Reasoning · Syllogism
Syllogism — a reliable method
6 min read
How to handle 'all', 'some' and 'no' statements without guessing, plus the possibility cases that catch people out.
Syllogism rewards method over intuition. The rule that matters most: you must accept the statements as true even when they contradict the real world.
Draw Venn diagrams rather than reasoning verbally. Three statement types cover almost everything:
All A are B — circle A sits entirely inside circle B. Some A are B — circles A and B overlap. No A are B — circles A and B are separate.
Standard conclusions: All A are B does NOT give All B are A. It does give Some B are A. Some A are B gives Some B are A. It does not give All. No A are B gives No B are A.
The part that decides most questions is "possibility". A conclusion holds only if it is true in EVERY valid diagram, not merely one. If you can draw a single arrangement satisfying all statements where the conclusion fails, the conclusion does not follow.
Either-or pairs. When two conclusions individually fail but together cover all possibilities, and they concern the same pair of terms, the answer is "either I or II follows". This typically appears when one conclusion says Some A are B and the other says No A are B.
Practical approach: draw the most restrictive diagram first, test each conclusion, then try to draw an alternative that breaks it. If you cannot break it, it follows.