Mind Your Logic
Edition: 2
Copyright: 2007
Pages: 220
Edition: 2
Copyright: 2007
Pages: 222
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Sometimes it is helpful to reflect upon how we do the things we do. Reasoning logically is one of the things we do, and in this book we will reflect upon how we do it.
Mind Your Logic is designed for the introductory logic student, it contains a treatment of the essential ingredients of an introductory course: the nature, strengths, and limitations of logic; induction vs. deduction; the relation between language and logic; informal fallacies; the classical logic of the categorical proposition and categorical syllogism; symbolic or truth-functional logic including the truth-table method of testing arguments, formal proof of validity, and a brief introduction to quanti?cation.
Exercises are provided for each major point covered, and in addition to traditional “problem-solving” exercises, there are many invitations to the student to explain in a brief paragraph the concept just discussed. This latter sort of exercise is designed to provide a “reality check” to be sure the student is not simply memorizing formulas and de?nitions. Working through the exercises serves the dual purpose of providing practice in careful writing and learning key logical concepts in other than a rote manner. Answers to all the exercises in the text, in addition to some extra exercises for practice, will be found at the end of the book.
Some distinctive features of Mind Your Logic include the following:
- Emphasis is given to the role logic plays in our lives with regard to both its strengths and limitations.
- Analogies are frequently employed to make difficult concepts easier to understand.
- Philosophical controversies in logic, while not ignored, are mentioned only brie?y for what they are, namely issues which primarily concern professionals and advanced students in the ?eld.
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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 De?ning 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 Premisses
5.8 Quanti?cation: 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