(From Book One, The Science of Logic)
When we say of things that they are finite, we understand thereby that they not only have a determinateness, that their quality is not only a reality and an intrinsic determination, that finite things are not merely limited — as such they still have determinate being outside their limit — but that, on the contrary, non-being constitutes their nature and being. Finite things are, but their relation to themselves is that they are negatively self-related and in this they are negatively self-related and in this very self-relation send themselves away beyond themselves, beyond their being. They are, but the truth of this being is their end.
The finite not only alters, like something in general, but it ceases to be; and its ceasing to be is not merely a possibility, so that it could be without ceasing to be, but the being as such of finite things is to have the germ of decease as their being-within-self: the hour of their birth is the hour of their death.
[a] The Immediacy of Finitude
The thought of the finitude of things brings this sadness with it because it is qualitative negation pushed to its extreme, and in the singleness of such determination there is no longer left to things an affirmative being distinct from their destiny to perish. Because of this qualitative singleness of the negation, which has gone back to the abstract opposition of nothing and ceasing-to-be as opposed to being, finitude is the most stubborn category of the understanding; negation in general, constitution and limit, reconcile themselves with their other, with determinate being; and even nothing, taken abstractly as such, is given up as an abstraction; but finitude is the negation as fixed in itself, and it therefore stands in abrupt contrast to its affirmative. The finite, it is true, lest itself be brought into flux, it is itself this, to be determined or destined to its end, but only to its end — or rather, it is the refusal to let itself be brought affirmatively to its affirmative, to the infinite, and to let itself be united with it; it is therefore posited as inseparable from its nothing, and is thereby cut off from all reconciliation with its other, the affirmative. The determination or destiny of finite things takes them no further than their end. The understanding persists in this sadness of finitude by making non-being the determination of things and at the same time making it imperishable and absolute. Their transitoriness could only pass away or perish in their other, in the affirmative; their finitude would then be parted from them; but it is their unalterable quality, that is, their quality which does not pass over into its other, that is, into its affirmative; it is thus eternal
This is a very important consideration; but certainly no philosophy or opinion, or understanding, will let itself be tied to the standpoint that the finite is absolute; the very opposite is expressly present in the assertion of the finite; the finite is limited, transitory, it is only finite, not imperishable; this is directly implied in its determination and expression. But the point is, whether in thinking of the finite one holds fast to the being of finitude and lets the transitoriness continue to be, or whether the transitoriness and the ceasing-to-be cease to be. But it is precisely in that view of the finite which makes ceasing-to-be the final determination of the finite, that this does not happen. It is the express assertion that the finite is irreconcilable with the infinite and cannot be united with it, that the finite is utterly opposed to the infinite. Being, absolute being, is ascribed to the infinite; confronting it, the finite thus remains held fast as its negative; incapable of union with the infinite, it remains absolute on its own side; from the affirmative, from the infinite, it would receive affirmation, and would thus cease to be; but a union with the infinite is just what is declared to be impossible. If it is not to remain fixed in its opposition to the infinite but is to cease to be, then, as we have already said, just this ceasing-to-be is its final determination, not the affirmative which would be only the ceasing to be of the ceasing-to-be. If, however, the finite is not to pass way in the affirmative, but its end is to be grasped as the nothing, then we should be back again at that first, abstract nothing which itself has long since passed away.
(From Chapter C:Infinity
Remark 1: The Infinite Progress…
Remark 2: Idealism
The proposition that the finite is ideal [ideell] constitutes idealism. The idealism of philosophy consists in nothing else than in recognising that the finite has no veritable being. Every philosophy is essentially an idealism or at least has idealism for its principle, and the question then is only how far this principle is actually carried out. This is as true of philosophy as of religion; for religion equally does not recognise finitude as a veritable being, as something ultimate and absolute or as something underived, uncreated, eternal. Consequently the opposition of idealistic and realistic philosophy has no significance. A philosophy which ascribed veritable, ultimate, absolute being to finite existence as such, would not deserve the name of philosophy; the principles of ancient or modern philosophies, water, or matter, or atoms are thoughts, universals, ideal entities, not things as they immediately present themselves to us, that is, in their sensuous individuality — not even the water of Thales. For although this is also empirical water, it is at the same time also the in-itself or essence of all other things, too, and these other things are not self-subsistent or grounded in themselves, but are posited by, are derived from, an other, from water, that is they are ideal entities. Now above we have named the principle or the universal the ideal (and still more must the Notion, the Idea, spirit be so named); and then again we have described individual, sensuous things as ideal in principle, or in their Notion, still more in spirit, that is, as sublated; here we must note, in passing, this twofold aspect which showed itself in connection with the infinite, namely that on the one hand the ideal is concrete, veritable being, and on the other hand the moments of this concrete being are no less ideal — are sublated in it; but in fact what is, is only the one concrete whole from which the moments are inseparable…)