Karnataka II PUC Logic (KSEAB): Categorical Syllogism and Fallacies

What this domain tests

This is the highest-scoring unit: identify the three terms and the figure, test validity by rules or Venn diagram, and name the fallacy when a syllogism fails.

Structure

Three terms - major (predicate of the conclusion), minor (subject of the conclusion), middle (in both premises, never in the conclusion) - and three propositions: major premise, minor premise, conclusion. Figures are fixed by the position of the middle term; mood is the letter sequence, e.g. AAA-1.

Rules that catch most errors

1. Exactly three terms.
2. The middle term must be distributed at least once.
3. No term may be distributed in the conclusion unless distributed in a premise.
4. Two negative premises yield no conclusion.
5. A negative premise requires a negative conclusion; two affirmatives give an affirmative conclusion.
6. Two particular premises yield no conclusion.

Fallacies

Undistributed middle; illicit major; illicit minor; four terms (equivocation); exclusive premises; drawing an affirmative conclusion from a negative premise.

Worked example

"All dogs are mammals; all mammals are animals; therefore all dogs are animals." The middle term "mammals" is distributed in the second premise, since A distributes its subject, so rule 2 is met. "Dogs" and "animals" are distributed only where the conclusion needs them. Mood and figure AAA-1 (Barbara) - valid.

Traps that cost marks

Forgetting that the predicate of an A proposition is undistributed, the commonest source of illicit minor; counting a complemented term as a fourth term; accepting a conclusion that merely re-words a premise.