## Methods of LogicThis widely used textbook of modern formal logic now offers a number of new features. Incorporating updated notations, selective answers to exercises, expanded treatment of natural deduction, and new discussions of predicate- functor logic and the affinities between higher set theory and the elementary logic of terms, Quine's new edition will serve admirably both for classroom and for independent use. |

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### Contents

Introduction | 1 |

TRUTH FUNCTIONS | 7 |

Negation Conjunction and Alternation | 9 |

Truth Functions | 16 |

The Conditional | 21 |

Grouping | 27 |

TruthValue Analysis | 33 |

Consistency and Validity | 40 |

GENERAL THEORY OF QUANTIFICATION | 165 |

Schemata Extended | 167 |

Substitution Extended | 174 |

Pure Existentials | 182 |

The Main Method | 190 |

Application | 195 |

Completeness | 203 |

Lowenheims Theorem | 209 |

Implication | 45 |

Words into Symbols | 53 |

Equivalence | 60 |

Alternational Normal Schemata | 68 |

Simplification | 74 |

Duality | 79 |

Axioms | 85 |

GENERAL TERMS AND QUANTIFIERS | 91 |

Categorical Statements | 93 |

Venns Diagrams | 98 |

Syllogisms | 102 |

Limits of These Methods | 109 |

Boolean Schemata | 114 |

Tests of Validity | 121 |

Some Boolean Incidentals | 128 |

The Bound Variable | 132 |

Quantification | 136 |

Rules of Passage Monadic Schemata | 142 |

Prenexity and Purity | 148 |

Validity Again | 154 |

Substitution | 160 |

Decisions and the Undecidable | 213 |

Functional Normal Forms | 219 |

Herbrands Method | 224 |

Other Methods for Validity | 232 |

Deduction | 237 |

Soundness | 245 |

Deductive Strategy | 248 |

GLIMPSES BEYOND | 257 |

Singular Terms | 259 |

Identity | 265 |

Descriptions | 274 |

Elimination of Singular Terms | 278 |

Elimination of Variables | 283 |

Classes | 288 |

Number | 294 |

Axiomatic Set Theory | 300 |

Partial Answers to Exercises | 305 |

320 | |

327 | |

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### Common terms and phrases

3x Fx affirmative alternational normal antecedent axioms biconditional Boolean existence Boolean term schemata Cerberus clausal UG clause comes out true component compound conclusion conjunctional normal form consistency decision procedure deduction Diagram equivalent example EXERCISES existence schemata existential conditionals existential quantifiers F are G false fell swoop free variables functional normal forms functors HISTORICAL NOTE identity implies instantial variable interpretation ix)Fx logic main method means monadic negation normal schema notation object ordinary language p v q paraphrasing polyadic premises prenex form proof procedure pure existential quantificational schemata relettering rules of passage set theory singular terms step substitution syllogism term abstracts term letters term schema theorem tion truth functions truth value truth-functional truth-functionally valid truth-value analysis universal quantifiers unquantified instances valid schemata Vx(Fx