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The number sense does not represent numbers, but cardinality comparisons
1Department of Philosophy, Texas A&M University, College Station, TX77843, USA. jbermudez@tamu.edu.
The Behavioral and Brain Sciences
|December 15, 2021
Summary
The approximate number system (ANS) likely represents quantity comparisons, not natural or rational numbers. This suggests basic arithmetic is not fundamental to quantity representation.
Area of Science:
- Cognitive Science
- Psychology
- Number Representation
Background:
- The approximate number system (ANS) is crucial for understanding numerical cognition.
- Clarke and Beck proposed that the ANS represents natural and rational numbers.
- This proposal implies a foundational link between the ANS and basic arithmetic.
Purpose of the Study:
- To re-evaluate the representational capacity of the approximate number system (ANS).
- To challenge the notion that the ANS represents natural and rational numbers.
- To propose an alternative, weaker thesis for ANS representation.
Main Methods:
- Analysis of existing experimental evidence on the approximate number system (ANS).
- Theoretical comparison of number representation versus cardinality comparison models.
- Evaluation of the arithmetical properties associated with each proposed representation.
Main Results:
- Experimental data are more consistent with the ANS representing cardinality comparisons.
- Cardinality comparisons do not inherently possess arithmetical relations.
- The ability to perform cardinality comparisons does not necessitate basic arithmetic operations.
Conclusions:
- The approximate number system (ANS) likely represents quantity comparisons, not abstract number types.
- This challenges the view that basic arithmetic is a prerequisite for numerical cognition.
- A weaker model of ANS function better explains current empirical findings.
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