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 as the 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. Illustration: 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. The same relation may be indicated by a small pad being placed on top of a larger pad. Then the whole of the smaller pad could be thought of as being identical with that part of the larger pad which is immediately underneath. In the case of the second proposition a part of the “men” class is identical with a portion of the “wise” class. The two circles indicating this relation must intersect each other so that a portion of each may be common ground, as in Fig. 2 where the shaded part represents the identity. Illustration: Fig. 2. Thus we see that the law of identity underlies all affirmative propositions. Absolute identity making possible the truism and definition, and relative identity conditioning all the universal and particular affirmative propositions which are neither truisms nor definitions. The three forms may be symbolized as follows: (1) A is A――Absolute complete (2) _A_ is A――Absolute incomplete (3) A is B――Relative. The student will note that the “A’s” of absolute incomplete differ in form. =3. LAW OF CONTRADICTION.=