Without the indivisible unity of consciousness, no intelligent subject is conceivable. Every intelligent being requires this link to unite the variety of phenomena of which it is the subject. If this unity fail, the phenomena become an informal aggregation, unrelated among themselves: intellectual acts without an intelligent being. The tendency to unity originates in the perfection of our mind, and is itself a perfection; but it needs to be carefully watched, lest it go astray, and seek real unity there, where only a factitious unity can be found. This exaggeration is the cause of pantheism, the fatal error of our day. Our mind is one, so also is the infinite essence, cause of all finite beings; but the aggregation of these beings is not one, for even when united by many ties, they cease not to be distinct. There is in the world unity of order, of harmony, of origin, and of end; but there is no absolute unity. Number also enters into unity of harmony, but it is incompatible with absolute unity, as reason and experience both show. CHAPTER V. GENERATION OF THE IDEA OF NUMBER. 37. Unity is the first element of number, but does not of itself alone constitute number, which is not unity, but the collection of unities. 38. _Two_ is a number. What is our idea of the number _two_? Evidently it is not confounded with its sign, for signs are many and very different, but it is one and always the same. 39. It would seem at first sight that the idea of two is independent of the mode of its generation, and that, being one, it may be formed by addition or subtraction, by adding one to one, or taking one from three: 1 + 1 = 2; 3-1 = 2. But if we reflect upon these two expressions, we shall see that the latter is impossible without the former. We should not know that 3-1 = 2 if we did not previously know that two entered into the composition of three, and how it entered. We could know nothing of this had we not already the idea of two, and this idea is nothing else than the perception of this sum. 40. The idea of two is no sensation, for it extends alike to the sensible and the non-sensible, to the simultaneous and the successive. In itself it is simple, its object is composite. 41. Since the collection of objects is small in two, the imagination can easily figure to itself what the understanding perceives; and the idea seems clearer to us because made sensible by a representation. The idea of addition made, _in facto_, that is, the idea of the sum, enters into that of two, but not of addition _in fieri_. Our idea of this number is perfectly clear, and yet we do not continually think of one plus one. 42. The idea of two refers to the simultaneous as well as to the successive; but our mind does not discover it until after it has the idea of succession. The object of this perception is the relation of united things; the understanding perceives them as such, and then only has it the idea of two.