Law of Syllogism

Law of Syllogism

  • If given statements are:

    • p → q

    • q → r

  • Then we conclude:

    • p → r

Purpose of Law of Syllogism

  • The Law of Syllogism is used to make conclusions from multiple conditional statements.

  • It helps determine if a conclusion is possible based on the preceding conditional statements.

  • Enables writing conclusions based on multiple IF-THEN statements.

  • Writing the Law of Syllogism symbolically will be a focus area.

  • Learning Intention Success Criteria guide this process.

Components of a Valid Syllogism

  • True conditional statements: At least two true statements are required to form an argument.

  • Hypotheses and Conclusions: The conclusion of the first statement becomes the hypothesis of the next.

  • Canceling Repeated Parts: The repeated components help simplify the argument.

  • Example structure:

    • p → q

    • q → r

    • Conclusion: p → r

Examples of Syllogism

Example 1

  • Statements:

    • If you study, then you get smart.

    • If you get smart, then you are happy.

  • Conclusion:

    • If you study, then you are happy.

Example 2

  • Statements:

    • If you are kind, then people like you.

    • If people like you, then you are successful.

  • Conclusion:

    • If you are kind, then you are successful.

Identifying Patterns in Syllogism

  • Look for patterns in IF-THEN statements.

  • You should find that:

    • The conclusion of one statement acts as the hypothesis of the following one.

  • No need for complex language; recognize the structural pattern.

Substituting Statements

  • Any variable can replace p, q, and r as long as:

    • The conclusion of one statement serves as the next hypothesis.

Expanding the Argument

  • Multiple statements may exist in an argument beyond just two.

  • Example of extended syllogism:

    • p → q

    • q → r

    • r → s

    • s → t

  • Conclusion: p → t

Fun Example: Mr. Clean

  • Statement Structure:

    • p → q:

      • If you don’t buy Mr. Clean Magic Erasers, then your house will be dirty.

    • q → r:

      • If your house is dirty, then people won’t want to come over.

    • r → s:

      • If people won’t want to come over, then you’ll grow a stinky beard down to your knees.

    • Conclusion:

      • If you don’t buy Mr. Clean Magic Erasers, then you’ll grow a stinky beard down to your knees.

  • Note: These may not be factually true, but syllogisms are typically expected to hold true.