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Numerosities are not ersatz numbers.

Catarina Dutilh Novaes1, César Frederico Dos Santos1,2

  • 1Department of Philosophy, Vrije Universiteit Amsterdam, De Boelelaan 1105, 1081 HV, Amsterdam, Netherlands. c.dutilhnovaes@vu.nlhttps://www.cdutilhnovaes.com.

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This summary is machine-generated.

Numerosity, the perception of quantity, is distinct from number, which measures it. This study clarifies that numerosity is the cognitive magnitude, while number is the scale used for measurement.

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Area of Science:

  • Cognitive Science
  • Philosophy of Mathematics
  • Psychology

Background:

  • Existing definitions of numerosity, such as "ersatz number," overlook a key conceptualization.
  • Numerosity is often discussed without clearly distinguishing it from the mathematical concept of number.

Purpose of the Study:

  • To propose a clearer definition of numerosity.
  • To distinguish numerosity from number by defining numerosity as magnitude and number as a measurement scale.

Main Methods:

  • Conceptual analysis of numerosity and number.
  • Philosophical argumentation regarding mathematical cognition.

Main Results:

  • Numerosity is the cognitive counterpart to mathematical cardinality (magnitude).
  • Number serves as a scale to measure numerosity/cardinality.

Conclusions:

  • The distinction between numerosity as magnitude and number as a scale is crucial for understanding quantity representation.
  • This refined conceptualization offers a more robust framework for cognitive and mathematical research.