PREFACEINTRODUCTIONPART I-PRINCIPLES OF INFERENCE AND DEFINITION 1. THE SENTENTIAL CONNECTIVES1.1 Negation and Conjunction1.2 Disjunction1.3 Implication: Conditional Sentences1.4 Equivalence: Biconditional Sentences1.5 Grouping and Parentheses1.6 Truth Tables and Tautologies1.7 Tautological Implication and Equivalence 2. SENTENTIAL THEORY OF INFERENCE2.1 Two Major Criteria of Inference and Sentential Interpretations2.2 The Three Sentential Rules of Derivation2.3 Some Useful Tautological Implications2.4 Consistency of Premises and Indirect Proofs 3. SYMBOLIZING EVERYDAY LANGUAGE3.1 Grammar and Logic3.2 Terms3.3 Predicates3.4 Quantifiers3.5 Bound and Free Variables3.6 A Final Example 4. GENERAL THEORY OF INFERENCE4.1 Inference Involving Only Universal Quantifiers4.2 Interpretations and Validity4.3 Restricted Inferences with Existential Quantifiers4.4 Interchange of Quantifiers4.5 General Inferences4.6 Summary of Rules of Inference 5. FURTHER RULES OF INFERENCE5.1 Logic of Identity5.2 Theorems of Logic5.3 Derived Rules of Inference 6. POSTSCRIPT ON USE AND MENTION6.1 Names and Things Named6.2 Problems of Sentential Variables6.3 Juxtaposition of Names 7. TRANSITION FROM FORMAL TO INFORMAL PROOFS7.1 General Considerations7.2 Basic Number Axioms7.3 Comparative Examples of Formal Derivations and Informal Proofs7.4 Examples of Fallacious Informal Proofs7.5 Further Examples of Informal Proofs 8. THEORY OF DEFINITION8.1 Traditional Ideas8.2 Criteria for Proper Definitions8.3 Rules for Proper Definitions8.4 Definitions Which are Identities8.5 The Problem of Divison by Zero8.6 Conditional Definitions8.7 Five Approaches to Division by Zero8.8 Padoa's Principle and Independence of Primitive SymbolsPART II-ELEMENTARY INTUITIVE SET THEORY 9. SETS9.1 Introduction9.2 Membership9.3 Inclusion9.4 The Empty Set9.5 Operations on Sets9.6 Domains of Individuals9.7 Translating Everyday Language9.8 Venn Diagrams9.9 Elementary Principles About Operations on Sets 10. RELATIONS10.1 Ordered Couples10.2 Definition of Relations10.3 Properties of Binary Relations10.4 Equivalence Relations10.5 Ordering Relations10.6 Operations on Relations 11. FUNCTIONS11.1 Definition11.2 Operations on Functions11.3 Church's Lambda Notation 12. SET-THEORETICAL FOUNDATIONS OF THE AXIOMATIC METHOD12.1 Introduction12.2 Set-Theoretical Predicates and Axiomatizations of Theories12.3 Ismorphism of Models for a Theory12.4 Example: Profitability12.5 Example: MechanicsINDEX