ISBN-10:
0195155033
ISBN-13:
9780195155037
Pub. Date:
05/28/1999
Publisher:
Oxford University Press, USA
The Many Worlds of Logic / Edition 2

The Many Worlds of Logic / Edition 2

by Paul Herrick

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Product Details

ISBN-13: 9780195155037
Publisher: Oxford University Press, USA
Publication date: 05/28/1999
Edition description: REV
Pages: 688
Sales rank: 969,775
Product dimensions: 9.40(w) x 6.40(h) x 1.20(d)

About the Author

Shoreline Community College

Table of Contents

To the Instructor
To the Student
Acknowledgements
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
Implication
Logical Equivalence
Necessity
Ideals
Appendix: Some Logical Puzzles
Glossary
PART I TRUTH-FUNCTIONAL LOGIC
Chapter 2 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
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
Glossary
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
Glossary
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
Glossary
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
Glossary
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
Proofs
Glossary
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
Glossary
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?
Glossary
Chapter 11 Indirect and Conditional Proofs with Replacement Rules
Indirect Proofs with Replacement Rules
Conditional Proof with Replacement Rules
Proving Tautologies
Glossary
PART II TWO INFORMAL TOPICS
Chapter 12 Definition
The Purposes of Definition
Five Types of Definition
Two Types of Meaning
Constructing a Definition: Techniques
Rules for Intensional Definitions
Glossary
Chapter 13 Informal Fallacies
Fallacies of No Evidence
Fallacies of Little Evidence
Fallacies of Language
Glossary
A Summary of the Fallacies
PART III ARISTOTELIAN CATEGORICAL LOGIC
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
Glossary
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
Enthememes
Refutation by Logical Analogy
Appendix: Rules for Evaluating Categorical Syllogisms
PART IV MODERN QUANTIFICATIONAL LOGIC
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?
Glossary
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
Glossary
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
Glossary
Chapter 19 Interpretations, Invalidity, and Semantics
Interpretations of Multiply Quantified Sentences
Using Interpretations to Show Invalidity
Semantics
The Monadic Predicate Test
Glossary
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
Glossary
PART V MODAL LOGIC
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
Glossary
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
Glossary
PART VI INDUCTION
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?
Glossary
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
Glossary
Appendices
1. Truth-Trees
2. Truth
Answers to Selected Exercises
Index

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