Contents

  1. About the Textbook

  2. Reviewer's Notes

  3. Dedication

  4. Copyright

    Jenna Woodrow

  5. Introduction
  6. Part 0: Truth Tables

    1. 1. The Purpose of a Truth Table

    2. 2. Atomic Sentences

    3. 3. Logical Operators

    4. 4. Creating a Truth Table

    5. 5. Filling in a Truth Table

    6. 6. Filling in a Truth Table - Another Example

    7. 7. Filling in a Truth Table - An Alternative Approach

    8. 8. Testing for Validity

    9. 9. Testing for Validity - Example

    10. 10. Truth Tables for Single Statements

    11. 11. Answers for Truth Tables for Single Statements

    12. 12. Questions on Truth Tables for Arguments

    13. 13. Answers for Questions on Truth Tables for Arguments

  7. Part I: Propositional Logic

    1. 1. Developing a Precise Language

      1. 1.1 Starting with sentences
      2. 1.2 Precision in sentences
      3. 1.3 Atomic sentences
      4. 1.4 Syntax and semantics
      5. 1.5 Logical connectives
      6. 1.6 Key Concepts
      7. 1.7 Exercises

    2. 2. “If…then…” and “It is not the case that...”

      1. 2.1 The Conditional
      2. 2.2 Alternative phrasings in English for the conditional. Only if.
      3. 2.3 Test your understanding of the conditional
      4. 2.4 Alternative symbolizations for the conditional
      5. 2.5 Negation
      6. 2.6 Alternative symbolizations for negation
      7. 2.7 How to Make a Truth Table
      8. 2.8 Key Concepts
      9. 2.9 Exercises

    3. 3. Good Arguments

      1. 3.1  A historical example
      2. 3.2  Arguments
      3. 3.3  Checking arguments semantically
      4. 3.4 Returning to our historical example
      5. 3.5  Other kinds of arguments 1:  Scientific reasoning
      6. 3.6 Other kinds of arguments 2:  Probability
      7. 3.7 Key Concepts
      8. 3.8 Exercises

    4. 4. Proofs

      1. 4.1  A problem with semantic demonstrations of validity
      2. 4.2  Direct proof
      3. 4.3  Other inference rules
      4. 4.4  An example
      5. 4.5 How to Make a Direct Proof
      6. 4.6 Key Concepts
      7. 4.7  Exercises

    5. 5. “And”

      1. 5.1  The conjunction
      2. 5.2  Alternative phrasings, and a different “and”
      3. 5.3  Inference rules for conjunctions
      4. 5.4  Reasoning with conjunctions
      5. 5.5  Alternative symbolizations for the conjunction
      6. 5.6 Complex sentences
      7. 5.7 Key Concepts
      8. 5.8 Exercises

    6. 6. Conditional Derivations

      1. 6.1  An argument from Hobbes
      2. 6.2  Conditional derivation
      3. 6.3  Some additional examples
      4. 6.4  Theorems
      5. 6.5 How to Make a Conditional Proof
      6. 6.6  Key Concepts
      7. 6.7  Exercises

    7. 7. “Or”

      1. 7.1  A historical example:  The Euthryphro argument
      2. 7.2  The disjunction
      3. 7.3  Alternative forms
      4. 7.4  Reasoning with disjunctions
      5. 7.5  Alternative symbolizations of disjunction
      6. 7.6 Key Concepts
      7. 7.7  Exercises

    8. 8. Reductio ad Absurdum

      1. 8.1  A historical example
      2. 8.2  Indirect proofs
      3. 8.3  Our example, and other examples
      4. 8.4 How to Make an Indirect Proof
      5. 8.5 Key Concepts
      6. 8.6 Exercises

    9. 9. “… if and only if …”, Using Theorems

      1. 9.1  A historical example
      2. 9.2  The biconditional
      3. 9.3 Alternative phrases
      4. 9.4  Reasoning with the biconditional
      5. 9.5  Returning to Hume
      6. 9.6  Some examples
      7. 9.7 Using theorems
      8. 9.8 How to Make a Biconditional Proof and How to Prove a Theorem
      9. 9.9 Key Concepts
      10. 9.10  Exercises

    10. 10. Summary of Propositional Logic

      1. 10.1 Elements of the language
      2. 10.2 Reasoning with the language
  8. Part II: First Order Logic

    1. 11. Names and Predicates

      1. 11.1 A limitation of the propositional logic
      2. 11.2  Symbolic terms:  proper names
      3. 11.3  Predicates
      4. 11.4  First order logic sentences
      5. 11.5  Exercises

    2. 12. “all” and “some”

      1. 12.1  The challenge of translating “all” and “some”
      2. 12.2  A new syntax
      3. 12.3  Common sentence forms for quantifiers
      4. 12.4  Exercises

    3. 13. Reasoning with Quantifiers

      1. 13.1  Using the universal quantifier
      2. 13.2  Showing the existential quantifier
      3. 13.3  Using the existential quantifier
      4. 13.4  Exercises

    4. 14. Universal Derivation

      1. 14.1  An example:  the Meno
      2. 14.2  A familiar strangeness
      3. 14.3  Universal derivation
      4. 14.4  Two useful theorems:  quantifier equivalence
      5. 14.5  Illustrating invalidity
      6. 14.6  Exercises

    5. 15. Relations, Functions, Identity, and Multiple Quantifiers

      1. 15.1  Relations
      2. 15.2  Functions
      3. 15.3  Identity
      4. 15.4  Examples using multiple quantifiers
      5. 15.5  Capturing specific quantities
      6. 15.6  Exercises

    6. 16. Summary of First Order Logic

      1. 16.1 Elements of the language
      2. 16.2  Syntax of the language
      3. 16.3  Semantics of the language
      4. 16.4 Reasoning with the Language
      5. 16.5  Some advice on translations using quantifiers

    7. First Order Logic Questions for UI and EG

    8. Answers to First Order Logic Questions for UI and EG

    9. First Order Logic Questions for All Rules

    10. Answers for First Order Logic Questions for All Rules

    11. More First Order Logic Questions

    12. Answers for More First Order Logic Questions

  9. Part III: A Look Forward
  10. Chapter Answer Keys

    1. Chapter 1 Answer Key

      1. Full Exercise Question Sets

    2. Chapter 2 Answer Keys

      1. 2.9 Exercises

    3. Chapter 3 Answer Key

      1. 3.8 Exercises

    4. Chapter 4 Answer Key

      1. 4.7 Exercises

    5. Chapter 5 Answer Key

      1. 5.7 Exercises

    6. Chapter 6 Answer Key

      1. 6.6 Exercises

    7. Chapter 7 Answer Key

      1. 7.7 Exercises

    8. Chapter 8 Answer Key

      1. 8.6 Exercises

    9. Chapter 9 Answer Key

      1. 9.10 Exercises

  11. Bibliography

  12. About the Author

  13. About Open SUNY Textbooks