Logic: Techniques of Formal Reasoning / Edition 2

by Donald Kalish, Richard Montague, Gary Mar

Overview

Logic: Techniques of Formal Reasoning, 2/e is an introductory volume that teaches students to recognize and construct correct deductions. It takes students through all logical steps—from premise to conclusion—and presents appropriate symbols and terms, while giving examples to clarify principles. Logic, 2/e uses models to establish the invalidity of arguments, and includes exercise sets throughout, ranging from easy to challenging. Solutions are provided to selected exercises, and historical remarks discuss major contributions to the theories covered.

Product Details

ISBN-13:	9780195155044
Publisher:	Oxford University Press
Publication date:	04/16/1980
Edition description:	REV
Pages:	544
Product dimensions:	9.58(w) x 6.60(h) x 0.97(d)

About the Author

State University of New York, Stony Brook

Table of Contents

Chapter I: "Not" and "If"1. Symbols and sentences2. From symbols to English and back3. Derivability and validity of symbolic arguments4. Validity of English arguments5. Fallacies6. Theorems7. Historical remarks8. AppendixChapter II: "And," "Or," "If and Only If"1. Symbols and sentences2. Translation and symbolization3. Inference rules and derivability4. Theorems with unabbreviated proofs5. Abbreviated derivations6. Theorems with unabbreviated proofs7. Arguments8. Truth-value analysis of sentences9. Truth-value analysis of arguments10. Historical remarks11. Appendix: list of theorems of chapters I and II12. Appendix: solutions to selected exercisesChapter III: "All" and "Some"1. Variables, quantifiers, formulas2. Bondage and freedom3. Informal notational conventions4. Translation and symbolization5. Inference rules6. Derivations7. Theorems with unabbreviated proofs8. Abbreviated derivations9. Fallacies10. Theorems with abbreviated proofs11. Arguments12. Invalidity: truth-functional expansions and models13. Historical remarks14. Appendix: list of theorems of chapter III15. Appendix: solutions to selected exercises16. Appendix: summary of the system of logic developed in chapters I-IIIChapter IV: "All" and "Some," continued1. Terms and formulas2. Bondage and freedom3. Informal notational conventions4. Translation and symbolization5. Revised inference rules6. Theorems7. Invalidity: truth-functional expansions and models8. Invalidity: false arithmetical translations9. Arguments of English10. Historical remarks11. Appendix: list of theorems of chapter IV12. Appendix: solutions to selected exercisesChapter V: "Is" (in one sense)1. Terms and formulas2. Translation and symbolization3. Inference rules4. Theorems5. Invalidity6. Historical remarks7. Appendix: list of theorems of chapter V8. Appendix: solutions to selected exercisesChapter VI: "The"1. Descriptive phrases, terms, formulas2. Bondage and freedom3. Informal notational conventions4. Translation and symbolization5. Inference rules6. Theorems7. Invalidity8. Arguments of English9. Historical remarks10. Appendix: list of theorems of chapter VI11. Appendix: solutions to selected exercisesChapter VII: Additional Derivational Procedures1. Alphabetic variance2. Substitution3. Abbreviated derivations reconsidered; biconditional derivations4. Formulas without overlay and prenex normal form, again5. Abbreviated derivations justified; generalized priciples of interchange6. Historical remarks7. Appendix: list of theorems of chapter VII8. Appendix: solutions to selected exercises9. Appendix: summary of the system of logic developed in chapters I-VIIChapter VIII: "The" again: A Russellian Theory of Descriptions1. The Fregean theory of chapter VI reconsidered2. A Russellian theory of descriptions3. Historical remarks4. Appendix: list of theorems of chapter VIII5. Appendix: solutions to selected exercises6. Appendix: summary of the Russellian system of logic developed in chapter VIIIChapter IX: Automatic Procedures1. Introduction2. Tautologies reconsidered3. Tautological implication; generalized indirect derivation4. A proof procedure for prenex formulas5. A derivation procedure for prenex arguments6. Conversion to prenex form7. A derivation procedure for arbitrary symbolic arguments8. A decision procedure for certain prenex formulas9. A decision procedure for certain prenex arguments10. Historical remarksChapter X: Definitions: Formal Theories1. The vocabulary of formal languages2. Bondage and freedom; proper substitution; alphabetic varianc3. Informal notational conventions4. Derivability5. Formal theories; the theory of commutative ordered fields6. Extensions of theories; the theory of real numbers7. DefinitionsChapter XI: Variable-Binding Operators1. Definitions reconsidered2. The theory of convergence3. A sketch of further developments4. Historical remarks5. Appendix: list of constants used in chapters X and XI6. Appendix: list of axioms, definitions, and theorems of chapters X and XIBibliographyIndex of Proper NamesIndex of Subjects