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The Many Worlds of Logic

Second Edition

Paul Herrick

Publication Date - May 1999

ISBN: 9780195155037

688 pages
6-1/2 x 9-1/4 inches

Retail Price to Students: $114.95


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.

* 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

Previous Publication Date(s)

January 1994

Table of Contents

    To the Instructor
    To the Student
    Chapter 1 Fundamentals
    Recognizing Arguments
    Some Typical Conclusion Indicators
    Some Typical Premise Indicators
    Distinguishing Sentences and Statements
    Two General Categories of Argument: Deductive and Inductive Arguments
    Deductive and Inductive Indicator Words
    Evaluating Inductive Arguments: The Strong, the Weak, and the Inductively Sound
    Evaluating Deductive Arguments: The Valid, the Invalid, and the Dedictively Sound
    Deciding Whether an Argument is Valid or Invalid
    Consistency and Inconsistency
    Logical Equivalence
    Appendix: Some Logical Puzzles
    Chapter 2 Introductory Truth-Functional Logic
    Simple and Compound Sentences, Sentence Operators, and the Conjunction
    Truth-Functions and Truth-Functional Compound Sentences
    Conditional Sentences
    Biconditional Sentences
    Chapter 3 Translating English into Logical Symbols
    Symbolizing Sentences Containing More than One Operator
    Throwing the Tilde into the Mix
    From And to Or and Back Again--With a Few Nots Thrown In
    Some General Hints on Symbolizing
    Translating Conditionals and Biconditionals
    Symbolizing Necessary and Sufficient Conditions
    Chapter 4 Our New Language Gets a Name and a Formal Syntax
    The Language TL
    How to Calculate the Truth-Value of the Whole from the Values of the Parts
    Chapter 5 Truth-Table Analysis
    Constructing a Truth-Table for a Formula
    Eight-Row Tables
    How to Make Your Own Tautology Detector Using Just Paper and Pencil
    How to Make an Inexpensive Contradiction Detector for Home or Office
    The Contingency Detector: Don't Leave Home without It
    Testing an Argument for Validity
    Showing an Argument Invalid with a Partial Truth-Table
    Testing a Pair of Sentences for Equivalences
    Chapter 6 The Concept of Logical Form
    Sentence Forms
    Argument Forms
    The Disjunctive Syllogism Form
    The Modus Ponens Form
    The Modus Tollens Form
    The Hypothetical Syllogism Form
    Valid Argument Forms
    Invalid Argument Forms
    Concluding Comments
    Appendix: Contradictory and Tautological Sentence Forms
    Chapter 7 Truth-Functional Natural Deduction
    The Disjunctive Syllogism Rule
    The Modus Ponens Rule
    The Modus Tollens Rule
    The Hypothetical Syllogism Rule
    Proving that a Conclusion Validly Follows
    The System TD
    Chapter 8 Four More Inference Rules
    The Simplification Rule
    The Conjunction Rule
    The Addition Rule
    The Constructive Dilemma Rule
    Some Unsolicited Advice on Learning to Construct Proofs
    Proof Strategies
    Some Additional Suggestions Concerning Strategy
    Appendix: Some Common Deduction Errors
    Chapter 9 Indirect Proofs and Conditional Proofs
    The Indirect Proof Rule
    The Conditional Proof Rule
    Nested Proofs
    Proving Sentences Tautological
    The Law of Noncontradiction
    Chapter 10 Replacement Rules
    The Commutative Rule
    The Associative Rule
    The Double Negation Rule
    DeMorgan's Rule
    The Distribution Rule
    Five More Replacement Rules
    The Transposition Rule
    The Implication Rule
    The Exportation Rule
    The Tautology Rule
    The Equivalence Rule
    Are Replacement Rules Worth the Bother?
    Chapter 11 Indirect and Conditional Proofs with Replacement Rules
    Indirect Proofs with Replacement Rules
    Conditional Proof with Replacement Rules
    Proving Tautologies
    Chapter 12 Definition
    The Purposes of Definition
    Five Types of Definition
    Two Types of Meaning
    Constructing a Definition: Techniques
    Rules for Intensional Definitions
    Chapter 13 Informal Fallacies
    Fallacies of No Evidence
    Fallacies of Little Evidence
    Fallacies of Language
    A Summary of the Fallacies
    Chapter 14 The Logic of Categorical Statements
    Categorical Sentences
    Quality and Quantity
    The Traditional Square of Opposition
    Translating English Sentences into Standard Categorical Forms
    Equivalence Rules for Aristotelian Logic
    Dropping the Assumption of Existential Import
    The Modern Square of Opposition
    Chapter 15 Categorical Syllogisms
    Logical Form
    Venn Diagrams
    Testing a Categorical Syllogism for Validity with Venn Diagrams
    Diagramming Aristotelian Categorical Syllogisms
    Diagramming from the Boolean Standpoint
    The Sorites
    Testing a Sorites with Venn Diagrams
    Refutation by Logical Analogy
    Appendix: Rules for Evaluating Categorical Syllogisms
    Chapter 16 Quantificational Logic I: The Language QL
    Two Types of Sentences
    General Sentences
    A Syntax for our New Language
    The Vocabulary of QL
    Symbolizing General Sentences
    Categorical Sentences
    The Old "Quantifier Switch" Trick
    Switching Quantifiers on Categoricals
    Symbolizing Complicated General Sentences
    Denying Existence
    The Only Way to Go
    What is a Cat-Dog?
    Chapter 17 The Language of Quantificational Logic II: Relations
    Sentences with a Quantifier-Dyadic Predicate Combo
    Any and Every
    Reflexive Sentences
    Sentences with Overlapping Quantifiers
    "What Are You Talking About?" The Universe of Discourse
    Dean Martin, Universal Love, and a Summary of Logic Relations
    To Be or Not To Be: The Logic of Identity
    The Identity Sign
    Appendix: Properties of Relations
    Chapter 18 Proofs with Monadic Predicates
    The Universal Instantiation Rule
    Existential Generalization
    Existential Instantiation
    Memories of Geometry Class: Universal Generalization
    One New Replacement Rule: Quantifier Exchange
    Naming Our System
    Chapter 19 Interpretations, Invalidity, and Semantics
    Interpretations of Multiply Quantified Sentences
    Using Interpretations to Show Invalidity
    The Monadic Predicate Test
    Chapter 20 Conditional and Indirect Quantifier Proofs
    Adding Truth-Functional Replacement Rules to the Mix
    Putting QD on a Diet: A Reduced Set of Quantifier Rules
    Proving Logical Truths
    Chapter 21 Proofs with Overlapping Quantifiers
    Properties of Relations
    Chapter 22 Proofs with Identity
    Properties of the Identity Relation
    Chapter 23 Introductory Modal Logic
    To Shave or Not to Shave: That Is the Question
    Five Modal Properties
    Possible Truths, Possible Falsehoods, Contingencies
    Necessary Truths
    Necessary Falsehoods
    Putting Statements into Symbols
    Translating English Sentences into Modal Symbols
    A Name and Syntax for our Modal Language
    The Vocabulary for ML
    The Grammar for ML
    Linking Modal Operators
    "It Ain't Necessarily So," Or, Trading a Diamond for a Box and a Box for a Diamond
    Modal Operators Need Scope, Too
    Modal Relations
    Scopes of the Dyadic Modal Operators
    Symbolizing with Dyadic Operators
    Modal Operators Are Not Truth-Functional
    Appendix: There's Nothing New under the Sun
    Chapter 24 Modal Logic: Methods of Proof
    Five Modal Principles
    Six Inference Rules
    The Possibility to Necessity Rule
    The Necessitation Rule
    Four Modal Replacement Rules
    Validity in S5
    Proving Theorems of S5
    Another Inference Rule: The Tautology Necessitation Rule
    Appendix 1: Putting an S5 Formula on a Diet: S5 Reduction
    Appendix 2: The Modal Fallacy
    Chapter 25 Inductive Reasoning
    Analogical Reasoning
    Evaluating Analogical Arguments
    Analogies as Models
    Enumerative Induction
    Statistical Inductive Generalization
    Inference to the Best Explanation
    What Makes One Explanation Better than Another?
    Chapter 26 Scientific Reasoning
    Scientific Reasoning
    Comments on the Steps
    Confirming and Disconfirming Scientific Hypotheses
    The Confirmation of a Scientific Hypothesis
    The Disconfirmation of a Scientific Hypothesis
    The Fact of the Cross
    What Makes One Hypothesis Better than Another?
    Case Studies
    Cause and Effect and Mill's Method
    Cause and Effect
    Mill's Method of Agreement
    Mill's Method of Difference
    The Joint Method of Agreement and Difference
    Mill's Method of Residues
    Mill's Method of Concomitant Variation
    1. Truth-Trees
    2. Truth
    Answers to Selected Exercises