## 24 Nov 2008

### Hegel, Science of Logic, Vol 1, Bk 1, Sect 2: Magnitude (Quantity), Ch 2 "Quantum," §§437-442

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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)

Chapter 2 Quantum

§ 437

A quantum is a quantity with a determinateness or limit. Quantum in its complete determinateness is number. Quantum subdivides into
1) extensive quantum, "in which the limit is a limitation of the determinately existent plurality;" and
2) intensive quantum or degree, "the determinate being having made the transition into being-for-self." The intensive quantum has an "indifferent limit," thus it is at the same time both "for itself" and "outside itself."

As this manifest contradiction of being determined simply within itself yet having its determinateness outside it, pointing outside itself for it, quantum posited as being in its own self external to itself, passes over thirdly, into quantitative infinity.

A. NUMBER

§ 438

Quantity is quantum, or has a limit, both as continuous and as discrete magnitude.

§ 439

Quantity is indifferent to its limit, but it also contains within itself unity (or "the one"), which is absolutely determined.

§ 440

The one is the "principle of quantum." It is firstly a unitary continuity. It is secondly a discrete plurality of ones, "which is implicit in continuous, or explicit in discrete magnitude." The one is thirdly a "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." Thus the one is
[a] self-relating,
[b] enclosing and
[c] other-excluding limit.

§ 441

When we posit quantum in these above determinations, we consider it as number, which appears both as a discrete magnitude as well as a unitary continuity.

§ 442

In quantum as number, the limit is posited as a manifold within itself. Amount is the "form taken by discreteness in number" and the unit is "the continuity of the amount. Amount and unit constitute the moments of number."

From the original text of the translation:
Chapter 2 Quantum
§ 437
Quantum, which to begin with is quantity with a determinateness or limit in general is, in its complete determinateness, number. Quantum differentiates itself secondly, into (a) extensive quantum, in which the limit is a limitation of the determinately existent plurality; and (b) intensive quantum or degree, the determinate being having made the transition into being-for-self. Intensive quantum as both for itself and at the same time immediately outside itself — since it is an indifferent limit — has its determinateness in an other. As this manifest contradiction of being determined simply within itself yet having its determinateness outside it, pointing outside itself for it, quantum posited as being in its own self external to itself, passes over thirdly, into quantitative infinity.
A. NUMBER
§ 438
Quantity is quantum, or has a limit, both as continuous and as discrete magnitude. The difference between these two kinds has here, in the first instance, no immediate significance.
§ 439
The very nature of quantity as sublated being-for-self is ipso facto to be indifferent to its limit. But equally, too, quantity is not unaffected by the limit or by being, a quantum; for it contains within itself as its own moment the one, which is absolutely determined and which, therefore, as posited in the continuity or unity of quantity, is its limit, but a limit which remains what it has become, simply a one.
§ 440
This one is thus the principle of quantum, but as the one of quantity. Hence, first, it is continuous, it is a unity; secondly, it is discrete, a plurality of ones, which is implicit in continuous, or explicit in discrete magnitude, the ones having equality with one another, possessing the said continuity, the same unity. Thirdly, this one is also a 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. Thus the one is [a] self-relating, [b] enclosing and [c] other-excluding limit.
§ 441
Quantum completely posited in these determinations is number. The complete positedness lies in the existence of the limit as a plurality and so in its distinction from the unity. Consequently, number appears as a discrete magnitude, but in the unity it equally possesses continuity. It is, therefore, also quantum in its complete determinateness, for its principle the one, the absolutely determinate. Continuity, in which the one is present only in principle, as a sublated moment — posited as a unity — is the form of indeterminateness.
§ 442
Quantum, merely as such, is limited generally; its limit is an abstract simple determinateness of it. But in quantum as number, this limit is posited as manifold within itself. It contains the many ones which constitute its determinate being, but does not contain them in an indeterminate manner, for the determinateness of the limit falls in them; the limit excludes other determinate being, that is, other pluralities and the ones it encloses are a specific aggregate, the amount — which is the form taken by discreteness in number — the other to which is the unit, the continuity of the amount. Amount and unit constitute the moments of number.
Hegel. Science of Logic. Transl. A.V. Miller. George Allen & Unwin, 1969.
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