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.
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.