Module 10. Conditional and Indirect Proof

This module introduces three new rules for propositional logic which make use of temporary or provisional assumptions: conditional proof, indirect proof, and disjunction elimination. It also proves the validity of two other rules, hypothetical syllogism and exportation. These rules work together to make it easier and quicker to complete proofs.

• 10.1 Conditional Proof
  • 10.1.1 Provisional Assumptions
    • For the Sake of Argument
    • Tracking Assumptions
    • No Going Back
  • 10.1.2 Method of Conditional Proof
    • Conditional Proof (CP)
    • An Example
    • Using Conditional Proof with Symbolized Arguments (CP)
  • 10.1.3 Practice with Conditional Introduction
    • How to Remember CP
  • Submodule 10.1 Quiz
• 10.2  Hypothetical Syllogism and Exportation
  • 10.2.1 Disjunction Elimination Rule
    • Two Paths Converge
    • Using Disjunction Elimination
  • 10.2.2 The Rule of Hypothetical Syllogism
    • A Chain of Conditionals
  • 10.2.3 The Rule of Exportation
    • The Rule of Exportation (EXPO)
    • Proving the Rule is Valid
    • Examples of Exportation
  • Submodule 10.2 Quiz
• 10.3 Indirect Proof
  • 10.3.1 Principle of Indirect Proof
    • Indirect Proof
    • Proof by Contradiction
  • 10.3.2 Negation Introduction
    • Negation Introduction (~I)
    • Examples with Negation Introduction
  • 10.3.3 Negation Elimination
    • Negation Elimination (~E)
    • Examples with Negation Elimination
    • Warnings
  • Submodule 10.3 Quiz
• 10.4 Applications of Conditional and Indirect Proof
  • 10.4.1 Modeling Arguments as Conditional Proofs
    • Reconstructing a Conditional Argument
  • 10.4.2 Modeling Arguments as Indirect Proofs
    • Reconstructing a Proof by Contradiction
  • 10.4.3 Three Proof Strategies
    • Completing Proofs
    • The CP Strategy
    • The IP Strategy
    • Concluding Advice
  • Submodule 10.4 Quiz