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

by George Hastings McNair

In general the law of identity implies a certain permanency throughout the material world. That door is a door and always will be a door till the conditions change. If it were not for this law, that everything ispermanently identical with itself, it would be impossible to think at all. For example: Take away the notion of permanency from the door and thought becomes at once ridiculous. Suppose that while we are asserting that the object is a door, it changes to a tree, and while we insist that the object is now a tree, it changes to a cow, etc. We can readily see that it would hardly be worth while to think at all.

The law of identity may be stated in three ways: (1) Whatever is, is; (2) Everything remains identical with itself; (3) The same is the same.

ABSOLUTE IDENTITY—COMPLETE AND INCOMPLETE.

Applying the law of identity to the affirmative judgment expressed in the form of a proposition, we find two kinds of identity, absolute and relative. In the propositions, “Socrates is Socrates,” “dogs are dogs,” “honesty is honesty,” the subject is absolutely identical with the predicate—the same in form and meaning. If we were to illustrate the subject and predicate by two circles they would be of the same size and shape, the one coinciding with the other point to point.

This kind of absolute identity which makes possible all truisms we may term, for want of a better name, complete absolute identity. This would imply that there is an incomplete absolute identity and such seems to be the case. Examining the definition, “A man is a rational animal,” we observe that the notion man has the same content or meaning as the notion rational animal. In meaning, then, the two notions are absolutely identical. The one includes just as many objects or qualities asthe other, and if we were to draw two circles representing them, they would be of the same size. In form, in mode of expression, however, the notions differ and the circles, though coinciding, would need to differ in form, the boundary of one might be a solid line, the other a dotted. This we may call incomplete absolute identity. All logical definitions illustrate identities of this kind.

RELATIVE IDENTITY.

Relative identity is best understood by thinking of it as partial identity, just as we may think of absolute identity as total identity. In relative identity the whole of one notion may be affirmed of a part of another notion; or a part of one notion may be affirmed of a part of another notion. To illustrate: (1) All men are mortal; (2) Some men are wise. These and their like are made possible because of the law of relative identity. In the first proposition all of the “men” class is identical with a part of the “mortal” class. If we were to represent this relation by circles, the “men” circle would be made smaller than the “mortal” circle and placed inside it, as in [Fig. 1.]

Fig. 1.

Be it remembered that circles are surfaces, and in [Fig. 1] the men circle is identical with that portion of the mortal circle which is immediately underneath it.