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 ofeach 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.
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.