The conceptual basis of numerical abilities: One-to-one correspondence versus the successor relation
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophical Psychology 21 (4):459 – 473 (2008)
In recent years, neologicists have demonstrated that Hume's principle, based on the one-to-one correspondence relation, suffices to construct the natural numbers. This formal work is shown to be relevant for empirical research on mathematical cognition. I give a hypothetical account of how nonnumerate societies may acquire arithmetical knowledge on the basis of the one-to-one correspondence relation only, whereby the acquisition of number concepts need not rely on enumeration (the stable-order principle). The existing empirical data on the role of the one-to-one correspondence relation for numerical abilities is assessed and additional empirical tests are proposed. In the final part, it is argued that the fact that the successor relation and the one-to-one correspondence relation can play independent roles in number concept acquisition may be a complication for testing the Whorfian hypothesis.
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References found in this work BETA
David Hume (1739/2000). A Treatise of Human Nature. Oxford University Press.
Crispin Wright (1983). Frege's Conception of Numbers as Objects. Aberdeen University Press.
Gottlob Frege (1964). The Basic Laws of Arithmetic. Berkeley, University of California Press.
Elizabeth M. Brannon (2002). The Development of Ordinal Numerical Knowledge in Infancy. Cognition 83 (3):223-240.
Rochel Gelman & Brian Butterworth (2005). Number and Language: How Are They Related? Trends in Cognitive Sciences 9 (1):6-10.
Citations of this work BETA
Helen De Cruz & Johan De Smedt (2010). The Innateness Hypothesis and Mathematical Concepts. Topoi 29 (1):3-13.
Wojciech Krysztofiak (2012). Indexed Natural Numbers in Mind: A Formal Model of the Basic Mature Number Competence. [REVIEW] Axiomathes 22 (4):433-456.
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