El artículo documenta y analiza las vicisitudes en torno a la incorporación de Hilbert de su famoso axioma de completitud, en el sistema axiomático para la geometría euclídea. Esta tarea es emprendida sobre la base del material que aportan sus notas manuscritas para clases, correspondientes al período 1894–1905. Se argumenta que este análisis histórico y conceptual no sólo permite ganar claridad respecto de cómo Hilbert concibió originalmentela naturaleza y función del axioma de completitud en su versión geométrica, sino que además (...) permite disipar equívocos en cuanto a la relación de este axioma con la propiedad metalógica de completitud de un sistema axiomático, tal como fue concebida por Hilbert en esta etapa inicial.The paper reports and analyzes the vicissitudes around Hilbert’s inclusion of his famous axiom of completeness, into his axiomatic system for Euclidean geometry. This task is undertaken on the basis of his unpublished notes for lecture courses, corresponding to the period 1894–1905. It is argued that this historical and conceptual analysis not only sheds new light on how Hilbert conceived originally the nature of his geometrical axiom of completeness, but also it allows to clarify some misunderstandings regarding this axiom and the metalogical property of completeness of an axiomatic system, as it was understoodby Hilbert in this initial stage. (shrink)

Sobre la base que aportan las notas manuscritas de David Hilbert para cursos sobre geometría, el artículo procura contextualizar y analizar una de las contribuciones más importantes y novedosas de su célebre monografía Fundamentos de la geometría, a saber: el cálculo de segmentos lineales. Se argumenta que, además de ser un resultado matemático importante, Hilbert depositó en su aritmética de segmentos un destacado significado epistemológico y metodológico. En particular, se afirma que para Hilbert este resultado representaba un claro ejemplo de (...) uno de los rasgos más fructíferos y atractivos de su nuevo método axiomático formal, o sea, la capacidad de descubrir y exhibir conexiones estructurales o internas entre diferentes teorías matemáticas. On the basis of a set of unpublished notes for lecture courses on geometry, the paper seeks to contextualize and analyze one of the most important and original contributions of David Hilbert's celebrated monograph Foundations of Geometry, namely its arithmetic of line segments. It is argued that Hilbert attributed to his arithmetic of segments an important epistemological and methodological meaning, in addition to its relevance as an original mathematical result. In particular, it is claimed that for Hilbert his arithmetic of segments represented a clear example of one of the most fruitful and attractive traits of his new formal axiomatic method, i.e., the power to discover and exhibit inner or structural connections among different mathematical theories. (shrink)

The paper surveys different notions of implicit definition. In particular, we offer an examination of a kind of definition commonly used in formal axiomatics, which in general terms is understood as providing a definition of the primitive terminology of an axiomatic theory. We argue that such “structural definitions” can be semantically understood in two different ways, namely as specifications of the meaning of the primitive terms of a theory and as definitions of higher-order mathematical concepts or structures. We analyze these (...) two conceptions of structural definition both in the history of modern axiomatics and in contemporary philosophical debates. Based on that, we give a systematic assessment of the underlying semantics of these two ways of understanding the definiens of such definitions, by considering alternative model-theoretic and inferential accounts of meaning. (shrink)

A theory of magnitudes involves criteria for their equivalence, comparison and addition. In this article we examine these aspects from an abstract viewpoint, by focusing on the so-called De Zolt’s postulate in the theory of equivalence of plane polygons (“If a polygon is divided into polygonal parts in any given way, then the union of all but one of these parts is not equivalent to the given polygon”). We formulate an abstract version of this postulate and derive it from some (...) selected principles for magnitudes. We also formulate and derive an abstract version of Euclid’s Common Notion 5 (“The whole is greater than the part”), and analyze its logical relation to the former proposition. These results prove to be relevant for the clarification of some key conceptual aspects of Hilbert’s proof of De Zolt’s postulate, in his classicalFoundations of Geometry(1899). Furthermore, our abstract treatment of this central proposition provides interesting insights for the development of a well-behaved theory ofcompatiblemagnitudes. (shrink)

El artículo examina una de las contribuciones más importantes a los fundamentos de la geometría euclídea elemental lograda por David Hilbert en su obra Fundamentos de la geometría, a saber: la reconstrucción de la teoría euclídea de las proporciones y de los triángulos semejantes. Se argumenta que dicha reconstrucción no sólo estuvo motivada por la identificación de Hilbert de suposiciones implícitas en la teoría de Euclides, sino que además estuvo esencialmente ligada a la preocupación por la 'pureza del método'. Más (...) aún, se afirma que, en este caso específico, el requerimiento de Hilbert por la pureza del método posee un carácter general o fundacional, esto es, no se refiere a la demostración de un teorema en particular, sino más bien es planteado respecto de la construcción axiomática de la teoría misma. (shrink)

The paper outlines an interpretation of one of the most important and original contributions of David Hilbert’s monograph Foundations of Geometry , namely his internal arithmetization of geometry. It is claimed that Hilbert’s profound interest in the problem of the introduction of numbers into geometry responded to certain epistemological aims and methodological concerns that were fundamental to his early axiomatic investigations into the foundations of elementary geometry. In particular, it is shown that a central concern that motivated Hilbert’s axiomatic investigations (...) from very early on was the aim of providing an independent basis for geometry. Accordingly, these concerns about an independent grounding for elementary geometry determined very clear methodological constraints in the process of embedding it into a formal axiomatic system. It is argued that Hilbert not only sought to show that geometry could be considered a pure mathematical theory, once it was presented as a formal axiomatic system; he also aimed at showing that in the construction of such an axiomatic system one could proceed purely geometrically, avoiding concept formations borrowed from other mathematical disciplines like arithmetic or analysis. (shrink)

This paper provides a detailed study of David Hilbert’s axiomatization of the theory of plane area, in the classical monograph Foundation of Geometry. On the one hand, we offer a precise contextualization of this theory by considering it against its nineteenth-century geometrical background. Specifically, we examine some crucial steps in the emergence of the modern theory of geometrical equivalence. On the other hand, we analyze from a more conceptual perspective the significance of Hilbert’s theory of area for the foundational program (...) pursued in Foundations. We argue that this theory played a fundamental role in the general attempt to provide a new independent basis for Euclidean geometry. Furthermore, we contend that our examination proves relevant for understanding the requirement of “purity of the method” in the tradition of modern synthetic geometry. (shrink)

This paper analyzes the theory of area developed by Euclid in the Elements and its modern reinterpretation in Hilbert’s influential monograph Foundations of Geometry. Particular attention is bestowed upon the role that two specific principles play in these theories, namely the famous common notion 5 and the geometrical proposition known as De Zolt’s postulate. On the one hand, we argue that an adequate elucidation of how these two principles are conceptually related in the theories of Euclid and Hilbert is highly (...) relevant for a better understanding of the respective geometrical practices. On the other hand, we claim that these conceptual relations unveil interesting issues between the two main contemporary approaches to the study of area of plane rectilinear figures, i.e., the geometrical approach consisting in the geometrical theory of equivalence and the metrical approach based on the notion of measure of area. Finally, in an appendix logical relations among equivalence, comparison and addition of magnitudes are examined schematically in an abstract setting. (shrink)

El artículo presenta una interpretación del abordaje axiomático temprano a la geometría de David Hilbert, i.e., el desarrollado entre 1891 y 1905. Se sostiene que diversos aspectos de este abordaje, a primera vista problemáticos, se pueden comprender mejor si se contrastan con una de sus influencias más importantes en este periodo: la teoría pictórica [Bildtheorie] de Heinrich Hertz. En particular se argumenta que un análisis de la concepción axiomática de Hilbert a la luz de la teoría de Hertz permite aliviar (...) ciertas tensiones en la concepción hilbertiana; más precisamente, las tensiones que surgen de mantener, al mismo tiempo, una posición axiomática abstracta o formal y una concepción empirista de la geometría, que la considera una ciencia natural. (shrink)

Theoria, Volume 88, Issue 3, Page 629-652, June 2022.

El artículo ofrece una interpretación de las contribuciones de David Hilbert a la teoría de las magnitudes poligonales, desarrollada en su influyente monografía Fundamentos de la geometría, publicada en 1899. Se argumenta que la construcción de esta parte central de la geometría euclidiana represento para Hilbert un desafío muy significativo, en razón de su objetivo general de proporcionar una axiomatización estrictamente sintética de esta teoría geométrica; es decir, en virtud de sus conocidos requerimientos metodológicos y epistemológicos de construir la geometría (...) elemental evitando toda apelación esencial a presupuestos numéricos. Se sostiene además que dicho desafío consistió en ofrecer un nuevo fundamento lógicamente sólido para la teoría del área poligonal, pero que al mismo tiempo pueda ser considerado como puramente geométrico. The paper offers an interpretation of David Hilbert's contributions to the theory of polygonal magnitudes, developed in his influential monograph Foundations of Geometry, published in 1899. It is argued that the construction of this central part of Euclidean geometry presented an appealing challenge to Hilbert's general aim of providing a purely synthetic axiomatization of this geometrical theory; in other words, to his epistemological and methodological concerns of constructing elementary geometry without resorting to any kind of numerical assumption. Moreover, it is claimed this challenge consisted in offering a new foundation for the theory of polygonal area, which could be considered at the same time as logically sound and purely geometrical. (shrink)

El artículo presenta y analiza un conjunto de notas manuscritas de clases para cursos sobre geometría, dictados por David Hilbert entre 1891 y 1905. Se argumenta que en estos cursos el autor elabora la concepción de la geometría que subyace a sus investigaciones axiomáticas en Fundamentos de la geometría . Por un lado, afirmo que lo que caracteriza esta concepción de la geometría es: i) una posición axiomática abstracta o formal; ii) una posición empirista respecto del origen de la geometría (...) y de su lugar dentro de las distintas teorías matemáticas. Por otro lado, sostengo que el papel que Hilbert le confiere a la intuición geométrica en el proceso de axiomatización de esta teoría, permite apreciar claramente su oposición respecto de las posiciones formalistas con las que habitualmente es identificado. (shrink)

This paper aims to offer an interpretation of the Transcendental Deduction of the Categories which puts together two of its most distinctive and fundamental traits: the constant reference to the temporal character of the human consciousness and the use of the analytic method of exposition. We will defend the thesis that the connection between both traits is essential, i. e., it will be argued that it is precisely the usage of the analytic method what confers to the pure consciousness of (...) time a significant role in the structure of the argument. With this thesis an alternative reading of the A-Deduction is pursued, one which moves away from the predominant one which claims that Kant's persistent allusion in it to the pure time representation - and to the synthesis which make it possible - is just a direct consequence of its psychological character.El objetivo del artículo es ofrecer una interpretación de la Deducción Transcendental de las Categorías que ponga en relación dos de sus aspectos más distintivos y fundamentales: la referencia permanente al carácter temporal de la conciencia humana, y la utilización del método analítico de exposición. Se defenderá la tesis de que la conexión entre ambos aspectos es esencial, en tanto que es precisamente la adopción del método analítico lo que determina que se le confiera a la conciencia pura del tiempo un rol fundamental en la estructura del argumento. Con esta tesis se intenta ofrecer una lectura alternativa de la Deducción A, que se diferencie de la habitual según la cual la apelación constante de Kant a la representación pura del tiempo - y a las síntesis que lo hacen posible - es una consecuencia directa del carácter psicologista que la distingue. (shrink)

The logics of formal inconsistency are logics tolerant to some amount of contradiction, but in which some versions of explosion still hold. The main result of this paper is a reconstruction of two such logics in the dialogical framework. By doing so, we achieve two things. On the one hand, we provide a formal approach to argumentative situations where some contradictions may occur while keeping the idea that there may still be situations in which some propositions are ‘safe’ in the (...) sense of immunity to the contradictions. On the other hand, we open a new line of study on these logics, in the context of the game-theoretical approach to semantics born in the 1960s, with various interesting perspectives, some of which are discussed at the end of this article. (shrink)

This paper seeks to highlight the methodological contributions developed by Michel Foucault in regard to a critical history. We propose a tour through various passages of the thinker´s work, with the aim of bashing the main elements that allegedly make up his method. From this exercise we maintain that, in order to record the existence of a Foucauldian method, it is necessary to reproblematize this notion beyond the displacements around the well-known three moments of his work -archeological/genealogical/ethical-, reorienting the look (...) towards the critical tension possible to peer around the unique place that occupies the question of history in his work. The novelty of our proposal is to point out that, beyond the well-known substantial contributions foreshadowed around Foucault's conceptual rig, his work must be understood as an eminently practical historical-philosophical methodology, aimed at disarticulating the canonical principles that legitimize knowledge produced by the historiographic method, thus opening a region of indiscernibility and rarity in historical practice that, we maintain, can be thought of in the vicinity of a parahistory. In sum, we propose the thesis that the displacement in Foucault's work takes on a singular power from the introduction of a strategic artifice ― anonymous ―, aimed at forcing a fold of history on itself, showing how historiographical plots actively tax to sustain and legitimize the regimes of knowledge, power and truth present in them. (shrink)

A theory of magnitudes involves criteria for their comparison, equivalence and addition. We examine these aspects from an abstract viewpoint, stressing independence and definability. These considerations are triggered by the so-called De Zolt’s principle in the theory of equivalence of plane polygons.

No. 135: LOS VALORES DEL PAISAJE Ponencias del Seminario del Paisaje (2008) que abordan con distintos puntos de vista los valores del paisaje, buscando entender mejor los significados del paisaje en el horizonte de la modernidad, las cualidades que se le atribuyen y el sentido que de esa manera adquiere.

O texto situa em seu contexto as Conferências Públicas e apresenta o seu papel no projeto de Instrução Pública e Organização do Ensino, proposto por Jean Antoine Nicolas de Caritat, marquês de Condorcet , que deu origem ao decreto sobre Instrução Pública aprovado na Assembléia Nacional da França Revolucionária em 1792. Ao final, caberá uma breve comparação entre os objetivos das Conferências Públicas dispostos por Condorcet com o recente programa Escola da Família, do governo do Estado de São Paulo, para (...) evidenciar o contraste entre duas políticas liberais para a educação. The essay places in context the Public conferences and presented his paper on the design of Public Instruction and Education Organization, proposed by Jean Antoine Nicolas de Caritat, Marquis de Condorcet , which led to the decree on Public Instruction approved National Assembly of Revolutionary France in 1792. In the end, it will be a brief comparison between the objectives of Public Conferences arranged by Condorcet at the recent Family School program, the state government of St. Paul, to highlight the contrast between two liberal policies for education. (shrink)

Desde que Hegel declarara el arte como “cosa del pasado”, diversas posturas han discutido sus posibilidades de existencia y ocaso, mientras el arte mismo se ha visto en la incomodidad de la indefinición de sus condiciones ontológicas y de sus espacios de circulación. Esa indefinición, no obstante, permitió que ciertas operaciones y modos de hacer artísticos se desplazaran hacia escenarios abiertos y no institucionales. Una vez trazada una ruta hermenéutica desde la estética hegeliana hasta la actualidad, a partir de modelos (...) de análisis como los Estudios visuales, la teoría de Boris Groys o Nicolas Bourriaud, o el sistema modal de Jordi Claramonte, es posible pensar las condiciones de posibilidad actuales del arte en la medida de sus entrecruzamientos y del desplazamiento de su objeto desde la creación hacia la circulación. Sin que haya desaparecido la plataforma de legitimación institucional, las variaciones en las que se despliegan los códigos artísticos en la cultura visual contemporánea desestiman la posibilidad de reclamarse como obras de arte, y se limitan a hacer un uso táctico de formas de relación y producción. De ahí que la demarcación de los escenarios de supervivencia del arte pueda resumirse en el traslado de la categoría arte, como sustantivo, hacia la movilidad versátil del adjetivo artístico. (shrink)

This paper demonstrates the central role of the Socratic elenchus in the Sophist. In the first part, I defend the position that the Stranger describes the Socratic elenchus in the sixth division of the Sophist. In the second part, I show that the Socratic elenchus is actually used when the Stranger scrutinizes the accounts of being put forward by his predecessors. In the final part, I explain the function of the Socratic elenchus in the argument of the dialogue. By contrast (...) with standard scholarly interpretations, this way of reading the text provides all the puzzles about being (241c4–251a4) with a definite function in the dialogue. It also reveals that Plato’s methodology includes a plurality of method and is more continuous than what is often believed. (shrink)

Nicolas Weill propose une lecture stimulante de ces textes qui constituent une des découvertes philosophiques les plus importantes de ces dernières années. La publication des "Cahiers" redonne une actualité brûlante à la question qui divise épigones et détracteurs du penseur allemand : comment continuer à philosopher avec Heidegger sans tenir compte d'une éventuelle contamination de cette philosophie par l'idéologie nazie? Par une analyse sans concession des "Cahiers", en se concentrant sur les Réflexions (tenues par Heidegger de 1931 à 1941) mais (...) tout en cherchant à en dégager les éléments proprement philosophiques, cet ouvrage invite à une approche équilibrée, quitte à "penser avec Heidegger, contre Heidegger", comme le suggérait Jürgen Habermas dès le début des années 1950. Il montre notamment comment l'auteur d'Etre et temps, en inventant une nouvelle forme de philosopher, a poursuivi et prolongé dans ces carnets la critique de la modernité telle qu'elle a été formulée par la "révolution conservatrice" allemande et par Oswald Spengler, le théoricien du déclin de l'Occident. (shrink)

This book is the first extensive treatment of Husserl's phenomenology of time-consciousness. Nicolas de Warren uses detailed analysis of texts by Husserl, some only recently published in German, to examine Husserl's treatment of time-consciousness and its significance for his conception of subjectivity. He traces the development of Husserl's thinking on the problem of time from Franz Brentano's descriptive psychology, and situates it in the framework of his transcendental project as a whole. Particular discussions include the significance of time-consciousness for other (...) phenomenological themes: perceptual experience, the imagination, remembrance, self-consciousness, embodiment, and the consciousness of others. The result is an illuminating exploration of how and why Husserl considered the question of time-consciousness to be the most difficult, yet also the most central, of all the challenges facing his unique philosophical enterprise"--Provided by publisher. (shrink)

What semantics should we attribute to nouns like "wisdom" and "generosity", which are derived from gradable adjectives? We show that, from a morphosyntactic standpoint, these nouns are mass nouns. This leads us to consider and answer the following questions. How are these nouns interpreted in their various uses? What formal representations may one associate with their interpretations? How do these depend on the semantics of the adjective? And where lies the semantic unity of nouns like wisdom and generosity with the (...) more familiar concrete mass nouns, like wine and furniture? (shrink)

Eduardo Arroyo, Armelle Auris, François Boissonnet, Paul HENRY, Pierre-Jean LABARRIERE, MATIEU, Gilles AILLAUD, Gérad THALMANN, Nicole MATHIEU, Jacques VIMARD, Michel QUAREZ, Leonardo CREMONINI, L'atelier d'Eduardo Arryo: Le carré blanc du ring, Rue Descartes, No. 7, Logiques de l'éthique (Juin 1993), pp. 149-168.

In this article, we discuss how we used institutional ethnography (Institutional ethnography as practice, Rowman & Littlefield, Lanham, MD and 2006) to map out powerful ruling relations that organize nurses’ wound care work. In recent years, the growing number of people living with wounds that heal slowly or not at all has presented substantial challenges for those managing the demands on Canada's publicly insured health‐care system. In efforts to address this burden, Canadian health‐care administrators and policy‐makers rely on scientific evidence (...) about how wounds heal and what treatments are most effective. Advanced wound care exemplifies the growing authorization of particular forms of evidence that change the ways in which nurses come to know about and conduct their work. The focus of this paper's nursing inquiry is a critique of registered nurses’ wound work as it arises within the established uptake of scientific evidence. (shrink)

This volume collects a number of important and revealing interviews with Richard Rorty, spanning more than two decades of his public intellectual commentary, engagement, and criticism. In colloquial language, Rorty discusses the relevance and nonrelevance of philosophy to American political and public life. The collection also provides a candid set of insights into Rorty's political beliefs and his commitment to the labor and union traditions in this country. Finally, the interviews reveal Rorty to be a deeply engaged social thinker and (...) observer. (shrink)

This paper focuses on the extension of AGM that allows change for a belief base by a set of sentences instead of a single sentence. In [FH94], Fuhrmann and Hansson presented an axiomatic for Multiple Contraction and a construction based on the AGM Partial Meet Contraction. We propose for their model another way to construct functions: Multiple Kernel Contraction, that is a modification of Kernel Contraction, proposed by Hansson [Han94] to construct classical AGM contractions and belief base contractions. This construction (...) works out the unsolved problem pointed out by Hansson in [Han99, pp. 369]. (shrink)

In this paper we claim that pragmatist philosophical practice is incompatible with scientistic philosophy. The kind of pragmatism used for making this case follows the spirit and method of philosophical pragmatists such as William James, John Dewey, Richard Rorty, and a related pragmatic tradition, Confucian Philosophy. Pragmatism starts from immediate experience, and refuses to cleave off the reality and salience of what is found in such experience in the process of thinking. Pragmatism also concerns itself with social problems, broadly conceived. (...) In contrast to this focus on immediate experience, the influence of science in much philosophizing involves a kind of scientism through which the relevance, value, and even reality of experience is brought into question. It also concerns itself with a narrowly defined set of so-called philosophical problems. In this regard, pragmatist philosophical practice is fundamentally opposed to scientistic philosophical practice. We will start by modelling the kind of philosophical practice that stems from pragmatism, and the role of immediate experience in it. Subsequently, we will introduce two modes of philosophizing that diminish if not negate the role of experience. One is bald naturalist philosophizing, and the other is a priori scientific philosophizing. In the last section, we will show how main commitments of both of these traditions are incompatible with a pragmatist philosophy that remains committed to the original impulse of pragmatism. (shrink)

Adding a transparent truth predicate to a language completely governed by classical logic is not possible. The trouble, as is well-known, comes from paradoxes such as the Liar and Curry. Recently, Cobreros, Egré, Ripley and van Rooij have put forward an approach based on a non-transitive notion of consequence which is suitable to deal with semantic paradoxes while having a transparent truth predicate together with classical logic. Nevertheless, there are some interesting issues concerning the set of metainferences validated by this (...) logic. In this paper, we show that this logic, once it is adequately understood, is weaker than classical logic. Moreover, the logic is in a way similar to the paraconsistent logic LP. (shrink)

Until now, North American and European philosophies have been engaged in debates about the possibility of a postmetaphysical philosophy and the consequences of the linguistic turn for the assessment of modernity; they have done so, however, without departing from the narrow horizons of their respective nationalistic perspectives. In this incisive critique, Dussel demonstrates how most of thse philosophies have either failed to give historically faithful analyses of the genesis of the "myth" of modernity, or have never engaged in a serious (...) questioning of their own Eurocentric presuppositions. He shows how North American and European philosophers have presupposed a no-longer-acceptable philosophy of history that has led them to fall into a "developmental fallacy," the belief that there is a linear sequence that moves from the premodern, underdeveloped, or on the way to industrialization, to the modern, developed, and industrialized. (shrink)