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Preface to the Eleventh Edition | p. ix |
Preface to the Tenth Edition | p. xi |
Introduction | p. 1 |
The Elements of an Argument | p. 1 |
Deduction and Induction | p. 5 |
Deductive Argument Forms | p. 7 |
Truth and Validity | p. 8 |
Soundness | p. 11 |
Consistency | p. 12 |
Contexts of Discovery and Justification | p. 14 |
The Plan of This Book | p. 14 |
Key Terms | p. 16 |
Sentential Logic | p. 17 |
Symbolizing in Sentential Logic | p. 19 |
Atomic and Compound Sentences | p. 20 |
Truth-Functions | p. 21 |
Conjunctions | p. 21 |
Non-Truth-Functional Connectives | p. 25 |
Variables and Constants | p. 25 |
Negations | p. 27 |
Parentheses and Brackets | p. 28 |
Use and Mention | p. 29 |
Disjunctions | p. 30 |
"Not Both" and "Neither . . . Nor" | p. 33 |
Material Conditionals | p. 35 |
Material Biconditionals | p. 38 |
"Only If" and "Unless" | p. 40 |
Symbolizing Complex Sentences | p. 41 |
Alternative Sentential Logic Symbols | p. 48 |
Key Terms | p. 50 |
Truth Tables | p. 53 |
Computing Truth-Values | p. 53 |
Logical Form | p. 58 |
Tautologies, Contradictions, and Contingent Sentences | p. 63 |
Logical Equivalences | p. 69 |
Truth Table Test of Validity | p. 70 |
Truth Table Test of Consistency | p. 73 |
Validity and Consistency | p. 74 |
The Short Truth Table Test for Invalidity | p. 76 |
The Short Truth Table Test for Consistency | p. 80 |
A Method of Justification for the Truth Tables | p. 81 |
Key Terms | p. 85 |
Proofs | p. 86 |
Argument Forms | p. 86 |
The Method of Proof: Modus Ponens and Modus Tollens | p. 88 |
Disjunctive Syllogism and Hypothetical Syllogism | p. 91 |
Simplification and Conjunction | p. 93 |
Addition and Constructive Dilemma | p. 94 |
Principles of Strategy | p. 97 |
Double Negation and DeMorgan's Theorem | p. 103 |
Commutation, Association, and Distribution | p. 106 |
Contraposition, Implication, and Exportation | p. 107 |
Tautology and Equivalence | p. 107 |
More Principles of Strategy | p. 111 |
Common Errors in Problem Solving | p. 115 |
Key Terms | p. 122 |
Conditional and Indirect Proofs | p. 123 |
Conditional Proofs | p. 123 |
Indirect Proofs | p. 132 |
Strategy Hints for Using CP and IP | p. 137 |
Zero-Premise Deductions | p. 138 |
Proving Premises Inconsistent | p. 139 |
Adding Valid Argument Forms | p. 141 |
An Alternative to Conditional Proof? | p. 142 |
The Completeness and Soundness of Sentential Logic | p. 144 |
Introduction and Elimination Rules | p. 146 |
Key Terms | p. 149 |
Sentential Logic Truth Trees | p. 151 |
The Sentential Logic Truth Tree Method | p. 151 |
The Truth Tree Rules | p. 152 |
Details of Tree Construction | p. 154 |
Normal Forms and Trees | p. 160 |
Constructing Tree Rules for Any Function | p. 161 |
Key Terms | p. 163 |
Predicate Logic | p. 165 |
Predicate Logic Symbolization | p. 167 |
Individuals and Properties | p. 167 |
Quantifiers and Free Variables | p. 171 |
Universal Quantifiers | p. 172 |
Existential Quantifiers | p. 177 |
Basic Predicate Logic Symbolizations | p. 178 |
The Square of Opposition | p. 180 |
Common Pitfalls in Symbolizing with Quantifiers | p. 180 |
Expansions | p. 183 |
Symbolizing "Only," "None but," and "Unless" | p. 186 |
Key Terms | p. 190 |
Predicate Logic Semantics | p. 191 |
Interpretations in Predicate Logic | p. 191 |
Proving Invalidity | p. 193 |
Using Expansions to Prove Invalidity | p. 196 |
Consistency in Predicate Logic | p. 197 |
Validity and Inconsistency in Predicate Logic | p. 198 |
Key Terms | p. 199 |
Predicate Logic Proofs | p. 200 |
Proving Validity | p. 200 |
The Four Quantifier Rules | p. 202 |
The Five Main Restrictions | p. 209 |
Precise Formulation of the Four Quantifier Rules | p. 213 |
Mastering the Four Quantifier Rules | p. 216 |
Quantifier Negation | p. 220 |
Key Term | p. 225 |
Relational Predicate Logic | p. 226 |
Relational Predicates | p. 226 |
Symbolizations Containing Overlapping Quantifiers | p. 229 |
Expansions and Overlapping Quantifiers | p. 229 |
Places and Times | p. 234 |
Symbolizing "Someone," "Somewhere," "Sometime," and So On | p. 235 |
Invalidity and Consistency in Relational Predicate Logic | p. 240 |
Relational Predicate Logic Proofs | p. 241 |
Strategy for Relational Predicate Logic Proofs | p. 248 |
Theorems and Inconsistency in Predicate Logic | p. 250 |
Predicate Logic Metatheory | p. 253 |
A Simpler Set of Quantifier Rules | p. 254 |
Rationale Behind the Precise Formulation of the Four Quantifier Rules | p. 257 |
Cases Involving the Five Major Restrictions | p. 257 |
One-to-One Correspondence Matters | p. 260 |
Accidentally Bound Variables and Miscellaneous Cases | p. 264 |
Predicate Logic Proofs with Flagged Constants | p. 269 |
Predicate Logic Truth Trees | p. 272 |
Introductory Remarks | p. 272 |
General Features of the Method | p. 273 |
Specific Examples of the Method | p. 273 |
Some Advantages of the Trees | p. 278 |
Example of an Invalid Argument with at Least One Open Path | p. 279 |
Metatheoretic Results | p. 280 |
Strategy and Accounting | p. 283 |
Key Terms | p. 285 |
Identity and Philosophical Problems of Symbolic Logic | p. 286 |
Identity | p. 286 |
Definite Descriptions | p. 292 |
Properties of Relations | p. 294 |
Higher-Order Logics | p. 297 |
Limitations of Predicate Logic | p. 299 |
Philosophical Problems | p. 303 |
Logical Paradoxes | p. 310 |
Key Terms | p. 317 |
Syllogistic Logic | p. 319 |
Categorical Propositions | p. 322 |
Existential Import | p. 322 |
The Square of Opposition | p. 323 |
Conversion, Obversion, Contraposition | p. 326 |
Syllogistic Logic - Not Assuming Existential Import | p. 329 |
Venn Diagrams | p. 332 |
Syllogisms | p. 334 |
Determining Syllogism Validity | p. 336 |
Venn Diagram Proofs of Validity or Invalidity | p. 337 |
Five Rules for Determining Validity or Invalidity | p. 342 |
Syllogistics Extended | p. 345 |
Enthymemes | p. 348 |
Sorites | p. 349 |
Technical Restrictions and Limitations; Modern Logic and Syllogistic Logic Compared | p. 351 |
Key Terms | p. 355 |
Answers to Even-Numbered Exercise Items | p. 358 |
Bibliography | p. 419 |
Special Symbols | p. 421 |
Index | p. 423 |
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