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**