Hegel, Science of Logic, Vol 1, Bk 1, Sect 2: Magnitude (Quantity), Ch 1 "Quantity," A: Pure Quantity, §395-§398

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.]

Volume One: The Objective Logic

Book One: The Doctrine of Being

Section 2: Magnitude (Quantity)

Chapter 1 Quantity

A. PURE QUANTITY

§ 395

Quantity comes about when something is related to something else in such a way that both are taken to be identical. Given that they are numerically different, they in a sense repel each other. But there is also an attraction between the two whereby they are taken as qualitatively identical even if they are not numerically identical. Thus each one unifies with its "self-externality" (its qualitatively but not quantitatively identical counterpart), and hence "Attraction is in this way the moment of continuity in quantity."

§ 396

Continuity is a non-immediate unity of ones. What differentiates the ones does not interrupt their sequence. Continuity is the "the self-continuation of the different ones into those from which they are distinguished."

§ 397

The discreteness in continuity is a "coalescent discreteness" in which the units are not conjoined by a void or negativity; rather they are connected by their own continuity.

§ 398

What comes out of one unit is likewise another unit, so the continuity is at the same time a plurality that remains self-identical.

Note, in § 401 Hegel quotes the Scholium of Proposition 15 of Spinoza's Ethics, whose content resembles Spinoza's Letter 12, sixth paragraph. § 401 reads:

It is the notion of pure quantity as opposed to the mere image of it that Spinoza, for whom it had especial importance, has in mind when he speaks of quantity as follows:

'Quantity is conceived by us in two manners, to wit, abstractly and superficially, as an offspring of imagination or as a substance, which is done by the intellect alone. If, then, we look at quantity as it is in the imagination, which we often and very easily do, it will be found to be finite, divisible, and composed of parts; but if we look at it as it is in the intellect and conceive it, in so far as it is a substance, which is done with great difficulty, then as we have already sufficiently shown, it will be found to be infinite, without like, and indivisible. This, to all who know how to distinguish between the imagination and the intellect, will be quite clear.'

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From the original text of the translation:

Chapter 1 Quantity

A. PURE QUANTITY

§ 395

Quantity is sublated being-for-self; the repelling one which related itself only negatively to the excluded one, having passed over into relation to it, treats the other as identical with itself, and in doing so has lost its determination: being-for-self has passed over into attraction. The absolute brittleness of the repelling one has melted away into this unity which, however, as containing this one, is at the same time determined by the immanent repulsion, and as unity of the self-externality is unity with itself. Attraction is in this way the moment of continuity in quantity.

§ 396

Continuity is, therefore, simple, self-same self-relation, which is not interrupted by any limit or exclusion; it is not, however, an immediate unity, but a unity of ones which possess being-for-self. The asunderness of the plurality is still contained in this unity, but at the same time as not differentiating or interrupting it. In continuity, the plurality is posited as it is in itself; the many are all alike, each is the same as the other and the plurality is, consequently, a simple, undifferentiated sameness. Continuity is this moment of self-sameness of the asunderness, the self-continuation of the different ones into those from which they are distinguished.

§ 397

In continuity, therefore, magnitude immediately possesses the moment of discreteness — repulsion, as now a moment in quantity. Continuity is self-sameness, but of the Many which, however, do not become exclusive; it is repulsion which expands the selfsameness to continuity. Hence discreteness, on its side, is a coalescent discreteness, where the ones are not connected by the void, by the negative, but by their own continuity and do not interrupt this self-sameness in the many.

§ 398

Quantity is the unity of these moments of continuity and discreteness, but at first it is so in the form of one of them, continuity, as a result of the dialectic of being-for-self, which has collapsed into the form of self-identical immediacy. Quantity is, as such, this simple result in so far as being-for-self has not yet developed its moments and posited them within itself. It contains them to begin with as being-for-self posited as it is in truth. The determination of being-for-self was to be a self-sublating relation-to-self, a perpetual coming-out-of-itself. But what is repelled is itself; repulsion is, therefore, the creative flowing away of itself. On account of the self-sameness of what is repelled, this distinguishing or differentiation is an uninterrupted continuity; and because of the coming-out-of-itself this continuity, without being interrupted, is at the same time a plurality, which no less immediately remains in its self-identicalness.

§ 401

It is the notion of pure quantity as opposed to the mere image of it that Spinoza, for whom it had especial importance, has in mind when he speaks of quantity as follows:

'Quantity is conceived by us in two manners, to wit, abstractly and superficially, as an offspring of imagination or as a substance, which is done by the intellect alone. If, then, we look at quantity as it is in the imagination, which we often and very easily do, it will be found to be finite, divisible, and composed of parts; but if we look at it as it is in the intellect and conceive it, in so far as it is a substance, which is done with great difficulty, then as we have already sufficiently shown, it will be found to be infinite, without like, and indivisible. This, to all who know how to distinguish between the imagination and the intellect, will be quite clear.'

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

Text available online at:

http://www.marxists.org/reference/archive/hegel/index.htm