It is well for the psychologist to note the privileged position of what we term the unity-type, or simply 1. It originates in experience, because unity, even when concrete, and apprehended by gross perception, appears as a primitive element, special and irreducible. So long as the mind confines itself to perceiving or imagining, there is in the passage from one object to two, three, or four objects, or inversely in the passage from four objects to three, two, or only one, an augmentation or diminution. But below unity in the first case, and above unity in the second, there is no longer any mental representation; unity seems to border on nonentity and to be an absolute beginning. From this privileged point the mind can follow two opposite directions, by an identical movement: the one towards the infinitely great, with constant augmentation; the other towards the infinitely small, with constant diminution—but in one sense or the other, infinity is a never exhausted possibility. Here we reach the much disputed question of infinite number: psychology is not concerned with this. For some, infinite number has an _actual_ existence. For others, it only exists potentially, i. e., as an intellectual operation which may, as was said above, add or subtract, without end or intermission.[96] III. The importance of signs, as the instruments of abstraction and generalisation, is nowhere so well shown as in their multiple applications to discrete or continuous quantity. The history of the mathematical sciences is in part that of the invention, and use of symbols of increasing complexity, whose efficacy is clearly manifested in their theoretical or practical results. In the first place, words were substituted for the things that were held to be numerable; next, particular signs, or figures; later still, with the invention of algebra, letters took the place of figures, or at any rate assumed their function and part in the problem to be solved; later still, the consideration of geometrical figures was replaced by that of their equations; finally, the use of new symbols corresponded with calculations for infinitesimal quantities, negative quantities, and imaginary numbers. These symbols are such a powerful auxiliary to the labor of the mathematicians that those among them who affect philosophy have gladly discoursed upon their nature and intrinsic value. They seem to be divided into two camps.