, Volume 29, Issue 1, pp 3–13 | Cite as

The Innateness Hypothesis and Mathematical Concepts

  • Helen De Cruz
  • Johan De Smedt


In historical claims for nativism, mathematics is a paradigmatic example of innate knowledge. Claims by contemporary developmental psychologists of elementary mathematical skills in human infants are a legacy of this. However, the connection between these skills and more formal mathematical concepts and methods remains unclear. This paper assesses the current debates surrounding nativism and mathematical knowledge by teasing them apart into two distinct claims. First, in what way does the experimental evidence from infants, nonhuman animals and neuropsychology support the nativist hypothesis? Second, granting that infants have some elementary mathematical skills, does this mean that such skills play an important role in the development of mathematical knowledge?


Innate knowledge Nativism Mathematical knowledge Developmental psychology Arithmetic 



This research is supported by grant 3H070815 from the Research Foundation Flanders and grant COM07/PWM/001 from Ghent University. We thank Leon Horsten for comments on an earlier version of this paper.


  1. Antell SE, Keating DP (1983) Perception of numerical invariance in neonates. Child Dev 54:697–701CrossRefGoogle Scholar
  2. Benacerraf P (1973) Mathematical truth. J Philos 70:661–680CrossRefGoogle Scholar
  3. Berger A, Tzur G, Posner M (2006) Infant brains detect arithmetic errors. Proc Natl Acad Sci USA 103:12649–12653CrossRefGoogle Scholar
  4. Biro D, Matsuzawa T (2001) Chimpanzee numerical competence: cardinal and ordinal skills. In: Matsuzawa T (ed) Primate origins of human cognition and behavior. Springer, Tokyo, pp 199–225Google Scholar
  5. Brannon EM (2002) The development of ordinal numerical knowledge in infancy. Cognition 83:223–240CrossRefGoogle Scholar
  6. Butterworth B, Reeve R, Reynolds F, Lloyd D (2008) Numerical thought with and without words: evidence from indigenous Australian children. Proc Natl Acad Sci USA 105:13179–13184CrossRefGoogle Scholar
  7. Carey S (2004) Bootstrapping and the origin of concepts. Daedalus 133:59–68CrossRefGoogle Scholar
  8. Cohen LB, Marks KS (2002) How infants process addition and subtraction events. Dev Sci 5:186–212CrossRefGoogle Scholar
  9. Davis PJ, Hersh R (1981) The mathematical experience. Birkhauser, BostonGoogle Scholar
  10. De Cruz H (2008) An extended mind perspective on natural number representation. Philos Psychol 21:475–490CrossRefGoogle Scholar
  11. De Cruz H (2009) An enhanced argument for innate elementary geometric knowledge and its philosophical implications. In: Van Kerkhove B (ed) New perspectives on mathematical practices. Essays in philosophy and history of mathematics. World Scientific, New Jersey, pp 185–206Google Scholar
  12. Decock L (2008) The conceptual basis of numerical abilities: one-to-one correspondence versus the successor relation. Philos Psychol 21:459–473CrossRefGoogle Scholar
  13. Dehaene S, Izard V, Spelke E, Pica P (2008) Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures. Science 320:1217–1220CrossRefGoogle Scholar
  14. Descartes R (1988) 1637, Le discours de la méthode, la dioptrique, les météores et la géometrie. In: Alquie F (ed) Œuvres philosophiques de Descartes. Classiques Garnier, Paris, pp 549–761Google Scholar
  15. Feigenson L, Dehaene S, Spelke ES (2004) Core systems of number. Trends Cogn Sci 8:307–314CrossRefGoogle Scholar
  16. Flombaum JI, Junde JA, Hauser MD (2005) Rhesus monkeys (Macaca mulatta) spontaneously compute addition operations over large numbers. Cognition 97:315–325CrossRefGoogle Scholar
  17. Frank MC, Everett DL, Fedorenko E, Gibson E (2008) Number as a cognitive technology: evidence from Pirahã language and cognition. Cognition 108:819–824CrossRefGoogle Scholar
  18. Gallistel CR, Gelman R (2000) Non-verbal numerical cognition: from reals to integers. Trends Cogn Sci 4:59–65CrossRefGoogle Scholar
  19. Gilmore CK, McCarthy SE, Spelke ES (2007) Symbolic arithmetic knowledge without instruction. Nature 447:589–591CrossRefGoogle Scholar
  20. Gordon P (2004) Numerical cognition without words: evidence from Amazonia. Science 306:496–499CrossRefGoogle Scholar
  21. Grabiner JV (1986) Is mathematical truth time-dependent? In: Tymoczko T (ed) New directions in the philosophy of mathematics. Birkhauser, Boston, pp 201–213Google Scholar
  22. Greiffenhagen C, Sharrock W (2006) Mathematical relativism: logic, grammar and arithmetic in cultural comparison. J Theory Soc Behav 36:97–117CrossRefGoogle Scholar
  23. Haith MM (1998) Who put the cog in infant cognition? Is rich interpretation too costly? Infant Behav Dev 21:167–179CrossRefGoogle Scholar
  24. Halberda J, Mazzocco MM, Feigenson L (2008) Individual differences in non-verbal number acuity correlate with maths achievement. Nature 455:665–668CrossRefGoogle Scholar
  25. Jordan KE, Brannon EM (2006) The multisensory representation of number in infancy. Proc Natl Acad Sci USA 103:3486–3489CrossRefGoogle Scholar
  26. Kant I (2005) In: Guyer P, Wood AW (eds) 1781, Critique of pure reason. Cambridge University Press, CambridgeGoogle Scholar
  27. Kobayashi T, Hiraki K, Mugitani R, Hasegawa T (2004) Baby arithmetic: one object plus one tone. Cognition 91:B23–B34CrossRefGoogle Scholar
  28. Koechlin E, Dehaene S, Mehler J (1998) Numerical transformations in five-month-old human infants. Math Cogn 3:89–104CrossRefGoogle Scholar
  29. Laurence S, Margolis E (2005) Number and natural language. In: Carruthers P, Laurence S, Stich S (eds) The innate mind. Structure and contents. Oxford University Press, Oxford, pp 216–235Google Scholar
  30. Le Corre M, Carey S (2007) One, two, three, four, nothing more: an investigation of the conceptual sources of the verbal counting principles. Cognition 105:395–438CrossRefGoogle Scholar
  31. Leibniz GW (2001) In: Remnant P, Bennett JF (eds) 1765, New essays on human understanding. Cambridge University Press, CambridgeGoogle Scholar
  32. Mameli M, Bateson P (2006) Innateness and the sciences. Biol Philos 21:155–188CrossRefGoogle Scholar
  33. McCrink K, Wynn K (2004) Large-number addition and subtraction by 9-month-old infants. Psychol Sci 15:776–781CrossRefGoogle Scholar
  34. Meck WH, Church RM (1983) A mode control model of counting and timing processes. J Exp Psychol Anim Behav Process 9:320–334CrossRefGoogle Scholar
  35. Piaget J (1952) The child’s conception of number. Norton, New YorkGoogle Scholar
  36. Plato: ca. 380 B.C. (2000) Meno. In: Cahn SM (ed) Exploring philosophy. An introductory anthology. Oxford University Press, New York, pp 117–151Google Scholar
  37. Resnik MD (1982) Mathematics as the science of patterns: epistemology. Noûs 16:95–105CrossRefGoogle Scholar
  38. Rips L, Bloomfield A, Asmuth J (2008) From numerical concepts to concepts of number. Behav Brain Sci 31:623–642CrossRefGoogle Scholar
  39. Samuels R (2002) Nativism in cognitive science. Mind Lang 17:233–265Google Scholar
  40. Samuels R (2004) Innateness in cognitive science. Trends Cogn Sci 8:136–141CrossRefGoogle Scholar
  41. Saxe GB (1985) Effects of schooling on arithmetic understandings: studies with Oksapmin children in Papua New Guinea. J Educ Psychol 77:503–513CrossRefGoogle Scholar
  42. Shapiro S (1997) Philosophy of mathematics: structure and ontology. Oxford University Press, OxfordGoogle Scholar
  43. Siegler RS, Booth JL (2004) Development of numerical estimation in young children. Child Dev 75:428–444CrossRefGoogle Scholar
  44. Spelke ES, Kinzler KD (2007) Core knowledge. Dev Sci 10:89–96CrossRefGoogle Scholar
  45. Thune CE (1978) Numbers and counting in Loboda: an example of a non-numerical oriented culture. Papua New Guinea J Educ 14:69–80Google Scholar
  46. Thurston W (2006) On proof and progress in mathematics. In: Hersh R (ed) 18 Unconventional essays on the nature of mathematics. Springer, New York, pp 37–55CrossRefGoogle Scholar
  47. Tudusciuc O, Nieder A (2007) Neuronal population coding of continuous and discrete quantity in the primate posterior parietal cortex. Proc Natl Acad Sci USA 104:14513–14518CrossRefGoogle Scholar
  48. Uller C, Jaeger R, Guidry G, Martin C (2003) Salamanders (Plethodon cinereus) go for more: rudiments of number in an amphibian. Anim Cogn 6:105–112Google Scholar
  49. Venkatraman V, Ansari D, Chee MWL (2005) Neural correlates of symbolic and non-symbolic arithmetic. Neuropsychologia 43:744–753CrossRefGoogle Scholar
  50. Wassmann J, Dasen PR (1994) Yupno number system and counting. J Cross Cult Psychol 25:78–94CrossRefGoogle Scholar
  51. Whalen J, Gallistel C, Gelman R (1999) Nonverbal counting in humans: the psychophysics of number representation. Psychol Sci 10:130–137CrossRefGoogle Scholar
  52. Wynn K (1992) Addition and subtraction by human infants. Nature 358:749–750CrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Centre for Logic and Analytical PhilosophyKatholieke Universiteit LeuvenLeuvenBelgium
  2. 2.Department of Philosophy and EthicsGhent UniversityGhentBelgium

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