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Mind Your Logic
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Table of Contents

  • Chapter One: What Logic Is and Is Not
  • 1.1 What Logic Can and Cannot Do
  • 1.2 Arguments
  • 1.3 Statements and Sentences
  • 1.4 Defining Inductive and Deductive Arguments
  • 1.5 Induction
  • 1.6 Deduction
  • Chapter Two: Everyday Mistakes in Reasoning
  • 2.1 Logical vs. Psychological Mistakes
  • 2.2 Some Typical Psychological Mistakes: A discussion of some typical "informal fallacies"
  • 2.3 How Can Mistakes in Reasoning be Avoided?
  • Chapter Three: Classical Logic
  • 3.1 Aristotle and His Importance
  • 3.2 Classes and Categorical Propositions
  • 3.3 The Square of Opposition
  • 3.4 A Sketch of Some Related Philosophical Issues
  • 3.5 Symbolizing and Diagramming the Categorical Propositions
  • 3.6 Putting the Pieces Together: Categorical Syllogisms
  • 3.7 Testing Categorical Syllogisms for Validity: Venn Diagrams
  • 3.8 Testing Categorical Syllogisms for Validity: Aristotle's Way
  • 3.9 Getting the Most Out of Classical Logic
  • Chapter Four: Contemporary Logic
  • 4.1 Why Classical Logic Has Not Been Rendered Obsolete
  • 4.2 Advantages of Constructing a Symbolic Language
  • 4.3 Symbolic Logic as a Game
  • 4.4 Learning the Game: What Gets Symbolized?
  • 4.5 Truth Tables for Conjunction, Disjunction, and Negation
  • 4.6 Punctuation in Symbolic Logic
  • 4.7 Material Implication and Its Truth Table
  • 4.8 Testing Arguments With Truth Tables
  • 4.9 Tautologies, Contradictions, and Contingent Statements
  • 4.10 Material and Logical Equivalence
  • Chapter Five: Formal Proof of the Validity of Arguments
  • 5.1 How Truth Tables Can Get Complicated
  • 5.2 Truth Tables and Formal Proof Compared
  • 5.3 The Rules of Inference and Substitution Instances
  • 5.4 Putting Together Formal Proofs
  • 5.5 The Rule of Replacement and Its Role in Formal Proof
  • 5.6 Formal Proof and Invalid Arguments
  • 5.7 Validity and Inconsistent Premises
  • 5.8 Quantification: Classical and Contemporary Logic Meet
  • Chapter Six: Some Further Considerations
  • 6.1 The Applicability of Logic to Our Lives
  • 6.2 Why Mr. Data is Not the Captain of the Enterprise
  • 6.3 Why Mr. Data is Important to the Enterprise
  • Glossary of Common Terms
  • Answers to All Exercises
  • More Exercises for Practice

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