Where mathematics comes from : how the embodied mind brings mathematics into being /
Lakoff, George,
Where mathematics comes from : how the embodied mind brings mathematics into being / How the embodied mind brings mathematics into being George Lakoff, Rafael E. Núñez. - xvii, 493 pages : illustrations ; 23 cm
Includes bibliographical references (pages 453-472) and index.
Introduction: Why Cognitive Science Matters to Mathematics -- Part I. The embodiment of basic arithmetic -- The Brain's Innate Arithmetic -- A Brief Introduction to the Cognitive Science of the Embodied Mind -- Embodied Arithmetic: The Grounding Metaphors -- Where Do the Laws of Arithmetic Come From? -- Part II. Algebra, logic, and sets -- Essence and Algebra -- Boole's Metaphor: Classes and Symbolic Logic -- Sets and Hypersets -- Part III. The embodiment of infinity -- The Basic Metaphor of Infinity -- Real Numbers and Limits -- Transfinite Numbers -- Infinitesimals -- Part IV. Banning space and motion : the discretization program that shaped modern mathematics -- Points and the Continuum -- Continuity for Numbers: The Triumph of Dedekind's Metaphors -- 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 -- The Theory of Embodied Mathematics -- The Philosophy of Embodied Mathematics -- Part VI. A case study of the cognitive structure of classical mathematics -- Analytic Geometry and Trigonometry -- What Is e? -- What Is i? -- e[superscript [pi]i] + 1 = 0 -- How the Fundamental Ideas of Classical Mathematics Fit Together. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Case Study 1. Case Study 2. Case Study 3. Case Study 4.
A study of the cognitive science of mathematical ideas.
0465037704 9780465037704 0465037712 9780465037711
00034216
Number concept.
Mathematics--Psychological aspects
Mathematics--Philosophy.
QA141.15 / .L37 2000
510
Where mathematics comes from : how the embodied mind brings mathematics into being / How the embodied mind brings mathematics into being George Lakoff, Rafael E. Núñez. - xvii, 493 pages : illustrations ; 23 cm
Includes bibliographical references (pages 453-472) and index.
Introduction: Why Cognitive Science Matters to Mathematics -- Part I. The embodiment of basic arithmetic -- The Brain's Innate Arithmetic -- A Brief Introduction to the Cognitive Science of the Embodied Mind -- Embodied Arithmetic: The Grounding Metaphors -- Where Do the Laws of Arithmetic Come From? -- Part II. Algebra, logic, and sets -- Essence and Algebra -- Boole's Metaphor: Classes and Symbolic Logic -- Sets and Hypersets -- Part III. The embodiment of infinity -- The Basic Metaphor of Infinity -- Real Numbers and Limits -- Transfinite Numbers -- Infinitesimals -- Part IV. Banning space and motion : the discretization program that shaped modern mathematics -- Points and the Continuum -- Continuity for Numbers: The Triumph of Dedekind's Metaphors -- 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 -- The Theory of Embodied Mathematics -- The Philosophy of Embodied Mathematics -- Part VI. A case study of the cognitive structure of classical mathematics -- Analytic Geometry and Trigonometry -- What Is e? -- What Is i? -- e[superscript [pi]i] + 1 = 0 -- How the Fundamental Ideas of Classical Mathematics Fit Together. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Case Study 1. Case Study 2. Case Study 3. Case Study 4.
A study of the cognitive science of mathematical ideas.
0465037704 9780465037704 0465037712 9780465037711
00034216
Number concept.
Mathematics--Psychological aspects
Mathematics--Philosophy.
QA141.15 / .L37 2000
510