| 0 Preface?
| vii
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| Organization and New Features
| viii
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| Traditional areas of Logic
| ix
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| Part I — Reasoning and language
| 1
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| 1 Truth and validity
| 2
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| 1.1 Arguments?
| 3
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| 1.2 Recognizing arguments
| 6
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| 1.3 Good arguments
| 17
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| 1.4 Reliability
| 20
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| 1.5 Implication and equivalence
| 24
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| 1.6 Logical properties of sentences
| 29
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| 1.6.1 Contingent sentences
| 29
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| 1.6.2 Tautological sentences
| 29
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| 1.6.3 Contradictory sentences
| 30
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| 1.6.4 Satisfiable sentences
| 30
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| 2 Evidence and relevance
| 37
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| 2.0.1 Evidence violation
|
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| 2.0.2 Relevance violation
|
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| 2.1 Begging the question
| 38
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| 2.2 Complex questions
| 43
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| 2.3 Relevance—refutations
| 46
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| 2.3.1 Abusive Ad Hominem
| 47
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| 2.3.2 Circumstantial Ad Hominem
| 48
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| 2.3.3 Tu Quoque
| 50
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| 2.4 Relevance—confusing the issue
| 56
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| 2.4.1 Red Herrings
| 57
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| 2.4.2 Straw Man
| 58
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| 3 Grounding?
| 62
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| 3.1 Appeals to emotion
| 64
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| 3.1.1 Appeal to the People (or Gallery)
| 65
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| 3.2 Practical Fallacies
| 69
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| 3.2.1 Appeal to Common Practice
| 70
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| 3.3 Superficiality
| 78
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| 3.3.1 Appeal to Ignorance
| 78
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| 3.1.2 Appeal to Authority
| 79
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| 3.1.3 Incomplete Enumeration
| 82
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| 3.1.4 Accident
| 83
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| 4 Meaning
| 90
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| 4.1 Equivocation
| 90
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| 4.2 Amphiboly
| 93
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| 4.3 Accent
| 99
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| 4.4 Composition and division
| 101
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| 4.5 Traditional criteria for definitions
| 104
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| Part II Sentential Logic
| 113
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| 5 Sentences
| 114
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| 5.1 Sentence connectives
| 114
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| 5.2 A sentential language
| 117
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| 5.3 Truth functions
| 121
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| 5.4 Symbolization
| 125
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| 6 Truth tables
| 139
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| 6.1 Truth table for formulas
| 139
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| 6.2 Other uses of truth tables
| 145
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| 7 Semantic tableaux
| 155
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| 7.1 Rules for Negation, Conjunction and Disjunction
| 161
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| 7.1.1 Negation
| 161
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| 7.1.2 Conjunction
| 162
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| 7.1.3 Disjunction
| 163
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| 7.1.4 Policies
| 164
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| 7.2 Rules for the conditional and biconditional
| 167
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| 7.2.1 →L (Conditional Left)
| 167
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| 7.2.2 →R (Conditional Right)
| 168
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| 7.2.3 ↔L (Biconditional Left)
| 168
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| 7.2.4 ↔R (Biconditional Right)
| 168
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| 7.3 Decision procedures
| 172
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| 7.3.1 Test for argument form validity (and implication)
| 173
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| 7.3.2 Test for equivalence
| 175
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| 7.3.3 Test for logical truth
| 176
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| 7.3.4 Test for contradiction or satisfiability
| 176
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| 8 Deduction
| 186
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| 8.1 Proofs
| 186
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| 8.1.1 Rules of inference
| 187
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| 8.1.2 Proof format
| 187
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| 8.1.2.1 Proof lines
| 187
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| 8.1.2.2 Proof
| 188
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| 8.1.2.3 Assumption
| 188
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| 8.2 Conjunction and negation rules
| 188
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| 8.2.1 Conjunction
| 188
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| 8.2.1.1 Simplification (S)
| 189
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| 8.2.1.2 Conjunction (C)
| 190
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| 8.2.1.3 Consequent Conjunction (CC)
| 191
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| 8.2.2 Negation
| 191
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| 8.2.2.1 Double negation (DN)
| 192
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| 8.2.3 Replacement
| 192
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| 8.3 Conditional and biconditional rules
| 193
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| 8.3.1 The conditional
| 193
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| 8.3.1.1 Modus ponens (MP)
| 194
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| 8.3.1.2 Self-implication (SI)
| 194
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| 8.3.2 The biconditional
| 195
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| 8.3.2.1 Biconditional (B)
| 195
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| 8.4 Disjunction rules
| 197
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| 8.4.1.1 Addition (Ad)
| 197
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| 8.4.1.2 Constructive dilemma (CD)
| 198
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| 8.4.1.3 Material conditional
|
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| 8.4.1.4 Commutativity of Disjunction (Cm)
| 199
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| 8.4.1.5 Associativity of Disjunction (As)
| 199
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| 8.5 Rules of Definition
| 201
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| 8.5.1 De Morgan’s Laws
| 201
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| 8.5.1.1 De Morgan’s Law #1 (DM)
| 202
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| 8.5.1.2 De Morgan’s Law #2 (DM)
| 202
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| 8.5.2 Rules applying only to entire formulas
| 203
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| 8.5.2.1 Assumption
| 203
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| 8.5.2.2 Simplification (S)
| 203
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| 8.5.2.3 Conjunction (C)
| 203
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| 8.5.2.4 Consequent conjunction (CC)
| 203
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| 8.5.2.5 Modus ponens (MP)
| 204
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| 8.5.2.6 Self-implication (SI)
| 204
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| 8.5.2.7 Addition (Ad)
| 204
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| 8.5.2.8 Constructive dilemma (CD)
| 204
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| 8.5.3 Invertible Rules
|
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| 8.5.3.1 Double negation (DN)
| 204
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| 8.5.3.2 Biconditional (B)
| 204
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| 8.5.3.3 Commutativity of disjunction (Cm)
| 205
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| 8.5.3.4 Associativity of disjunction
| 205
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| 8.5.3.5 De Morgan’s Law # 1 (DM)
| 205
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| 8.5.3.6 De Morgan’s Law # 2 (DM)
| 205
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| 8.5.3.7 Material conditional (MC)
| 205
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| 8.6 Derived rules
| 208
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| 8.6.1 Negations of complex formulas
| 208
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| 8.6.1.1 Negated conditional (NC)
| 209
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| 8.6.1.2 Negated biconditional (NB)
| 209
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| 8.6.2 Order and grouping
|
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| 8.6.2.1 Commutativity of conjunction (Cm)
| 210
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| 8.6.2.2 Associativity of conjunction (As)
| 210
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| 8.6.2.3 Idempotence (I)
| 211
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| 8.6.3 Abbreviations
| 211
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| 8.6.3.1 Modus tollens (MT)
| 211
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| 8.6.3.2 Hypothetical syllogisms (HS)
| 213
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| 8.6.3.3 Transposition (Tr)
| 213
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| 8.6.3.4 Biconditional exploitation (BE)
| 214
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| 8.6.3.5 Disjunctive syllogism (DS)
| 215
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| 8.6.3.6 Distribution (D)
| 215
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| 8.6.3.7 Weakening (W)
| 216
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| 8.6.3.8 Contradiction (!)
| 216
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| 8.6.4 Rules applying only to entire formulas
|
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| 8.6.4.1 Modus Tollens (MT)
| 216
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| 8.6.4.2 Hypothetical Syllogism (HS)
| 217
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| 8.6.4.3 Biconditional Exploitation (BE)
| 217
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| 8.6.4.4 Disjunctive Syllogism
| 217
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| 8.6.4.5 Weakening (W)
| 217
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| 8.6.4.6 Contradiction (!)
| 217
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| 8.6.5 Invertible Rules
| 218
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| 8.6.5.1 Negated Conditional (NC)
| 218
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| 8.6.5.2 Negated Biconditional (NB)
| 218
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| 8.6.5.3 Commutativity of Conjunction (Cm)
| 218
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| 8.6.5.4 Associativity of Conjunction
| 218
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| 8.6.5.5 Indempotence (I)
| 218
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| 8.6.5.6 Transposition (Tr)
| 218
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| 8.6.5.7 Distribution (D)
| 219
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| 8.6.6 Strategy
| 219
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| 8.7 Indirect proof
| 225
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| 8.7.1.1 Indirect Proof (Hypothetical)
| 226
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| 8.7.1.2 Indirect Proof (Categorical)
| 226
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| Part III Predicate Logic
| 229
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| 9 Syllogisms
| 230
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| 9.0 Categorical Syllogism
| 231
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| 9.1 Categorical sentences
| 236
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| 9.2 Diagramming categorical sentence forms
| 242
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| 9.3 Immediate inference
| 253
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| 9.4 Syllogisms
| 263
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| 9.5 Rules for validity
| 276
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| 9.6 Expanding the Aristotelian language
| 276
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| 10 Quantifiers
| 289
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| 10.1 Constants and quantifiers
| 290
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| 10.2 Categorical sentence forms
| 294
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| 10.3 Polyadic predicates
| 298
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| 10.4 The language QL
| 303
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| 11 Symbolization
| 311
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| 11.1 Noun phrases
| 311
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| 11.2 Verb phrases
| 322
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| 11.3 Definitions
| 331
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| 12 Quantified tableaux
| 340
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| 12.1 Quantifier tableaux rules
| 340
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| 12.2 Strategies
| 344
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| 13 Quantified deduction
| 358
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| 13.1 Deduction rules for quantifiers
| 358
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| 13.2 Universal generalization
| 366
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| 13.3 Formulas with overlapping quantifiers
| 372
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| 13.4 Quantifiers and connectives
| 376
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| Part IV Inductive Reasoning
| 393
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| 14 Generalizations
| 394
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| 14.1 Inductive reliability
| 395
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| 14.2 Enumeration
| 398
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| 14.3 Evaluating enumerations
| 400
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| 14.4 Statistical generalizations
| 403
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| 14.5 Analogies
| 412
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| 15 Causes
| 425
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| 15.1 Kinds of causes
| 425
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| 15.2 Agreement and difference
| 431
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| 15.3 Residues and concomitant variation
| 440
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| 15.4 Causal fallacies
| 447
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| 16 Explanations
| 450
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| 16.1 Explanations and hypothetical reasoning
| 450
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| 16.2 Scientific theories
| 458
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| 16.3 Evaluating explanations
| 464
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| [PART V] DEDUCTION STYLES
| 472
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| APPENDIX I DEDUCTION: STYLE TWO
| 472
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| A: Sentential Logic
| 472
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| A.1 Proofs
| 472
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| A.2 Conjunction and Negation Rules
| 475
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| A.3 Conditional and Biconditional Rules
| 481
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| A.4 Disjunction Rules
| 484
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| A.5 Derived Rules
| 486
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| B: Adding Quantifiers
| 501
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| B.1 Deduction Rules for Quantifiers
| 501
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| B.2 Universal Generalization
| 506
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| B.3 Formulas with Overlapping Quantifiers
| 508
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| B.4 Derived Rules for Quantifiers
| 512
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| APPENDIX II DEDUCTION: STYLE THREE
| 518
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| A: Sentential Logic
| 518
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| A.1 Proofs
| 518
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| A.2 Conjunction and Negation Rules
| 522
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| A.3 Conditional and Biconditional Rules
| 529
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| A.4 Disjunction Rules
| 533
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| A.5 Derived Rules
| 535
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| B: Adding Quantifiers
| 551
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| B.1 Deduction Rules for Quantifiers
| 551
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| B.2 Universal Proof
| 556
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| B.3 Derived Rules for Quantifiers
| 557
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| Bibliography
| 563
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| Answers to Selected Problems
| 565
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| Index
| 699
|
