This collection of newly commissioned essays by international contributors offers a representative overview of the most important developments in contemporary philosophical logic. Written by experts from a variety of different logical and philosophical perspectives, the volume presents controversies in philosophical implications and applications of formal symbolic logic.
Each section features contributors currently active in research who explain the central ideas of their special field and take a philosophical stand on recent issues in the intersection of logic and analytic philosophy. Taken together the essays survey major trends and offer original insights to advance research and philosophical discussion. A Companion to Philosophical Logic provides a comprehensive state-of-the-art handbook for students and professional researchers in philosophical logic.
A Companion to Philosophical Logic......Page 5
Contents......Page 7
List of Contributors......Page 10
Preface......Page 13
Acknowledgments......Page 15
Introduction: Logic, Philosophy, and Philosophical Logic......Page 17
Part I Historical Development of Logic......Page 25
1 Ancient Greek Philosophical Logic......Page 27
2 History of Logic: Medieval......Page 40
3 The Rise of Modern Logic......Page 51
Part II Symbolic Logic and Ordinary Language......Page 65
4 Language, Logic, and Form......Page 67
5 Puzzles about Intensionality......Page 89
6 Symbolic Logic and Natural Language......Page 102
Part III Philosophical Dimensions of Logical Paradoxes......Page 119
7 Logical Paradoxes......Page 121
8 Semantical and Logical Paradox......Page 131
9 Philosophical Implications of Logical Paradoxes......Page 147
Part IV Truth and Definite Description in Semantic Analysis......Page 159
10 Truth, the Liar, and Tarski’s Semantics......Page 161
11 Truth, the Liar, and Tarskian Truth Definition......Page 180
12 Descriptions and Logical Form......Page 193
13 Russell’s Theory of Definite Descriptions as a Paradigm for Philosophy......Page 210
Part V Concepts of Logical Consequence......Page 241
14 Necessity, Meaning, and Rationality: The Notion of Logical Consequence......Page 243
15 Varieties of Consequence......Page 257
16 Modality of Deductively Valid Inference......Page 272
Part VI Logic, Existence, and Ontology......Page 279
17 Quantifiers, Being, and Canonical Notation......Page 281
18 From Logic to Ontology: Some Problems of Predication, Negation, and Possibility......Page 297
19 Putting Language First: The ‘Liberation’ of Logic from Ontology......Page 309
Part VII Metatheory and the Scope and Limits of Logic......Page 321
20 Metatheory......Page 323
21 Metatheory of Logics and the Characterization Problem......Page 335
22 Logic in Finite Structures: Definability, Complexity, and Randomness......Page 348
Part VIII Logical Foundations of Set Theory and Mathematics......Page 365
23 Logic and Ontology: Numbers and Sets......Page 367
24 Logical Foundations of Set Theory and Mathematics......Page 381
25 Property-Theoretic Foundations of Mathematics......Page 393
Part IX Modal Logics and Semantics......Page 405
26 Modal Logic......Page 407
27 First-Order Alethic Modal Logic......Page 426
28 Proofs and Expressiveness in Alethic Modal Logic......Page 438
29 Alethic Modal Logics and Semantics......Page 458
30 Epistemic Logic......Page 494
31 Deontic, Epistemic, and Temporal Modal Logics......Page 507
Part X Intuitionistic, Free, and Many-Valued Logics......Page 527
32 Intuitionism......Page 529
33 Many-Valued, Free, and Intuitionistic Logics......Page 547
34 Many-Valued Logic......Page 561
Part XI Inductive, Fuzzy, and Quantum Probability Logics......Page 579
35 Inductive Logic......Page 581
36 Heterodox Probability Theory......Page 598
37 Why Fuzzy Logic?......Page 611
Part XII Relevance and Paraconsistent Logics......Page 623
38 Relevance Logic......Page 625
39 On Paraconsistency......Page 644
40 Logicians Setting Together Contradictories: A Perspective on Relevance, Paraconsistency, and Dialetheism......Page 667
Part XIII Logic, Machine Theory, and Cognitive Science......Page 681
41 The Logical and the Physical......Page 683
42 Modern Logic and its Role in the Study of Knowledge......Page 696
43 Actions and Normative Positions: A Modal-Logical Approach......Page 710
Part XIV Mechanization of Logical Inference and Proof Discovery......Page 723
44 The Automation of Sound Reasoning and Successful Proof Finding......Page 725
45 A Computational Logic for Applicative Common LISP......Page 740
46 Sampling Labeled Deductive Systems......Page 758
Resources for Further Study......Page 787
Index......Page 792
