Save in extremely rare cases,—supposing such to occur at all, as perhaps in the instant of surprise, and in states approximating to pure sensation,—save in such extremely rare cases, where the mind, like a mirror, passively reflects external impressions, intellectual activity may always be reduced to one of the two following types: associating, combining, unifying, or dissociating, isolating, and separating. These cardinal operations underlie all forms of _cognition_, from the lowest to the highest, and constitute its unity of composition. Abstraction belongs to the second type. It is a normal and necessary process of the mind, dependent on attention, i. e., on the limitation, willed or spontaneous, of the field of consciousness. The act of abstraction implies in its genesis both negative and positive conditions, and is the result of these. The negative conditions consist essentially in the fact that we cannot apprehend more than one quality or one aspect, varying according to the circumstances, in any complex whole,—because consciousness, like the retina, is restricted to a narrow region of clear perception. The positive condition is a state which has been appropriately termed a “psychical reinforcement” of that which is being abstracted, and it is naturally accompanied by a weakening of that which is abstracted from. The true characteristic of abstraction is this partial increment of intensity. While involving elimination, it is actually a positive mental process. The elements or qualities of a percept, or a representation, which we omit do not necessarily involve such suppression. We leave them out of account simply because they do not suit our ends for the moment, and are complementary.[2] Abstraction being, then, in spite of negative appearances, a positive operation, how are we to conceive it? Attention is necessary to it, but it is more than attention. It is an augmentation of intensity, but it is more than an augmentation of intensity. Suppose a group of representations _a + b + c = d_. To abstract from _b_ and _c_ in favor of _a_, would ostensibly give _a = d - (b + c)_. If this were so, _b_ and _c_ would be retained unaltered in consciousness; there would be no abstraction. On the other hand, since it is impossible for the whole representation _d_ to be suppressed outright, _b_ and _c_ cannot be totally obliterated. They subsist, accordingly, in a residual state which may be termed _x_, and the abstract representation is hence not _a_ but _a + x_ or _A_. Thus the elements of abstract representations are the same as those of concrete representations; only some are strengthened, others weakened: whence arise new groupings. Abstraction, accordingly, consists in the formation of new groups of representations which, while strengthening certain elements of the concrete representations, weaken other elements of the same.[3]