This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.
Author(s): Graham Priest
Series: Cambridge Introductions to Philosophy
Edition: 2nd
Publisher: Cambridge University Press
Year: 2008
Language: English
Pages: 647
Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface to the First Edition......Page 19
On Part I......Page 23
On Part II......Page 25
Book Website......Page 28
0.1 Set-theoretic Notation......Page 29
0.2 Proof by Induction......Page 31
0.3 Equivalence Relations and Equivalence Classes......Page 32
Part I Propositional Logic......Page 35
1.1 Introduction......Page 37
1.2 The Syntax of the Object Language......Page 38
1.3 Semantic Validity......Page 39
1.4 Tableaux......Page 40
1.5 Counter-models......Page 44
1.6 Conditionals......Page 45
1.7 The Material Conditional......Page 46
1.8 Subjunctive and Counterfactual Conditionals......Page 47
1.9 More Counter-examples......Page 48
1.10 Arguments for …......Page 49
1.11 Proofs of Theorems......Page 50
1.14 Problems......Page 52
2.2 Necessity and Possibility......Page 54
2.3 Modal Semantics......Page 55
2.4 Modal Tableaux......Page 58
2.6 Modal Realism......Page 62
2.7 Modal Actualism......Page 63
2.8 Meinongianism......Page 64
2.9 Proofs of Theorems......Page 65
2.10 History......Page 67
2.12 Problems......Page 68
3.2 Semantics for Normal Modal Logics......Page 70
3.3 Tableaux for Normal Modal Logics......Page 72
3.4 Infinite Tableaux......Page 76
3.5 S5......Page 79
3.6 Which System Represents Necessity?......Page 80
3.6a The Tense Logic Kt......Page 83
3.6b Extensions of Kt......Page 85
3.7 Proofs of Theorems......Page 90
3.10 Problems......Page 94
4.2 Non-normal Worlds......Page 98
4.3 Tableaux for Non-normal Modal Logics......Page 99
4.4 The Properties of Non-normal Logics......Page 101
4.4a S0.5......Page 103
4.6 The Paradoxes of Strict Implication......Page 106
4.7 ... and their Problems......Page 107
4.8 The Explosion of Contradictions......Page 108
4.9 Lewis' Argument for Explosion......Page 110
4.10 Proofs of Theorems......Page 111
4.11 History......Page 113
4.13 Problems......Page 114
5.2 Some More Problematic Inferences......Page 116
5.3 Conditional Semantics......Page 118
5.4 Tableaux for C......Page 120
5.5 Extensions of C......Page 121
5.6 Similarity Spheres......Page 124
5.7 C1 and C2......Page 128
5.8 Further Philosophical Reflections......Page 131
5.9 Proofs of Theorems......Page 132
5.10 History......Page 134
5.12 Problems......Page 135
6.2 Intuitionism: The Rationale......Page 137
6.3 Possible-world Semantics for Intuitionism......Page 139
6.4 Tableaux for Intuitionist Logic......Page 141
6.5 The Foundations of Intuitionism......Page 146
6.6 The Intuitionist Conditional......Page 147
6.7 Proofs of Theorems......Page 148
6.8 History......Page 150
6.10 Problems......Page 151
7.2 Many-valued Logic: The General Structure......Page 154
7.3 The 3-valued Logics of Kleene and Lukasiewicz......Page 156
7.4 LP and RM3......Page 158
7.5 Many-valued Logics and Conditionals......Page 159
7.6 Truth-value Gluts: Inconsistent Laws......Page 161
7.7 Truth-value Gluts: Paradoxes of Self-reference......Page 163
7.8 Truth-value Gaps: Denotation Failure......Page 164
7.9 Truth-value Gaps: Future Contingents......Page 166
7.10 Supervaluations, Modality and Many-valued Logic......Page 167
7.11 Proofs of Theorems......Page 171
7.12 History......Page 173
7.14 Problems......Page 174
8.2 The Semantics of FDE......Page 176
8.3 Tableaux for FDE......Page 178
8.4 FDE and Many-valued Logics......Page 180
8.4a Relational Semantics and Tableaux for L3 and RM3......Page 183
8.5 The Routley Star......Page 185
8.6 Paraconsistency and the Disjunctive Syllogism......Page 188
8.7 Proofs of Theorems......Page 189
8.10 Problems......Page 195
9.2 Adding $arrow $......Page 197
9.3 Tableaux for K4......Page 198
9.4 Non-normal Worlds Again......Page 200
9.5 Tableaux for N4......Page 202
9.6 Star Again......Page 203
9.7 Impossible Worlds and Relevant Logic......Page 205
9.7a Logics of Constructible Negation......Page 209
9.8 Proofs of Theorems......Page 213
9.9 History......Page 218
9.11 Problems......Page 219
10.2 The Logic B......Page 222
10.3 Tableaux for B......Page 224
10.4 Extensions of B......Page 228
10.4a Content Inclusion......Page 231
10.5 The System R......Page 237
10.6 The Ternary Relation......Page 240
10.7 Ceteris Paribus Enthymemes......Page 242
10.8 Proofs of Theorems......Page 245
10.9 History......Page 250
10.10 Further Reading......Page 251
10.11 Problems......Page 252
11.2 Sorites Paradoxes......Page 255
11.3 ... and Responses to Them......Page 256
11.4 The Continuum-valued Logic L......Page 258
11.5 Axioms for LN......Page 261
11.6 Conditionals in L......Page 264
11.7 Fuzzy Relevant Logic......Page 265
11.7a Appendix: t-norm Logics......Page 268
11.8 History......Page 271
11.9 Further Reading......Page 272
11.10 Problems......Page 273
11a.2 General Structure......Page 275
11a.3 Illustration: Modal Lukasiewicz Logic......Page 277
11a.4 Modal FDE......Page 278
11a.5 Tableaux......Page 281
11a.6 Variations......Page 284
11a.7 Future Contingents Revisited......Page 285
11a.8 A Glimpse Beyond......Page 288
11a.9 Proofs of Theorems......Page 289
Postcript: An Historical Perspective on Conditionals......Page 293
Part II Quantification and Identity......Page 295
12.2 Syntax......Page 297
12.3 Semantics......Page 298
12.4 Tableaux......Page 300
12.5 Identity......Page 306
12.6 Some Philosophical Issues......Page 309
12.7 Some Final Technical Comments......Page 311
12.8 Proofs of Theorems 1......Page 312
12.9 Proofs of Theorems 2......Page 317
12.10 Proofs of Theorems 3......Page 319
12.12 Further Reading......Page 321
12.13 Problems......Page 322
13.2 Syntax and Semantics......Page 324
13.3 Tableaux......Page 325
13.4 Free Logics: Positive, Negative and Neutral......Page 327
13.5 Quantification and Existence......Page 329
13.6 Identity in Free Logic......Page 331
13.7 Proofs of Theorems......Page 334
13.8 History......Page 338
13.10 Problems......Page 339
14.2 Constant Domain K......Page 342
14.3 Tableaux for CK......Page 343
14.4 Other Normal Modal Logics......Page 348
14.5 Modality De Re and De Dicto......Page 349
14.6 Tense Logic......Page 352
14.7 Proofs of Theorems......Page 354
14.8 History......Page 359
14.9 Further Reading......Page 360
14.10 Problems......Page 361
15.2 Prolegomenon......Page 363
15.3 Variable Domain K and its Normal Extensions......Page 364
15.4 Tableaux for VK and its Normal Extensions......Page 365
15.5 Variable Domain Tense Logic......Page 369
15.6 Extensions......Page 370
15.7 Existence Across Worlds......Page 373
15.8 Existence and Wide-Scope Quantifiers......Page 375
15.9 Proofs of Theorems......Page 376
15.11 Further Reading......Page 380
15.12 Problems......Page 381
16.1 Introduction......Page 383
16.2 Necessary Identity......Page 384
16.3 The Negativity Constraint......Page 386
16.4 Rigid and Non-rigid Designators......Page 388
16.5 Names and Descriptions......Page 391
16.6 Proofs of Theorems 1......Page 392
16.7 Proofs of Theorems 2......Page 396
16.9 Further Reading......Page 398
16.10 Problems......Page 399
17.2 Contingent Identity......Page 401
17.3 SI Again, and the Nature of Avatars......Page 407
17.4 Proofs of Theorems......Page 410
17.7 Problems......Page 416
18.2 Non-normal Modal Logics and Matrices......Page 418
18.3 Constant Domain Quantified L......Page 419
18.4 Tableaux for Constant Domain L......Page 420
18.5 Ringing the Changes......Page 421
18.6 Identity......Page 425
18.7 Proofs of Theorems......Page 427
18.10 Problems......Page 431
19.2 Constant and Variable Domain C......Page 433
19.3 Extensions......Page 437
19.4 Identity......Page 442
19.5 Some Philosophical Issues......Page 447
19.6 Proofs of Theorems......Page 449
19.9 Problems......Page 453
20.2 Existence and Construction......Page 455
20.3 Quantified Intuitionist Logic......Page 456
20.4 Tableaux for Intuitionist Logic 1......Page 458
20.5 Tableaux for Intuitionist Logic 2......Page 461
20.6 Mental Constructions......Page 465
20.7 Necessary Identity......Page 466
20.8 Intuitionist Identity......Page 468
20.9 Proofs of Theorems 1......Page 471
20.10 Proofs of Theorems 2......Page 482
20.13 Problems......Page 487
21.2 Quantified Many-valued Logics......Page 490
21.3 $forall$ and $exists$......Page 491
21.4 Some 3-valued Logics......Page 493
21.5 Their Free Versions......Page 495
21.6 Existence and Quantification......Page 496
21.7 Neutral Free Logics......Page 499
21.8 Identity......Page 501
21.9 Non-classical Identity......Page 502
21.10 Supervaluations and Subvaluations......Page 503
21.11 Proofs of Theorems......Page 505
21.12 History......Page 507
21.14 Problems......Page 508
22.2 Relational and Many-valued Semantics......Page 510
22.3 Tableaux......Page 513
22.4 Free Logics with Relational Semantics......Page 515
22.5 Semantics with the Routley......Page 517
22.6 Identity......Page 520
22.7 Proofs of Theorems 1......Page 523
22.8 Proofs of Theorems 2......Page 527
22.9 Proofs of Theorems 3......Page 533
22.12 Problems......Page 536
23.1 Introduction......Page 538
23.3 N4......Page 539
23.4 N......Page 542
23.5 K4 and K......Page 544
23.6 Relevant Identity......Page 546
23.7 Relevant Predication......Page 549
23.8 Logics with Constructible Negation......Page 551
23.9 Identity for Logics with Constructible Negation......Page 555
23.10 Proofs of Theorems 1......Page 557
23.11 Proofs of Theorems 2......Page 561
23.12 Proofs of Theorems 3......Page 564
23.14 Further Reading......Page 566
23.15 Problems......Page 567
24.2 Quantified B......Page 569
24.3 Extensions of B......Page 571
24.4 Restricted Quantification......Page 575
24.5 Semantics vs Proof Theory......Page 577
24.6 Identity......Page 582
24.7 Properties of Identity......Page 587
24.8 Proofs of Theorems 1......Page 589
24.9 Proofs of Theorems 2......Page 593
24.11 Further Reading......Page 595
24.12 Problems......Page 596
25.1 Introduction......Page 598
25.3 Validity in LN......Page 599
25.4 Deductions......Page 604
25.5 The Sorites Again......Page 606
25.6 Fuzzy Identity......Page 607
25.7 Vague Objects......Page 610
25.8 Appendix: Quantification and Identity in t-norm Logics......Page 612
25.9 History......Page 615
25.11 Problems......Page 616
Postcript: A Methodological Coda......Page 618
References......Page 621
Index of Names......Page 637
Index of Subjects......Page 641
