Understanding Symbolic Logic

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