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Numbers, numerosities, and new directions

Published online by Cambridge University Press:  15 December 2021

Sam Clarke
Affiliation:
Department of Philosophy & Centre for Vision Research, York University, Toronto, ONM3J 1P3, Canada.spclarke@yorku.ca; http://www.sampclarke.netjbeck@yorku.ca; http://www.jacobbeck.org
Jacob Beck
Affiliation:
Department of Philosophy & Centre for Vision Research, York University, Toronto, ONM3J 1P3, Canada.spclarke@yorku.ca; http://www.sampclarke.netjbeck@yorku.ca; http://www.jacobbeck.org

Abstract

In our target article, we argued that the number sense represents natural and rational numbers. Here, we respond to the 26 commentaries we received, highlighting new directions for empirical and theoretical research. We discuss two background assumptions, arguments against the number sense, whether the approximate number system (ANS) represents numbers or numerosities, and why the ANS represents rational (but not irrational) numbers.

Type
Authors’ Response
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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