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.

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)

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)

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)

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)

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)

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.".

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.

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.

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)

Since the 1980s, society's wealthiest members have claimed an ever-expanding share of income and property. It has been a true counterrevolution, says Pierre Rosanvallon--the end of the age of growing equality launched by the American and French revolutions. And just as significant as the social and economic factors driving this contemporary inequality has been a loss of faith in the ideal of equality itself. An ambitious transatlantic history of the struggles that, for two centuries, put political and economic equality (...) at their heart, The Society of Equals calls for a new philosophy of social relations to reenergize egalitarian politics. For eighteenth-century revolutionaries, equality meant understanding human beings as fundamentally alike and then creating universal political and economic rights. Rosanvallon sees the roots of today's crisis in the period 1830-1900, when industrialized capitalism threatened to quash these aspirations. By the early twentieth century, progressive forces had begun to rectify some imbalances of the Gilded Age, and the modern welfare state gradually emerged from Depression-era reforms. But new economic shocks in the 1970s began a slide toward inequality that has only gained momentum in the decades since. There is no returning to the days of the redistributive welfare state, Rosanvallon says. Rather than resort to outdated notions of social solidarity, we must instead revitalize the idea of equality according to principles of singularity, reciprocity, and communality that more accurately reflect today's realities. (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 ...

Bien des difficultés que nous éprouvons à comprendre les oeuvres philosophiques des Anciens proviennent souvent du fait que nous commmettons en les interprétant un double anachronisme: nous croyons que, comme beaucoup d'oeuvres modernes, elles sont destinées à communiquer des informations concernant un contenu conceptuel donné et que nous pouvons aussi en tirer directement des renseignements clairs sur la pensée et la psychologie de leur auteur. Mais en fait, elles sont très souvent des exercices spirituels que l'auteur pratique lui-même et fait (...) pratiquer à son lecteur. Elles sont destinées à former les âmes. Elles ont une valeur psychagogique. (shrink)

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)

Résumé La localisation des implantations des grands éléments d’infrastructure collective pose des problèmes de légitimation juridique spécifique. Ils délimitent en effet plusieurs territoires distincts en fonction de la nature des impacts qu’ils provoquent, lesquels, chacun, sont soumis à leurs propres législations et rentrent dans les compétences d’autorités différentes, y compris celle dont dépend la décision sur l’infrastructure envisagée. De telles situations normatives complexes empêchent la sémantisation légitimante que le droit est censé assurer dans les décisions de l’appareil étatique: elle sera (...) toujours partielle, voire lacunaire. Les compensations ne peuvent être que procédurales, et celles-ci sont insuffisantes à atteindre l’idéal postulé par le principe de légalité des activités publiques. Mais il ne peut en aller autrement pour ces infrastructures. (shrink)

« La métaphysique d’Aristote n’est, au sens aristotélicien, dialectique et par là incapable de tout achèvement déductif, que parce qu’elle est une métaphysique du mouvement, c’est-à-dire de la scission. » Le propos de l’auteur est simple : sans vouloir rajouter et apporter du nouveau sur Aristote, il tente au contraire de désapprendre tout ce que la tradition a ajouté à l’aristotélisme primitif. Car l’aristotélisme que nous connaissons est surtout celui des commentateurs grecs. L’image ainsi révélée est celle d’un Aristote aporétique, (...) mais « cette voix qui parle est celle plus fraternelle qui continue de chercher en nous ce qu’est l’être et de se taire parfois ». (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)

Cet ouvrage présente le destin de la métaphysique au siècle des Lumières. Derrière le schéma classique d'une substitution de l'anthropologie à la métaphysique caractérisant les Lumières, les études réunies dans ce volume montrent l'évolution du champ de la métaphysique, sa redéfinition, ses métamorphoses au sein d'une modernité en pleine évolution. L'intérêt est de dévoiler comment la métaphysique évolue, s'adapte à de nouvelles problématiques, et cela en tenant compte de la complexité des situations particulières propres aux Lumières européennes.

Les sociétés contemporaines tendent à ne plus connaître que les réalités individuelles et une perspective générale hors déterminations spécifiées. D'où la mise à l'écart de toute tradition, religieuse ou culturelle, et un refoulement de ce qui les portait. Cet ouvrage entend promouvoir une reconnaissance de la pluralité des voies de l'humain, mais sans juxtaposition communautariste, et préconise la mise en place de conditions de confrontations sur fond de différends fructueux et d'hétérogénéité foncière. C'est peut-être notre seule chance pour l'avènement de (...) chacun et un renouvellement social. Cela passera par des enjeux à faire réapparaître à l'encontre d'insidieuses neutralisations, et requiert des régimes de raison divers mais tous développés suivant un mode de rationalité publique. Sont ici en cause nos identités, nos rapports au passé et nos imaginations d'avenir, ainsi que ce qui nous y mobilise. (shrink)

L'erreur du populisme politique est de croire que la souveraineté du peuple est le fondement de la démocratie. On le sait, c'est plutôt le respect des Droits de l'Homme qui est déterminant : il en résulte le principe de la laïcité, qui a fait obstacle à la volonté de puissance de la chrétienté traditionnelle. Or, voici qu'aujourd'hui le fanatisme religieux renaît de ses cendres, ici ou là, et s'acoquine avec le populisme pour se légitimer. Comment se distancer, par la réflexion (...) critique, de ce genre de phénomène? L'intention de dominer autrui, quand on le rencontre, peut céder la place au sens de la réciprocité. Guidée par l'esprit de géométrie, la réflexion formelle le montre. Et l'alternative entre la violence et la bienveillance se répète au niveau des structures mentales : il n'est pas nécessaire de penser que tout, dans le monde humain, se réduit à des rapports de force ; il n'est pas nécessaire de s'en tenir à de telles simplifications idéologiques. On peut aussi se montrer un peu plus fin, et, pour s'y habituer, relire les origines de la philosophie démocratique moderne, de Hobbes (1588-1679) à Locke (1632-1704). (shrink)

L'usage éthique des logoi philosophoi -- Les écrits de Marc Aurèle sont des logoi -- Marc Aurèle et les logoi stoïciens -- La grande alternative -- Qu'est-ce que la vérité ? -- Qu'est-ce que le soi ? -- Le soi est social -- Les philosophes n'ont pas le monopole de l'enseignement éthique -- Le roman de la conversion de Marc Aurèle -- Qu'était-ce qu'être philosophos pour l'aristocratie impériale ? -- Qu'est-ce que l'âme ? -- La recherche de Paequanimitas -- L'éthique (...) est une esthétique -- Les pensées sont des images -- Les affects -- Affects humains -- Affects d'empereur -- Le désir de l'otium graecum -- La "vérité héroïque" et la mélancolie -- L'usage éthique des logoi philosophoi : mode d'emploi -- Les dogmata -- L'efficacité de la rhétorique -- La technique de dévaluation -- Échapper aux mots des autres -- La trousse à pharmacie -- Les dieux -- Présence des dieux dans les logoi -- Les doutes de Marc Aurèle -- Le devenir-dieu -- Le démon -- Épilogue. (shrink)

Cambrai, Bibl. munic. 940, ff. 1-59 [integralement reproduit]--Bibl. Vatic. Reg. Lat. 689 A, ff. 334-353.--Bibl. Vatic. Reg. Lat. 1653, ff, 1v-2v (feuilles de garde), ff. 3r, 29r-35r.--Pièces justificatives.

Recognized as a masterpiece of Nietzsche scholarship, NIETZSCHE AND THE VICIOUS CIRCLE is available here for the first time in English. Author Pierre Klossowski suggests that Nietzsche's ideas and beliefs did not stem from his personal pathology, but rather were applied in a pathological manner. Thereby Nietzsche's beliefs resonated dynamically and intellectually with his alternating lucidity and delirium.

Est-il aujourd’hui possible d’expliquer le mental à partir du cerveau? Où est le problème, diront les uns, puisque la mécanique neuronale est celle qui le crée? Comment seulement espérer, rétorqueront les autres, que la complexité de l’esprit puisse être fondée sur le seul fonctionnement cérébral? S’appuyant sur des siècles d’histoire et de philosophie des sciences, et surtout sur un examen des données expérimentales récentes, Pierre Buser établit ici une sorte de bilan, dégageant plusieurs problématiques distinctes et bien actuelles : (...) comment définir la conscience, ce site supposé abriter notre vécu subjectif, à nouveau reconnu comme instance fondamentale de l’esprit chez l’homme et aussi chez l’animal? Que sait-on aujourd’hui de l’inconscient, ce domaine où se trouvent amassés tant d’acquis de notre intellect, de notre vie cognitive et affective? Et que nous apprennent, par exemple, l’hypnose ou la méditation sur le fonctionnement de notre esprit? Pierre Buser est professeur émérite de neurosciences de l’université Pierre-et-Marie-Curie de Paris. Il est membre de l’Académie des sciences. Il a notamment publié Cerveau de soi, cerveau de l’autre, L’Inconscient aux mille visages et Le Temps, instant et durée (en collaboration avec Claude Debru). (shrink)

Dans les deux textes composant ce volume, on confronte Descartes pour qui la liberte est un fait certain et plus clair qu'aucun autre avec Hobbes qui recuse la validite de ce fait au nom de la necessite universelle qui gouverne aussi bien les evenements naturels que les actions humaines. On cherche a montrer ensuite quue la liberte ne serait pas le pouvoir ou la perfection propre a chacun de nous sans l'epreuve de la resistance que le corps propre oppose a (...) l'effort (Maine de Biran), sans une confrontation de tous les instants avec ce que Ricoeur nomme l'involontaire, engageant ainsi une discussion de fond, feconde et exigeante, avec Descartes auteur d'un Traite des passions. Le croisement entre le point de vue phenomenologique et celui du physicien sur l'affectivite montre aussi qu'expliquer et comprendre ne sont pas comme des mondes paralleles. Pierre Guenancia est professeur d'histoire de la philosophie moderne a l'universite de Bourgogne. Apres plusieurs livres et articles sur Descartes et la pensee classique, il a publie recemment Le Regard de la pensee. Philosophie de la representation (PUF 2009), Descartes chemin faisant (Encre Marine, 2010), Divertissements pascaliens (Hermann, 2011), ainsi que la reedition de Descartes et l'ordre politique (Tel, Gallimard 2012). A la suite de plusieurs textes sur le cosmopolitisme, il prepare un essai sur les Prolegomenes a une philosophie du cosmopolitisme. (shrink)

Entré en khâgne pour y devenir traducteur de Virgile et d'Homère, Pierre Magnard reçut de Jean Beaufret l'interpellation de Heidegger, qui fit vaciller ses certitudes et certaine manière d'être chrétien. Ce vacillement le conduisit vers Pascal, dont l'angoisse colore la foi d'une manière inoubliable, lequel Pascal le conduisit à Montaigne, ami de toute une vie. Deux figures en miroir entre lesquelles il lui parut urgent de ne jamais choisir, et auxquelles il consacra beaucoup de son industrie, comme à ces (...) philosophes de la fin de Moyen Age et de la Renaissance que Char eût dit des Matinaux. Un humanisme faisant l'épreuve du néant en l'homme et du silence de Dieu était possible, dont Maître Eckhart et Nicolas de Cues montrent le chemin ; un christianisme aussi, fondé non sur l'usage d'une raison dogmatique mais d'une raison joueuse, laquelle, tout en sachant que c'est le coeur qui lui donne ses principes, se déploiera en toute liberté. Le chemin d'un philosophe, professeur émérite en Sorbonne, jusqu'à la couleur du matin profond. (shrink)

In the debates on phenomenal consciousness that occurred over the last 20 years, Sartre’s analysis of pre-reflective consciousness has often been quoted in defence of a distinction between first- and third-personal modes of givenness that naturalists reject. This distinction aims both at determining the specificity of the access one has to their own thoughts, beliefs, intentions, or desires, and at justifying the particular privilege that one enjoys while making epistemic claims about their own mental states. This chapter defends an interpretation (...) of Sartre’s theory of pre-reflective consciousness that does not put him completely at odds with the naturalist critique and stresses that one’s pre-reflective experience should not be understood in terms of first-/third-person differentiation. This pre-reflective dimension of experience nevertheless allows a peculiar access to oneself, which grants no infallible epistemic privilege to the first-person, but lays the ground for a transformative process that makes self-knowledge possible. (shrink)