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Mathematics as verbal behavior.

M Jackson Marr1

  • 1GEORGIA TECH, School of Psychology, Georgia Tech, Atlanta, GA 30332-0170, 404-894-2635, United States.

Behavioural Processes
|January 18, 2015
PubMed
Summary
This summary is machine-generated.

Mathematics is understood as acquired verbal behavior, not a transcendental discovery. This perspective explains its effectiveness in science by examining its structural and functional features, including abstraction and intuition.

Keywords:
AbstractionEmpiricismIntuitionMathematicsPlatonismShapingVerbal behavior

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Area of Science:

  • * Philosophy of Mathematics
  • * Cognitive Science
  • * Behavioral Psychology

Background:

  • * Philosophers debate the nature of mathematics, questioning if it's discovered or invented.
  • * The effectiveness of pure mathematics in science and engineering remains a long-standing question.
  • * B.F. Skinner's work on verbal behavior provides a framework for analyzing complex human activities.

Purpose of the Study:

  • * To propose that mathematics can be understood as a form of acquired verbal behavior.
  • * To address the philosophical questions regarding the discovery versus invention of mathematical truths.
  • * To explain the efficacy of mathematics in scientific and engineering applications through a behavioral lens.

Main Methods:

  • * Analysis of the history and practice of mathematics.
  • * Application of Skinner's principles of verbal behavior.
  • * Examination of concepts such as verbal operants, rule-governed behavior, and relational frames.
  • * Discussion of abstraction and the development of mathematical intuition.

Main Results:

  • * Mathematical concepts and operations are framed as specific instances of verbal behavior.
  • * The structure and function of mathematical practice align with principles of learned behavior.
  • * The effectiveness of mathematics in describing nature stems from its basis in acquired verbal repertoires.

Conclusions:

  • * Mathematics is not a transcendental realm but a product of human verbal behavior.
  • * Understanding mathematics through a behavioral framework demystifies its "special nature."
  • * The inherent connection between language and nature explains mathematics' applicability to the natural world.