The Quantum, therefore, dispatches itself beyond itself; this other which it becomes is firstly itself a Quantum; but equally as a limit non-beënt, that drives itself beyond itself. The limit which in this transition has again arisen is, therefore, directly only such a one as again sublates itself and passes into another, and so on into the infinite.

C.

QUANTITATIVE INFINITUDE.

a. Its Notion.

The Quantum alters itself and becomes another Quantum; the further determination of this alteration, that it proceeds in infinitum, lies in this, that the Quantum is constituted as contradicting itself in itself. The Quantum becomes another; it continues itself, however, into its otherwiseness: the other, therefore, is also a Quantum. But this is the other not only of a, but of the Quantum itself, the negative of it as of a limited something; consequently, its unlimitedness, infinitude. The Quantum is a Sollen, a To-be-to; it implies to-be-determined-for-itself, and such self-determinedness is rather determinedness in another; and conversely it is sublated determinedness in another, it is indifferent self-subsistence.

Finitude and Infinitude receive thus at once each in itself a double, and that an opposed import. The Quantum is finite, firstly, as limited in general; secondly, as self-dispatch beyond itself, as determinedness in another. Its Infinitude, again, is, firstly, nonlimitedness; secondly, its return into itself, indifferent Being-for-self. If we directly compare these moments, there results, that the determination of the Finitude

of the Quantum, the self-dispatch into another, in which its determination is supposed to lie (and lies), is equally determination of the Infinite; the negation of the limit is the same Beyond over the determinateness, in such wise that the Quantum has in this negation, the Infinite, its ultimate determinateness. The other moment of the Infinitude is the Being-for-self that is indifferent to the limit; the Quantum itself, however, is just so limited, that it is what is for itself indifferent to its limit, and so to other Quanta and its Beyond. The Finite and the Infinite (that Infinite which is to be separated from the Finite, the spurious Infinite) have, in Quantum, each already in it the moment of the other.

The qualitative and the quantitative Infinites distinguish themselves by this, that in the former the antithesis of Finite and Infinite is qualitative, and the transition of the Finite into the Infinite, or the reference of both to each other, lies only in the notion, only in the In itself. The qualitative determinateness is as immediate, and refers itself to the otherwiseness essentially as to a something that is other to it; it is not explicit as having in itself its negation, its other. Quantity, on the contrary, is, as such, sublated determinateness; it is explicit as being unequal with itself and indifferent to itself, and so as alterable. The qualitative Finite and Infinite stand, therefore, absolutely, i. e., abstractly opposed to each other; their unity is the internal reference that is implied at bottom: the Finite continues itself, therefore, only in itself, and not in it, into its other. On the contrary, the quantitative Finite refers itself in itself into its infinite, in which it has its absolute determinateness. This their reference is set out at first hand in the Quantitative Infinite Progress.

b. The Quantitative Infinite Progress.

The Progress into the Infinite is in general the expression of contradiction, here of that contradiction which the quantitative Finite or Quantum in general implies. It is that alternation of Finite and Infinite which was considered in the qualitative sphere, with the difference that, as just remarked above, in the quantitative sphere, the limit dispatches itself and continues itself in itself into its Beyond; consequently, conversely also the quantitative Infinite is explicit as having the Quantum in itself, for the Quantum is in its Beingout-of-self at the same time itself; its externality belongs to its determination.

The infinite Progress is indeed only the expression of this contradiction, not its solution; but because of the continuity of the one determinateness into its other, it brings forward an apparent solution in a union of both. As this progress is first expressed, it is the Aufgabe of the Infinite (i.e. at once the giving up and the problem proposed; both sides of the English puzzle or riddle are, as it were, glanced at), not the attainment of the same, its recurrent production, without getting beyond the Quantum itself, and without the Infinite becoming positive and present. The Quantum has it in its notion to have a Beyond of itself. Beyond is, firstly, the abstract moment of the nonbeing of the Quantum; this latter eliminates itself in itself; thus it refers itself to its Beyond as to its Infinitude, as in the qualitative moment of the antithesis. But, secondly, the Quantum stands in continuity with this Beyond; the Quantum consists just in this, to be the other of itself, to be external to its own self: this, that is external, therefore, is just so not another

This

than the Quantum; the Beyond or the Infinite is therefore itself a Quantum. The Beyond is in this way recalled from its flight, and the Infinite reached. But because this now become a here from a Beyond, a cis or citra from an ultra-is again a Quantum, only a new limit has been made again explicit; this new limit, as Quantum, is again fled from by itself, is as Quantum beyond itself, and has repelled itself into its non-being, into its Beyond of or from its own self, which Beyond equally recurrently becomes Quantum, and as that repels itself from itself into the Beyond again.

The continuity of the Quantum into its other occasions the union of both in the expression of an infinitely great or infinitely small. As both have the determination of Quantum still in them, they remain alterable, and the absolute determinateness, which were a Beingfor-self, is therefore not reached. This Being-out-ofitself of the determination is explicit in the double Infinite, which is self-opposed according to a more or a less, the infinitely great and the infinitely small. In each of them Quantum is maintained in constantlyrecurring antithesis to its Beyond. The great, however much extended, vanishes together into inconsiderableness; in that it refers itself to the Infinite as to its non-being, the antithesis is qualitative: the extended Quantum has, therefore, won from the Infinite nothing; the latter, after as before, is the non-being of the former. Or, the aggrandisement of the Quantum is no nearing to the Infinite, for the difference of the Quantum and of its Infinite has essentially also this moment, that it is not a quantitative difference. It is only the expression of the contradiction driven closer into the straits; it is to be at once great, i. e. a

Quantum, and infinite, i.e. no Quantum. In the same manner, the infinitely small is as small a Quantum, and remains therefore absolutely, that is to say, qualitatively, too great for the Infinite, and is opposed to it. The contradiction of the infinite progress, which was to have found its goal in them, remains preserved in both.

This Infinite, which is persistently determined as the Beyond of the Finite, is to be described as the spurious quantitative infinite. It is, like the qualitative spurious Infinite, the perpetual crossing hence and thence from the one member of the persisting contradiction to the other, from the limit to its non-being, and from the latter anew back to the limit. In the quantitative progress, what is advanced to is indeed not an abstract other, but a Quantum that is expressed as different; but it remains equally in antithesis to its negation. The Progress, therefore, is equally not a progress, but a repetition of one and the same,-position, sublation, re-position and re-sublation; (the equating setzend with ponens and aufhebend with tollens is conspicuously plain here)-an impotence of the negative to which what it sublates returns through its very sublation as a Constant. There are two so connected that they directly mutually flee themselves; and even in fleeing cannot separate, but are in their mutual flight conjoined.'

REMARK 1.

The High Repute of the Progressus in Infinitum.

This Remark turns largely on certain declarations of Kant; but it is not of such a nature as to suggest reservation, as is usual where Kant is in question.

'The bastard Infinite-especially in its quantitative form, this perpetual transcendence of the limit and