Categorical Syllogism: Rules, Figures and Moods
Structure
A categorical syllogism has three categorical propositions and exactly three terms: major (P), minor (S), and middle (M). The major premise contains P; the minor contains S; the conclusion relates S and P. Mood records the A/E/I/O forms of major, minor, and conclusion; figure records the position of the middle term.
Rules and figures
Key rules: the middle term must be distributed at least once; no term may be distributed in the conclusion unless distributed in its premise; two negative premises yield no conclusion; a negative premise requires a negative conclusion; two particular premises yield no conclusion; a particular conclusion cannot follow from two universal premises in the standard rules. The four figures place M as subject or predicate in each premise.
Worked example
All mammals are animals. All whales are mammals. Therefore all whales are animals. This is AAA-1, called Barbara. M (“mammals”) is predicate in the major premise and subject in the minor, so it is figure 1. M is distributed in the major premise, and no term is illicitly distributed. The mood and figure are valid.
Traps that cost marks
- Confusing mood with figure.
- Checking only the conclusion’s truth instead of the syllogistic form.
- Missing an undistributed middle term.
- Forgetting that a negative conclusion needs a negative premise.
- Treating a valid syllogism as sound even when a premise is false.