Understanding Symbolic Logic

by Klenk, Virginia, Ph.D.

• ISBN13: 9780132051521
• ISBN10: 0132051524
• Edition: 5th
• Format: Paperback
• Copyright: 2007-04-19
• Publisher: Pearson

Summary

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.

Table of Contents

Sentential Logic

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

The Structure of Sentential Logic Simple and Compound Sentences Sentential Operators

The Structure and Symbolism of Sentential Logic

Definitions Study

Questions

Exercises

Computing Truth Values Truth Tables for the Operators

Computing Truth Values Truth-functional Operators

Non-truth-functional Operators

Definitions Study

Questions

Exercises

Symbolizing English Sentences Simple Sentences Truth-functional and Non-truth-functional

Compounds Symbolizing Truth-functional

English Operators Symbolizing Multiply Complex Sentences

Exercises

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

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

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

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

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

Monadic Predicate Logic

Singular Sentences

Singular Sentences and Propositional

Functions Symbolizing Singular Sentences

Definitions

Exercises

Quantifiers Universal and Existential Quantifiers

Free and Bound Variables; Scope of a Quantifier Negated Quantifiers

Definitions

Exercises

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

Complex Subjects and Predicates Complex

Subjects and Predicates Equivalent Symbolizations

Exercises

Quantifier Form and Truth-Functional

Compounds of Quantifier Statements Quantifier

Form Truth-functional Compounds and Quantifier

Form Symbolizing Truth-functional Compounds

Definitions

Exercises

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

Invalidity in Quantifier Logic

The Natural Interpretation Method Truth Conditions for Quantifier Statements

The Model Universe Method Definitions Exercises

Relational Predicate Logic

Symbolization in Relational Predicate Logic

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