Provability, Computability and Reflection (eBook)

Front Cover 1
The Axiomatic Method, Volume 27 4
Copyright Page 5
CONTENTS 6
Preface 8
PART I: FOUNDATIONS OF GEOMETRY 14
Chapter 1. Die Mannigfaltigkeit der Direktiven für die Gestaltung geometrischer Axiomensysteme 14
Chapter 2. What is elementary geometry ? 29
Chapter 3. Some metamathematical problems concerning elementary hyperbolic geometry 43
Chapter 4. Dimension in elementary Euclidean geometry 66
Chapter 5. Binary relations as primitive, notions in elementary geometry 81
Chapter 6. Remarks on primitive notions for elementary Euclidean and non Euclidean plane geometry 99
Chapter 7. Direct introduction of Weierstrass homogeneous coordinates in the hyperbolic plane, on the basis of the endcalculus of Hilbert 110
Chapter 8. Axiomatischer aufbau der ebenen absoluten Geometrie 127
Chapter 9. New metric postulates for elliptic n-space 140
Chapter 10. Axioms for geodesics and their implications 159
Chapter 11. Axioms for intuitionistic plane affine geometry 173
Chapter 12. Grundlagen der Geometrie vom Standpunkt der allgemeinen Topologie aus 187
Chapter 13. Lattice-theoretic approach to projective and affine geometry 201
Chapter 14. Conventionalism in geometry 217
PART II: FOUNDATIONS OF PHYSICS 236
Chapter 15. How much rigor is possible in physics ? 238
Chapter 16. La finitude en mécanique classique, ses axiomes et leurs implications 251
Chapter 17. The foundations of rigid body mechanics and the derivation of its laws from those of particle mechanics 263
Chapter 18. The foundations of classical mechanics in the light of recent advances in continuum mechanics 279
Chapter 19. Zur Axiomatisierung der Mechanik 295
Chapter 20. Axioms for relativistic kinematics with or without parity 304
Chapter 21. Axioms for cosmology 321
Chapter 22. Axiomatic method and theory of relativity . equivalent observers and special principle of relativity 335
Chapter 23. On the foundations of quantum mechanics 346
Chapter 24. The mathematical meaning of operationalism in quantum mechanics 354
Chapter 25. Quantum theory from non-quantal Postulates 366
Chapter 26. Quantenlogik und das kommutative gesetz 378
Chapter 27. Logical structure of physical theories 389
Chapter 28. Physico-logical problems 403
PART III: GENERAL PROBLEMS AND APPLICATIONS OF THE AXIOMATIC METHOD 420
Chapter 29. Studies in the foundations of genetics 421
Chapter 29. Axiomatizing a scientific system by axioms in the form of identifications 442
Chapter 30. Definable terms and primitives in axiom systems 456
Chapter 31. An axiomatic theory of functions and fluents 467
Chapter 32. Axiomatics and the development of creative talent 487