The Philosophy of Mathematical PracticeOUP Oxford, 19 jun 2008 - 447 pagina's Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, and developments at the intersection of history and philosophy of mathematics. But anyone familiar with contemporary philosophy of mathematics will be aware of the need for new approaches that pay closer attention to mathematical practice. Thisbook is the first attempt to give a coherent and unified presentation of this new wave of work in philosophy of mathematics. The new approach is innovative at least in two ways. First, it holds that there are important novel characteristics of contemporary mathematics that are just as worthy ofphilosophical attention as the distinction between constructive and non-constructive mathematics at the time of the foundational debates. Secondly, it holds that many topics which escape purely formal logical treatment - such as visualization, explanation, and understanding - can nonetheless be subjected to philosophical analysis.The Philosophy of Mathematical Practice comprises an introduction by the editor and eight chapters written by some of the leading scholars in the field. Each chapter consists of short introduction to the general topic of the chapter followed by a longer research article in the area. The eight topics selected represent a broad spectrum of contemporary philosophical reflection on different aspects of mathematical practice: diagrammatic reasoning and representation systems; visualization;mathematical explanation; purity of methods; mathematical concepts; the philosophical relevance of category theory; philosophical aspects of computer science in mathematics; the philosophical impact of recent developments in mathematical physics. |
Inhoudsopgave
Introduction | 1 |
1 Visualizing in Mathematics | 22 |
2 Cognition of Structure | 43 |
3 DiagramBased Geometric Practice | 65 |
4 The Euclidean Diagram 1995 | 80 |
Why it Matters | 134 |
6 Beyond Unification | 151 |
7 Purity as an Ideal of Proof | 179 |
Fruitfulness and Naturalness | 276 |
11 Computers in Mathematical Inquiry | 302 |
12 Understanding Proofs | 317 |
13 What Structuralism Achieves | 354 |
Visual and Structural Geometry in Arithmetic | 370 |
15 The Boundary Between Mathematics and Physics | 407 |
Strategies of Assimilation | 417 |
Index of Names | 441 |
8 Reflections on the Purity of Method in Hilberts Grundlagen der Geometrie | 198 |
9 Mathematical Concepts and Definitions | 256 |
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