Unit 5: Testing Syllogism Validity

This unit provides two methods for testing whether a syllogism is Valid or Invalid.

Copi's Six Rules for Testing Syllogisms

A categorical syllogism is valid if, and only if, it follows all of these six rules. If it breaks even one rule, it is invalid, and the rule it breaks is the fallacy it commits.

Rules of Distribution

These rules relate to the terms (S, P, M).

Rule 1: The middle term (M) must be distributed at least once.

Fallacy: Fallacy of the Undistributed Middle.
(Example: "All P are M. All S are M." Here M is the predicate in two A-propositions and is never distributed. We can't link S and P.)

Rule 2: If a term (S or P) is distributed in the conclusion, it must also be distributed in its premise.

This rule has two associated fallacies:

Fallacy: Fallacy of Illicit Major.
(The Major Term, P, is distributed in the conclusion but not in the major premise.)

Fallacy: Fallacy of Illicit Minor.
(The Minor Term, S, is distributed in the conclusion but not in the minor premise.)

Rules of Quality

These rules relate to affirmative and negative propositions.

Rule 3: No conclusion can be drawn from two negative premises.

Fallacy: Fallacy of Exclusive Premises.
(If both premises are "No..." or "Some...not...", they just state exclusion. We can't mediate a link.)

Rule 4: If one premise is negative, the conclusion must be negative. (And vice-versa: If the conclusion is negative, one premise must be negative).

Fallacy: Fallacy of Drawing an Affirmative Conclusion from a Negative Premise (or vice-versa).

Rules of Quantity

These rules relate to universal and particular propositions. (Note: These rules are sometimes combined with the others).

Rule 5: If both premises are universal, the conclusion cannot be particular.

(This rule is only for the Boolean (modern) interpretation. In the traditional Aristotelian view, this is not a fallacy. This is the "Existential Fallacy" problem.)

Rule 6: No conclusion can be drawn from two particular premises.

Fallacy: (This often breaks another rule, like Undistributed Middle, but it's a good rule of thumb.)

(Note: Your syllabus likely follows Copi's rules, which are sometimes listed as 4 or 5. Rules 1-4 are the core of Aristotelian logic. The "Fallacy of Four Terms" - having more than 3 terms - is also a rule, but it's usually assumed a syllogism has only 3 terms.)

Summary of Rules and Fallacies

Rule	Fallacy if Broken
1. Middle term (M) must be distributed at least once.	Undistributed Middle
2. A term (S or P) distributed in conclusion must be distributed in its premise.	Illicit Major (for P) or Illicit Minor (for S)
3. Cannot have two negative premises.	Exclusive Premises
4. A negative premise requires a negative conclusion (and vice-versa).	Affirmative from Negative (or vice-versa)