فضای ریاضیات ۲۰۱۲
The Space of Mathematics 2012

1. Acknowledgments

2. Introductory afterthoughts

1. Structural Dimensions

4. The Protean Character of Mathematics

5. Categories of Space and of Quantity

6. Structural Analogies Between Mathematical and Empirical Theories

7. Reduction and Explanation: Science vs. Mathematics

8. Reality, Truth, and Confirmation in Mathematics – Reflections on the Quasi-empiricist Programme

9. Tacit Knowledge in Mathematical Theory

10. Structure-similarity as a Cornerstone of the Philosophy of Mathematics

2. Dimensions of Applicability

12. Applying Mathematics and the Indispensibility Argument

13. Mathematical Structures and Physical Necessity

14. The Role of Mathematics in Physical Science

15. The Status of Set-theoretic Axioms in Empirical Theories

16. Suppes Predicates for Classical Physics

17. Mathematics in Philosophy

3. Historical Dimensions

19. Are There Revolutions in Mathematics?

20. Observations, Problems, and Conjectures in Number Theory – The History of the Prime Number Theorem

21. Historical Aspects of the Foundations of Error Theory

22. A Structuralist View of Lagrange’s Algebraic Analysis and the German Combinatorial School

23. Constructivism and Objects of Mathematical Theory

24. Turing’s “Oracle”: From Absolute to Relative Computability – And Back

25. Computers and Mathematics: The Search for a Discipline of Computer Science

4. Global Dimensions of Knowledge: Information, Implementation, and Intertheoretic Relations

27. Theories and the Flow of Information

28. Structuralism and Scientific Discovery

29. Towards a Typology of Intertheoretical Relations

30. Index of Names