## 25 Nov 2008

### Hegel, Science of Logic, Section 2: Magnitude (Quantity) §479-§481

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[Below is summary. At the end I cite the text in full. My interpretations not informed by a complete read of the text.]

Hegel

Science of Logic

Volume One: The Objective Logic

Book One: The Doctrine of Being

Section 2: Magnitude (Quantity)

B. EXTENSIVE AND INTENSIVE QUANTUM

(b) Identity of Extensive and Intensive Magnitude

§ 479

Intensive magnitude is a “unitary one of a plurality.” An intensive magnitude may come in a variety of different degrees, but that magnitude is neither a simple one with no numerical value, nor is it a plurality, because its value is taken together. It obtains its value through it relations to other degrees. Hence something of the 10th degree is half that of something that is of the 20th degree. The 10 degrees of a 10-degree-intensive-magnitude are contained within the whole value, but as a continuity.

§ 480

Intensive magnitudes are determined in two ways. They are determined by other intensive quanta that it is continuous with. So the 10th degree is 10 because it stops before reaching what lies beyond that value. Thus in this way it obtains its determinateness through its exclusion of other values.

Intensive magnitudes also receive their determinate value by being a value in itself. So the 20th degree contains 20 within itself which determines its value.

But as soon as we consider the 20th degree as having 20 degrees within it, that value of 20 taken on its own is an amount, making the degrees it describes an extensive quantum rather than an intensive one, because intensive quanta are continuous.

§ 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 the other having amount outside itself.

An extensive magnitude passes over into an intensive one when its internal plurality collapses into oneness, leaving plurality to lie outside it. Conversely, the intensive magnitude passes over into an extensive one when its “differently determined intensities” are considered in terms of an external amount.

From the original text:

##### (b) Identity of Extensive and Intensive Magnitude

§ 479

Degree is not external to itself within itself. Nevertheless, it is not the indeterminate one, the principle of number as such, which is not amount save in the negative sense of not being any particular amount. Intensive magnitude is primarily a unitary one of a plurality; there are many degrees, but they are determined neither as a simple one nor as a plurality, but only in the relation of this self-externality, or in the identity of the one and the plurality. if, therefore, the many as such are indeed outside the simple, unitary degree, nevertheless the determinateness of the degree consists in its relation to them; it thus contains amount. just as twenty, as an extensive magnitude, contains the twenty ones as discrete within it, so does the specific degree contain them as the continuity which this determinate plurality simply is; it is the twentieth degree, and is the twentieth degree only by virtue of this amount, which as such is outside it.

§ 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 contains 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 the other having amount outside 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.

§ 482

With this identity, the qualitative something makes its appearance, for the identity is the unity which is self-related through the negation of its differences; these differences, however, constitute the determinate being of the quantitative determinateness; this negative identity is therefore a something, and a something which is indifferent to its quantitative determinateness. Something is a quantum; but now the qualitative determinate being, as it is in itself, is posited as indifferent to quantum. Quantum, number as such, and so forth, could be spoken of without any mention of its having a something as substrate. But the something now confronts these its determinations, through the negation of which it is mediated with itself, as existing for itself and, since it has a quantum, as something which has an extensive and an intensive quantum. Its one determinateness which it has as quantum is posited in the differentiated moments of unit and amount; this determinateness is not only in itself one and the same, but its positing in these differences as extensive and intensive quantum is the return into this unity which, as negative, is the something posited as indifferent to it.

Hegel. Science of Logic. Transl. A.V. Miller. George Allen & Unwin, 1969.
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