Philosophical Psychology 21 (4):459 – 473 (2008)

Lieven Decock
VU University Amsterdam
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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DOI 10.1080/09515080802285255
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References found in this work BETA

The Basic Laws of Arithmetic.Gottlob Frege - 1893 - Berkeley: University of California Press.
General Theory of Natural Equivalences.Saunders MacLane & Samuel Eilenberg - 1945 - Transactions of the American Mathematical Society:231-294.
Number and Language: How Are They Related?Rochel Gelman & Brian Butterworth - 2005 - Trends in Cognitive Sciences 9 (1):6-10.

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Situated Counting.Peter Gärdenfors & Paula Quinon - 2020 - Review of Philosophy and Psychology 12 (4):1-24.
Situated Counting.Peter Gärdenfors & Paula Quinon - 2021 - Review of Philosophy and Psychology 12 (4):721-744.

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