Methods of LogicThis widely used textbook of modern formal logic now offers a number of new features. Incorporating updated notations, selective answers to exercises, expanded treatment of natural deduction, and new discussions of predicate-functor logic and the affinities between higher set theory and the elementary logic of terms, W. V. Quine's new edition will serve admirably for both classroom and independent use. |
Contents
Introduction | 1 |
TRUTH FUNCTIONS | 7 |
Negation Conjunction and Alternation | 9 |
Truth Functions 3 The Conditional 16 | 26 |
Grouping | 27 |
TruthValue Analysis | 33 |
Consistency and Validity | 40 |
Implication | 45 |
Substitution | 160 |
Pure Existentials | 182 |
The Main Method | 190 |
Application | 195 |
Completeness | 203 |
Löwenheims Theorem | 209 |
Decisions and the Undecidable | 213 |
Functional Normal Forms | 219 |
Words into Symbols | 53 |
Equivalence | 60 |
Alternational Normal Schemata | 68 |
Simplification | 74 |
Duality | 79 |
Axioms | 85 |
GENERAL TERMS AND QUANTIFIERS | 91 |
Categorical Statements | 93 |
Venns Diagrams | 98 |
Syllogisms | 102 |
Limits of These Methods | 109 |
Boolean Schemata | 114 |
Tests of Validity | 121 |
Some Boolean Incidentals | 128 |
The Bound Variable | 132 |
Quantification | 136 |
Prenexity and Purity | 148 |
Validity Again | 154 |
Herbrands Method | 224 |
Other Methods for Validity | 232 |
Deduction | 237 |
Soundness | 245 |
Deductive Strategy | 248 |
GLIMPSES BEYOND | 257 |
Singular Terms | 259 |
Identity | 268 |
Descriptions | 274 |
Elimination of Singular Terms | 278 |
Elimination of Variables | 283 |
Classes | 288 |
Number | 294 |
Partial Answers to Exercises | 305 |
| 320 | |
| 327 | |
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Common terms and phrases
3x Fx alternational normal schema antecedent axioms biconditional Boolean existence schemata Boolean statement Boolean term schemata Cerberus clause comes out true component compound conclusion conjunctional normal form consistency decision procedure deduction Diagram dual duality equivalent example EXERCISES existential conditionals existential quantifiers F are G fell swoop free variable functional normal forms functors HISTORICAL NOTE inconsistent interpretation logic main method means modus ponens monadic negation notation objects ordinary language p v q pq v pr preceding chapter premises prenex form proof procedure quantificational schemata relettering rendered rules of inference rules of passage S₁ set theory singular terms statement schema substitution syllogism term abstraction term letters term schema theorem tion truth functions truth value truth-functional schemata truth-value analysis universal quantifiers valid schemata Vx Fx Vx(Fx