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Where mathematics comes from : how the embodied mind brings mathematics into being / George Lakoff, Rafael E. Núñez.

By: Contributor(s): Material type: TextTextPublisher: New York, NY : Basic Books, [2000]Copyright date: ©2000Description: xvii, 493 pages : illustrations ; 23 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 0465037704
  • 9780465037704
  • 0465037712
  • 9780465037711
Other title:
  • How the embodied mind brings mathematics into being
Subject(s): Additional physical formats: Online version:: Where mathematics comes from.; No titleDDC classification:
  • 510 23
LOC classification:
  • QA141.15 .L37 2000
Contents:
Introduction: Why Cognitive Science Matters to Mathematics -- Part I. The embodiment of basic arithmetic -- 1. The Brain's Innate Arithmetic -- 2. A Brief Introduction to the Cognitive Science of the Embodied Mind -- 3. Embodied Arithmetic: The Grounding Metaphors -- 4. Where Do the Laws of Arithmetic Come From? -- Part II. Algebra, logic, and sets -- 5. Essence and Algebra -- 6. Boole's Metaphor: Classes and Symbolic Logic -- 7. Sets and Hypersets -- Part III. The embodiment of infinity -- 8. The Basic Metaphor of Infinity -- 9. Real Numbers and Limits -- 10. Transfinite Numbers -- 11. Infinitesimals -- Part IV. Banning space and motion : the discretization program that shaped modern mathematics -- 12. Points and the Continuum -- 13. Continuity for Numbers: The Triumph of Dedekind's Metaphors -- 14. Calculus Without Space or Motion: Weierstrass's Metaphorical Masterpiece -- Le trou normand: a classic paradox of infinity -- Part V. Implications for the philosophy of mathematics -- 15. The Theory of Embodied Mathematics -- 16. The Philosophy of Embodied Mathematics -- Part VI. A case study of the cognitive structure of classical mathematics -- Case Study 1. Analytic Geometry and Trigonometry -- Case Study 2. What Is e? -- Case Study 3. What Is i? -- Case Study 4. e[superscript [pi]i] + 1 = 0 -- How the Fundamental Ideas of Classical Mathematics Fit Together.
Summary: A study of the cognitive science of mathematical ideas.
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Includes bibliographical references (pages 453-472) and index.

Introduction: Why Cognitive Science Matters to Mathematics -- Part I. The embodiment of basic arithmetic -- 1. The Brain's Innate Arithmetic -- 2. A Brief Introduction to the Cognitive Science of the Embodied Mind -- 3. Embodied Arithmetic: The Grounding Metaphors -- 4. Where Do the Laws of Arithmetic Come From? -- Part II. Algebra, logic, and sets -- 5. Essence and Algebra -- 6. Boole's Metaphor: Classes and Symbolic Logic -- 7. Sets and Hypersets -- Part III. The embodiment of infinity -- 8. The Basic Metaphor of Infinity -- 9. Real Numbers and Limits -- 10. Transfinite Numbers -- 11. Infinitesimals -- Part IV. Banning space and motion : the discretization program that shaped modern mathematics -- 12. Points and the Continuum -- 13. Continuity for Numbers: The Triumph of Dedekind's Metaphors -- 14. Calculus Without Space or Motion: Weierstrass's Metaphorical Masterpiece -- Le trou normand: a classic paradox of infinity -- Part V. Implications for the philosophy of mathematics -- 15. The Theory of Embodied Mathematics -- 16. The Philosophy of Embodied Mathematics -- Part VI. A case study of the cognitive structure of classical mathematics -- Case Study 1. Analytic Geometry and Trigonometry -- Case Study 2. What Is e? -- Case Study 3. What Is i? -- Case Study 4. e[superscript [pi]i] + 1 = 0 -- How the Fundamental Ideas of Classical Mathematics Fit Together.

A study of the cognitive science of mathematical ideas.

Machine converted from AACR2 source record.

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