Given that, through some association, the image of the line _a_ calls up that of the line _b_, and both are associatively ranged together, we have still not made the real synthesis _a_ + _b_ = _c_. For to think of _a_ and _b_ side by side is not the same thing as thinking of _c_, as we shall readily see if we square them. The squares of _a_ and _b_ thought of beside one another, that is, _a_2 and _b_2, are something quite different from the square of the really synthetised _a_ and _b_, which is (_a_ + _b_)2 = _a_2 + 2_ab_ + _b_2, or _c_ 2. This requires quite a new view, a spontaneous synthesis, which is an action and not a mere experience. The Ego. It was customary in earlier psychology, as it still is in all apologetic psychology, to regard the soul as a unified, immaterial, indivisible and therefore indestructible _substance_, as a monad, which, as a unity without parts, superior to its own capacities and the changes of its states, is at all times one and the same subject. Many attempts have been made since the time of Plotinus to accumulate proofs of this substantial unity. We may leave this question untouched here, and need not even inquire whether these definitions are not themselves things of the external world employed as images and analogies and pushed too far. But there are three factors which may be established in regard to the psychical in spite of all naturalistic opposition; and those who have attempted to find proofs for the traditional idea we have noted, have usually really had these three in mind, and quite rightly so: they are, self-consciousness, the unity of consciousness, and the consciousness of the ego. Self-Consciousness.