That these methods, however indispensable and brilliantly successful in their own province, are unserviceable for philosophical cognition, is self-evident. They have pre-suppositions; and their style of cognition is that of understanding, proceeding under the canon of formal identity. In Spinoza, who was especially addicted to the use of the geometrical method, we are at once struck by its characteristic formalism. Yet his ideas were speculative in spirit; whereas the system of Wolf, who carried the method out to the height of pedantry, was even in subject-matter a metaphysic of the understanding. The abuses which these methods with their formalism once led to in philosophy and science have in modern times been followed by the abuses of what is called 'Construction.' Kant brought into vogue the phrase that mathematics 'construes' its notions. All that was meant by the phrase was that mathematics has not to do with notions, but with abstract qualities of sense-perceptions. The name 'Construction (construing) of notions' has since been given to a sketch or statement of sensible attributes which were picked up from perception, quite guiltless of any influence of the notion, and to the additional formalism of classifying scientific and philosophical objects in a tabular form on some pre-supposed rubric, but in other respects at the fancy and discretion of the observer. In the background of all this, certainly, there is a dim consciousness of the Idea, of the unity of the notion and objectivity,—a consciousness, too, that the idea is concrete. But that play of what is styled 'construing' is far from presenting this unity adequately—a unity which is none other than the notion properly so called: and the sensuous concreteness of perception is as little the concreteness of reason and the idea.

Another point calls for notice. Geometry works with the sensuous but abstract perception of space; and in space it experiences no difficulty in isolating and defining certain simple analytic modes. To geometry alone therefore belongs in its perfection the synthetical method of finite cognition. In its course, however (and this is the remarkable point), it finally stumbles upon what are termed irrational and incommensurable quantities; and in their case any attempt at further specification drives it beyond the principle of the understanding. This is only one of many instances in terminology, where the title rational is perversely applied to the province of understanding, while we stigmatise as irrational that which shows a beginning and a trace of rationality. Other sciences, removed as they are from the simplicity of space or number, often and necessarily reach a point where understanding permits no further advance: but they get over the difficulty without trouble. They make a break in the strict sequence of their procedure, and assume whatever they require, though it be the reverse of what preceded, from some external quarter,—opinion, perception, conception or any other source. Its inobservancy as to the nature of its methods and their relativity to the subject-matter prevents this finite cognition from seeing that, when it proceeds by definitions and divisions, &c., it is really led on by the necessity of the laws of the notion. For the same reason it cannot see when it has reached its limit; nor, if it have transgressed that limit, does it perceive that it is in a sphere where the categories of understanding, which it still continues rudely to apply, have lost all authority.

232.] The necessity, which finite cognition produces in the Demonstration, is, in the first place, an external necessity, intended for the subjective intelligence alone. But in necessity as such, cognition itself has left behind its presupposition and starting-point, which consisted in accepting its content as given or found. Necessity quâ necessity is implicitly the self-relating notion. The subjective idea has thus implicitly reached an original and objective determinateness,—a something not-given, and for that reason immanent in the subject. It has passed over into the idea of Will.

The necessity which cognition reaches by means of the demonstration is the reverse of what formed its starting-point. In its starting-point cognition had a given and a contingent content; but now, at the close of its movement, it knows its content to be necessary. This necessity is reached by means of subjective agency. Similarly, subjectivity at starting was quite abstract, a bare tabula rasa. It now shows itself as a modifying and determining principle. In this way we pass from the idea of cognition to that of will. The passage, as will be apparent on a closer examination, means that the universal, to be truly apprehended, must be apprehended as subjectivity, as a notion self-moving, active, and form-imposing.

(ß) Volition.

233.] The subjective idea as original and objective determinateness, and as a simple uniform content, is the Good. Its impulse towards self-realisation is in its behaviour the reverse of the idea of truth, and rather directed towards moulding the world it finds before it into a shape conformable to its purposed End.—This Volition has, on the one hand, the certitude of the nothingness of the pre-supposed object; but, on the other, as finite, it at the same time pre-supposes the purposed End of the Good to be a mere subjective idea, and the object to be independent.

234.] This action of the Will is finite: and its finitude lies in the contradiction that in the inconsistent terms applied to the objective world the End of the Good is just as much not executed as executed,—the end in question put as unessential as much as essential,—as actual and at the same, time as merely possible. This contradiction presents itself to imagination as an endless progress in the actualising of the Good; which is therefore set up and fixed as a mere 'ought,' or goal of perfection. In point of form however this contradiction vanishes when the action supersedes the subjectivity of the purpose, and along with it the objectivity, with the contrast which makes both finite; abolishing subjectivity as a whole and not merely the one-sidedness of this form of it. (For another new subjectivity of the kind, that is, a new generation of the contrast, is not distinct from that which is supposed to be past and gone.) This return into itself is at the same time the content's own 'recollection' that it is the Good and the implicit identity of the two sides,—it is a 'recollection' of the pre-supposition of the theoretical attitude of mind (§ 224) that the objective world is its own truth and substantiality.

While Intelligence merely proposes to take the world as it is, Will takes steps to make the world what it ought to be. Will looks upon the immediate and given present not as solid being, but as mere semblance without reality. It is here that we meet those contradictions which are so bewildering from the standpoint of abstract morality. This position in its 'practical' bearings is the one taken by the philosophy of Kant, and even by that of Fichte. The Good, say these writers, has to be realised: we have to work in order to produce it: and Will is only the Good actualising itself. If the world then were as it ought to be, the action of Will would be at an end. The Will itself therefore requires that its End should not be realised. In these words, a correct expression is given to the finitude of Will. But finitude was not meant to be the ultimate point: and it is the process of Will itself which abolishes finitude and the contradiction it involves. The reconciliation is achieved, when Will in its result returns to the pre-supposition made by cognition. In other words, it consists in the unity of the theoretical and practical idea. Will knows the end to be its own, and Intelligence apprehends the world as the notion actual. This is the right attitude of rational cognition. Nullity and transitoriness constitute only the superficial features and not the real essence of the world. That essence is the notion in posse and in esse: and thus the world is itself the idea. All unsatisfied endeavour ceases, when we recognise that the final purpose of the world is accomplished no less than ever accomplishing itself. Generally speaking, this is the man's way of looking; while the young imagine that the world is utterly sunk in wickedness, and that the first thing needful is a thorough transformation. The religious mind, on the contrary, views the world as ruled by Divine Providence, and therefore correspondent with what it ought to be. But this harmony between the 'is' and the 'ought to be' is not torpid and rigidly stationary. Good, the final end of the world, has being, only while it constantly produces itself. And the world of spirit and the world of nature continue to have this distinction, that the latter moves only in a recurring cycle, while the former certainly also makes progress.

235.] Thus the truth of the Good is laid down as the unity of the theoretical and practical idea in the doctrine that the Good is radically and really achieved, that the objective world is in itself and for itself the Idea, just as it at the same time eternally lays itself down as End, and by action brings about its actuality. This life which has returned to itself from the bias and finitude of cognition, and which by the activity of the notion has become identical with it, is the Speculative or Absolute Idea.