Other possible conclusions are, “_All trees are men_,” “_All men are trees_” and “_Some men are trees_.” It is thus seen that no definite conclusion can be drawn. It may now be said that when the major and minor terms are used in two negative premises the connection between them is _indeterminate_. This violation of rule “5” may be termed the fallacy of _two negatives_. (6) _If one premise be negative the conclusion must be negative; and conversely, to prove a negative conclusion one of the premises must be negative._ Referring to the first part of this rule, it may be said of two terms that if one is affirmed and the other denied of a third term, then the two terms must be denied of each other. The attending syllogism and its “circled” representation will throw light upon this: No men are immortal, All Americans are men, ∴ No Americans are immortal. Illustration: FIG. 14. Since none of the “men” circle belongs to the “immortal” circle and all of the “American” circle is inside the “men” circle, it is evident that none of the “American” circle can belong to any part of the “immortal” circle. Thus it is manifest that an affirmative conclusion like, “All Americans are immortal,” is invalid. 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. (8) Hence a conclusion from I and O is untenable. The same may be said of “OI.” “II” considered.