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What’s new: innovation and enculturation of arithmetical practices

  • Jean-Charles PellandEmail author
S.I.: MathCogEncul
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Abstract

One of the most important questions in the young field of numerical cognition studies is how humans bridge the gap between the quantity-related content produced by our evolutionarily ancient brains and the precise numerical content associated with numeration systems like Indo-Arabic numerals. This gap problem is the main focus of this paper. The aim here is to evaluate the extent to which cultural factors can help explain how we come to think about numbers beyond the subitizing range. To do this, I summarize Clark’s (Analysis 58:7–19, 1998) notion of a difference maker in explaining complex causation that criss-crosses between mind and world and apply it to Menary’s (In: Metzinger T, Windt JM (eds) Open MIND. MIND Group, Frankfurt, 2015a) discussion of mathematical cognition as a case of enculturation. I argue that while Menary’s views on enculturation can help explain what makes the difference between numerate and anumerate cultures, it cannot help specify what makes the difference between numerate and anumerate individuals. I argue that features of enculturation do not provide an account of innovation capable of explaining how individuals manage to improve and modify the practices of their cultural niche. This is because Menary’s construal of the role of enculturation in the development of mathematical cognition focuses mostly on the inheritance and transmission of practices, not on their origins, which involve individual-level understanding, rather than population-level practices and pressures. The upshot is that culture provides the necessary background conditions against which individuals can innovate. This role is crucial in the development of numerical abilities—crucial, but explanatorily limited.

Keywords

Numerical cognition Enculturation Innovation Richard Menary Cultural Niche Cognitive Niche 4E cognition Extended cognition Arithmetical practices History of numeration systems Approximate number system Culture and cognition Cultural evolution Arithmetic Numerals Developmental psychology 

Notes

Acknowledgements

Research for this article was supported by Grant 163129 from the Fonds de recherche du QuébecSociété et culture (FRQSC). Many thanks to Catarina Dutilh Novaes, Markus Pantsar, Max Jones, Regina Fabry, Richard Menary and other participants of the ESPP 2016 Symposium for helpful and engaging discussion on these topics. I also want to thank Brian Ball, Mathieu Marion, and two anonymous reviewers for helpful comments on earlier versions of this work.

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.New College of the HumanitiesLondonUK
  2. 2.McGill UniversityMontrealCanada
  3. 3.Université du Québec à MontréalMontrealCanada

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