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The number sense represents (rational) numbers

Published online by Cambridge University Press:  12 April 2021

Sam Clarke  and
Jacob Beck Open the ORCID record for Jacob Beck [Opens in a new window]
Sam Clarke
Affiliation:
Department of Philosophy & Centre for Vision Research, York University, Toronto, ONM3J 1P3, Canada. [email protected]; http://[email protected]; http://www.jacobbeck.org
Jacob Beck
Affiliation:
Department of Philosophy & Centre for Vision Research, York University, Toronto, ONM3J 1P3, Canada. [email protected]; http://[email protected]; http://www.jacobbeck.org
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Abstract

On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system (ANS), that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for number, such as “numerosities” or “quanticals,” as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind(s) of number being represented. In response, we propose that the ANS represents not only natural numbers (e.g., 7), but also non-natural rational numbers (e.g., 3.5). It does not represent irrational numbers (e.g., √2), however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research.

Keywords

analog magnitude systemapproximate number systemnumber sensenumerical cognitionnumerosity
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Behavioral and Brain Sciences , Volume 44 , 2021 , e178
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Copyright © The Author(s), 2021. Published by Cambridge University Press

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