Chapter 2 - Quantum

Summary

Quantum, which in the first instance is quantity with a determinateness or limit in general, in its complete determinateness is number. Second, quantum divides first into extensive quantum, in which limit is the limitation of a determinately existent plurality; and then, inasmuch as the existence of this plurality passes over into being-for-itself, into intensive quantum or degree. This last is for-itself but also, as indifferent limit, equally outside itself. It thus has its determinateness in an other. Third, as this posited contradiction of being determined simply in itself yet having its determinateness outside itself and pointing outside itself for it, quantum, as thus posited outside itself within itself, passes over into quantitative infinity.

NUMBER

Quantity is quantum, or has a limit, both as continuous and discrete magnitude. The distinction between these two species has here, in the first instance, no significance.

As the sublated being-for-itself, quantity is already in and for itself indifferent to its limit. But, equally, the limit or to be a quantum is not thereby indifferent to quantity; for quantity contains within itself as its own moment the absolute determinateness of the one, and this moment, posited in the continuity or unity of quantity, is its limit, but a limit which remains as the one that quantity in general has become.

This one is therefore the principle of quantum, but as the one of quantity. For this reason it is, first, continuous, it is a unity; second, it is discrete, a plurality (implicit in continuous magnitude or posited in discrete magnitude) of ones that have equality with one another, the said continuity, the same unity. Third, this one is also the negation of the many ones as a simple limit, an excluding of its otherness from itself, a determination of itself in opposition to other quanta. The one is thus (α) self-referring, (β) enclosing, and (ϒ) other-excluding limit.

Thus completely posited in these determinations, quantum is number. The complete positedness lies in the existence of the limit as a plurality and so in its being distinguished from the unity. Number appears for this reason as a discrete magnitude, but in unity it has continuity as well.