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The number sense represents (rational) numbers.

Sam Clarke1, Jacob Beck1

  • 1Department 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.

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Summary
This summary is machine-generated.

Humans and animals possess a number sense, or approximate number system (ANS), representing quantities. This study defends the ANS against critiques and proposes it represents natural and rational numbers, but not irrational ones.

Keywords:
analog magnitude systemapproximate number systemnumber sensenumerical cognitionnumerosity

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Area of Science:

  • Cognitive Science
  • Comparative Psychology
  • Philosophy of Mind

Background:

  • The orthodox view posits an approximate number system (ANS) for numerical representation in humans and animals.
  • Recent critiques challenge whether the ANS truly represents numbers or non-numerical confounds.

Purpose of the Study:

  • To evaluate critiques of the ANS and provide evidence for its genuine numerical representation.
  • To investigate the specific kinds of numbers the ANS represents.

Main Methods:

  • Analysis of critiques: arguments from congruency, confounds, and imprecision.
  • Theoretical proposal regarding the types of numbers represented by the ANS.

Main Results:

  • Critiques against the ANS were found to be unsuccessful.
  • The ANS is proposed to represent natural and non-natural rational numbers.
  • The ANS does not represent irrational numbers, thus not all real numbers.

Conclusions:

  • The ANS genuinely represents numbers, refuting claims of non-numerical representations.
  • The ANS represents a specific subset of numbers (natural and rational), refining our understanding.
  • This refined understanding of the ANS has implications for future research in numerical cognition.