## ELEMENTARY LOGICNow much revised since its first appearance in 1941, this book, despite its brevity, is notable for its scope and rigor. It provides a single strand of simple techniques for the central business of modern logic. Basic formal concepts are explained, the paraphrasing of words into symbols is treated at some length, and a testing procedure is given for truth-function logic along with a complete proof procedure for the logic of quantifiers. Fully one third of this revised edition is new, and presents a nearly complete turnover in crucial techniques of testing and proving, some change of notation, and some updating of terminology. The study is intended primarily as a convenient encapsulation of minimum essentials, but concludes by giving brief glimpses of further matters. |

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### Contents

Introduction | 1 |

STATEMENT COMPOSITION | 5 |

Conjunction | 8 |

Denial | 11 |

Or | 13 |

But although unless | 15 |

If | 17 |

General and Subjunctive Conditionals | 20 |

Implication between Schemata | 65 |

TruthFunctional Implication | 66 |

QUANTIFICATION | 71 |

Quantifiers | 73 |

Variables and Open Sentences | 75 |

Variants of Some | 78 |

Some Restricted | 79 |

No | 82 |

Because hence that | 22 |

Reduction to Conjunction and Denial | 24 |

Grouping | 26 |

Verbal Cues to Grouping | 28 |

Paraphrasing Inward | 30 |

TRUTHFUNCTIONAL TRANSFORMATIONS | 35 |

Instances | 39 |

Equivalent Schemata | 40 |

TruthFunctional Equivalence | 43 |

Replacement | 44 |

Transformation | 47 |

Proofs of Equivalence | 50 |

Alternation and Duality | 52 |

Normal Schemata | 55 |

Validity | 59 |

TruthFunctional Truth | 60 |

Inconsistency and TruthFunctional Falsity | 63 |

Every | 84 |

Variants of Every | 86 |

Persons | 89 |

Times and Places | 90 |

Quantification in Context | 93 |

QUANTIFICATIONAL INFERENCE | 97 |

Predicates | 99 |

Restraints on Introducing | 101 |

Substitution Extended | 104 |

Validity Extended | 107 |

Equivalence Extended | 109 |

Inconsistency Proofs | 112 |

Logical Arguments | 116 |

Identity and Singular Terms | 119 |

Membership | 122 |

127 | |

### Common terms and phrases

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