III.3.2. The Idea of Cognition

Life is the immediate Idea, or the Idea as its Notion which is not yet realized in itself. In its Judgment it is Cognition in general.

The Notion is as Notion for itself in so far as it exists freely as abstract universality, or as Kind. Thus it is its own pure self-identity, which distinguishes itself within itself in such a manner that that which is distinguished is not an objectivity, but has become freed so that it too is subjectivity or the form of simple self-equality; hence the object of the Notion is the Notion itself. Its reality in general is the form of its existence, and what matters is the determination of this form; upon this depends the distinction of that which the Notion is in itself or as subjective, and of what it is as submerged into Objectivity, and next in the Idea of Life. It is true that in the last it is distinct from its external reality and is posited for itself; but it has this its Being-for-Self only as the identity which is a relation to itself as submerged into its subordinate objectivity or to itself as indwelling and substantial form. The elevation of the Notion above Life means this, that its reality is the Notion-form freed so that it becomes universality. By means of this Judgment the Idea is duplicated—into the subjective Notion whose reality is itself, and into the objective Notion, which is as Life.—Thought, Spirit, and self-consciousness are determinations of the Idea in so far as it has itself for object and its Existence, that is, the determinateness of its Being, is its own distinction from itself.

The metaphysics of Spirit, or, as was the more usual term, of the soul, turned upon the determinations of substance, simplicity, and immateriality;—determinations, in which the general idea of spirit as it exists in empirical consciousness as subject was made the foundation, whereupon the question next was asked what predicates agree with the observed phenomena. This procedure could go no further than that of physics, which reduces the world of appearance to general laws and determinations of reflection, since here too Spirit has its foundation only in its appearance. Indeed this method necessarily fell short of the method of physical science, since Spirit not only is infinitely richer than Nature, but the absolute unity of opposites in the Notion constitutes its essence, and therefore in its appearance and its relation to externality it manifests contradiction in its highest determinateness. Consequently it must be possible to cite an experience for each of the opposite determinations of reflection, or to arrive, from experience, at contradictory determinations according to the method of the formal syllogism. The predicates which immediately result in appearance belong properly to empirical psychology, and therefore all that is left over for metaphysical consideration is some rather tenuous determinations of reflection.—Kant, in his criticism of the rational doctrine of the soul, nails down this metaphysics at this point, that, in so far as it is supposed to be a rational science, the smallest element which is introduced from perception into the general idea of self-consciousness makes this science empirical and taints its rational purity and complete independence of experience.—Thus, he argues, nothing remains but the simple idea (which in itself is quite void of content) of the Ego, of which it is impossible even to say that it is a concept, since it is a mere consciousness which accompanies all concepts. Now this Ego or It (the Thing), which thinks, represents nothing more (according to Kant’s further conclusions) than a transcendental subject of thoughts = x, which is known only through the thoughts that are its predicates, and of which by itself we can never have the slightest notion. At the same time this Ego, according to Kant’s own expression, is awkward in this respect, that we must always make use of it in order to make any judgment about it; for it is not an idea by which a particular object is distinguished so much as a form of ideation in general, in so far as it is to be called cognition.—The paralogism which according to Kant is committed by the rational doctrine of the soul consists in this, that modes of self-consciousness in thought are made into notions of the understanding which imply an object; the “I think” is taken as a thinking being or Thing-in-itself;—in consciousness the Ego always occurs as subject which is singular and, in spite of the multiplicity of ideation, identical, distinguishing its self from this multiplicity which is external; and hence the invalid conclusion is drawn in this manner that Ego is a substance, and further that it is qualitatively simple and one and exists independently of the things of space and time.—

I have set out this exposition in some detail because the nature of the old metaphysics of the soul, as well as the criticism which destroyed it, can clearly be seen in it.—The former attempted to determine the abstract essence of the soul; it began originally in this attempt with perception, and changed its empirical universality and the reflection-determination (which is altogether external to the individuality of the actual) into the form of the determinations of essence which have been recited.—Kant had in mind mainly the condition of contemporary metaphysics, which generally halted at such abstract and one-sided determinations, without dialectic; he neither considered nor investigated the truly speculative ideas of older philosophers about the notion of Spirit. In his criticism of these determinations he simply followed Hume’s sceptical manner: he holds fast to that which appears as Ego in self-consciousness, from which however (he insists) everything empirical must be omitted, since the aim is to know its essence, or the Thing-in-itself. Now nothing remains but the phenomenon of the “I think” which accompanies every idea; and nobody has the slightest notion of this “I think.”—It must certainly be admitted that it is impossible to have the slightest notion of Ego or anything else (the Notion included), if no Notion is formed and a halt is made at the simple, fixed general idea and name.—It is a strange thought (if it is to be called a thought) that Ego must make use of Ego in order to judge about Ego; the Ego which makes use of self-consciousness as a means in order to judge is indeed an x, of which (as also of this relation of making use) it is impossible to have the slightest notion. But it is ridiculous to call awkward and to stigmatize as circular this property of self-consciousness—that Ego thinks itself and that it cannot be thought unless it is Ego that thinks. It is by this very relation that its absolute and eternal nature, and that of the Notion, manifests itself in immediate empirical self-consciousness, and manifests itself because self-consciousness is precisely the existing and therefore empirically perceptible pure Notion, the absolute self-relation which, as separating Judgment, makes itself its own object and is just this process of thereby becoming a circle.—A stone does not suffer from this awkward property; if it is the object of thought or judgment it does not stand in its own way;—it is exempted from the trouble of being its own instrument in this operation; something else is outside it which must undertake this burden.

These ideas, which may be called barbarous, set it down as a defect that, in the process of thinking the Ego, Ego itself as subject cannot be omitted; and the same defect also appears conversely in this form, that Ego occurs only as subject of consciousness, or that Ego can only use itself as subject of a judgment, while the intuition is said to be lacking by which it could be given as an object; and further the Notion of a thing which can exist only as subject implies no objective reality.—If objectivity is said to demand external intuition determined in time and space, and it is this which is missing, it is quite clear that by objectivity only that kind of sensuous reality is meant which it is a condition of thought and truth to have superseded. But, of course, if Ego is taken not as a Notion but as bare and simple idea in the manner in which we pronounce I in everyday consciousness, then it is the abstract determination and not a self-relation having itself for object;—in this manner it is only one of the extremes, or one-sided subject without its objectivity; and it could also be object without subjectivity but for the implication of the awkward fact, already mentioned, that the thinking subject cannot be forced away from the Ego as object. But in fact the same awkwardness is also to be found in the first determination, or the Ego as subject: the Ego thinks something—either itself or something else. This inseparability of the two forms in which it opposes itself belongs to the most peculiar nature of its Notion and of the Notion itself; it is precisely that which Kant wishes to ward off in order to hold fast simply the general idea which does not distinguish itself within itself and therefore of course is Notion-less. Now it is true that such a Notion-less entity may oppose itself to the abstract determinations of reflection or categories of the earlier metaphysics;—for in respect of one-sidedness it stands on a level with them, although these are higher as products of thought; on the other hand it appears all the poorer and emptier compared with the profounder ideas of older philosophy with regard to the notion of the soul or of thought—for example, the truly speculative ideas of Aristotle. If Kant’s philosophy investigated these determinations of reflection, it ought still more to have investigated the abstraction of the empty Ego, which was held fast, and the supposed Idea of the Thing-in-itself, which, just because of its abstraction, shows itself to be wholly untrue; the experience of that awkwardness which was deplored is itself the empirical fact in which the untruth of this abstraction expresses itself.

Kant’s criticism of rational psychology mentions only Mendelssohn’s proof of the persistence of the soul; and I cite the refutation of this proof because of the remarkable nature of that which is opposed to it. The proof is based upon the simplicity of the soul, which is asserted to render it incapable of change, of a temporal transition into an Other. Qualitative simplicity is the form of abstraction in general which was considered above; as qualitative determinateness it was investigated in the sphere of Being, when it was shown that the Qualitative is such an abstractly self-relating determinateness, and as such is for that very reason of dialectic nature and only the transition into an Other. But under the Notion it was shown that, if the Notion is considered with respect to persistence, indestructibility, and imperishability, it is the eternal and that which is in and for itself, just because it is concrete and not abstract simplicity; not abstractly self-relating determinedness, but the unity of itself and its Other, into which accordingly it cannot pass over in such a manner as to undergo change in it, precisely because the Other, the determinedness, is itself, and therefore in this transition it only reaches itself.—Now Kant’s criticism opposes the quantitative determination of the Notion-unity to this qualitative. The soul (he says) is not a manifold of juxtaposed parts and contains no extensive magnitude; but still, consciousness has a degree, and the soul, like every existent, has an intensive magnitude; and hereby the possibility is posited of the transition into nothing by gradual disappearance.—Now what else is this refutation but the application to Spirit of a category of Being—to wit, Intensive Magnitude?—a determination which has no truth in itself and in fact is transcended in the Notion.

Metaphysics—even that kind which restricted itself to fixed notions of understanding without rising to the speculative and to the nature of the Notion and the Idea—had for its end the cognition of truth, and asked of the objects of its investigation whether they were something veritable or not, substances or phenomena. But the victory of Kant’s Critique over this consists rather in abolishing the investigation which has truth for end, together with this end itself; it does not ask the one question which is of interest, namely, whether a certain subject (in this instance the abstract Ego of imagination) has truth in and for itself. But to stand fast at appearance and the data given to mere sensuous representation in everyday consciousness is tantamount to a resignation of the Notion and of philosophy. What goes beyond this is given in Kant’s Critique the name of something extravagant, to which Reason has no title at all. The Notion does in fact range beyond the Notion-less, and its immediate title to this transgression is (a) itself and (b), from the negative side, the untruth of appearance and of sensuous representation, as well as of abstractions such as the Things-in-themselves and that Ego which is supposed not to be its own object.

In the connected course of our logical exposition it is from the Idea of Life that the Idea of Spirit has emerged; or, what is the same thing, the latter has proved itself to be the truth of the former. As being this result this Idea has its truth in and for itself, with which now the empirical element, or the Appearance of Spirit, may be compared, to see how far they agree; nevertheless the empirical itself can be grasped only through and from the standpoint of the Idea. We have seen of Life that it is the Idea, but at the same time Life showed itself to be not yet the true representation or fashion of the existence of the Idea. For in Life the reality of the Idea is as Individuality; Universality, or the Kind, is inner; consequently the truth of Life as absolute negative unity is that it transcends abstract or (what is the same thing) immediate individuality, and that, as identical, it is self-identical, and as Kind, self-equal. Now this Idea is Spirit.—But in this regard the further remark may be made that Spirit is here considered in that form which belongs to this Idea as logical. For the Idea has other shapes too, which may here be mentioned in passing, under which it must be considered in the concrete sciences of Spirit—namely as soul, consciousness, and Spirit as such.

The name of soul was formerly used of the individual finite spirit in general, and rational or empirical doctrine of the soul was intended to mean the same as doctrine of spirit. Where the expression “soul” is used, the idea is present that it is a thing like other things; its seat (the spatial determination whence its forces operate) is asked for, and the further question is put how this thing can be imperishable, subject as it is to the conditions of temporality but free from temporal change. The system of monads raises matter to the status of the soul: the soul in this view is an atom like the atoms of matter in general; it is said that the atom which rises as steam from the coffee-cup might, with luck, develop into a soul, and that it is only the greater obscurity of its process of mirroring that distinguishes it from the kind of thing that appears as a soul.—The Notion which is for itself is necessary also in immediate Existence; in this substantial identity with Life—in its immersion into its externality—it has to be considered in anthropology. But this metaphysics, where this form of immediacy becomes a soul-thing, an atom like the atoms of matter, must remain alien to anthropology too.—To anthropology those dark regions alone may be ceded where spirit stands under influences formerly called sidereal or terrestrial, living as a natural spirit in sympathy with nature and becoming aware of its changes in dreams and premonitions, and dwelling in brain, heart, ganglia, or liver, and so on; to which last part, according to Plato, the god gave that gift of prophecy above which self-conscious man is raised, in order that the unreasonable part too might partake of his goodness and have a share in higher things. To this unreasonable side belongs further the relation of sensuous representation, and of higher intellectual activity in so far as it is exposed in the individual subject to the play of wholly contingent corporeal nature, external influences and particular circumstances.

This is the lowest of the concrete forms in which Spirit is immersed in materiality; its immediately higher form is in consciousness. In this form the free Notion as Ego which is for itself is withdrawn out of objectivity, but it relates itself to objectivity as its Other, as opposed object. Here Spirit no longer is soul, but, in the certainty of itself, the immediacy of Being rather has the significance of something negative for it; hence the self-identity in which it remains in objectivity is at the same time only a show, since the objective also has still the form of something which is in itself. This stage is the object of the Phenomenology of Spirit—a science which stands midway between the sciences of Natural Spirit and of Spirit as such, and considers Spirit which is for itself at the same time in its relation to its Other (which thus, as was mentioned, is determined both as object which is in itself and also as negated object)—as appearing and as representing itself in its own opposite.

But the higher truth of this form is Spirit for itself, for which the object, which for consciousness is in itself, has the form of its own determination, or of sensuous representation in general; this Spirit, which operates upon determinations as determinations proper to itself—sensations, images, and thoughts—is, in so far, in itself and in its form infinite. The contemplation of this stage belongs to the doctrine proper of Spirit, which would comprise that which is the object of ordinary empirical psychology, yet cannot go to work in an empirical manner if it would be science of Spirit, but must be taken scientifically.—At this stage Spirit is finite Spirit, in so far as the content of its determinateness is immediate and given; the science which is concerned with it must present the process in which it sets itself free from this its determinateness and passes on to the comprehension of its truth, which is Infinite Spirit.

On the other hand the Idea of Spirit, which is an object of logic, is already within pure science, which therefore need not witness its progress where it is implicated in nature, in immediate determinateness and in matter, or in sensuous representation, which is what is considered in these three sciences; this progress it has already left behind, or (which is the same thing) it rather has it before it,—the former, in so far as logic is taken as the last science, the latter, in so far as it is taken as the first, out of which at last the Idea passes over into Nature. Consequently in the logical Idea of Spirit Ego forthwith is the free Notion (as appeared from the Notion of Nature as the truth of this Idea); the free Notion which in its Judgment is itself the object, or, the Notion as its Idea. But even in this form the Idea is not yet complete.

It is indeed the free Notion, which has itself for object; but, just because it is immediate, it is still immediately the Idea in its subjectivity, and therefore in its finitude in general. It is the End which is to realize itself; or, it is the Absolute Idea itself still in its appearance. What it seeks is the True, this identity of the Notion itself and reality, but, as yet, it merely is seeking; for here still (as it is at the beginning) it is subjective. Consequently the object which is object of the Notion is here also a given object, but it does not enter into the subject as an Object which operates upon it, or in its quality as object having a nature for itself, or as image: on the contrary the subject changes it into a Notion-determination; it is the Notion that sets itself to work in the object, relates itself to itself therein, and finds truth in giving itself its reality in the Object.

Thus at this point the Idea is one extreme of a Syllogism, as the Notion which as End has itself for subjective reality; the other extreme is the barrier of the subjective, namely, the objective world. The two extremes are identical in being the Idea; their unity, first, is that of the Notion, which in the one is only for itself and in the other only in itself; secondly, reality in the one is abstract and in the other in its concrete externality.—Now this unity is posited by Cognition; and, since it is the subjective Idea that starts from itself as End, this unity is at first only as middle,—The cognizing entity relates itself to an external world by means of the determinateness of its Notion (namely abstract Being-for-Self), but does so in absolute self-certainty in order to raise its own reality in itself (a formal truth) to real truth. In its Notion it has the whole essentiality of the objective world; its process is, to posit the concrete content of the objective world for itself as identical with the Notion, and conversely the latter as identical with the objectivity.

Immediately the Idea of appearance is theoretic Idea, or Cognition as such. For immediately the objective world has the form of immediacy or of Being for the Notion which is for itself, while the latter at first is to itself only the abstract Notion of itself, bound up as yet in itself. The Notion consequently is only as form\ its reality, which it has in itself, is no more than its simple determinations of Universality and Particularity: this form receives from without Individuality or determinate determinateness, or, its content.

At first the subjective Idea is impulse. For it is this contradiction in the Notion, that it has itself for object, and is its own reality, while at the same time the object is not as an Other, independent of the Notion, nor again has the distinction of itself from itself the essential determination of difference and of indifferent Existence. Consequently the impulse has the determinateness of cancelling its own subjectivity, of making concrete its reality (which was abstract at first), and of filling it, for content, with the world which is presupposed by its subjectivity.—From the other side it determines itself in the following manner by this process: the Notion is absolute self-certainty, but its Being-for-Self is faced by its presupposition of a world which is in itself, whose indifferent otherness, however, has the significance only of something unessential for this self-certainty. In so far the Notion is the impulse to transcend this otherness and to contemplate self-identity in contemplating the Object. In so far as this intro-Reflection is transcended opposition and posited individuality which has been effected for the subject (and which at first appears as presupposed Being-in-Self), it is the self-identity of the form, which has been constructed out of the opposition,—an identity which thereby is determined as indifferent to the form in its distinctness, and is content.

This impulse consequently is impulse of truth in so far as truth lies in Cognition—of truth therefore as theoretic Idea in its proper sense.—Objective truth is the Idea itself as the reality which corresponds to the Notion, and in so far an object may or may not have truth in it; but the more definite meaning of truth is this, that it is for or in the subjective Notion, or, in knowledge. Truth is the relation of the Notion-judgment, which proved to be the formal judgment of truth; for in it the predicate is not only the objectivity of the Notion, but is also the relating comparison of the Notion of the fact and its actuality.—This realization of the Notion is theoretic in so far as the Notion, as form, still has the determination of something subjective, or the determination, for the subject, of belonging to it. Cognition is the Idea as End or as subjective, and so the negation of the world which is presupposed as being in itself is first negation; the conclusion, where the objective is posited as subjective, at first therefore signifies only that that which is in itself is posited only as subjective or is only posited in the Notion-determination, but, in consequence, is not there in and for itself. In so far the conclusion reaches merely a neutral unity or a synthesis, that is, a unity of terms which originally are separate and are connected in this manner only externally.—Consequently, when in this Cognition the Notion posits the Object as being its own, the Idea at first merely gives itself a content whose foundation is given and in which only the form of externality has been transcended. In so far this Cognition retains its finitude in its Realized End; in its End it has, at the same time, not reached its End, and in its truth has not yet arrived at truth. For in so far as the content in the result is still determined as given, the presupposed Being-in-Self standing against the Notion is not transcended; equally therefore the unity of Notion and reality, or truth, is not contained in it.—Strangely -enough this side of finitude has latterly been seized upon and has been taken to be the absolute relation of Cognition—as though the finite as such was to be the absolute! At this point of view the Object is assigned the property of being an unknown Thing-in-itself behind all knowledge, which property, together with truth, is considered an absolute Beyond for Cognition. The determinations of thought in general, the categories and the determinations of reflection as well as the formal Notion and its moments, are here given the position not that they are finite determinations in and for themselves, but that they are so in the sense that they are subjective as against that empty Thinghood-in-itself: the error of taking this relation of the untruth of Cognition as valid has become the universal opinion of modern times.

It is immediately obvious from this determination of finite Cognition that it is a contradiction which cancels itself—the contradiction of a truth which at the same time is not to be truth, of cognizing that which is while it does not cognize the Thing-in-itself. In the collapse of this contradiction its content, namely subjective Cognition and the Thing-in-itself, collapses, that is, proves itself to be untrue. But Cognition must by its own process resolve its finitude and therefore its contradiction. The contemplation to which we subject it is an external reflection; but Cognition is itself the Notion which is its own End and accordingly is realized in its realization, and in this realization transcends its subjectivity and the presupposed Being-in-Self.—Cognition must therefore be considered by itself in its positive activity. This Idea, as was shown, is the impulse of the Notion to realize itself for itself consequently its activity is to determine the Object and in this process to relate itself in the Object identically to itself. The Object is just simply the determinable, and in the Idea it has the essential side that it is not opposed in and for itself to the Notion. This Cognition still is finite and not speculative, and therefore the presupposed objectivity has not yet for it the form of being simply in itself the Notion, containing nothing particular for itself as against the Notion. But now that objectivity is counted as a Beyond which is in itself, the determination of being determinable by the Notion is essential in it—for this reason, because the Idea is the Notion which is for itself and that which is utterly infinite in itself, wherein the Object is transcended in itself and the End now only is to transcend it for itself. Consequently, although the Object is presupposed by the Idea of Cognition as being in itself, yet it is so essentially in this relation, that, being certain of itself and of the nullity of this opposition, the Idea is to reach the realization of its Notion in the Object.

In the syllogism in which now the subjective Idea combines with objectivity, the first premiss is that same form of immediate seizure and relation of the Notion to the Object that we saw in the End-relation. The determining activity of the Notion upon the Object is an immediate communication; it spreads itself upon the Object unresisted. Here the Notion remains in its pure self-identity; but this its immediate intro-Reflection equally has the determination of objective immediacy; that which for it is its own determination is equally a Being, for it is the first negation of the presupposition. The posited determination consequently counts equally as a presupposition which is merely found or as the taking up of something which is given, wherein the activity of the Notion itself is rather said to consist in this, that it is negative as against itself, restraining itself in face of the given and making itself passive, so that the given may be able to show itself as it is in itself and not as determined by the subject.

In this premiss therefore this Cognition does not at all appear as an application of logical determinations: it merely accepts and apprehends them as found, and its activity appears as restricted to the removal of a subjective obstacle or external husk from the object. This is Analytic Cognition.

It is sometimes stated that the difference between Analytic and Synthetic Cognition is that the one proceeds from known to unknown, while the other proceeds from unknown to known. But if this distinction is more closely considered, it will be found difficult to discover in it any definite thought, much less a Notion. It may be said that Cognition altogether begins with the realm of the unknown, since one does not become acquainted with what is known already. And conversely Cognition begins also with the known. This is a tautology;—that with which it begins (and which therefore it actually cognizes) is, for that very reason, known; that which is not yet, and still remains to be, cognized, is still unknown. In so far it must be said that Cognition, once it has begun, always proceeds from known to unknown.

The distinguishing part of Analytic Cognition has already determined itself to the effect that, since it is the first premiss of the whole syllogism, mediation does not yet belong to it, but that it is the immediate communication of the Notion, not yet containing otherness: here the activity resigns its negativity. But this immediacy of the relation is itself mediation, since it is the negative relation of the Notion to the Object, which relation however annuls itself and thereby makes itself simple and identical. This intro-Reflection is merely subjective, because in its mediation the distinction is present only as presupposed and being in itself, as differentiation of the Object within itself. Consequently the determination which results from this relation is the form of simple identity or abstract universality. Consequently Analytic Cognition has this identity for its general principle, and the transition into other, the connexion of different terms, is excluded from itself and from its activity.

If now Analytic Cognition is further considered, its beginning is made from a presupposed (and therefore individual) and concrete object; an object either ready for sensuous representation or else a problem—given only in its circumstances and conditions, but not yet developed out of these by itself and presented in simple independence. Now the analysis of such an object cannot consist merely in its dissolution into the various ideas which may be contained in it; such a dissolution and its comprehension are a business which does not belong to Cognition, but would merely concern a closer acquaintance, a determination within the sphere of sensuous representation. Analysis has the Notion for its foundation, and therefore has for products essentially Notion-determinations—namely, those which are immediately contained in the object. It has resulted from the nature of the Idea of Cognition that the activity of the subjective Notion from the one side is to be regarded merely as the development of what already is in the Object, since the Object itself is just the totality of the Notion. It is one-sided to imagine analysis in such a manner as though nothing were in the object except what has been put into it; and it is equally one-sided to think that the determinations which result are simply taken out of it. The former idea is of course the thesis of subjective idealism, which in analysis takes the activity of Cognition only as a one-sided positing, beyond which the Thing-in-itself remains hidden; the latter idea belongs to so-called realism, which takes the subjective Notion as an empty identity that absorbs the thought-determinations from without.—Analytic Cognition, or the transformation of the given material into logical determinations, has shown itself to be two in one—a positing which equally immediately determines itself as a presupposing; and therefore, because of the latter, the logical element can appear as something ready in the object, and, because of the former, as the product of a merely subjective activity. But the two moments cannot be separated; in its abstract form, into which analysis elaborates it, the logical is certainly present only in Cognition; while conversely it is not only something posited but also something which is in itself.

Now in so far as Analytic Cognition is the transformation which has just been pointed out, it passes through no further intermediate terms: the determination in so far is immediate and has this meaning, that it is peculiar to the object and in itself belongs to it: it is therefore taken up out of it without subjective mediation.—But further, Cognition is to be a progress, or a development of distinctions. Now according to its present determination it is Notion-less and undialectical; the distinction which it has is therefore only given, and its progress takes place solely along the determinations of the material. It appears to have an immanent progress only in so far as the derivative thought-determinations can be analysed afresh in their quality as concrete: the highest and final stage of this process of analysis is the abstract highest essence or abstract subjective identity—and, opposed to it, variety. But this progress is nothing further than the repetition of the original activity of analysis, namely, the iterated determination as concrete of the term which has already been taken up into the abstract Notion-form; which action is followed by its analysis, after which the resultant abstract is determined anew as concrete, and so forth.—The thought-determinations appear, however, to contain a transition in themselves also. If the object has been determined as whole, then it is true that a progress has been made from that to the other determination, the part, and from the cause to the other determination of effect, and so on. But here this is no progress, in so far as whole and parts, and cause and effect, are relations—relations which for this kind of formal Cognition are ready in such a manner that one determination is found in an essential connexion with the other. The object which has been determined as cause or as part is, by this fact, determined already by the whole of the relation, and by both sides of it. Although in itself it may be synthetic, still this connexion, for Analytic Cognition, is given as much as any other connexion of its material, and therefore does not belong to its peculiar business. Whether such a connexion is otherwise determined as a priori or a posteriori is here indifferent in so far as it is taken as found, or, as it has been called, as a fact of consciousness—namely, the fact that the determination “part” is connected with the determination “whole,” and so on. When Kant advances his profound observation of synthetic principles a priori, and recognizes that their root is the unity of self-consciousness and therefore the self-identity of the Notion, he nevertheless takes up the determinate connexion (the relation-notions and the synthetic principles themselves) from formal logic as given. They ought to have been deduced by the exposition of the transition of this simple unity of self-consciousness into these its determinations and distinctions; but Kant spared himself the trouble of demonstrating this veritably synthetic progress—the self-producing Notion.

Arithmetic and the more general sciences of discrete magnitude are of course by preference called analytic science, and analysis. And indeed their method of cognition is in the most immanent manner analytic; and the foundation of this fact must briefly be considered.—Elsewhere Analytic Cognition begins with a concrete material which contains a contingent manifold; from this every distinction of content and progress to further content depends. On the other hand, arithmetical and algebraic material has already been made something wholly abstract and indeterminate, where every peculiarity of relation has been expunged, so that every determination and connexion is external. Such is the principle of discrete magnitude, or the One. This relationless and atomic unit can be increased to a plurality and can be determined externally and unified into an amount; this multiplication and limitation are an empty progress and determining, which do not move beyond the same principle of the abstract One. The composition and separation of numbers further depends wholly upon the positing activity of the cognizing being. The general category within which these determinations are made is magnitude, which is determinateness made indifferent, so that the object has no determinateness which is immanent in it and therefore given to Cognition. Now in so far as Cognition has given itself a contingent variety of numbers, these merely constitute material for a further treatment and for manifold relations. Such relations and their discovery and treatment do not indeed appear as something immanent in Analytic Cognition—they appear as contingent and given; and indeed these relations and the relative operations are generally set forth in a series and as different, without intimation of any inner connexion. However, it is easy to recognize a guiding principle: it is the immanent element of analytic identity which appears as equality in variety; and progress is the reduction of the unequal to an ever greater equality. To give an example in the first elements, addition is the comprehension of quite contingently unequal numbers, while multiplication comprehends equal numbers; the relation of equality of amount and unit appears later, and, with it, the power-relation.

Now the determinateness of the object and of the relations is a posited determinateness, and therefore the further operation with them is wholly analytical; whence analytic science has problems but no theorems. The analytic theorem contains the problem as already solved for itself; and the wholly external distinction between the two sides which it equates is so unessential that such a theorem would appear as a trivial identity. Kant indeed declared the proposition 5 + 7 = 12 to be synthetic because the same thing is represented on one side in the form of a plurality (5 and 7) and on the other in the form of a one (12). But unless analytic is to mean the quite abstractly identical and tautological statement 12 = 12, and if there is to be any progress in it at all, then there must be some distinction,—a distinction, however, which is founded on no quality, nor determinateness of reflection, nor (much less) of Notion. 5 + 7, and 12, are entirely the same content; the former side also expresses the demand that 5 and 7 are to be comprehended into one expression, that is, that, five being the end, arbitrarily reached, of a series which might equally have been prolonged, so now the process of enumeration is to be continued, with the provision that the ones which are to be added are to number seven. Thus 12 is the result of 5 and 7 and of an operation which is already posited according to its nature as a wholly external and thoughtless activity, an activity which may for that reason be left to a machine. There is here not the least transition to an Other; it is a mere continuation, that is, repetition, of the same operation that created 5 and 7.

If such a proposition were synthetic it would demand a proof; and such a proof would consist merely in the operation of counting on from 5 with the determination of 7, and in the recognition that the result thus reached agrees with what otherwise is known as 12 and in fact is nothing else than this particular process of counting. Consequently, in place of the form of theorem the form of problem is at once chosen—the demand for the operation, that is, the enunciation of the one side only of the equation, which would constitute the theorem and whose other side is now to be found. The problem includes the content and indicates the particular operation which is to be undertaken with it. The operation is not restricted by any stubborn material having specific relations for properties, but is an external subjective activity whose determinations are accepted with indifference by the material in which they are posited. The only distinction between the conditions set in the problem and the result in the solution is this, that in the latter these unions and separations have actually taken place in the required manner as they were indicated in the former.

The application of the form of geometrical method relating to synthetic propositions, and the addition of a proof to the solution of the problem, is here therefore an entirely superfluous framework. The proof can only express the tautology that the solution is correct because the operation has been concluded as was prescribed. The problem being to add together certain numbers, the solution is to add them; the proof shows that the solution is correct because the problem was to add and addition has taken place. If the problem contains more composite determinations and operations (for example to multiply decimal numbers), and the solution indicates merely the mechanical procedure, then a proof does become necessary; but the proof can be nothing else but the analysis of these determinations and of the operation whence the solution emerges by itself. This separation of the solution as a mechanical procedure and the proof as a recollection of the nature of the object which was to be treated and of the operation itself, leads to the loss of the advantage of the analytic problem, which is that the construction can be derived immediately from the problem and therefore can be represented as reasonable in and for itself; while the other way expressly affects the construction with a flaw which is peculiar to the synthetic method.—In the higher analysis, where, with the power-relation, relations of discrete magnitude appear which are chiefly qualitative and depend on notion-determinatenesses, the problems and theorems certainly contain synthetic determinations; there other determinations and relations must be taken as intermediate terms, than are indicated immediately in the problem or theorem. But even these auxiliary determinations must be of such a kind that they are founded upon the consideration and development of one side of the problem or theorem; the synthetic appearance arises solely from the fact that the problem or theorem does not itself announce this side.—For example, the problem of finding the sum of the powers of the roots of an equation is solved by the consideration and subsequent connexion of the functions which are the coefficients of the equation of the roots. The determination of the functions of the coefficients and their connexion, which here is employed, is not already expressed in the problem; but for the rest the development itself is wholly analytical. Another synthetic solution is the solution of the equation xᵐ⁻¹ = 0 by the help of the sine, and also the immanent algebraic solution through the consideration of the residuum of xᵐ⁻¹ − 1 divided by m and of the so-called primitive roots;—this was of course discovered by Gauss, and is one of the most important modern extensions of analysis. And these solutions are synthetic because the determinations employed—the sine, or the consideration of the residua—are not determinations of the problem itself.

The nature of the analysis which considers the so-called infinitesimal differences of variable magnitudes—the differential and integral calculus—was treated at greater length in the first part of this Logic. It was shown there that the foundation of this is a qualitative determination of magnitude which can be apprehended through the Notion alone. The transition to this from magnitude as such is no longer analytic; whence to this day mathematics has failed in justifying these operations, which are based upon this transition, through themselves, that is, in a mathematical manner: for the transition is not of mathematical nature. Leibniz is given the credit of having transformed the arithmetic of the infinitesimal differences into a calculus; but (as was shown in the same place) he made the transition in the most inadequate manner, a manner both thoroughly notionless and unmathematical: once, however, the transition is presupposed—and in the present state of the science it is no more than a presupposition—the further course is nothing but a series of ordinary operations.

It was mentioned that analysis becomes synthetic when it reaches determinations which are no longer posited by the problems themselves. But the general transition from Analytic to Synthetic Cognition is implied in the necessary transition from the form of immediacy to mediation, from abstract identity to distinction. The analytic function halts in its activity at the determinations in general in so far as they are self-related; but by reason of their determinateness they have the essential property of relating themselves to an Other. It has already been mentioned that, although Analytic Cognition proceeds upon relations which are not a material given externally, but thought-determinations, it still remains analytic, since for it these relations too are given relations. But the abstract identity which is the peculiar object of this Cognition, is essentially identity of distincts; hence this identity even as such must belong to this Cognition; while the connexion must both be posited by and become identical with the subjective Notion.

Analytic Cognition is the first premiss of the whole syllogism,—the immediate relation of the Notion to the Object. Consequently identity is the determination which it recognizes as its own: it is only the apprehension of what is. Synthetic Cognition endeavours to form a Notion of what is, that is, to seize the multiplicity of determinations in their unity. Hence it is the second premiss of the syllogism in which terms various as such are related. Its goal is therefore necessity in general.—The terms which are connected are partly related, and then, although related, they are also independent and indifferent to one another; and partly they are knit together in the Notion, which is their simple but determinate unity. Now in so far as Synthetic Cognition passes over from abstract identity to relation, or from Being to Reflection, it is not the absolute Reflection of the Notion which the Notion cognizes in its object: the reality which it gives itself is the next stage, namely the identity (already indicated) of various terms as such, which consequently is also still inner (and only necessity) and not subjective and existing for itself, and is not yet, therefore, the Notion as such. Consequently, although Synthetic Cognition has the Notion-determinations for its content, and the Object is posited in these, yet they are merely related to one another or are in immediate unity, which unity for this very reason is not that by which the Notion is as Subject.

This constitutes the finitude of this Cognition: this real side of the Idea in it still possesses identity as inner; and therefore the determinations of the latter are still external for themselves. It is not as subjectivity, and therefore that peculiar entity which the Notion has in its object still lacks individuality; and it is no longer the abstract but the determinate form (that is, the particular element of the Notion) which corresponds to it in the Object, while the individual part of it is still a given content. Consequently, although this Cognition transforms the objective world into Notions, it gives it only a form according to the Notion-determinations and must discover the Object in its individuality or determinate determinateness: it is not yet itself determinant. Similarly it finds propositions and laws and demonstrates their necessity, but not as a necessity of the case in and for itself (that is, out of the Notion), but of Cognition which progresses along given determinations (the distinctions of appearance) and cognizes for itself the proposition as unity and relation, or cognizes out of appearance the ground of appearance.

The further moments of Synthetic Cognition must now be considered.

First of all the objectivity (which still is given) is transformed into the simple and first form, that is, into the form of the Notion. Consequently the moments of this apprehension are just the moments of the Notion, namely, universality, particularity, and individuality.—The individual is the Object itself as immediate image, or that which is to be defined. The universal aspect of its Object has turned out in the determination of the objective judgment or the Judgment of Necessity to be the Kind and further to be the next term, namely, the universal plus that determinateness which at the same time is the principle for the distinction of the particular. This distinction exists in the object as specific difference which makes it a certain species and is the basis of its disjunction as against the other species.

In this manner Definition leads back the object to its Notion, and in doing so strips off those of its externals which are requisite for existence; it abstracts from that which in its realization is added to the Notion, by means of which it emerges first into the Idea and secondly into external existence. Description is for imagination, and absorbs this further content which belongs to reality. But Definition reduces this wealth of the manifold determinations of intuited existence to the simplest moments; it is implied in the Notion what is the form of these simple elements and how they are determined relatively to one another. Thus, as has been indicated, the object is taken as universal which at the same time is essentially determinate. The object itself is the third term, the individual, in which genus and particularization are posited in one: here something immediate is posited, which is external to the Notion, since the latter is not yet self-determining.

In these determinations—the form-distinction of Definition—the Notion finds itself and has the reality which corresponds to it. But the intro-Reflection of the Notion-moments, or individuality, is not yet contained in this reality; the Object, accordingly, in so far as it lies in Cognition, is not yet determined as subjective; and hence, relatively to it, Cognition is subjective and has an external beginning; or again it is subjective because it has an external beginning in the individual. Consequently the content of the Notion is given and contingent. Hence the concrete Notion is itself contingent, in a dual aspect: (1) in its content generally, and (2) according to the content-determinations which are selected for the Notion from the manifold qualities which the object has in external existence, and are made to constitute its moments.

The latter respect demands further consideration. Individuality is determinedness in and for itself, and therefore lies outside the peculiar Notion-determination of Synthetic Cognition. Consequently there is no principle to determine which sides of the object are to be looked upon as belonging to its Notion-determination and which as belonging merely to external reality. This constitutes a difficulty in Definitions which cannot be removed for this kind of Cognition. A distinction however must here be made.—Firstly, it is easy to discover the definition of products of self-conscious aim at an End; for the End which they are to serve is a determination which is created out of subjective resolution and constitutes that essential particularization or form of the existing which here alone is important. The further nature of its material and other external properties is contained in its determination in so far as they correspond to the End; and the others are unessential.

Secondly, geometrical objects are abstract spatial determinations; the fundamental abstraction (so-called absolute space) has lost all further concrete determinations, and now has only such shapes and figurations as are posited in it: they are therefore essentially only what they ought to be; their Notion-determination, and, more precisely, the specific difference, has its simple unimpeded reality in them; in so far they are the same as the products of external adequacy to End, and they also agree with arithmetical objects in this respect; for in these too only that determination which was posited in them is fundamental.—It is true that space has further determinations; it has three dimensions, and continuity and divisibility, which are not posited in it by the external determination. But these belong to the material which is absorbed and are immediate presuppositions; and synthetic relations and laws are produced only by the connexion and complication of these subjective determinations with this peculiar nature of the soil into which they were introduced.—With numerical determinations the simple principle of the unit is the foundation, and therefore the connexion and further determination are entirely posited; whereas the determinations in space, which, for itself, is a continuous juxtaposition, spread themselves still further, and have a reality different from their Notion but no longer belonging to the immediate Definition.

But, thirdly, the Definition of concrete objects of nature as well as of spirit is a wholly different matter. For sensuous representation such objects are things of many properties. And it is here important to apprehend what is their nearest genus, and then what is their specific difference. It must consequently be determined which of the many properties belongs to the object as genus and which as species, and further which of these properties is the essential one; and, for the latter end, it is necessary to understand their inter-connexion and whether the positing of one implies that of another. But no criterion is given for this end except their existence itself.—The essentiality of a property for Definition (where it is to be posited as simple undeveloped determinateness) is its universality. But in existence this is merely empirical,—a temporal universality, where the property is permanent while the others show themselves transitory in the persistence of the whole,—or a universality which emerges from the comparison with other concrete wholes and in so far does not go further than community. Now if comparison presents the total habitus, as it offers itself empirically, as common foundation, then it is the office of reflection to collect it into a simple thought-determination and to apprehend the simple character of such a totality. The attestation, however, that a thought-determination or any one of the immediate properties constitutes the simple and determinate essence of the object, can only consist in a derivation of such a determination from the concrete quality. But this would require an analysis which transforms into thoughts the immediate qualities and reduces their concrete element to something simple; an analysis which is higher than that which has just been considered, because it ought not to abstract but ought to preserve in the universal the determinate part of the concrete, uniting it and showing it as dependent upon the simple thought-determination.

But the relations of the manifold determinations of immediate existence to the simple Notion would be Propositions requiring proof. But Definition is the first and, as yet, undeveloped Notion, and therefore, when it is required to apprehend the simple determinateness of the object (which apprehension is to be immediate), it can use only one of its immediate so-called properties—a determination of sensible existence or of sensuous representation; its individualization, which takes place through abstraction, thus constitutes its simplicity, while for universality and essentiality the Notion is referred to empirical universality, to persistence in changed circumstances, and to reflection, which looks for the Notion-determination in external existence and in sensuous representation—where precisely it cannot be found.—Consequently Definition automatically renounces proper Notion-determinations, which would essentially be the principles of the objects, and is satisfied with characteristics, that is, determinations in which essentiality is indifferent for the object itself, their end being to furnish tokens for external reflection.—Such an individual and external determinateness is so inadequate to the concrete totality and to the nature of its Notion that it cannot be selected for its own sake nor taken in such a manner that a concrete whole could have its true expression and determination in it.—Blumenbach, for example, observed that the lobe of the ear is absent in all other animals, whence, according to the ordinary phrases about common and distinguishing characteristics, it might be used with perfect correctness as the differentiating mark in the definition of physical man. But such a wholly external determination immediately shows itself to be utterly inadequate to the idea of the total habitus of physical man, and to the demand that the Notion-determination is to be something essential. It is quite contingent whether the characteristics admitted into Definition are such pure makeshifts or approach more closely to the nature of a principle. Also their externality proclaims that no beginning was made from them in Notion-cognition; in fact some dim feeling, some indefinite although profounder sense, some premonition of the essential, preceded the discovery of genera in Nature and in Spirit; a determinate externality was sought only subsequently for understanding.—In existence the Notion has entered into externality, and thus is unfolded into its distinctions; it cannot therefore be entirely attached to any one of such properties. Properties, as the externality of the thing, are external to themselves; and in the sphere of Appearance (under the Thing of many Properties) it was shown that for this reason they even became independent matters; and Spirit, considered from this same standpoint of appearance, becomes an aggregate of many independent forces. The individual property or force, even when it is posited as indifferent to the others, ceases, through this standpoint, to be a characterizing principle; and then the determinateness, as determinateness of the Notion in general, disappears.

Further, besides the differences between properties, the distinction between the Notion and its actualization emerges in concrete things. In Nature and in Spirit the Notion has an external representation, where its determinateness shows itself as dependence upon the external, as transitoriness and inadequacy. Thus although the actual something shows in itself what it ought to be, it can equally show (according to the negative Notion-judgment) that its actuality corresponds to this Notion but imperfectly, or that it is bad. Now Definition must indicate the determinateness of the Notion in some immediate property; and there is no property against which some instance could not be adduced in which the whole habitus allows the concrete entity (which is to be defined) to be known, while at the same time the property which is taken for the mark of the entity appears crude or stunted. In a bad plant or bad animal genus, a contemptible man or a bad State, some sides of existence are defective or wholly obliterated which otherwise might be taken as the distinguishing mark and essential determinateness for Definition in the existence of such a concrete entity. But a bad plant or animal (and so on) still remains a plant or animal. If therefore the bad is to be admitted into the Definition, then all those properties which empirical search wished to regard as essential, elude it through instances of malformation which lack those properties. Thus, for example, the brain is proved unessential for physical man by the occurrence of acephalous births, and the protection of life and property unessential for the State by instances of despotic States and tyrannous governments.—If the Notion is asserted against the instance, and the latter is styled a bad specimen as measured against that standard, then the Notion ceases to be certified by Appearance. But the independence of the Notion is antithetical to the meaning of Definition, which is supposed to be the immediate Notion, and so can take up its determinations for objects only out of the immediacy of existence and can justify itself only in its discoveries.—Whether its content in and for itself is truth or contingency is a question that lies outside the sphere of Definition; but formal truth, or the agreement between the Notion which is subjectively posited in the Definition, and some object which is actual outside it, cannot be established, since the individual object may also be bad.

The content of Definition in general comes from immediate existence, and, because it is immediate, it has no justification, and the question after its necessity is set aside through the origin; for this question pronounces the Notion to be merely immediate, and therewith renounces the attempt to conceive the Notion itself. Consequently Definition represents nothing but the form-determination of the Notion upon a given content, without any intro-Reflection of the Notion, that is, without its Being-for-Self.

But immediacy in general only emerges out of mediation, and must therefore pass over into the latter. In other words the content-determinateness which Definition contains is not only immediate because it is determinateness, but it is mediated through other terms. Hence Definition can comprehend its object only through the opposite determination, and consequently must pass over to Classification,

The universal must particularize itself: in so far the universal implies the necessity of Classification. But Definition itself already begins with the particular, and therefore the particular implies its necessary transition to Classification, since for itself the particular points on to another particular. Conversely the particular distinguishes itself from the universal in that the determinateness is held fast in the need for its distinction from that which is its other; thus the universal is presupposed for Classification. Thus the process is this, that the individual content of Definition rises through particularity to the extreme, or universality; but the latter must now be taken as objective foundation; and, from this foundation, Classification is presented as disjunction of the universal as prius.

Hereby a transition has arisen which takes place from universal to particular and therefore is determined through the form of the Notion. By itself Definition is individual; a plurality of definitions belongs to a plurality of objects. The progress from universal to particular, which belongs to the Notion, is the foundation and possibility of a synthetic science, of a system and of systematic Cognition.

The first requisite for this is, as has been shown, that a beginning shall be made with the object in the form of a universal. In actuality (either natural or spiritual) the concrete individuality is the first thing that is given to subjective and natural Cognition; but in Cognition (which is a process of forming Notions at least in so far as it has the form of the Notion for foundation) the simple term segregated from the concrete must be the prius, because the object has in this form alone the form of a self-relating universal and of something immediate according to the Notion. It may be objected to this scientific process that, since intuition is easier than Cognition, that which can be intuited (concrete actuality) should be made the beginning of science; and it may be added that this course is more natural than that which begins from the object in its abstraction and thence follows the opposite course to its particularization and concrete individualization.—But, where Cognition is demanded, comparison with intuition has already been judged and surrendered, and the only question can be what is to be the first thing within the process of Cognition and what is to be the nature of the sequel: a cognitive progress, and no longer a natural, is now required.—If ease is the only question, then it is self-evident that it is easier for Cognition to seize the abstract simple thought-determination than the concrete, which is a manifold concatenation of such thought-determinations and their relations: and this is the manner in which the concrete is to be apprehended, not as it is in intuition. In and for itself the universal is the first Notion-moment, since it is the simple, and the particular comes after, because it is mediated; conversely the simple is the more universal, and the concrete, since it is differentiated in itself and consequently mediated, is that which presupposes the transition from a first term.—This observation applies not only to the order of the progress in the determinate forms of Definitions, Classifications, and Propositions, but also to the order of Cognition in general and merely with respect to the general distinction between abstract and concrete.—Consequently, for example, where reading is learnt, the beginning, rightly, is not made with whole words or even syllables, but with the elements of words and syllables and with the symbols of abstract sounds. In written characters the analysis of the concrete word into its abstract sounds and their symbols has already been completed; for this very reason a reading lesson is a first occupation with abstract objects. In geometry a beginning must be made not with a concrete three-dimensional figure, but with the point and the line and next with plane figures; and among those not with polygons but with the triangle, and, among curves, with the circle. In physics the several natural properties or matters must be set free from the manifold complications which beset them in concrete actuality, and must be represented with their simple and necessary conditions: they too, like three-dimensional figures, may be intuited; but first the way for their intuition must be cleared by causing them to appear, and be held fast, free from all modifications through circumstances external to their peculiar determinateness. Magnetism, electricity, various kinds of gas, and the like, are such objects as admit of determinate Cognition only if they are taken as removed out of those concrete circumstances in which they appear in actuality. It is true that experiment presents them to intuition in a concrete example; but, in order to be scientific, an experiment (a) must admit only the necessary conditions and (b) must multiply itself in order to show that the inseparable concretion of these conditions is unessential, since they appear first in one and then in another concrete shape, so that for Cognition only their abstract form remains.—To mention one more example, it might have appeared natural and profound to consider colour first in the concrete appearance to the subjective animal sense, next as a spectral appearance suspended outside the subject, and finally as fixed upon objects in external actuality. But, for Cognition, the universal and therefore truly prior form is the middle one of the above-mentioned, where colour stands midway between subjectivity and objectivity as the well-known spectrum, unentangled as yet with either subjective or objective circumstances. The latter merely disturb the pure contemplation of the nature of colour, for they operate as active causes and therefore make it impossible to decide whether the definite changes, transitions, and relations which take place in a colour are grounded in its own specific nature, or must rather be ascribed either to the abnormal specific quality of these circumstances, to the particular affections and effects, healthy or diseased, of the organs of the subject, or to the chemical, vegetable, and animal forces of the objects.—Several further examples might be cited from the cognition of organic nature and of the world of spirit: the abstract must everywhere constitute the beginning and the element in which and from which the particularities and rich shapes of the concrete spread out.

Now in Classification (or in the particular) the distinction between it and the universal arises; but this universal is itself already determinate and thus is only a member of a Classification. Hence there is for it some higher universal; but there is again a higher universal for the latter, and so, at this point, to infinity. The Cognition which is here considered has no immanent limit, since it starts from what is given and the form of abstract universality is peculiar to its first term. Accordingly any object which seems to have an elementary universality is made the object of a particular science, and is an absolute beginning in so far as imagination is presupposed to be acquainted with it and for itself it is taken not to need any derivation. Definition takes it as immediate.

Next the further progress from this term is Classification. For this progress only an immanent principle, that is, a beginning from the universal and the Notion, would be required; but the Cognition which has here been considered lacks this, because it pursues only the form-determination of the Notion without its intro-Reflection: it consequently takes the content-determinateness out of what is given. There is no peculiar ground for the particular which arises in Classification, either in regard to that which is to constitute the basis of Classification or to the definite relation which is to subsist between the members of the disjunction. Consequently in this respect the office of Cognition can only be, partly to order the particular which is discovered in the empirical material, and partly to find its universal determinations by means of comparison. The latter determinations then count as grounds of Classification; and there is a similar number of Classifications accordingly. The mutual relation of the members of a Classification (the species) has only this general determination, that they must be determinate as against one another in accordance with the ground of Classification which has been assumed; if their variety rested upon a different consideration they would not be co-ordinated upon a level basis.

Since a principle of determinedness for self is lacking, the laws which are employed for this operation of Classification can consist only of formal and empty rules which lead nowhere.—Thus the rule is set up that the Classification should exhaust the Notion; but in fact each individual member of the Classification must exhaust the Notion. Really however the determinateness of the Notion is meant, and this it is which is to be exhausted; but, since species here have an empirical multiplicity which in itself is without determination, the number, greater or less, of species which are discovered does not contribute to the exhaustion of the Notion. For example it does not concern the exhaustion of the genus whether a further dozen is discovered in addition to the existing sixty-seven species of parrots. The demand for exhaustion can mean only the tautological proposition that all species should be specified completely.—Now with the growth of empirical knowledge it may well happen that species are discovered which do not lie under the determination of the genus which has been adopted; for the latter is adopted more frequently in accordance with a dim idea of the general habitus than in accordance with the more or less individual characteristic which is expressly designed to serve for its determination.—In such a case the genus would have to be changed, and a justification would have to be furnished for regarding some other number of species as species of a new genus; that is, the genus would be determined in accordance with a collection made under some respect which is accepted as unity, and this respect itself would here be the basis of Classification. Conversely, if the determinateness which originally was accepted were held fast as the peculiarity of the genus, that material would be excluded which it was desired to comprehend in one as species with former species. This Notionless activity, which first assumes a determinateness to be an essential moment of a genus and accordingly subordinates or excludes particulars, but next begins with the particular and, in arranging it, is guided by some other determinateness, produces an appearance of arbitrariness, to which it is left to determine what part or side of the concrete it shall hold fast and arrange accordingly.—Physical nature offers of itself such a contingency in the principles of Classification; because of its dependent and external actuality it stands in a connexion which is manifold and is given for it too. Consequently a multitude of principles is found to which it must conform, following one in one of the series of its forms and another in another, and producing hybrids which simultaneously diverge in opposite directions. It thus results that in one series of natural objects characteristics emerge as extremely expressive and essential, which become insignificant and purposeless in others, so that it becomes impossible to retain a principle of Classification of this kind.

The general determinateness of empirical species can be only this, that they are generally different from one another without being opposite. The disjunction of the Notion has already been demonstrated in its determinateness; if particularity, without the negative unity of the Notion, is accepted as immediate and given, then the distinction does not move beyond the reflection-form of difference in general, which has already been considered. That externality, which is the peculiar habitat of the Notion in Nature, introduces the total indifference of the distinction; consequently a common determination for Classification is derived from number.

However contingent the particular is here as against the universal, and therefore against Classification in general, it may be ascribed to an instinct of reason if Classifications and grounds for Classification are found in this Cognition which, so far as sensuous properties admit, show themselves to be more adequate to the Notion. Thus for animals the organs of eating (teeth and claws) are used in the various systems as a comprehensive ground of Classification; at first they are taken merely as sides in which the characteristics for the subjective purpose of Cognition are more easily designated. But in fact these organs not only contain a distinction which belongs to external reflection, but also they are the vital centre of animal individuality, where it posits itself, in distinction from external nature (its Other), as self-relating individuality, separating itself from the continuity with Other.—For the plant the fructifying organs constitute the highest point of vegetable life, by which it intimates the transition to sexual differentiation and thus to distinct individuality. Systems therefore have rightly turned to this point as a ground for Classification which, if not wholly adequate, goes far, and have thus based themselves on a determinateness which is not only a determinateness for external and comparative reflection, but is also in and for itself the highest that a plant admits.

I, The third stage of this Cognition, which progresses in accordance with the Notion-determinations, is the transition of particularity into individuality; the latter constitutes the content of the Proposition (or Theorem). What must here be considered is the self-relating determinateness, the internal distinction of the object and the relation to one another of the distinct determinatenesses. Definition contains one determinateness only, and Classification one determinateness as against others: in individualization the object has fallen apart within itself. Just as Definition does not go beyond the general Notion, so in Propositions the object is cognized in its reality, in the conditions and forms of its real existence. Thus, joined to Definition, it represents the Idea, which is the unity of Notion and Reality. But the Cognition which is here considered and is still engaged in search does not reach this representation in so far as Reality with it does not emerge out of the Notion, and so the dependence of Reality upon the Notion, and therefore the unity itself, is not cognized.

Now according to the determination which has been indicated the Proposition is the properly synthetic part of an object, in so far as the relations of its determinatenesses are necessary, that is, are founded upon the inner identity of the Notion. In Definition and Classification the synthetic element is a combination admitted from outside; what is found given is reduced into the form of the Notion, but, as given, the whole content is merely pointed at, whereas the Proposition ought to be demonstrated. This Cognition does not deduce the content of its Definitions and determinations of Classification, so that it might seem that it could also spare itself the proof of these relations, which are expressed by Propositions, remaining satisfied with perception in this respect too. But Cognition is distinguished from bare perception and sensuous representation by the Notional form generally which it imparts to the content; this is the work of Definition and Classification. Now the content of the Proposition is derived from the Notion-moment of individuality, and consequently it consists in determinations of reality which no longer have merely the simple and immediate Notion-determinations for their relation; in individuality the Notion has passed over to otherness, to the Reality by virtue of which it becomes Idea. Thus the synthesis which is contained in the Proposition no longer has the Notional form for justification: it is a combination of various terms; consequently the unity, which has not yet been posited, remains to be demonstrated,—so that proof becomes actually necessary for this Cognition.

Here the first difficulty which arises is to distinguish accurately between the determinations of the object which can be admitted into the Definition and those which must be relegated to the Propositions. There can be no principle which governs this. A principle appears to lie in the fact that that which immediately belongs to the object belongs to the Definition, while the rest, being mediated, must first have its mediation exposed. But the content of Definition is determinate in general, and therefore is essentially mediated itself; its immediacy is merely subjective, that is, the subject makes an arbitrary beginning and allows the object to count as presupposition. Now the object is an object concrete in general in itself; it must also be classified, and thus a number of determinations result which by their nature are mediated, and are taken as immediate and undemonstrated,—not by virtue of a principle, but only by subjective determination.—Even in Euclid, who has always been justly recognized as the master of this synthetic kind of Cognition, a presupposition about parallel lines is found, under the name of axiom, which has been thought to require proof; and attempts have been made in various ways to supply this want. In several other theorems it has been thought that presuppositions have been discovered which should not have been assumed immediately but should have been proved. With regard to the axiom about parallel lines, it may be observed that it is a clear example of the justness of thought of Euclid, who accurately valued the element and nature of his science. The proof of this axiom might have been deduced from the Notion of parallel lines; but such a proof is no more part of his science than the deduction of his definitions and axioms or of his subject in general, namely, space and its first determinations, the dimensions. Such a deduction can only be made out of the Notion, and the Notion lies outside the peculiar sphere of Euclid’s science; these therefore are necessarily presuppositions for it, or relative priora.

The axioms may be mentioned in this connexion; they are members of the same class. As a rule they are incorrectly taken as absolute priora, as though in and for themselves they required no proof. If this were in fact the case they would be mere tautologies, since only in abstract identity is there no variety and consequently no need for mediation. But if the axioms are more than tautologies they are propositions of some other science, since they are to be presuppositions for the science in which they serve as axioms. Consequently they are really theorems, and generally logical ones. The axioms of geometry are such lemmata, or logical propositions which approximate to tautology since they refer to magnitude only, so that qualitative distinctions are extinguished in them; the capital axiom—the purely quantitative Syllogism—has been mentioned above.—Thus the axioms, considered in and for themselves, require proof as much as Definitions and Classifications, and the reason why they are not made into Propositions (or theorems) is only that they are taken as relatively first for a certain standpoint and therefore as presuppositions.

With respect to the content of Propositions a further distinction is to be made. The content consists in a relation of determinatenesses of the reality of the Notion: consequently these relations may be more or less incomplete and individual relations of the object, or else may be such a relation as comprehends the whole content of the reality and expresses its determinate relation. But the unity of the complete content-determinatenesses is equal to the Notion: consequently a proposition which contains them is in turn a Definition, which however expresses the Notion not only as taken up immediately but as developed into its determinate and real distinctions; it expresses the complete existence of the Notion. Consequently the two together are the Idea.

If the Propositions of a synthetic science, and especially of geometry, are more closely compared, the distinction will be observed that some of its Propositions contain only single relations of the object, and others contain such as express the full determinateness of the object. It is a very superficial view which holds that all propositions have the same value because each contains a truth anyhow, and each is equally essential in the formal demonstrative progress or train of proof. The distinction with regard to the content of Propositions has the closest connexion with this progress; some further observations upon the latter will serve to elucidate this distinction and also the nature of Synthetic Cognition. We will take for example Euclidean geometry, as representative of the synthetic method, of which it furnishes the most perfect model; it has always been praised for the consecutive arrangement of its Propositions, whereby for each theorem those other propositions which its construction and proof require are always discovered to have been already demonstrated. This circumstance relates to formal consecutiveness; and however important this is, it rather regards external arrangement for convenience, and for itself has no relation to the essential distinction between Notion and Idea, which involves a higher principle of necessary progression.—For the Definitions with which a beginning is made take the sensible object as immediately given, and determine it according to its nearest genus and specific difference; and these too are the simple immediate determinatenesses of the Notion, Universality and Particularity, whose relation is not further developed. Now the first Propositions can only have recourse to such immediate determinations as are contained in the Definitions; moreover their reciprocal dependence can only regard this general point, that one is, generally, determined through the other. Thus Euclid’s first theorems about triangles regard only their equality, that is, the number of pieces in a triangle which must be determined in order that the other pieces of the same triangle (or the whole) shall be altogether determined. The comparison of two triangles with each other and the plan of placing equality in coincidence is a detour required by a method which is forced to use sensuous coincidence in place of the concept of determinedness. Considered otherwise by themselves, these theorems themselves contain two parts, one of which may be regarded as the Notion and the other as the Reality, or that which completes the former into Reality. For that which completely determines (for example the two sides and the included angle) is already the whole triangle for understanding; nothing further is wanted for its complete determinateness, and the remaining two angles and third side are the excess of Reality over the determinateness of the Notion. Thus the work of these theorems is really to reduce the sensuous triangle (which of course does require three sides and three angles) to the simplest conditions; the Definition had mentioned only the three lines which enclose the plane figure and make it a triangle: the Proposition at length contains expressly the determinedness of the angles through the determinedness of the sides; and the other Propositions contain the dependence of three further parts on three such parts.—The complete determinateness of the magnitude of a triangle within itself according to its sides is contained in the theorem of Pythagoras: this is the equation of the sides of a triangle, whereas previously the sides achieve only a general determinateness of its parts relatively to one another, and not an equation. Consequently this Proposition is the perfect and real Definition of the triangle, and primarily of the right-angled triangle, which in its distinctions is simplest and most regular.—With this Proposition Euclid ends the first book; and indeed it is a perfect determinateness which has here been reached. And similarly, after he has reduced to uniformity the triangles which are not right-angled and are affected with greater inequality, he ends the second book with the reduction of the rectangle to the square,—which is the equation of the self-equal (the square) and the self-unequal (the rectangle). Similarly the hypotenuse (which corresponds to the right angle, or self-equal) in the theorem of Pythagoras constitutes one side of the equation, while the other side is constituted by the self-unequal, namely the two catheters. This equation between square and rectangle is the basis of the second definition of the circle—which in turn is the theorem of Pythagoras just in so far as the catheters are taken as variable magnitudes. The first equation of the circle bears the same relation of sensuous determinateness to equation as the two different definitions of conic sections in general bear to each other.

This true synthetic progress is a transition of the universal to individuality, namely to that which is determined in and for itself or to the unity of the object within itself, in so far as the latter has fallen apart and has been distinguished into its essential real determinatenesses. In other sciences however the usual and wholly incomplete progress is that, while the beginning is made from a universal, its individualization and concretion are only the application of the universal to material which is introduced from elsewhere. In this manner the truly individual element of the Idea is an empirical addition.

But however complete or incomplete, more or less, the content of a Proposition is, it must be proved. It is a relation of real determinations which have not the relation of Notion-determinations; if they have this relation (as can be demonstrated in those Propositions which we called second or real Definitions), then for this very reason these (a) are Definitions; but (b) because their content at the same time consists in a relation of real determinations and not merely in the relation of a universal and of simple determinateness, they are both in need and capable of a proof in comparison with such a first Definition. They are real determinatenesses, and as such have the form of entities persisting indifferent and various; consequently they are not immediately one, and for this reason their mediation must be exposed. The immediate unity in the first Definition is that in accordance with which the particular is in the universal.

2. The mediation must now be more closely considered. It may be simple, or may pass through several mediations. The members which mediate are connected with those which are to be mediated; but it is not the Notion out of which the mediation and Proposition are reduced in this Cognition—the transition into opposite being altogether alien to the Notion—, and therefore the mediating determinations must be produced from somewhere, without the notion of connexion, as a provisional material for the framework of the proof. This preliminary procedure is the construction.

Among the relations of the content of the Proposition, which may be extremely various, only those must now be enumerated and made imaginable which are used in the proof. It is only in the proof that this collection of material achieves a meaning: in itself it appears blind and Notionless. After the proof it is of course seen that it was suitable to draw such further lines, for example, in a geometrical figure as are indicated in the construction; but in the construction it demands blind obedience, so that this operation for itself is without understanding, since the end which guides it has not yet been expressed.—It is indifferent whether it is a theorem proper or a problem for which the construction is undertaken: such as it appears before the proof, it is something not derived out of the determination given in the theorem or problem, and is therefore a meaningless activity for anyone who does not yet know the end; always it is ruled by an external end.

This temporary secret emerges in the proof. As has been stated, the proof contains the mediation of that which the Proposition enunciated as connected; it is only through this mediation that this connexion appears necessary. The construction by itself is without the subjectivity of the Notion; and the proof similarly is a subjective activity without objectivity. For the content-determinations of the Proposition are not also posited as Notion-determinations, but as given and indifferent parts which stand in manifold external relations to one another; and therefore the necessity shows itself only in the formal and external Notion. The proof is not a genesis of the relation which constitutes the content of the Proposition; the necessity exists only for intellectual discernment, and the whole proof for the subjective purpose of Cognition. For this reason it is altogether an external reflection which goes from without inwards, that is, draws conclusions about the inner nature of the relation from external circumstances. The circumstances which the construction represented, followed from the nature of the object: here conversely they become ground and mediating relations. Consequently the middle or third term, in which the terms connected in the Proposition represent themselves in their unity—it is the nerve of the proof—is only an entity in which this connexion appears and is external. The consequence which this proof pursues is the converse of the nature of the thing, and therefore that which there is regarded as ground is a subjective ground from which the nature of the thing emerges for Cognition only.

What has been said so far makes clear the necessary limit of this Cognition, which very frequently has been misunderstood. The brilliant example of the synthetic method is the science of geometry,—but it has been improperly applied to other sciences, and even to philosophy. Geometry is a science of magnitude, and therefore formal syllogizing most fittingly belongs to it. Here the merely quantitative determination is considered, and abstraction is made from the qualitative determination; it can therefore remain within formal identity or Notionless unity, which is equality and belongs to external abstracting reflection. The object (spatial determinations) is such an abstract object as has been prepared for the end of having a complete finite and external determinateness. By virtue of its abstract object this science has on the one hand the sublime quality that in its void and silent spaces colour is extinguished and every other sensuous property has vanished, and that every other appeal is silent which speaks more intimately to living individuality. On the other hand the abstract object still remains space, an unsensuously sensuous entity;—intuition is raised into its abstraction. It is a form of intuition, but still it is intuition;—it is sensuous, the external juxtaposition of sensuousness itself, its pure Notionlessness.—Enough has been heard in our time about the excellence of geometry from this side;—the fact that it has sensuous intuition for its foundation has been declared its greatest advantage, and it has been thought that this is even the basis of its high standing as a science, and that its proofs rest upon intuition. This shallow observation must be met by the platitude that no science is made through intuition, but through thought alone. Geometry, by virtue of its still sensuous material, rests to some extent on intuition; but this gives it only that kind of evidence which the sensuous in general has for spirit without thought. And, by a pitiful error, this very sensuousness of material has been counted an advantage which in fact marks the lowness of its standpoint. It owes its capacity for a higher scientific quality to the abstraction of its sensuous object alone; hence also its great advantage over all the other collections of pieces of knowledge which men are likewise pleased to call sciences and which have for content a concrete and perceptible sensuous, showing a dim foreboding and allusion to the demands of the Notion only through the order which they attempt to introduce.

Geometrical space is the abstraction and -void of external juxtaposition; only by virtue of this is it possible that the configurations can be plotted into its indeterminateness in such a manner that their determinations remain separate in stable fixity and contain no transition into opposite. The science of geometry is thus simple science of the finite which is compared according to magnitude, and whose unity is external, or is equality. But in this process of figuration a start is made at the same time from different sides and principles, and the various figures arise each for itself; and thus being compared they still show qualitative unlikeness and incommensurability. These properties are the force which drives geometry from finitude, where it was pursuing its safe and regular advance, to infinity—a region where entities which are qualitatively different are posited as like. Here its self-evidence ceases in this respect, that elsewhere it is based upon fixed finitude and has nothing to do with the Notion and its Appearance, which is the transition that has just been mentioned. Finite science has here reached its limit, since the necessity and mediation of the synthetic element are no longer founded upon merely positive, but upon negative, identity.

Geometry, like algebra, soon strikes upon its limit with its abstract objects of mere understanding; and with other sciences the synthetic method proves from the beginning all the more inadequate—most of all with philosophy. With respect to Definition and Classification what is required has already resulted; and this would be the place for a discussion of the Proposition and proof only; but, apart from the presupposition of Definition and Classification, which demands and presupposes the proof, the inadequacy consists in their general attitude to the Propositions. This attitude is chiefly remarkable with the empirical sciences (physics for example) when they attempt to assume the form of synthetic sciences. The following method is used. Reflection-determinations about particular forces or other internal and essential forms which result from the manner in which empirical data are analysed, and can justify themselves only as results, must be given the prior place, in order that a general foundation may thus be obtained which may afterwards be applied to and demonstrated in the individual. These general foundations have no foothold for themselves; they are postulated for the time being; and it is noticed only in the conclusions derived that the said conclusions are the real ground of these foundations. It is now seen that the so-called explanation and proof of the concrete element which is brought into Propositions is partly a tautology and partly a confusion of the true relation; further it is seen that this confusion served to disguise the trick of Cognition, which took up empirical data one-sidedly (the only manner in which it could reach its simple definitions and formulae), and eludes empirical refutation by examining experience and allowing it validity not in its concrete totality but as example, and only in that direction which is serviceable for the hypotheses and the theory. Concrete experience being thus subordinated to the presupposed determinations, the foundation of the theory is obscured, and is exhibited only from that side which is in conformity with the theory; and altogether this method makes it much more difficult to contemplate without bias concrete perceptions by themselves. Only if the entire course which has been followed is inverted does the whole obtain the right relation, where the connexion between ground and consequence and the correctness of the transformation of perception into thought may be checked. Consequently one of the main difficulties in the study of such sciences is, to penetrate into them; and this can be done only if certain presuppositions are blindly granted, and the determinations are, for the time being, memorized, about the forces and matters which are assumed, together with their hypothetical formations, directions, and rotations, while as yet it is impossible to form a Notion about them or even a definite image—at best a confused mental picture can be made. If the necessity and the Notion of the presuppositions are demanded before they are accepted and counted as valid, then no progress can be made beyond the beginning.

The occasion arose above of speaking about the impropriety of applying the synthetic method to strictly analytic science. Wolf extended this application to every possible kind of knowledge, and drew them all into philosophy and mathematics,—knowledge which partly is of wholly analytic nature and partly of a contingent and merely professional kind. Such a material, which by its nature is easily apprehended and admits of no strict and scientific treatment, being contrasted with the stiff circumlocution and armour of science, automatically demonstrated and discredited the clumsiness of such an application. Nevertheless this abuse could not extinguish the belief in the fitness and essentiality of this method for scientific exactness in philosophy; and Spinoza’s example in the presentation of his philosophy was long held ‘to be a pattern. But in fact Kant and Jacobi overturned the whole manner of the older metaphysics, and with the manner the method. Kant, in his own fashion, proved of the content of these metaphysics that it led by strict demonstration to antinomies, whose further nature has been examined at the proper places. But he did not reflect upon the nature of this demonstration, which is bound to a finite content; yet the two stand and fall together. In his Foundations of Natural Science he has himself given an example of treating as a science of reflection, and by the method appropriate to such, a science which he had intended to reclaim for philosophy by the other means.—Of the older metaphysics Kant chiefly attacked the matter, while Jacobi attacked its method of demonstration, elaborating in the clearest and profoundest manner the point which is of chief importance—namely, that such a method of demonstration is simply bound within the circle of the rigid necessity of the finite, and that freedom (that is, the Notion, and whatever is true) lies beyond its sphere and scope.—According to Kant’s result it is the peculiar material of metaphysics that leads it into contradictions, and the inadequacy of Cognition consists in its subjectivity; according to Jacobi’s it is the method and entire nature of Cognition itself, which seizes only a connexion of conditionedness and dependence, thus proving itself inadequate to that which is in and for itself and is the absolutely true. And indeed the principle of philosophy is the infinite free Notion, and all its content rests upon this alone; and thus the method of Notionless finitude does not fit the Notion. The synthesis and mediation of this method (that is, the process of proof) achieve only a necessity which is the opposite of freedom,—that is, an identity of the dependent which is only in itself whether it is taken as internal or as external, where that which constitutes the real element (that which is distinct and has entered into existence) remains something which is just independently different and therefore finite. Here this identity does not reach existence and remains the merely internal; or, it is that which is merely external, its determinate content being given it. In both views it is abstract and does not contain the side of reality within itself, and is not posited as identity which is determined in and for itself. Thus the Notion is excluded from this Cognition, and it is the Notion which is the only goal and is the infinite in and for itself.

Thus in Synthetic Cognition the Idea reaches its end only in so far as the Notion now is for the Notion according to its moments of identity and the real determinations, or according to universality and the particular distinctions, and, further, as identity which is connexion and dependence of the different. But this its object is not adequate to it; for the Notion does not become unity with itself in its object or its reality. In necessity its identity is for it; but in this identity the necessity is not itself determinateness, but is a material external to it, that is, not determined by the Notion, so that in it the Notion does not cognize itself. Thus altogether the Notion is not determined for itself, not determined both in and for itself according to its unity. Hence in this Cognition the Idea does not yet reach truth because of the inadequacy of the object to the subjective Notion.—But the sphere of Necessity is the highest point of Being and of Reflection; in and for itself it passes over into the freedom of the Notion, while the inner identity passes over into its manifestation, which is the Notion as Notion. It was shown under the heading of Necessity how the transition from the sphere of this latter into the Notion takes place in itself; and indeed this transition presented itself as the genesis of the Notion at the beginning of this Book. Here Necessity has this position, that it is the reality or object of the Notion, while the Notion into which it passes over is now as object of this same. But the transition itself remains unchanged. Here too it is only in itself, and as yet lies outside Cognition in our reflection; that is, it is the Necessity (which as yet is inner) of this Cognition. Only the result is for it. The Idea, in so far as the Notion is now for itself the Notion determinate in and for itself, is the Practical Idea, or Action.

Since the Notion which is its own object is determined in and for itself, the subject is determined for itself as individual. As subjective the Notion has again the presupposition of an otherness which is in itself; it is the impulse to realize itself, or the end which tries to give itself objectivity in the objective world, and to execute itself, through itself In the Theoretical Idea the subjective Notion stands opposed, as the universal which is indeterminate in and for itself, to the objective world, from which it draws determinate content and fulfilment. But in the Practical Idea it stands opposed as actual to the actual. But the self-certainty which the subject has in the fact of its determinedness in and for itself, is a certainty of its own actuality and of the non-actuality of the world; what is null for it is not only the world’s otherness as abstract universality, but its individuality and the determinations of its individuality. The subject has here appropriated objectivity for itself; its determinateness within itself is the objective, for it is universality which equally is just determinate; the heretofore objective world, on the other hand, is only something posited, something immediately determined in manifold ways; but, because it is only immediately determined, it lacks the unity of the Notion within itself and for itself is null.

This determinateness, which is contained in the Notion, and is equal to it, and includes within itself the demand of the individual external actuality, is the Good. It appears with the dignity of absoluteness, because it is the totality of the Notion within itself—the objective in the form simultaneously of free unity and subjectivity. This Idea is higher than the Idea of Cognition which has already been considered, for it has not only the dignity of the universal but also of the simply actual.—It is impulse in so far as this actual is still subjective and posits itself and has not at the same time the form of immediate presupposition; its impulse towards self-realization is not really the impulse to give itself objectivity (for this it has in itself), but is only this empty form of immediacy.—Consequently the activity of the end is not directed against itself, for the purpose of absorbing and assimilating a given determination; it aims rather at positing its own determination, and, by transcending the determinations of the external world, at giving itself reality in the form of external actuality.—The Idea of Will as self-determining for itself has the content within itself. This content is determinate, and as such is finite and restricted: self-determination is essentially particularization, since the intro-Reflection of Will as negative unity in general is also individuality in the sense of the exclusion and presupposing of an Other. But still the particularity of the content is at this point infinite through the form of the Notion whose peculiar determinateness it is, while in it the Notion has negative self-identity and therefore not only a particularity, but also its infinite individuality. The finitude of content in the Practical Idea, which has been mentioned, is therefore identical with the fact that as yet it is not realized Idea; for the content, the Notion is that which is in and for itself; here it is the Idea in the form of objectivity which is for itself. For this reason (1) the subjective is no longer merely posited, arbitrary, or contingent, but is absolute; but (2) this form of existence, or Being-for-Self, has not yet also the form of Being-in-Self. That which purely formally appears as opposition appears as simple determinateness of the content in the content, which is the form of the Notion reflected so as to be simple identity; hence, although valid in and for itself, the Good is some particular end, which however is not merely to receive its truth through its realization, but already is the true for itself.

The syllogism of immediate realization itself requires here no further exposition; it is nothing whatever but the syllogism of external adequacy to End which was considered above; the only distinction lies in the content. In external adequacy to End (since it is formal) this content was merely indeterminate and finite in general; and although here too it is finite, it also has, as such, absolute validity. But a further distinction arises in regard to the conclusion, that is, the Realized End. In the process of realization the finite End equally reaches only the Means; and, since in its beginning it is not already an End determinate in and for itself, it remains in its realization something which is not in and for itself. And if the Good in turn is fixed as finite and is essentially so, then, in spite of its internal infinity, it cannot escape the fate of finitude—a fate which appears in more forms than one. The realized Good is good by virtue of what it is already in the Subjective End, in its Idea; realization gives it an external existence; but this existence is determined only as an externality which in and for itself is null, and therefore in it the Good has reached only an existence which is contingent and subject to destruction, and not a realization corresponding to its idea.—And further, since with respect to its content it is restricted, there are varieties of Good; the existent Good is subject to destruction not only through external contingency and through evil, but also through the collision and conflict of the Good itself. An objective world is presupposed to the Good, a world which constitutes the subjectivity and finitude of the Good and, as being other, pursues its own course: and in it even the realization of the Good is exposed to obstacles, which may sometimes be insuperable. Thus the Good remains an Ought; it is in and for itself, but Being, as last and abstract immediacy, remains determined against it as a Not-being too. Although the Idea of the perfected Good is an absolute postulate, it is no more than a postulate,—that is, the absolute infected with the determinateness of subjectivity. The two worlds still remain in opposition; one a realm of subjectivity in the pure spaces of transparent thought, the other a realm of objectivity in the element of an externally manifold actuality, which is an unexplored realm of darkness. The complete development of the unresolved contradiction, of that absolute end which the barrier of this actuality insuperably opposes, has been considered more closely in the Phenomenology of Spirit (Eng. tr., pp. 610 sqq.).—Since now the Idea contains the moment of perfect determinateness, the other Notion, to which this Notion stands related in the Idea, contains in its subjectivity the moment of an Object; consequently the Idea here enters into the shape of self-consciousness and, in this one respect, coincides with the presentation of the latter.

The Practical Idea still, however, lacks the moment of real consciousness, which would mean that the moment of actuality in the Notion had reached for itself the determination of external Being.—This lack may also be considered in this way, that the Practical Idea is still wanting the moment of the Theoretical Idea. For in the latter it is only the determination of universality that stands on the side of the subjective Notion which comes to be intuited by the Notion within itself; Cognition knows itself only as apprehension, as the self-identity of the Notion, which for itself is indeterminate: fulfilment, that is, objectivity determined in and for itself, is given to it, and that which truly is is the actuality that is present independently of subjective positing. The Practical Idea on the other hand counts this actuality (which at the same time opposes it as an insuperable barrier) as that which in and for itself is null, which is to receive its true determination and sole value through the ends of the Good. Will itself consequently bars the way to its own goal in so far as it separates itself from Cognition and external actuality does not, for it, obtain the form of that which truly is; consequently the Idea of the Good can find its complement only in the Idea of the True.

But it makes this transition through itself. In the syllogism of action one premiss is the immediate relation of the good end to actuality, of which it makes itself master, directing it (in the second premiss) as external means against external actuality. For the subjective Notion the Good is the objective; actuality in its existence opposes it as insuperable barrier only in so far as itself still has the determination of immediate existence, and not of something objective in the sense of Being-in-and-for-Self; rather, actuality is either the evil or the indifferent and merely determinable, which does not contain its value in itself. But the Practical Idea has itself already transcended this abstract Being which stands opposed to the Good in the second premiss; the first premiss of its action is the immediate objectivity of the Notion, according to which the end communicates itself to actuality without any resistance and is thus in simple and identical relation with it. In so far, then, only the meanings of its two premisses need be brought together. That which in the first premiss is already immediately consummated by the objective Notion, is only complemented in the second by being posited through mediation and hence for the objective Notion. In the End-relation in general the Realized End is also only a Means, but conversely the Means is also the Realized End; and similarly in the syllogism of the Good the second premiss is immediately present implicitly in the first; but this immediacy does not suffice, and the second premiss is already postulated for the first Good;—the realization of the Good in the teeth of an opposing and other actuality is the mediation which is essential for the immediate relation and actualization of the Good. For it is only the first negation or the otherness of the Notion,—an objectivity which would mean that the Notion was submerged in externality. The second negation is the transcendence of this otherness, whereby now the immediate realization of the end becomes actuality of the Good as Notion which is for itself, since here the Notion is posited as identical with itself, not with an Other, and therefore alone as free. If now in spite of this the end of the Good should not be realized, then this is a relapse of the Notion to the standpoint which the Notion has before its activity—the standpoint of that actuality which was determined as null and yet was presupposed as real. This relapse becomes a progress to bad infinity; it has its only ground in the fact (1) that in the transcendence of this abstract reality the transcendence is equally immediately forgotten, or (2) that it is forgotten that this reality has already been presupposed as non-objective actuality which is null in and for itself. This repetition of the presupposition of the non-realized end after the actual realization of the end consequently also determines itself in the following manner: the subjective attitude of the objective Notion is reproduced and perpetuated, whence the finitude of the Good as permanent truth (with respect to both its form and its content), as well as its actualization, still appears merely as an individual and not as a universal act.—In fact this determinateness has transcended itself in the actualization of the Good. The objective Notion is still limited by its own view of itself, which vanishes by its reflection upon what its actualization is in itself. By this view it stands only in its own way, and in this matter must turn, not against any outer actuality, but against itself.

For in the second premiss only a one-sided Being-for-Self is produced, whence the product appears as subjective and individual, so that in it the first presupposition is repeated; and in truth this activity is equally the positing of the identity (which is in itself) of the objective Notion and the immediate actuality. By the presupposition the latter is determined as having a reality of appearance only, being null in and for itself, and utterly determinable by the objective Notion. By the activity of the objective Notion its external actuality is altered, and its determination is accordingly transcended; and by this very process it loses merely apparent reality, external determinability, and nullity, and it is thus posited as being in and for itself. Presupposition in general is here transcended,—that is, the determination of the Good as an end which is merely subjective and restricted in its content, the necessity of realizing it by subjective activity, and this activity itself. In the result mediation transcends itself; the result is an immediacy which is not the reconstitution of the presupposition but rather the fact of its transcendedness. The Idea of the Notion which is determined in and for itself is thus posited no longer merely in the active subject, but equally as an immediate actuality; and the latter conversely is posited as it is in Cognition, as objectivity which is veritable. Hereby the individuality of the subject, with which it was affected by its presupposition, has disappeared; it is thus now as free and universal self-identity; for it the objectivity of the Notion is given, and immediately present for the subject, just as much as the subject knows itself to be the Notion determined in and for itself. In this result then Cognition is reconstructed and united with the Practical Idea; the actuality which is found as given is at the same time determined as the realized absolute end,—not however (as in inquiring Cognition) merely as objective world without the subjectivity of the Notion, but as objective world whose inner ground and actual persistence is the Notion. This is the Absolute Idea.