24 Nov 2008

Hegel, Science of Logic, Vol 1, Bk 1, Sect 2: Magnitude (Quantity), Ch 1 "Quantity," B: Continuous and Discrete Magnitude, §§429-431

by Corry Shores
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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 1 Quantity


§ 429

1. Quantity contains two moments: continuity and discreteness. Quantity is the immediate unity of the two, but it is posited firstly in continuity only, and as such it is "continuous magnitude."

§ 430

Quantity is the concrete unity of discrete moments taken together as a whole. Thus quantity itself is a continuous magnitude.

§ 431

Quantity is posited in terms of the determinateness immanent in it, which is "the one." So Quantity itself is also a discrete magnitude. And yet, quantity is internally divided. In quantities that are continuous magnitudes, the internal divisions continue without negation on account of the "self-same connectedness" that blends all the divisions into one another. In discrete magnitudes, the internal divisions are interrupted by each other; they are discontinuous. But they are not incohesive. Each discrete unit is itself a one, so there is a continuum of ones in a discrete magnitude.

From the text of the original translation:

§ 429
1. Quantity contains the two moments of continuity and discreteness. It is to be posited in both of them as determinations of itself. It is already their immediate unity, that is, quantity is posited at first only in one of its determinations, continuity, and as such is continuous magnitude.
§ 430
Or we may say that continuity is indeed one of the moments of quantity which requires the other moment, discreteness, to complete it. But quantity is a concrete unity only in so far as it is the unity of distinct moments. These, are, therefore, also to be taken as distinct, but are not to be resolved again into attraction and repulsion, but are to be taken as they are in their truth, each remaining in its unity with the other, that is, remaining the whole. Continuity is only coherent, compact unity as unity of the discrete; posited as such it is no longer only a moment but the whole of quantity, continuous magnitude.
§ 431
2. Immediate quantity is continuous magnitude. But quantity is not an immediate at all; immediacy is a determinateness the sublatedness of which is quantity itself. It is, therefore, to be posited in the determinateness immanent in it, and this is the one. Quantity is discrete magnitude.
Discreteness is, like continuity, a moment of quantity but it is itself also the whole of quantity just because it is a moment in it, in the whole, and therefore as a distinct moment it does not stand outside the whole, outside its unity with the other moment. Quantity is in itself asunderness, and continuous magnitude is this asunderness continuing itself without negation as an internally self-same connectedness. But discrete magnitude is this asunderness as discontinuous, as interrupted. With this plurality of ones, however, we are not again in the presence of the plurality of atoms and the void, repulsion in general. Because discrete magnitude is quantity, its discreteness is itself continuous. This continuity in the discrete consists in the ones being the same as one another, or in having the same unity. Discrete magnitude is, therefore, the asunderness of the manifold one as self-same, not the manifold one in general but posited as the many of a unity.

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