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Clear focus on its application of formal logic to ordinary English is the most distinctive feature of this textbook for the introductory course in deductive logic. Great care is taken with the appropriate translation into logical languages of ordinary English sentences. Evaluation of these translations promotes a more effective use of ordinary language.



The Principles of Deductive Logic presents symbolic logic in a fuller and more leisurely fashion than other introductory textbooks. Early chapters cover informal material, including definition and informal fallacies. The remainder of the text is devoted to the treatment of four distinct artificial languages. The Categorical language is the language of syllogistic logic. The Extended Categorical language enriches this first language with the symbolic connectives for conjunction and negation. The Propositional Connective language and the First-Order language (with identity) are the two basic languages of modern logic. Each language is accompanied by a deductive system, and is used as an instrument for exploring ordinary language, including ordinary arguments



The book contains a large number of exercises whose answers are supplied in the back of the book, and many more that can be assigned as homework. A solution's manual is available to instructors upon their request. The request must be written on college or university letterhead.

Tabla de contenidos provista por Syndetics

• Preface
• 1 Applied Logic: What We Hope To Accomplish
• 1-0 Summary
• 1-1 The Nature of Logic
• 1-2 Talking About Words
• 1-3 Speech Acts
• 1-4 A Language is a Complex System
• 1-5 Logically Important Semantic Features
• 1-6 Applied Logic
• 1-7 Philosophy of Logic
• 2 Some Preliminary Matters
• 2-0 Summary
• 2-1 Definitions (Opt)
• 2-2 Inferences and Arguments
• 2-3 Informal Fallacies (Opt)
• 3 Sentences About Individuals
• 3-0 Summary
• 3-1 Looking Ahead
• 3-2 Individuals
• 3-3 Quantified Phrases
• 3-4 Universal Sentences
• 3-5 Some Other Universal Sentences
• 3-6 Singular Sentences
• 4 The Artificial-Language Strategy
• 4-0 Summary
• 4-1 Artificial Languages
• 4-2 Logical Form
• 4-3 Evaluation
• 4-4 The Languages to be Developed
• 5 The Categorical Language
• 5-0 Summary
• 5-1 Categorical Sentences
• 5-2 Semantics
• 5-3 Logical Form
• 5-4 The Complement of an Expression
• 5-5 Some Syntactic Relations
• 5-6 Implication and Equivalence
• 5-7 Logical Truth
• 5-8 Venn Diagrams
• 5-9 Incompatibility
• 5-10 Syllogisms
• 5-11 The Categorical Deductive System
• 5-12 Proving Incompatibility
• 5-13 Venn Diagrams for Many-Place Relations
• 5-14 Formal Fallacies (Opt)
• 6 Applying an Artificial Language
• 6-0 Summary
• 6-1 What We Want in a Translation
• 6-2 The Features We Test for
• 6-3 Negative Outcomes
• 7 Applying the Categorical Language to English
• 7-0 Summary
• 7-1 Translating English Sentences
• 7-2 Expressing Existential Force
• 7-3 Detecting Semantic Features of Existence Claims
• 7-4 Evaluating English Sentences and Arguments
• 7-5 Achieving Comparable Translations
• 7-6 Incorporating Semantic Features in Logical Form
• 7-7 Enthymemes
• 7-8 What Comes Next
• 8 The Extended Categorical Language
• 8-0 Summary
• 8-1 The Changes We Want
• 8-2 What We Will Keep
• 8-3 Small Change
• 8-4 The Sign of Negation
• 8-5 Reasoning with Negative Sentences
• 8-6 Translating Negated Sentences
• 8-7 Singular Sentences
• 8-8 Reasoning with Singular Sentences
• 9 The Propositional Connective Language
• 9-0 Summary
• 9-1 A Mixed Language
• 9-2 The Syntax and Semantics of the PC Language
• 9-3 Variables and Formulas
• 9-4 Evaluating Sentences of the PC Languge
• 9-5 Two-Place Relations
• 9-6 Many-Place Relations
• 9-7 Indirect Tests
• 9-8 The Quick Method of Determining if a Formula is a Tautology
• 10 The Pc Deductive System
• 10-0 Summary
• 10-1 A Deductive System
• 10-2 Proofs from Hypotheses
• 10-3 The Easy Rules
• 10-4 More Rules
• 10-5 Proofs within Proofs
• 10-6 Properties of the PC System
• 10-7 Proofs without Hypotheses
• 10-8 Metatheorems and Derived Rules
• 10-9 Our First Metatheorems (Opt)
• 10-10 More Metatheorems (Opt)
• 10-11 Still More Metatheorems (Opt)
• 10-12 Rules to Shorten Proofs
• 10-13 Proving Incompatibility
• 10-14 Refutation
• 10-15 What to do Next
• The Original and Derived Rules of the PC Deductive System
• 11 Applying the PC Language to English
• 11-0 Summary
• 11-1 Translating within a Single Language
• 11-2 Translating with the Negation Sign
• 11-3 Translating with '&'
• 11-4 Translations with 'v'
• 11-5 Translations with the Horseshoe
• 11-6 Some Additional Translations
• 11-7 The Scope of a Connective
• 11-8 Identifying Sentences
• 11-9 A Further Look at the Difference Between Ordinary Conditional Sentences and Horseshoe Sentences (Opt)
• 11-10 Testing for Analyticity
• 11-11 Incompatibility
• 11-12 Entailment and Validity
• 11-13 An Important Exception
• 11-14 Incorporating Semantic Features in Logical Form
• 11-15 Enthymemes
• 12 The First-Order Language
• 12-0 Summary
• 12-1 A Purely Artificial Language
• 12-2 The Truth Conditions of Atomic Sentences
• 12-3 New Varieties of Variables
• 12-4 Quantifiers
• 12-5 Multiple Quantification
• 12-6 Restricted Domains
• 12-7 A More Careful Description of the First-Order Language
• 13 The First-Order Deductive System
• 13-0 Summary
• 13-1 Adapting the PC System
• 13-2 Some Derived Rules
• 13-3 A Notation for Substitution
• 13-4 An Additional Notation
• 13-5 Change of Bound Variables
• 13-6 Universal Quantifier Elimination
• 13-7 Universal Quantifier Introduction
• 13-8 Existential Quantifier Introduction
• 13-9 Existential Quantifier Elimination
• 13-10 Identity Rules
• 13-11 More Derived Rules
• 13-12 Refutation
• 13-13 Incompatibilty
• Rules and Derived Rules of the First-Order Deductive System
• 14 Applying the First-Order Language to English
• 14-0 Summary
• 14-1 The Expressive Power of the First-Order Language
• 14-2 Predicates and Singular Terms
• 14-3 Quantified Phrases in English
• 14-4 Indefinite Sentences
• 14-5 Universal Sentences
• 14-6 Only
• 14-7 Another Use of 'Any'
• 14-8 Generalized Conditionals
• 14-9 Analytic Sentences
• 14-10 Incompatibility
• 14-11 Entailment and Validity
• 14-12 Comparable Translations
• 14-13 Supplementing Our Translations
• Afterword Reflections On Logic
• Answers to Starred Questions
• Index

Notas de autor provistas por Syndetics

John T. Kearns is Professor of Philosophy at State University of New York at Buffalo. He is author of Using Language: The Structures of Speech Acts , also published by SUNY Press.