Philosophy of Logic

Dov M. Gabbay, Paul Thagard, John Woods

• Publisher: North Holland
• Year: 2006
• eBook ISBN: 9780080466637
• Topic: Mathematics
• Subtopic: Logic in Mathematics
• Index: Mathematics

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

Table of contents

• Front Cover
• Philosophy of Logic
• Copyright Page
• Table of Contents
• General Preface
• Preface
• List of Contributors
• Introduction: Philosophy of Logic Today
• What is Logic?
• The Scope and Limits of Logic
• Logic in Philosophy
• Informal Logic and The Concept of Argument
• On the Relation of Informal to Symbolic Logic
• Vagueness and the Logic of Ordinary Language
• Logic and Semantic Analysis
• Justificatory Irrelevance of Formal Semantics
• A Brief History of Truth
• Truth and Paradox: A Philosophical Sketch
• Hilbert’s Program Then and Now
• Logicism and its Contemporary Legacy
• Classical Logic’s Coming of Age
• Infinity
• Löwenheim–Skolem Theorems
• The Mathematics of Skolem’s Paradox
• Objectual and Substitutional Interpretations of the Quantifiers
• Many-Valued Logics
• Relevance Logics
• Paraconsistent Logics and Paraconsistency
• Extensional vs. Intensional Logic
• Logically Possible Worlds and Counterpart Semantics for Modal Logic
• Modal Realism and its Roots in Mathematical Realism
• Free Logics
• Fictions and their Logic
• Counterfactuals, Causation, and Preemption
• Logic, Mathematics, and the Natural Sciences
• Default Reasoning
• Index