After the publication of Begriffsschrift, a conflict erupted between Frege and Schröder regarding their respective logical systems which emerged around the Leibnizian notions of lingua characterica and calculus ratiocinator. Both of them claimed their own logic to be a better realisation of Leibniz’s ideal language and considered the rival system a mere calculus ratiocinator. Inspired by this polemic, van Heijenoort (1967b) distinguished two conceptions of logic—logic as language and logic as calculus—and presented them as opposing views, but did not explain (...) Frege’s and Schröder’s conceptions of the fulfilment of Leibniz’s scientific ideal. -/- In this paper I explain the reasons for Frege’s and Schröder’s mutual accusations of having created a mere calculus ratiocinator. On the one hand, Schröder’s construction of the algebra of relatives fits with a project for the reduction of any mathematical concept to the notion of relative. From this stance I argue that he deemed the formal system of Begriffsschrift incapable of such a reduction. On the other hand, first I argue that Frege took Boolean logic to be an abstract logical theory inadequate for the rendering of specific content; then I claim that the language of Begriffsschrift did not constitute a complete lingua characterica by itself, more being seen by Frege as a tool that could be applied to scientific disciplines. Accordingly, I argue that Frege’s project of constructing a lingua characterica was not tied to his later logicist programme. (shrink)

Recent historical studies have investigated the first proponents of methodological structuralism in late nineteenth-century mathematics. In this paper, I shall attempt to answer the question of whether Peano can be counted amongst the early structuralists. I shall focus on Peano’s understanding of the primitive notions and axioms of geometry and arithmetic. First, I shall argue that the undefinability of the primitive notions of geometry and arithmetic led Peano to the study of the relational features of the systems of objects that (...) compose these theories. Second, I shall claim that, in the context of independence arguments, Peano developed a schematic understanding of the axioms which, despite diverging in some respects from Dedekind’s construction of arithmetic, should be considered structuralist. From this stance I shall argue that this schematic understanding of the axioms anticipates the basic components of a formal language. (shrink)

In contemporary historical studies, Peano is usually included in the logical tradition pioneered by Frege. In this paper, I shall first demonstrate that Frege and Peano independently developed a similar way of using logic for the rigorous expression and proof of mathematical laws. However, I shall then suggest that Peano also used his mathematical logic in such a way that anticipated a formalisation of mathematical theories which was incompatible with Frege’s conception of logic.

In contemporary historical studies, Peano is usually included in the logical tradition pioneered by Frege. In this paper, I shall first demonstrate that Frege and Peano independently developed a similar way of using logic for the rigorous expression and proof of mathematical laws. However, I shall then suggest that Peano also used his mathematical logic in such a way that anticipated a formalisation of mathematical theories which was incompatible with Frege’s conception of logic.

It is well known that the formal system developed by Frege in Begriffsschrift is based upon the distinction between function and argument—as opposed to the traditional distinction between subject and predicate. Almost all of the modern commentaries on Frege's work suggest a semantic interpretation of this distinction, and identify it with the ontological structure of function and object, upon which Grundgesetze is based. Those commentaries agree that the system proposed by Frege in Begriffsschrift has some gaps, but it is taken (...) as an essentially correct formal system for second-order logic: the first one in the history of logic. However, there is strong textual evidence that such an interpretation should be rejected. This evidence shows that the nature of the distinction between function and argument is stated by Frege in a significantly different way: it applies only to expressions and not to entities. The formal system based on this distinction is tremendously flexible and is suitable for making explicit the logical structure of contents as well as of deductive chains. We put forward a new reconstruction of the function-argument scheme and the quantification theory in Begriffsschrift. After that, we discuss the usual semantic interpretation of Begriffsschrift and show its inconsistencies with a rigorous reading of the text. (shrink)

In Begriffsschrift, Frege presented a formal system and used it to formulate logical definitions of arithmetical notions and to deduce some noteworthy theorems by means of logical axioms and inference rules. From a contemporary perspective, Begriffsschrift’s deductions are, in general, straightforward; it is assumed that all of them can be reproduced in a second-order formal system. Some deductions in this work present—according to this perspective—oddities that have led many scholars to consider it to be Frege’s inaccuracies which should be amended. (...) In this paper, we continue with the analysis of Begriffsschrift’s logic undertaken in an earlier work and argue that its deductive system must not be reconstructed as a second-order calculus. This leads us to argue that Begriffsschrift’s deductions do not need any correction but, on the contrary, can be explained in coherence with a global reading of this work and, in particular, with its fundamental distinction between function and argument. (shrink)

"Mille Plateaux (Paris, Éditions de Minuit, 1980) est le second des deux volumes ayant pour sous-titre Capitalisme et schizophrénie issu de la collaboration entre le philosophe Gilles Deleuze et le philosophe et psychanalyste Félix Guattari. Cet ouvrage continue à explorer par des voies inédites - en s'attaquant notamment à une série d'erreurs afférentes selon les auteurs à l'arborescence, à l'État, au langage... - la question déjà avancée dans L'Anti-Œdipe (premier volume) d'une ontologie révolutionnaire des devenirs ("presque imperceptibles") qui ne cessent (...) de défaire l'histoire des identités ("primauté des lignes de fuite") et de produire des "coups" imprévisibles au sociologue et au militant. Sans doute le livre politique de Deleuze et Guattari le plus important, grâce à sa conception originale du pluralisme (l'individu n'y est pas conçu comme fondement de l'organisation sociale : les subjectivités sociales sont toujours au-dessus ou en dessous du niveau de l'individu, composant et décomposant des collectivités de toutes sortes)"--Wikipedia = Mille Plateaux (Paris: Editions de Minuit, 1980) is the second of two volumes which comes in the series of Capitalism and Schizophrenia is a result of collaboration between the philosopher Gilles Deleuze and Felix Guattari, philosopher and psychoanalyst. This book continues to explore new paths - including addressing a series of errors by the authors related to the tree, the state, the language... - that are already dealt with in Anti-Oedipus (first volume) of an ontology of revolutionary futures; the latter continues to unravel the history of identities ("primacy of lines of flight") and produce "coups" unforeseeable to the sociologist and activist. No doubt the political book of Deleuze and Guattari's is the most important, with its original conception of pluralism (the individual is not conceived as the foundation of social organization: social subjectivities are always above or below of the individual level, composing and decomposing communities of all kinds).". (shrink)

Selon une psychologie empiriste, aucune vie mentale inconsciente n'existe ; la conscience devrait être vue comme intérieure au sujet. Au contraire, la psychologie idéaliste soutient une philosophie de l'inconscient (et non pas de l'inconscience). La multiplicité et la finalité ne sont pas représentables comme des produits de l'évolution ou du destin des individus ; notre image du monde est conscience du monde. Nietzsche (1874), le premier, réagit contre cette thèse ; il y voit un tourbillon de consciences étroites : "l'homme (...) historique qui se laisse transformer en miroir historique." La psychologie idéaliste tendrait-elle vers une idolâtrie de l'histoire ? Il nous semble qu'une éthique et une philosophie sociale idéalistes, bâties sur les principes du droit, aident à former des hypothèses plausibles, notamment celle d'une solidarité inconsciente. L'expérience moniste d'unité entre notre représentation et notre volonté peut plaider pour une compréhension du monde sur le terrain de valeurs axiologiques, sans maladie historique. Elle explique une soif universelle de culture et de religion. Réexaminons l'utilité et l'inconvénient d'élargir la reconnaissance réciproque des sujets, vers un don de soi au monde. (shrink)

Los trabajos que aquí se presentan ofrecen una gran panorámica sobre la reflexión en torno a la vida humana y vienen a continuación de los expuestos en el libro Dimensiones de la vida humana tal como las ofrece la antropología española. Ahora se abordan esas dimensiones desde tres vertientes diferenciadas, la historia, la literatura y la hermenéutica. La vida humana es plural y así son también las vistas sobre ella. Un primer conjunto de textos trata de la imagen del ser (...) humano en diversos momentos de la historia de la filosofía. Un segundo grupo nos acerca a la reflexión filosófica que se da en la literatura, ya que los escritores exploran las posibilidades de la vida humana, con lo que sus creaciones son un excelente mirador que el antropólogo filósofo no puede ignorar. Por último aparece un bloque de investigaciones que se centran en la hermenéutica -con una importante presencia de Paul Ricoeur- y en M. Merleau-Ponty, con motivo de su centenario en 2008. La cantidad de trabajos aquí recogidos es una buena muestra de los estudios que sobre antropología filosófica se están realizando en nuestro país. Cada texto es una ventana abierta que permite una mirada sobre el ser humano, sobre su imagen o sus imágenes. Sobre los autores: Javier San Martín, catedrático de Filosofía en la UNED, ha centrado su investigación en la fenomenología, antropología filosófica y filosofía de Ortega y Gasset. Tomás Domingo Moratalla, profesor de Ética en la Universidad Complutense de Madrid, se ha centrado en la filosofía de Paul Ricoeur, la antropología filosófica y la filosofía práctica en clave hermenéutica. (shrink)

Antropología y filosofía Los textos aquí reunidos son sólo pensamientos en voz alta, a la vez que propuestas para pensar, que más que aportar soluciones presentan problemas. Todos son textos programáticos, sin pretensión dogmática, dirigidos a mostrar que la reflexión científica sobre el ser humano pide, si ha de ser auténtica, su continuidad en la filosofía.

Collected articles on Burmese linguistic and literature.

On the qualities considered to be negative in a woman as per Islamic teachings.

For each natural number n, let C(n) be the closed and unbounded proper class of ordinals α such that Vα is a Σn elementary substructure of V. We say that κ is a C(n)-cardinal if it is the critical point of an elementary embedding j : V → M, M transitive, with j(κ) in C(n). By analyzing the notion of C(n)-cardinal at various levels of the usual hierarchy of large cardinal principles we show that, starting at the level of superstrong (...) cardinals and up to the level of rank-into-rank embeddings, C(n)-cardinals form a much finer hierarchy. The naturalness of the notion of C(n)-cardinal is exemplified by showing that the existence of C(n)-extendible cardinals is equivalent to simple reflection principles for classes of structures, which generalize the notions of supercompact and extendible cardinals. Moreover, building on results of Bagaria et al. (2010), we give new characterizations of Vopeňka’s Principle in terms of C(n)-extendible cardinals. (shrink)

On concepts of current existence of Burmese Theravada Buddhists.

School violence is a burning issue these days. This book provides an in-depth analysis of violence prevention programs and an assessment of their effectiveness, using data from observations, individual interviews, and focus groups, as well as published data from the schools. It is distinguished by its focus on the cultural and structural context of school violence and violence prevention efforts. Where most other researchers use quantitative measures, such as surveys, to assess the effectiveness of violence prevention programs, the authors of (...) this book use qualitative research and ethnography to study the environment where such programs take place. Thus, this work--one of only a few ethnographic studies of violence prevention programs in schools--links previous quantitative research on the topic and critical ethnography. _Preventing Violence in Schools: A Challenge to American Democracy_: *includes voices of school students, accused of practicing violence, who have been participants in violence prevention programs; *analyzes a citywide peer mediation program ; *examines the kinds of violence recognized in schools and the ways schools themselves may perpetuate violence; and *describes a violence prevention program for students at an alternative school. _Preventing Violence in Schools: A Challenge to American Democracy_ is highly relevant for students in courses on urban education, foundations of education, education and social policy, youth and the law, and qualitative research, and for teachers, administrators, and other professionals, such as school psychologists and guidance counselors, at the middle and high school levels. (shrink)

El humanismo, asociado históricamente a la educación –la paideia griega- merece ser repensado y recuperado para la educación en un momento de cambio tecnológico tan acelerado y tan influyente en la condición humana que ya hay quien habla de “transhumanismo”. Se analiza la riqueza polisémica de la noción de humanismo y el valor de la formación humanística al servicio de la justicia; y finalmente, su valor como aprendizaje del goce mismo de vivir. En suma, su alto valor educativo. Palabras clave: (...) Humanismo, educación, transhumanismo, justicia, goce de vivir. (shrink)

La religion, qui a irrigué la culture occidentale pendant deux mille ans, perd son influence sur tous les plans. La chrétienté ne se retire pas seule, mais avec elle ses fruits sécularisés, qui constituaient une architecture signifiante. Quel est le destin de notre représentation du monde à forée de cet effacement? Certains désignent le relativisme, voire le nihilisme. qui s'instaurent dans l'oubli des référents fondateurs. Ce livre veut montrer que le nihilisme n'est qu'une brève transition, que le relativisme reflète une (...) apparence. L'époque présente atteste plutôt la réinstauration de modes d'être et de pensée comparables à ceux qui précédèrent l'Occident chrétien et à ceux qui se déploient partout hors l'Occident chrétien : des sagesses et des paganismes, déjà à l'ouvre sous la texture déchirée de nos anciennes convictions. transcendantes ou immanentes. Ces sagesses se nourrissent de renoncement, lequel forme aujourd'hui l'essentielle disposition de notre esprit. Renoncement à la quête de la vérité, renoncement au progrès, à la royauté de l'homme, à la liberté personnelle. Les conséquences en sont, par un lent processus, le remplacement du vrai par le bien, des dogmes par vies mythe, du temps fléché par un retour au temps circulaire, du monothéisme par le paganisme ou le panthéisme, de l'humanisme de liberté par un humanisme de protection, de la démocratie par le consensus, de la ferveur par le lâcher prise. C'est une métamorphose radicale, et ce renoncement est un retournement, non seulement de nos pensées, mais aussi de nos modes d'être et de nos institutions. Après une histoire de deux mille ans, sous de multiples signes réapparaît l'appel à une résignation sereine dont les hommes sans Dieu n'ont jamais cessé de rêver. (shrink)