Put the distribution rules and the quality rules together with one more, and you have the six rules for a standard-form syllogism (on the modern reading). Each broken rule has a name.
| Rule | Fallacy when broken |
|---|---|
| 1. The middle term is distributed at least once. | Undistributed middle |
| 2. A term distributed in the conclusion is distributed in its premise. | Illicit major / illicit minor |
| 3. Not both premises negative. | Exclusive premises |
| 4. A negative premise needs a negative conclusion, and the reverse. | Affirmative conclusion from a negative premise / negative conclusion from affirmative premises |
| 5. (Modern reading) Two universal premises cannot give a particular conclusion. | Existential fallacy |
| A syllogism must have exactly three terms. | Four terms |
Key idea
A syllogism is valid (modern reading) exactly when it breaks none of the rules. Check every rule: one syllogism can break several, and each name points to a different flaw.
Why it works
The existential fallacy is the rule we have not met yet. On the modern reading, universal premises say only that regions are empty, so they put no X in the diagram. A particular conclusion needs an X. So two universal premises can never prove a particular conclusion, unless we add the traditional assumption that some class has members (the last lesson of this unit).
Worked examples
Worked example: Two fallacies
Name every fallacy: "All bakers are skaters. All early risers are bakers. So no early risers are skaters."
- Distribution: the conclusion (E) distributes skaters, but the major premise (A) does not: illicit major.
- Quality: both premises affirmative, conclusion negative: negative conclusion from affirmative premises.
- The middle term is distributed (premise 1) and the minor term is fine.
Answer: illicit major; negative conclusion from affirmative premises
Worked example: Four terms
What is wrong with: "All chess players are thinkers. All chess fans are viewers. So all chess players are viewers"?
- Count the terms: chess players, thinkers, chess fans, viewers. That is four.
- With no shared middle term, the premises cannot connect anything.
Answer: four terms
Common mistake
Stopping at the first broken rule. The question "which fallacies?" wants all of them. Check all five rules in order (middle, major, minor, the negatives, universals to a particular) every time.