46. The ideas of being, distinction, and similarity enter into that of two. The idea of being, because nothing cannot be counted: that of distinction, or negation of the one being the other, because the identical does not constitute number: that of similarity, because things are only numbered when abstraction is made of their difference. Being is the basis of perception; distinction, of comparison; and similarity, of union. Perception begins with unity, proceeds with distinction, and ends with similarity, which is a kind of unity. The perception of this similarity unites what is distinct; but the union need not always be of the things, but may be in the idea comprising them. There are two poles of the world, but they are not united. The perception of the number two requires something more than the simple perception of objects; they must be susceptible of comparison, and consequently united in a common idea. This perception, therefore, demands comparison and abstraction, and this is why animals cannot numerate; they can neither compare nor generalize. 47. The analysis of the idea of two is the analysis of all numbers; the difference is not of nature, but of more and less; in the repetition of the same perception. 48. If any one now ask whether number be in the things, or in the mind alone, we reply that it is in things as in its foundation, because both distinction and similarity are in the things; that is, the one is not the other, and both have something in common; but it is the mind that sees all this. 49. After having perceived the distinction and union of two objects, we can also perceive another object, which will be neither the one nor the other of them, and will yet be comprehended in one general idea with them. This is the perception or idea of the number _three_. No matter how many numbers be imagined, nothing will ever be discovered in any of them except a simultaneous perception of objects, distinction of objects, and similarity of objects. If these be determinate, we shall have concrete number; if they be comprised in the general idea of being, of thing, we shall have abstract number.