No CrossRef data available.
Article contents
The number sense does not represent numbers, but cardinality comparisons
Published online by Cambridge University Press: 15 December 2021
Abstract
Against Clarke and Beck's proposal that the approximate number system (ANS) represents natural and rational numbers, I suggest that the experimental evidence is better accommodated by the (much weaker) thesis that the ANS represents cardinality comparisons. Cardinality comparisons do not stand in arithmetical relations and being able to apply them does not involve basic arithmetical concepts and operations.
- Type
- Open Peer Commentary
- Information
- Copyright
- Copyright © The Author(s), 2021. Published by Cambridge University Press
References
Barth, H., La Mont, K., Lipton, J., & Spelke, E. S. (2005). Abstract number and arithmetic in preschool children. Proceedings National Academy of Sciences, 102(39), 14116–14121. doi:10.1073/pnas.0505512102.CrossRefGoogle ScholarPubMed
Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74(1), B1–B11.CrossRefGoogle ScholarPubMed
Target article
The number sense represents (rational) numbers
Related commentaries (26)
A rational explanation for links between the ANS and math
Constructing rationals through conjoint measurement of numerator and denominator as approximate integer magnitudes in tradeoff relations
Contents of the approximate number system
Distinguishing the specific from the recognitional and the canonical, and the nature of ratios
Non-symbolic and symbolic number and the approximate number system
Not so rational: A more natural way to understand the ANS
Numbers in action
Numerical cognition needs more and better distinctions, not fewer
Numerical cognition: Unitary or diversified system(s)?
Numerosities are not ersatz numbers
Numerosity, area-osity, object-osity? Oh my
Perceived number is not abstract
Positing numerosities may be metaphysically extravagant; positing representation of numerosities is not
Ratio-based perceptual foundations for rational numbers, and perhaps whole numbers, too?
Real models: The limits of behavioural evidence for understanding the ANS
Representation of pure magnitudes in ANS
Second-order characteristics don't favor a number-representing ANS
Sizes, ratios, approximations: On what and how the ANS represents
The approximate number system represents magnitude and precision
The approximate number system represents rational numbers: The special case of an empty set
The number sense does not represent numbers, but cardinality comparisons
The number sense represents multitudes and magnitudes
The perception of quantity ain't number: Missing the primacy of symbolic reference
Unwarranted philosophical assumptions in research on ANS
Weighted numbers
What are we doing when we perceive numbers?
Author response
Numbers, numerosities, and new directions