This chapter investigates the second developmental stage in number concept acquisition–calculation–and its role in the ontogenetic and historical reification of numbers. While early numerical competence is grounded in the mastery of number words and counting, calculation introduces new cognitive and linguistic structures that promote treating numerals as referring to abstract objects. The chapter argues that the widespread tendency to speak of numbers as objects arises not from their ontological status but from the projection of object-based linguistic frameworks onto numerical discourse. This reification is traced through developmental, historical, and philosophical perspectives, offering a cognitive account of how numbers come to be treated as independent entities within mathematics and everyday language.

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The Reification of Number Concepts

  • César Frederico dos Santos

摘要

This chapter investigates the second developmental stage in number concept acquisition–calculation–and its role in the ontogenetic and historical reification of numbers. While early numerical competence is grounded in the mastery of number words and counting, calculation introduces new cognitive and linguistic structures that promote treating numerals as referring to abstract objects. The chapter argues that the widespread tendency to speak of numbers as objects arises not from their ontological status but from the projection of object-based linguistic frameworks onto numerical discourse. This reification is traced through developmental, historical, and philosophical perspectives, offering a cognitive account of how numbers come to be treated as independent entities within mathematics and everyday language.