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...

A general introduction to the celebrated foundational crisis, discussing how the characteristic traits of modern mathematics (acceptance of the notion of an “arbitrary” function proposed by Dirichlet; wholehearted acceptance of infinite sets and the higher infinite; a preference “to put thoughts in the place of calculations” and to concentrate on “structures” characterized axiomatically; a reliance on “purely existential” methods of proof) provoked extensive polemics and alternative approaches. Going beyond exclusive concentration on the paradoxes, it also discusses the role of the (...) axiom of Choice, issues of predicativity, and goes on to present the ideas of intuitionism and Hilbert's program. The essay closes with Gödel's contributions and the aftermath. (shrink)

Building on evidence for embodied representations, we investigated whether Spanish spatial terms map onto the NEAR/FAR perceptual division of space. Using a long horizontal display, we measured congruency effects during the processing of spatial terms presented in NEAR or FAR space. Across three experiments, we manipulated the task demands in order to investigate the role of endogenous attention in linguistic and perceptual space mapping. We predicted congruency effects only when spatial properties were relevant for the task but not when attention (...) was allocated to other features. Results showed faster responses for words presented in Near-space in all experiments. Consistent with our hypothesis, congruency effects were observed only when a reaching estimate was requested. Our results add important evidence for the role of top-down processing in congruency effects from embodied representations of spatial terms. (shrink)

Building on evidence for embodied representations, we investigated whether Spanish spatial terms map onto the NEAR/FAR perceptual division of space. Using a long horizontal display, we measured congruency effects during the processing of spatial terms presented in NEAR or FAR space. Across three experiments, we manipulated the task demands in order to investigate the role of endogenous attention in linguistic and perceptual space mapping. We predicted congruency effects only when spatial properties were relevant for the task but not when attention (...) was allocated to other features. Results showed faster responses for words presented in Near-space in all experiments. Consistent with our hypothesis, congruency effects were observed only when a reaching estimate was requested. Our results add important evidence for the role of top-down processing in congruency effects from embodied representations of spatial terms. (shrink)

Review of: José Ferreirós. 2016. Mathematical knowledge and the interplay of practices. Princeton: Princeton University Press.

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 ofrece dos formas -en su filosofía en último análisis complementarias- de caracterizar al idealismo: La primera es próxima a la concepción habitual de idealismo previa a Kant, a saber: como una posición que considera que aquello que conocemos es una modificación de la propia conciencia. La segunda descansa en la tesis de la nulidad de lo finito; según esto, ?idealista? es la filosofía que considera que lo finito no tiene en cuanto tal realidad; ?realista?, a la inversa, es la (...) filosofía que toma el ser de las cosas determinadas como algo fijo y definitivo. Hegel denomina a este idealismo ?absoluto?.El idealismo absoluto es el modelo teórico que interrelaciona la tesis del carácter intrínsecamente ideal de los objetos de conocimiento y la tesis de que las cosas singulares que constituyen el mundo real surgen como una autodeterminación del ser. La premisa que permite tal vínculo es la tesis defendida por Hegel de que ser y pensar nunca se han separado y que su separación es el resultado de una concepción posterior errónea de la mente humana sobre la naturaleza de su actividad cognitiva. La hipostasiación de la disociación que la forma cognitiva de la representación introduce en la unidad indiferenciada de ser y pensar de la que parte la actividad de conocimiento en el sentimiento y la intuición sensibles es para Hegel la que provoca la ilusión retroactiva de que ambos -ser y pensar, mundo conocido y mente que conoce- se diferencian y contraponen. Por el contrario, desde el momento que la sensación es también ella misma un modo particular de la actividad continua e ininterrumpida del pensamiento, en el itinerario que va de la percepción sensible a la comprensión del objeto no hay para Hegel un punto en donde pueda introducirse una fractura que disuelva la unidad primigenia entre el ser y el pensar. En esta precisa medida, el momento final de la actividad de conocimiento, es decir, la actividad de comprender el mundo, es a un tiempo la singularización de los contenidos universales que constituyen la teoría del sujeto sobre el mundo y la autodeterminación de la unidad ser-pensar de la que parte y en todo momento permanece el sujeto que elabora esa teoría. Arribados al punto de vista del concepto, la dicotomía realismo-idealismo queda develada como un corolario de la autoconcepción representacionalista de la subjetividad cognoscente. Esta concepción define al paradigma general del realismo, el cual incluye para Hegel como el anverso y reverso de un mismo modelo teórico tanto lo que tradicionalmente ha sido entendido como realismo como al idealismo que resulta de una universalización de la idealidad de la conciencia singular, ya sea en la variante propuesta por Berkeley, ya sea en la del idealismo trascendental de Kant. A ojos de Hegel, por el contrario, el idealismo no puede ser sino absoluto, es decir, debe incluir en sí mismo el momento del ser y, con él, la realidad de las cosas que el sujeto conoce: la tarea esencial de la filosofía no consiste para Hegel más que en tomar conciencia de la co-pertenencia y unidad intrínseca de ambos. (shrink)

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.

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)

Reductive intellectualists hold that knowledge-how is a kind of knowledge-that. For this thesis to hold water, it is obviously important that knowledge-how and knowledge-that have the same epistemic properties. In particular, knowledge-how ought to be compatible with epistemic luck to the same extent as knowledge-that. It is argued, contra reductive intellectualism, that knowledge-how is compatible with a species of epistemic luck which is not compatible with knowledge-that, and thus it is claimed that knowledge-how and knowledge-that come apart.

Aristotle is widely regarded as the greatest of all philosophers; indeed, he is traditionally referred to simply as `the philosopher'. Today, after more than two millennia, his arguments and ideas continue to stimulate philosophers and provoke them to controversy. In this book J.L. Ackrill conveys the force and excitement of Aristotle's philosophical investigations, thereby showing why contemporary philosophers still draw from him and return to him. He quotes extensively from Aristotle's works in his own notably clear English translation, and a (...) picture emerges of a lucid, lively, subtle and tough-minded thinker of astonishing range and penetration. Professor Ackrill identifies many striking connections between Aristotle's ideas and ideas in recent philosophy; he also raises philosophical questions of his own, and exemplifies the way in which Aristotle can still be argued with and learned from. (shrink)

This paper examines the Aristotelian roots of the mechanics of naval architecture, beginning with Mechanical Problems, through its various interpretations by Renaissance mathematicians including Vettor Fausto and Galileo at the Venice Arsenal, and culminating in the first synthetic works of naval architecture by the French navy professor Paul Hoste at the end of the seventeenth century.

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.

Como parte de las sucesivas modificaciones al marco jurídico que regula el sistema educativo mexicano, la rendición de cuentas basada en evidencias se ha convertido en una nueva responsabilidad para los docentes del nivel básico. No obstante, se sabe poco acerca de qué significa para los docentes, cómo la han asumido, más aún, qué efectos ha provocado en la práctica cotidiana. Por tal motivo, se realizó un estudio cuyo propósito fue analizar los efectos de la rendición de cuentas en el (...) trabajo docente, con particular atención a la dimensión pedagógica. Mediante entrevistas semiestructuradas a diez docentes de escuelas públicas de la Ciudad de México, se encontró lo que denominamos una autonomía relativa, limitada y mediada por múltiples disposiciones normativas; la invención de realidades como estrategia para cumplir con la entrega de informes y toda clase de evidencias requeridas por diversas autoridades; una idoneidad multitarea, reflejada en una multiplicidad de actividades más allá de la enseñanza; finalmente una profesionalización mecanicista, es decir, una búsqueda constante de cursos y talleres por cuenta propia pero siempre sobre temas y contenidos instrumentales. (shrink)

La presente comunicación tiene como principal objetivo poner sobre la mesa algunos de los problemas que latían de fondo en algunas de las charlas del anterior VII Congreso sobre Pensamiento Filosófico Contemporáneo de la Sociedad Asturiana de Filosofía. No pretendo, sin embargo, exponer tesis alguna, sino que procuraré dialogar con las ideas del pasado Congreso de la SAF, y así poder ganar distancia para orientar mejor la mirada o proponer una actitud diferente ante las cuestiones. Comenzaré centrándome en una de (...) las comunicaciones, concretamente la de Virginia Ballesteros. A continuación, procuraré señalar los presupuestos fundamentales que latían de fondo a partir de las investigaciones de Felipe Martínez Marzoa, con el que intentaré mostrar qué elementos se encuentran a la base de la violencia ontológica en nuestras sociedades. Finalmente, y sólo para señalar posibles líneas de investigación, indicaré brevemente una probable relación alternativa entre fenomenología y medicina. (shrink)

The aim of this paper is to argue that there existed relevant interactions between mechanics and geometry during the first half of the nineteenth century, following a path that goes from Gauss to Riemann through Jacobi. By presenting a rich historical context we hope to throw light on the philosophical change of epistemological categories applied by these authors to the fundamental principles of both disciplines. We intend to show that presentations of the changing status of the principles of mechanics as (...) a mere epiphenomenon of the emergence of non-Euclidean geometries are inaccurate, that the relations between the two disciplines were richer than what is usually considered in the literature. These claims will be based on historical and philosophical arguments, starting from the fact that disciplinary boundaries at the time were not rigid as we are used today. It is widely known that the main figures we target worked in different areas, which is a first piece of evidence for the plausibility of our main thesis. (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)

Guest Editors’ introduction to the Monographic Section.

A historical investigation of the exclusion of Africa and Asia from modern histories of philosophy.

This comprehensive and important volume includes contributions by activists, journalists, lawyers and scholars from twenty-one countries. The essays map the directions the movement for women's rights is taking--and will take in the coming decades--and the concomittant transformation of prevailing notions of rights and issues. They address topics such as the rapes in former Yugoslavia and efforts to see that a War Crimes Tribunal responds; domestic violence; trafficking of women into the sex trade; the persecution of lesbians; female genital mutilation; and (...) reproductive rights. (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)

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)

Presents general information about meteorology, weather, and climate and includes more than thirty activities to help study these topics, including making a ...

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)

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)

This paper argues that for the purposes of any sort of serious discussion about immoral conduct in sport very little is illuminated by claiming that the conduct in question is cheating. In fact, describing some behavior as cheating is typically little more than expressing strong, but thoroughly vague and imprecise, moral disapproval or condemnation of another person or institution about a wide and ill-defined range of improper advantage-seeking behavior. Such expressions of disapproval fail to distinguish cheating from many other types (...) of immoral conduct. The discussion shows that we should set the concept aside and assess the moral disapproval implied by claims of cheating by reference to the moral and other principles that underlie the practice of sport. This allows us to consider carefully the complexity of the issues that are raised when allegations of cheating are made and not be distracted by the emotionally loaded, conversation-stopping tendency of the concept. This means that some types of disputes in sport will be messy and demand more effort to resolve, but the payoff will be better informed and more thoughtful discussions and greater awareness of the moral complexity of sport and of its principled underpinnings. (shrink)