Hegel: Intensive And Extensive Magnitude

The correlated terms of intensive and extensive abstraction have another antecedent in the reflections of G.W.F Hegel on intensive and extensive “magnitude.”  The following fragments can be found in Hegel’s “Science of Logic- Identity of Intensive and Extensive Magnitude” – sections 480, 481 and 483:

“480. The determinateness of intensive magnitude is, therefore, to be considered from two sides. Intensive magnitude is determined by other intensive quanta and is  continuous with its otherness, so that its determinateness consists in this relation to its otherness. Now in the first place, in so far as it is a simple determinateness it is determinate relatively to other degrees;  it excludes them from itself and has its determinateness in this exclusion. But, secondly, it is determinate in its own self; this it is in the amount as its own amount, not in the amount as excluded, nor in the amount of other degrees. The twentieth degree contents the twenty within itself;  it is not only determined as distinguished from the nineteenth, twenty-first and so on, but its determinateness is its own amount. But in so far as the amount is its own—and the determinateness is at the same time essentially an amount—the degree is an extensive quantum.”

“481. Extensive and intensive magnitude are thus one and the same determinateness of quantum; they are only distinguished by the one having amount within itself and other having amount outside of itself. Extensive magnitude passes over into intensive magnitude because its many spontaneously collapse into oneness, outside which the many stand. But conversely, this unitary degree has its determinateness only in the amount, and that too in its own amount; as indifferent to the differently determined intensifies it has within itself the externality of the amount; and so intensive magnitude is equally essentially an extensive magnitude. “

“483. Extensive and intensive quantum are usually distinguished in the ordinary conception of them as kinds of magnitude, as if some objects had only intensive, others only extensive magnitude. In addition we have the conception of a philosophical science of Nature in which what is a plurality or extensive—for example, in the fundamental property of matter to occupy space, and in other concepts too—is converted into something intensive, meaning thereby that the intensive aspect as dynamic is the true determination; density, or the specific filling of space, for example, must essentially be understood not as a certain aggregate and amount of material parts in a quantum of space, but as a certain degree of the space-filling force of matter.”

Usually Hegel’s difficult prose and his constant attempt at exhausting every concept discourage the reader, but from the fragments above it should be enough to retain that the great thinker very closely associated intensive and extensive concepts as being interrelated and co-dependent. Thinking intensive and extensive magnitude are shown to be inseparable. (See: Hegel’s Science of Logic, translated by A. V. Miller, London, Allen and Unwin, 1969 ).