A Class Room Logic / Deductive and Inductive, with Special Application to the Science and Art of Teaching

by George Hastings McNair

A term is said to be distributed when it is referred to as a definite whole.

In the proposition, “All men are mortal,” the subject all men is considered as a whole. “All men” stands for every specimen of the human race; not a single one has been left out. Again, the whole is definite; any one, if he were given the time and opportunity, could ascertain by actual count just how many “all men” represented.

It should be observed that if the word definite is not incorporated in the definition of a distributed term, thereis afforded an opportunity for error. The attending illustrations will make this clear:

1. “All the students except John and James are dismissed.”

2. “All the students except John, James, etc., are dismissed.”

The subject of the first proposition is distributed, while the subject of the second is undistributed. Reasons: The first subject, “All the students except John and James,” is referred to as a whole and that whole is definite, therefore, it is distributed; the second subject, “All the students except John, James, etc.,” is referred to as a whole, but as the whole is not definite, the term is not distributed. Because all is the quantity sign of the second subject the casual observer might easily be misled in designating it as a distributed term.

Here it may be well to explain that when reference is made to subject or predicate the logical subject or predicate is meant. Unless this is constantly kept in mind error results; e. g., in the proposition, “All white men are Caucasians,” the logical subject is “white men,” not “men.” If the subject were “men,” it would be undistributed, as the whole of the man family is not considered, but the actual subject, being “white men,” is distributed because the predicate refers to all white men.

Recurring to the illustration, “All men are mortal,” we have concluded that the subject “all men” is distributed. The predicate, “mortal,” however, is undistributed, as reference is made to it only in part; i. e., there are other beings aside from men that are mortal, such as “trees,”“horses,” “dogs,” etc. In all A propositions of the type of “all men are mortal,” the subject is distributed while the predicate is undistributed. This relation is clearly shown by the diagrammatical illustration, [Fig. 1]. Here all of the “men” circle is identical with only a part of the “mortal” circle. In other words, the whole of the “men” circle is considered, while reference is made to only a part of the “mortal” circle.

In the case of the co-extensive A both subject and predicate are distributed. Relative to the co-extensive “All men are rational animals,” it could likewise be said that “all rational animals are men,” or that “all men are all of the rational animals.” Reference is thus made to all of the definite predicate as well as to all of the definite subject.

In the E propositions, such as “No men are immortal,” the whole of the subject is excluded from the whole of the predicate. This makes evident the fact that both terms are distributed. See [Fig. 2].