Principles of Deductive Logic

Clear focus on its application of formal logic to ordinary English is the most distinctive feature of this textbook for the introductory course in deductive logic. Great care is taken with the appropriate translation into logical languages of ordinary English sentences. Evaluation of these translations promotes a more effective use of ordinary language.

The Principles of Deductive Logic presents symbolic logic in a fuller and more leisurely fashion than other introductory textbooks. Early chapters cover informal material, including definition and informal fallacies. The remainder of the text is devoted to the treatment of four distinct artificial languages. The Categorical language is the language of syllogistic logic. The Extended Categorical language enriches this first language with the symbolic connectives for conjunction and negation. The Propositional Connective language and the First-Order language (with identity) are the two basic languages of modern logic. Each language is accompanied by a deductive system, and is used as an instrument for exploring ordinary language, including ordinary arguments

The book contains a large number of exercises whose answers are supplied in the back of the book, and many more that can be assigned as homework. A solution's manual is available to instructors upon their request. The request must be written on college or university letterhead.

Table of Contents:

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