Categorical Syllogisms: Rules and Validity Testing Notes

Overview of Categorical Syllogisms and Validity Testing

  • Focus of this week: Rules and fallacies within categorical syllogisms and the Venn diagram method.
  • Two methods to test validity: Venn diagrams and rules/fallacies.

Venn Diagram Method

  • Fill in the Venn diagram according to the premises.
  • Check if the conclusion matches the diagram.
  • Valid if the conclusion is represented; invalid otherwise.

Rules for Categorical Syllogisms

Rule 1: Distribution of Middle Term
  • The middle term must be distributed at least once in the premises.
  • Middle term: Appears once in each premise and not in the conclusion.
  • Example:
    • Premise 1: All cats are mammals (Middle term = cats).
    • Premise 2: All mammals are animals.
    • Conclusion: All animals are mammals.
  • Validity Check: Circle distributed terms to confirm the middle term is represented.
Rule 2: Distribution of Terms in Conclusion
  • Any term that is distributed in the conclusion must also be distributed in at least one premise.
  • Example: If the conclusion states "All animals are mammals", check that 'animals' is circled (it must be in a premise).
  • If the term is not distributed in the premises, the argument is invalid (e.g., illicit major/minor).
Rule 3: Negative Premises
  • An argument with two negative premises is always invalid. ("No" statements)
  • Example: Premises of the form "No R are P" cannot exist together.
Rule 4: Negative Statements' Requirements
  • Negative premises must correspond with negative conclusions.
  • Negative conclusion requires at least one negative premise.
  • Fallacy: Drawing an affirmative conclusion from a negative premise (denoted as DAP).
  • Fallacy: Drawing a negative conclusion from affirmative premises (denoted as DNP).
Rule 5: Universal Premises and Conclusions
  • If both premises are universal statements, the conclusion must also be universal.
  • If conclusions are particular while premises are universal, the argument is invalid.

Examples of Valid and Invalid Arguments

Example 1: Valid Argument
  1. All cats are mammals. (A)
  2. All mammals are animals. (A)
  3. Conclusion: All cats are animals.
  • Process:
    • Middle term 'cats' is distributed.
    • No broken rules.
  • Validity: Confirmed through both Venn diagrams and rules.
Example 2: Invalid Argument
  1. Some dogs are not cats. (O)
  2. Some cats are mammals.
  3. Conclusion: Some mammals are not dogs.
  • Process:
    • The conclusion does not align with the premises.
    • Rule 4: negative premise and an affirmative conclusion.
  • Invalidity: Checked through broken rules and Venn diagrams.

Final Note

  • Important to circle distributed terms in arguments to ensure stepwise clarity in checking validity.
  • Always refer to the rules during assessments for easier validation.
  • Study Tip: Create a quick reference sheet containing rules and their associated fallacies to utilize during quizzes and exams.