Logic

Techniques of Formal Reasoning

Kalish, Montague, Mar (Autoren)

Buch | Hardcover

538 Seiten

1980 | 2nd edition
Oxford University Press Inc (Verlag)
978-0-19-515504-4 (ISBN)

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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: 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.

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

Verlagsort	New York
Sprache	englisch
Gewicht	985 g
Themenwelt	Geisteswissenschaften ► Philosophie ► Logik
ISBN-10	0-19-515504-1 / 0195155041
ISBN-13	978-0-19-515504-4 / 9780195155044
Zustand	Neuware