PREFACE

INTRODUCTION 
PART IPRINCIPLES OF INFERENCE AND DEFINITION 

1. THE SENTENTIAL CONNECTIVES 


1.1 Negation and Conjunction 


1.2 Disjunction 


1.3 Implication: Conditional Sentences 


1.4 Equivalence: Biconditional Sentences 


1.5 Grouping and Parentheses 


1.6 Truth Tables and Tautologies 


1.7 Tautological Implication and Equivalence 

2. SENTENTIAL THEORY OF INFERENCE 


2.1 Two Major Criteria of Inference and Sentential Interpretations 


2.2 The Three Sentential Rules of Derivation 


2.3 Some Useful Tautological Implications 


2.4 Consistency of Premises and Indirect Proofs 

3. SYMBOLIZING EVERYDAY LANGUAGE 


3.1 Grammar and Logic 


3.2 Terms 


3.3 Predicates 


3.4 Quantifiers 


3.5 Bound and Free Variables 


3.6 A Final Example 

4. GENERAL THEORY OF INFERENCE 


4.1 Inference Involving Only Universal Quantifiers 


4.2 Interpretations and Validity 


4.3 Restricted Inferences with Existential Quantifiers 


4.4 Interchange of Quantifiers 


4.5 General Inferences 


4.6 Summary of Rules of Inference 

5. FURTHER RULES OF INFERENCE 


5.1 Logic of Identity 


5.2 Theorems of Logic 


5.3 Derived Rules of Inference 

6. POSTSCRIPT ON USE AND MENTION 


6.1 Names and Things Named 


6.2 Problems of Sentential Variables 


6.3 Juxtaposition of Names 

7. TRANSITION FROM FORMAL TO INFORMAL PROOFS 


7.1 General Considerations 


7.2 Basic Number Axioms 


7.3 Comparative Examples of Formal Derivations and Informal Proofs 


7.4 Examples of Fallacious Informal Proofs 


7.5 Further Examples of Informal Proofs 

8. THEORY OF DEFINITION 


8.1 Traditional Ideas 


8.2 Criteria for Proper Definitions 


8.3 Rules for Proper Definitions 


8.4 Definitions Which are Identities 


8.5 The Problem of Divison by Zero 


8.6 Conditional Definitions 


8.7 Five Approaches to Division by Zero 


8.8 Padoa's Principle and Independence of Primitive Symbols 
PART IIELEMENTARY INTUITIVE SET THEORY 

9. SETS 


9.1 Introduction 


9.2 Membership 


9.3 Inclusion 


9.4 The Empty Set 


9.5 Operations on Sets 


9.6 Domains of Individuals 


9.7 Translating Everyday Language 


9.8 Venn Diagrams 


9.9 Elementary Principles About Operations on Sets 

10. RELATIONS 


10.1 Ordered Couples 


10.2 Definition of Relations 


10.3 Properties of Binary Relations 


10.4 Equivalence Relations 


10.5 Ordering Relations 


10.6 Operations on Relations 

11. FUNCTIONS 


11.1 Definition 


11.2 Operations on Functions 


11.3 Church's Lambda Notation 

12. SETTHEORETICAL FOUNDATIONS OF THE AXIOMATIC METHOD 


12.1 Introduction 


12.2 SetTheoretical Predicates and Axiomatizations of Theories 


12.3 Ismorphism of Models for a Theory 


12.4 Example: Profitability 


12.5 Example: Mechanics 
INDEX 

