Abstract
This chapter is devoted to the discovery of the core abilities underlying human numerical cognition. Neuroscientists hypothesises that human beings are born with a “number sense” that they share with other animals and that this instinct is the expression of the functioning of a “mental organ”, a set of brain circuits that exist also in other species. According to neuroscientist Stanislas Dehaene, this “mental organ” works as an accumulator, namely a kind of approximate counting device that allows us to perceive, store, and compare numerical quantities.
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Antell, S. E., & Keating, L. E. (1983). Perception of numerical invariance by neonates. Child Development, 54, 695–701.
Beran, M. J., & Beran, M. M. (2004). Chimpanzees remember the results of onebyone addition of food items to sets over extended time periods. Psychological Science, 15, 94–99.
Bijeljac-Babic, R., Bertoncini, J., & Mehler, J. (1993). How do 4-day-old infants categorize multisyllabic utterances? Developmental Psychology, 29(4), 711–721.
Biro, D., & Matsuzawa, T. (2001). Use of numerical symbols by the chimpanzee (Pan troglodytes): Cardinals, ordinals, and the introduction of zero. Animal Cognition, 4, 193–199.
Boysen, S. T., & Berntson, G. G. (1989). Numerical competence in a chimpanzee. Journal of Comparative Psychology, 103(1), 23–31.
Brannon, E. M. (2002). The development of ordinal numerical knowledge in infancy. Cognition, 83, 223–240.
Brannon, E. M., & Terrace, H. S. (1998). Ordering of the numerosities 1 to 9 by monkeys. Science, 282, 746–749.
Brannon, E. M., & Terrace, H. S. (2000). Representation of the numerosities 1-9 by rhesus macaques (macaca mulatta). Journal of Experimental Psychology: AnimalBehavior Processes, 26(1), 31–49.
Cantlon, J. F., & Brannon, E. M. (2006). The effect of heterogeneity on numerical ordering in rhesus monkeys. Infancy, 9, 173–189.
Clearfield, M. W., & Mix, K. S. (1999). Number versus contour length in infants’ discrimination of small visual sets. Psychological Science, 10(5), 408–411.
Cohen, L. B., & Marks, K. (2002). How infants process addition and subtraction events. Developmental Science, 5(2), 186–201.
Davis, H., & Albert, M. (1987). Failure to transfert or train a numerical discrimination using sequential visual stimuli in rats. Bulletin of the Psychonomic Society, 25, 472–474.
Davis, H., & Perusse, R. (1988). Numerical competence in animals: Definitional issues, current evidence and a new research agenda. Behavioural Brain Science, 11, 561–579.
Dehaene, S. (1997). The number sense. New York, Cambridge (UK): Oxford University Press, Penguin Press.
Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1–42.
Dehaene, S. (2011). The number sense. How the mind creates mathematics. Revised and updated edition. New York: Oxford University Press.
Devlin, K. (2005). The math instinct. Why you’re a mathematical genius. New York: Thunder’s Mouth press.
Emmerton, J., & Delius, J.D. (1993). Beyond sensation: Visual cognition in pigeons. In H. P. Zeigler & H. Bischof (Eds.), Vision, brain, and behavior in birds (pp. 377–390). Cambridge, MA: MIT Press.
Emmerton, J., Lohmann, A., & Niemann, J. (1997). Pigeon’s serial ordering of numerosity with visual arrays. Animal Learning and Behavior, 25, 234–244.
Feigenson, L. (2005). A double-dissociation in infants’ representations of object arrays. Cognition, 95, 37–48.
Feigenson, L., Carey, S., & Hauser, M. D. (2002). The representations underlying infants’ choice of more: Object files versus analog magnitudes. Psychological Science, 13(2), 150–156.
Feigenson, L., Dehaene, S., & Spelke, E. S. (2004). Core systems of number. Trends in Cognitive Sciences, 8, 307–314.
Fernandes, D. M., & Church, R. H. (1982). Discrimination of the number of sequential events by rats. Animal Learning and Behavior, 10(2), 171–176.
Flombaum, J. I., Junge, J. A., & Hauser, M. D. (2005). Rhesus monkeys (Macaca mulatta) spontaneously compute addition operations over large numbers. Cognition, 97, 315–325.
Gallistel, C. R., & Gelman, R. (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences, 4, 59–65.
Hanus, D., & Call, J. (2007). Discrete quantity judgments in the great apes (Pan paniscus, Pan troglodytes, Gorilla gorilla, Pongo pygmaeus). Journal of Comparative Psychology, 121(3), 241–249.
Hauser, M. D., & Spelke, E. S. (2004). Evolutionary and developmental foundations of human knowledge: A case study of mathematics. In M. Gazzaniga (Ed.), The cognitive neurosciences (Vol. 3). Cambridge: MIT Press.
Jaakkola, K., Fellner, W., Erb, L., Rodriguez, A. M., & Guarino, E. (2005). Understanding of the concept of numerically “less” by bottlenose dolphins (Tursiops truncatus). Journal of Comparative Psychology, 119, 296–303.
Jordan, K. E., & Brannon, E. M. (2006). Weber’s law influences numerical representations in rhesus macaques (Macaca mulatta). Animal Cognition, 9, 159–172.
Kilian, A., Yaman, S., Fersen, L., & Gunturkun, O. (2003). A bottlenose dolphin (Tursiops truncates) discriminates visual stimuli differing in numerosity. Learning and Behaviour, 31, 133–142.
Kilian, A., Von Fersen, L., & Güntürkün, O. (2005). Left hemispheric advantage for numerical abilities in the bottlenose dolphin. Behavioural Processes, 68, 179–184.
Kobayashi, T., Hiraki, K., & Hasegawa, T. (2005). Auditory-visual intermodal matching of small numerosities in 6-month-old infants. Developmental Science, 8, 409–419.
Leslie, A., Xu, F., Tremoulet, P., & Scholl, B. (1998). Indexing and the object concept: Developing what and where systems. Trends in Cognitive Science, 2(1), 10–18.
Lipton, J. S., & Spelke, E. S. (2003). Origins of number sense: Large-number discrimination in human infants. Psychological Science, 14(5), 396–401.
Lyon, B. E. (2003). Egg recognition and counting reduce costs of avian conspecific brood parasitism. Nature, 422, 495–499.
Marler, P., & Tamura, M. (1962). Song dialects in three populations of Whitecrowned sparrows. Condor, 64, 368–377.
McComb, K., Packer, C., & Pusey, A. (1994). Roaring and numerical assessment in the contests between groups of female lions, Panther leo. Animal Behaviour, 47, 379–387.
McCrink, K., & Wynn, K. (2004). Large number addition and subtraction by 9-month-old infants. Psychological Science, 15(11), 776–781.
Mechner, F. (1958). Probability relations within response sequences under ratio reinforcement. Journal of the Experimental Analysis of Behaviour, 1, 109–122.
Mechner, F., & Guevrekian, L. (1962). Effects of deprivation upon counting and timing in rats. Journal of the Experimental Analysis of Behavior, 5(4), 463–466.
Meck, W. H., & Church, R. M. (1984). Simultaneous temporal processing. Journal of Experimental Psychology: Animal Behavior Processes, 10(1), 1–29.
Moore, D., Benenson, J., Reznick, J. S., Peterson, M., & Kagan, J. (1987). Effect of auditory numerical information on infants’ looking behavior: Contradictory evidence. Developmental Psychology, 23, 665–670.
Pepperberg, I. (2006). Grey parrot numerical competence: A review. Animal Cognition, 9, 377–391.
Piaget, J. (1952). The child’s conception of number. New York: Norton.
Piazza, M., Izard, V., Pinel, P., Bihan, D. L., & Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44(3), 547–555.
Platt, J. R., & Johnson, D. M. (1971). Localization of position within a homogeneous behaviour chain: Effects of error contingencies. Learning and Motivation, 2, 386–414.
Robins, A., Lippolis, G., Bisazza, A., Vallortigara, G., & Rogers, L. J. (1998). Lateralized agonistic responses and hind-limb use in toads. Animal Behaviour, 56, 875–881.
Rugani, R., Regolin, L., & Vallortigara, G. (2007). Rudimental numerical competence in 5-day-old domestic chicks: Identification of ordinal position. Journal of Experimental Psychology: Animal Behavior Processes, 33(1), 21–31.
Rumbaugh, D. M., Savage-Rumbaugh, S., & Hegel, M. T. (1987). Summation in the chimpanzee (pan troglodytes). Journal of Experimental Psychology: Animal Behavior Processes, 13, 107–115.
Santos, L. R., Barnes, J. L., & Mahajan, N. (2005). Expectations about numerical events in four lemur species. Animal Cognition, 8, 253–262.
Simon, T. J. (1999). The foundations of numerical thinking in a brain without numbers. Trends in Cognitive Sciences, 3(10), 363–364.
Spelke, E. S., Kestenbaum, R., Simons, D. J., & Wein, D. (1995). Spatio-temporal continuity, smoothness of motion and object identity in infancy. British Journal of Developmental Psychology, 13, 113–142.
Starkey, P., & Cooper, R. G. (1980). Perception of numbers by human infants. Science, 210, 1033–1035.
Starkey, P., Spelke, E. S., & Gelman, R. (1983). Detection of intermodal numerical correspondences by human infants. Science, 222(4620), 179–181.
Starkey, P., Spelke, E. S., & Gelman, R. (1990). Numerical abstraction by human infants. Cognition, 36, 97–128.
Sulkowski, G. M., & Hauser, M. D. (2001). Can rhesus monkeys spontaneously substract? Cognition, 79, 239–262.
Uller, C., Hauser, M. D., & Carey, S. (2001). Spontaneous representation of number in cotton-top tamarins. Journal of Comparative Psychology, 115, 1–10.
Uller, C., Jaeger, R., Guidry, G., & Martin, C. (2003). Salamanders (Plethodon cinereus) go for more: Rudiments of number in a species of basal vertebrate. Animal Cognition, 6, 105–112.
Wilson, M. L., Hauser, M. D., & Wrangham, R. W. (2001). Does participation in intergroup conflict depend on numerical assessment, range, location, or rank for wild chimpanzees? Animal Behaviour, 61, 1203–1216.
Wood, J. N., & Spelke, E. S. (2005). Infants’ enumeration of actions: numerical discrimination and its signature limits. Developmental Science, 8, 173–181.
Woodruff, G., & Premack, D. (1981). Primative (sic) mathematical concepts in the chimpanzee: Proportionality and numerosity. Nature, 293, 568–570.
Wynn, K. (1990). Children’s understanding of counting. Cognition, 36, 155–193.
Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358, 749–750.
Wynn, K., Bloom, P., & Chiang, W. (2002). Enumeration of collective entities by 5-month-old infants. Cognition, 83, B55–B62.
Xu, F., & Arriaga, R. I. (2007). Number discrimination in 10-month-old infants. British Journal of Developmental Psychology, 25, 103–108.
Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74, 1–11.
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Graziano, M. (2018). The System 1. In: Dual-Process Theories of Numerical Cognition. SpringerBriefs in Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-319-96797-4_2
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