Categorical Syllogism and Fallacies
What the exam tests
A categorical syllogism has three terms and three propositions. The exam tests figure and mood, the distribution rules, valid moods, and the formal fallacies that arise when a rule is broken.
Core rules
- Major term (P) is predicate of conclusion; minor term (S) is subject; middle term (M) appears in both premises but not the conclusion.
- Figures: Fig. 1 M–P / S–M; Fig. 2 P–M / S–M; Fig. 3 M–P / M–S; Fig. 4 P–M / M–S.
- Rules: M must be distributed at least once; no term may be distributed in the conclusion unless distributed in a premise; two negative premises yield no conclusion; if one premise is negative, the conclusion is negative; two affirmative premises yield an affirmative conclusion; a particular conclusion requires a particular premise.
- Valid moods include Barbara (AAA-1), Celarent (EAE-1), Darii (AII-1), Ferio (EIO-1), Cesare (EAE-2), Camestres (AEE-2), Disamis (IAI-3), and Calemes (AEE-4).
Worked example
“All mammals are animals; all dogs are mammals; therefore all dogs are animals.” This is AAA-1 (Barbara). The middle term “mammals” is distributed in the major premise because it is the subject of an A proposition. “Animals,” the major term, is undistributed in the premise and undistributed in the conclusion (predicate of A). “Dogs,” the minor term, is distributed in both minor premise and conclusion. No rule is broken, so the syllogism is valid.
Traps
Do not assume that a true conclusion makes an argument valid. Check distribution of the predicate in A: it is undistributed. A frequent error is the undistributed middle, as in “All cats are mammals; all dogs are mammals; therefore all dogs are cats.” Also avoid illicit process: distributing S or P in the conclusion when it was undistributed in its premise.