43. Neither the successive nor simultaneous perception of two objects unaccompanied by relation is the idea of two. Hence the saying: a man and a horse do not make two, but only one and one; and the reason of this is that the man and the horse are represented to the understanding by their difference, not by their resemblance; and things must be presented to the mind under a common idea in order to give number. Thus, if we abstract their difference, and consider them only as animals, or corporeal beings, or beings simply, or things, they will make two. 44. In objects, then, totally unlike, or not comprehended under some common idea, there can be no number. Abstract number is number by excellence; because it eliminates all that distinguishes the things numbered, and considers them only as beings, consequently as similar, as contained in the general idea of being. Concrete numbers are only numbers so far as they participate in this property. _Two_ is applicable to one horse and another horse, but not to a horse and a man, unless we identify them under the idea of animal, and abstract rationality and irrationality. Concrete number requires a common denomination; otherwise it is not number. 45. The idea of distinction, that is, that the one is not the other, enters into the idea of two, so that this idea necessarily involves an affirmation and a negation. The affirmation is of the real, possible, or imaginary existence of the things counted; the negation is of the one with respect to the other. Affirmation without distinction or negation involves identity. The idea of two, as well as that of every other number, includes the ideas of identity and distinction. The identity is of each extreme with itself; the distinction is of the extremes among themselves. Identity in the thing is the thing itself: identity in the idea is the simple perception of the thing. Distinction in the thing is the negation of it with respect to others: distinction in the idea is the perception of negation. We always perceive a thing as identical, and consequently every perception includes the idea of unity. But we do not always, when we perceive a thing, observe its negation with respect to others, and consequently do not always perceive number. The idea of number originates in comparison, when we see an object which _is not_ another.