Module 6. Universals and Existentials

Categorical logic studies the logic of claims about all members (universals) or some members (existentials) of a category. This module discusses the distinction between existentials and universals, some of the basic rules which apply to each, and the fifteen valid forms of categorical syllogism. Specific Topics are:

1. Distinguishing Existential and Universal Claims;
2. Using Venn Diagrams to model claims and prove validity;
3. Basic rules for Existentials and Universals;
4. Relationships of contradiction and logical equivalence between categorical claims;
5. Constants, Variables, and Identity;
6. Categorical Syllogisms, including Standard Form, Mood, Figure, and the 15 Valid Forms.

• 6.1 Existentials and Universals with Venn Diagrams
  • 6.1.1 Existential and Universal Claims
    • Categorical Logic
    • Existentials (SOME)
    • Universals (ALL)
    • Using Capital Letters as Abbreviations
  • 6.1.2 Modeling Existentials with Venn Diagrams
    • Basic Venn Diagrams
    • Existentials with Two Circles
    • Existentials with Three Circles
  • 6.1.3 Modeling Universals with Venn Diagrams
    • Universals with Two Circles
    • Contradictory Claims: The Square of Opposition
    • Universals with Three Circles
  • 6.1.4 Using Venn Diagrams to Prove Validity
    • Step 1: Create the Venn Diagram
    • Step 2: Diagram any Universal Claims in the Premises
    • Step 3: Diagram any Particular Claims in the Premises
    • Step 4: See if the Conclusion must be true given the Diagram
    • Important Notes
  • Submodule 6.1 Quiz
• 6.2 Rules for Universals and Existentials
  • 6.2.1 Basic Rules for Universals and Existentials
    • Applied Universal Instantiation (AUI)
    • Existential Generalization (EG)
  • 6.2.2 Conversion, Obversion, and Contraposition
    • Four Categories of Categorical Propositions
    • Conversion (CONV)
    • Obversion (OBV)
    • Contraposition of Categoricals (CTRA-CG)
    • Summary
  • 6.2.3 Identities
    • The Law of Identity (=i)
    • The Indiscernibility of Identicals (=E)
  • 6.2.4 Variables
    • Variables
    • Existential Instantiation (EI)
    • Fallacies of Existential Instantiation
  • Submodule 6.2 Quiz
• 6.3 Categorical Syllogisms
  • 6.3.1 Three Valid Forms of Categorical Syllogism
    • Three Valid Forms of Categorical Syllogism (CS)
    • The Form of a Categorical Syllogism
    • What Categorical Syllogisms are Valid?
  • 6.3.2 Fallacies and Categorical Syllogisms
    • Fallacies of Categorical Syllogism
    • The Fallacy of Four Terms
    • Undistributed Middle
    • Illicit Major or Minor
      • Illicit Minor
      • Illicit Major
    • Exclusive Premises
    • Affirmative from Negative
    • Existential Fallacy
  • 6.3.3 Mood and Figure for Categorical Syllogism
    • Standard Form
    • Mood
    • Figure
    • Here is a summary of the four figures
  • 6.3.4 Valid Categorical Syllogisms of the First Figure
    • First Figure
  • 6.3.5 Valid Categorical Syllogisms of the Second Figure
    • Second Figure
  • 6.3.6 Valid Categorical Syllogisms of the Third Figure
    • Third Figure
  • 6.3.7 Valid Categorical Syllogisms of the Fourth Figure
    • Fourth Figure
  • Submodule 6.3 Quiz
• 6.4 Practice with Universals and Existentials
  • 6.4.1 Three Valid Forms of Categorical Syllogism
  • 6.4.2 Three Valid Forms of Categorical Syllogism
    • Quantifier Negation Laws (QN)
  • 6.4.3 Three Valid Forms of Categorical Syllogism
  • Submodule 6.4 Quiz