Philosophy of Logic

The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.

- Written by leading logicians and philosophers
- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic
- Clear, in-depth expositions of technical detail
- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics
- Presents current work in symbolic logic within a unified framework
- Accessible to students, engaging for experts and professionals
- Insightful philosophical discussions of all aspects of logic
- Useful bibliographies in every chapter

General Preface (Dov Gabbay, Paul Thagard and John Woods)

Preface

List of Contributors

Introduction: Philosophy of Logic Today (Dale Jacquette)

What is Logic? (Jaakko Hintikka and Gabriel Sandu)

The Scope and Limits of Logic (Wilfrid Hodges)

Logic in Philosophy (Johan van Benthem)

Informal Logic and the Concept of Argument (David Hitchcock)

On the Relation of Informal to Symbolic Logic (Dale Jacquette)

Vagueness and the Logic of Ordinary Language (Roy A. Sorensen)

Logic and Semantic Analysis (Ernest Lepore and Matthew Stone)

Justificatory Irrelevance of Formal Semantics (Charles F. Kielkopf)

A Brief History of Truth (Stewart Candlish and Nic Damnjanovic)

Truth and Paradox: A Philosophical Sketch (J.C. Beall)

Hilbert's Program Then and Now (Richard Zach)

Logicism and its Contemporary Legacy (Herbert Hochberg)

Classical Logic's Coming of Age (John W. Dawson, Jr.)

Infinity (Peter Fletcher)

Löwenheim-Skolem Theorems (Heinz-Dieter Ebbinghaus)

The Mathematics of Skolem's Paradox (Timothy Bays)

Objectual and Substitutional Interpretations of the Quantifiers (Michael Hand)

Many-Valued Logics (Siegfried Gottwald)

Relevance Logics (Katalin Bimbó)

Paraconsistent Lgoics and Paraconsistency (Newton C.A. da Costa, Otávio Bueno and Décio Krause)

Extensional vs Intensional Logic (Jaroslav Peregrin)

Logically Possible Worlds and Counterpart Semantics for Modal Logic (Marcus Kracht and Oliver Kutz)

Modal Realism and its Roots in Mathematical Realism (Charles S. Chihara)

Free Logics (John Nolt)

Fictions and their Logic (John Woods)

Counterfactuals, Causation, and Preemption (John Collins)

Logic, Mathematics, and the Natural Sciences (Neil Tennant)

Default Reasoning (Nicholas Rescher)

Index