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)

Subjects classified visible 2-digit numbers as larger or smaller than 55. Target numbers were preceded by masked 2-digit primes that were either congruent (same relation to 55) or incongruent. Experiments 1 and 2 showed prime congruency effects for stimuli never included in the set of classified visible targets, indicating subliminal priming based on long-term semantic memory. Experiments 2 and 3 went further to demonstrate paradoxical unconscious priming effects resulting from task context. For example, after repeated practice classifying 73 as larger (...) than 55, the novel masked prime 37 paradoxically facilitated the “larger” response. In these experiments task context could induce subjects to unconsciously process only the leftmost masked prime digit, only the rightmost digit, or both independently. Across 3 experiments, subliminal priming was governed by both task context and long-term semantic memory. (shrink)

‘Number sense’ is a short‐hand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence suggesting that number sense constitutes a domain‐specific, biologically‐determined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence of a homology (...) between the animal, infant, and human adult abilities for number processing; and the existence of a dedicated cerebral substrate. In adults of all cultures, lesions to the inferior parietal region can specifically impair number sense while leaving the knowledge of other cognitive domains intact. Furthermore, this region is demonstrably activated during number processing. I postulate that higher–level cultural devel‐opments in arithmetic emerge through the establishment of linkages between this core analogical representation (the ‘number line’ ) and other verbal and visual representations of number notations. The neural and cognitive organization of those representations can explain why some mathematical concepts are intuitive, while others are so difficult to grasp. Thus, the ultimate foundations of mathematics rests on core representations that have been internalized in our brains through evolution. (shrink)

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)

Can we ever experimentally disentangle phenomenal consciousness from the cognitive accessibility inherent to conscious reports? In this commentary, we suggest that (1) Block's notion of phenomenal consciousness remains intractably entangled with the need to obtain subjective reports about it; and (2) many experimental paradigms suggest that the intuitive notion of a rich but non-reportable phenomenal world is, to a large extent illusory – in a sense that requires clarification.

‘Number sense’ is a short‐hand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence suggesting that number sense constitutes a domain‐specific, biologically‐determined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence of a homology (...) between the animal, infant, and human adult abilities for number processing; and the existence of a dedicated cerebral substrate. In adults of all cultures, lesions to the inferior parietal region can specifically impair number sense while leaving the knowledge of other cognitive domains intact. Furthermore, this region is demonstrably activated during number processing. I postulate that higher–level cultural devel‐opments in arithmetic emerge through the establishment of linkages between this core analogical representation (the ‘number line’ ) and other verbal and visual representations of number notations. The neural and cognitive organization of those representations can explain why some mathematical concepts are intuitive, while others are so difficult to grasp. Thus, the ultimate foundations of mathematics rests on core representations that have been internalized in our brains through evolution. (shrink)

‘Number sense’ is a short‐hand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence suggesting that number sense constitutes a domain‐specific, biologically‐determined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence of a homology (...) between the animal, infant, and human adult abilities for number processing; and the existence of a dedicated cerebral substrate. In adults of all cultures, lesions to the inferior parietal region can specifically impair number sense while leaving the knowledge of other cognitive domains intact. Furthermore, this region is demonstrably activated during number processing. I postulate that higher–level cultural devel‐opments in arithmetic emerge through the establishment of linkages between this core analogical representation (the ‘number line’ ) and other verbal and visual representations of number notations. The neural and cognitive organization of those representations can explain why some mathematical concepts are intuitive, while others are so difficult to grasp. Thus, the ultimate foundations of mathematics rests on core representations that have been internalized in our brains through evolution. (shrink)

Quartz & Sejnowski's constructivist manifesto promotes a return to an extreme form of empiricism. In defense of learning by selection, we argue that at the neurobiological level all the data presented by Q&S in support of their constructive model are in fact compatible with a model comprising multiple overlapping stages of synaptic overproduction and selection. We briefly review developmental studies at the behavioral level in humans providing evidence in favor of a selectionist view of development.

Cohen Kadosh & Walsh (CK&W) neglect the solid empirical evidence for a convergence of notation-specific representations onto a shared representation of numerical magnitude. Subliminal priming reveals cross-notation and cross-modality effects, contrary to CK&W's prediction that automatic activation is modality and notation-specific. Notation effects may, however, emerge in the precision, speed, automaticity, and means by which the central magnitude representation is accessed.

The position of the Belgian prime minister is hardly mentioned in the Belgian Constitution. lt was only after almost 140 years, in 1970 he was mentioned for the first time. lts power is rather a matter of common law. Since 1831 through the years, the position and power of the PM changed strongly. This often happened together with changes concerning the power of the King: the weaker the King, the stronger the PM.The existence of coalition governments puts forward bis role (...) as coordinator and even as arbitrator, whereas the federalisation process since the seventies places him as a conciliator between Regions and Communities. The growing importance of the European Council of Head of States have made him the most important decision-maker among the national politicians in the European integration process. The PM's skills concerning timing and agendasetting are very important because it is one of his most important power instruments. Other key skills are bis profound knowledge in certain issues but mostly as a generalist, his insisting on good minister nominations by the party leaders, the way he can motivate his cabinet members, a good team spirit among the government members and the existence of a clear government contract. In order to avoid a strongdependency on or tutelage from the political parties of the majority it is important to have their top politicians in the government. (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.

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)

Reviews the book 'The Cognitive Neuroscience of Consciousness', edited by Stanislas Dehaene.

A breathtaking look at the new science that can track consciousness deep in the brain How does our brain generate a conscious thought? And why does so much of our knowledge remain unconscious? Thanks to clever psychological and brain-imaging experiments, scientists are closer to cracking this mystery than ever before. In this lively book, Stanislas Dehaene describes the pioneering work his lab and the labs of other cognitive neuroscientists worldwide have accomplished in defining, testing, and explaining the brain events (...) behind a conscious state. We can now pin down the neurons that fire when a person reports becoming aware of a piece of information and understand the crucial role unconscious computations play in how we make decisions. The emerging theory enables a test of consciousness in animals, babies, and those with severe brain injuries. A joyous exploration of the mind and its thrilling complexities, Consciousness and the Brain will excite anyone interested in cutting-edge science and technology and the vast philosophical, personal, and ethical implications of finally quantifying consciousness. (shrink)

Frege writes in Numbers and Arithmetic about kindergarten-numbers and “an a priori mode of cognition” that they may have “a geometrical source.” This resembles recent findings on arithmetical cognition. In my paper, I explore this resemblance between Gottlob Frege’s later position concerning the geometrical source of arithmetical knowledge, and some current positions in the literature dedicated to arithmetical cognition, especially that of Stanislas Dehaene. In my analysis, I shall try to mainly see to what extent logicism is compatible with (...) intuitionism. (shrink)

The relation between the constitutionally founded supremacy of the parliament and the authoriy of the Prime Minister based on common law, is of a great importance in the Low Countries. This relation constitutes the difference between parliamentary and presidential regimes. It is the PM's duty to take care of the permanent support ofthe parliamentary majority. This is not an easy exercise. Members of parliament are not always as positive about the PM's parliamentary performances. Characteristics of the parliamentary activity of the (...) Belgian PM's Wilfried Martens, Jean-Luc Dehaene and the Dutch Ruud Lubbers are handled as: the frequency and the extent of the PM's parliamentary performances, the topics handled by the PM's in parliament, the PM's opponents in parliamentary debate and finally more generally the PM's parliamentary role behaviour. Due to the different position of both the parliament and the PM in the Belgian and the Dutch political system, the characteristics of the parliamenty activity of the Belgian and the Dutch PM are not always very similar. Additionally, remarkable differences occur between the parliamentary activity of different PM'swithin the same country. (shrink)

Frege writes in Numbers and Arithmetic about kindergarten-numbers and “an a priori mode of cognition” that they may have “a geometrical source.” This resembles recent findings on arithmetical cognition. In my paper, I explore this resemblance between Gottlob Frege’s later position concerning the geometrical source of arithmetical knowledge, and some current positions in the literature dedicated to arithmetical cognition, especially that of Stanislas Dehaene. In my analysis, I shall try to mainly see to what extent (Frege’s) logicism is compatible (...) with (Dehaene’s) intuitionism. (shrink)

This introductory chapter attempts to clarify the philosophical, empirical, and theoretical bases on which a cognitive neuroscience approach to consciousness can be founded. We isolate three major empirical observations that any theory of consciousness should incorporate, namely (1) a considerable amount of processing is possible without consciousness, (2) attention is a prerequisite of consciousness, and (3) consciousness is required for some specific cognitive tasks, including those that require durable information maintenance, novel combinations of operations, or the spontaneous generation of intentional (...) behavior. We then propose a theoretical framework that synthesizes those facts: the hypothesis of a global neuronal workspace. This framework postulates that, at any given time, many modular cerebral networks are active in parallel and process information in an unconscious manner. An information becomes conscious, however, if the neural population that represents it is mobilized by top-down attentional amplification into a brain-scale state of coherent activity that involves many neurons distributed throughout the brain. The long-distance connectivity of these `workspace neurons' can, when they are active for a minimal duration, make the information available to a variety of processes including perceptual categorization, long-term memorization, evaluation, and intentional action. We postulate that this global availability of information through the workspace is what we subjectively experience as a conscious state. A complete theory of consciousness should explain why some cognitive and cerebral representations can be permanently or temporarily inaccessible to consciousness, what is the range of possible conscious contents, how they map onto specific cerebral circuits, and whether a generic neuronal mechanism underlies all of them. We confront the workspace model with those issues and identify novel experimental predictions. Neurophysiological, anatomical, and brain-imaging data strongly argue for a major role of prefrontal cortex, anterior cingulate, and the areas that connect to them, in creating the postulated brain-scale workspace. (shrink)

Amidst the many brain events evoked by a visual stimulus, which are specifically associated with conscious perception, and which merely reflect non-conscious processing? Several recent neuroimaging studies have contrasted conscious and non-conscious visual processing, but their results appear inconsistent. Some support a correlation of conscious perception with early occipital events, others with late parieto-frontal activity. Here we attempt to make sense of those dissenting results. On the basis of a minimal neuro-computational model, the global neuronal workspace hypothesis, we propose a (...) taxonomy which distinguishes between vigilance and access to conscious report, as well as between subliminal, preconscious and conscious processing. We suggest that these distinctions map onto different neural mechanisms, and that conscious perception is systematically associated with a sudden surge of parieto-frontal activity causing top-down amplification. (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.

A uniquely integrative work, this volume provides a much needed compilation of primary source material to researchers from basic neuroscience, psychology, developmental science, neuroimaging, neuropsychology and theoretical biology. * The ...

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)

Whether unconscious stimuli can modulate the preparation of a cognitive task is still controversial. Using a backward masking paradigm, we investigated whether the modulation could be observed even if the prime was made unconscious in 100% of the trials. In two behavioral experiments, subjects were instructed to initiate a phonological or semantic task on an upcoming word, following an explicit instruction and an unconscious prime. When the SOA between prime and instruction was sufficiently long , primes congruent with the task (...) set instruction led to speedier responses than incongruent primes. In the other condition , no task set priming was observed. Repetition priming had the opposite tendency, suggesting the observed task set facilitation cannot be ascribed solely to perceptual repetition priming. Our results therefore confirm that unconscious information can modulate cognitive control for currently active task sets, providing sufficient time is available before the conscious decision. (shrink)

‘Number sense’ is a short‐hand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence suggesting that number sense constitutes a domain‐specific, biologically‐determined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence of a homology (...) between the animal, infant, and human adult abilities for number processing; and the existence of a dedicated cerebral substrate. In adults of all cultures, lesions to the inferior parietal region can specifically impair number sense while leaving the knowledge of other cognitive domains intact. Furthermore, this region is demonstrably activated during number processing. I postulate that higher–level cultural devel‐opments in arithmetic emerge through the establishment of linkages between this core analogical representation and other verbal and visual representations of number notations. The neural and cognitive organization of those representations can explain why some mathematical concepts are intuitive, while others are so difficult to grasp. Thus, the ultimate foundations of mathematics rests on core representations that have been internalized in our brains through evolution. (shrink)