Syllogistic Reasoning
Structure
A categorical syllogism has exactly three terms - major (predicate of the conclusion), minor (subject of the conclusion) and middle (appears in both premises) - and three categorical propositions. Mood records the forms of the three propositions (e.g., AAA); figure records the position of the middle term:
- 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 of validity
- The middle term must be distributed in at least one premise.
- No term may be distributed in the conclusion unless it was distributed in a premise (no illicit major or minor).
- Two negative premises yield no conclusion.
- If one premise is negative, the conclusion must be negative, and conversely.
- Two particular premises yield no conclusion; a particular conclusion requires a particular premise.
Worked example
“All dogs are animals; all cats are animals; therefore all cats are dogs.” Mood AAA, figure 2. The middle term “animals” is the predicate of two affirmative premises, so it is undistributed throughout - undistributed middle. Invalid. Compare Barbara: “All M are P; all S are M; therefore all S are P” - figure 1, mood AAA, satisfies every rule.
Traps that cost marks
Students memorise moods but ignore figure, so they misplace the middle term. Watch illicit process: in “All dogs are animals; no cats are dogs; therefore no cats are animals,” “animals” is distributed in the conclusion but not in its premise.