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""Not"" and ""If"" | |
Symbols and sentences | |
From symbols to English and back | |
Derivability and validity of symbolic arguments | |
Validity of English arguments | |
Fallacies | |
Theorems | |
Historical remarks | |
Appendix | |
""And,"" ""Or,"" ""If and Only If"" | |
Symbols and sentences | |
Translation and symbolization | |
Inference rules and derivability | |
Theorems with unabbreviated proofs | |
Abbreviated derivations | |
Theorems with unabbreviated proofs | |
Arguments | |
Truth-value analysis of sentences | |
Truth-value analysis of arguments | |
Historical remarks | |
Appendix: list of theorems of chapters I and II | |
Appendix: solutions to selected exercises | |
""All"" and ""Some"" | |
Variables, quantifiers, formulas | |
Bondage and freedom | |
Informal notational conventions | |
Translation and symbolization | |
Inference rules | |
Derivations | |
Theorems with unabbreviated proofs | |
Abbreviated derivations | |
Fallacies | |
Theorems with abbreviated proofs | |
Arguments | |
Invalidity: truth-functional expansions and models | |
Historical remarks | |
Appendix: list of theorems of chapter III | |
Appendix: solutions to selected exercises | |
Appendix: summary of the system of logic developed in chapters I-III | |
""All"" and ""Some,"" continued | |
Terms and formulas | |
Bondage and freedom | |
Informal notational conventions | |
Translation and symbolization | |
Revised inference rules | |
Theorems | |
Invalidity: truth-functional expansions and models | |
Invalidity: false arithmetical translations | |
Arguments of English | |
Historical remarks | |
Appendix: list of theorems of chapter IV | |
Appendix: solutions to selected exercises | |
""Is"" (in one sense) | |
Terms and formulas | |
Translation and symbolization | |
Inference rules | |
Theorems | |
Invalidity | |
Historical remarks | |
Appendix: list of theorems of chapter V | |
Appendix: solutions to selected exercises | |
""The"" | |
Descriptive phrases, terms, formulas | |
Bondage and freedom | |
Informal notational conventions | |
Translation and symbolization | |
Inference rules | |
Theorems | |
Invalidity | |
Arguments of English | |
Historical remarks | |
Appendix: list of theorems of chapter VI | |
Appendix: solutions to selected exercises | |
Additional Derivational Procedures | |
Alphabetic variance | |
Substitution | |
Abbreviated derivations reconsidered | |
biconditional derivations | |
Formulas without overlay and prenex normal form, again | |
Abbreviated derivations justified | |
generalized priciples of interchange | |
Historical remarks | |
Appendix: list of theorems of chapter VII | |
Appendix: solutions to selected exercises | |
Appendix: summary of the system of logic developed in chapters I-VII | |
""The"" again: A Russellian Theory of Descriptions | |
The Fregean theory of chapter VI reconsidered | |
A Russellian theory of descriptions | |
Historical remarks | |
Appendix: list of theorems of chapter VIII | |
Appendix: solutions to selected exercises | |
Appendix: summary of the Russellian system of logic developed in chapter VIII | |
Automatic Procedures | |
Introduction | |
Tautologies reconsidered | |
Tautological implication | |
generalized indirect derivation | |
A proof procedure for prenex formulas | |
A derivation procedure for prenex arguments | |
Conversion to prenex form | |
A derivation procedure for arbitrary symbolic arguments | |
A decision procedure for certain prenex formulas | |
A decision procedure for certain prenex arguments | |
Historical remarks | |
Definitions: Formal Theories | |
The vocabulary of formal languages | |
Bondage and freedom | |
proper substitution | |
alphabetic varianc | |
Informal notational conventions | |
Derivability | |
Formal theories | |
the theory of commutative ordered fields | |
Extensions of theories | |
the theory of real numbers | |
Definitions | |
Variable-Binding Operators | |
Definitions reconsidered | |
The theory of convergence | |
A sketch of further developments | |
Historical remarks | |
Appendix: list of constants used in chapters X and XI | |
Appendix: list of axioms, definitions, and theorems of chapters X and XI | |
Bibliography | |
Index of Proper Names | |
Index of Subjects | |
Table of Contents provided by Publisher. All Rights Reserved. |
The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.