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| Document Type: | Book |
|---|---|
| All Authors / Contributors: |
Alan Hausman; Howard Kahane; Paul Tidman |
| ISBN: | 9780495601586 0495601586 |
| OCLC Number: | 259265754 |
| Description: | xiii, 434 pages : illustrations ; 24 cm |
| Contents: | ch. One: Introduction -- 1. The elements of an argument -- 2. Deduction and induction -- 3. Deductive argument forms -- 4. Truth and validity -- 5. Soundness -- 6. Consistency -- 7. Contexts of discovery and justification -- 8. The plan of this book -- Key terms. pt. I: Sentential logic -- ch. Two: Symbolizing in sentential logic -- 1. Atomic and compound sentences -- 2. Truth-functions -- 3. Conjunctions -- 4. Non-truth-functional connectives -- 5. Variables and constants -- 6. Negations -- 7. Parentheses and brackets -- 8. Use and mention -- 9. Disjunctions -- 10. "Not both" and "neither ... nor" -- 11. Material conditionals -- 12. Material biconditionals -- 13. "Only if" and "unless" -- 14. Symbolizing complex sentences -- 15. Alternative sentential logic symbols -- Key terms. ch. Three: Truth tables -- 1. Computing truth-values -- 2. Logical form -- 3. Tautologies, contradictions, and contingent sentences -- 4. Logical equivalences -- 5. Truth table test of validity -- 6. Truth table test of consistency -- 7. Validity and consistency -- 8. The short truth table test for invalidity -- 9. The short truth table test for consistency -- 10. A method of justification for the truth tables -- Key terms. ch. Four: Proofs -- 1. Argument forms -- 2. The method of proof: modus ponens and modus tollens -- 3. Disjunctive syllogism and hypothetical syllogism -- 4. Simplification and conjunction -- 5. Addition and constructive dilemma -- 6. Principles of strategy -- 7. Double negation and DeMorgan's Theorem -- 8. Commutation, association and distribution -- 9. Contraposition, implication, and exportation -- 10. Tautology and equivalence -- 11. More principles of strategy -- 12. Common errors in problem solving -- Key terms. ch. Five: Conditional and indirect proofs -- 1. Conditional proofs -- 2. Indirect proofs -- 3. Strategy hints for using CP and IP -- 4. Zero-premise deductions -- 5. Proving premises inconsistent -- 6. Adding valid argument forms -- 7. An alternative to conditional proof? -- 8. The completeness and soundness of sentential logic -- 9. Introduction and elimination rules -- Key terms. ch. Six: Sentential logic truth trees -- 1. The sentential logic truth tree method -- 2. The truth tree rules -- 3. Details of tree construction -- 4. Normal forms and trees -- 5. Constructing tree rules for any function -- Key terms. pt. II: Predicate logic -- ch. Seven: Predicate logic symbolization -- 1. Individuals and properties -- 2. Quantifiers and free variables -- 3. Universal quantifiers -- 4. Existential quantifiers -- 5. Basic predicate logic symbolizations -- 6. The square of opposition -- 7. Common pitfalls in symbolizing with quantifiers -- 8. Expansions -- 9. Symbolizing "only," "none but," and "unless" -- Key terms. ch. Eight: Predicate logic semantics -- 1. Interpretations in predicate logic -- 2. Proving invalidity -- 3. Using expansions to prove invalidity -- 4. Consistency in predicate logic -- 5. Validity and inconsistency in predicate logic -- Key terms. ch. Nine: Predicate logic proofs -- 1. Proving validity -- 2. The four quantifier rules -- 3. The five main restrictions -- 4. Precise formulation of the four quantifier rules -- 5. Mastering the four quantifier rules -- 6. Quantifier negation -- Key terms. ch. Ten: Relational predicate logic -- 1. Relational predicates -- 2. Symbolizations containing overlapping quantifiers -- 3. Expansions and overlapping quantifiers -- 4. Places and times -- 5. Symbolizing "someone," "somewhere," "sometime," and so on -- 6. Invalidity and consistency in relational predicate logic -- 7. Relational predicate logic proofs -- 8. Strategy for relational predicate logic proofs -- 9. Theorems and inconsistency in predicate logic -- 10. Predicate logic metatheory -- 1. A simpler set of quantifier rules. ch. Eleven: Rationale behind the precise formulation of the four quantifier rules -- 1. Cases involving the five major restrictions -- 2. One-to-one correspondence matters -- 3. Accidentally bound variables and miscellaneous cases -- 4. Predicate logic proofs with flagged constants. ch. Twelve: Predicate logic truth trees -- 1. Introductory remarks -- 2. General features of the method -- 3. Specific examples of the method -- 4. Some advantages of the trees-- 5. Example of an invalid argument with at least one open path -- 6. Metatheoretic results -- 7. Strategy and accounting -- Key terms. ch. Thirteen: Identity and philosophical problems of symbolic logic -- 1. Identity -- 2. Definite descriptions -- 3. Properties of relations -- 4. Higher-order logics -- 5. Limitations of predicate logic -- 6. Philosophical problems -- 7. Logical paradoxes -- Key terms. ch. Fourteen: Syllogistic logic -- 1. Categorical propositions -- 2. Existential import -- 3. The square of opposition -- 4. Conversion, obversion, contraposition -- 5. Syllogistic logic: not assuming existential import -- 6. Venn Diagrams -- 7. Syllogisms -- 8. Determining syllogism validity -- 9. Venn Diagram proofs of validity or invalidity -- 10. Five rules for determining validity or invalidity -- 11. Syllogistics extended -- 12. Enthymemes -- 13. Sorites -- 14. Technical restrictions and limitations -- Moder logic and syllogistic logic compared -- Key terms. |
| Responsibility: | Alan Hausman, Howard Kahane, Paul Tidman. |
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