Past, Present, and Future

Preface ......Page 4
Table of contents ......Page 6
1. McTaggart’s A series (past, present, future) and B series (earlier, later) ......Page 10
2. McTaggart’s argument against the reality of the A series ......Page 13
3. Broad’s criticism of McTaggart; temporal predicates and tenses ......Page 16
4. Findlay’s tense-logical laws ......Page 17
5. Smart’s argument that events do not change ......Page 19
6. Reichenbach on the time of speech and the time of reference; the nature of presentness ......Page 21
7. Time and truth in ancient and medieval logic ......Page 24
8. Symbolism and metaphysics ......Page 26
1. The tense-logical basis of Diodorean modal logic ......Page 29
2. A matrix for Diodorean modality ......Page 31
3. Modal systems between S4 and S5 ......Page 32
4. Kripke’s ‘branching time’ matrix for S4, and Lemmon’s for S4.2 ......Page 36
5. Dummett’s formula in D but not S4.3, and its assumption of discreteness ......Page 38
1. Analysis of the Master-argument of Diodorus ......Page 41
2. Some early postulates for past and future ......Page 43
3. Corresponding postulates in the logic of the B series ......Page 47
4. U-calculi and modal logics ......Page 51
5. Hamblin’s 15-tenses theorem and its basis ......Page 54
6. Cocchiarella’s tense-logic, and differences between linear and branching time ......Page 59
7. Further simplifications by Scott and Lemmon ......Page 64
8. Correction of Hume on past and future ......Page 66
1. Theses which assume that time is either discrete or circular ......Page 68
2. Postulates for circular time ......Page 72
3. Postulates for the next and the last moment, in discrete time ......Page 75
4. The logic of ‘and then’ ......Page 79
5. Mere denseness and Dedekindian continuity ......Page 80
6. Postulates for beginning and ending time ......Page 81
7. Tense-logic as giving the cash-value of assertions about time ......Page 83
1. The de-trivializing of modality: ‘the world’ ......Page 86
2. Instantaneous world-states ......Page 88
4. Non-repetition, repetition, and world-state-hood ......Page 91
5. The definition of tenses in terms of Diodorean modalities ......Page 94
6. Development of the Z7-calculus within the theory of world-states ......Page 97
7. ‘States’ consisting of combinations of Hamblin tenses ......Page 101
1. The syntax of intervals ......Page 104
2. Postulates for metric tense-logic ......Page 106
3. Interaction of the A series and the B series ......Page 110
4. The logic of dates ......Page 112
5. Metric circular time ......Page 114
6. Enlargement of tense-logic to make metric concepts definable ......Page 115
7. Geach’s definitions of Kamp’s constants ......Page 120
1. Arguments for the incompatibility of foreknowledge (and fore-truth) and indeterminism ......Page 122
2. Formalization of these arguments ......Page 126
3. The classical answers to these arguments ......Page 130
4. Formalization of the Ockhamist answer ......Page 131
5. Ultimately converging time ......Page 136
6. Formalization of the Peircean answer, and comparison with the Ockhamist ......Page 137
7. The Peircean senses of ‘will’ ......Page 141
8. Propositions that are neither true nor false ......Page 144
1. Modalized and tensed predicate logic: the standard systems ......Page 146
2. Ancient, medieval, and modern objections to coming to be, being brought into being, and being prevented from being ......Page 147
3. Ampliation ......Page 152
4. Objections to standard modal logic suggested by Myhill, Ramsey, and Chrysippus ......Page 154
5. Moore on what might not have existed, and on what once did not exist ......Page 158
6. Arguments against some common principles of modal and tense-logic ......Page 160
7. The modal system Q, its modifications, and its adaptation to tense-logic ......Page 163
8. Tensed predicate logic with now-empty names, in Cocchiarella, Rescher, and Hamblin ......Page 167
9. Tensed ontology ......Page 171
10. Internal and external complexity in systems with free individual variables ......Page 176
11. The difficulties of doing without non-existents ......Page 178
12. The admission of past existents but not future ones ......Page 180
13. Summary of possible positions ......Page 181
3. Systems between T and S5 ......Page 184
5. Standard enlargements of the minimal system ......Page 185
7. Systems for the next moment (T) and the last moment (Y) ......Page 187
9. Correspondences between U-calculi, modal logics, and tense-logics ......Page 188
1. Von Wright’s ‘and next’ and ‘and then’ calculi; ‘and next’ and metric tense-logic ......Page 191
3. On the range of world-variables, and the interpretation of U-calculi in world-calculi ......Page 196
4. The uniqueness of the time-series ......Page 207
5. The tense-logical discrimination of special from general relativity ......Page 212
6. Alternative axioms for non-branching ......Page 214
7. Tenses defined in terms of Diodorean modalities ......Page 216
8. Independence proofs for Kt ......Page 219
9. Anticipations of later developments in Los’s calculus of instants ......Page 221
Index ......Page 224