The Many Worlds of Logic / Edition 2

by Paul Herrick

Overview

With clear explanations and many examples drawn right out of day-to-day life, Paul Herrick untangles the complexities of logical theory in The Many Worlds of Logic. This new edition adds new chapters on informal logic and critical thinking. It also breaks out longer chapters from the previous edition into shorter, more focused chapters. Herrick has added many new explanations and examples; in each chapter, he covers the fundamentals completely before moving on to more challenging areas.

Features
* Difficult terms are highlighted and explained carefully
* End-of-chapter glossaries help students remember important terms
* Hundreds of examples demonstrate the application of concepts
* Hundreds of exercises help students learn logic by actually doing it
* Truth-trees in an appendix help students go beyond the basics

Product Details

ISBN-13:	9780195155037
Publisher:	Oxford University Press
Publication date:	05/28/1999
Edition description:	REV
Pages:	690
Product dimensions:	9.52(w) x 6.60(h) x 1.42(d)

About the Author

Shoreline Community College

Table of Contents

To the InstructorTo the StudentAcknowledgementsChapter 1 FundamentalsRecognizing ArgumentsSome Typical Conclusion IndicatorsSome Typical Premise IndicatorsDistinguishing Sentences and StatementsTwo General Categories of Argument: Deductive and Inductive ArgumentsDeductive and Inductive Indicator WordsEvaluating Inductive Arguments: The Strong, the Weak, and the Inductively SoundEvaluating Deductive Arguments: The Valid, the Invalid, and the Dedictively SoundDeciding Whether an Argument is Valid or InvalidConsistency and InconsistencyImplicationLogical EquivalenceNecessityIdealsAppendix: Some Logical PuzzlesGlossaryPART I TRUTH-FUNCTIONAL LOGICChapter 2 Introductory Truth-Functional LogicSimple and Compound Sentences, Sentence Operators, and the ConjunctionNegationDisjunctionTruth-Functions and Truth-Functional Compound SentencesConditional SentencesBiconditional SentencesGlossaryChapter 3 Translating English into Logical SymbolsSymbolizing Sentences Containing More than One OperatorThrowing the Tilde into the MixFrom And to Or and Back Again—With a Few Nots Thrown InSome General Hints on SymbolizingTranslating Conditionals and BiconditionalsSymbolizing Necessary and Sufficient ConditionsGlossaryChapter 4 Our New Language Gets a Name and a Formal SyntaxThe Language TLHow to Calculate the Truth-Value of the Whole from the Values of the PartsGlossaryChapter 5 Truth-Table AnalysisConstructing a Truth-Table for a FormulaEight-Row TablesHow to Make Your Own Tautology Detector Using Just Paper and PencilHow to Make an Inexpensive Contradiction Detector for Home or OfficeThe Contingency Detector: Don't Leave Home without ItTesting an Argument for ValidityShowing an Argument Invalid with a Partial Truth-TableTesting a Pair of Sentences for EquivalencesGlossaryChapter 6 The Concept of Logical FormSentence FormsArgument FormsThe Disjunctive Syllogism FormThe Modus Ponens FormThe Modus Tollens FormThe Hypothetical Syllogism FormValid Argument FormsInvalid Argument FormsConcluding CommentsAppendix: Contradictory and Tautological Sentence FormsGlossaryChapter 7 Truth-Functional Natural DeductionThe Disjunctive Syllogism RuleThe Modus Ponens RuleThe Modus Tollens RuleThe Hypothetical Syllogism RuleProving that a Conclusion Validly FollowsThe System TDProofsGlossaryChapter 8 Four More Inference RulesThe Simplification RuleThe Conjunction RuleThe Addition RuleThe Constructive Dilemma RuleSome Unsolicited Advice on Learning to Construct ProofsProof StrategiesSome Additional Suggestions Concerning StrategyAppendix: Some Common Deduction ErrorsChapter 9 Indirect Proofs and Conditional ProofsThe Indirect Proof RuleThe Conditional Proof RuleNested ProofsProving Sentences TautologicalThe Law of NoncontradictionGlossaryChapter 10 Replacement RulesThe Commutative RuleThe Associative RuleThe Double Negation RuleDeMorgan's RuleThe Distribution RuleFive More Replacement RulesThe Transposition RuleThe Implication RuleThe Exportation RuleThe Tautology RuleThe Equivalence RuleAre Replacement Rules Worth the Bother? GlossaryChapter 11 Indirect and Conditional Proofs with Replacement RulesIndirect Proofs with Replacement RulesConditional Proof with Replacement RulesProving TautologiesGlossaryPART II TWO INFORMAL TOPICSChapter 12 DefinitionThe Purposes of DefinitionFive Types of DefinitionTwo Types of MeaningConstructing a Definition: TechniquesRules for Intensional DefinitionsGlossaryChapter 13 Informal FallaciesFallacies of No EvidenceFallacies of Little EvidenceFallacies of LanguageGlossaryA Summary of the FallaciesPART III ARISTOTELIAN CATEGORICAL LOGICChapter 14 The Logic of Categorical StatementsCategorical SentencesQuality and QuantityThe Traditional Square of OppositionTranslating English Sentences into Standard Categorical FormsEquivalence Rules for Aristotelian LogicDropping the Assumption of Existential ImportThe Modern Square of OppositionGlossaryChapter 15 Categorical SyllogismsLogical FormVenn DiagramsTesting a Categorical Syllogism for Validity with Venn DiagramsDiagramming Aristotelian Categorical SyllogismsDiagramming from the Boolean StandpointThe SoritesTesting a Sorites with Venn DiagramsEnthememesRefutation by Logical AnalogyAppendix: Rules for Evaluating Categorical SyllogismsPART IV MODERN QUANTIFICATIONAL LOGICChapter 16 Quantificational Logic I: The Language QLTwo Types of SentencesGeneral SentencesA Syntax for our New LanguageThe Vocabulary of QLSymbolizing General SentencesCategorical SentencesThe Old "Quantifier Switch" TrickSwitching Quantifiers on CategoricalsSymbolizing Complicated General SentencesDenying ExistenceThe Only Way to GoWhat is a Cat-Dog? GlossaryChapter 17 The Language of Quantificational Logic II: RelationsSentences with a Quantifier-Dyadic Predicate ComboAny and EveryReflexive SentencesSentences with Overlapping Quantifiers"What Are You Talking About?" The Universe of DiscourseDean Martin, Universal Love, and a Summary of Logic RelationsTo Be or Not To Be: The Logic of IdentityThe Identity SignAppendix: Properties of RelationsGlossaryChapter 18 Proofs with Monadic PredicatesThe Universal Instantiation RuleExistential GeneralizationExistential InstantiationMemories of Geometry Class: Universal GeneralizationOne New Replacement Rule: Quantifier ExchangeNaming Our SystemGlossaryChapter 19 Interpretations, Invalidity, and SemanticsInterpretations of Multiply Quantified SentencesUsing Interpretations to Show InvaliditySemanticsThe Monadic Predicate TestGlossaryChapter 20 Conditional and Indirect Quantifier ProofsAdding Truth-Functional Replacement Rules to the MixPutting QD on a Diet: A Reduced Set of Quantifier RulesProving Logical TruthsChapter 21 Proofs with Overlapping QuantifiersProperties of RelationsChapter 22 Proofs with IdentityProperties of the Identity RelationGlossaryPART V MODAL LOGICChapter 23 Introductory Modal LogicTo Shave or Not to Shave: That Is the QuestionFive Modal PropertiesPossible Truths, Possible Falsehoods, ContingenciesNecessary TruthsNecessary FalsehoodsPutting Statements into SymbolsTranslating English Sentences into Modal SymbolsA Name and Syntax for our Modal LanguageThe Vocabulary for MLThe Grammar for MLLinking Modal Operators"It Ain't Necessarily So," Or, Trading a Diamond for a Box and a Box for a DiamondModal Operators Need Scope, TooModal RelationsScopes of the Dyadic Modal OperatorsSymbolizing with Dyadic OperatorsModal Operators Are Not Truth-FunctionalAppendix: There's Nothing New under the SunGlossaryChapter 24 Modal Logic: Methods of ProofFive Modal PrinciplesSix Inference RulesThe Possibility to Necessity RuleThe Necessitation RuleFour Modal Replacement RulesValidity in S5Proving Theorems of S5Another Inference Rule: The Tautology Necessitation RuleAppendix 1: Putting an S5 Formula on a Diet: S5 ReductionAppendix 2: The Modal FallacyGlossaryPART VI INDUCTIONChapter 25 Inductive ReasoningAnalogical ReasoningEvaluating Analogical ArgumentsAnalogies as ModelsEnumerative InductionStatistical Inductive GeneralizationInference to the Best ExplanationWhat Makes One Explanation Better than Another? GlossaryChapter 26 Scientific ReasoningScientific ReasoningComments on the StepsConfirming and Disconfirming Scientific HypothesesThe Confirmation of a Scientific HypothesisThe Disconfirmation of a Scientific HypothesisThe Fact of the CrossWhat Makes One Hypothesis Better than Another? Case StudiesCause and Effect and Mill's MethodCause and EffectMill's Method of AgreementMill's Method of DifferenceThe Joint Method of Agreement and DifferenceMill's Method of ResiduesMill's Method of Concomitant VariationGlossaryAppendices1. Truth-Trees2. TruthAnswers to Selected ExercisesIndex