Coherent, well-organized text familiarizes readers with complete theory of logical inference and its applications to math and the empirical sciences. Part I deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Last section introduces numerous examples of axiomatically formulated theories.

Table of Contents for Introduction to Logic

PREFACE
INTRODUCTION
PART I-PRINCIPLES 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 II-ELEMENTARY 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. RELA
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. SET-THEORETICAL FOUNDATIONS OF THE AXIOMATIC METHOD
12.1 Introduction
12.2 Set-Theoretical Predicates and Axiomatizations of Theories
12.3 Ismorphism of Models for a Theory
12.4 Example: Profitability
12.5 Example: Mechanics
INDEX

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