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


Table of Contents



 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
    Study Questions

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

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

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

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

 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
    Four Kinds of Truth Table Problems and the Relations Between Them
    Study Questions

 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

 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

 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
    Truth and Proof
    Summary of Rules of Conditional Proof and Indirect Proof



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

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

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

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

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

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

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



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

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

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

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



21. Well-Formed Formulas for Sentential Logic

22. Proof Trees for Sentential Logic

23. Using Venn Diagrams to Prove Validity

24. Proof Trees for Predicate Logic

Answers to Starred Exercises