Essentials of Symbolic Logic

by Simpson, R. L.

• ISBN13: 9780415018715
• ISBN10: 0415018714
• Format: Paperback
• Copyright: 1989-03-01
• Publisher: Routledge

Table of Contents

Chapter One
The Aims of this Book	1	(2)
Primarily for the Student	3	(1)
Primarily for the Instructor	4	(3)
Chapter Two
The Fundamentals	7	(1)
Truth Functions	8	(1)
Sentence Letters and Symbols	9	(2)
Metalanguage	11	(1)
Well-Formed Formulas	12	(1)
Exercises	13	(1)
Simple Translation: Negation	14	(1)
Simple Translation: Conjunction	15	(2)
Simple Translation: Disjunction	17	(1)
Simple Translation: the Horseshoe	18	(2)
Simple Translation: the Triplebar	20	(1)
Translating Complicated Sentences	21	(3)
Exercises	24	(2)
Defining the Operators	26	(3)
Truth Tables	29	(3)
Exercises	32	(1)
Types of Formulas	32	(3)
Truth-Functional Equivalences	35	(4)
Exercises	39	(1)
Arguments	39	(4)
Exercises	43	(2)
Translating Arguments	45	(5)
Exercises	50	(1)
Summary of Topics	51	(4)
Chapter Three
What a Derivation Is	55	(2)
Conjunction Introduction	57	(2)
Conjunction Elimination	59	(2)
Negation Elimination	61	(1)
Disjunction Introduction	62	(2)
Horseshoe Elimination	64	(2)
Triplebar Elimination	66	(1)
Exercises	67	(1)
Constructing Derivations	68	(11)
Exercises	79	(1)
Assumptions	80	(2)
Reiteration	82	(2)
Horseshoe Introduction	84	(4)
Triplebar Introduction	88	(3)
Negation Introduction	91	(4)
Disjunction Elimination	95	(2)
Exercises	97	(2)
More Derivation Construction	99	(13)
Exercises	112	(1)
Indirect Proof	113	(8)
Exercises	121	(2)
Categorical Derivations	123	(3)
Exercises	126	(1)
Summary of Topics	127	(6)
Chapter Four
Individuals and Predicates	133	(2)
One-Place and Multi-Place Predicates	135	(2)
Choices in Translation	137	(1)
Exercises	138	(1)
Quantifiers	139	(1)
The Existential Quantifier	140	(2)
The Universal Quantifier	142	(2)
Using Both Quantifiers	144	(3)
Exercises	147	(1)
People and Things	148	(1)
Exercises	149	(1)
Identity	150	(4)
Translation Problems and Domains	154	(5)
Exercises	159	(1)
Arguments in Predicate Logic	160	(3)
Exercises	163	(2)
Simple Interpretations	165	(6)
Exercises	171	(3)
Summary of Topics	174	(3)
Chapter Five
Predicate Logic Derivations	177	(1)
Existential Quantifier Introduction	178	(3)
Universal Quantifier Elimination	181	(2)
Existential Quantifier Elimination	183	(3)
Universal Quantifier Introduction	186	(4)
Identity Introduction	190	(1)
Identity Elimination	191	(1)
Exercises	192	(2)
Derivation Strategies	194	(9)
Exercises	203	(1)
More Derivation Strategies	204	(11)
Exercises	215	(2)
Categorical Derivations in Predicate Logic	217	(3)
Exercises	220	(1)
Summary of Topics	220	(3)
Chapter Six
The Scope of the Text	223	(1)
Existence and Translation Problems	224	(1)
The Names of the Rules	224	(1)
Unfamiliar Terminology and Symbols	225	(3)
Additional Derivation Rules	228	(1)
Replacement Rules	229	(1)
Avoiding Reiteration	230	(1)
Joint Denial and the Sheffer Stroke	231	(2)
Consistency and Truth Trees	233	(6)
INDEX
Technical Terms	239