62. By generalization we unite many similar things in one idea. The general idea is a kind of formula. Numeration unites in one sign many things contained in a general idea, but this sign has, at the same time, its own distinctive character. Thus the general idea belongs as a predicate to each of its particular objects; number belongs to no one in particular, but to all joined. We perceive in abstraction a common property, and lay aside all the particular objects which it presents; in numeration, we perceive similarity, but always with distinction. Abstraction is the result of comparison, but not comparison. Numeration implies a permanent comparison, or the recollection of it. 63. The idea of number is not conventional; a hundred is always a hundred with all its properties and relations, and this, too, prior to all convention and even to all human perception. The sign, and the sign only, is conventional. Were there no intellectual creature, and a hundred beings distinct among themselves were to exist, there would really be this number. The number three exists in the august mystery of the Trinity, from all eternity, and of absolute necessity. Number requires only the existence of distinct things; since, however unlike they may be, they always have something in common being, which may be included in a general idea, and consequently they fulfil the two conditions necessary to number. 64. The perception of being and of distinction, that is, of substantive being and of relative not-being, is the perception of number. The science of the relations of every collection, with its measure, which is unity, is the science of numbers. BOOK SEVENTH. ON TIME. CHAPTER I. IMPORTANCE AND DIFFICULTY OF THE SUBJECT. 1. The explanation of the idea of time is not a matter of mere curiosity, but of the highest importance. To convince ourselves of this we have only to consider that the explanation of the whole edifice of human cognitions is based upon it. The most fundamental and indispensable principle which supports all others, includes the idea of time. A thing cannot be and not be at the same time: "impossibile est idem simul esse et non esse." The impossibility of being and of not-being regards only the _simul, the same time_. Therefore, the idea of time necessarily enters into the very principle of contradiction. 2. The idea of time is involved in all our perceptions; it extends to many more objects than does the idea of space. We estimate not only the movements of bodies by time, but also the operations of the mind. We know that a series of thoughts may be measured by time the same as a series of corporal movements.