What is a Mathematical Concept?Elizabeth de Freitas, Nathalie Sinclair, Alf Coles Responding to widespread interest within cultural studies and social inquiry, this book addresses the question 'what is a mathematical concept?' using a variety of vanguard theories in the humanities and posthumanities. Tapping historical, philosophical, sociological and psychological perspectives, each chapter explores the question of how mathematics comes to matter. Of interest to scholars across the usual disciplinary divides, this book tracks mathematics as a cultural activity, drawing connections with empirical practice. Unlike other books in this area, it is highly interdisciplinary, devoted to exploring the ontology of mathematics as it plays out in different contexts. This book will appeal to scholars who are interested in particular mathematical habits - creative diagramming, structural mappings, material agency, interdisciplinary coverings - that shed light on both mathematics and other disciplines. Chapters are also relevant to social sciences and humanities scholars, as each offers philosophical insight into mathematics and how we might live mathematically. |
Contents
Introduction | 1 |
Platonism and Induction | 19 |
Mathematical Concepts? The View from Ancient History | 36 |
Notes on the Syntax and Semantics Distinction or Three | 55 |
Concepts as Generative Devices | 76 |
Bernhard Riemanns Conceptual Mathematics and | 93 |
Contents | 108 |
Homotopy Type Theory and the Vertical Unity of Concepts | 125 |
Mathematics Concepts in the News | 175 |
Concepts and Commodities in Mathematical Learning | 189 |
A Relational View of Mathematical Concepts | 205 |
Cultural Concepts Concretely | 223 |
Ideas as Species | 237 |
Inhabiting Mathematical Concepts | 251 |
Some Conceptual Commentary | 269 |
| 285 | |
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What is a Mathematical Concept? Elizabeth de Freitas,Nathalie Sinclair,Alf Coles Limited preview - 2017 |
Common terms and phrases
abstract adic algebraic algebraic variety approach Archimedes Archimedes Palimpsest argued Arkady Plotnitsky Bloor Cantor cepts chapter cognition cohomology complex concept of number conceptualisable character concrete construction context Corfield cube Cuisenaire rods cultural curriculum defined Deleuze differential discourses drawing ematical entities epistemology étale cohomology example existence finitist framing Freitas function Galois Gattegno geometry Greek mathematics groupoid Guattari homotopy type theory human ideas infinite infinity Lakatos Lautman logic manifold math mathematical concepts mathematical problems mathematicians mathematics education matics meaning finitism meaning finitist memeplexes memes memetics metaphor nature Netz notion number line p-adic p-adic Hodge theory particular perfectoid spaces philosophy philosophy of mathematics physical plane of immanence polyhedra polyhedron proof proposition pyjamas question relation representation Riemann Scholze Scholze’s school mathematics sense social specific structure teacher theorem theory of problems things thinking thought tion understanding University Press virtual Žižek