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.

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.

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)

This article claims that one has to distinguish between X° reflexives which do not bear phi-features, such as number, and XP complex reflexive - which do bear such features. The presence/vs absence of features, it is argued, explains the behavior of so called long distance reflexives - first observed, within the generative tradition, in scandinavian languages - but present all over. The observation according to which XP reflexives are clause bound, while X° reflexives in argument position are not, is some (...) times refered to as "Pica's generalization" (see Burzio (1987) which stressed correctly that is was the first time that such a correlatiion betwen reflexives structure, binding domains, and the role of a cycle was observed. The behavioir of reflexives it is argued derives from the properties of abstratc movement at the level of Logical Form. (shrink)

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)

Cross cultural studies have played a pivotal role in elucidating the extent to which behavioral and mental characteristics depend on specific environmental influences. Surprisingly, little field research has been carried out on a fundamentally important perceptual ability, namely the perception of biological motion. In this report, we present details of studies carried out with the help of volunteers from the Mundurucu indigene, a group of people native to Amazonian territories in Brazil. We employed standard biological motion perception tasks inspired by (...) over 30 years of laboratory research, in which observers attempt to decipher the walking direction of point-light (PL) humans and animals. Do our effortless skills at perceiving biological activity from PL animations, as revealed in laboratory settings, generalize to people who have never before seen representational depictions of human and animal activity? The results of our studies provide a clear answer to this important, previously unanswered question. Mundurucu observers readily perceived the coherent, global shape depicted in PL walkers, and experienced the classic inversion effects that are typically found when such stimuli are turned upside down. In addition, their performance was in accord with important recent findings in the literature, in the abundant ease with which they extracted direction information from local motion invariants alone. We conclude that the effortless, veridical perception of PL biological motion is a spontaneous and universal perceptual ability, occurring both inside and outside traditional laboratory environments. (shrink)

The article shows that the arugument of a verb can be projected in diffrent ways according to the meaning (agentive or not) of the predicate. An analysis is developed which suggests a modification of the projection principle according to which this principle is in part an interpretative principle, not a principle of the core grammmar.

Article Authors Metrics Comments Media Coverage Abstract Author Summary Introduction Results Discussion Supporting information Acknowledgments Author Contributions References Reader Comments (0) Media Coverage (0) Figures Abstract During language processing, humans form complex embedded representations from sequential inputs. Here, we ask whether a “geometrical language” with recursive embedding also underlies the human ability to encode sequences of spatial locations. We introduce a novel paradigm in which subjects are exposed to a sequence of spatial locations on an octagon, and are asked to (...) predict future locations. The sequences vary in complexity according to a well-defined language comprising elementary primitives and recursive rules. A detailed analysis of error patterns indicates that primitives of symmetry and rotation are spontaneously detected and used by adults, preschoolers, and adult members of an indigene group in the Amazon, the Munduruku, who have a restricted numerical and geometrical lexicon and limited access to schooling. Furthermore, subjects readily combine these geometrical primitives into hierarchically organized expressions. By evaluating a large set of such combinations, we obtained a first view of the language needed to account for the representation of visuospatial sequences in humans, and conclude that they encode visuospatial sequences by minimizing the complexity of the structured expressions that capture them. (shrink)

Nous distinguons deux types d'anaphores en montrant que la comprehension des relations à longue distance met en jeu plusieurs propriétés de la grammaire comme l'association, ou non, avec un rôle thématique, ou à une position argumentale, et montrons comment les mécanismes mis en jeu sont universels - et ont des conséquences sur l'architecture de la grammaire (sur la définition de la notion de c-commande par exemple). L'article montre en particulier qu'il ne peut y avoir de réciproque ou de clitique lié (...) a longue distance. (shrink)

It is claimed that the English genitive marker 's' suprisingly mirrors- at least in some dialects of English - the three main different usage of the mono-morphemic reflexives such as 'se' in French. A solution to this paradox already noted by Jespersen (1918) is proposed drawing on Watkins paradox according to which the study of what looks like 'social' parameters might be relevant for linguistics.

We argue that there exist two kinds of passive structures, a) one generated in the base b) the other transformationally derived by the structure preserving-rule of move-NP. Assuming a Case theory along the lmines of Chomsky (1978), we want to argue a) that some oblique Cases are assigned in the base b) that NP movement can move an oblique Case assigned in the base c) that movement should not be defined in terms of Case but in terms of Government.

It is suggested that the notion of truth value plays a role in syntactic theory and should be incorporated in the appropriate formulation of conditions on transformations.

In this paper, we show that many of the dramatic changes that took place in the course of the history of the English complementation system are the result of a simple morphological Change in the determiner system. We propose that Old English (OE) evolved from a system in which 'complements' clauses, relative clauses and DP were interpreted as adverbials to a system in which they are interpreted as arguments of the verb. As the determiner acquired certain certain type of morphological (...) feature , a complementation system developed. We show that this claim is is reinforced by the fact that apparently unrelated changes all follow from the nature of the determiner system. (shrink)

It is claimed that the notion of reflexive pronoun involves, in indo-european and amerindian languages, a name or a morphological mark related to the expression of an inalienable relationship.

Epithets and pronominals 'en' and 'y' in French have a variety of Binding properties that are unexpected on conventional approach to Binding Theory. We argue that the linguistic variety observed cross-linguistically (and perhaps, more surprinsingly, within a single language) - derives from the morphological properties of the anaphoric element - which we claim lack number features. Epithets and pronominal like 'en' and 'y' are predicates modifying null but semantically active nouns, and must theefore refer to the Speaker. These properties, we (...) claim, explain why these elements must be employed in what we define as an Epistemic Context, and are subject to Condition C of Binding Theory. (shrink)

Une théorie de la littérature s'appuyant sur les contraintes de langue mises en évidence par la grammaire chomskyenne est-elle envisageable ? Une telle théorie peut-elle reprendre en des termes nouveaux le programme de recherche envisagé - en termes sémiotiques - par Jakobson, qui tentait de constituer une théorie générale du langage, de la poésie et de l'art ? -/- Une théorie linguistique peut-elle participer à la découverte de nouvelles formes littéraires dont elle s'enrichirait en retour ? C'est ce que suggère (...) ce volume d'hommages à Mitsou Ronat. L'avant-propos montre que son travail pourrait bien constituer une conception différente du programme actuel des sciences cognitives, dont il recoupe en partie l'objet de recherche, tout en y englobant certaines expériences sur l'écriture. (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.

We propose that the restrictive/non restrictive distinction found in relative clauses corresponds to the Inalienable vs Alienable distinction of the Nominal Possessive constructions. We propose to extend this distinction to adjectives suggesting that is not construction specific.

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)

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)

"What is at stake in this book is nothing less than a dramatically new way of approaching literature, one which in its unostentatious, low key way scandalously smashes a whole range of liberal humanist icons." --Terry Eagleton Who is more important: the reader, or the writer? Originally published in French in 1966, Pierre Macherey's first and most famous work, A Theory of Literary Production dared to challenge perceived wisdom, and quickly established him as a pivotal figure in literary theory. (...) In this provocative work, Macherey puts the focus as much on the reader as the writer, stating that the very act of reading is a form of production in its own right, generating interpretation and meanings which are beyond the control of the author. Part of the birth of a whole new branch of post-structuralist theory, Macherey's work also influenced a new generation of critics among them Jacques Derrida, his contemporary, and Terry Eagleton. His ideas have also led some observers to claim that he announced the death of the author fully two years before Roland Barthes' famous essay. The reissue of this work as a Routledge Classic brings some radical ideas to a new audience, and argues persuasively for a totally new way of reading. As such, it is an essential work for anyone interested in the development of literary theory. (shrink)

Les études présentées dans ce volume portent sur des sujets empruntés à des domaines très divers : ceux-ci mettent en jeu des questions concernant la vie, la réalité sociale, la connaissance dont le traitement relève en particulier des compétences de l'anthropologie, de l'histoire des sciences, de la philosophie, et même de la littérature qui s'est intéressée à sa façon à ces questions. Les traverse l'hypothèse suivante : les contenus auxquels ces questions se rapportent, si différents soient les plans sur lesquels (...) ils se situent, ont en commun de n'exister qu'"à l'essai", c'est-à-dire en cours d'élaboration, en travail, dans l'effort, à la peine, à travers des formes inachevées, donc en étant confrontés en permanence au risque de la crise, ce qui n'empêche qu'ils soient entraînés dans un élan continu sans qu'on sache où celui-ci conduit ni même s'il conduit quelque part. Or, pour rendre compte de ces réalités en devenir, marquées d'incertitude à un certain degré, le mieux était de procéder identiquement "à l'essai", en lançant une dynamique d'investigation qui ne suive pas un chemin déjà tout tracé conformément à un idéal de rectitude. De là une démarche systématiquement sinueuse, appuyée sur des lectures pratiquées comme autant d'expérimentations qui mettent à l'épreuve, cas par cas, l'hypothèse de départ telle qu'elle vient d'être évoquée. Sont ainsi esquissés, pour voir, sous réserve d'examen, les linéaments d'une philosophie pratique qui permet d'évacuer certaines alternatives traditionnelles comme celles du réel et de la pensée, du corporel et du mental, des faits et des valeurs, de la nature et de la culture, de la nécessité et de la liberté"--Page 4 of cover. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Chacun croit savoir, pour l'avoir appris à l'école, ce qu'était la philosophie antique : la naissance de la Raison, avec la critique du mythe et de la religion ; l'invention de l'éthique, avec le " souci de soi " et les " exercices spirituels " ; et bien sûr une galerie de bustes blancs vénérables : Socrate, Platon, Aristote, etc. Pierre Vesperini propose de mettre en suspens ce " grand récit ", et d'aller directement aux sources, en leur posant (...) une question simple : qu'appelait-on philosophia dans l'Antiquité? Tout d'un coup, le musée laisse place à un territoire luxuriant de couleurs et d'histoires, où le familier retrouve son étrangeté, où l'inconnu fait son entrée.0L'histoire ici, loin de s'opposer à la philosophie, la déplace. Car en proposant une reconstitution de l'expérience antique de la philosophia, du " temps des sages " à la christianisation, l'auteur invite aussi à prendre conscience de ce qui a été perdu, pour inventer d'autres façons de concevoir le savoir et la pensée. (shrink)

Long undervalued in France, philosophical anthropology has played an essential role in Germany, helping to address some of the most important issues straddling philosophy and the social sciences: humanity's place in nature and in history; the individual and others; and relations between human groups.

La modernité, dès ses débuts, attribue un rôle-clef aux passions : qu’elles soient hostiles à la Raison ou au contraire ses alliées, dangereuses ou fascinantes, elles marquent le rôle du corps, du désir, du langage et de l’imagination dans la nature de l’homme. La même époque voit se développer différentes variantes du matérialisme. Presque toutes réévaluent ce que la raison classique avait tendance à réprimer ou à considérer comme révélateur de la faiblesse humaine : le corps et tout ce qui, (...) dans l’âme ou dans la société, porte les traces de l’activité et de la positivité du corps. On peut donc s’attendre à ce que les matérialistes fassent un sort particulier aux passions, à ce qu’ils y reconnaissent des lois et non pas seulement des manques ou des vices, à ce qu’ils essaient d’en repérer l’efficace dans l’ensemble des activités humaines. Encore faut-il se demander comment chaque matérialisme procède, par quelle configuration propre il rend compte de ces phénomènes ou comment il dévie les discours de la théorie classique pour les forcer à passer par les objets qui sont les siens. Plutôt que de supposer l’existence d’une théorie matérialiste unique, une enquête s’impose donc qui prenne en vue la diversité de ces auteurs, les situe dans leur contexte et repère les points d’inflexion que rencontre chez chacun d’entre eux cette problématique générale des passions qui semble avoir gouverné plusieurs siècles. (shrink)