Every standard form categorical syllogism can be classified by its mood (which proposition types appear) and its figure (where the middle term appears). Together, mood and figure uniquely identify a syllogism's logical form.
1
Mood
The mood of a syllogism is simply the sequence of proposition types — A, E, I, or O — for the major premise, minor premise, and conclusion, in that order. It tells you what kind of claims the argument is making, but not how the terms are arranged.
All M are P. A
All S are M. A
∴ All S are P. A
Mood →
AAA
Major · Minor · Conclusion read in order, top to bottom
2
Figure
Figure 1
M – P
S – M
S – P
M is subject of major, predicate of minor. The most "natural" figure.
Figure 2
P – M
S – M
S – P
M is predicate of both premises. Good for exclusion arguments.
Figure 3
M – P
M – S
S – P
M is subject of both premises. Always yields a particular conclusion.
Figure 4
P – M
M – S
S – P
M is predicate of major, subject of minor. The most "indirect" figure.
3
Mood + Figure Together
A syllogism's full form is expressed as mood followed by figure. This gives a compact, precise way to name any standard form syllogism — and to look up whether it's valid.
All M are P. A · M is subject of major → Fig. 1
All S are M. A · M is predicate of minor → Fig. 1
∴ All S are P. A
Mood
AAA
Figure
1
Full form
AAA-1
"Barbara" — valid ✓
4
The 15 Valid Forms
There are 256 possible mood-figure combinations, but only 15 are valid (24 if you count the weakened forms). Medieval logicians gave them names to aid memorization — the vowels encode the mood. Here they are by figure: