John T. Kearns is Professor of Philosophy at State University of New York at Buffalo. He is author of Using Language: The Structures of Speech Acts, also published by SUNY Press.

"It is hard to say what I like most about the book because there are so many things I like. One of the things is that it incorporates so much of what has been happening in logic recently. It does not attempt to rewrite or copy Copi, and it is beautifully written." — S. Jack Odell, University of Maryland"The discussion of translation is especially good. Examples are well chosen, the pace is excellent, and there are lots of illustrations to support the text. The book is also very well organized." — Paolo Dau, University of California, San Diego

• PREFACE 1. APPLIED LOGIC: WHAT WE HOPE TO ACCOMPLISH 1-0 Summary1-1 The Nature of Logic1-2 Talking About Words1-3 Speech Acts1-4 A Language is a Complex System1-5 Logically Important Semantic Features1-6 Applied Logic1-7 Philosophy of Logic 2. SOME PRELIMINARY MATTERS 2-0 Summary2-1 Definitions (Opt)2-2 Inferences and Arguments2-3 Informal Fallacies (Opt) 3. SENTENCES ABOUT INDIVIDUALS 3-0 Summary3-1 Looking Ahead3-2 Individuals3-3 Quantified Phrases3-4 Universal Sentences3-5 Some Other Universal Sentences3-6 Singular Sentences 4. THE ARTIFICIAL-LANGUAGE STRATEGY 4-0 Summary4-1 Artificial Languages4-2 Logical Form4-3 Evaluation4-4 The Languages to be Developed 5. THE CATEGORICAL LANGUAGE 5-0 Summary5-1 Categorical Sentences5-2 Semantics5-3 Logical Form5-4 The Complement of an Expression5-5 Some Syntactic Relations5-6 Implication and Equivalence5-7 Logical Truth5-8 Venn Diagrams5-9 Incompatibility5-10 Syllogisms5-11 The Categorical Deductive System5-12 Proving Incompatibility5-13 Venn Diagrams for Many-Place Relations5-14 Formal Fallacies (Opt) 6. APPLYING AN ARTIFICIAL LANGUAGE 6-0 Summary6-1 What We Want in a Translation6-2 The Features We Test for6-3 Negative Outcomes 7. APPLYING THE CATEGORICAL LANGUAGE TO ENGLISH 7-0 Summary7-1 Translating English Sentences7-2 Expressing Existential Force7-3 Detecting Semantic Features of Existence Claims7-4 Evaluating English Sentences and Arguments7-5 Achieving Comparable Translations7-6 Incorporating Semantic Features in Logical Form7-7 Enthymemes7-8 What Comes Next 8. THE EXTENDED CATEGORICAL LANGUAGE 8-0 Summary8-1 The Changes We Want8-2 What We Will Keep8-3 Small Change8-4 The Sign of Negation8-5 Reasoning with Negative Sentences8-6 Translating Negated Sentences8-7 Singular Sentences8-8 Reasoning with Singular Sentences 9. THE PROPOSITIONAL CONNECTIVE LANGUAGE 9-0 Summary9-1 A Mixed Language9-2 The Syntax and Semantics of the PC Language9-3 Variables and Formulas9-4 Evaluating Sentences of the PC Languge9-5 Two-Place Relations9-6 Many-Place Relations9-7 Indirect Tests9-8 The Quick Method of Determining if a Formula is a Tautology 10. THE PC DEDUCTIVE SYSTEM 10-0 Summary10-1 A Deductive System10-2 Proofs from Hypotheses10-3 The Easy Rules10-4 More Rules10-5 Proofs within Proofs10-6 Properties of the PC System10-7 Proofs without Hypotheses10-8 Metatheorems and Derived Rules10-9 Our First Metatheorems (Opt)10-10 More Metatheorems (Opt)10-11 Still More Metatheorems (Opt)10-12 Rules to Shorten Proofs10-13 Proving Incompatibility10-14 Refutation10-15 What to do NextTHE ORIGINAL AND DERIVED RULES OF THE PC DEDUCTIVE SYSTEM 11. APPLYING THE PC LANGUAGE TO ENGLISH 11-0 Summary11-1 Translating within a Single Language11-2 Translating with the Negation Sign11-3 Translating with '&'11-4 Translations with 'v'11-5 Translations with the Horseshoe11-6 Some Additional Translations11-7 The Scope of a Connective11-8 Identifying Sentences11-9 A Further Look at the Difference Between Ordinary Conditional Sentences and Horseshoe Sentences (Opt)11-10 Testing for Analyticity11-11 Incompatibility11-12 Entailment and Validity11-13 An Important Exception11-14 Incorporating Semantic Features in Logical Form11-15 Enthymemes 12. THE FIRST-ORDER LANGUAGE 12-0 Summary12-1 A Purely Artificial Language12-2 The Truth Conditions of Atomic Sentences12-3 New Varieties of Variables12-4 Quantifiers12-5 Multiple Quantification12-6 Restricted Domains12-7 A More Careful Description of the First-Order Language 13. THE FIRST-ORDER DEDUCTIVE SYSTEM 13-0 Summary13-1 Adapting the PC System13-2 Some Derived Rules13-3 A Notation for Substitution13-4 An Additional Notation13-5 Change of Bound Variables13-6 Universal Quantifier Elimination13-7 Universal Quantifier Introduction13-8 Existential Quantifier Introduction13-9 Existential Quantifier Elimination13-10 Identity Rules13-11 More Derived Rules13-12 Refutation13-13 IncompatibiltyRULES AND DERIVED RULES OF THE FIRST-ORDER DEDUCTIVE SYSTEM 14. APPLYING THE FIRST-ORDER LANGUAGE TO ENGLISH 14-0 Summary14-1 The Expressive Power of the First-Order Language14-2 Predicates and Singular Terms14-3 Quantified Phrases in English14-4 Indefinite Sentences14-5 Universal Sentences14-6 Only14-7 Another Use of 'Any'14-8 Generalized Conditionals14-9 Analytic Sentences14-10 Incompatibility14-11 Entailment and Validity14-12 Comparable Translations14-13 Supplementing Our Translations AFTERWORD: REFLECTIONS ON LOGIC ANSWERS TO STARRED QUESTIONS INDEX

John T. Kearns is Professor of Philosophy at State University of New York at Buffalo. He is author of Using Language: The Structures of Speech Acts, also published by SUNY Press.

"It is hard to say what I like most about the book because there are so many things I like. One of the things is that it incorporates so much of what has been happening in logic recently. It does not attempt to rewrite or copy Copi, and it is beautifully written." — S. Jack Odell, University of Maryland"The discussion of translation is especially good. Examples are well chosen, the pace is excellent, and there are lots of illustrations to support the text. The book is also very well organized." — Paolo Dau, University of California, San Diego

• PREFACE 1. APPLIED LOGIC: WHAT WE HOPE TO ACCOMPLISH 1-0 Summary1-1 The Nature of Logic1-2 Talking About Words1-3 Speech Acts1-4 A Language is a Complex System1-5 Logically Important Semantic Features1-6 Applied Logic1-7 Philosophy of Logic 2. SOME PRELIMINARY MATTERS 2-0 Summary2-1 Definitions (Opt)2-2 Inferences and Arguments2-3 Informal Fallacies (Opt) 3. SENTENCES ABOUT INDIVIDUALS 3-0 Summary3-1 Looking Ahead3-2 Individuals3-3 Quantified Phrases3-4 Universal Sentences3-5 Some Other Universal Sentences3-6 Singular Sentences 4. THE ARTIFICIAL-LANGUAGE STRATEGY 4-0 Summary4-1 Artificial Languages4-2 Logical Form4-3 Evaluation4-4 The Languages to be Developed 5. THE CATEGORICAL LANGUAGE 5-0 Summary5-1 Categorical Sentences5-2 Semantics5-3 Logical Form5-4 The Complement of an Expression5-5 Some Syntactic Relations5-6 Implication and Equivalence5-7 Logical Truth5-8 Venn Diagrams5-9 Incompatibility5-10 Syllogisms5-11 The Categorical Deductive System5-12 Proving Incompatibility5-13 Venn Diagrams for Many-Place Relations5-14 Formal Fallacies (Opt) 6. APPLYING AN ARTIFICIAL LANGUAGE 6-0 Summary6-1 What We Want in a Translation6-2 The Features We Test for6-3 Negative Outcomes 7. APPLYING THE CATEGORICAL LANGUAGE TO ENGLISH 7-0 Summary7-1 Translating English Sentences7-2 Expressing Existential Force7-3 Detecting Semantic Features of Existence Claims7-4 Evaluating English Sentences and Arguments7-5 Achieving Comparable Translations7-6 Incorporating Semantic Features in Logical Form7-7 Enthymemes7-8 What Comes Next 8. THE EXTENDED CATEGORICAL LANGUAGE 8-0 Summary8-1 The Changes We Want8-2 What We Will Keep8-3 Small Change8-4 The Sign of Negation8-5 Reasoning with Negative Sentences8-6 Translating Negated Sentences8-7 Singular Sentences8-8 Reasoning with Singular Sentences 9. THE PROPOSITIONAL CONNECTIVE LANGUAGE 9-0 Summary9-1 A Mixed Language9-2 The Syntax and Semantics of the PC Language9-3 Variables and Formulas9-4 Evaluating Sentences of the PC Languge9-5 Two-Place Relations9-6 Many-Place Relations9-7 Indirect Tests9-8 The Quick Method of Determining if a Formula is a Tautology 10. THE PC DEDUCTIVE SYSTEM 10-0 Summary10-1 A Deductive System10-2 Proofs from Hypotheses10-3 The Easy Rules10-4 More Rules10-5 Proofs within Proofs10-6 Properties of the PC System10-7 Proofs without Hypotheses10-8 Metatheorems and Derived Rules10-9 Our First Metatheorems (Opt)10-10 More Metatheorems (Opt)10-11 Still More Metatheorems (Opt)10-12 Rules to Shorten Proofs10-13 Proving Incompatibility10-14 Refutation10-15 What to do NextTHE ORIGINAL AND DERIVED RULES OF THE PC DEDUCTIVE SYSTEM 11. APPLYING THE PC LANGUAGE TO ENGLISH 11-0 Summary11-1 Translating within a Single Language11-2 Translating with the Negation Sign11-3 Translating with '&'11-4 Translations with 'v'11-5 Translations with the Horseshoe11-6 Some Additional Translations11-7 The Scope of a Connective11-8 Identifying Sentences11-9 A Further Look at the Difference Between Ordinary Conditional Sentences and Horseshoe Sentences (Opt)11-10 Testing for Analyticity11-11 Incompatibility11-12 Entailment and Validity11-13 An Important Exception11-14 Incorporating Semantic Features in Logical Form11-15 Enthymemes 12. THE FIRST-ORDER LANGUAGE 12-0 Summary12-1 A Purely Artificial Language12-2 The Truth Conditions of Atomic Sentences12-3 New Varieties of Variables12-4 Quantifiers12-5 Multiple Quantification12-6 Restricted Domains12-7 A More Careful Description of the First-Order Language 13. THE FIRST-ORDER DEDUCTIVE SYSTEM 13-0 Summary13-1 Adapting the PC System13-2 Some Derived Rules13-3 A Notation for Substitution13-4 An Additional Notation13-5 Change of Bound Variables13-6 Universal Quantifier Elimination13-7 Universal Quantifier Introduction13-8 Existential Quantifier Introduction13-9 Existential Quantifier Elimination13-10 Identity Rules13-11 More Derived Rules13-12 Refutation13-13 IncompatibiltyRULES AND DERIVED RULES OF THE FIRST-ORDER DEDUCTIVE SYSTEM 14. APPLYING THE FIRST-ORDER LANGUAGE TO ENGLISH 14-0 Summary14-1 The Expressive Power of the First-Order Language14-2 Predicates and Singular Terms14-3 Quantified Phrases in English14-4 Indefinite Sentences14-5 Universal Sentences14-6 Only14-7 Another Use of 'Any'14-8 Generalized Conditionals14-9 Analytic Sentences14-10 Incompatibility14-11 Entailment and Validity14-12 Comparable Translations14-13 Supplementing Our Translations AFTERWORD: REFLECTIONS ON LOGIC ANSWERS TO STARRED QUESTIONS INDEX

John T. Kearns is Professor of Philosophy at State University of New York at Buffalo. He is author of Using Language: The Structures of Speech Acts, also published by SUNY Press.

"It is hard to say what I like most about the book because there are so many things I like. One of the things is that it incorporates so much of what has been happening in logic recently. It does not attempt to rewrite or copy Copi, and it is beautifully written." — S. Jack Odell, University of Maryland"The discussion of translation is especially good. Examples are well chosen, the pace is excellent, and there are lots of illustrations to support the text. The book is also very well organized." — Paolo Dau, University of California, San Diego

• PREFACE 1. APPLIED LOGIC: WHAT WE HOPE TO ACCOMPLISH 1-0 Summary1-1 The Nature of Logic1-2 Talking About Words1-3 Speech Acts1-4 A Language is a Complex System1-5 Logically Important Semantic Features1-6 Applied Logic1-7 Philosophy of Logic 2. SOME PRELIMINARY MATTERS 2-0 Summary2-1 Definitions (Opt)2-2 Inferences and Arguments2-3 Informal Fallacies (Opt) 3. SENTENCES ABOUT INDIVIDUALS 3-0 Summary3-1 Looking Ahead3-2 Individuals3-3 Quantified Phrases3-4 Universal Sentences3-5 Some Other Universal Sentences3-6 Singular Sentences 4. THE ARTIFICIAL-LANGUAGE STRATEGY 4-0 Summary4-1 Artificial Languages4-2 Logical Form4-3 Evaluation4-4 The Languages to be Developed 5. THE CATEGORICAL LANGUAGE 5-0 Summary5-1 Categorical Sentences5-2 Semantics5-3 Logical Form5-4 The Complement of an Expression5-5 Some Syntactic Relations5-6 Implication and Equivalence5-7 Logical Truth5-8 Venn Diagrams5-9 Incompatibility5-10 Syllogisms5-11 The Categorical Deductive System5-12 Proving Incompatibility5-13 Venn Diagrams for Many-Place Relations5-14 Formal Fallacies (Opt) 6. APPLYING AN ARTIFICIAL LANGUAGE 6-0 Summary6-1 What We Want in a Translation6-2 The Features We Test for6-3 Negative Outcomes 7. APPLYING THE CATEGORICAL LANGUAGE TO ENGLISH 7-0 Summary7-1 Translating English Sentences7-2 Expressing Existential Force7-3 Detecting Semantic Features of Existence Claims7-4 Evaluating English Sentences and Arguments7-5 Achieving Comparable Translations7-6 Incorporating Semantic Features in Logical Form7-7 Enthymemes7-8 What Comes Next 8. THE EXTENDED CATEGORICAL LANGUAGE 8-0 Summary8-1 The Changes We Want8-2 What We Will Keep8-3 Small Change8-4 The Sign of Negation8-5 Reasoning with Negative Sentences8-6 Translating Negated Sentences8-7 Singular Sentences8-8 Reasoning with Singular Sentences 9. THE PROPOSITIONAL CONNECTIVE LANGUAGE 9-0 Summary9-1 A Mixed Language9-2 The Syntax and Semantics of the PC Language9-3 Variables and Formulas9-4 Evaluating Sentences of the PC Languge9-5 Two-Place Relations9-6 Many-Place Relations9-7 Indirect Tests9-8 The Quick Method of Determining if a Formula is a Tautology 10. THE PC DEDUCTIVE SYSTEM 10-0 Summary10-1 A Deductive System10-2 Proofs from Hypotheses10-3 The Easy Rules10-4 More Rules10-5 Proofs within Proofs10-6 Properties of the PC System10-7 Proofs without Hypotheses10-8 Metatheorems and Derived Rules10-9 Our First Metatheorems (Opt)10-10 More Metatheorems (Opt)10-11 Still More Metatheorems (Opt)10-12 Rules to Shorten Proofs10-13 Proving Incompatibility10-14 Refutation10-15 What to do NextTHE ORIGINAL AND DERIVED RULES OF THE PC DEDUCTIVE SYSTEM 11. APPLYING THE PC LANGUAGE TO ENGLISH 11-0 Summary11-1 Translating within a Single Language11-2 Translating with the Negation Sign11-3 Translating with '&'11-4 Translations with 'v'11-5 Translations with the Horseshoe11-6 Some Additional Translations11-7 The Scope of a Connective11-8 Identifying Sentences11-9 A Further Look at the Difference Between Ordinary Conditional Sentences and Horseshoe Sentences (Opt)11-10 Testing for Analyticity11-11 Incompatibility11-12 Entailment and Validity11-13 An Important Exception11-14 Incorporating Semantic Features in Logical Form11-15 Enthymemes 12. THE FIRST-ORDER LANGUAGE 12-0 Summary12-1 A Purely Artificial Language12-2 The Truth Conditions of Atomic Sentences12-3 New Varieties of Variables12-4 Quantifiers12-5 Multiple Quantification12-6 Restricted Domains12-7 A More Careful Description of the First-Order Language 13. THE FIRST-ORDER DEDUCTIVE SYSTEM 13-0 Summary13-1 Adapting the PC System13-2 Some Derived Rules13-3 A Notation for Substitution13-4 An Additional Notation13-5 Change of Bound Variables13-6 Universal Quantifier Elimination13-7 Universal Quantifier Introduction13-8 Existential Quantifier Introduction13-9 Existential Quantifier Elimination13-10 Identity Rules13-11 More Derived Rules13-12 Refutation13-13 IncompatibiltyRULES AND DERIVED RULES OF THE FIRST-ORDER DEDUCTIVE SYSTEM 14. APPLYING THE FIRST-ORDER LANGUAGE TO ENGLISH 14-0 Summary14-1 The Expressive Power of the First-Order Language14-2 Predicates and Singular Terms14-3 Quantified Phrases in English14-4 Indefinite Sentences14-5 Universal Sentences14-6 Only14-7 Another Use of 'Any'14-8 Generalized Conditionals14-9 Analytic Sentences14-10 Incompatibility14-11 Entailment and Validity14-12 Comparable Translations14-13 Supplementing Our Translations AFTERWORD: REFLECTIONS ON LOGIC ANSWERS TO STARRED QUESTIONS INDEX