A Companion to Philosophical Logic

Dale Jacquette is Professor of Philosophy at the Pennsylvania State University. He is the author of Philosophy of Mind (1994), Meinongian Logic: The Semantics of Existence and Nonexistence (1996), Wittgenstein's Thought in Transition (1998), Symbolic Logic (2001), David Hume's Critique of Infinity (2001), and On Boole: Logic as Algebra (2001), as well as numerous articles on logic, metaphysics, philosophy of mind, and Wittgenstein. He is editor of Philosophy of Mathematics: An Anthology (Blackwell 2001) and Philosophy of Logic: An Anthology (Blackwell 2001).

List of Contributors viii

Preface xi

Acknowledgments xiii

Introduction: Logic, Philosophy, and Philosophical Logic – Dale Jacquette 1

Part I Historical Development of Logic 9

11 Ancient Greek Philosophical Logic – Robin Smith 11

12 History of Logic: Medieval – E. P. Bos and B. G. Sundholm 24

13 The Rise of Modern Logic – Rolf George and James Van Evra 35

Part II Symbolic Logic and Ordinary Language 49

14 Language, Logic, and Form – Kent Bach 51

15 Puzzles about Intensionality – Nathan Salmon 73

16 Symbolic Logic and Natural Language – Emma Borg and Ernest Lepore 86

Part III Philosophical Dimensions of Logical Paradoxes 103

17 Logical Paradoxes – James Cargile 105

18 Semantical and Logical Paradox – Keith Simmons 115

19 Philosophical Implications of Logical Paradoxes – Roy A. Sorensen 131

Part IV Truth and Definite Description in Semantic Analysis 143

10 Truth, the Liar, and Tarski’s Semantics – Gila Sher 145

11 Truth, the Liar, and Tarskian Truth Definition – Greg Ray 164

12 Descriptions and Logical Form – Gary Ostertag 177

13 Russell’s Theory of Definite Descriptions as a Paradigm for Philosophy – Gregory Landini 194

Part V Concepts of Logical Consequence 225

14 Necessity, Meaning, and Rationality: The Notion of Logical Consequence – Stewart Shapiro 227

15 Varieties of Consequence – B. G. Sundholm 241

16 Modality of Deductively Valid Inference – Dale Jacquette 256

Part VI Logic, Existence, and Ontology 263

17 Quantifiers, Being, and Canonical Notation – Paul Gochet 265

18 From Logic to Ontology: Some Problems of Predication, Negation, and Possibility – Herbert Hochberg 281

19 Putting Language First: The ‘Liberation’ of Logic from Ontology – Ermanno Bencivenga 293

Part VII Metatheory and the Scope and Limits of Logic 305

20 Metatheory – Alasdair Urquhart 307

21 Metatheory of Logics and the Characterization Problem – Jan Wole´nski 319

22 Logic in Finite Structures: Definability, Complexity, and Randomness – Scott Weinstein 332

Part VIII Logical Foundations of Set Theory and Mathematics 349

23 Logic and Ontology: Numbers and Sets – José A. Benardete 351

24 Logical Foundations of Set Theory and Mathematics – Mary Tiles 365

25 Property-Theoretic Foundations of Mathematics – Michael Jubien 377

Part IX Modal Logics and Semantics 389

26 Modal Logic – Johan van Benthem 391

27 First-Order Alethic Modal Logic – Melvin Fitting 410

28 Proofs and Expressiveness in Alethic Modal Logic – Maarten de Rijke and Heinrich Wansing 422

29 Alethic Modal Logics and Semantics – Gerhard Schurz 442

30 Epistemic Logic – Nicholas Rescher 478

31 Deontic, Epistemic, and Temporal Modal Logics – Risto Hilpinen 491

Part X Intuitionistic, Free, and Many-Valued Logics 511

32 Intuitionism – Dirk van Dalen and Mark van Atten 513

33 Many-Valued, Free, and Intuitionistic Logics – Richard Grandy 531

34 Many-Valued Logic – Grzegorz Malinowski 545

Part XI Inductive, Fuzzy, and Quantum Probability Logics 563

35 Inductive Logic – Stephen Glaister 565

36 Heterodox Probability Theory – Peter Forrest 582

37 Why Fuzzy Logic? – Petr Hájek 595

Part XII Relevance and Paraconsistent Logics 607

38 Relevance Logic – Edwin D. Mares 609

39 On Paraconsistency – Bryson Brown 628

40 Logicians Setting Together Contradictories: A Perspective on Relevance, Paraconsistency, and Dialetheism – Graham Priest 651

Part XIII Logic, Machine Theory, and Cognitive Science 665

41 The Logical and the Physical – Andrew W. Hodges 667

42 Modern Logic and its Role in the Study of Knowledge – Peter A. Flach 680

43 Actions and Normative Positions: A Modal-Logical Approach – Robert Demolombe and Andrew J. I. Jones 694

Part XIV Mechanization of Logical Inference and Proof Discovery 707

44 The Automation of Sound Reasoning and Successful Proof Finding – Larry Wos and Branden Fitelson 709

45 A Computational Logic for Applicative Common LISP – Matt Kaufmann and J. Strother Moore 724

46 Sampling Labeled Deductive Systems – D. M. Gabbay 742

Resources for Further Study 771

Index 776