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Logic and philosophy : a modern introduction

Author: Alan Hausman; Howard Kahane; Paul Tidman
Publisher: Australia ; Boston, MA : Thomson Wadsworth/Cengage learning, ©2010.
Edition/Format:   Book : English : 11th edView all editions and formats
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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 p. : ill. ; 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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schema:description"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 --"@en
schema:description"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 --"@en
schema:description"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 --"@en
schema:description"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 --"@en
schema:description"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 --"@en
schema:description"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 --"@en
schema:description"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 --"@en
schema:description"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 --"@en
schema:description"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 --"@en
schema:description"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 --"@en
schema:description"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 --"@en
schema:description"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 --"@en
schema:description"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."@en
schema:description"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 --"@en
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