Hegel’s Science of Logic
Ideality can be called the quality of infinity; but it is essentially the process of becoming, and hence a transition — like that of becoming in determinate being — which is now to be indicated. As a sublating of finitude, that is, of finitude as such, and equally of the infinity which is merely its opposite, merely negative, this return into self is self-relation, being. As this being contains negation it is determinate, but as this negation further is essentially negation of the negation, the self-related negation, it is that determinate being which is called being-for-self.
Remark 1: The Infinite Progress
The infinite — in the usual meaning of the spurious infinity — and the progress to infinity are, like the ought, the expression of a contradiction which is itself put forward as the final solution. This infinite is a first elevation of sensuous conception above the finite into thought, the content of which, however, is only nothing, that is, it is expressly in the form of not-being — a flight beyond limited being which does not inwardly collect itself and does not know how to bring the negative back to the positive. This incomplete reflection has completely before it both determinations of the genuine infinite: the opposition of the finite and infinite, and their unity, but it does not bring these two thoughts together; the one inevitably evokes the other, but this reflection lets them only alternate.
This alternation, the infinite progress, is exhibited whenever one remains fixed in the contradiction of the unity of two determinations and of their opposition. The finite is the sublating of itself, it includes within itself its negation, infinity — the unity of both; there is a movement away from the finite to the infinite, to the beyond of the finite — the separation of both; but beyond the infinite is another finite — the beyond; the infinite contains finitude-the unity of both; but this finite, too, is a negative of the infinite-the separation of both; and so on. Thus, in the causal relation, cause and effect are inseparable; a cause which had no effect would not be a cause, just as an effect which had no cause would no longer be an effect. This relation yields, therefore, the infinite progress of causes and effects; something is determined as cause, but as finite (and it is finite for the very reason that it is separated from its effect) it, too, has a cause, that is, it is also an effect; hence the same thing that was determined as cause is also determined as effect — the unity of cause and effect; now that which is determined as effect again has a cause, that is, the cause has to be separated from its effect and posited as a different something; but this fresh cause is itself only an effect — the unity of cause and effect; it has an other for its cause — the separation of both determinations, and so on to infinity.
Thus the progress can be put in the following more characteristic form. The assertion is made: the finite and infinite are a single unity; this false assertion must be corrected by the opposite: they are absolutely different and opposed to each other; this must be corrected again by declaring that they are inseparable, that the determination of each lies in the other, by the assertion of their unity, and so on to infinity. What is required in order to see into the nature of the infinite is nothing difficult: it is to be aware that the infinite progress, the developed infinite of the understanding, is so constituted as to be the alternation of the two determinations, of the unity and the separation of both moments and also to be aware that this unity and this separation are themselves inseparable.
The resolution of this contradiction is not the recognition of the equal correctness and equal incorrectness of the two assertions — this is only another form of the abiding contradiction — but the ideality of both, in which as distinct, reciprocal negations, they are only moments. The said monotonous alternation is actually the negation of their unity and also of their separation. In it, also actually, there is present what was pointed out above: that the beyond of the finite is the infinite, but equally beyond the infinite again the finite finds itself reborn; consequently, in this process the finite is united only with itself, and the same is true of the infinite — so that the same negation of the negation results in an affirmation, this result thus proving itself to be their truth and primary determination. In this being which is thus the ideality of the distinct moments, the contradiction has not vanished abstractly, but is resolved and reconciled, and the thoughts are not only complete, but they are also brought together. In this detailed example, there is revealed the specific nature of speculative thought, which consists solely in grasping the opposed moments in their unity. Each moment actually shows that it contains its opposite within itself and that in this opposite it is united with itself; thus the affirmative truth is this immanently active unity, the taking together of both thoughts, their infinity — the relation to self which is not immediate but infinite.
Thinkers have often placed the essence of philosophy in the answering of the question: how does the infinite go forth from itself and become finite? This it is supposed, cannot be made comprehensible. In the course of this exposition the infinite, the Notion of which we have reached, will further determine itself and will show in all its varied forms what is demanded, that is, how (if we want so to express it) the infinite becomes finite. Here we are considering this question only in its immediacy and with respect to the meaning considered above which is usually attached to the infinite.
It is supposed that it depends altogether on the answering of this question whether there is a philosophy; and while people pretend that they are willing to let the decision rest on this, they also believe themselves to possess in the question itself a sort of puzzle, an invincible talisman, by which they are firmly secured against the answering of the question and consequently against philosophy and the entering of its portals. Even in other subjects, to understand how to put questions presupposes a certain education, and this holds good even in the case of philosophical topics if one is to obtain a better answer than that the question is an idle one. ®
With such questions it is usually claimed as a reasonable assumption that the matter does not depend on the words, but that the point at issue can be understood from one or other of the ways in which the question is expressed. Expressions of sensuous conception like going forth and suchlike, which are used in the question, arouse the suspicion that they spring from the level of ordinary conception and that for the answer, too, conceptions which are current in everyday life are expected and in the form of a sensuous simile.
If instead of the infinite being as such is taken, then the determining of being, a negation or finitude in it, seems easier to understand. Being, it is true, is itself the indeterminate; but that it is the opposite of determinate being, this is not directly expressed in it. In the infinite, on the other hand, this is expressed; it is the not-finite. The unity of the finite and infinite thus seems to be directly excluded, and that is why incomplete reflection is most stubbornly opposed to this unity.
But it has been shown that it is at once evident without going into further detail about the determination of the finite and infinite, that the infinite as understood by said reflection, namely, as opposed to the finite, has in it its other, just because it is opposed to the finite, and therefore is already limited and itself finite — the spurious infinite. The answer, therefore, to the question: how does the infinite become finite? is this: that there is not an infinite which is first of all infinite and only subsequently has need to become finite, to go forth into finitude; on the contrary, it is on its own account just as much finite as infinite. The question assumes that the infinite, on the one side, exists by itself, and that the finite which has gone forth from it into a separate existence — or from whatever source it might have come — is in its separation from the infinite truly real; but it should rather be said that this separation is incomprehensible. Neither such a finite nor such an infinite has truth; and what is untrue is incomprehensible. But equally it must be said that they are comprehensible, to grasp them even as they are in ordinary conception, to see that in the one there lies the determination of the other, the simple insight into their inseparability, means to comprehend them; this inseparability is their Notion. But the separate self-subsistence of the said infinite and finite assumed in the question is an untrue content, and the question already implies an untrue connection between them. Instead, therefore, of answering the question, we must deny the false presuppositions contained in it, that is, the question itself. The question as to the truth of the said infinite and finite involves a change of standpoint and this change will cause a recoil upon the first question of the embarrassment it was intended to produce. This question of ours is something new for the reflection which is the source of the first question, since such reflection does not contain the speculative interest which, for its own sake and before it connects determinations, sets out to ascertain whether these, as presupposed, are something true. But in so far as the falsity of that abstract infinite, and of the finite which equally is supposed to remain standing on its side, is recognised, there is this to be said about the coming or going forth of the finite from the infinite: the infinite goes forth out of itself into finitude because, being grasped as an abstract unity, it has no truth, no enduring being within it; and conversely the finite goes into the infinite for the same reason, namely that it is a nullity. Or rather it should be said that the infinite has eternally gone forth into finitude, that, solely by itself and without having its other present within it, the infinite no more is than pure being is.
The question as to how the infinite goes forth to the finite can contain still another presupposition, namely that the infinite in itself includes the finite, hence is in itself the unity of itself and its other, so that the difficulty is connected chiefly with the separating of them, which is in opposition to the presupposed unity of both. In this presupposition, the opposition which is insisted on merely has another form; the unity and the differentiation are separated and isolated from each other. But if the former is taken, not as the abstract indeterminate unity but, as it already is in the presupposition, as the determinate unity of the finite and the infinite, then the differentiation of both is already present in it too — a differentiation which is thus at the same time not a releasing of them into a separate self-subsistence, but which leaves them as ideal moments in the unity. This unity of the finite and infinite and the distinction between them are just as inseparable as are finitude and infinity.
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