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What Is a Mathematical Concept? by de Freitas, Elizabeth; Sinclair, Nathalie; Coles, Alf is a book available to read on EtoBox.

What is What Is a Mathematical Concept? about?

Cover 1 Half-title 3 Title page 5 Copyright information 6 Table of contents 7 List of images 9 Notes on contributors 11 Introduction 15 The Context for This Book: Philosophy and Cognition 16 Themes and Chapters 20 On Reading the Book 28 References 28 Part I 31 1 Of Polyhedra and Pyjamas: Platonism and Induction in Meaning-Finitist Mathematics 33 Introduction 33 Strong Program Meaning Finitism 35 Induction 39 Platonism 44 Conclusion 47 Acknowledgments 48 References 48 2 Mathematical Concepts? The View from Ancient History 50 Introduction 50 Infinity, Actually 52 Indeed, It’s Not That They Couldn’t 59 What We Share 62 References 64 Part II 67 3 Notes on the Syntax and Semantics Distinction, or Three Moments in the Life of the Mathematical Drawing 69 Introduction 69 Two Subgenres 69 First Moment: The Euclidean Diagram 72 Second Moment: “What Is the Hand?” 80 Third Moment: The Incidental Drawing 84 Conclusion 86 Acknowledgements 87 References 88 4 Concepts as Generative Devices 90 Proposition 1: Concepts Are Not Merely Metaphors or Representations 90 Proposition 2: Concepts Are Not Mental Constructs Abstracted from the Material World 91 Proposition 3: Concepts Are Vibrant and Indetermi

Author

de Freitas, Elizabeth; Sinclair, Nathalie; Coles, Alf

Language

EN