Principles of Deductive Logic

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.

PREFACE

1. APPLIED LOGIC: WHAT WE HOPE TO ACCOMPLISH
1-0 Summary
1-1 The Nature of Logic
1-2 Talking About Words
1-3 Speech Acts
1-4 A Language is a Complex System
1-5 Logically Important Semantic Features
1-6 Applied Logic
1-7 Philosophy of Logic

2. SOME PRELIMINARY MATTERS
2-0 Summary
2-1 Definitions (Opt)
2-2 Inferences and Arguments
2-3 Informal Fallacies (Opt)

3. SENTENCES ABOUT INDIVIDUALS
3-0 Summary
3-1 Looking Ahead
3-2 Individuals
3-3 Quantified Phrases
3-4 Universal Sentences
3-5 Some Other Universal Sentences
3-6 Singular Sentences

4. THE ARTIFICIAL-LANGUAGE STRATEGY
4-0 Summary
4-1 Artificial Languages
4-2 Logical Form
4-3 Evaluation
4-4 The Languages to be Developed

5. THE CATEGORICAL LANGUAGE
5-0 Summary
5-1 Categorical Sentences
5-2 Semantics
5-3 Logical Form
5-4 The Complement of an Expression
5-5 Some Syntactic Relations
5-6 Implication and Equivalence
5-7 Logical Truth
5-8 Venn Diagrams
5-9 Incompatibility
5-10 Syllogisms
5-11 The Categorical Deductive System
5-12 Proving Incompatibility
5-13 Venn Diagrams for Many-Place Relations
5-14 Formal Fallacies (Opt)

6. APPLYING AN ARTIFICIAL LANGUAGE
6-0 Summary
6-1 What We Want in a Translation
6-2 The Features We Test for
6-3 Negative Outcomes

7. APPLYING THE CATEGORICAL LANGUAGE TO ENGLISH
7-0 Summary
7-1 Translating English Sentences
7-2 Expressing Existential Force
7-3 Detecting Semantic Features of Existence Claims
7-4 Evaluating English Sentences and Arguments
7-5 Achieving Comparable Translations
7-6 Incorporating Semantic Features in Logical Form
7-7 Enthymemes
7-8 What Comes Next

8. THE EXTENDED CATEGORICAL LANGUAGE
8-0 Summary
8-1 The Changes We Want
8-2 What We Will Keep
8-3 Small Change
8-4 The Sign of Negation
8-5 Reasoning with Negative Sentences
8-6 Translating Negated Sentences
8-7 Singular Sentences
8-8 Reasoning with Singular Sentences

9. THE PROPOSITIONAL CONNECTIVE LANGUAGE
9-0 Summary
9-1 A Mixed Language
9-2 The Syntax and Semantics of the PC Language
9-3 Variables and Formulas
9-4 Evaluating Sentences of the PC Languge
9-5 Two-Place Relations
9-6 Many-Place Relations
9-7 Indirect Tests
9-8 The Quick Method of Determining if a Formula is a Tautology

10. THE PC DEDUCTIVE SYSTEM
10-0 Summary
10-1 A Deductive System
10-2 Proofs from Hypotheses
10-3 The Easy Rules
10-4 More Rules
10-5 Proofs within Proofs
10-6 Properties of the PC System
10-7 Proofs without Hypotheses
10-8 Metatheorems and Derived Rules
10-9 Our First Metatheorems (Opt)
10-10 More Metatheorems (Opt)
10-11 Still More Metatheorems (Opt)
10-12 Rules to Shorten Proofs
10-13 Proving Incompatibility
10-14 Refutation
10-15 What to do Next
THE ORIGINAL AND DERIVED RULES OF THE PC DEDUCTIVE SYSTEM

11. APPLYING THE PC LANGUAGE TO ENGLISH
11-0 Summary
11-1 Translating within a Single Language
11-2 Translating with the Negation Sign
11-3 Translating with '&'
11-4 Translations with 'v'
11-5 Translations with the Horseshoe
11-6 Some Additional Translations
11-7 The Scope of a Connective
11-8 Identifying Sentences
11-9 A Further Look at the Difference Between Ordinary Conditional Sentences and Horseshoe Sentences (Opt)
11-10 Testing for Analyticity
11-11 Incompatibility
11-12 Entailment and Validity
11-13 An Important Exception
11-14 Incorporating Semantic Features in Logical Form
11-15 Enthymemes

12. THE FIRST-ORDER LANGUAGE
12-0 Summary
12-1 A Purely Artificial Language
12-2 The Truth Conditions of Atomic Sentences
12-3 New Varieties of Variables
12-4 Quantifiers
12-5 Multiple Quantification
12-6 Restricted Domains
12-7 A More Careful Description of the First-Order Language

13. THE FIRST-ORDER DEDUCTIVE SYSTEM
13-0 Summary
13-1 Adapting the PC System
13-2 Some Derived Rules
13-3 A Notation for Substitution
13-4 An Additional Notation
13-5 Change of Bound Variables
13-6 Universal Quantifier Elimination
13-7 Universal Quantifier Introduction
13-8 Existential Quantifier Introduction
13-9 Existential Quantifier Elimination
13-10 Identity Rules
13-11 More Derived Rules
13-12 Refutation
13-13 Incompatibilty
RULES AND DERIVED RULES OF THE FIRST-ORDER DEDUCTIVE SYSTEM

14. APPLYING THE FIRST-ORDER LANGUAGE TO ENGLISH
14-0 Summary
14-1 The Expressive Power of the First-Order Language
14-2 Predicates and Singular Terms
14-3 Quantified Phrases in English
14-4 Indefinite Sentences
14-5 Universal Sentences
14-6 Only
14-7 Another Use of 'Any'
14-8 Generalized Conditionals
14-9 Analytic Sentences
14-10 Incompatibility
14-11 Entailment and Validity
14-12 Comparable Translations
14-13 Supplementing Our Translations

AFTERWORD: REFLECTIONS ON LOGIC

ANSWERS TO STARRED QUESTIONS

INDEX