The converse of rule 6, “To prove a negative conclusion, one of the premises must be negative,” may be explained by the general principle in logic that when two terms are known to disagree, one must agree with a third term while the other must disagree. If both agreed with a third, then the conclusion would of necessity be affirmative. If both disagreed no conclusion could be drawn. A violation of rule 6 may be called the fallacy of negative conclusion.
(7) No conclusion can be drawn from two particular premises. Proof:
(1) All the possible combinations of the two particular premises I and O are, (1) IO, (2) OI, (3) II, (4) OO.
“IO” considered.
(2) Since O is a negative premise the conclusion would have to be negative according to rule 6. (If one premise is negative, the conclusion must be negative.)
(3) If the conclusion is negative, then its predicate, which is the major term, must be distributed. (All negative propositions distribute their predicates.)
(4) If the major term is distributed in the conclusion, it must be distributed in the major premise, rule 4. (No term must be distributed in the conclusion, which is not also distributed in one of the premises.)
(5) Hence two terms must be distributed in the premises, the major term according to (4) and the middle term according to rule 3.
(6) But I distributes neither term and O distributes its predicate only; I and O together, then, distribute but one term.
(7) To draw a negative conclusion the premises must distribute two terms, the middle and the major, according to the foregoing.