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Embodied and Extended Numerical Cognition

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Explorations in Archaeology and Philosophy

Part of the book series: Synthese Library ((SYLI,volume 433))

Abstract

In this chapter we consider the theories of embodied cognition and extended mind with respect to the human ability to engage in numerical cognition. Such an enquiry requires first distinguishing between our innate number sense and the sort of numerical reasoning that is unique to humans. We provide anthropological and linguistic research to defend the thesis that places the body at the center of our development of numerical reasoning. We then draw on archaeological research to suggest a rough date for when ancient humans first were able to represent numerical information beyond the body and in enduring material artifacts. We conclude by briefly describing how these capacities for embodied and extended numerical cognition shaped our world.

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Notes

  1. 1.

    This does not mean, of course, that a parent would not, say, be able to tell that one of her six children is missing from a lineup. Similarly, if we saw a map of the United States with (say) Florida missing, we would surely notice. This does not require us to count to 49 or suggest we are using numerical concepts. In neither of these cases does the recognition that something is missing require numerical reasoning but visual recognition that something is off from the norm. Visual recognition only goes so far, however, and very large families in our society may resort to counting to make sure the entire family is present on certain occasions. Thanks to Sean Allen-Hermanson for posing the question with the first example.

  2. 2.

    It is not clear if Malafouris mistakenly believes that Chalmers and Clark (1998) hold the view the Otto’s notebook plays a ‘mere’ causal role rather than a constitutive one, or if he believes this paper (which, as of publication, has over 5000 citations) is one of the ‘rare’ exceptions to philosophers allegedly overlooking this possibility.

  3. 3.

    Thanks to Anton Killin for raising this point.

References

  • Adams F, Aizawa K (2008) Why the mind is still in the head. In: Robbins P, Aydede M (eds) Cambridge handbook of situated cognition. Cambridge University Press, Cambridge, pp 78–95

    Google Scholar 

  • Agrillo C (2015) Numerical and arithmetic abilities in non-primate species. In: Kadosh RC, Dowker A (eds) Oxford handbook of numerical cognition. Oxford University Press, Oxford, pp 214–236

    Google Scholar 

  • Anderson ML (2003) Embodied cognition: a field guide. Artificial Intelligence 149:91–130

    Google Scholar 

  • Ansary T (2009) Destiny disrupted: a history of the world through Islamic eyes. Public Affairs, New York

    Google Scholar 

  • Atherton M (1994) Women philosophers of the early modern period. Hackett, Cambridge

    Google Scholar 

  • Bowern C, Zentz J (2012) Diversity in the numeral systems of Australian languages. Anthropological Linguistics 54:133–160

    Article  Google Scholar 

  • Brannon E, Park J (2015) Phylogeny and ontogeny of mathematical and numerical understanding. In: Kadosh RC, Dowker A (eds) Oxford handbook of numerical cognition. Oxford University Press, Oxford, pp 203–213

    Google Scholar 

  • Carey S (2009) The origin of concepts. Oxford University Press, Oxford

    Book  Google Scholar 

  • Chalmers D, Clark A (1998) The extended mind. Analysis 58(1):7–19

    Article  Google Scholar 

  • Chemero A (2009) Radical embodied cognitive science. MIT Press, Cambridge, MA

    Google Scholar 

  • Churchland P (2017) Neurophilosophy. In: Smith DL (ed) How biology shapes philosophy. Cambridge University Press, Cambridge, pp 72–94

    Chapter  Google Scholar 

  • Clark A (1997) Being there: putting brain, body, and world together again. MIT Press, Cambridge, MA

    Google Scholar 

  • Clark A (2008) Supersizing the mind. Oxford University Press, Oxford

    Google Scholar 

  • Comrie B (2013) Numeral bases.. The World Atlas of Language Structures. http://wals.info/chapter/131

    Google Scholar 

  • De Cruz H (2008) An extended mind perspective on natural number representation. Philos Psychol 21(4):475–490

    Article  Google Scholar 

  • De Smedt J, De Cruz H (2011) The role of material culture in human time representation: calendrical systems as extensions of mental time travel. Adapt Behav 19:63–76

    Article  Google Scholar 

  • D’Errico F (1998) Paleolithic origins of artificial memory systems: an evolutionary perspective. In: Renfrew C, Scarre C (eds) Cognition and material culture: the archaeology of symbolic storage. McDonald Institute, Cambridge, pp 19–50

    Google Scholar 

  • D’Errico F, Henshilwood C, Lawson G, Vanhaeren M et al (2003) Archaeological evidence for the emergence of language, symbolism, and music—an alternative multidisciplinary perspective. J World Prehist 17(1):1–70

    Article  Google Scholar 

  • D’Errico F, Doyon L, Colagé I, Queffelec A et al (2018) From number sense to number symbols: an archaeological perspective. Philos Trans R Soc B. https://doi.org/10.1098/rstb.2016.0518

  • Dehaene S (1997) The number sense: how the mind creates mathematics. Oxford University Press, Oxford

    Google Scholar 

  • Everett C (2015) Lexical and grammatical number are cognitively and historically dissociable. Curr Anthropol 57:351

    Article  Google Scholar 

  • Everett C (2017) Numbers and the making of us. Harvard University Press, Cambridge, MA

    Book  Google Scholar 

  • Everett C, Madora K (2012) Quantity recognition among speakers of an anumeric language. Cogn Sci 36:130–141

    Article  Google Scholar 

  • Flegg G (2002) Numbers: their history and meaning. Dover, New York

    Google Scholar 

  • Franzon F, Zanini C, Rugani R (2019) Do non-verbal systems shape grammar? Numerical cognition and number morphology compared. Mind and Language 34:37–58

    Article  Google Scholar 

  • Gleitman L, Newport E (1995) The invention of language by children: environmental and biological influences on the acquisition of language. In: Gleitman L, Liberman M (eds) Language: an invitation to cognitive science, 2nd edn. MIT Press, Cambridge, MA

    Chapter  Google Scholar 

  • Gomez-Robles A (2019) Dental evolutionary rates and its implications for the neanderthal-modern human divergence. Sci Adv. https://doi.org/10.1126/sciadv.aaw1268

  • Harman G (1973) Thought. Princeton University Press, Princeton

    Book  Google Scholar 

  • Hauser M, Chomsky N, Fitch W (2002) The faculty of language: what is it, who has it, and how did it evolve? Science 298(5598):1569–1579

    Article  Google Scholar 

  • Izard V, Sann C, Spelke E, Streri A (2009) Newborn infants perceive abstract numbers. Proc Natl Acad Sci 106:10382–10385

    Article  Google Scholar 

  • MacFarquhar L (2018) Mind expander: a philosopher asks where we begin and where we end. The New Yorker. April 2, 2018, pp 62–73.

    Google Scholar 

  • Malafouris L (2013) How things shape the mind. MIT Press, Cambridge, MA

    Book  Google Scholar 

  • Marshack A (1991) The roots of civilization: the cognitive beginnings of man’s first art, symbol and notation. Moyer Bell Limited, Rhode Island

    Google Scholar 

  • Menary R (2015) Mathematical cognition: a case of enculturation. In: Metzinger T, Windt JM (eds) Open mind: 25. Frankfurt am Main. https://doi.org/10.15502/9783958570818

  • Nathan N (2014) Grounded mathematical reasoning. In: Shapiro L (ed) Routledge handbook of embodied cognition. Routledge, Oxon/New York, pp 171–183

    Google Scholar 

  • Núñez R (2017) Is there really an evolved capacity for number? Trends Cogn Sci 21(6):409–424

    Article  Google Scholar 

  • Overmann K (2015) Numerosity structures the expression of quantity in lexical numbers and grammatical number. Curr Anthropol 56:638–653

    Article  Google Scholar 

  • Piantadosi S (2016) A rational analysis of the approximate number system. Psychon Bull Rev 23:877–886

    Article  Google Scholar 

  • Prinz J (2008) Is consciousness embodied? In: Robbins P, Aydede M (eds) Cambridge handbook of situated cognition. Cambridge University Press, Cambridge, pp 419–436

    Google Scholar 

  • Renfrew C, Bahn P (2012) Archaeology: theories, methods, practice. Thames & Hudson, London

    Google Scholar 

  • Rescorla M (2017) The computational theory of mind. In: Zalta EN (ed) The Stanford encyclopedia of philosophy, spring 2017 edn. https://plato.stanford.edu/archives/spr2017/entries/computational-mind

    Google Scholar 

  • Revell T (2017) Celebrate pi day with 9 trillion more digits than ever before. New Scientist. March 14, 2017

    Google Scholar 

  • Spaepen E, Coppola M, Spelke E, Carey S, Goldin-Meadow S (2011) Number without a language model. Proc Natl Acad Sci 108:3163–3168

    Article  Google Scholar 

  • Tomasello M (1999) The cultural origins of human cognition. Harvard University Press, Cambridge, MA

    Google Scholar 

  • Wheeler M (2005) Reconstructing the cognitive world. MIT Press, Cambridge, MA

    Google Scholar 

  • Wynn K (1992) Addition and subtraction by human infants. Nature 358:749–750

    Article  Google Scholar 

  • Xu F, Spelke E (2000) Large number discrimination in 6-month-old infants. Cognition 74:B1–B11

    Article  Google Scholar 

  • Zahidi K, Myin E (2016) Radically enactive numerical cognition. In: Etzelmuller G, Tewes C (eds) Embodiment in evolution and culture. Mohr-Siebrek, Tübingen, pp 57–71

    Google Scholar 

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Acknowledgements

We would like to thank Sean Allen-Hermanson, Francesco d’Errico, Peter Godfrey-Smith, Anton Killin, and Ronald Planer for their helpful comments on the paper.

Author information

Authors and Affiliations

  1. Department of Philosophy, University of San Diego, San Diego, CA, USA

    Marilynn Johnson

  2. Department of Anthropology, University of Miami, Miami, FL, USA

    Caleb Everett

Authors
  1. Marilynn Johnson
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  2. Caleb Everett
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Correspondence to Marilynn Johnson .

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Editors and Affiliations

  1. Department of Philosophy, Mount Allison University, Sackville NB, Canada, School of Philosophy and Centre of Excellence for the Dynamics of Language, Australian National University, Acton ACT, Australia, Acton, ACT, Australia

    Anton Killin

  2. Department of Philosophy, Florida International University, Miami, FL, USA

    Sean Allen-Hermanson

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Johnson, M., Everett, C. (2021). Embodied and Extended Numerical Cognition. In: Killin, A., Allen-Hermanson, S. (eds) Explorations in Archaeology and Philosophy. Synthese Library, vol 433. Springer, Cham. https://doi.org/10.1007/978-3-030-61052-4_8

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