Logic

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