Module 4. Foundations of Argumentation

Formal logic studies the abstract form of an argument rather than its content. This module studies the assumptions of classical logic, how to clarify claims in order to symbolize them, and how to use very basic truth tables and Venn Diagrams to model validity. Topics studied in this module include:

1. Applying Formal Logic only to statements;
2. Symbolizing Simple Positive and Negative Claims;
3. The Laws of Non-Contradiction and Excluded Middle;
4. The Rules of Reiteration and Double Negation;
5. Introduction to Basic Truth Tables;
6. Introduction to Basic Venn Diagrams;
7. Making Sentences more Precise;
8. Making Sentences more Concise;
9. Distinguishing the Explicit, Literal Meaning of Logical Connectives from Implicatures;
10. Testing the Validity of Rules of Inference;
11. Making use of formal tools to reason more methodically;
12. Making use of formal tools to more objectively approach controversial topics.

• 4.1 The Form of an Argument
  • 4.1.1 Introduction to Formal Logic
    • Formal Logic
    • Symbolizing
    • Rules of Inference
  • 4.1.2 What to Symbolize
    • Symbolize Statements
    • Single, Complete Sentences
    • Breaking Up Sentences
  • 4.1.3 Symbolization: Positive Claims
    • Writing a Dictionary
    • Simple Statements
    • The Rule of Reiteration (Reit.)
    • Proving the Validity of Reiteration (Reit.)
  • 4.1.4 Symbolization: Negative Claims
    • Negation
    • Symbolizing Negation
  • Submodule 4.1 Quiz
• 4.2  True and False
  • 4.2.1 The Laws of Non-Contradiction and Excluded Middle
    • Two Truth Values
    • Two Laws of Logic
  • 4.2.2 Truth Tables: Positive and Negative Claims
    • Truth Tables and Negation
  • 4.2.3 Negation and Double Negation
    • Truth Tables for Multiple Negations
    • Double Negation (DN)
  • Submodule 4.2 Quiz
• 4.3 Clarifying Claims
  • 4.3.1 More Precisely
    • Making Claims Precise
  • 4.3.2 More Concisely
    • Concise Translations
  • 4.3.3 More Explicitly
    • Literally Speaking
  • 4.3.4 More Methodically
    • Rules for Thinking Slower
    • Step by Step
  • Submodule 4.3 Quiz
• 4.4 Modeling Validity
  • 4.4.1 Validity and Truth Tables
    • Step 1: Symbolize the Argument
    • Step 2: One Row Per Truth Value Assignment
    • Step 3: Calculate Truth Values for Premises
    • Step 4: Calculate Truth Values for Conclusion
    • Step 5: Highlight all Rows Where All Premises are True
    • Step 6: Check if the Conclusion is true in all Highlighted Rows
    • Invalid Arguments
    • Extending Truth Tables
  • 4.4.2 Validity and Venn Diagrams
    • Representing Categorical Claims
    • Testing for Validity
  • 4.4.3 Rules of Inference
    • Justifying Rules of Inference
    • The Validity of DN
    • Truth-Functional Equivalence
    • Proving a Rule is Invalid
  • 4.4.4 Controversy
    • Controversy and Abstraction
  • Submodule 4.4 Quiz