C. BEING-FOR-SELF IN MEASURE

§ 738

1. In the form of specified measure just considered, the quantitative element of both sides is qualitatively determined (both in the ratio of powers); hence they are moments of one measure-determinateness of qualitative nature.

At the same time, however, the two sides are so far posited only as immediate, merely different qualities, which do not themselves stand in the same relationship as their quantitative determinatenesses; that is, they cannot be said to have no meaning or existence outside that relationship, as is the case in the determinateness of quantity as a ratio of powers.

The qualitative element thus masks itself, specifying not itself but the quantitative determinateness; only in the latter is it posited, remaining on its own account an immediate quality as such which, beside the fact that it explicitly differentiates the magnitude and beside its relation to its other, still has an independent determinate being of its own. Thus space and time, apart from that specification contained in their quantitative determinateness in the descent of a falling body, or in the absolutely free motion, count as space in general and time in general, space having an enduring existence of its own apart from and without time, and time flowing on its own independently of space.

§ 739

This immediacy of the qualitative element as against its specific measure relation is, however, just as much bound up with a quantitative immediacy and with the indifference of this quantitative aspect in it towards this its relation; the immediate quality has also a merely immediate quantum.

Consequently, the specific measure has also a side which is, to begin with, subject to external alteration in the sense of a merely arithmetical progression unaffected by the specific measure and in which falls the external, hence only empirical, determinateness of magnitude. Quality and quantum as thus also appearing outside the specific measure are at the same time correlated with it; immediacy is a moment of those sides which themselves belong to measure. Thus the immediate qualities also belong to measure, are likewise in relation and stand in a quantitative relationship which, as outside the specified determination, the ratio of powers, is itself only a direct ratio and an immediate measure. This conclusion and its import is to be indicated in more detail.

§ 740

2. Even though the immediately determined quantum as such is, in virtue of its being a moment of measure, established as in itself determinable by the Notion, it is still with reference to the specific measure an externally given quantum. But the immediacy which is thus posited is the negation of the qualitative determination of measure; this has already been demonstrated in respect of the sides of this determination of measure which for that reason appeared as independent qualities. Such negation and the return to the immediate determination of quantity lies in the qualitatively determined relation, for the relation of distinct terms as such implies their correlation as one determinateness which latter, in distinction from the determination of the relation, is here in the sphere of quantity a quantum. As a negation of the distinct qualitatively determined sides, this exponent is a being-for-self or absolute determinedness; but it is such being-for-self only in principle [an sich]; as a determinate being it is a simple immediate quantum which is the quotient or exponent of a direct ratio between the sides of the measure, but in general is the unit appearing as empirical, in the quantitative side of measure. In the motion of failing bodies the spaces traversed are proportional to the squares of the elapsed times, s = at2. This is the specifically determined relation of space and time, a ratio of powers. The other, the direct ratio, would concern space and time as mutually indifferent qualities; it is supposed to be the ratio of the space traversed to the first unit of time. The same coefficient a remains in all the following units of time — the unit being an ordinary quantum, while the amount is determined by the specifying measure. This unit at the same time counts as the exponent of that direct ratio which belongs to the imaginary, spurious velocity i.e. the merely formal velocity which is not specifically determined by the Notion. Such a velocity does not exist here, any more than the one previously mentioned which is supposed to accrue to the falling body at the end of a unit of time. That velocity was ascribed to the first unit of time in the motion of a falling body; but this so-called unit of time is itself only an assumed unit and has as such atomic point no real being.

The beginning of the motion — the alleged smallness of it could make no difference — is straightway a magnitude and one specified by the law of descent of a falling body. The said empirical quantum is attributed to the force of gravity, on the supposition that this force itself has no connection with the actual specification, with the ratio of powers characteristic of a determination of measure. The immediate moment, that in the motion of a falling body the amount of some fifteen spatial units, taken as feet, is traversed in a unit — the so-called first unit — of time, a second, is an immediate measure, like the measurements of the limbs of the human body, the distances and diameters of the planets and so forth. The determination of such a measure falls elsewhere than in the qualitative measure determination itself, here in the law of descent of a falling body; however, the concrete sciences have so far failed to throw any light on the basis of determination of such numbers, which are only immediate and consequently are the empirical embodiment of a measure. Here we are concerned only with the determinateness specified by the Notion, namely, that the said empirical coefficient constitutes the moment of being-for-self in the measure-determination, and that too only in so far as this moment is unexplicated [an sich], and hence an immediacy. The second moment is the developed side of this being-for-self, the specific measure determinateness of the sides. In the motion of falling, a motion which is still half-conditioned and half-free, gravity, according to this second moment, is to be regarded as a force of nature, so that the relationship expressed by the law of descent of a falling body is determined by the nature of space and time, and consequently the said specification, namely, the ratio of powers, falls within gravity; the above-mentioned simple direct ratio expresses only a mechanical relationship between space and time in the [merely] formal velocity which is externally produced and determined.

§ 741

3. Measure has now acquired the character of a specified quantitative relation which, as qualitative, has in it the ordinary external quantum; but this is not a quantum in general, but essentially a determinant of the relation as such; hence in the sense of an exponent, and by virtue of the immediacy of its determination, of a fixed exponent, namely that of the already mentioned direct ratio between the same qualities whose quantitative relationship is at the same time specifically determined by the ratio. This direct ratio is, so to speak, anticipated and assumed as given in the example used of a measure, namely the law of descent of a falling body; but still, as we remarked, it does not exist in this motion. The fact, however, that the two sides of measure are themselves measures, the one immediate and external, and the other immanently specified, both being contained within the unity of measure itself, means that measure is now further determined, is realised. As this unity, measure contains the relation in which the magnitudes are determined and posited as differently specified by the nature of the qualities; its determinateness is accordingly wholly immanent and self-subsistent, and has at the same time collapsed into the being-for-self of an immediate quantum, the exponent of a direct ratio. The self-determination of the relation is thus negated, for in this its other it has its final, explicit determinateness; and conversely, the immediate measure which is supposed to be in its own self qualitative, possesses in truth such qualitative determinateness only in the other side of the relation. This negative unity is a real being-for-self, the category of a something as a unity of qualities which are related as measures — a completely self-subsistent something. The two sides which have presented themselves as distinct relations also immediately possess a twofold existence; or, to put it more explicitly, a self-subsistent whole of this kind, just because it is a real being-for-self, is at the same time a repulsion into distinct self-subsistent somethings whose qualitative nature and subsistence (materiality) lies in their measure determinateness.

§ 774

The system of natural numbers already shows a nodal line of qualitative moments which emerge in a merely external succession. It is on the one hand a merely quantitative progress and regress, a perpetual adding or subtracting, so that each number has the same arithmetical relation to the one before it and after it, as these have to their predecessors and successors, and so on. But the numbers so formed also have a specific relation to other numbers preceding and following them, being either an integral multiple of one of them or else a power or a root. In the musical scale which is built up on quantitative differences, a quantum gives rise to an harmonious relation without its own relation to those on either side of it in the scale differing from the relation between these again and their predecessors and successors. While successive notes seem to be at an ever-increasing distance from the keynote, or numbers in succeeding each other arithmetically seem only to become other numbers, the fact is that there suddenly emerges a return, a surprising accord, of which no hint was given by the quality of what immediately preceded it, but which appears as an actio in distans, as a connection with something far removed. There is a sudden interruption of the succession of merely indifferent relations which do not alter the preceding specific reality or do not even form any such, and although the succession is continued quantitatively in the same manner, a specific relation breaks in per saltum.

§ 775

Such qualitative nodes and leaps occur in chemical combinations when the mixture proportions are progressively altered; at certain points in the scale of mixtures, two substances form products exhibiting particular qualities. These products are distinguished from one another not merely by a more or less, and they are not already present, or only perhaps in a weaker degree, in the proportions close to the nodal proportions, but are bound up with these nodes themselves. For example, different oxides of nitrogen and nitric acids having essentially different qualities are formed only when oxygen and nitrogen are combined in certain specific proportions, and no such specific compounds are formed by the intermediate proportions. Metal oxides, e.g. the lead oxides, are formed at certain quantitative points of oxidation and are distinguished by colours and other qualities. They do not pass gradually into one another; the proportions lying in between these nodes do not produce a neutral or a specific substance. Without having passed through the intervening stages, a specific compound appears which is based on a measure relation and possesses characteristic qualities. Again, water when its temperature is altered does not merely get more or less hot but passes through from the liquid into either the solid or gaseous states; these states do not appear gradually; on the contrary, each new state appears as a leap, suddenly interrupting and checking the gradual succession of temperature changes at these points. Every birth and death, far from being a progressive gradualness, is an interruption of it and is the leap from a quantitative into a qualitative alteration.

§ 776

It is said, natura non facit saltum [there are no leaps in nature]; and ordinary thinking when it has to grasp a coming-to-be or a ceasing-to-be, fancies it has done so by representing it as a gradual emergence or disappearance. But we have seen that the alterations of being in general are not only the transition of one magnitude into another, but a transition from quality into quantity and vice versa, a becoming-other which is an interruption of gradualness and the production of something qualitatively different from the reality which preceded it. Water, in cooling, does not gradually harden as if it thickened like porridge, gradually solidifying until it reached the consistency of ice; it suddenly solidifies, all at once. It can remain quite fluid even at freezing point if it is standing undisturbed, and then a slight shock will bring it into the solid state.

§ 777

In thinking about the gradualness of the coming-to-be of something, it is ordinarily assumed that what comes to be is already sensibly or actually in existence; it is not yet perceptible only because of its smallness. Similarly with the gradual disappearance of something, the non-being or other which takes its place is likewise assumed to be really there, only not observable, and there, too, not in the sense of being implicitly or ideally contained in the first something, but really there, only not observable. In this way, the form of the in-itself, the inner being of something before it actually exists, is transformed into a smallness of an outer existence, and the essential difference, that of the Notion, is converted into an external difference of mere magnitude. The attempt to explain coming-to-be or ceasing-to-be on the basis of gradualness of the alteration is tedious like any tautology; what comes to be or ceases to be is assumed as already complete and in existence beforehand and the alteration is turned into a mere change of an external difference, with the result that the explanation is in fact a mere tautology. The intellectual difficulty attendant on such an attempted explanation comes from the qualitative transition from something into its other in general, and then into its opposite; but the identity and the alteration are misrepresented as the indifferent, external determinations of the quantitative sphere.

§ 778

In the moral sphere, in so far as it is considered under the categories of being, there occurs the same transition from quantity into quality and different qualities appear to be based in a difference of magnitude.

It is through a more or less that the measure of frivolity or thoughtlessness is exceeded and something quite different comes about, namely crime, and thus right becomes wrong and virtue vice. Thus states, too, acquire through their quantitative difference, other things being assumed equal, a distinct qualitative character. With the expansion of the state and an increased number of citizens, the laws and the constitution acquire a different significance. The state has its own measure of magnitude and when this is exceeded this mere change of size renders it liable to instability and disruption under that same constitution which was its good fortune and its strength before its expansion.

C The Measureless

Chapter 3: The Becoming of Essence

A Absolute Indifference B Indifference as an Inverse Ratio of its Factors Remark: Centripetal and Centrifugal Force

C Transition into Essence

§ 803

Absolute indifference is the final determination of being before it becomes essence; but it does not attain to essence. It reveals itself as still belonging to the sphere of being through the fact that, determined as indifferent, it still contains difference as an external, quantitative determination; this is its determinate being, contrasted with which absolute indifference is determined as being only implicitly the absolute, not the absolute grasped as actuality. In other words, it is external reflection which stops short at conceiving the differences in themselves or in the absolute as one and the same, thinking of them as only indifferently distinguished, not as intrinsically distinct from one another. The further step which requires to be made here is to grasp that this reflection of the differences into their unity is not merely the product of the external reflection of the subjective thinker, but that it is the very nature of the differences of this unity to sublate themselves, with the result that their unity proves to be absolute negativity, its indifference to be just as much indifferent to itself, to its own indifference, as it is indifferent to otherness.

§ 804

But we are already familiar with this self-sublating of the determination of indifference; in the development of its positedness, this determination has shown itself to be from every aspect a contradiction. It is in itself the totality in which every determination of being is sublated and contained; it is thus the substrate, but at first only in the one-sided determination of the in-itself, and consequently the differences, namely, the quantitative difference and the inverse ratio of factors, are present in it only in an external manner. As thus the contradiction of itself and its determinedness, of its implicit determination and its posited determinateness, it is the negative totality whose determinatenesses have sublated themselves in themselves and in so doing have sublated this fundamental one-sidedness of theirs, their [merely] implicit being [Ansichsein]. The result is that indifference is now posited as what it in fact is, namely a simple and infinite, negative relation-to-self, its inherent incompatibility with itself, a repelling of itself from itself. The process of determining and being determined is not a transition, nor an external alteration, nor an emergence of determinations in the indifference, but is its own self-relating which is the negativity of itself, of its [merely] implicit being.

§ 805

Now these repelled determinations do not possess themselves, do not emerge as self-subsistent or external determinations, but first, as moments belonging to the implicit unity, they are not expelled from it but are borne by it as the substrate and are filled solely by it; secondly, as determinations which are immanent in the explicated unity, they are only through their repulsion from themselves. The being of the determinations is no longer simply affirmative as in the entire sphere of being, but is now a sheer positedness, the determinations having the fixed character and significance of being related to their unity, each consequently being related to its other and with negation; this is the mark of their relativity.

§ 806

Thus we see that being in general and the being or immediacy of the distinct determinatenesses, no less than the implicit being, has vanished and the unity is being, an immediate presupposed totality such that it is this simple self-relation only as a result of the sublating of this presupposition, and this presupposedness and immediate being is itself only a moment of its repelling, the original self-subsistence and self-Identity is only as the resulting coming together with itself. Being, in its determining, has thus determined itself to essence, a being which, through the sublating of being, is a simple being-with-itself. ®

ESSENCE - Second Part of The Logic