An Introduction to Logic
Using Natural Deduction, Real Arguments, a Little History, and Some Humour
  • Publication Date: November 30, 2016
  • ISBN: 9781554813322 / 1554813328
  • 456 pages; 6½" x 9"

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An Introduction to Logic

Using Natural Deduction, Real Arguments, a Little History, and Some Humour

  • Publication Date: November 30, 2016
  • ISBN: 9781554813322 / 1554813328
  • 456 pages; 6½" x 9"

In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python.

A previous edition of this book appeared under the title Natural Deduction. This new edition adds clarifications of the notions of explanation, validity and formal validity, a more detailed discussion of derivation strategies, and another rule of inference, Reiteration.


“Richard Arthur’s book offers a fresh new perspective on the pedagogy of introductory logic instruction and its underlying philosophy. Its approach makes informal logic and critical thinking mesh smoothly and intuitively with formal logic, thus clarifying the relevance of formal logic to the assessment of natural argument. My experience of teaching from the first edition was very positive; the book genuinely makes a majority of students build an appetite for logic. With its many conceptual, technical, and pedagogical improvements, the second edition should prove to be a sound choice as an introductory logic text.” — Nicolas Fillion, Simon Fraser University

Praise for the first edition:

“This excellent text covers all the standard topics and more. Its real strength lies in the clarity and humour of exposition and in the richness of examples and exercises. The illustrations are invariably interesting, since often they are related to current events or the history of philosophy and science or are drawn from Monty Python. The last of these provides several memorable fallacies. Arthur’s … is one of the finest introductions to logic available today.” — James Robert Brown, University of Toronto

  • Preface for Students
  • Preface for Instructors
  • Acknowledgements
    • Chapter 1: Arguments
      • Introduction
      • Identifying Arguments
        • Inference Indicators
        • Explanations
        • Implicit Arguments
        • Enthymemes
      • Natural Arguments
        • Argument and Inference
        • Techniques of Diagramming
    • Chapter 2: Validity
      • Validity
        • Defining Validity
        • Soundness
      • Argument Forms and Formal Validity
      • Evaluating Natural Arguments
    • Chapter 3: Statements and Conditionals
      • Statements and Compounds
        • Statements
        • Compounds
        • Statement Operators
      • Conditional Statements
      • Modus Ponens
        • Argument Form and Substitution Instance
        • Affirming the Consequent
    • Chapter 4: Negation
      • Symbolizing Negations
        • Negations
        • Contradictories
      • Modus Tollens
        • Modus Tollens and Double Negation
        • Denying the Antecedent
      • Inference and Implication
    • Chapter 5: Conjunction
      • Symbolizing Conjunctions
      • Rules of Inference for Conjunction
      • Evaluating Extended Arguments
    • Chapter 6: Disjunction
      • Symbolizing Disjunctions
      • Rules of Inference for Disjunctions
        • Disjunctive Syllogism
        • Disjunction
        • De Morgan’s Laws
    • Chapter 7: 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 8: Biconditionals
      • Necessary and Sufficient Conditions
        • ‘Only If’
        • Necessary and Sufficient Conditions
      • Biconditionals
        • Symbolizing
        • Conversational Implicature
        • Rules of Inference
    • Chapter 9: Dilemmas
      • Dilemmas
      • Natural Dilemmas
    • Chapter 10: Reductio Arguments
      • Reductio ad Absurdum
      • Natural Reductio Arguments
    • Chapter 11: Review and Consolidation
      • Rules of Inference
        • Rules of Inference and Equivalence Rules
        • Two Simplifying Modifications
        • Proof Strategies
      • Derived Rules
    • Chapter 12: 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
    • Chapter 13: Truth Tables
      • Truth Tables and Statements
        • Truth Tables
        • Material Implication
        • Tautologies, Contradictions, and Contingent Statements
        • Logical Equivalence
      • Truth Tables and Validity
        • The Full Truth Table Method
        • Invalid Argument Forms
      • The Brief Truth Table Method
    • Chapter 14: Truth Trees for SL
      • Truth Trees
        • The Truth Tree Method
        • Decomposition Rules
      • Statements, Consistency, and Completeness
        • Tautologies, Contradictions, and Logical Equivalence
        • Consistency and Completeness
    • Chapter 15: 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 16: Universal Quantification
      • Universal and Singular Statements
        • Universal Quantification
        • ‘Only’ and ‘Nothing But’
        • Singular Statements and Individual Names
      • Rules of Inference: UI and UG
    • Chapter 17: Existential Quantification
      • Particular Statements
        • Existential Quantification
      • Rules of Inference
        • Existential Instantiation
        • Existential Generalization
        • Proof Strategy
    • Chapter 18: 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 19: Asyllogistic Arguments
      • More on Symbolizing
        • Non-Classical Statements
        • ‘Any’
      • Asyllogistic Proofs: QN
      • Predicate Logic as a Formal System
        • Symbols, Formulas, and Wffs
        • Propositional Functions and Quantifier Scope
    • Chapter 20: Relational Logic
      • The Logic of Relations
        • Relations
        • Symbolizing Relations
        • Nested Quantifiers
        • Relational Proofs
      • Properties of Binary Relations
        • Transitivity, Symmetry, and Reflexivity
        • Equivalence Relations
    • Chapter 21: 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
    • Chapter 22: Relational Arguments
      • More on Symbolizing Relational Statements
        • A Method for Symbolizing
        • Prenex Forms
      • Relational Arguments
        • Arguments beyond the Scope of Traditional Logic
        • Ambiguities and the Quantifier Shift Fallacy
    • Chapter 23: 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
    • Chapter 24: Other Logics
      • Second Order Logic
      • Modal Logic
      • Deontic Logic
      • Quantum Logic
      • Intuitionistic Logic

      Appendix 1: The Paradoxes of Material Implication
      Appendix 2: A Little History: Consequentiae
      Appendix 3: Logic Diagrams

Richard T.W. Arthur is Professor of Philosophy at McMaster University.

For a sample chapter of Introduction to Logic click here (opens as a PDF).