Logic : Techniques of Formal Reasoning Book

Chapter I: "Not" and "If"
1. Symbols and sentences
2. From symbols to English and back
3. Derivability and validity of symbolic arguments
4. Validity of English arguments
5. Fallacies
6. Theorems
7. Historical remarks
8. Appendix
Chapter II: "And," "Or," "If and Only If"
1. Symbols and sentences
2. Translation and symbolization
3. Inference rules and derivability
4. Theorems with unabbreviated proofs
5. Abbreviated derivations
6. Theorems with unabbreviated proofs
7. Arguments
8. Truth-value analysis of sentences
9. Truth-value analysis of arguments
10. Historical remarks
11. Appendix: list of theorems of chapters I and II
12. Appendix: solutions to selected exercises
Chapter III: "All" and "Some"
1. Variables, quantifiers, formulas
2. Bondage and freedom
3. Informal notational conventions
4. Translation and symbolization
5. Inference rules
6. Derivations
7. Theorems with unabbreviated proofs
8. Abbreviated derivations
9. Fallacies
10. Theorems with abbreviated proofs
11. Arguments
12. Invalidity: truth-functional expansions and models
13. Historical remarks
14. Appendix: list of theorems of chapter III
15. Appendix: solutions to selected exercises
16. Appendix: summary of the system of logic developed in chapters I-III
Chapter IV: "All" and "Some," continued
1. Terms and formulas
2. Bondage and freedom
3. Informal notational conventions
4. Translation and symbolization
5. Revised inference rules
6. Theorems
7. Invalidity: truth-functional expansions and models
8. Invalidity: false arithmetical translations
9. Arguments of English
10. Historical remarks
11. Appendix: list of theorems of chapter IV
12. Appendix: solutions to selected exercises
Chapter V: "Is" (in one sense)
1. Terms and formulas
2. Translation and symbolization
3. Inference rules
4. Theorems
5. Invalidity
6. Historical remarks
7. Appendix: list of theorems of chapter V
8. Appendix: solutions to selected exercises
Chapter VI: "The"
1. Descriptive phrases, terms, formulas
2. Bondage and freedom
3. Informal notational conventions
4. Translation and symbolization
5. Inference rules
6. Theorems
7. Invalidity
8. Arguments of English
9. Historical remarks
10. Appendix: list of theorems of chapter VI
11. Appendix: solutions to selected exercises
Chapter VII: Additional Derivational Procedures
1. Alphabetic variance
2. Substitution
3. Abbreviated derivations reconsidered; biconditional derivations
4. Formulas without overlay and prenex normal form, again
5. Abbreviated derivations justified; generalized priciples of interchange
6. Historical remarks
7. Appendix: list of theorems of chapter VII
8. Appendix: solutions to selected exercises
9. Appendix: summary of the system of logic developed in chapters I-VII
Chapter VIII: "The" again: A Russellian Theory of Descriptions
1. The Fregean theory of chapter VI reconsidered
2. A Russellian theory of descriptions
3. Historical remarks
4. Appendix: list of theorems of chapter VIII
5. Appendix: solutions to selected exercises
6. Appendix: summary of the Russellian system of logic developed in chapter VIII
Chapter IX: Automatic Procedures
1. Introduction
2. Tautologies reconsidered
3. Tautological implication; generalized indirect derivation
4. A proof procedure for prenex formulas
5. A derivation procedure for prenex arguments
6. Conversion to prenex form
7. A derivation procedure for arbitrary symbolic arguments
8. A decision procedure for certain prenex formulas
9. A decision procedure for certain prenex arguments
10. Historical remarks
Chapter X: Definitions: Formal Theories
1. The vocabulary of formal languages
2. Bondage and freedom; proper substitution; alphabetic varianc
3. Informal notational conventions
4. Derivability
5. Formal theories; the theory of commutative ordered fields
6. Extensions of theories; the theory of real numbers
7. Definitions
Chapter XI: Variable-Binding Operators
1. Definitions reconsidered
2. The theory of convergence
3. A sketch of further developments
4. Historical remarks
5. Appendix: list of constants used in chapters X and XI
6. Appendix: list of axioms, definitions, and theorems of chapters X and XI Bibliography Index of Proper Names Index of Subjects