general-unequal, therefore, in general: the putting together or numbering of such is Addition. The next determination is, that the Numbers are equal in general; they constitute thus one Unity, and there is present an Amount of such unities: to number such numbers is to Multiply ;-and here it is indifferent how the moments of Amount and Unity are apportioned in the two numbers, the Factors, indifferent which is taken as Amount, and which again as Unity. The third characteristic determinateness is finally the Equality of Amount and Unity. The numbering together of numbers so characterised, is the raising into powers, and first of all into the square. Further potentiation is the formal repetition of the multiplication of the number with itself which runs out again into the indefinite Amount. As in this third form, the complete equality of the sole present difference, of Amount and Unity, is attained, there cannot be more than these three operations in Arithmetic. There corresponds to the numbering together, a resolution of the Numbers according to the same determinatenesses. With the three operations mentioned, which may be so far named positive, there are, therefore, also three negative. c. Degree. The limit is identical with the whole of the Quantum itself; as multiple in itself, it is extensive as simple in itself, intensive magnitude: the latter is also named Degree. The difference of continuous and discrete from extensive and intensive magnitudes consists, therefore, in this, that the former concern Quantity in general—the latter, on the other hand, the limit, or the determinate ness of Quantity as such. Extensive and intensive magnitudes are, in like manner, not two sorts of which the one should possess a distinction which the other wanted; what is extensive is equally intensive, and vice versa. In degree the notion of Quantum is in explicit position. It is magnitude as indifferently independent and simple, but so that it has the determinateness by which it is Quantum directly out of it in other magnitudes. In this contradiction, viz. that the beënt-for-self indifferent limit is absolute Externality, the infinite quantitative Progress is expressly explicit,-an immediacy which immediately strikes round into its counterpart, mediatedness (a going over and beyond the Quantum that has just been posited), and vice versâ. A Number is thought, but thought as a Beingness completely external to its own self. It belongs not to perception because it is thought, but it is the thought which has for its characterisation the externality of perception. The Quantum not only may therefore be increased or diminished ad infinitum; it itself is through its Notion this dispatch of itself beyond itself. The infinite quantitative Progress is just the thoughtless repetition of one and the same contradiction which the Quantum in general is, and Quantum as Degree, or expressly set in its determinateness. As regards the superfluousness of enunciating this contradiction in the form of the infinite Progress, Zeno in Aristotle says justly it is the same thing to say something once, and to say it always. This outerliness of Quantum to its own self in its beënt-for-self determinateness constitutes its Quality; in it it is just itself and referred to itself. In it are united, Externality, i.e. Quantitativeness, and Being for-self, i. e. Qualitativeness. Quantum thus put is in itself the Quantitative Relation,-determinateness which is no less immediate Quantum, the Exponent, than mediatedness, namely, the reference of some one Quantum to another, the two sides of the relation, which at the same time are not valid in their immediate value, but have their value only in this reference. The sides of the relation are still immediate Quanta, the qualitative and the quantitative moments still external to each other. Their truth, however, viz. that the Quantitativeness itself is in its externality reference to itself, or that the Being-for-self and the indifference of the determinateness are united, is Measure. VI. THE COMMENTATORS OF HEGEL: SCHWEGLER, In the interest of one's own self-seeking to demonstrate the shortcomings of one's predecessors, is a procedure now so vulgar that it would, perhaps, have been better taste to have left to others the task which is here begun. Any plea in excuse can found only on the important aid which may be so afforded to a general understanding of the single theme, and is only to be made good by the result. There are many other Commentators of Hegel, but we have selected these examples, too, of feelings impartial, partial, and hostile-as the latest and most generally-acknowledged best. Now, each of the three has devoted a vast amount of labour and time to the study of Hegel, and all of them have, more or less, attained to a very considerable relative knowledge. It is not, then, what is in general meant by ignorance that we would object here, but only a peculiar and insufficient state of knowledge in this way, that the path of this knowledge has been ever on the outside, from particular to particular, with darkness and incoherences between, and without perception of the single light in which the whole should show-without attainment of the single Rück, of the single turn, stir, touch by which the painful and unreachable Many should kaleidoscopically collapse into the held and intelligible One. In a word, whatever general connexion they may have perceived between Hegel and Kant, and however often they may have used, each of them, the word Begriff, they have all failed to detect that literal one connexion and that literal one signification which have been accentuated in the preceding pages. Hegel was literal with Idealism; the whole is Thought, and the whole life of it is Thought; and, therefore, what is called the History of Philosophy will be in externality and contingency, but a Gesetztseyn of Thought, but an explicitment, a setting of one thought the other. So it was that Spinoza was Substance, Hume Causality, Kant Reciprocity, and Hegel the Notion-the Notion as set by Kant, and as now to be developed subjectively by Hegel into the Subjective Logic which ends in the Idea. So it was that he, as it were, anallegorised actual history, even contemporary history, even his own position, into the plastic dialectic of his abstract Logic. Hegel was literal with Idealism up to the last invisible negation of the negation-up to the ultimate pure Negativity within which even the triple muscle of the Notion lay a hidden Nisus, retracted into transparency. To Hegel even the very way which had led to this was, so far, false; it was but the chain of the finite categories; and their whole truth was this negative One. Thus it was that Hegel completed the whole movement of which Kant, Fichte, and Schelling had been successive vital knots; but still this completion he reached only by making good his attachment directly to the first of them. This was effected by the entire realisation and vitalisation of Logic, even scholastic Logic (which Kant had begun), by reduction simply of the All into the simply |