## Where Mathematics Come From: How The Embodied Mind Brings Mathematics Into BeingThis book is about mathematical ideas, about what mathematics means-and why. Abstract ideas, for the most part, arise via conceptual metaphor-metaphorical ideas projecting from the way we function in the everyday physical world. Where Mathematics Comes From argues that conceptual metaphor plays a central role in mathematical ideas within the cognitive unconscious-from arithmetic and algebra to sets and logic to infinity in all of its forms. |

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#### LibraryThing Review

User Review - jcopenha - LibraryThingI've never ready anything about cognitive science and as this book is a look at Mathematics from the Cognitive Scientist point of view it was difficult to start. By the end of the book I was pretty ... Read full review

#### LibraryThing Review

User Review - fpagan - LibraryThingCan be summarized by the dust-jacket slogans "Mathematics is not built into the universe" and "The portrait of mathematics has a human face." Meaty and quite absorbing, even though it goes against my sometime Platonist sympathies. Read full review

### Contents

The Brains Innate Arithmetic | 15 |

A Brief Introduction to the Cognitive Science of the Embodied Mind | 27 |

Embodied Arithmetic The Grounding Metaphors | 50 |

Where Do the Laws of Arithmetic Come From? | 77 |

Essence and Algebra | 107 |

Booles Metaphor Classes and Symbolic Logic | 121 |

Sets and Hypersets | 140 |

The Basic Metaphor of Infinity | 155 |

Continuity for Numbers The Triumph of Dedekinds Metaphors | 292 |

Calculus Without Space or Motion Weierstrasss Metaphorical Masterpiece | 306 |

A Classic Paradox of Infinity | 325 |

The Theory of Embodied Mathematics | 337 |

The Philosophy of Embodied Mathematics | 364 |

Case Study 1 Analytic Geometry and Trigonometry | 383 |

Case Study 2 What Is e? | 399 |

Case Study 3 What Is i? | 420 |

Real Numbers and Limits | 181 |

Transfinite Numbers | 208 |

Infinitesimals | 223 |

Points and the Continuum | 259 |

Case Study 4 e𝝅𝙞 + 1 0 How the Fundamental Ideas of Classical Mathematics Fit Together | 433 |

453 | |

473 | |

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### Common terms and phrases

abstract actual infinity addition algebra Basic Metaphor bers Boole's branches of mathematics bumpy curve calculation Cartesian plane Chapter characterize classes closure cognitive mechanisms cognitive perspective cognitive science Commutative law complex numbers complex plane conceptual blend conceptual metaphors conceptual system Container schemas corresponding Dedekind defined diameter disc discrete elements Entailment entities equation essence everyday example exponential function finite formal geometry given granular numbers grounding metaphors hyperreals image schemas infinite decimal infinite sequence infinite set infinitesimals innate arithmetic integers inversive geometry least upper bound length limit logic mathe mathematical idea analysis mathematicians matics means Metaphor of Infinity metaphorical mapping motion multiplication natural numbers negative numbers neural nine axioms number line Number-Line blend object collection one-to-one operations ordered pairs physical segments point-locations properties rational numbers real numbers rotation set theory structure subitizing subject matter subtraction symbols tion transcendent mathematics transfinite understanding unique unit circle Weierstrass zero