Being as Indifference. Centripetal and Centrifugal Force

⁷⁹²

2. As this indifference, being [existence] is now the specification of measure no longer in its immediacy, but measure as developed in the manner just indicated.

Being is indifference as:

1. The whole of the determinations of being which are resolved into this unity

2. A determinate being

This is a totality of the posited realisation, in which the moments themselves are implicitly the totality of the indifference, borne by this latter as their unity.

But because the unity is only an indifference, and hence is held fast only as an implicit unity, and the moments are not yet explicitly self-determined, i.e. are not yet determined as sublating themselves into a unity within themselves and through one another, what is here present is simply the indifference of the unity itself towards itself as a developed determinateness.

⁷⁹³

This self-subsistent measure is thus indivisible.

It is immanent in all its determinations and in them remains in unity with itself and unaffected by them.

But [a] as remaining implicitly the totality, it possesses the determinatenesses which are sublated in it, only as groundlessly emerging in it.

The implicit being of the indifference and this real being of the latter are unconnected; the deterininatenesses show themselves in the indifference in an immediate manner and the indifference is wholly present in each of them.

Consequently, the difference between them is posited in the first place as sublated, therefore as only quantitative, but not as the self-repulsion of the indifference, and the indifference is not posited as self-determining but as being determinate and determined only externally.

[b] The 2 moments are in an inverted quantitative relation-a to and fro in the scale of magnitude.

But this fluctuation is determined not by the indifference, which is just the indifference of this fluctuation, but is determined herewith only externally.

The principle of determination resides not in the indifference, but in something lying outside it. The absolute, as indifference, has in this aspect the second defect of the quantitative form, namely that the determinateness of the difference is not determined by the absolute itself; just as it has the first defect in the fact that the differences simply emerge in it, that is to say, the absolute’s positing is immediate in character, is not the mediation of the absolute with itself.

[c] The quantitative determinateness of the moments which are now sides of the relation constitutes this mode of their subsistence; through this indifference their determinate being is freed from the transition of the qualitative sphere.

But in distinction from this their real being, they have an implicit subsistence in the fact that they are in themselves the indifference itself, each being itself the unity of the 2 qualities into which the qualitative moment splits itself.

The difference between the two sides is restricted to this, that one quality is posited in the one side with a more and in the other with a less, and the other quality similarly, but conversely. Hence each side is in its own self the totality of the indifference.

Each of the two qualities taken singly on its own account also remains the same sum which the indifference is; it continues itself out of the one side into the other and is not bounded by the quantitative limit which is thereby posited in it.

In consequence of this the determinations come into immediate opposition and this develops itself into a contradiction which we have now to consider.

⁷⁹⁴

3. Each quality enters within each side into relation to the other.

It does so in such a way that, as has been determined, this relation too is to be only a quantitative difference.

If the 2 qualities are self-subsistent — taken, say, as if they were sensuous things independent of each other — then the whole determinateness of indifference falls asunder; their unity and totality would be empty names. But they are at the same time expressly determined as comprised in a single unity, as inseparable, each as having meaning and reality only in this one qualitative relation to the other. But now, because their quantitativity is simply and solely of this qualitative nature, each reaches only as far as the other.

If the qualities are regarded simply as distinct quanta, then the one would reach beyond the other and would have in its more an indifferent determinate being which the other would not have. But in their qualitative connectedness, each is only in so far as the other is.

It follows that they are in equilibrium – as one increases, the other likewise would increase in the same proportion.

⁷⁹³ Therefore on the basis of their qualitative connection there can be no question of a quantitative difference or of a more of the one quality. The more by which one of the correlated moments would exceed the other would only be a baseless determination, or else this more would only be the other itse@ again; but in this their equality, both would have vanished, for their determinate being was supposed to be based solely on the inequality of their quantum.

Each of these hypothetical factors vanishes, whether it is supposed to be beyond or equal to the other. This vanishing appears to quantitative conception as a disturbance of the equilibrium so that the one factor becomes greater than the other; thus there is posited the sublating of the quality of the other and its lack of any support. One factor becomes preponderant as the other diminishes with an accelerated velocity and is overpowered by the first, which therefore constitutes itself the sole self-subsistent quality; but this being so, there are no longer two specific moments and factors but only the one whole.

⁷⁹⁶ This unity thus posited as the totality of the process of determining, in which it is itself determined as indifference, is a contradiction in every respect; it therefore has to be posited as sublating this its contradictory nature and acquiring the character of a self-determined, self-subsistent being which has for its result and truth not the unity which is merely indifferent, but that immanently negative and absolute unity which is called essence.

Remark: Centripetal and Centrifugal Force

⁷⁹⁷ The relationship of a whole which is supposed to have its determinateness in the quantitative difference of two factors determined qualitatively against each other, is applied to the elliptical motion of the celestial bodies. This example exhibits primarily only two qualities in inverse relation to each other, not two sides, each of which is itself the unity of both and their inverse relation.

The fact, the inverse relation, rests on a firm empirical foundation, but the theoretical explanation of it involves a consequence which is overlooked, namely the destruction of the basic fact; or if, as is proper, the fact is retained it escapes notice that the theory proves to be meaningless in face of the fact.

The ignoring of this consequence allows the fact and the theory conflicting with it to exist calmly side by side. The simple fact is that in the elliptical motion of the celestial bodies their velocity is accelerated as they approach perihelion and retarded as they approach aphelion.

The quantitative side of this fact has been accurately ascertained by the untiring diligence of observation, and further, it has been reduced to its simple law and formula.

⁷⁹⁸ Hence all that can properly be required of a theory has been accomplished.

But to reflective understanding this did not appear sufficient.

For the purpose of a so-called explanation of the phenomenon and its law a centripetal and a centrifugal force are assumed as qualitative moments of the curvilinear motion.

Qualitatively, their difference consists in the opposed direction of the moments.

Quantitatively, their difference consists in:

• the moments being determined as unequal
• the fact that as the one increases the other is supposed to decrease, and vice versa
• their relationship being reversed again so that after a period during which the centripetal force has been increasing and the centrifugal force decreasing, a point is reached where the former decreases and the latter increases.

But this way of representing the matter is contradicted by the essentially qualitative relation between their respective determinatenesses which makes their separation from each other completely out of the question.

Each has meaning only with reference to the other; consequently, in so far as the one had an excess over the other, to that extent it would have no relation to it and the other would no longer exist.

If it is assumed that one of them is at one time greater than the other, being related to it as the greater to the smaller, then what was said above applies, namely, that the greater would acquire absolute preponderance and the other would vanish; the other would be posited as a vanishing moment without any support; and nothing would be altered by supposing the vanishing to take place only gradually any more than by supposing that by as much as the vanishing moment decreases in magnitude the other increases, for the latter, too, is destroyed with the former, since it is what it is, only in so far as the other is.

It requires but little consideration to see that if, for example, as is alleged, the body’s centripetal force increases as it approaches perihelion, while the centrifugal force is supposed to decrease proportionately, the latter would no longer be able to tear the body away from the former and to set it again at a distance from its central body; on the contrary, for once the former has gained the preponderance, the other is overpowered and the body is carried towards its central body with accelerated velocity. Just as conversely, if the centrifugal force gains the upper hand when infinitely near to aphelion, it is equally contradictory that now, in the aphelion itself, it should be overpowered by the weaker force.

⁷⁹⁹ It would be an alien force which effected this reversal; and this means that this alternation of accelerated and retarded velocity of the motion cannot be ascertained or, as it is said, explained from the assumed determination of the factors although these have been assumed for the express purpose of explaining this difference.

The conclusion which follows from the vanishing of one or the other direction and hence of the elliptical motion altogether, is ignored and concealed because of the undeniable fact that this motion does go on and pass from the accelerated into the retarded velocity. The assumed transformation of the weakness of the centripetal force in aphelion into a preponderant strength over the centrifugal force, and conversely in perihelion, implies first the conclusion arrived at above, namely, that each side of the inverse relation is in its own self the whole inverse relation; for the side of the motion from aphelion to perihelion (when the centripetal force is supposed to be preponderant) is still supposed to contain the centrifugal force which, however, diminishes as the other increases, while on the side of the retarded motion the centrifugal force is assumed to be present in that same inverse relation in an ever-increasing preponderance over the centripetal force.

Consequently, on neither side has either force vanished but only become increasingly smaller up to the point of its transformation into a preponderance over the other. All that recurs then on either side is the defect characteristic of this inverse relation, namely, either each force is credited with an independent self-subsistence, the pair being merely externally associated in a motion (as in the parallelogram of forces), in which case the unity of the Notion, the nature of the thing itself, is left out of account; or else, since each is qualitatively related to the other by the Notion, neither can attain an indifferent independent subsistence in face of the other, a subsistence supposedly imparted to it by a more. The form of intensity, the so-called dynamic factor, does not help, because this too has its determinateness in quantum and consequently can express only as much force (which is the measure of its existence) as is opposed to it by the opposite force.

Secondly, this sudden change round from a preponderance into its opposite implies the alternation of the qualitative determination of positive and negative; an increase in the one means an equivalent loss in the other. In the theory, the inseparable qualitative connectedness of this qualitative opposition is distorted into a succession in time; but it fails thereby to give an explanation of this alternation and more particularly of this distortion itself. The semblance of unity which is still implied in the increasing of one side with an equivalent decreasing of the other vanishes here completely; what is alleged is a merely external succession of the sides which only contradicts what is necessarily implied in their qualitative connectedness, namely that with the preponderance of one side the other must disappear.

⁸⁰⁰ The same relationship has been applied to the forces of attraction and repulsion for the purpose of explaining the different densities of bodies; and the inverse ratio of sensibility and irritability has also been invoked to explain from the inequality of these factors of life the various determinations of the whole and of health and also the variety of living species.

This mode of explanation was supposed to form a basis for the natural philosophy of physiology, nosology and also zoology, but the confused hotchpotch of nonsense in which it became entangled through the uncritical use of these determinations of the Notion soon led to the abandonment in these spheres of this formalism which, however, is practised without restraint in the other sciences, particularly in physical astronomy.

⁸⁰¹ Since absolute indifference may seem to be the fundamental determination of Spinoza’s substance, we may add that this is indeed the case in so far as in both every determination of being, like every further concrete differentiation of thought and extension and so forth, is posited as vanished.

If we stop short at the abstraction [of substance] then it is a matter of complete indifference what something looked like in reality before it was swallowed up in this abyss.

But when substance is conceived as indifference, it is tied up with the need for determining it and for taking this determining into consideration; it is not to remain Spinoza’s substance, the sole determination of which is the negative one that everything is absorbed in it. With Spinoza, the moment of difference — attributes, thought and extension, then the modes too, the affections, and every other determination — is introduced quite empirically; it is intellect, itself a mode, which is the source of the differentiation.

⁸⁰² The relationship of the attributes to substance and to one another is not specified further than that they express the whole of substance, and their content, the order of things as extended and as thoughts, is the same. But by the determination of substance as indifference, the difference too, comes to be reflected on; whereas with Spinoza, the difference is an external, and more precisely a quantitative difference only by implication, now it is posited as such.

The indifference does indeed, like substance, remain immanent in the differentiated moments, but only abstractly so, only implicitly; the difference is not immanent in the indifference, for as quantitative it is rather the opposite of immanence, and the quantitative indifference is rather the self-externality of the unity. Thus the difference is also not grasped qualitatively; substance is not determined as selfdifferentiating, not as subject.

The immediate consequence with respect to the category of indifference itself is that in it the difference of quantitative or qualitative determination falls apart as we found in the explication of indifference; it is the dissolution of measure, in which both moments were directly posited as one.