Sethy S.S. Introduction to Logic and Logical Discourse

Singapore: Springer Nature, 2021. — 283 p.Preface
Acknowledgements
Contents
About the Author
Logic and Language
Definition, Nature, and Scope of Logic
What is Logic?
Definition of Logic
Methods to Acquire Valid Knowledge
Logic, Language, and Reasoning
Ideas Versus Thoughts
Thinking, Asserting, and Judging
Usage of Logic in Everyday Life
Form and Matter
Formal Logic and Material Logic
Deductive Logic and Inductive Logic
Language, Logic, and Concepts
Interrelation between Logic and Language
Syntax, Semantics, and Grammar
Natural Language, Metalanguage, Logically Perfect Language
Functions of Language: Directive, Informative, and Expressive
Formation of Abstract and Concrete Concepts: The Role of Logic
Classification of Logical Propositions
What is a Word?
Types of Words
Words Versus Terms
Types of Terms
Sentence Versus Proposition
Propositions and Theories of Truth
Types of Logical Propositions
Formal and Material Proposition: Their Truth-Value Determination
Identifying Formal and Material Arguments
Categorical Propositions: A, E, I, O
Distribution of Terms
Square of Opposition of Propositions
Sub-alternation
Contrary
Sub-contrary
Contradictory
Truth and Validity of SOP
Modern Interpretations of SOP
Fundamental Principles of Logic (The Laws of Thought)
The Law of Identity
The Law of Excluded Middle
The Law of Non-contradiction
The Law of Sufficient Reason
Logical Paradoxes
What is a Paradox?
Classification of the Paradoxes
Differences among Paradox, Ambiguity, and Vagueness
Russell’s Paradox
Liar’s Paradox
Barber’s Paradox
Zeno’s Paradox
The Paradox of the Stone
Grelling’s Paradox
Immediate and Mediate Inference
Immediate Inference
Conversion
Obversion
Contraposition
Converting Sentences to Categorical Propositions for Immediate Inference
Mediate Inference (Syllogism)
Figures of Syllogism
Moods of Syllogism
Rules of Syllogism
Determining the Valid Moods of Syllogism
Valid Moods of the First Figure
Valid Moods of the Second Figure
Valid Moods of the Third Figure
Valid Moods of the Fourth Figure
Formal Fallacy Versus Material Fallacy
Informal Fallacies
Pure and Mixed Syllogism
Pure Categorical Syllogism
Dictum de Omni et Nullo
Enthymemes
Sorites
Pure Hypothetical Syllogism
Pure Disjunctive Syllogism
Hypothetical Categorical Syllogism
Disjunctive Categorical Syllogism
Dilemma
Forms of Dilemma
Symbolic Logic
Symbolic Logic-01
Birth of Symbolic Logic
Ideograms Versus Phonograms
Propositional Variables and Logical Connectives
Translation of Logical Propositions into Symbolic Propositions
Truth Functions and Truth Table Method
The Conjunctive Function and the Disjunctive Function
Implicative Function and Equivalence Function
Dagger Function and Stroke Function
Truth-Value: Tautology, Contradiction, and Contingent
Symbolic Logic-02
Indirect Method of Truth Table Decision
Beth Tree (Truth Tree)
Propositional Derivation Formulae
Disjunctive Normal Form (DNF)
Conjunctive Normal Form (CNF)
Proving the Validity of Arguments
Predicate Logic
Predicate Logic
What is Predicate Logic?
Universal Quantifier
Existential Quantifier
Atomic Proposition
Opposition of Propositions
Translation of Logical Propositions to Predicate Logic
Proving Validity of Arguments
Basic Sets and Laws of Algebra
Basic Sets
Introduction to Set Theory
Notation
Forms of a Set
Equality of Sets and the Null Set
Subset, Proper Subset, and Superset
Universal Set, Power Set, and Comparability of Sets
A Set of Sets, and Finite and Infinite Sets
Disjoint Sets
Line Diagram
Venn Diagram
Basic Set Operations
Union and Intersection
Relative Complement
Absolute Complement and Double Complement
Some Proofs
Laws of the Algebra of Sets
Exercises
Induction
Induction
What is Induction?
Types of Induction
Scientific and Unscientific Induction
Induction by Analogy and Enumerative Induction
Induction by Simple Enumeration
Induction by Complete Enumeration
David Hume and the Problem of Induction
Induction and Probability
J S Mill’s Inductive Methods
J S Mill’s Proposal on Inductive Methods
The Method of Agreement
The Method of Difference
The Joint Method of Agreement and Difference
The Method of Residues
The Method of Concomitant Variations
Science and Hypothesis
What is a Hypothesis?
Definition, Nature, and Importance of ‘Hypothesis’
Sources of a Hypothesis
Types of Hypothesis
Verification of a Hypothesis
References