Chapter 9

  • The Rules of Validity
    • There are 5 Rules to apply.
      1. The middle term must be distributed in at least one premise.
      2. If a term is distributed in the conclusion, then it must be distributed in the premise in which it appears.
      3. Both premises cannot be negative.
      4. If the conclusion is negative, then exactly one premise must be negative, and vice versa.
      5. If the conclusion is a particular, then exactly one premise must be particular, and vice versa.

    • If a categorical syllogism fails even a single Rule, it is invalid.

      • For example,

        All X are T
        Some T are not U
        No X are U

      • Let's apply the Rules.
        1. The middle term must be distributed in at least one premise. Fails! T is the middle term, but it is not distributed in either premise.
        2. If a term is distributed in the conclusion, then it must be distributed in the premise in which it appears.Passes. Both terms in the conclusion are distributed and each is distributed in its premise.
        3. Both premises cannot be negative.Passes. The first premise is not negative.
        4. If the conclusion is negative, then exactly one premise must be negative, and vice versa.Passes. One premise is negative, and so is the conclusion
        5. If the conclusion is a particular, then exactly one premise must be negative, and vice versa.Fails! One premise is a particular, but the conclusion is a universal.

      • The argument is invalid, since it failed Rules 1 and 5.

Rules of Validity | Venn Diagrams | Question? | Self-test | Logic Page 1