Where Mathematics Come From: How The Embodied Mind Brings Mathematics Into BeingThis book is about mathematical ideas, about what mathematics meansand why. Abstract ideas, for the most part, arise via conceptual metaphormetaphorical 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 unconsciousfrom arithmetic and algebra to sets and logic to infinity in all of its forms. 
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LibraryThing Review
User Review  mykls  LibraryThingInteresting followup to Lakoff's Metaphors We Live By. The thesis here is that all language is metaphorical expression, which is based on conceptual metaphors determined by the brain as well as by ... Read full review
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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 NumberLine blend object collection onetoone operations ordered pairs physical segments pointlocations properties rational numbers real numbers rotation set theory structure subitizing subject matter subtraction symbols tion transcendent mathematics transfinite understanding unique unit circle Weierstrass zero