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Arthur R.T.W.. An Introduction to Logic: Using Natural Deduction, Real Arguments, a Little History, and Some Humour. Broadview Press,2016. — 456 p.. 2016

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EQUIVALENCE RULES
Contents
Preface for Students
Preface for Instructors
Acknowledgements
PART I ARGUMENTS
Chapter One Arguments
INTRODUCTION
IDENTIFYING ARGUMENTS
INFERENCE INDICATORS
EXPLANATIONS
IMPLICIT ARGUMENTS
Enthymemes
NATURAL ARGUMENTS
ARGUMENT AND INFERENCE
TECHNIQUES OF DIAGRAMMING
Chapter Two Validity
VALIDITY
DEFINING VALIDITY
SOUNDNESS
ARGUMENT FORMS AND FORMAL VALIDITY
EVALUATING NATURAL ARGUMENTS
PART II STATEMENT LOGIC
Chapter Three Statements and Conditionals
STATEMENTS AND COMPOUNDS
STATEMENTS
COMPOUNDS
STATEMENT OPERATORS
CONDITIONAL STATEMENTS
MODUS PONENS
ARGUMENT FORM AND SUBSTITUTION INSTANCE
AFFIRMING THE CONSEQUENT
Chapter Four Negation
SYMBOLIZING NEGATIONS
NEGATIONS
CONTRADICTORIES
MODUS TOLLENS
MODUS TOLLENS AND DOUBLE NEGATION
DENYING THE ANTECEDENT
INFERENCE AND IMPLICATION
Conjunction
SYMBOLIZING CONJUNCTIONS
RULES OF INFERENCE FOR CONJUNCTION
EVALUATING EXTENDED ARGUMENTS
RULES OF INFERENCE FOR DISJUNCTIONS
DISJUNCTIVE SYLLOGISM
DISJUNCTION
Conditional Proof
MORE ON SYMBOLIZING
DISJUNCTIONS IN CONDITIONALS
‘UNLESS’
OTHERWISE,’ ‘ELSE’
MORE RULES INVOLVING CONDITIONALS
CONDITIONAL PROOF AND SUPPOSITION
THE HYPOTHETICAL SYLLOGISM
SUPPOSITION IN NATURAL ARGUMENT
Chapter Eight Biconditionals
NECESSARY AND SUFFICIENT CONDITIONS
ONLY IF’
NECESSARY AND SUFFICIENT CONDITIONS
BICONDITIONALS
SYMBOLIZING
CONVERSATIONAL IMPLICATURE (ADVANCED LEVEL MATERIAL)
RULES OF INFERENCE
NATURAL DILEMMAS
Chapter Ten Reductio Arguments
Reductio ad absurdum
Review and Consolidation
RULES OF INFERENCE
RULES OF INFERENCE AND EQUIVALENCE RULES
TWO SIMPLIFYING MODIFICATIONS (OPTIONAL)1
PROOF STRATEGIES
DERIVED RULES
Chapter Twelve SL as a Formal System
RULES OF FORMATION
SYMBOLS, FORMULAS, AND WFFS
CONSISTENCY AND COMPLETENESS
SEQUENTS, THEOREMS, AND AXIOMS
sequents and theorems
AXIOMS AND THE PROPOSITIONAL CALCULUS (CHALLENGE LEVEL)
Chapter Thirteen Truth Tables
TRUTH TABLES AND STATEMENTS
TRUTH TABLES
TRUTH TABLES AND VALIDITY
THE FULL TRUTH TABLE METHOD
INVALID ARGUMENT FORMS
THE BRIEF TRUTH TABLE METHOD
Chapter Fourteen Truth Trees for SL
TRUTH TREES
THE TRUTH TREE METHOD
DECOMPOSITION RULES
STATEMENTS, CONSISTENCY, AND COMPLETENESS
TAUTOLOGIES, CONTRADICTIONS, AND LOGICAL EQUIVALENCE
CONSISTENCY AND COMPLETENESS (challenge level)
PART III PREDICATE LOGIC
Chapter Fifteen Syllogistic Logic
CATEGORY LOGIC
ARISTOTLE’S LOGIC
A-, E-, I-, AND O-STATEMENTS
AMBIGUOUS STATEMENTS
CARROLL DIAGRAMS
CARROLL’S DIAGRAMS
EXISTENCE AND NON-EXISTENCE
CONVERSION
EVALUATING VALIDITY OF SYLLOGISMS
Chapter Sixteen Universal Quantification
UNIVERSAL AND SINGULAR STATEMENTS
UNIVERSAL QUANTIFICATION
ONLY’ AND 6NOTHING BUT’
SINGULAR STATEMENTS AND INDIVIDUAL NAMES
RULES OF INFERENCE: UI AND UG
Chapter Seventeen Existential Quantification
PARTICULAR STATEMENTS
EXISTENTIAL QUANTIFICATION
RULES OF INFERENCE
EXISTENTIAL INSTANTIATION
EXISTENTIAL GENERALIZATION
PROOF STRATEGY
Chapter Eighteen Advanced Class Logic
ARGUMENTS WITH MORE THAN 3 PREDICATES
CARROLL DIAGRAMS FOR 4 OR 5 CATEGORIES
SORITES
EXISTENTIAL IMPORT
ON GIVING UNIVERSAL STATEMENTS EXISTENTIAL IMPORT
Penevalid arguments
NON-EMPTINESS OF THE UD
Chapter Nineteen Asyllogistic Arguments
MOREON SYMBOLIZING
NON-CLASSICAL STATEMENTS
Asyllogistic proofs: qn
PREDICATE LOGIC AS A FORMAL SYSTEM
SYMBOLS, FORMULAS, AND WFFS
PROPOSITIONAL FUNCTIONS AND QUANTIFIER SCOPE
Chapter Twenty Relational Logic
THE LOGIC OF RELATIONS
RELATIONS
SYMBOLIZING RELATIONS
NESTED QUANTIFIERS
PROPERTIES OF BINARY RELATIONS
TRANSITIVITY, SYMMETRY, AND REFLEXIVITY
EQUIVALENCE RELATIONS
Chapter Twenty-One Logic with Identity
IDENTITY AND QUANTITY
SYMBOLIZING IDENTITIES AND QUANTITIES
RUSSELL’S THEORY OF DEFINITE DESCRIPTIONS
INFERENCES INVOLVING IDENTITY
THE RULE OF INFERENCE SI
PROPERTIES OF IDENTITY
ORDERING RELATIONS
RELATIONAL ARGUMENTS
ARGUMENTS BEYOND THE SCOPE OF TRADITIONAL LOGIC
AMBIGUITIES AND THE QUANTIFIER SHIFT FALLACY
Chapter Twenty-Three Truth Trees for PL
PREDICATE LOGIC TRUTH TREES
TRUTH TREE RULES FROM STATEMENT LOGIC
ADDITIONAL TRUTH TREE RULES FOR QUANTIFICATIONS
NEGATED QUANTIFIER DECOMPOSITION RULES
EFFECTIVE COMPLETENESS
TREES FOR RELATIONAL LOGIC AND IDENTITY
TRUTH TREE RULES IN RELATIONAL LOGIC
ADDITIONAL TRUTH TREE RULES FOR IDENTITY AND DIVERSITY
Other Logics
You now have behind you a course in elementary symbolic logic and its application to argument.
SECOND ORDER LOGIC
MODAL LOGIC
DEONTIC LOGIC
QUANTUM LOGIC
Intuitionistic logic
Appendix One The Paradoxes of Material Implication
Appendix Two A Little History: Consequentiae
Appendix Three Logic Diagrams
Glossary
Index

Books and textbooks on the discipline Logic:

  1. Artemov S., Fitting M.. Justification Logic: Reasoning with Reasons. Cambridge: Cambridge University Press,2019. — 271 p. - 2019 ãîä
  2. Arp R., Barbone S., Bruce M. (eds.). Bad arguments: 100 of the most important fallacies in Western philosophy. New York: Wiley-Blackwell,2018. — 450 p. - 2018 ãîä
  3. Arun Sharma. How to prepare for Logical Reasoning for the CAT. McGraw-Hill Education series,2012. — 1111 p. - 2012 ãîä
  4. Albrecht Karl. Brain building: Easy games to develop your problem-solving skills. Prentice Hall Trade,1984. — 92 p. - 1984 ãîä
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