Review by A. Kanamori, Boston University (author of The Higher Infinite), review in The Bulletin of Symbolic Logic: “Notwithstanding and braving the daunting complexities of this labyrinth, José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in (...) mathematics from the early nineteenth century. Much of history is in the details, and much of good history is in tone, emphasis, and the drawing together of different strands. Without being Whiggish, Ferreirós is never far from major synthetic themes, themes that in the main work toward balance and pull back from excesses of emphasis of some recent histories. The main criticism of the book would have to be on matters of broad interpretation. Yet, Ferreirós brings a considerable mathematical acuity and expertise to his enterprise, and this makes his viewpoints the more compelling.” . (shrink)

On knowledge and practices: a manifesto -- The web of practices -- Agents and frameworks -- Complementarity in mathematics -- Ancient Greek mathematics: a role for diagrams -- Advanced math: the hypothetical conception -- Arithmetic certainty -- Mathematics developed: the case of the reals -- Objectivity in mathematical knowledge -- The problem of conceptual understanding.

This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research and how a number of historical accounts can be deepened by embracing philosophical questions.

Abstract: According to Hegel, comprehension proper is the ostensible self-determination of thinking with the determinations that spontaneously present themselves as independent objects. By positing objective determinations as the own determinations of thought, comprehension reveals thinking as an activity that is practical. For Hegel, comprehending allegedly extrinsic objects, and free willing of the own determinations of the thinking and willing subject, are in essence the same activity: only subjects who can choose between the determinations that determine them can comprehend objects. To (...) elucidate: only subjects who are able to actively determine themselves with the determinations that spontaneously determine them are able to analyse and comprehend the objects of their knowing activity. Thought that can think itself defines, according to Hegel, the true nature of the human spirit. (shrink)

Adorno asocia la concepción hegeliana del espíritu a la concepción en última instancia formal de la subjetividad de Kant y del Fichte de la Grundlage. La subjetividad no puede ser infinita: al sujeto siempre se le opone el objeto. Aunque pretende superar el subjetivismo de la concepción kantiana y fichteana del sujeto, la unidad del sujeto y el objeto que define al "espíritu" de Hegel es todavía un sujeto; fuera de este sujeto resiste siempre algo no-idéntico que le es irreductible; (...) un idealismo absoluto es como tal, pues, imposible. En una línea con esto, Adorno considera que la Lógica hegeliana carece de contenido y permanece, a pesar de sus pretensiones materiales, una teoría puramente formal. Ahora bien, Adorno no ofrece un análisis detallado de la argumentación de Hegel en contra de la concepción formal de la subjetividad que proponen Kant y el primer Fichte. Hegel diferencia la subjetividad vacía obtenida por abstracción a partir del sujeto empírico respecto de la subjetividad absoluta o espíritu. Adorno rastrea la esencia del idealismo absoluto en la relación entre sensibilidad e inteligibilidad; para Hegel, sin embargo, la clave del idealismo absoluto reside en la unidad entre ser y pensar, o, lo que para Hegel es en última instancia lo mismo, entre ser y determinidad. (shrink)

ABSTRACTWe discuss the thesis of universality of geometric notions and offer critical reflections on the concept of “natural geometry” employed by Spelke and others. Promoting interdisciplinary wor...

The place of Richard Dedekind in the history of logicism is a controversial matter. The conception of logic incorporated in his work is certainly old-fashioned, in spite of innovative elements that would play an important role in late 19th and early 20th century discussions. Yet his understanding of logic and logicism remains of interest for the light it throws upon the development of modern logic in general, and logicist views of the foundations of mathematics in particular. The paper clarifies Dedekind's (...) views and their relation to transcendental logic, makes explicit the role of the principle of comprehension (unrestricted) and offers a reconstrucion ot his dichotomy conception. The last section explores the differences with Frege (half epistemic, half metaphysical) making clear that there were different brands of logicism, and that logicism does not necessarily lead to singularism or “essentialistic objectualism”. (shrink)

This paper defends a conceptualistic version of structuralism as the most convincing way of elaborating a philosophical understanding of structuralism in line with the classical tradition. The argument begins with a revision of the tradition of “conceptual mathematics”, incarnated in key figures of the period 1850 to 1940 like Riemann, Dedekind, Hilbert or Noether, showing how it led to a structuralist methodology. Then the tension between the ‘presuppositionless’ approach of those authors, and the platonism of some recent versions of philosophical (...) structuralism, is presented. In order to resolve this tension, we argue for the idea of ‘logical objects’ as a form of minimalist realism, again in the tradition of classical authors including Peirce and Cassirer, and we introduce the basic tenets of conceptual structuralism. The remainder of the paper is devoted to an open discussion of the assumptions behind conceptual structuralism, and—most importantly—an argument to show how the objectivity of mathematics can be explained from the adopted standpoint. This includes the idea that advanced mathematics builds on hypothetical assumptions (Riemann, Peirce, and others), which is presented and discussed in some detail. Finally, the ensuing notion of objectivity is interpreted as a form of particularly robust intersubjectivity, and it is distinguished from fictional or social ontology. (shrink)

This chapter can be considered as made up of two parts, a general discussion of the notion of mathematical practice and the limits of its use, comprised by the first three sections, and a particular case study that is presented in order to exemplify the idea of the web of practices, which occupies the remaining three. The presentation of my approach to the notion of mathematical practice is brief and synthetic but more articulated theoretically than in a previous book (Ferreirós (...) 2016). Considerations in Sect. 3 about mathematical cognition and ethnomathematics have to do with the “limits” of mathematical practice, i.e., with practices that do not fall under that rubric.The case study concerns the evolution of the function concept, which offers a complex example of the web-of-practices approach. We start with early Modern developments that led to the eighteenth-century idea of function (as “analytical expression”) and the nineteenth-century “logical” idea of function, showing how complex is the spiderweb of interrelated mathematical and scientific practices knotted around the function concept. In the last section, I consider the difficult question of the most basic practices and cognitive experiences that form the basis of the idea of function. I propose that two conceptions – a dynamic and an algebraic or operational one – coalesced to give rise to the early Modern idea of function. (shrink)

Delusions are one of the most classical symptoms described in schizophrenia. However, despite delusions are often emotionally charged, they have been investigated using tasks involving non-affective material, such as the Beads task. In this study we compared 30 patients with schizophrenia experiencing delusions with 32 matched controls in their pattern of responses to two versions of the Beads task within a Bayesian framework. The two versions of the Beads task consisted of one emotional and one neutral, both with ratios of (...) beads of 60:40 and 80:20, considered, respectively, as the “difficult” and “easy” variants of the task. Results indicate that patients showed a greater deviation from the normative model, especially in the 60:40 ratio, suggesting that more inaccurate probability estimations are more likely to occur under uncertainty conditions. Additionally, both patients and controls showed a greater deviation in the emotional version of the task, providing evidence of a reasoning bias modulated by the content of the stimuli. Finally, a positive correlation between patients’ deviation and delusional symptomatology was found. Impairments in the 60:40 ratio with emotional content was related to the amount of disruption in life caused by delusions. These results contribute to the understanding of how cognitive mechanisms interact with characteristics of the task in the context of delusional thinking. These findings might be used to inform improved intervention programs in the domain of inferential reasoning. (shrink)

David Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here. I consider strong evidence for the fact that Hilbert was a logicist at that time, following upon Dedekind’s footsteps in his understanding of pure mathematics. This insight makes it possible to throw new light on the evolution of Hilbert’s foundational ideas, including his early contributions to the foundations of geometry and the real number system. The context of Dedekind-style logicism makes it possible to offer a new (...) analysis of the emergence of Hilbert’s famous ideas on mathematical existence, now seen as a revision of basic principles of the “naive logic” of sets. At the same time, careful scrutiny of his published and unpublished work around the turn of the century uncovers deep differences between his ideas about consistency proofs before and after 1904. Along the way, we cover topics such as the role of sets and of the dichotomic conception of set theory in Hilbert’s early axiomatics, and offer detailed analyses of Hilbert’s paradox and of his completeness axiom (Vollständigkeitsaxiom). (shrink)

Historiographical studies have provided a wealth of information on the naturalistic background of medieval political thought, having incorporated Aristotle’s thesis resulting from the reception of Politics. The goal of our study is to provide the hermeneutics of this natural philosophy using as a common thread the body as an attribute of the human constitution which imposes certain needs and from which emerge certain impulses that determine its social and political condition. Specifically, we will analyze the treatises De regno ad regem (...) Cypri and Defensor pacis by Saint Thomas Aquinas and Marsilius of Padua, respectively, regarding how the notion of body is especially important because it is the center of a series of activities which are decisive for life. (shrink)

We formulate and discuss a “great antinomy” between theoreticist/foundationist conceptions and pragmatist conceptions, in relation to a wide diversity of scientific and/or philosophical approaches. The contrast is illustrated in particular with the concept of time, considering the ‘timelessness crowd’ that has been guided by a theoreticist vision.

Logicism finds a prominent place in textbooks as one of the main alternatives in the foundations of mathematics, even though it lost much of its attraction from about 1950. Of course the neologicist trend has revitalized the movement on the basis of Hume’s Principle and Frege’s Theorem, but even so neologicism restricts itself to arithmetic and does not aim to account for all of mathematics. The present contribution does not focus on the classical logicism of Frege and Dedekind, nor on (...) the Russell-Carnap period, and also not on recent neologicism; its aim is to call attention to some forms of heritage from logicism that normally go quite unnoticed. In the 1920s, 1930s and 1940s, the logicist thesis became a stimulus for some deep innovations in the field of mathematical logic. One can argue, in particular, that two key ideas linked with formal semantics had their origins in the conception of logic associated with the logicist trend – the expansion of metamathematics brought about by Tarski, opening the way to model theory, and the insistence on the “full” set-theoretic semantics as “standard” for second-order logic. The paper proposes an analysis of those inheritances and argues that that logical theory ought to avoid some of their implications. (shrink)

On knowledge and practices: a manifesto -- The web of practices -- Agents and frameworks -- Complementarity in mathematics -- Ancient Greek mathematics: a role for diagrams -- Advanced math: the hypothetical conception -- Arithmetic certainty -- Mathematics developed: the case of the reals -- Objectivity in mathematical knowledge -- The problem of conceptual understanding.

"Esta guía se organiza a partir de ejercicios prácticos que estimulan la participación, interacción y curiosidad con y a partir de la ciudad; en donde cada ejercicio toma como referencia la manera enque algunos filósofos, cineastas, fotógrafos, artistas y arquitectos contemporáneos se han aproximado al espacio urbano. Cada ejercicio contiene un instructivo de cómo llevar a cabo las acciones de observación, registro ytoma de evidencia, cada uno ilustrado por el autor. Escrito con un estilo anecdótico, el libro se convierte en (...) una herramienta con la cual caminar la ciudad sintiéndose acompañado, en un atravesí que promueve una aproximación lúdica a nuestro entorno."-- Cubierta trasera. (shrink)

Proponemos una revisión crítica a una corriente interpretativa de base lingüística de las religiones prerromanas del área indo-europea de la Península Ibérica que se ha venido desarrollando durante los últimos quince años; para ello tomamos como referencia un reciente trabajo de B.M. Prósper (Lenguas y religiones del occidente de la Península Ibérica, Salamanca, 2002) en el que se exponen los puntos de vista de dicha hipótesis interpretativa. Nuestro trabajo revisa sus tres planteamientos metodológicos básicos: su consideración de dichas religiones como (...) cultos idolátricos, su base evolucionista decimonónica y su manifiesto anti-dumezilianismo. Nuestra propuesta consiste en integrar el aporte de la lingüística dentro del ámbito de la Historia de las Religiones como un tipo de análisis que contribuya, con otros, a la construcción de hipótesis explicativas del fenómeno religioso de dichas sociedades. (shrink)

This paper aims to outline an analysis and interpretation of the process that led to First-Order Logic and its consolidation as a core system of modern logic. We begin with an historical overview of landmarks along the road to modern logic, and proceed to a philosophical discussion casting doubt on the possibility of a purely rational justification of the actual delimitation of First-Order-Logic. On this basis, we advance the thesis that a certain historical tradition was essential to the emergence of (...) modern logic; this traditional context is analyzed as consisting in some guiding principles and, particularly, a set of exemplares (i.e., paradigmatic instances). Then, we proceed to interpret the historical course of development reviewed in section 1, which can broadly be described as a two-phased movement of expansion and then restriction of the scope of logical theory. We shall try to pinpoint ambivalencies in the process, and the main motives for subsequent changes. Among the latter, one may emphasize the spirit of modern axiomatics, the situation of foundational insecurity in the 1920s, the resulting desire to find systems well-behaved from a proof-theoretical point of view, and the metatheoretical results of the 1930s. Not surprisingly, the mathematical and, more specifically, the foundational context in which Firs-Order-Logic matured will be seen to have played a primary role in its shaping. (shrink)

Nach den Kriterien einer einflußreichen (vor allem in den englischsprachigen Ländern vertretenen) Deutung der neuzeitlichen Philosophie enthält das Denken Kants die maximale Dosis an Idealismus, die eine Philosophie vertragen kann, ohne inkonsistent zu werden. Die Radikalisierung des idealistischen Ansatzes durch Fichte, Schelling und Hegel wird demnach als eine Abkehr von den geltenden Vernunftstandards betrachtet. Ausgangspunkt dieser Einschätzung ist nicht selten die Verwechslung des nachkantischen Idealismus mit einer überspannten Variante des Idealismus von Berkeley. Diese Lesart des postkantischen Idealismus läßt sich aber (...) weder exegetisch noch konzeptuell rechtfertigen. Der Grundsatz der Einheit von Sein und Denken, dessen erste explizite Aufstellung und Entfaltung Hegel zufolge Fichte zu verdanken ist, impliziert in keiner Weise, daß man dadurch die Existenz der Welt verneinen muß. Was dieser Grundsatz zum Ausdruck bringt, ist eigentlich nur die Notwendigkeit, ein komplexes theoretisches Modell auszuarbeiten, das imstande ist, zu erklären, wie sich die Existenz von wirklichen Dingen behaupten läßt, die vom Subjekt durch seine eigenen Erkenntnisakte erkannt werden, dabei aber zugleich vom Subjekt selbst verschieden sind. Hegels erkenntnistheoretischer Hauptansatz ist, daß die Verbindung von Denken und Sein, von Geist und Welt, strukturell ist. Das Sein kommt zu den Denkinhalten insofern nicht synthetisch hinzu; es sind hingegen die nur vorgestellten Erkenntnisinhalte, welche unter bestimmten Bedingungen der strukturellen Einheit des Geistes mit der Welt zugeschrieben werden. (shrink)

El artículo intenta promover una recepción más amplia de los trabajos recientes sobre filosofía de la actividad científica experimental. Primero se comentarán los orígenes y las características de la tradición teoreticista predominante, criticando sus presupuestos y sus "miserias". Se analizará luego la función de los instrumentos, proponiendo una tipología de la actividad experimental, aunque elemental --esperamos-- útil. Tras analizar la estructura del experimento, empleando contribuciones de Pickering y otros, discutiremos la dinámica de la experimentación: los procesos de formación de datos. (...) Ésta es, obviamente, la cuestión más crucial y debatida, de la que depende la especificidad y fiabilidad de los métodos científicos. /// This paper attempts to promote a more widespread reception of recent work on the philosophy of experimental scientific activity. First, we comment on the origins and character of the predominant theoreticist tradition, offering critical remarks on its assumptions and "poverty". Then we analyze the function of instruments, proposing a coarse but hopefully useful typology of experimental activity. After analyzing the structure of experiment, drawing on work by Pickering and others, we discuss the dynamics of experimentation --the processes of data formation. This is obviously the most crucial and disputed issue, on which the specificity and reliability of scientific methods depends. (shrink)

La doctrina del choque (Anstoß), que Fichte desarrolla ante todo en el Fundamento de toda la Doctrina de la Ciencia, pero también en otros escritos de la época de Jena, ha sido desde antaño objeto de crítica tanto por los admiradores como por los detractores de la filosofía fichteana. Existen al menos dos modos específicamente diferentes y aparentemente contrapuestos de comprender su sentido: según una lectura, el choque sería una autoafección del propio Yo; según otra, un residuo realista, en última (...) instancia incompatible con los compromisos idealistas del pensamiento de Fichte. La tensión entre ambos modos de comprender la tesis del choque pueden reeconcontrarse en la confrontación entre las interpretaciones así llamadas epistemológica y ontológica de la tesis de la “cosa en sí” en la filosofía de Kant –tesis con la que de hecho suele asociarse la tesis fichteana del choque. En este contexto, Hegel parecería a primera vista presentarse –por ejemplo, si se considera el escrito de la Diferencia entre los sistemas de filosofía de Fichte y Schelling– como partidario de una interpretación robusta, ontológica, de la tesis del choque; sin embargo, si se analiza el corpus hegeliano en su conjunto la posición de Hegel resulta ser más matizada y próxima a una interpretación por así llamarla epistemológica de dicha tesis. Con todo, aun así la postura de Hegel sobre el sentido de la tesis fichteana del choque en el contexto de una filosofía idealista continúa siendo crítica. (shrink)

A down-to-earth admission of abstract objects can be based on detailed explanation of where the objectivity of mathematics comes from, and how a ‘thin’ notion of object emerges from objective mathematical discourse or practices. We offer a sketch of arguments concerning both points, as a basis for critical scrutiny of the idea that mathematical and social objects are essentially of the same kind—which is criticized. Some authors have proposed that mathematical entities are indeed institutional objects, a product of our collective (...) imposition of function onto reality (the phrase comes from Searle) and of surrogation or hypostasis. Yet there are significant disanalogies between the typical social objects and mathemata, on which basis I argue that one should make a clear distinction between both. The comparison of mathematical with social objects helps understanding how non-physical objects can figure prominently in our explanations of reality. Yet mathematical objects have a different kind of cognitive grounding, and the more elementary of them emerge under relatively very simple sociocultural conditions. The differences are also reflected in the wide scope of use of mathematical concepts, and the much higher degree of variation found among social objects. On the basis of all of these features, I defend the thesis that one can significantly distinguish degrees of objectivity, and I use the distinction to articulate a graded ontology where one can locate the different kinds of mathematical and social objects. (shrink)

Dedekind’s methodology, in his classic booklet on the foundations of arithmetic, has been the topic of some debate. While some authors make it closely analogue to Hilbert’s early axiomatics, others emphasize its idiosyncratic features, most importantly the fact that no axioms are stated and its careful deductive structure apparently rests on definitions alone. In particular, the so-called Dedekind “axioms” of arithmetic are presented by him as “characteristic conditions” in the _definition_ of the complex concept of a _simply infinite_ system. Making (...) sense of Dedekind’s method may be dependent on an analysis of the classical model of deductive science, as presented by authors from the eighteenth and early nineteenth centuries. Studying the modern reconstructions of Euclidean geometry, we show that they did not presuppose deductive independence of the axioms from the definitions. Authors like Wolff elaborated a mathematics _based on definitions_, and the Wolffian model of deductive science shows significant coincidences with Dedekind’s method, despite the great differences in content and approach. Wolff had a conception of definitions as _genetic_, which bears some similarities with Kant’s idea of synthetic definitions: they are understood as positing the content of mathematical concepts and introducing thought objects (_Gedankendinge_) that are the objects of mathematics. The emphasis on the spontaneity of the understanding, which can be found in this philosophical tradition, can also be fruitfully related with Dedekind’s idea of the “free creation” of mathematical objects. (shrink)

Set theory deals with the most fundamental existence questions in mathematics—questions which affect other areas of mathematics, from the real numbers to structures of all kinds, but which are posed as dealing with the existence of sets. Especially noteworthy are principles establishing the existence of some infinite sets, the so-called “arbitrary sets.” This paper is devoted to an analysis of the motivating goal of studying arbitrary sets, usually referred to under the labels of quasi-combinatorialism or combinatorial maximality. After explaining what (...) is meant by definability and by “arbitrariness,” a first historical part discusses the strong motives why set theory was conceived as a theory of arbitrary sets, emphasizing connections with analysis and particularly with the continuum of real numbers. Judged from this perspective, the axiom of choice stands out as a most central and natural set-theoretic principle (in the sense of quasi-combinatorialism). A second part starts by considering the potential mismatch between the formal systems of mathematics and their motivating conceptions, and proceeds to offer an elementary discussion of how far the Zermelo—Fraenkel system goes in laying out principles that capture the idea of “arbitrary sets”. We argue that the theory is rather poor in this respect. (shrink)

La actividad teórica y la actividad práctica han sido tradicionalmente entendidas como complementarias en el sentido que mediante la actividad teórica el sujeto se apropiaría idealmente de los objetos del mundo externo, mientras que mediante la actividad práctica realizaría sus propias metas subjetivas en el mundo. Sin embargo, dicho modelo plantea un conjunto de graves problemas exegéticos y conceptuales sobre la estructura y significado de la entera filosofía del espíritu de Hegel. En este artículo buscaremos esclarecer qué es a ojos (...) de Hegel lo propiamente específico de la actividad teórica y de la actividad práctica, para, sobre esa base, ofrecer un modelo exegético que logre dar satisfactoriamente cuenta de la particular periodización general que Hegel propone sobre las diferentes formas de actividad del espíritu humano. (shrink)

Hegel weist das Weltbild zurück, nach dem das erkennende Subjekt ein Ding unter den Dingen ist, das alle Dinge – dabei also auch sich selbst – kausal widerspiegelt, und schlägt stattdessen ein neues Paradigma vor, in dem das erkennende Subjekt als die Einheit der Erkenntnistätigkeit (des „Subjekts“ vom alten Paradigma) und des durch sie Erkannten (des „Objekts“) aufgefasst wird. Für diese neue Auffassung gehört das Objekt nicht zum Anderen der erkennenden Subjektivität, die es daher als ein Fremdes widerspiegelt; Objekt und (...) Subjekt sind vielmehr strukturelle und strukturierende Momente des Erkennens bzw. des Denkens selbst, welches nun als der „Raum“ verstanden wird, in dem Objekt und Subjekt, Welt und Geist vorkommen. Das Ziel des vorliegenden Beitrags besteht darin, Hegels Ansatz gegen die repräsentationalistische Auffassung der Erkenntnis zu analysieren und in diesem Kontext den Sinn hervorzuheben, den seine These über die praktischen Tätigkeit als Wesen und Wahrheit der kognitiven Tätigkeit hat. (shrink)

This is my introduction to a bilingual Spanish-German edition of selected writings by Bernhard Riemann. Published in Madrid: CSIC, 2000.

As early as 1784, sharp-eyed engineers and scientists noted striking similarities between the dynamics of seagoing vessels and aerial vehicles. By the early twentieth century, naval engineers and scientists were developing and designing airplanes and dirigibles using empirical principles derived from naval architecture. Several key researchers in aerodynamics began their career as naval architects (David A. Taylor, William F. Durand and Jerome C. Hunsaker) and carried out their experiments in ship testing facilities. By the 1930s, however, the transfer of knowledge (...) was irrevocably reversed as empiricism gave way to more fundamental, physics-based research. The rapid evolution of complex aircraft systems and flight envelopes led to new theoretical developments in aerodynamics and maneuvering, which quickly found their way into naval ship design. The theoretical and experimental results for airfoils, rigid airships and fixed-wing aircraft developed by Ludwig Prandtl, Theodore von Kármán, Max M. Munk and Hilda M. Lyon were employed in the hydrodynamic development of surface ships and submarines. This paper examines how the ideas, concepts and data from one discipline influenced the other and explores the processes by which that knowledge was transferred between disciplines. (shrink)

Review of M. Giaquinto, The Search for Certainty: A Philosophical Account of Foundations of Mathematics (Osford, 2002).

Ao analisar a teoria da memória mecânica de Hegel, a maioria dos intérpretes considerou apenas dois aspectos da memorização mecânica: o desaparecimento do significado nas palavras mecânicamente memorizadas ou a internalização totalmente abstrata da mente que as memoriza. No primeiro caso, a interpretação concentrou-se na relação entre o significante e o significado das palavras; no segundo caso, concentrou-se na relação entre o signo linguístico como um todo e a mente. Entretanto, a posição específica da memória mecânica na sistematização das atividades (...) cognitivas de Hegel não se baseia nessas duas relações, mas na relação entre o significado de cada palavra e o significado das outras palavras. Ao memorizar de cor fileiras de palavras que não estão conectadas umas às outras por seus significados, mas apenas pela força da mente que decide memorizá-las juntas, a mente se liberta de qualquer conteúdo dado externamente e sublima a referência linear do conteúdo representacional de cada significado à intuição em sua origem. A atualização do poder da mente de interconectar conteúdos de acordo com as próprias regras lógicas da mente realiza, para Hegel, a transição para o pensamento propriamente dito. (shrink)

Die Poesie ist für Hegel die Endform der Kunst, in der die Kunst im Allgemeinen durch die Religion überwunden wird. Die These, dass die Poesie den anderen Künsten, d.h. der Architektur, der Skulptur, der Malerei und der Musik, überlegen ist, spricht von einer besonderen Hierarchisierung und Periodisierung, die Hegel zwischen die verschiedenen Kunstformen einführt. Das Kriterium für diese Hierarchisierung und Periodisierung ist offensichtlich das gleiche, nach dem Hegel die Kunst wiederum als eine der Religion und der Philosophie unterlegene Form betrachtet. (...) Dass die Poesie eine den anderen Künsten überlegene Kunstform ist, ist auf den ersten Blick eine überraschende These; und sie wirkt noch überraschender, wenn man sie durch die These ergänzt, dass die Kunst wiederum durch die Religion und die Philosophie als weitere Phasen eines linearen Prozesses aufgehoben wird. Um was für einen linearen Prozess handelt es sich hier eigentlich? Ein linearer Prozess wohin? Der Prozess, von dem Hegel in diesem Kontext spricht, ist ein Erkenntnisprozess, und zwar ein ziemlich spezifischer Erkenntnisprozess, nämlich Erkenntnis des Absoluten. Die Poesiegattung, die für Hegel die Endphase der Kunst ausmacht, ist das moderne Drama, in dessen Zentrum die Darstellung des Charakters und der Handlungen seiner verschiedenen Gestalten steht. Was hat das alles aber mit dem Absoluten zu tun? Was haben das Drama und seine Subgattungen - der Tragödie, der Komödie, der Satire usw. - mit Religion und Philosophie zu tun? Hegel verbindet außerdem die Kunst mit dem Absoluten als eine Erkenntnisform desselben. Aber in welchem Sinne ist die Kunst Erkenntnis? Ist Kunst nicht eher Darstellung und Ausdruck subjektiver Gefühle und Ideen - und eben nicht ein Erfassen der Realität, eben nicht eine Erkenntnisform der Wirklichkeit? Um den allgemeinen Sinn von Hegels Ästhetik und dadurch die besondere Rolle, die er darin der Poesie zuschreibt, verstehen zu können, ist es unentbehrlich, die oben gestellten Fragen zu beantworten. Ein theoretisches und exegetisches Modell zu liefern, das imstande ist, eine solche Aufgabe zu erfüllen, ist das Ziel dieses Beitrags. (shrink)

La exterioridad de una cosa o de un estado de cosas configurados por el ser humano no implica para Hegel que esa cosa o ese estado de cosas deban ya por ello ser considerados como formas del espíritu objetivo, mientras que en contrapartida las formas del espíritu absoluto estarían entonces conformadas por contenidos ideales del pensamiento. La diferencia entre espíritu objetivo y espíritu absoluto no radica en la diferencia entre lo que el espíritu humano “hace” y lo que “conoce”. En (...) efecto, las obras de arte, es decir, configuraciones exteriores hechas por el ser humano utilizando, por ejemplo, piedras, metales, colores o sonidos, son para Hegel instancias del espíritu absoluto, mientras que, por su parte, realidades que en cuanto tales no son intuibles, como, por ejemplo, los contratos o la organización estatal, son instancias del espíritu objetivo. Que Hegel considere al arte como una forma del espíritu absoluto pone de manifiesto que, a sus ojos, las cosas que intuimos en el universo son, en rigor, productos del propio sujeto que las conoce. Espontáneamente el sujeto cognoscente piensa que lo que intuye es algo que recibe desde un mundo externo; sostener que el arte es una forma de conocimiento es justamente el modo como Hegel está expresando que lo intuido es en todos los casos un contenido producido por el propio espíritu, que es, por así decirlo, una obra de arte humano. En el arte mismo, sin embargo, la producción de la cosa intuible es insuficiente, dado que el material que el espíritu utiliza para sus configuraciones conserva en mayor o menor medida, según el caso, una determinidad propia que resiste a la determinidad que el espíritu busca conferirle. Por esta razón, las obras de arte se presentan inicialmente como productos arbitrarios. Recién cuando integra sus intuiciones en la actividad de comprensión -actividad cognitiva con la que opera la filosofía- y media con ello completamente la determinidad de los contenidos intuidos, el espíritu configura finalmente un universo que le es propio y específico. El objetivo de mi ponencia es reconstruir desde el marco teórico recién expuesto el sentido y función que Hegel le atribuye al arte en su teoría del conocimiento. (shrink)