The Many Worlds of Logic

by Herrick, Paul

• ISBN13: 9780195155037
• ISBN10: 0195155033
• Edition: 2nd
• Format: Hardcover
• Copyright: 1999-05-28
• Publisher: Oxford University Press

Summary

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

Table of Contents

To the Instructor

To the Student

Acknowledgements

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 Implication

Logical Equivalence

Necessity

Ideals

Appendix: Some Logical Puzzles

Glossary

Truth-Functional Logic

Introductory Truth-Functional Logic

Simple and Compound Sentences, Sentence Operators, and the Conjunction

Negation

Disjunction

Truth-Functions and Truth-Functional Compound Sentences

Conditional Sentences

Biconditional Sentences

Glossary

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

Glossary

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

Glossary

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

Glossary

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

Glossary

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

Proofs

Glossary

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

Indirect Proofs and Conditional Proofs

The Indirect Proof Rule

The Conditional Proof Rule

Nested Proofs

Proving Sentences Tautological

The Law of Noncontradiction

Glossary

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?

Glossary

Indirect and Conditional Proofs with Replacement Rules

Indirect Proofs with Replacement Rules

Conditional Proof with Replacement Rules

Proving Tautologies

Glossary

Two Informal Topics

Definition

The Purposes of Definition

Five Types of Definition

Two Types of Meaning

Constructing a Definition: Techniques

Rules for Intensional Definitions

Glossary

Informal Fallacies

Fallacies of No Evidence

Fallacies of Little Evidence

Fallacies of Language

Glossary

A Summary of the Fallacies

Aristotelian Categorical Logic

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

Glossary

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

Enthememes

Refutation by Logical Analogy

Appendix: Rules for Evaluating Categorical Syllogisms

Modern Quantificational Logic

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?

Glossary

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

Glossary

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

Glossary

Interpretations, Invalidity, and Semantics

Interpretations of Multiply Quantified Sentences

Using Interpretations to Show Invalidity

Semantics

The Monadic Predicate Test

Glossary

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

Proofs with Overlapping Quantifiers

Properties of Relations

Proofs with Identity

Properties of the Identity Relation

Glossary

Modal Logic

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

Glossary

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

Putting an S5 Formula on a Diet: S5 Reduction

The Modal Fallacy

Glossary

Induction

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?

Glossary

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

Glossary

Appendices

Truth-Trees

Truth

Answers to Selected Exercises

Index

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