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Contents of the approximate number system
1Department of Philosophy, University of Glasgow, GlasgowG12 8QQ, UK. Jack.Lyons@glasgow.ac.uk; https://sites.google.com/view/jack-lyons/home.
The Behavioral and Brain Sciences
|December 15, 2021
Summary
The approximate number system (ANS) likely represents natural numbers and their ratios, not rational numbers. This research suggests ANS representations are inherently approximate.
Area of Science:
- Cognitive Science
- Mathematical Cognition
- Psychology
Background:
- The approximate number system (ANS) is a cognitive mechanism for representing numerical quantities.
- Existing theories propose the ANS represents rational numbers (e.g., fractions, decimals).
Purpose of the Study:
- To challenge the theory that the ANS represents rational numbers.
- To propose an alternative interpretation of the ANS.
Main Methods:
- Critical analysis of existing evidence on the ANS.
- Theoretical argumentation.
Main Results:
- Evidence does not support the representation of rational numbers by the ANS.
- The ANS is better understood as representing natural numbers and ratios.
Conclusions:
- The contents of ANS representations should be considered genuinely approximate.
- Reinterpreting the ANS as representing natural numbers and ratios offers a more parsimonious explanation.
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