Introduction to Logic and Logical Discourse

Preface
Acknowledgements
Contents
About the Author
Part I Logic and Language
1 Definition, Nature, and Scope of Logic
1.1 What is Logic?
1.2 Definition of Logic
1.3 Methods to Acquire Valid Knowledge
1.4 Logic, Language, and Reasoning
1.5 Ideas Versus Thoughts
1.6 Thinking, Asserting, and Judging
1.7 Usage of Logic in Everyday Life
1.8 Form and Matter
1.9 Formal Logic and Material Logic
1.10 Deductive Logic and Inductive Logic
2 Language, Logic, and Concepts
2.1 Interrelation between Logic and Language
2.2 Syntax, Semantics, and Grammar
2.3 Natural Language, Metalanguage, Logically Perfect Language
2.4 Functions of Language: Directive, Informative, and Expressive
2.5 Formation of Abstract and Concrete Concepts: The Role of Logic
3 Classification of Logical Propositions
3.1 What is a Word?
3.2 Types of Words
3.3 Words Versus Terms
3.4 Types of Terms
3.5 Sentence Versus Proposition
3.6 Propositions and Theories of Truth
3.7 Types of Logical Propositions
3.8 Formal and Material Proposition: Their Truth-Value Determination
3.9 Identifying Formal and Material Arguments
3.10 Categorical Propositions: A, E, I, O
3.11 Distribution of Terms
4 Square of Opposition of Propositions
4.1 Sub-alternation
4.2 Contrary
4.3 Sub-contrary
4.4 Contradictory
4.5 Truth and Validity of SOP
4.6 Modern Interpretations of SOP
5 Fundamental Principles of Logic (The Laws of Thought)
5.1 The Law of Identity
5.2 The Law of Excluded Middle
5.3 The Law of Non-contradiction
5.4 The Law of Sufficient Reason
6 Logical Paradoxes
6.1 What is a Paradox?
6.2 Classification of the Paradoxes
6.3 Differences among Paradox, Ambiguity, and Vagueness
6.4 Russell’s Paradox
6.5 Liar’s Paradox
6.6 Barber’s Paradox
6.7 Zeno’s Paradox
6.8 The Paradox of the Stone
6.9 Grelling’s Paradox
Part II Immediate and Mediate Inference
7 Immediate Inference
7.1 Conversion
7.2 Obversion
7.3 Contraposition
7.4 Converting Sentences to Categorical Propositions for Immediate Inference
8 Mediate Inference (Syllogism)
8.1 Figures of Syllogism
8.2 Moods of Syllogism
8.3 Rules of Syllogism
8.4 Determining the Valid Moods of Syllogism
8.5 Valid Moods of the First Figure
8.6 Valid Moods of the Second Figure
8.7 Valid Moods of the Third Figure
8.8 Valid Moods of the Fourth Figure
8.9 Formal Fallacy Versus Material Fallacy
8.10 Informal Fallacies
9 Pure and Mixed Syllogism
9.1 Pure Categorical Syllogism
9.2 Dictum de Omni et Nullo
9.3 Enthymemes
9.4 Sorites
9.5 Pure Hypothetical Syllogism
9.6 Pure Disjunctive Syllogism
9.7 Hypothetical Categorical Syllogism
9.8 Disjunctive Categorical Syllogism
9.9 Dilemma
9.10 Forms of Dilemma
Part III Symbolic Logic
10 Symbolic Logic-01
10.1 Birth of Symbolic Logic
10.2 Ideograms Versus Phonograms
10.3 Propositional Variables and Logical Connectives
10.4 Translation of Logical Propositions into Symbolic Propositions
10.5 Truth Functions and Truth Table Method
10.6 The Conjunctive Function and the Disjunctive Function
10.7 Implicative Function and Equivalence Function
10.8 Dagger Function and Stroke Function
10.9 Truth-Value: Tautology, Contradiction, and Contingent
11 Symbolic Logic-02
11.1 Indirect Method of Truth Table Decision
11.2 Beth Tree (Truth Tree)
11.3 Propositional Derivation Formulae
11.4 Disjunctive Normal Form (DNF)
11.5 Conjunctive Normal Form (CNF)
11.6 Proving the Validity of Arguments
Part IV Predicate Logic
12 Predicate Logic
12.1 What is Predicate Logic?
12.2 Universal Quantifier
12.3 Existential Quantifier
12.4 Atomic Proposition
12.5 Opposition of Propositions
12.6 Translation of Logical Propositions to Predicate Logic
12.7 Proving Validity of Arguments
Part V Basic Sets and Laws of Algebra
13 Basic Sets
13.1 Introduction to Set Theory
13.2 Notation
13.3 Forms of a Set
13.4 Equality of Sets and the Null Set
13.5 Subset, Proper Subset, and Superset
13.6 Universal Set, Power Set, and Comparability of Sets
13.7 A Set of Sets, and Finite and Infinite Sets
13.8 Disjoint Sets
13.9 Line Diagram
13.10 Venn Diagram
14 Basic Set Operations
14.1 Union and Intersection
14.2 Relative Complement
14.3 Absolute Complement and Double Complement
14.4 Some Proofs
14.5 Laws of the Algebra of Sets
14.6 Exercises
Part VI Induction
15 Induction
15.1 What is Induction?
15.2 Types of Induction
15.3 Scientific and Unscientific Induction
15.4 Induction by Analogy and Enumerative Induction
15.5 Induction by Simple Enumeration
15.6 Induction by Complete Enumeration
15.7 David Hume and the Problem of Induction
15.8 Induction and Probability
16 J. S. Mill’s Inductive Methods
16.1 J. S. Mill’s Proposal on Inductive Methods
16.2 The Method of Agreement
16.3 The Method of Difference
16.4 The Joint Method of Agreement and Difference
16.5 The Method of Residues
16.6 The Method of Concomitant Variations
17 Science and Hypothesis
17.1 What is a Hypothesis?
17.2 Definition, Nature, and Importance of ‘Hypothesis’
17.3 Sources of a Hypothesis
17.4 Types of Hypothesis
17.5 Verification of a Hypothesis
References