The mood does not tell the whole shape of a syllogism. "All M are P" and "All P are M" are both A, but they place the middle term differently. The figure records where the middle term sits.
| Figure | Major premise | Minor premise | Middle term is… |
|---|---|---|---|
| 1 | M – P | S – M | subject, then predicate |
| 2 | P – M | S – M | predicate twice |
| 3 | M – P | M – S | subject twice |
| 4 | P – M | M – S | predicate, then subject |
Key idea
Figure 1: the middle term is the subject of the major premise and the predicate of the minor. Figure 2: predicate of both. Figure 3: subject of both. Figure 4: predicate of the major, subject of the minor. The form of a syllogism is its mood and figure, such as AII-3.
Why it works
The figure matters because it changes which terms are distributed where. "All M are P" distributes M, but "All P are M" does not. With 64 moods and 4 figures there are 256 forms, and each one is either always valid or never valid, whatever its terms.
Worked examples
Worked example: Figure 2
Find the figure: "No mammals are reptiles. All snakes are reptiles. So no snakes are mammals."
- The conclusion's predicate is mammals, so "No mammals are reptiles" is the major premise. The middle term is reptiles.
- In the major premise, M is the predicate.
- In the minor premise "All snakes are reptiles", M is the predicate again.
- Predicate twice is figure 2.
Answer: figure 2 (form EAE-2, Cesare)
Worked example: Figure 3
Find the figure: "All knitters are climbers. All knitters are runners. So some runners are climbers."
- Middle term: knitters.
- It is the subject of both premises.
Answer: figure 3 (form AAI-3)
Common mistake
Mixing up figures 1 and 4. In figure 1 the middle term is the subject of the major premise and the predicate of the minor (M–P, S–M); figure 4 is the reverse (P–M, M–S). Check: put the premises in standard order first, then trace where M sits in each line.