Applying Mathematics and the Indispensability Argument

Kapitel in diesem Buch

1. Frontmatter i
2. Table of Contents v
3. Acknowledgments vii
4. Introductory afterthoughts ix
5. Structural Dimensions
6. The Protean Character of Mathematics 3
7. Categories of Space and of Quantity 14
8. Structural Analogies Between Mathematical and Empirical Theories 31
9. Reduction and Explanation: Science vs. Mathematics 47
10. Reality, Truth, and Confirmation in Mathematics – Reflections on the Quasi-Empiricist Programme 60
11. Tacit Knowledge in Mathematical Theory 79
12. Structure-Similarity as a Cornerstone of the Philosophy of Mathematics 91
13. Dimensions of Applicability
14. Applying Mathematics and the Indispensability Argument 115
15. Mathematical Structures and Physical Necessity 132
16. The Role of Mathematics in Physical Science 141
17. The Status of Set-theoretic Axioms in Empirical Theories 156
18. Suppes Predicates for Classical Physics 168
19. Mathematics in Philosophy 192
20. Historical Dimensions
21. Are There Revolutions in Mathematics? 205
22. Observations, Problems and Conjectures in Number Theory – The History of the Prime Number Theorem 230
23. Historical Aspects of the Foundations of Error Theory 253
24. A Structuralist View of Lagrange’s Algebraic Analysis and the German Combinatorial School 280
25. Constructivism and Objects of Mathematical Theory 296
26. Turing’s “Oracle”: From Absolute to Relative Computability – and Back 314
27. Computers and Mathematics: The Search for a Discipline of Computer Science 349
28. Global Dimensions of Knowledge: Information, Implementation, and Intertheoretic Relations
29. Theories and the Flow of Information 367
30. Structuralism and Scientific Discovery 379
31. Towards a Typology of Intertheoretical Relations 403
32. Index of Names 413
33. 423-424 423