It is usual to give this as one of the General Canons of the Syllogism; but we have seen ([chap. vi. § 6]) that it is of wider application. Indeed, 'not to go beyond the evidence' belongs to the definition of formal proof. A breech of this rule in a syllogism is the fallacy of Illicit Process of the Minor, or of the Major, according to which term has been unwarrantably distributed. The following parasyllogism illicitly distributes both terms of the conclusion:
All poets are pathetic;
Some orators are not poets:
∴ No orators are pathetic.
(4) The Middle Term must be distributed at least once in the premises (in order to prove a conclusion in the given terms).
For the use of mediate evidence is to show the relation of terms that cannot be directly compared; this is only possible if the middle term furnishes the ground of comparison; and this (in Logic) requires that the whole denotation of the middle should be either included or excluded by one of the other terms; since if we only know that the other terms are related to some of the middle, their respective relations may not be with the same part of it.
It is true that in what has been called the "numerically definite syllogism," an inference may be drawn, though our canon seems to be violated. Thus:
60 sheep in 100 are horned;
60 sheep in 100 are blackfaced:
∴ at least 20 blackfaced sheep in 100 are horned.
But such an argument, though it may be correct Arithmetic, is not Logic at all; and when such numerical evidence is obtainable the comparatively indefinite arguments of Logic are needless. Another apparent exception is the following:
Most men are 5 feet high;
Most men are semi-rational:
∴ Some semi-rational things are 5 feet high.
Here the Middle Term (men) is distributed in neither premise, yet the indisputable conclusion is a logical proposition. The premises, however, are really arithmetical; for 'most' means 'more than half,' or more than 50 per cent.
Still, another apparent exception is entirely logical. Suppose we are given, the premises—All P is M, and All S is M—the middle term is undistributed. But take the obverse of the contrapositive of both premises: