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Many Worlds of Logic

ISBN-10: 0195155033

ISBN-13: 9780195155037

Edition: 2nd 2000 (Revised)

Authors: Paul Herrick

List price: $114.95
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Book details

List price: $114.95
Edition: 2nd
Copyright year: 2000
Publisher: Oxford University Press, Incorporated
Publication date: 5/28/1999
Binding: Hardcover
Pages: 688
Size: 6.50" wide x 9.25" long x 1.25" tall
Weight: 2.288
Language: English

To the Instructor
To the Student
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
Appendix: Some Logical Puzzles
Truth-Functional Logic
Introductory Truth-Functional Logic
Simple and Compound Sentences, Sentence Operators, and the Conjunction
Truth-Functions and Truth-Functional Compound Sentences
Conditional Sentences
Biconditional Sentences
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
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
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
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
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
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
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?
Indirect and Conditional Proofs with Replacement Rules
Indirect Proofs with Replacement Rules
Conditional Proof with Replacement Rules
Proving Tautologies
Two Informal Topics
The Purposes of Definition
Five Types of Definition
Two Types of Meaning
Constructing a Definition: Techniques
Rules for Intensional Definitions
Informal Fallacies
Fallacies of No Evidence
Fallacies of Little Evidence
Fallacies of Language
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
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
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?
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
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
Interpretations, Invalidity, and Semantics
Interpretations of Multiply Quantified Sentences
Using Interpretations to Show Invalidity
The Monadic Predicate Test
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
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
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
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?
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
Answers to Selected Exercises