Developing earlier studies of the system of numbers in Mundurucu, this paper argues that the Mundurucu numeral system is far more complex than usually assumed. The Mundurucu numeral system provides indirect but insightful arguments for a modular approach to numbers and numerals. It is argued that distinct components must be distinguished, such as a system of representation of numbers in the format of internal magnitudes, a system of representation for individuals and sets, and one-to-one correspondences between the numerosity expressed by (...) the number and its metrics. It is shown that while many-number systems involve a compositionality of units, sets and sets composed of units, few-number languages, such as Mundurucu, do not have access to sets composed of units in the usual way. The nonconfigurational character of the Mundurucu language, which is related to a property for which we coin the term 'low compositionality power', accounts for this and explains the curious fact that Mundurucus make use of marked one-to-one correspondence strategies in order to overcome the limitations of the core system at the perceptual/motor interface of the language faculty. We develop an analysis of a particular construction, parallel numbers, which has not been studied before, elucidating the whole system. This analysis, we argue, sheds new light on classical philosophical, psychological and linguistic debates about numbers and numerals and their relation to language, and more particularly, sheds light on few-number languages. (shrink)

Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers larger than 4 (...) or 5. Our results imply a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic. (shrink)

The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and logarithmic (...) mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education. (shrink)

Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that (...) are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ∼180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics. (shrink)

Does geometry constitues a core set of intuitions present in all humans, regarless of their language or schooling ? We used two non verbal tests to probe the conceptual primitives of geometry in the Munduruku, an isolated Amazonian indigene group. Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms.

Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS : the fact that all numbers can be generated by (...) a successor function and the fact that equality between numbers can be defined in an exact fashion. We discuss some recent findings assessing how speakers of Munduruc (an Amazonian language), and young Western children (3-4 years old) understand these fundamental properties of numbers. (shrink)

The relationship between language and conceptual thought is an unresolved problem in both philosophy and psychology. It remains unclear whether linguistic structure plays a role in our cognitive processes. This special issue brings together cognitive scientists and philosophers to focus on the role of language in numerical cognition: because of their universality and variability across languages, number words can serve as a fruitful test case to investigate claims of linguistic relativism.

Our paper presents a novel theory of weak crossover effects, based entirely on quantifier scope preferences and their consequences for variable binding. The structural notion of 'crossover' play no role. We develop a theory of scope preferences which ascribes a central role to the AGR-P System.

Geometry defines entities that can be physically realized in space, and our knowledge of abstract geometry may therefore stem from our representations of the physical world. Here, we focus on Euclidean geometry, the geometry historically regarded as “natural”. We examine whether humans possess representations describing visual forms in the same way as Euclidean geometry – i.e., in terms of their shape and size. One hundred and twelve participants from the U.S. (age 3–34 years), and 25 participants from the Amazon (age (...) 5–67 years) were asked to locate geometric deviants in panels of 6 forms of variable orientation. Participants of all ages and from both cultures detected deviant forms defined in terms of shape or size, while only U.S. adults drew distinctions between mirror images (i.e. forms differing in “sense”). Moreover, irrelevant variations of sense did not disrupt the detection of a shape or size deviant, while irrelevant variations of shape or size did. At all ages and in both cultures, participants thus retained the same properties as Euclidean geometry in their analysis of visual forms, even in the absence of formal instruction in geometry. These findings show that representations of planar visual forms provide core intuitions on which humans’ knowledge in Euclidean geometry could possibly be grounded. (shrink)

All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to mathematics education. (...) By comparing Mundurucú subjects with and without access to schooling, we found that education significantly enhances the acuity with which sets of concrete objects are estimated. These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction. (shrink)

Geometry, etymologically the “science of measuring the Earth”, is a mathematical formalization of space. Just as formal concepts of number may be rooted in an evolutionary ancient system for perceiving numerical quantity, the fathers of geometry may have been inspired by their perception of space. Is the spatial content of formal Euclidean geometry universally present in the way humans perceive space, or is Euclidean geometry a mental construction, specific to those who have received appropriate instruction? The spatial content of the (...) formal theories of geometry may depart from spatial perception for two reasons: first, because in geometry, only some of the features of spatial figures are theoretically relevant; and second, because some geometric concepts go beyond any possible perceptual experience. Focusing in turn on these two aspects of geometry, we will present several lines of research on US adults and children from the age of three years, and participants from an Amazonian culture, the Mundurucu. Almost all the aspects of geometry tested proved to be shared between these two cultures. Nevertheless, some aspects involve a process of mental construction where explicit instruction seem to play a role in the US, but that can still take place in the absence of instruction in geometry. (shrink)

La connaissances noyau de la géométrie euclidienne est liée au raisonnement déductif et non à la reconnaissance de motifs perceptuels.

The performance of the Mundurucu on the number-space task may exemplify a general competence for drawing analogies between space and other linear dimensions, but Mundurucu participants spontaneously chose number when other dimensions were available. Response placement may not reflect the subjective scale for numbers, but Cantlon et al.'s proposal of a linear scale with scalar variability requires additional hypotheses that are problematic.

Des branches entières des mathématiques sont fondées sur des liens posés entre les nombres et l’espace : mesure de longueurs, définition de repères et de coordonnées, projection des nombres complexes sur le plan… Si les nombres complexes, comme l’utilisation de repères, sont apparus relativement récemment (vers le XVIIe siècle), la mesure des longueurs est en revanche un procédé très ancien, qui remonte au moins au 3e ou 4e millénaire av. J-C. Loin d’être fortuits, ces liens entre les nombres et l’espace (...) reflèteraient une intuition fondamentale, universelle, façonnée au cours des millénaires par la sélection naturelle, et qui aurait servi de guide et d’inspiration aux mathématiciens au fil des siècles. (shrink)

We agree with Nuñez that the Mundurucu do not master the formal propreties of number lines and logarithms, but as the term "intuition" implies, they spontaneously experience a logarithmic mapping of number to space as natural and "feeling right.".

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an intuition of a more complex calculation, division, exists in an indigene group in the Amazon, the Mundurucu, whose language includes no words for large numbers. Mundurucu children were presented with a video event (...) depicting a division transformation of halving, in which pairs of objects turned into single objects, reducing the array's numerical magnitude. Then they were tested on their ability to calculate the outcome of this division transformation with other large-number arrays. The Mundurucu children effected this transformation even when non-numerical variables were controlled, performed above chance levels on the very first set of test trials, and exhibited performance similar to urban children who had access to precise number words and a surrounding symbolic culture. We conclude that a halving calculation is part of the suite of intuitive operations supported by the ANS. (shrink)

Qu'est-ce que la 'déconstruction'? Quelles sont les origines philosophiques de ce mot magique, brandi par tous ceux dont le but, déclaré ou non, est de criminaliser l'Occident en le réduisant à une expression du racisme, de l'esclavagisme, de l' 'hétéro-patriarcat' et de l'impérialisme colonial? Cette civilisation redoutable dont les proies seraient les peuples dominés, racisés, opprimés, et les minorités essentialisées en tant que victimes systémiques? Ainsi la civilisation occidentale se trouve-t-elle convoquée devant un nouveau grand Tribunal de l'Histoire pour répondre (...) de ses crimes, imaginaires ou réels, et, surtout, elle est la seule civilisation à être mise au banc des accusés. Au croisement de la recherche universitaire et du militantisme politique, le décolonialisme, l'intersectionnalité, la 'théorie critique de la race', la 'théorie queer', la 'théorie du genre', mais aussi le 'wokisme', né d'une corruption idéologique de l'antiracisme et du féminisme importée des campus étatsuniens, se sont peu à peu diffusés dans les médias et dans la société tout entière grâce à une propagande violente et culpabilisante puisant dans un imaginaire victimaire. Dans ce livre incisif et documenté, qui part d'une réflexion sur la pensée de Nietzsche et sur ses mésusages par les disciples français de Heidegger, Pierre-André Taguieff analyse ces théories aussi foisonnantes qu'inconsistantes et dénonce l'émergence de ce nouvel esprit totalitaire qu'il faut se garder de réduire à ses effets les plus médiatisés, comme ces 'déboulonnages' spectaculaires illustrant la violence purificatrice de la 'cancel culture'. De fait, ce néo-puritanisme obscurantiste, inquisitorial et punitif représente, dans les démocraties occidentales, un défi majeur pour les défenseurs de la liberté d'expression, de pensée et de création."--Back cover. (shrink)

Comment devient-on philosophe? Par quel sursaut un Aristoclès se fait-il Platon, jusqu'à s'imposer dans la liste des " auteurs philo " Il faut enquêter, non pas sur la vie privée, mais sur la vie intime : rumination intellectuelle, ton sur lequel on parle, motivations amoureuses... Ce qui fait un philosophe, c'est un immense travail sur soi, et la rencontre d'autres philosophes, vivants, de leurs problématiques. Mémoire sémantique + obsession métaphysique, voilà le code génétique du philosophe. Il débute par un attentat (...) religieux, puisqu'il commence sa carrière en niant tel ou tel sacré. Bien sûr, il vaut mieux être mâle, communiquer par les livres adopter la langue dominante, écrire quand on est célibataire. Comment gagner sa vie? Pas forcément en étant enseignant, comme c'est le cas aujourd'hui. Le profil du philosophe nous le révèle orphelin, vivant à l'étranger, souvent laid, jamais fou, et serial thinker, prêt à changer de philosophie pourvu qu'il reste, lui, à menacer le monde donnera ou donnera pas du sens à notre vie? Le philosophe est l'être inquiet qui pense inquiéter l'Être par deux trois mots bien aiguisés. (shrink)

Synthesizing forty years' work by France's leading sociologist, this book exemplifies Bourdieu's unique ability to link sociological theory, historical information, and philosophical thought. It makes explicit the presuppositions of a state of 'scholasticism', a certain leisure liberated from the urgencies of the world. Philosophers have brought these presuppositions into the order of discourse, more to legitimate than analyze them, and this is the primary systematic, epistemological, ethical, and aesthetic error that Bourdieu subjects to methodological critique. Pascalian because he, too, was (...) concerned with symbolic power, he refused the temptation of foundationalist thinking, attended to 'ordinary people', and was determined to seek the reason for seemingly illogical behavior rather than simply condemning it. Bourdieu charts a negative philosophy, whose intellectual debt to such other 'heretical' philosophers as Wittgenstein, Austin, Dewey, and Peirce, renews traditional questioning of concepts of violence, power, time, history, the universal, and the purpose and direction of existence. (shrink)

During the last two decades, sociologist Pierre Bourdieu has become a dominant force in cultural activity ranging from taste in music and art to choices in food and lifestyles. _The Field of Cultural Production_ brings together Bourdieu's major essays on art and literature and provides the first introduction to Bourdieu's writings and theory of a cultural field that situates artistic works within the social conditions of their production, circulation, and consumption. Bourdieu develops a highly original approach to the study (...) of literary and artistic works, addressing many of the key issues that have preoccupied literary art and cultural criticism in the last twentieth century: aesthetic value and canonicity, intertextuality, the institutional frameworks of cultural practice, the social role of intellectuals and artists, and structures of literary and artistic authority. Bourdieu elaborates a theory of the cultural field which situates artistic works within the social conditions of their production, circulation, and consumption. He examines the individuals and institutions involved in making cultural products what they are: not only the writers and artists, but also the publishers, critics, dealers, galleries, and academies. He analyzes the structure of the cultural field itself as well as its position within the broader social structures of power. The essays in his volume examine such diverse topics as Flaubert's point of view, Manet's aesthetic revolution, the historical creation of the pure gaze, and the relationship between art and power. The Field of Cultural Porduction will be of interest to students and scholars from a wide range of disciplines: sociology and social theory, literature, art, and cultural studies. (shrink)

Written with verve and intensity (and a good bit of wordplay), this is the long-awaited study of Flaubert and the modern literary field that constitutes the ...

Over the last four decades, the French sociologist Pierre Bourdieu produced one of the most imaginative and subtle bodies of social theory of the postwar era. When he died two years ago, he was considered to be a thinker on a par with Foucault, Barthes, and Lacan--a public intellectual as influential to his generation as Sartre was to his. Science of Science and Reflexivity will be welcomed as a companion volume to Bourdieu's now seminal An Invitation to Reflexive Sociology (...) . In this posthumous work, Bourdieu declares that science is in danger of becoming a handmaiden to biotechnology, medicine, genetic engineering, and military research--that it risks falling under the control of industrial corporations that seek to exploit it for monopolies and profit. Science thus endangered can become detrimental to mankind. The line between pure and applied science, therefore, must be subjected to intense theoretical scrutiny. Bourdieu's goals in Science of Science and Reflexivity are to identify the social conditions in which science develops in order to reclaim its objectivity and to rescue it from relativism and the forces that might exploit it. In the grand tradition of scientific reflections on science, Bourdieu provides a sociological analysis of the discipline as something capable of producing transhistorical truths he presents an incisive critique of the main currents in the study of science throughout the past half century and he offers a spirited defense of science against encroaching political and economic forces. A masterful summation of the principles underlying Bourdieu's oeuvre and a memoir of his own scientific journey, Science of Science and Reflexivity is a capstone to one of the most important and prodigious careers in the field of sociology. (shrink)

Replete with madwomen, murderers, musicians, and mystics, "Lonely Woman" dramatically interweaves the lives of five women. It remains Takako Takahashi's most sustained and multifaceted fictional realization of her concept of "loneliness.".

This study investigated subjective experiences of nine men who had been psychiatrically hospitalized upon being assessed as "dangerous-to-others-due-to-a-mental-illness." Using a phenomenological interviewing approach, researchers helped subjects construct narratives of their pre-hospitalization experiences. The research illuminated aspects of life-contexts that were shared among all or nearly all subjects: feeling ostracized and alone; struggling with longstanding and pervasive feelings of inadequacy; experiencing a sense or a fear of having little or no control or options in life; and feeling emotionally depressed, misunderstood, and (...) uncared for. Situations immediately preceding hospitalization were characterized by subjects experiencing threats to their sense of self-esteem that were of heightened intensity. In five cases, subjects reported anxiety related to self-fragmentation or becoming "nothing." Perceived threats to self-worth and self-structure were accompanied by anger and aggressive acts or impulses. In all cases, aggressive impulses and threats, and violence appeared to be in the service of self-validation and self-empowerment. In cases of violent behavior, an apparent function of the subjects' behaviors was toward self-consolidation. Based on findings, the researchers discuss implications consistent with humanistic psychology and existential psychotherapy principles and practices. (shrink)

The Meditations of Marcus Aurelius are treasured today--as they have been over the centuries--as an inexhaustible source of wisdom. And as one of the three most important expressions of Stoicism, this is an essential text for everyone interested in ancient religion and philosophy. Yet the clarity and ease of the work's style are deceptive. Pierre Hadot, eminent historian of ancient thought, uncovers new levels of meaning and expands our understanding of its underlying philosophy. Written by the Roman emperor for (...) his own private guidance and self-admonition, the Meditations set forth principles for living a good and just life. Hadot probes Marcus Aurelius's guidelines and convictions and discerns the hitherto unperceived conceptual system that grounds them. Abundantly quoting the Meditations to illustrate his analysis, the author allows Marcus Aurelius to speak directly to the reader. And Hadot unfolds for us the philosophical context of the Meditations, commenting on the philosophers Marcus Aurelius read and giving special attention to the teachings of Epictetus, whose disciple he was. The soul, the guiding principle within us, is in Marcus Aurelius's Stoic philosophy an inviolable stronghold of freedom, the "inner citadel." This spirited and engaging study of his thought offers a fresh picture of the fascinating philosopher-emperor, a fuller understanding of the tradition and doctrines of Stoicism, and rich insight on the culture of the Roman empire in the second century. Pierre Hadot has been working on Marcus Aurelius for more than twenty years; in this book he distills his analysis and conclusions with extraordinary lucidity for the general reader. (shrink)

Tied to the apron strings of the church -- Researcher, teacher, philosopher -- Philosophical discourse -- Interpretation, objectivity and nonsense -- Unitary experience and philosophical life -- Philosophical discourse as spiritual exercise -- Philosophy as life and as a quest for wisdom -- From Socrates to Foucault : a long tradition -- Inacceptable? -- The present alone is our happiness.

The authors develop an analysis of education. They show how education carries an essentially arbitrary cultural scheme which is actually based on power. More widely, the reproduction of culture through education is shown to play a key part in the reproduction of the whole social system.

This work by Pierre Bourdieu develops the anthropological theory which has formed the basis of his scientific research. It discusses the problems posed by "structuralist" philosophers in order to solve or dissolve them.

_Democracy Past and Future_ is the first English-language collection of Pierre Rosanvallon's most important essays on the historical origins, contemporary difficulties, and future prospects of democratic life. One of Europe's leading political thinkers, Rosanvallon proposes in these essays new readings of the history, aims, and possibilities of democratic theory and practice, and provides unique theoretical understandings of key moments in democracy's trajectory, from the French Revolution and the struggles for universal suffrage to European unification and the crises of the (...) present. In so doing, he lays out an influential new theory of how to write the history of politics. Rosanvallon's historical and philosophical approach examines the "pathologies" that have curtailed democracy's potential and challenges the antitotalitarian liberalism that has dominated recent political thought. All in all, he adroitly combines historical and theoretical analysis with an insistence on the need for a new form of democracy. Above all, he asks what democracy means when the people rule but are nowhere to be found. Throughout his career, Rosanvallon has resisted simple categorization. Rosanvallon was originally known as a primary theorist of the "second left", which hoped to stake out a non-Marxist progressive alternative to the irresistible appeal of revolutionary politics. In fact, Rosanvallon revived the theory of "civil society" even before its usage by East European dissidents made it globally popular as a non-statist politics of freedom and pluralism. His ideas have been shaped by a variety of influences, ranging from his work with an influential French union to his teachers François Furet and Claude Lefort. Well known throughout Europe as a historian, political theorist, social critic, and public intellectual, Pierre Rosanvallon was recently elected to a professorship at the Collège de France, Paris, a position held at various times by Claude Lévi-Strauss, Michel Foucault, and Pierre Bourdieu. _Democracy Past and Future_ begins with Rosanvallon's groundbreaking and synthetic lecture that he delivered upon joining this institution. Throughout the volume, Rosanvallon illuminates and invigorates contemporary political and democratic thought. (shrink)

This paper describes the semantic mapping methodology we applied to define an integration model for describing the stages of an outdoor and indoor route within the historic center of Naples, dating back to between the 17th and 18th Centuries. We detailed the side concerning the selection and connection of cultural contents, as well as that concerning the transformation of data into an interoperable format. From both perspectives, the working methodologies are illustrated, and issues and opportunities are highlighted. The semantic model (...) can be applied to any project that needs to integrate heterogeneous data for the fruition of cultural heritage in a well-defined sequence of stages. (shrink)

A lot of attention has been devoted to the study of discoveries in high energy physics, but less on measurements aiming at improving an existing theory like the standard model of particle physics, getting more precise values for the parameters of the theory or establishing relationships between them. This paper provides a detailed and critical study of how measurements are performed in recent HEP experiments, taking examples from differential cross section measurements with the ATLAS detector at the LHC. This study (...) will be used to provide an elucidation of the concept of event used in HEP, in order to determine what constitutes an observation and what does not. It will highlight the essential place taken by theory-ladenness in order to produce observational facts, and will show how uncertainty and sensitivity estimates constitute an operational approach to robustness, inside the practice of science, avoiding potential circularity problem traditionally implied by theory-ladenness. This is in contrast to robustness analyses typically considered in the literature. A careful analysis of systematic uncertainty estimates and of statistical tests used to set empirical conclusions from the observations will however demonstrate that quantitative statements obtained from these statistical tests cannot be more than simple guiding arguments for the production of knowledge, but do not determine it. This indicates that the frontier between theory and observation is blurry and that the dichotomy theory-experiment should be revised. (shrink)

An English translation of Pierre Bayle's posthumous last book, Entretiens de Maxime et de Themiste (1707), in which Bayle defends his skeptical position on the problem of the evil. This book is often cited and attacked by G.W. Leibniz in his Theodicy (1710). Over one hundred pages of original philosophical and historical material introduce the translation, providing it with context and establishing the work's importance.

Les émotions ont un rôle important dans nos interactions sociales. Sans émotions, nous avons du mal à faire des choix. Quand notre environnement déçoit nos attentes de manière répétée, nos émotions nous signalent qu'il serait rationnel de changer nos attentes, c'est-à-dire de procéder à des révisions. Le partage des émotions, qui est la clé de notre sentiment d'appartenance à une communauté, nous amène à révéler nos valeurs, parce qu'il permet de résister face à un monde décevant. Si même une fois (...) révisées nos croyances, nos émotions se maintiennent, elles manifestent alors des attentes bien enracinées, qui sont nos valeurs réelles. Pour étudier les valeurs collectives, il faut donc étudier les émotions, la manière dont elles incitent à des révisions, et comment leur partage collectif renforce nos résistances. La rationalité morale s'appuie sur les émotions. Celles-ci sont sensibles aux détails des situations, et cette rationalité dépend des contextes, si bien qu'elle propose des arguments qui restent révisables quand le contexte change. Ne résistent à toute révision que nos sentiments d'injustice. L'originalité de ce livre est donc d'étudier les émotions et les valeurs, individuelles et collectives, dans la dynamique de leurs changements, de leurs révisions et de leurs résistances, et d'utiliser ce lien entre émotions et révisions pour mieux définir la spécificité d'une rationalité morale. (shrink)