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 ExercisesIndex