Cognitive Processing

, Volume 12, Issue 1, pp 1–11 | Cite as

The redundancy of recursion and infinity for natural language



An influential line of thought claims that natural language and arithmetic processing require recursion, a putative hallmark of human cognitive processing (Chomsky in Evolution of human language: biolinguistic perspectives. Cambridge University Press, Cambridge, pp 45–61, 2010; Fitch et al. in Cognition 97(2):179–210, 2005; Hauser et al. in Science 298(5598):1569–1579, 2002). First, we question the need for recursion in human cognitive processing by arguing that a generally simpler and less resource demanding process—iteration—is sufficient to account for human natural language and arithmetic performance. We argue that the only motivation for recursion, the infinity in natural language and arithmetic competence, is equally approachable by iteration and recursion. Second, we submit that the infinity in natural language and arithmetic competence reduces to imagining infinite embedding or concatenation, which is completely independent from the ability to implement infinite processing, and thus, independent from both recursion and iteration. Furthermore, we claim that a property of natural language is physically uncountable finity and not discrete infinity.


Recursion Iteration Language Brain Infinity Embedding Arithmetic 


  1. Abelson H, Sussman GJ, Sussman J (1996) Structure and interpretation of computer programs, 2nd edn. MIT, CambridgeGoogle Scholar
  2. Bickerton D (2009) Recursion: core of complexity or artifact of analysis? In: Givón T, Shibatani M (eds) Syntactic complexity: diachrony, acquisition, neuro-cognition, evolution. John Benjamins, Amsterdam, pp 531–543Google Scholar
  3. Birkhoff G, von Neumann J (1936) The logic of quantum mechanics. Ann Math 37(4):823–843CrossRefGoogle Scholar
  4. Chaiken M, Bohner J, Marler P (1994) Repertoire turnover and the timing of song acquisition in European starlings. Anim Behav 128(1–2):26–39Google Scholar
  5. Chang G, Sederberg TW (1998) Over and over again. The Mathematical Association of America, Washington, DCGoogle Scholar
  6. Chomsky N (1956) Three models for the description of language. IRE Transact Inform Theor 2:113–124CrossRefGoogle Scholar
  7. Chomsky N (1959) On certain formal properties of grammars. Inform Control 2:137–167CrossRefGoogle Scholar
  8. Chomsky N (1964 [1957]) Syntactic structures. Mouton, The HagueGoogle Scholar
  9. Chomsky N (1971 [1957]) Syntactic structures. Mouton, The HagueGoogle Scholar
  10. Chomsky N (1975) The logical structure of linguistic theory. Plenum, New YorkGoogle Scholar
  11. Chomsky N (1995) The minimalist program. MIT, CambridgeGoogle Scholar
  12. Chomsky N (2010) Some simple evo-devo theses: how true might they be for language? In: Larson RK, Yamakido H, Deprez V (eds) Evolution of human language: biolinguistic perspectives. Cambridge University Press, Cambridge, pp 45–61Google Scholar
  13. Christiansen MH (1992) The (non)necessity of recursion in natural language processing. In: Proceedings of the 14th annual conference of the Cognitive Science Society. Cognitive Science Society, Indiana University, Indiana, pp 665–670Google Scholar
  14. Christiansen MH, Chater N (2003) Constituency and recursion in language. In: Arbib MA (ed) The handbook of brain theory and neural networks, 2nd edn. MIT, Cambridge, pp 267–271Google Scholar
  15. Christiansen MH, Chater N (2008) Language as shaped by the brain. Behav Brain Sci 31:489–558. doi:10.1017/S0140525X08004998 PubMedGoogle Scholar
  16. Corballis MC (2007a) On phrase-structure and brain responses: a comment on Bahlmann, Gunter, and Friederici (2006). J Cogn Neurosci 19:1581–1583CrossRefPubMedGoogle Scholar
  17. Corballis MC (2007b) Recursion, language, and starlings. Cogn Sci 31:697–704CrossRefGoogle Scholar
  18. Cowan N (2001) The magical number 4 in short-term memory: a reconsideration of mental storage capacity. Behav Brain Sci 24(1):87–114 (discussion 114–185)CrossRefPubMedGoogle Scholar
  19. Donald M (1998) Mimesis and the executive suite: missing links in language evolution. In: Hurford JR, Studdert-Kennedy M, Knight C (eds) Approaches to the evolution of language: social and cognitive bases. Cambridge University Press, CambridgeGoogle Scholar
  20. Douglas RJ, Martin KA (2007) Mapping the matrix: the ways of neocortex. Neuron 56(2):226–238. doi:10.1016/j.neuron.2007.10.017 CrossRefPubMedGoogle Scholar
  21. Evans N, Levinson SC (2009) The myth of language universals: language diversity and its importance for cognitive science. Behav Brain Sci 32:429–492. doi:10.1017/S0140525X0999094X CrossRefPubMedGoogle Scholar
  22. Everett DL (2005) Cultural constraints on grammar and cognition in Pirahã. Curr Anthropol 46(4):621–646CrossRefGoogle Scholar
  23. Felleman DJ, Van Essen DC (1991) Distributed hierarchical processing in the primate cerebral cortex. Cereb Cortex 1(1):1–47CrossRefPubMedGoogle Scholar
  24. Fitch WT (2010) Three meanings of “recursion”: key distinctions for biolinguistics. In: Larson RK, Deprez V, Yamakido H (eds) The evolution of human language: biolinguistic perspectives. Cambridge University Press, Cambridge, pp 73–90Google Scholar
  25. Fitch WT, Hauser MD, Chomsky N (2005) The evolution of the language faculty: Clarifications and implications. Cognition 97(2):179–210. doi:10.1016/j.cognition.2005.02.005 (discussion 211–125)CrossRefPubMedGoogle Scholar
  26. Gentner TQ, Fenn KM, Margoliash D et al (2006) Recursive syntactic pattern learning by songbirds. Nature 440(7088):1204–1207. doi:10.1038/nature04675 CrossRefPubMedGoogle Scholar
  27. Gibson E (1998) Syntactic complexity: locality of syntactic dependencies. Cognition 68(1):1–76CrossRefPubMedGoogle Scholar
  28. Gibson E (2000) The dependency locality theory: a distance-based theory of linguistic complexity. In: Miyashita Y, Marantz AP, O’Neil W (eds) Image, language, brain. MIT, Cambridge, pp 95–126Google Scholar
  29. Hauser MD, Chomsky N, Fitch WT (2002) The faculty of language: what is it, who has it, and how did it evolve? Science 298(5598):1569–1579. doi:10.1126/science.298.5598.1569 CrossRefPubMedGoogle Scholar
  30. Heine B, Kuteva T (2007) The genesis of grammar: a reconstruction. Oxford University Press, New YorkGoogle Scholar
  31. Hurford JR (2004) Human uniqueness, learned symbols and recursive thought. Eur Rev 12(4):551–565CrossRefGoogle Scholar
  32. Jackendoff R, Pinker S (2005) The nature of the language faculty and its implications for evolution of language (reply to Fitch, Hauser, and Chomsky). Cognition 97(2):211–225. doi:10.1016/j.cognition.2005.04.006 CrossRefGoogle Scholar
  33. Johansson S (2006) Working backwards from modern language to proto-grammar. In: The evolution of language: proceedings of the 6th international conference on the evolution of language (evolang6). World Scientific, Singapore, pp 160–167Google Scholar
  34. Karlsson F (2007a) Constraints on multiple center-embedding of clauses. J Linguist 43(2):365–392. doi:10.1017/S0022226707004616 CrossRefGoogle Scholar
  35. Karlsson F (2007b) Constraints on multiple initial embedding of clauses. Int J Corpus Linguist 12(1):107–118. doi:10.1075/ijcl.12.1.07kar CrossRefGoogle Scholar
  36. Köhler O (1956) The ability of birds to “count”. In: Newman JR (ed) The world of mathematics, vol 1. Simon and Schuster, New YorkGoogle Scholar
  37. Leng G, Ludwig M (2006) Jacques Benoit lecture: information processing in the hypothalamus: peptides and analogue computation. J Neuroendocrinol 18(6):379–392. doi:10.1111/j.1365-2826.2006.01428.x CrossRefPubMedGoogle Scholar
  38. Lieberman P (2008) Cortico-striatal-cortical neural circuits, reiteration, and the “Narrow language faculty”. Behav Brain Sci 31:527–528CrossRefGoogle Scholar
  39. Lieberman P (2010) The creative capacity of language, in what manner is it unique, who had it? In: Larson RK, Deprez V, Yamakido H (eds) The evolution of human language: biolinguistic perspectives. Cambridge University Press, Cambridge, pp 163–175Google Scholar
  40. Marcus GF (2006) Language: startling starlings. Nature 440(7088):1117–1118CrossRefPubMedGoogle Scholar
  41. Marr D (1982) Vision: a computational investigation into the human representation and processing of visual information. W. H. Freeman and Company, San FransiscoGoogle Scholar
  42. Minsky M (1972) Computation: finite and infinite machines. Prentice-Hall International, LondonGoogle Scholar
  43. Moore AW (1990) The infinite. Routledge, LondonCrossRefGoogle Scholar
  44. Okanoya K (2007) Language evolution and an emergent property. Curr Opin Neurobiol 17(2):271–276. doi:10.1016/j.conb.2007.03.011 CrossRefPubMedGoogle Scholar
  45. Parker AR (2006) Evolving the narrow language faculty: was recursion the pivotal step? In: The evolution of language: proceedings of the 6th international conference on the evolution of language. World Scientific, Singapore, pp 239–246Google Scholar
  46. Pinker S, Jackendoff R (2005) The faculty of language: what’s special about it? Cognition 95(2):201–236. doi:10.1016/j.cognition.2004.08.004 CrossRefPubMedGoogle Scholar
  47. Premack D (2004) Psychology. Is language the key to human intelligence? Science 303(5656):318–320. doi:10.1126/science.1093993 CrossRefPubMedGoogle Scholar
  48. Premack D (2007) Human and animal cognition: Continuity and discontinuity. Proc Natl Acad Sci USA 104(35):13861–13867. doi:10.1073/pnas.0706147104 CrossRefPubMedGoogle Scholar
  49. Pullum GK, Stolz BC (2010) Recursion and the infinitude claim. In: Hulst Hvd (ed) Recursion in human language (studies in generative grammar 104). Mouton de Gruyter, Berlin, pp 113–138Google Scholar
  50. Putnam H (1975) Mathematics, matter, and method. Cambridge University Press, LondonGoogle Scholar
  51. Rogers H Jr (1987) The theory of recursive functions and effective computability. MIT, CambridgeGoogle Scholar
  52. Shannon CE, Weaver W (1964 [1949]) The mathematical theory of communication. The University of Illinois Press, UrbanaGoogle Scholar
  53. Sipser M (1997) Introduction to the theory of computation. PWS Publishing Company, BostonGoogle Scholar
  54. Studdert-Kennedy M (1998) The particulate origins of language generativity: from syllable to gesture. In: Hurford JR, Studdert-Kennedy M, Knight C (eds) Approaches to the evolution of language: social and cognitive bases. Cambridge University Press, Cambridge, pp 202–221Google Scholar
  55. Suzuki R, Buck JR, Tyack PL (2006) Information entropy of humpback whale songs. J Acoust Soc Am 119(3):1849–1866. doi:10.1121/1.424990 CrossRefPubMedGoogle Scholar
  56. Tomalin M (2007) Reconsidering recursion in syntactic theory. Lingua 117:1784–1800. doi:10.1016/j.lingua.2006.11.001 CrossRefGoogle Scholar
  57. Unsworth N, Engle RW (2007) The nature of individual differences in working memory capacity: active maintenance in primary memory and controlled search from secondary memory. Psychol Rev 114(1):104–132CrossRefPubMedGoogle Scholar
  58. von Neumann J (1948) The computer and the brain. Yale University Press, New HavenGoogle Scholar
  59. Warren T, Gibson E (2002) The influence of referential processing on sentence complexity. Cognition 85:79–112CrossRefPubMedGoogle Scholar
  60. Watanabe S, Huber L (2006) Animal logics: decisions in the absence of human language. Anim Cogn 9(4):235–245CrossRefPubMedGoogle Scholar
  61. Watanabe S, Sakamoto J, Wakita M (1995) Pigeons’ discrimination of paintings by Monet and Picasso. J Exp Anal Behav 63(2):165–174CrossRefPubMedGoogle Scholar
  62. Weisstein EW (2003) CRC concise encyclopedia of mathematics, 2nd edn. Chapman & Hall/CRC, Boca RatonGoogle Scholar

Copyright information

© Marta Olivetti Belardinelli and Springer-Verlag 2010

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of TartuTartuEstonia
  2. 2.Department of PhysiologyUniversity of TartuTartuEstonia
  3. 3.Department of Clinical BiochemistryBispebjerg HospitalCopenhagenDenmark
  4. 4.TartuEstonia

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