## Philosophy of LogicThe 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 |

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### Contents

1 | |

13 | |

41 | |

65 | |

101 | |

On the Relation of Informal to Symbolic Logic | 131 |

Vagueness and the Logic of Ordinary Language | 155 |

Logic and Semantic Analysis | 173 |

The Mathematics of Skolems Paradox | 615 |

Objectual and Substitutional Interpretations of the Quantifiers | 649 |

ManyValued Logics | 675 |

Relevance Logics | 723 |

Paraconsistent Logics and Paraconsistency | 791 |

Extensional vs Intensional Logic | 913 |

Logically Possible Worlds and Counterpart Semantics for Modal Logic | 943 |

Modal Realism and its Roots in Mathematical Realism | 997 |

Justificatory Irrelevance of Formal Semantics | 205 |

A Brief History of Truth | 227 |

A Philosophical Sketch | 325 |

Hilberts Program Then and Now | 411 |

Logicism and its Contemporary Legacy | 449 |

Classical Logics Coming of Age | 497 |

Infinity | 523 |

LoumlwenheimSkolem Theorems | 587 |

### Common terms and phrases

algebraic analysis argument arithmetic axiomatic axioms Benthem Bernays bijection calculus Cambridge cardinality claim classical logic concept consistency proof construction context countable deductive defined definition dialetheism dtrue Dummett entailment equivalent example expressions fact false finitary finite first-order logic formal formulas Frege function fuzzy given Gödel hence Hilbert Hintikka idea inference infinite infinity informal logic interpretation intuitive Kleene Kripke liar paradox liar sentence logicians Löwenheim-Skolem Theorem many-valued logic mathematics meaning modal modal logics natural numbers negation nontrivial notion objects ontological Oxford paracomplete paraconsistent paraconsistent logic philosophical postulates predicate principle problem propositions provable quantifiers question Quine reasoning recursive relation relevance logics rules Russell Russell’s semantics sense set theory Skolem’s Paradox statements structure symbols t-norm Tarski theorem theory of truth transfinite true truth degree truth value truthmaker University Press valid variables