Understanding Symbolic Logic by Virginia KlenkUnderstanding Symbolic Logic by Virginia Klenk

Understanding Symbolic Logic

byVirginia Klenk

Paperback | April 19, 2007

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This comprehensive introduction presents the fundamentals of symbolic logic clearly, systematically, and in a straightforward style accessible to readers. Each chapter, or unit, is divided into easily comprehended small “bites” that enable learners to master the material step-by-step, rather than being overwhelmed by masses of information covered too quickly. The book provides extremely detailed explanations of procedures and techniques, and was written in the conviction that anyone can thoroughly master its content. A four-part organization covers sentential logic, monadic predicate logic, relational predicate logic, and extra credit units that glimpse into alternative methods of logic and more advanced topics. For individuals interested in the formal study of logic.

Title:Understanding Symbolic LogicFormat:PaperbackDimensions:480 pages, 9.1 × 6.9 × 1.1 inPublished:April 19, 2007Publisher:Pearson EducationLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0132051524

ISBN - 13:9780132051521

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Table of Contents

I. SENTENTIAL LOGIC

 

 1. Introduction to Logic
    Why Study Logic?
    What Logic Is All About
    Induction and Deduction
    Form and Validity
    Truth and Validity
    The Nature of Symbolic Logic
    The Scope of Symbolic Logic
    Definitions
    Study Questions
    Exercises

 2. The Structure of Sentential Logic
    Simple and Compound Sentences
    Sentential Operators
    The Structure and Symbolism of Sentential Logic
    Definitions
    Study Questions
    Exercises

 3. Computing Truth Values
    Truth Tables for the Operators
    Computing Truth Values
    Truth-functional Operators
    Non-truth-functional Operators
    Definitions
    Study Questions
    Exercises

 4. Symbolizing English Sentences
    Simple Sentences
    Truth-functional and Non-truth-functional Compounds
    Symbolizing Truth-functional English Operators
    Symbolizing Multiply Complex Sentences
    Exercises

 5. Truth Tables for Testing Validity
    Constructing Base Columns for Truth Tables
    The Truth Table Test for Validity
    Shortcut Validity Tests
    Mechanical Decision Procedures
    Definitions
    Study Questions
    Exercises

 6. Further Applications of the Truth Table Method
    Tautologies, Contradictions, and Contingencies
    Logical Implication and Logical Equivalence
    Rules of Inference, Logical Implication, and Logical Equivalence
    Consistency
    Four Kinds of Truth Table Problems and the Relations Between Them
    Definitions
    Study Questions
    Exercises

 7. The Proof Method: Eight Basic Inference Rules
    Form and Substitution Instance
    The Proof Process
    Eight Basic Inference Rules
    Derivations and Proofs
    Constructing Simple Proofs
    Constructing More Complex Proofs
    Summary of Rules of Inference
    Definitions
    Exercises

 8. Replacement Rules
    The Structure of Replacement Rules
    The Ten Replacement Rules
    Constructing Simple Proofs with Replacement Rules
    Strategies for More Complex Proofs
    Summary of Replacement Rules
    Exercises

 9. Conditional Proof and Indirect Proof
    Conditional Proof
    Indirect Proof
    Discharging Assumptions; Restrictions on C.P. and I.P.
    Using C.P. and I.P.
    Proofs of Theorems
    Invalidity
    Truth and Proof
    Summary of Rules of Conditional Proof and Indirect Proof
    Definitions
    Exercises

II. MONADIC PREDICATE LOGIC

 

10. Singular Sentences
    Singular Sentences and Propositional Functions
    Symbolizing Singular Sentences
    Definitions
    Exercises

11. Quantifiers
    Universal and Existential Quantifiers
    Free and Bound Variables; Scope of a Quantifier
    Negated Quantifiers
    Definitions
    Exercises

12. Categorical Propositions
    The Four Categorical Propositions
    Individuals, Sets, and Properties
    Venn Diagrams
    Symbolizing Categorical Propositions
    Negated Categorical Propositions
    Deriving C.Q.N. Rules from Q.N. Rules
    Symbolizing English Categorical Sentences
    Summary of Categorical Propositions
    Definitions
    Exercises

13. Complex Subjects and Predicates
    Complex Subjects and Predicates
    Equivalent Symbolizations
    Exercises

14. Quantifier Form and Truth-Functional Compounds of Quantifier Statements
    Quantifier Form
    Truth-functional Compounds and Quantifier Form
    Symbolizing Truth-functional Compounds
    Definitions
    Exercises

15. Proofs in Predicate Logic
    Preliminary Statement of the Four Quantifier Rules
    Instances of Quantified Formulas
    The Rules of Universal Instantiation (U.I.) and Existential Generalization (E.G.)
    The Rules of Existential Instantiation (E.I.) adn Universal Generalization (U.G.); Flagging Restrictions
    Constructing Proofs for "Pure" Quantifier Arguments
    Constructing Proofs for Arguments Containing Truth-functional Compounds
    Constructing Proofs of Quantifier Theorems
    Statement of the Quantifier Rules, with All Necessary Restrictions
    Exercises

16. Invalidity in Quantifier Logic
    The Natural Interpretation Method
    Truth Conditions for Quantifier Statements
    The Model Universe Method
    Definitions
    Exercises

III. RELATIONAL PREDICATE LOGIC

 

17. Symbolization in Relational Predicate Logic
    Relational Predicates and Singular Sentences
    Multiple Quantifiers
    Quantifier Negation
    Categorical Relational Statements; Complex Subjects and Predicates
    Symbolizing English Sentences
    Exercises

18. Proofs and Invalidity for Relational Predicate Logic
    Proofs in Relational Predicate Logic
    Invalidity in Relational Predicate Logic
    Exercises

19. Identity and Definite Descriptions
    Identity Statements and Their Negations
    Exceptives and "Only" Statements
    Superlatives
    Numerical Statements
    Definite Descriptions
    Exercises

20. Proofs Involving Identity
    Rules for Identity
    Proofs Containing Identity Statements
    Summary of Identity Rules
    Exercises

IV. EXTRA CREDIT UNITS

 

21. Well-Formed Formulas for Sentential Logic
    Exercises

22. Proof Trees for Sentential Logic
    Exercises

23. Using Venn Diagrams to Prove Validity
    Exercises

24. Proof Trees for Predicate Logic
    Exercises

Answers to Starred Exercises

Index