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)

Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion of a (...) few inducer trials, in which participants are explicitly (and sometimes misleadingly) told that a given display contains 30 dots, is sufficient to calibrate their estimates on the whole range of stimuli. Based on these empirical results, we develop a model of the mapping between the numerical symbols and the representations of numerosity on the number line. (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)

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)

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)

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.".

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)

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.

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)

We argue that Cohen Kadosh & Walsh's (CK&W's) definitions of neural coding and of abstract representations are overly shallow, influenced by classical cognitive psychology views of modularity and seriality of information processing, and incompatible with the current knowledge on principles of neural coding. As they stand, the proposed dichotomies are not very useful heuristic tools to guide our research towards a better understanding of the neural computations underlying the processing of numerical quantity in the parietal cortex.

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.

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)

Geometrical intuitions spontaneously drive visuo-spatial reasoning in human adults, children and animals. Is their emergence intrinsically linked to visual experience, or does it reflect a core property of cognition shared across sensory modalities? To address this question, we tested the sensitivity of blind-from-birth adults to geometrical-invariants using a haptic deviant-figure detection task. Blind participants spontaneously used many geometric concepts such as parallelism, right angles and geometrical shapes to detect intruders in haptic displays, but experienced difficulties with symmetry and complex spatial (...) transformations. Across items, their performance was highly correlated with that of sighted adults performing the same task in touch (blindfolded) and in vision, as well as with the performances of uneducated preschoolers and Amazonian adults. Our results support the existence of an amodal core-system of geometry that arises independently of visual experience. However, performance at selecting geometric intruders was generally higher in the visual compared to the haptic modality, suggesting that sensory-specific spatial experience may play a role in refining the properties of this core-system of geometry. (shrink)

For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core cognitive systems for (...) representing the shapes of large-scale, navigable surface layouts and of small-scale, movable forms and objects. Each of these systems applies to some but not all perceptible arrays and captures some but not all of the three fundamental Euclidean relationships of distance (or length), angle, and direction (or sense). Like natural number (Carey, 2009), Euclidean geometry may be constructed through the productive combination of representations from these core systems, through the use of uniquely human symbolic systems. (shrink)

Leibovich et al. opened up an important discussion on the nature and origins of numerosity perception. The authors rightly point out that non-numerical features of stimuli influence this ability. Despite these biases, there is evidence that from birth, humans perceive and represent numerosities, and not just non-numerical quantitative features such as item size, density, and convex hull.

This paper aims to study the perception of color (representations, synesthesia, denominations, uses and classification) in specific writings such as recipe treatises written from 1520 to 1689. These treatises deal with the manufacture and stages of color in various objects (remedies, blushes and mainly gems). They reveals that color is not only an apparent surface but also a sensitive substance, in particular white and red colors. Although color is a principle of unity for diverse materials, it sometimes becomes contradictory when (...) it is associated with variable signified and signifiers, so that color also offers a play on naming: meaning is sometimes clear, sometimes obscure, and in any case mobile (azure, vermilion). The contemporary reader does not perceive color in the same way as the Renaissance craftsman. Finally, as a principle of classification, it shows an imbalance and hierarchy of colors which, while providing structure to recipes: it gives mainly a place of choice to red and its shades. (shrink)

When individual rights, especially constitutional rights, compete with other rights or with a public good, judges and politicians involved in the legislative process or jurisdictional process are expected to balance their decision in such a way that the gain from achieving the goal mitigates the costs of the resulting loss for the parties. Jurists speak of the doctrine of proportionality in connection with this process of balancing. In the proportionality calculus, judges have to evaluate whether the impact on individual rights (...) outweighs the public purpose pursued through a state’s legal activity. I will argue that the procedure of proportionality is similar to the procedure of reaching a compromise. More precisely, I will defend that compromise is a special case of the principle of proportionality, for it applies when claims cannot be balanced or in the absence of an overarching principle on which all the parties agree. With this, I aim to show the connection between the principle of proportionality and compromises without conflating these two concepts, and to offer new perspectives on the discussion of proportionality as it is used in the legal context. (shrink)

An error that medicine has long shared is to attribute to a desire or an effect of the mother’s imagination during gestation, the deformities, growths or spots that a child bears at birth. The imagination would be capable of imprinting external modifications on a matter and would have an impact on the perceptions and sensory development of the fetus. Returning briefly to the genealogy and posterity of the topos, this article focuses on the successes and refutations of the Malebranchist paradigm (...) in the 18th century, through a corpus of medical popularization texts where the debates oppose the supporters of the imagination for whom emotion alters the organs of the fetus and the detractors of this thesis who only see it as prejudice. Mechanistic systems had in common that they avoided the soul to explain life. Although each era has its hermeneutic system of representations, and that medicine—closely dependent on the philosophical and moral conceptions of its time—is also a cultural production, it is nevertheless not uninteresting to question on the fortune of a motive and the scientific topicality of the question. What does the baby perceive in utero? Does he feel his mother’s pain? If so, what is the biological impact? To what extent can the maternal imagination and experience mark the child’s body? Informed by functional imaging technologies, recent research returns to the symbiotic link of mother-fetus interactions. Convergences appear between this 18th century and our 21st century. In no case did we want to contrast today’s scientists who are firmly in touch with reality and their predecessors who are prey to imagination. Science, whatever the era, always feeds on imagination. (shrink)

L’article étudie comment l’humain peut être défini dans les rapports créés dans l’imaginaire entre le corps et l’alimentation. En s’appuyant sur des traités de médecine et de cuisine du Moyen Âge au xviie siècle, des essais d’humanistes et les travaux d’anthropologues, d’historiens et de sociologues contemporains, on découvre comment l’acte même de manger permet de définir et construire les frontières du corps humain et un imaginaire de l’alimentation : la nomination de l’aliment et la charge sémantique des métaphores empruntés à (...) l’alimentation définissent une éthique de l’humain et sa vision du corps humain et animal. Une approche médicale complète cette étude linguistique et montre que le fonctionnement des limites extérieures et internes du corps humain se modèle sur la représentation de l’aliment et de ses effets paradoxaux, bénéfiques et pathologiques. Enfin, le corps social du mangeur est délimité par la distance qui le sépare de l’aliment et le lieu assigné à l’animal destiné à être mangé. (shrink)

Parmi les petits objets qui nous sont parvenus de l’Antiquité, ceux que les archéologues classent ordinairement parmi les jouets, au sens moderne, forment une catégorie particulièrement énigmatique. La notion même de « jouet » est problématique car aucun terme grec (athurma, paignion) ni latin (ludicrum) ne correspond exactement à ce que recouvre aujourd’hui ce mot. Les études philologiques et linguistiques montrent que le champ de ce vocabulaire est polysémique et comprend tout ce qui fascin...

The French philosopher Renaud Barbaras remarked that late in Maurice Merleau-Ponty’s career, “The phenomenology of perception fulfills itself as a philosophy of expression.” In _Tracing Expression in Merleau-Ponty: Aesthetics, Philosophy of Biology, and Ontology, _Véronique M. Fóti_ _addresses the guiding yet neglected theme of expression in Merleau-Ponty’s thought. She traces Merleau-Ponty’s ideas about how individuals express creative or artistic impulses through his three essays on aesthetics, his engagement with animality and the “new biology” in the second of his lecture courses (...) on nature of 1957–58, and in his late ontology, articulated in 1964 in the fragmentary text of _Le visible et l’invisible _. With the exception of a discussion of Merleau-Ponty’s 1945 essay “Cezanne’s Doubt,” Fóti engages with Merleau-Ponty’s late and final thought, with close attention to both his scientific and philosophical interlocutors, especially the continental rationalists. Expression shows itself, in Merleau-Ponty’s thought, to be primordial, and this innate and fundamental nature of expression has implications for his understanding of artistic creation, science, and philosophy. (shrink)

After the ‘empirical turn’ in bioethics, few specific approaches have been developed for doing clinical ethics research in close connection with clinical decision-making on a daily basis. In this paper we describe the ‘committed researcher’ approach to research in clinical ethics that we have developed over the years. After comparing it to two similar research methodological approaches, the ‘embedded researcher’ and ‘deliberative engagement’, we highlight its main features: it is patient-oriented, it is implemented by collegial and multidisciplinary teams, it uses (...) an ethical grid to build the interview guide, and it is geared towards bringing the results to bear on the public debate surrounding the issue at stake. Finally, we position our methodological approach with respect to the ‘is vs. ought’ distinction. We argue that our ‘commitment researcher’ approach to clinical ethics research takes concerned people’s life-building values as the main data, and compares them to the larger normative framework underlying the medical practice at stake. (shrink)

L’exploration archéologique du site de l’Arkipiskopi dans la vieille ville de Nicosie, conduite par Fryni Hadjichristofi et son équipe (Département des Antiquités de Chypre) de 2009 à 2011 puis en 2016, a mis au jour les vestiges d’un puits à roue élévatrice appelé à Chypre αλακάτιν/alakatin et plus habituellement connu dans le monde méditerranéen sous le nom de sakieh. S’il en existe des exemplaires plus anciens dans l’île, c’est la première machine hydraulique à traction animale permettant de puiser l’eau dans (...) un puits profond fouillée à Nicosie pour les époques latine, ottomane et anglaise. Cette étude entend d’abord examiner et interpréter les vestiges de ces structures au regard des informations livrées par des documents d’archives et des récits de voyageurs, des dessins de la fin du xvie et du début du xviiie siècle, un plan de 1882 et le cadastre de 1948, afin d’en mieux saisir les contextes de fonctionnement sur une longue durée. Elle présente aussi les godets de terre fixés sur la roue pour le puisage de l’eau et qui, à de rares exceptions, ont complètement échappé aux études céramologiques conduites dans l’île. (shrink)

Is the principal concern of political philosophy the source of political authority? And, if so, can this source be located in individual consent? In this article I draw on Rousseau to answer the second question negatively; and in rejecting that answer, why we might answer the first question in the negative as well. We should be concerned with questions of legitimacy rather than with the source of authority and political obligation. Our principal concern, that is, should be with the question (...) how well political institutions meet the needs of individuals. I pursue these issues in the context of interpreting Rousseau's distinctive contribution to political thought. I start out by asking the question ‘What problem is the General Will designed to solve?’ I argue that Rousseau's challenge to Hobbes represents a crucial step in the move from the source of authority and political obligation to a focus on legitimacy. (shrink)

Is the principal concern of political philosophy the source of political authority? And, if so, can this source be located in individual consent? In this article I draw on Rousseau to answer the second question negatively; and in rejecting that answer, why we might answer the first question in the negative as well. We should be concerned with questions of legitimacy rather than with the source of authority and political obligation. Our principal concern, that is, should be with the question (...) how well political institutions meet the needs of individuals. I pursue these issues in the context of interpreting Rousseau's distinctive contribution to political thought. I start out by asking the question ‘What problem is the General Will designed to solve?’ I argue that Rousseau's challenge to Hobbes represents a crucial step in the move from the source of authority and political obligation to a focus on legitimacy. (shrink)

En septembre 2021 s’est tenu à Fribourg, en Suisse, le XVIe colloque du CIERGA, plusieurs fois reporté en raison de la pandémie. Comme toujours, c’est l’équipe locale prenant en charge l’organisation qui a donné l’impulsion de la thématique choisie. Or, depuis plusieurs années désormais, l’université de Fribourg accueille le projet européen Locus Ludi. The Cultural Fabric of Play and Games in Classical Antiquity, sous la direction de Véronique Dasen. Ce projet ambitieux envisage toutes les di...

Compromises are arrived at when, in spite of the efforts of those participating to mediate and defend their position in a rationally acceptable manner, each remains with his judgment while, at the same time, a decision must be made without further delay. What this means is that the parties agree to an option about which they are not, in their heart of hearts, entirely convinced. This article examines the notion of moral compromise, concentrating thereby on the case of political praxis. (...) It asks whether, in view of the complexity and multiplicity of morally relevant decisions encountered in a pluralist society, it is at all realistic to expect much else from political institutions than what Rawls dismissively refers to as a modus vivendi and whether a conception of justice that is true or reasonable only given the reasonable pluralism of comprehensive doctrines is still a conception of justice, and not simply a compromise between the contending doctrines. (shrink)

Dans une approche psycho-développementale et systémique, cet article examine l’expérience grand-parentale en contexte de troubles du spectre autistique ( tsa ) de l’enfant en considérant la pluralité des relations familiales (conjugale, co-grand-parentale, parents/enfant(s), grand(s)-parent(s)/petit(s)-enfant(s), etc.) dans lesquelles les grands-parents sont inscrits. L’analyse des entretiens menés auprès de six grands-parents (quatre familles) montre notamment l’important engagement et le soutien instrumental et émotionnel des grands-parents auprès des parents et de leur petit-enfant porteur de tsa. Ces résultats sont discutés en lien avec l’accompagnement (...) des enfants présentant un tsa et leurs familles, dans une perspective systémique. (shrink)

Meu intuito é tecer algumas considerações sobre a descoberta e relação de Voltaire com o newtonianismo, e a partir daí refletir de maneira mais geral sobre as possibilidades da aproximação entre filosofia e ciência.

As a tribute to Marie-Agnès Cathiard, this opening text which aims to recount the story of a journey and researcher’s commitment places her work around the major themes that structured it. “From the body of speech to imagined bodies”, its contributions and experimental investigations, attentive to the innovations of neuroscience, have influenced the center’s policy in terms of anthropological research, breaking down innovative avenues, particulary on the imagination of the brain and the amputated body. Her contributions have enabled the conjunction (...) between cognitive sciences and research on the imagination, between biology and culture. Her work has rethought mental images in the light of neurology. They considered the connectomes of the imagination associated with certain image complexes (levitation, alien presence). They compared the contributions of neuroscience to the most ancient mythological phenomenologies, developing a transalpine neurocognitive anthropology. Marie-Agnès’research has opened the way to a neural status of the imagination, a real epistemological upheaval. This reconstruction enterprise, more narrative than conceptual, nevertheless allows us to underline the importance of her pioneering work in cortical mapping. Being part of the lineage of Gilbert Durand whose hypotheses she corroborates (primacy of images in cognitive operations, biological rooting of images), she has made it possible to take a new look at this heritage and to breathe new life into it. (shrink)

Depuis la parution de son premier fascicule en 1877, le Bulletin de Correspondance Hellénique joue son rôle de passeur du savoir en faisant connaître à une vaste communauté de chercheurs les résultats des explorations archéologiques qui, dans le monde grec, dans les Balkans, à Chypre, renouvellent les connaissances par l’apport de documents inédits ou réinterprétés. Enraciné dans l’institution qui le publie, l’École française d’Athènes, il n’a cessé d’évoluer avec elle pour être toujours mieu...