditions. Following the Introduction by Toby Foshay, two of Derrida's essays on negative theology, Of an Apocalyptic Tone Newly Adopted in Philosophy and How to Avoid Speaking: Denials, are reprinted here. These are followed by essays from a Western perspective by Mark C. Taylor and Michel Despland, and essays from an Eastern perspective by David Loy, (...) a Buddhist, and Harold Coward, a Hindu. In the Conclusion, Jacques Derrida responds to these discussions. (shrink)

Traiter de la figure du Christ revient à interroger Dieu. Cette démarche peut réunir théologiens et littéraires autour du même objet ; la création romanesque, libre par essence si on se réfère à la théorie des genres, ne peut toutefois s’écarter des fondements du message évangélique sous peine de n’être prise au sérieux par personne. À travers l’analyse de quatre romans contemporains – que Jésus parle lui-même, se révèle dans la contemplation par autrui ou provoque les interrogations fondamentales autour de (...) sa résurrection –, apparaît l’image de Celui qui toujours se révèle de manière indirecte, dans le questionnement des hommes de bonne volonté. (shrink)

Este trabajo presenta una propuesta para la investigación y la enseñanza de la parasitología. La Metodología de los Programas de Investigación Científica está basada en la metodología de Imre Lakatos. El “núcleo tenaz” del programa en parasitología es “las características de comportamiento alimenticio de los hospedadores explica y predice la fauna de endoparásitos que ellos albergan “. Las hipótesis auxiliares del cinturón protector son: i) hipótesis de los ciclos biológicos y ii) hipótesis del desarrollo de comunidades de parásitos. Las pre-condiciones (...) iniciales necesarias para el establecimiento de la relación parásitohospedador son: a) existencia del parásito potencial, b) existencia del hospedador potencial y c) existencia del biotopo potencial. Se discute el papel de las anomalías y se sugieren modificaciones al tratamiento hecho por Lakatos. Creemos que las anomalías no deben archivarse y acumularse hasta que la comunidad científica comience a dudar y cuestionar el núcleo tenaz. Es mejor que el científico resuelva cada anomalía a medida que se le van presentando, pudiedo resultar en el futuro en caminos insospechables para el trabajo teórico y empírico, y de esta manera aumentar el poder predictivo y explicativo del programa. En definitiva esto estará aumentando el “contenido experimental” del programa.This paper presents a theoretical methodological proposal for research and teaching in parasitology. The Methodology of Scientific Research Program, , presented here is based on I. Lakatos’ methodology. The “hard core” in parasitology is: the characteristics of the trophic behavior of hosts explain and forecast the parasitic fauna which they harbour. The following hypotheses form the hard core’s safety belt of the auxiliary hypotheses: 1. the hypothesis of the biological cycles; 2. the hypothesis of parasite community development. The necessary initial physical pre-conditions for the establishment of a host-parasite relation are: a.- the existence of a potential parasite; b- the existence of a potential host, and c - the existence of a potential biotope. The role of anomalies in the development of any MSRP is discussed and a modification of Lakatos’ treatment is suggested. We believe that anomalies should not be set aside until they accumulate to the point where the scientific community begins to doubt their basic hard core. It is better for the scientist to resolve each controversial event as soon as it emerges since these events, may, in the future, give rise to unsuspected paths of theoretical and empiricalwork, or even improve and widen the predictive and explicative power of the MSRP itself. This, in brief, would deepen the “experimental content” of the program. (shrink)

The Cambridge Companion to Piaget provides a comprehensive introduction to different aspects of Jean Piaget's work.

Of laws in general -- Of laws directly derived from the nature of government -- Of the principles of the three kinds of government -- That the laws of education ought to be relative to the principles of government -- That the laws given by the legislator ought to be relative to the nature of government -- Consquences of the principles of different governments, with respect to the simplicity of civil and criminal laws, the form of judgements, and inflicting of (...) punishments -- Consquences of the different principles of the three governments, with respect to sumptuary laws, luxury, and the condition of women -- Of the corruption of the principles of the three governments -- Of the laws in the relation they bear to defensive force -- Of laws, in the relation they bear to offensive force. (shrink)

In recent decades we witnessed ongoing debates about the objectives of history education, with different underlying epistemological perspectives. This qualitative study explored prospective history teachers' beliefs about these objectives of history education. Prospective history teachers of six universities starting a teacher educational programme were invited to answer an open-ended questionnaire about history education. Six objectives were found: (1) memorising; (2) critical/explanatory; (3) constructivist; (4) perspective-taking; (5) moral; and (6) collective-identity objectives. Almost all prospective teachers mentioned several of these objectives. A (...) distinction between two epistemological perspectives on historical knowledge representation (factual or interpretive), was used as a framework for categorising the different objectives. More than half of the respondents mentioned objectives of history education that represent history as factual and objectives that represent history as interpretive. We propose that in actual practice most history teachers are combining epistemologically opposing objectives for pedagogical, political and religious motives. (shrink)

L'originalite du present recueil reside surtout dans le fait qu'il reflete dans toute sa diversite le champ mondial de l'attention philosophique au langage. Au lieu de se confiner dans un territoire particulier - que ce soit celui de l'hermeneutique allemande ou celui de l'analytisme anglo-saxon par exemple - il s'offre, tout au contraire, comme espace de confrontation authentiquement philosophique (et non de debat technique a l'interieur d'une ecole ou d'une tendance) dans lequel des pensees des langages se cotoient et se (...) rencontrent venues des horizons les plus heterogenes (informatique, theologique, hermeneutique, analytique, pragmatique, ideologique,...). Cette riche diversite manifeste aussi l'extraordinaire interet de la pensee contemporaine pour le langage, interet qui fonde peut-etre la veritable specificite de la philosophie du XXe siecle. (shrink)

Abstract.In Islam, the acquisition of knowledge is a form of worship. But human achievement must be exercised in conformity with God's will. Warnings against feelings of superiority often are coupled with the command to remain within the confines of God's laws and limits. Because of the fear of arrogance and disregard of the balance created by God, any new knowledge or discovery must be applied with careful consideration to maintaining balance in the creation. Knowledge must be applied to ascertain equity (...) and justice for all of humanity. Research in Islam must be linked to the broad ethical base set forth in the Qur'an and the Sunnah. Whether embryonic stem cell research or cloning is ethically acceptable in Islam depends on the benefits derived from such applications. What is most important for the scholars is to adhere to the concepts of compassion, mercy, and benefit to everyone. (shrink)

A collection of personal narratives and essays, Living Professionalism is designed to help medical students and residents understand and internalize various aspects of professionalism. These essays are meant for personal reflection and above all, for thoughtful discussion with mentors, with peers, with others throughout the health care provider community who care about acting professionally.