A Treatise on Time and Space
Originally published in 1976. This comprehensive study discusses in detail the philosophical, mathematical, physical, logical and theological aspects of our understanding of time and space. The text examines first the many different definitions of time that have been offered, beginning with some of the puzzles arising from our awareness of the passage of time and shows how time can be understood as the concomitant of consciousness. In considering time as the dimension of change, the author obtains a transcendental derivation of the concept of space, and shows why there has to be only one dimension of time and three of space, and why Kant was not altogether misguided in believing the space of our ordinary experience to be Euclidean.
The concept of space-time is then discussed, including Lorentz transformations, and in an examination of the applications of tense logic the author discusses the traditional difficulties encountered in arguments for fatalism. In the final sections he discusses eternity and the beginning and end of the universe.
The book includes sections on the continuity of space and time, on the directedness of time, on the differences between classical mechanics and the Special and General theories of relativity, on the measurement of time, on the apparent slowing down of moving clocks, and on time and probability.
Part 1: Time by Itself 1. The nature of time 2. Time and consciousness 3. Instants and intervals 4. The ever-shrinking present 5. Concepts and experience 6. Denseness and continuity 7. The topology of time 8. The direction of time 9. Cyclic time 10. The measurement of time 11. Calendars and clocks 12. The rational theory of clocks 13. Timelessness, permanence and omnitemporality 14 Facts and fiats 15. The tenuousness of time Part 2: The Argument from Time to Space 16. Space 17. Outline of the argument from time to space 18. Time, change and communication 19. Things 20. The argument from the possibility of communication to things 21. The argument from change to things 22. The argument from things and change to different sorts of qualities 23. Qualitative identity and numerical distinctness 24. Types and tokens 25. The Identity of Indiscernibles 26. Parameter space 27. Wireless metaphysics 28. Impenetrability 29. Dimensions and continuity Part 3: The Theology of Space 30. Newtonian space 31. Equivalence relations and groups 32. Digression into geometry 33. Interpretations 34. The measurement of space 35. Τὸ ἄπειρον 36. Reflections and rotations 37. The Euclidean group 38. Shapes and sizes 39. Pythagoreanism 40. Theodicy Part 4: Space and Time Together 41. The plenum 42. Newtonian mechanics and relativity 43. The Lorentz group of transformations 44. The transcendental derivation of the Lorentz transformations 45. A priori arguments and empirical truths 46. The dilatation of time 47 The Special and General Theories of Relativity 48. Athanasius intra mundum Part 5: Return to Time 49. Time reversibility in classical physics 50. Time and probability 51. Time and modality 52. Tenses 53. Dates and tenses 54. Future contingents and fatalism 55. Eternity 56. Alpha and omega