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Mathematical knowledge and the interplay of practices /
Annotation
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2015.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover
- Contents
- List of Illustrations
- Foreword
- 1 On Knowledge and Practices: A Manifesto
- 2 The Web of Practices
- 2.1. Historical Work on Practices
- 2.2. Philosophers Working on Practices
- 2.3. What Is Mathematical Practice, Then?
- 2.4. The Multiplicity of Practices
- 2.5. The Interplay of Practices and Its Basis
- 3 Agents and Frameworks
- 3.1. Frameworks and Related Matters
- 3.2. Interlude on Examplars
- 3.3. On Agents
- 3.4. Counting Practices and Cognitive Abilities
- 3.5. Further Remarks on Mathematics and Cognition
- 3.6. Agents and "Metamathematical" Views
- 3.7. On Systematic Links
- 4 Complementarity in Mathematics
- 4.1. Formula and Meaning
- 4.2. Formal Systems and Intended Models
- 4.3. Meaning in Mathematics: A Tentative Approach
- 4.4. The Case of Complex Numbers
- 5 Ancient Greek Mathematics: A Role for Diagrams
- 5.1. From the Technical to the Mathematical
- 5.2. The Elements: Getting Started
- 5.3. On the Euclidean Postulates: Ruling Diagrams (and Their Reading)
- 5.4. Diagram-Based Mathematics and Proofs
- 5.5. Agents, Idealization, and Abstractness
- 5.6. A Look at the Future-Our Past
- 6 Advanced Math: The Hypothetical Conception
- 6.1. The Hypothetical Conception: An Introduction
- 6.2. On Certainty and Objectivity
- 6.3. Elementary vs. Advanced: Geometry and the Continuum
- 6.4. Talking about Objects
- 6.5. Working with Hypotheses: AC and the Riemann Conjecture
- 7 Arithmetic Certainty
- 7.1. Basic Arithmetic
- 7.2. Counting Practices, Again
- 7.3. The Certainty of Basic Arithmetic
- 7.4. Further Clarifications
- 7.5. Model Theory of Arithmetic
- 7.6. Logical Issues: Classical or Intuitionistic Math?
- 8 Mathematics Developed: The Case of the Reals
- 8.1. Inventing the Reals
- 8.2. "Tenths" to the Infinite: Lambert and Newton
- 8.3. The Number Continuum.
- 8.4. The Reinvention of the Reals
- 8.5. Simple Infinity and Arbitrary Infinity
- 8.6. Developing Mathematics
- 8.7. Mathematical Hypotheses and Scientific Practices
- 9 Objectivity in Mathematical Knowledge
- 9.1. Objectivity and Mathematical Hypotheses: A Simple Case
- 9.2. Cantor's "Purely Arithmetical" Proofs
- 9.3. Objectivity and Hypotheses, II: The Case of p(N)
- 9.4. Arbitrary Sets and Choice
- 9.5. What about Cantor's Ordinal Numbers?
- 9.6. Objectivity and the Continuum Problem
- 10 The Problem of Conceptual Understanding
- 10.1. The Universe of Sets
- 10.2. A "Web-of-Practices" Look at the Cumulative Picture
- 10.3. Conceptual Understanding
- 10.4. Justifying Set Theory: Arguments Based on the Real-Number Continuum
- 10.5. By Way of Conclusion
- References
- Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- U
- V
- W
- Z.