We offer an analysis of the disciplinary transformations underwent by mathematical or symbolic logic since its emergence in the late 19th century. Examined are its origins as a hybrid of philosophy and mathematics, the maturity and institutionalisation attained under the label �logic and foundations,� a second wave of institutionalisation in the Postwar period, and the institutional developments since 1975 in connection with computer science and with the study of language and informatics. Although some �internal history� is discussed, the main focus (...) is on the emergence, consolidation and convolutions of logic as a discipline, through various professional associations and journals, in centers such as Torino, Göttingen, Warsaw, Berkeley, Princeton, Carnegie Mellon, Stanford, and Amsterdam. (shrink)

Dedekind used to refer to Riemann as his main model concerning mathematical methodology, particularly regarding the use of abstract notions as a basis for mathematical theories. So, in passages written in 1876 and 1895 he compared his approach to ideal theory with Riemann’s theory of complex functions. In this paper, I try to make sense of those declarations, showing the role of abstract notions in Riemann’s function theory, its influence on Dedekind, and the importance of the methodological principle of avoiding (...) ‘forms of representation’ in shaping ideal theory. In order to emphasize the abstract viewpoint of Riemann and Dedekind, I compare their work with that of their great german contemporaries, Weierstrass and Kronecker; so, an influential ‘Göttingen group’ is confronted with the ‘Berlin school’ of mathematics. Some light is also thrown on the relation between Riemann and Dedekind, particularly with respect to Dedekind’s interest on Riemann’s ideas --in function theory, geometry and topology--, beginning in the 1850s and through later works. The abstract approach of the ‘Göttingen group’ was determinant for the turn to abstract mathematics in our century, and the direct influence of Riemann on Dedekind shows how this approach developed. (shrink)

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.

El deporte como realización genuinamente humana, su evolución a través del tiempo y su configuración actual son algunas de las claves que plantea esta obra para tratar de aproximar al lector al complejo mundo de la realidad deportiva. A caballo entre el estudio científico y el ensayo, el libro resume a lo largo de sus cuatro capítulos todas las pautas y componentes que de alguna manera han podido influir en la historia pasada y presente; e incluso se nos muestran las (...) que pudieran intervenir en las futuras formas deportivas. Un estilo conciso y directo, junto a la brevedad de la exposición, constituyen alicientes añadidos para disfrutar de este trabajo. (shrink)

La evolución del rol del profesor en las aulas en las dos últimas décadas se ha destacado por la preocupación de cumplir con las grandes exigencias de las instituciones educativas: adquirir habilidades digitales que les permita alcanzar un nivel “óptimo” de conocimiento en el uso de los recursos tecnológicos informáticos e incorporar estos recursos en sus actividades en el aula. No obstante, aún no se encuentra la fórmula para que los profesores modifiquen el modelo de enseñanza (transmisor-receptor) vigente en las (...) escuelas y en el salón de clase. Sin embargo, aunque las actividades que se realizan en el aula se encierran en una aparente caja negra, en este trabajo se presentan modelos tecno-pedagógicos que han implementado profesores de educación superior en el aula y que propone un nuevo rol del profesor, el docente innovador. Un profesor que combina el curriculum, contenidos, didácticas, actitudes, habilidades digitales, y estilos de aprendizaje para innovar en su método didáctico y que da cuenta de su habilidad didáctica, su conocimiento y preparación profesional así como de una cultura digital que va más allá de saber usar los dispositivos digitales y que conjunta los saberes humanos y tecnológicos en un modelo tecno-pedagógica para construir nuevos entornos de aprendizaje y modelos de enseñanza. (shrink)

Understanding how people behave when facing hazardous situations, how intrinsic and extrinsic factors influence the risk taking (RT) decision making process and to what extent it is possible to modify their reactions externally, are questions that have long interested academics and society in general. In the spheres of Occupational Safety and Health (OSH), the military, finance and sociology, this topic has multidisciplinary implications because we all constantly face risk taking situations. Researchers have hitherto assessed risk taking profiles by conducting questionnaires (...) prior to and after the presentation of stimuli; however, this can lead to the production of biased, non-realistic, risk taking profiles. This is due to the reflexive nature of choosing an answer in a questionnaire, which is remote from the reactive, emotional and impulsive decision making processes inherent to real, risky situations. One way to address this question is to exploit VR capabilities to generate immersive environments that recreate realistic seeming but simulated hazardous situations. We propose VR as the next-generation tool to study risk taking processes, taking advantage of the big four families of metrics which can provide objective assessment methods with high ecological validity: the real-world risks approach (high presence VR environments triggering real-world reactions), embodied interactions (more natural interactions eliciting natural behaviours), stealth assessment (unnoticed real-time assessments offering efficient behavioural metrics) and physiological real-time measurement (physiological signals avoiding subjective bias). Additionally, VR can provide an invaluable tool, after the assessment phase, to train in skills related to risk taking due to its transferability to real-world situations. (shrink)

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)

La carta Placuit Deo es un documento preciso e iluminador para presentar una comprensión cristiana de la salvación. Se destacan sólo algunos aspectos, pero se explican en un conjunto que ofrece el esquema fundamental para una soteriología. En el documento aparecen contenidos básicos y criterios orientativos para una reflexión sobre la salvación.

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 is a contribution to the philosophy of experimental work, engaging with questions posed by Hacking, Franklin, Pickering, Schaffer and Collins. It focuses on the dynamics of experimentation and offers a detailed argument that one finds no "regress" of the kind posited by Collins. In particular, we reanalyze the celebrated series of experimental investigations by Newton on optical phenomena, taking into account Schaffer's partial reconstruction, and we show how it must be supplemented to obtain a more complete picture.

A long-awaited edition of Zermelo’s works Content Type Journal Article Pages 1-4 DOI 10.1007/s11016-011-9548-y Authors José Ferreirós, Instituto de Filosofia, CCHS-CSIC, Albasanz, 26-28, 28037 Madrid, Spain Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

El análisis de los sesgos de género en ciencia ha dado lugar a una revisión crítica del conocimiento científico y a un cuestionamiento en profundidad del modelo de ciencia existente. Lo que, a su vez, da paso al interés por investigar en torno a las claves epistémicas que harían posible una ciencia no sexista, racista o clasista, fraguando un debate epistemológico de gran alcance.Las pretensiones de estas epistemologías son, principalmente, mostrar que los valores contextuales, es decir, los considerados no cognitivos, (...) influyen en la ciencia, en las metáforas científicas, el lenguaje utilizado, los procesos y métodos de investigación, y en los conocimientos. En esta comunicación se abordará principalmente el tema de la Ciencia Sostenible como alternativa a la denominada ciencia tradicional, y también como disyuntiva a la denominada ciencia feminista. Las posturas que confluyen son las de tres autoras: D. Haraway, S. Harding y Londa Schiebinger. Las cuales, en conjunto, dan lugar a una actividad práctica en ciencia, además de a una forma de mirar diferente, que intenta elaborar propuestas novedosas para la mejora del quehacer científico. (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)

Some transhumanist authors make the prophecy of immortality thanks to the transfer of the human mind to a superintelligent computer that would guarantee the survival of the person. That immortality would mean a happy life. In this article we try to show that this supposed indefinite survival is not exactly what is usually understood by immortality. In addition, we try to think about what immortality is based on the theological understanding of eternity and personal communion in which the life of (...) God consists. The decisive questions in this dialogue with the postures of transhumanism are the meaning of the body for the human person and what happiness is. (shrink)

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

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)

info:eu-repo/semantics/publishedVersion.

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)

Desde la didáctica de la Historia, el análisis de los libros de texto es una de las líneas de investigación más arraigadas en los últimos años. Este trabajo analiza la forma en que se ha enseñado la Transición democrática a través de libros de texto de Bachillerato correspondientes a la asignatura de Historia de España, de diferentes editoriales, tanto confesionales como laicas.

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...

Traducción de "Ortega ante el lenguaje." en: Ortega y la cultura española. Madrid, Cincel 1985.

A book-length study of Riemann's multi-dimensional work (in Spanish), which considers his contributions to physics, philosophy and mathematics. Plus a bi-lingual edition (German-Spanish) of some of his landmark papers: the lecture on geometry, with Weyl's comments; the paper introducing the Riemann Conjecture, part of his 1857 paper on function theory; all of the philosophical fragments, etc. These different contributions, and their interconnections, are carefully studied in the introductory essay of 150 pages.

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)

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)

The present paper is a contribution to the history of logic and its philosophy toward the mid-20th century. It examines the interplay between logic, type theory and set theory during the 1930s and 40s, before the reign of first-order logic, and the closely connected issue of the fate of logicism. After a brief presentation of the emergence of logicism, set theory, and type theory, Quine’s work is our central concern, since he was seemingly the most outstanding logicist around 1940, though (...) he would shortly abandon that viewpoint and promote first-order logic as all of logic. Quine’s class-theoretic systems NF and ML, and his farewell to logicism, are examined. The last section attempts to summarize the motives why set theory was preferred to other systems, and first orderlogic won its position as the paradigm logic system after the great War. (shrink)

El objetivo de este artículo es el de explorar las principales características del ensayo como genus dicendi filosófico y cómo se cumplen en las obras de Ortega. En consecuencia, analizo en primer lugar las cuatro características principales del búsqueda de la verdad, valor cognitivo de las opiniones, rechazo del argumento de autoridad y tolerancia intelectual. Y, en segundo lugar, demuestro cómo se han tenido en cuenta en los escritos filosóficos de Ortega. ENGLISH: The aim of this paper is to explore (...) the main characteristics of the essay as philosophical genus dicendi and how they are fulfilled in Ortega’s works. Consequently, I firstly analyze the main four characteristics of the essay, namely, search for truth, cognitive value of opinions, rejection of the argument from authority, and intellectual tolerance. And secondly, I demonstrate how they have been taken into account by Ortega in his philosophical writing. (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)

El artículo explora la crítica de Santiago Ramírez a la clasificación de la analogía de Cayetano. Ramírez argumenta que la división tradicional de la analogía no refleja completamente la complejidad de las nociones de santo Tomás de Aquino. En particular, se introduce la "analogía de atribución intrínseca" como una categoría adicional dentro de la analogía de atribución. A través de un análisis detallado, el texto examina cómo esta forma de analogía mantiene elementos de la proporcionalidad y la atribución extrínseca, pero (...) se distingue por ser una atribución "según el ser" y "según la intención". Se destacan las implicaciones teológicas y filosóficas de esta distinción, especialmente en relación con la predicación del concepto de verdad respecto a Dios, las criaturas y los juicios humanos. (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)

We offer an analysis of the disciplinary transformations underwent by mathematical or symbolic logic since its emergence in the late 19 th century. Examined are its origins as a hybrid of philosophy and mathematics, the maturity and institutionalisation attained under the label “logic and foundations,” a second wave of institutionalisation in the Postwar period, and the institutional developments since 1975 in connection with computer science and with the study of language and informatics. Although some “internal history” is discussed, the main (...) focus is on the emergence, consolidation and convolutions of logic as a discipline, through various professional associations and journals, in centers such as Torino, Göttingen, Warsaw, Berkeley, Princeton, Carnegie Mellon, Stanford, and Amsterdam. (shrink)