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)
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)
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)
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.
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.
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.".
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 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)
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)
Does geometry constitute a core set of intuitions present in all humans, regardless of their language or schooling? We used two nonverbal tests to probe the conceptual primitives of geometry in the Mundurukú, an isolated Amazonian indigene group. Mundurukú children and adults spontaneously made use of basic geometric concepts such as points, lines, parallelism, or right angles to detect intruders in simple pictures, and they used distance, angle, and sense relationships in geometrical maps to locate hidden objects. 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. (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)
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.
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)
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)
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.
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.
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.
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)
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)
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)
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.