III.1.3. The Syllogism

It has resulted that the Syllogism is the reconstruction of the Notion in the Judgment, and is thus the unity and truth of both. The Notion as such holds its moments suspended in unity; in the Judgment this unity is internal, or, what is the same thing, it is external, and the moments, although related, are posited as independent extremes. In the Syllogism the Notion-determinations are posited like the extremes of the Judgment; at the same time their determinate unity is posited.

The Syllogism thus is the Notion posited in its completeness; consequently it is the Reasonable.—Understanding is taken to be the capacity of the determinate Notion, which is held fast for itself through abstraction and the form of universality. But in reason the determinate Notions are posited in their totality and unity. Consequently not only is the Syllogism reasonable, but whatever is reasonable is a Syllogism. To syllogize has for long been held to be the part of reason; on the other hand, reason in and for itself, and reasonable axioms and laws, are spoken of in a manner which leaves it dark how the former syllogizing reason is connected with the latter reason which is the source of laws and other eternal truths and absolute thoughts. If the former is supposed to be only formal reason, while the latter is supposed to produce the content, then, according to this distinction, it is precisely the form of reason, the Syllogism, that could not be lacking in the latter. In spite of this both are commonly kept apart, and when one is mentioned the other is neglected, so that the reason of absolute thoughts seems to be ashamed of the reason of the Syllogism, and the Syllogism to be cited only traditionally as an activity of reason. But, as has just been observed, logical reason, when it is considered as formal, plainly should be recognizable in that reason which concerns itself with a content: indeed, content can be reasonable only through the form of reason. It is impossible here to have recourse to common chat about reason, which refrains from stating what is to be understood by reason; this cognition which is supposed to be reasonable is generally so busy about its objects that it forgets to cognize reason itself, distinguishing and designating it only by those objects which are supposed to belong to it. If reason is supposed to be that cognition which has knowledge of God, freedom, right, duty, the infinite, the unconditioned, the supersensuous, or even yields only ideas and sentiments about them, then partly these latter are only negative objects, and partly the first question still remains, what it is in all these objects that makes them reasonable.—It is this:—that their infinite element is not empty abstraction from the finite, nor universality without content or determination: it is filled universality, the Notion which is determinate, and contains its determinateness in this veritable manner, that it distinguishes itself in itself and exists as the unity of these its rational and determinate distinctions. It is only thus that reason rises above the finite, conditioned, or sensuous, or however else it may be determined; in this negativity it is essentially full of content, for it is unity as unity of determinate extremes; but thus the reasonable is Syllogism and Syllogism only.

At first the Syllogism like the Judgment is immediate; hence its determinations (termini) are simple and abstract determinatenesses; thus it is the Syllogism of Understanding. If no progress is made beyond this form of it, its reasonableness, although present and posited in it, is insignificant. Its essential elements are the unity of the extremes, the middle term which unites and the ground which sustains them. Abstraction holds fast the independence of the extremes, and, in so doing, opposes to them this unity as a determinateness which is equally fixed and is for itself; in this manner it takes it as non-unity rather than as unity. The expression “middle” (medius terminus) has been introduced from spatial imagery, and contributes its part in preventing progress beyond the mutual externality of the determinations. Now if the Syllogism consists in this, that the unity of the extremes is posited in it, and if this unity is taken altogether (a) as a particular by itself, and (b) as a merely external relation, non-unity being made the essential relation of the Syllogism, then reason (and the Syllogism is reason) does not help to produce reasonableness.

First the Qualitative Syllogism, in which the determinations are thus immediately and abstractly determined, demonstrates in itself (because, like Judgment, it is their relation) that they are not such abstract determinations, but that each contains the relation to the other, and that the middle not only contains particularity as against the determinations of the extremes, but also contains particularity posited in itself.

Through this its dialectic it becomes the Syllogism of Reflection, the second Syllogism,—with determinations as such, in each of which essentially the other shows; in other words, they are posited as mediated, and this, according to the Syllogism, they are supposed to be.

Thirdly, this showing or mediatedness is intro-reflected, and thus the Syllogism is determined as Syllogism of Necessity, where the objective nature of the thing is the mediator. This Syllogism equally determines the extremes of the Notion as totalities; it has thus reached its truth—the correspondence of its Notion (or the middle) and its Existence (or the extreme distinctions). It has thus passed over from Subjectivity into Objectivity.

1. The Syllogism in its immediate state has for its moments the Notion-determinations as immediate. They thus are the abstract determinatenesses of the form; they have not yet been shaped by mediation into concreteness, but each is only an individual determinateness. The first is therefore the strictly formal Syllogism. The formalism of syllogizing consists in making a halt at the determination of this first Syllogism. The Notion, sundered into its abstract moments, has individuality and universality for its extremes, and it itself appears as the particularity which stands between them. Because of their immediacy, and as only self-relating determinatenesses, they are all together one individual content. Particularity at first constitutes the middle in so far as it immediately unites in itself the two moments of individuality and universality. It is determinate and therefore subsumed under the universal; on the other hand the individual (as against which it has universality) is subsumed under it. But at first this concretion is only a two-sidedness; in the immediate Syllogism the medius terminus is immediate and therefore is as simple determinateness; and the mediation which it constitutes is not yet posited. Now the dialectic movement of the Qualitative Syllogism consists in this, that the mediation, which alone constitutes the Syllogism, is to be posited in its moments.

The general scheme of the determinate Syllogism is I—P—U. Individuality joins itself with universality through particularity; and the individual is not immediately universal, but only through particularity; and conversely the universal is likewise not immediately individual, but lowers itself to individuality through particularity.—These determinations stand opposed to each other, as extremes, and are one in a different third term. Each is determinateness, and in this they are identical; and this their general determinateness is particularity. But they are extremes against the latter as much as against each other, because each is in its immediate determinateness.

The general meaning of this syllogism is that the individual (which as such is infinite self-relation, and therefore would be only inner) passes through particularity into Existence as into universality: here it no longer belongs to itself alone, but has external connexions. Conversely the individual severs itself into its determinateness as particularity; in this separation it is therefore concrete, and, as self-relation of determinateness, a universal self-relating entity, and therefore also one which is truly individual; in the extreme of universality it has passed out of externality into itself.—In the first syllogism, the objective significance of the Syllogism is present only in a superficial manner, for here the determinations are not yet posited as the unity which constitutes the essence of the Syllogism. The latter is still subjective in so far as the abstract meaning which its terms have is not in and for itself, but is thus isolated only in subjective consciousness.—For the rest, the relation between individuality, particularity, and universality is the necessary and essential form-relation (as was seen) of the determinations of the Syllogism; the fault does not consist in this determinateness of the form, but in the fact that under this form each individual determination is not also richer.—Aristotle clung rather to the bare relation of inherence when he described the nature of the Syllogism as follows:—‘“If three determinations are so related that one extreme is in the whole of the middle determination, and this middle determination is in the whole of the other extreme, then these two extremes are necessarily bound together.” What is here expressed is rather the repetition of the same relation of inherence (a) between one extreme and the middle and (b) between the middle and the other extreme, than the determinateness of the three terms to one another.—Now the Syllogism rests upon this their determinateness against one another, so that it is immediately plain that other relations of the terms which result from the other Figures can have validity as rational syllogisms only in so far as they can be reduced to this original relation. There are not various kinds of Figures standing by the side of the First Figure; but, first, in so far as they are supposed to be correct syllogisms, they rest only upon the essential form of the Syllogism in general, which is the First Figure; and next, in so far as they diverge from it, they are modifications into which this first abstract form necessarily passes over, whereby it determines itself further, and towards totality. The nature of this process will soon be seen.

The general formula of the Syllogism in its determinateness is, then, I—P—U. The individual is subsumed under the particular, and the particular under the universal; consequently the individual is also subsumed under the universal. Or, the particular inheres in the individual, and the universal in the particular; consequently the universal inheres also in the individual. In one direction (namely, as against the universal) the particular is subject; it is predicate as against the individual; or again it is individual as against the former and universal as against the latter. The two determinatenesses are united in it, and therefore the extremes are bound together through this their unity. The “consequently” appears as the conclusion which has taken place in the subject, and is supposed to be derived from subjective insight into the relation between the two immediate premisses. Subjective reflection asserts that the two relations of middle to extremes are particular and indeed immediate judgments or propositions; and thus the conclusion, as mediated relation, must be allowed to be a particular proposition; the “consequently” or “accordingly” expresses that it is the mediated proposition. But this “consequently” must not be considered as a determination external to this proposition, having its ground and seat only in subjective reflection: it is grounded in the very nature of the extremes, whose relation is again asserted to be mere judgment or proposition only as a makeshift by abstracting reflection, while their true relation is posited as the middle term.—Accordingly it is a merely subjective circumstance that “/ is U” is a judgment; the Syllogism is the very fact that this is not merely a judgment, that is, not a relation effected through the bare copula or the empty “is,” but through the determinate middle which is full of content.

If then the Syllogism is merely regarded as consisting of three judgments, this is a formal view which takes no account of the relation of determinations, which alone are important in the Syllogism. And altogether it is a merely subjective reflection which separates the relation of the terms into detached premisses and a conclusion distinct from them:—

All men are mortal,

Gaius is a man, therefore he is mortal. Boredom immediately descends when such a syllogism is heard approaching;—this is due to the otiose form, which gives an appearance of variety through the detached propositions that, in fact, is immediately dissolved. It is this subjective formation that chiefly causes syllogizing to appear as a subjective makeshift to which reason or understanding has recourse when it cannot cognize immediately.—The nature of things—the reasonable—does not indeed proceed by first setting up a major premiss (the relation of a particularity to a persisting universal), and next discovering a detached relation of an individuality to the particularity, whence at length and thirdly a new proposition comes to light.—This process of syllogizing which proceeds by detached propositions is just a subjective form: the nature of the situation is, that the distinct Notion-determinations of the thing are united in the essential unity. This reasonableness is not a makeshift; rather, in opposition to the immediacy of relation which still is found in the Judgment, it is the objective, while the immediacy of cognition is the merely subjective; the Syllogism, again, is the truth of the Judgment.—All things are a Syllogism, a universal which is bound together with individuality through particularity; but of course they are not wholes consisting of three propositions.

2. In the immediate Syllogism of understanding the terms have the form of immediate determinations; it must now be considered from this side, according to which its terms are content. So far it may be regarded as the Qualitative Syllogism; and the Judgment of Inherence has this same side of qualitative determination. Hence the terms of this Syllogism, like the terms of that Judgment, are individual determinatenesses; for, through its self-relation, the determinateness is posited as indifferent to form,—that is, as content. The individual is any immediate concrete object; particularity is one of its determinatenesses, properties, or relations; and universality is a still more abstract and more individual determinateness in the particular.—The subject is immediately determinate and therefore is not yet posited in its Notion; hence its concretion is not reduced to the essential Notion-determinations; consequently its self-relating determinateness is indeterminate and infinite manifoldness. In this immediacy the individual has an infinity of determinatenesses which belong to its particularity; consequently each of these can constitute a middle term for it in a syllogism. But through every other middle term it binds itself to another universal; through each of its properties it has a different contact and connexion with Existence.—Further, in comparison with the universal, the middle term is a concrete; it itself contains more than one predicate, and through the same middle term the individual may again be bound to more than one universal. Which of the many properties of a thing is taken up, so that it may serve to connect it with a predicate, is, therefore, a matter of pure contingency and caprice; other middle terms serve as links with other predicates, and even one and the same middle term may be the transition to various predicates; for, being particular as against the universal, it contains several determinations.

But it is not only true that for any one subject an indefinite number of syllogisms are equally possible, and any individual syllogism is in its content contingent: these syllogisms, which relate to the same subject, must further pass over into contradiction. For difference in general, which at first is indifferent variety, is equally essentially opposition. The concrete is no longer something which merely appears, but is concrete through the unity of opposites (which have determined themselves to be Notion-moments) in the Notion. Now, according to the qualitative nature of the terms in the formal syllogism, the concrete is taken up according to some particular one of the determinations, which is proper to it, and the syllogism allots to it the predicate which corresponds to this middle term. But, from some other side, a syllogism reaches the opposite determinateness, and thus the former conclusion shows itself to be false, although in themselves its premisses and also its consequence are quite correct.—If, from the middle term that a canvas has been painted blue, the conclusion is drawn that therefore it is blue, then this conclusion has been drawn correctly; but in spite of this conclusion the canvas may be green if it has also been covered with yellow colour (from which latter circumstance by itself it would follow that it was yellow).—If, from the middle term of sensuousness, it is concluded that man is neither good nor evil, because neither the one nor the other can be predicated of the sensuous, the syllogism is correct but the conclusion is false; for the middle term of spirituality is equally valid of man as the concrete.—From the middle term of the gravity of planets, satellites, and comets as against the sun, it follows correctly that these bodies are falling into the sun; but they do not do so, for they are each equally for itself a private centre of gravity, or, as the expression runs, they are driven by centrifugal force.—And similarly the community of goods among the citizens may be reached from the middle term of sociality, while the dissolution of the state follows from the middle term of individuality, if it is followed with equal abstractness; as has happened for example in the Holy Roman Empire, since men clung to the latter middle term.—Justly nothing is held to be more inadequate than such a formal syllogism, since it rests upon contingency or caprice which middle term is used. However prettily such a deduction has run through its syllogisms, and however completely its correctness may be admitted, it still leads nowhere, for it is always possible to find other middle terms from which the precise opposite can equally correctly be deduced.—Kant’s Antinomies of Reason are just this, that first one determination of a Notion is made the foundation of the Notion, and next, and with equal necessity, the other.—But this inadequacy and contingency of a syllogism must not be put to the account merely of the content, as though they were independent of the form, and the latter alone concerned logic. Rather it is implied in the form of the formal Syllogism that the content is such a one-sided quality; this one-sidedness is determined in it through the abstract form. For the content is one quality of the many qualities or determinations of a concrete object or Notion, since formally it is supposed to be nothing more than such an immediate and individual determinateness. The extreme of individuality, as abstract individuality, is the immediate Concrete, and consequently the infinitely or indeterminably Manifold; the middle is equally abstract particularity, and consequently is one individual quality among these manifold qualities; and, equally, the other extreme is the abstract universal. The formal Syllogism therefore is essentially something wholly contingent in its content because of its form; this is not because it is the case that it is contingent for the Syllogism whether this or some other object is submitted to it; logic abstracts from this content; but, in so far as a subject is the foundation, it is contingent what content-determinations the Syllogism infers from it.

3. The determinations of the Syllogism are content-determinations in so far as they are immediate, abstract, and intro-reflected determinations. But their essential element is that they are not such intro-reflected and mutually indifferent determinations, and that they are form-determinations: in so far they are essentially relations. These relations are, firstly, those of the extremes to the middle,—relations which are immediate (the premisses), partly of particular to universal [major premiss) and partly of individual to particular [minor premiss). Secondly, there is the relation between extreme and extreme: this is mediated [the conclusion). These immediate relations, the premisses, are propositions or judgments in general, and conflict with the nature of the Syllogism, according to which the distinct Notion-determinations are not immediately related: their unity too is supposed to be posited: the truth of the Judgment is the Syllogism. The premisses can remain immediate relations all the less, because their content consists of immediately distinct determinations, so that they are not immediately identical in and for themselves; unless they are pure identical propositions, that is, empty tautologies which lead to nothing.

It is therefore generally demanded of the premisses that they shall be proved, that is, that they too are to be represented as conclusions. Thus the two premisses provide two further syllogisms. But these two new syllogisms in turn provide altogether four premisses, which require four new syllogisms; these have eight premisses, whose eight syllogisms in turn for their sixteen premisses provide sixteen syllogisms, and so to infinity in geometrical progression.

Here again that progress to infinity re-emerges which before occurred in the lower sphere of Being but was no longer to be expected in the field of the Notion, of the absolute intro-Reflection out of the finite, and the region of free infinity and truth. It was shown in the sphere of Being that where bad infinity, whose manifestation the progress is, emerges, a contradiction is present between a qualitative Being and an impotent Ought which passes beyond it; the progress itself is the repetition of the demand for unity which has arisen as against the Qualitative, and the continued relapse into the barrier which is inadequate to this demand. Now in the formal Syllogism the immediate relation or the qualitative Judgment is the foundation, while the mediation of the Syllogism is that which is posited against it as the higher truth. The infinite process of demonstration of the premisses does not solve this contradiction, but only perpetually renews it: it is the repetition of one and the same original defect.—The truth of the infinite progress is rather that both it and the form which by it is determined as defective are to be transcended.—This form is the form of mediation as I—P—U. The two relations I—P and P—U are supposed to be mediated; if this is done in the same manner, the defective form I—P—U is doubled, and so to infinity. P also has to I the form-determination of a universal, and to U the form-determination of an individual, since it is the case that these relations are Judgments. They therefore require mediation; but when they have this form, that relation only arises again which is supposed to be transcended.

The mediation must therefore be made in some other manner. For the mediation of P—U, I is given; consequently the mediation must take the form P—I—U. To mediate I—P, U is given; consequently this mediation becomes the syllogism I-U-P.

If this transition is considered more closely, according to its Notion, then, first, the mediation of the formal Syllogism according to its content is contingent, as was shown above. In its determinatenesses the immediate individual has an indeterminable number of middle terms, and these in turn have altogether a similar number of determinatenesses; so that it lies with an external caprice, or, generally, in some external circumstance or contingent determination, which is the universal with which the subject of the Syllogism is to be bound together. According to its content therefore the mediation is nothing either necessary or universal; it is not grounded in the Notion of the thing: the ground of the Syllogism rather is that which is external in it, that is, the immediate; but, among the Notion-determinations, the immediate is the individual.

With respect to form similarly mediation has for presupposition the immediacy of relation; the former therefore is itself mediated—through the immediate, that is, the individual.—More precisely, through the conclusion of the first Syllogism the individual has become the mediator. The conclusion is I—U; it thus posits the individual as universal. In one of the premisses (the minor premiss, I—P) it already exists as particular, that is, as that in which these two determinations are united.—In other words, the conclusion in and for itself expresses the individual as universal; not in an immediate manner but through mediation, that is, as a necessary relation. Simple particularity was middle term; in the conclusion this particularity is developed and posited as the relation of the individual and of universality. But as yet the universal is a qualitative determinateness, a predicate of the individual; the individual, being determined as universal, is posited as the universality of the extremes, or as middle; for itself it is extreme of individuality, but it is now determined as universal, and therefore at the same time it is the unity of the two extremes.

1. The truth of the first qualitative Syllogism is that something is not bound together in and for itself with a qualitative determinateness as a universal determinateness, but is bound contingently or in an individuality. In such a quality the subject of the Syllogism has not returned into its Notion; a Notion is formed about it only in its externality. Immediacy constitutes the ground of the relation, and therefore the mediation: in so far the individual is in truth the middle.

But further the syllogism-relation is the transcendence of immediacy: the conclusion is not an immediate relation, but the relation is mediated by a third term; consequently the mediation is now determined to contain a negative moment.

In this second Syllogism the premisses are P—I and I—U; only the first of these premisses remains immediate; the second, I—U, already is mediated (by the first Syllogism): thus the second Syllogism presupposes the first, while conversely the first presupposes the second.—Here the two extremes are determined against each other as particular and universal; in so far the latter still has its place, it is predicate. The particular however has exchanged its place; it is subject, or is posited under the determination of extreme of individuality, while the individual is posited with the determination of middle or of particularity. Accordingly neither is now the abstract immediacy which it was in the first Syllogism. They are nevertheless not yet posited as concrete: because each stands in the place of the other, it is posited in its own determination and also (though only externally) in the other determination.

The determinate and objective meaning of this Syllogism is, that the universal is a definite particular not in and for itself (for in fact it is the totality of its particulars), but that it is thus one of its species through individuality; its other species are excluded from it through immediate externality. On the other hand the particular, in the same manner, is not immediately and in and for itself the universal, but negative unity strips it of determinateness and thus raises it into universality.—Individuality is negatively related to the particular in so far as it is supposed to be its predicate; it is not predicate of the particular.

2. As yet however the terms are each an immediate determinateness; through themselves they have not developed to any objective significance. The changed position which is given to two of them is formal, and at first it is external to them; therefore, as in the first Syllogism, each is a content indifferent to the other—two qualities which are connected by a contingent individuality and not in and for themselves.

The Syllogism of the First Figure was the immediate Syllogism, or, equally, it was Syllogism in so far as it is in its Notion, as abstract form which has not yet realized itself in its determinations. Now this pure form has passed over into another Figure; hence (1) this is the beginning of the realization of the Notion, the negative moment of mediation—and hence a further form-determinateness—being posited in the determinateness of the terms which so far is immediate and qualitative.—(2) At the same time the pure form of the Syllogism now becomes other; the Syllogism no longer completely corresponds to it, and the determinateness which is posited in its terms is different from the original form-determination.—In so far as it is considered only as a subjective Syllogism which takes place in an external reflection, it is reckoned as a species of Syllogism which should correspond to the genus, namely the general scheme of I—P—U. But at first it does not correspond to this; its two premisses are P—I (or I—P), and I—U; consequently the middle term is subsumed, or is subject, on each of the two occasions, so that the other two terms inhere in it; and it is therefore not a middle which is supposed first to subsume (or to be predicate) and next to be subsumed (or to be subject), or to inhere in the one term, while the other inheres in it.—This Syllogism does not correspond to the general form of the Syllogism; and the true meaning of this fact is, that the form has passed over into it, since its truth consists in being a subjective and contingent binding together. If the conclusion in the Second Figure (without recourse being had to the limitation which is about to be mentioned and which makes it to be something indeterminate) is correct, then it is correct because it is so for itself, and not because it is the conclusion of this Syllogism. But this is also the case with the conclusion of the First Figure; and it is this its truth which is posited by the Second Figure.—The opinion which holds that the Second Figure is only one species overlooks the necessary transition from the first into this second form, and a halt is made at the first as being the true form. Consequently, in so far as a correct syllogism, in this subjective sense, can be constructed in the Second Figure (which, from old habit, is, without reason given, quoted as the third), such a Syllogism ought to be conformable to the first; and, since the one premiss I—U has the relation of subsumption of the middle term under one extreme, the other premiss P—I must be given the relation opposite to that which it has; and it ought to be possible to subsume P under I. But such a relation would be the transcendence of the determinate judgment J is P, and could only take place in an indeterminate, or a particular, judgment; whence the conclusion in this figure can only be particular. But, as was observed above, the Particular Judgment is as well positive as negative—a conclusion to which for this reason no great value can be attached.—And in so far as particular and universal are extremes, and immediate and indifferent determinatenesses as against each other, their relation itself is indifferent; either one may arbitrarily be taken as major or as minor term, and consequently either premiss may be taken indifferently as major or minor.

3. The conclusion, being positive as well as negative, is a relation indifferent to these determinatenesses and therefore universal. More closely considered, the mediation of the first Syllogism was in itself contingent: in the second Syllogism this contingency is posited. It is thus a self-transcending mediation; the mediation has the determination of individuality and immediacy. What is bound together by this Syllogism must rather be identical in itself and immediately; for that middle (the immediate individuality) is infinitely manifold and external determinateness. Thus rather self-external mediation is posited in this mediation. But the externality of individuality is universality; and this mediation through the immediate individual points beyond itself to that which is other to it and which thus takes place through the universal.—Or what is to be united by the second Syllogism must be bound together immediately; the immediacy which is its foundation does not serve to effect a definite binding. The immediacy to which it points forward is other to its own immediacy (which is the transcended first immediacy of Being); it is therefore intro-reflected or self-existent immediacy, and abstract universal.

According to the side which has been considered, the transition of this Syllogism was a becoming other, like the transition of Being, because its foundation is the qualitative—immediate individuality. But according to the Notion, individuality binds together particular and universal in so far as it transcends the determinateness of the particular, which process manifests itself as the contingency of this Syllogism. The extremes are not bound together by their determinate relation, which is their middle term; consequently it is not their determinate unity, and that positive unity which does belong to it is only abstract universality. But the middle term being posited in this determination (which is its truth), a different form of the Syllogism has arisen.

1. This third Syllogism has no longer any immediate premiss; the relation I—U has been mediated by the first Syllogism, and the relation P—U by the second. Hence it pre-supposes the two first Syllogisms; but, conversely, these two presuppose it, and indeed each one presupposes the two others. Thus the determination in general of the Syllogism is completed in it.—What this reciprocal mediation contains is this, that each Syllogism is mediation for itself but is not in itself the totality thereof; it has in it an immediacy whose mediation lies outside it.

If the Syllogism I—U—P is considered in itself, it is the truth of the formal Syllogism. It expresses this, that the mediation of the latter is the abstractly universal, and that the extremes according to their essential determinateness are contained not in the middle but only according to their universality; so that precisely that which here is supposed to be mediated is not bound together in it. Thus that in which the formalism of the Syllogism consists is here posited; the terms of this Syllogism have a content immediate and indifferent to form, or (which is the same thing) they are form-determinations which have not yet reflected themselves so as to become content-determinations.

2. The middle of this Syllogism is the unity of the extremes; but in this unity abstraction is made from their determinateness: it is the indeterminate universal. This universal, however, at the same time is distinct (as abstract) from the extremes (as determinate); in so far, however, it is itself also determinate as against these, and the whole is a Syllogism, whose relation to its Notion must be considered. The middle as the universal is related as subsuming, or as predicate, to its two extremes: it is not also subsumed, nor is it subject. Consequently, in so far as this Figure is supposed to correspond to the Syllogism as being one species of Syllogism, this can happen only if the one relation I—U already has the due relationship while at the same time the other, U—P, also acquires the same relationship. This happens in a judgment where the relation of subject and predicate is indifferent, that is, in a negative judgment. Thus the Syllogism becomes legitimate, but the conclusion, necessarily, negative.

Thus also it has now become indifferent which of the two determinations of this proposition is taken as predicate and which as subject; and, in the conclusion, whether it is taken as extreme of individuality or of particularity—that is, whether it is taken as minor or as major term. According to the common assumption it depends upon this which of the two premisses is to be major and which minor; thus this has here become indifferent.—This is the ground of the ordinary Fourth Figure of the Syllogism; Aristotle was not acquainted with it, and indeed it deals with a wholly uninteresting and empty distinction. Here the immediate position of the terms is the reverse of their position in the First Figure; in the negative conclusion subject and predicate, according to the formal consideration of the Judgment, have not the determinate relation of subject and predicate, and one can take the place of the other; and therefore it is indifferent which term is taken as subject and which as predicate; and consequently it is equally indifferent which premiss is taken as major and which as minor.—This indifference, which is aided by the determination of particularity (especially in so far as it is remarked that it may be taken in the comprehensive sense), renders this Fourth Figure quite nugatory.

3. The objective meaning of the Syllogism where the universal is the middle is that the mediating term as unity of the extremes is essentially universal. But here this universality is only qualitative or abstract, and therefore does not contain the determinateness of the extremes. If it is to be brought about that they are bound together, this must have its ground in a mediation which lies outside this Syllogism; and, with respect to this ground, it is quite as contingent as in the previous forms of Syllogisms. But, since the universal is determined as the middle and does not contain the determinateness of the extremes, this determinateness is posited as completely indifferent and external.—From this bare abstraction a Fourth Figure of the Syllogism has, indeed, arisen—that of the relationless Syllogism, or U—U—U, which abstracts from the qualitative distinction of the terms, and thus has their merely external unity, namely their equality, for determination.

1. The Mathematical Syllogism runs: If two things or determinations are equal to a third, they are equal to each other,—Here the relation of inherence or subsumption of terms is extinct.

The mediating term here is a third term in general; but it has no determination whatever as against its extremes. Consequently each one of the three terms may equally well be the third term which mediates. Which shall be used to that end, and hence which of the three relations are to be taken as the immediate and which as the mediated, depends upon external circumstances and other conditions—namely, upon the question which two of them are the immediately given terms. But this determination does not concern the Syllogism itself and is entirely external.

2. In mathematics the Mathematical Syllogism counts as an axiom,—as an elementary and self-evident proposition which neither admits nor requires proof (that is, mediation), pre-supposes nothing beyond itself, and cannot be derived from anything.—When this its advantage of immediate self-evidence is more closely considered, it appears that it is implied in the formalism of this Syllogism, which abstracts from every qualitative variety of its determinations and accepts only their quantitative equality or inequality. But for this very reason it is not without presupposition and not unmediated; that quantitative determination which is alone regarded in it exists only by virtue of abstraction from qualitative distinction and Notion-determinations.—Lines or figures which are posited as equal to each other are understood only according to their magnitude: a triangle is said to be equal to a quadrilateral, but only in area and not because a triangle is a quadrilateral; and so on. And similarly the Notion and its determinations have no place in this syllogizing; it thus is in no way a notional process; understanding even has not so much as the formal and abstract Notion-determinations before itself; and the self-evident element of this Syllogism rests only upon the fact that it is so abstract and poor in thought-determination.

3. But the result of the Qualitative Syllogism is not merely this abstraction from every Notion-determinateness; the negativity of the immediate and abstract determinations, which emerged from it, has another and positive side, namely that where its other is posited into abstract determinateness, and it thereby has become concrete.

First, all Qualitative Syllogisms presuppose one another, and the extremes which are bound together in the conclusions are true and bound together in and for themselves only in so far as they are otherwise united by an identity which is grounded elsewhere; the middle term, having the nature which it has in these Syllogisms which have been considered, is supposed to be their Notion-unity, but in fact is only a formal determinateness which is not posited as their concrete unity. But this presupposed element in each of these mediations is not merely a given immediacy in general (as in the Mathematical Syllogism), but is itself a mediation—namely, for each of the other two Syllogisms. There is before us here, therefore, in fact a mediation founded, not upon a given immediacy, but upon mediation. Consequently this is the mediation of Reflection; not quantitative or abstracting from the form of mediation, but rather mediation relating itself to mediation. The circle of reciprocal presupposing which these Syllogisms form one with another is the self-return of this presupposing, which here forms a totality, having that Other, towards which each individual Syllogism points, not outside (which would be the work of abstraction), but included within the circle.

It has further appeared, from the side of the individual form-determinations, that in this Whole of the formal Syllogisms each individual determination has in turn had the place of middle. Immediately it was determined as particularity; it then determined itself by dialectic movement as individuality and universality. Similarly each of these determinations passed through the places of the two extremes. The merely negative result is the extinction of the qualitative form-determinations in the merely quantitative Mathematical Syllogism. What however is in truth given here is this positive result, that mediation does not take place through an individual qualitative form-determinateness, but through the concrete identity of the form-determinations. The deficiency and formalism of the three Syllogistic Figures which have been considered consists precisely in this, that such an individual determinateness was supposed to constitute their middle.—The mediation has thus determined itself as the indifference of the immediate or abstract form-determinations and as positive Reflection of one into the other. And now the immediate Qualitative Syllogism has passed over into the Syllogism of Reflection.

In the exposition of the nature of the Syllogism and its various forms, which has here been given, that element too was cursorily regarded which is of main interest in the ordinary consideration and treatment of Syllogisms, namely, the question how in each figure a correct syllogism may be made. However, only the chief moment was indicated, and those instances and complications were omitted which arise when the distinction between positive and negative judgments, together with quantitative determination (especially particularity), is also taken into consideration.—Some observations about the common view and treatment of the Syllogism in logic will not be out of place here.—It is well known that this system was developed to such a degree of exactitude that its so-called subtleties became universally tedious and disgusting. Natural understanding asserted itself against the unsubstantial forms of reflection in every field of intellectual development; and thus it came to revolt against this artificial cognition of the forms of reason, and thought that it might dispense with this science because it effected the individual operations of thought specified therein naturally by itself and without having to learn them for the purpose. Indeed, with regard to reasonable thought, if it depended upon the laborious study of syllogistic formulae, man would be in as sorry a case as he would be (as was observed in the Preface) if he could not walk or digest without a previous study of anatomy and physiology. The study of these sciences may not be without value in dietetics; and similarly the study of the forms of reason may doubtless be allowed to have an influence of even greater importance upon the correctness of thought. But even if this side (which concerns the formation of subjective thought and is therefore really an educational subject) is here neglected, it will have to be admitted that the study which concerns itself with the manners and laws by which reason operates must be of the greatest interest for itself,—at any rate not less than a knowledge of the laws of nature and their particular formations. It is esteemed no mean thing to have discovered some sixty species of parrots, one hundred and thirty-seven species of veronica, and so forth; but it must be considered much less a negligible matter to discover the forms of reason; for is not a syllogistic figure an infinitely higher matter than a species of parrot or of veronica?

If, therefore, it is to be regarded as just barbaric to despise all knowledge of the forms of Reason, still it must equally be admitted that the ordinary presentation of the Syllogism and of its particular formations is not a reasonable cognition; it does not present them as forms of reason, and the contempt which syllogistic lore suffered was due to its uselessness. Its flaw is this, that it just stops short at that syllogistic form of understanding according to which the Notion-determinations are taken as abstract formal determinations. It is all the more inconsistent to retain them as abstract qualities because in the Syllogism their relations constitute the essential part; it is already implicit in inherence and subsumption that the individual is itself universal because the universal inheres in it, and that the universal is itself individual because it subsumes the individual, while, more precisely, the Syllogism expressly posits this unity as middle, its determination being just mediation, which means that now the Notion-determinations are no longer external to each other (as in the Judgment) but rather have for foundation their unity.—The Notion of the Syllogism thus declares the imperfection of the formal Syllogism, in which the middle is to be held fast, not as unity of the extremes, but as a formal determination, abstract and qualitatively distinct from them.—And this consideration becomes further exhausted of content because such relations and judgments are still assumed to be complete relations, even though their formal determinations become indifferent (as in the Negative and the Particular Judgment) so that they approximate to propositions.—The qualitative form I—P—U is counted as the ultimate and absolute, so that the dialectic view of the Syllogism is altogether lost; the remaining Syllogisms accordingly are not considered as necessary mutations of this form, but as species.—It is here indifferent whether the first formal Syllogism is considered only as one species alongside the others, or as genus and species simultaneously; the latter happens when the other Syllogisms are reduced to the first. If this reduction is not performed expressly, the same formal relation of external subsumption which is expressed by the First Figure always lies at the bottom.

This formal Syllogism is a contradiction in this way, that the middle is supposed to be the determinate unity of the extremes, but exists not as this unity, but as a determination which is qualitatively distinct from those terms of which it is supposed to be the unity. The Syllogism is this contradiction, and therefore is dialectical in itself. Its dialectic movement presents it in the complete Notion-moments, and shows that not only this relation of subsumption (or particularity) but, equally essentially, negative unity and universality are moments of the process of binding together. Each of these, in so far as for itself it is only a one-sided moment of particularity, is likewise an incomplete middle; but, simultaneously, they constitute together the developed determinations of these. The entire course taken through the three Figures shows the middle in each of these determinations one after the other; and the true result which emerges is that the middle is not one from among them, but their totality.

The flaw of the formal Syllogism therefore is not in its form—which indeed is the form of reasonableness—but in the fact that it is only abstract, that is, notionless, form. It has been shown that abstract determination, because of its abstract self-relation, can equally be considered as content; in this regard the formal Syllogism only effects this, that the relation of a subject to a predicate follows or does not follow from a given middle term. To prove a proposition by such a Syllogism is useless; the middle term is abstractly determinate and is a notionless quality, and therefore there may equally be other middle terms from which the opposite follows, and it is even possible to derive opposite predicates, through further Syllogisms, from the same middle term.—The formal Syllogism not only effects very little, but also is extremely simple; the many rules which have been invented are tiresome both because they contrast so harshly with the simple nature of the thing in hand, and also because they refer to those cases where the formal content of the Syllogism is finally reduced through external form-determination,—chiefly that of particularity, especially since to this end it must be taken in the comprehensive sense; formally too only quite empty results are here produced.—But the justest and most important aspect of the disfavour into which Syllogistics have fallen is this, that they constitute a cumbrous and notionless occupation with an object whose only content is the Notion itself.—The multitude of syllogistic rules recalls the procedure of arithmeticians, who also give a multitude of rules about arithmetical operations, all of which presuppose that the Notion of the operations is not in the mind.—But numbers are a notionless material, and the operations of arithmetic are external processes of connexion or separation—a mechanical procedure: indeed, machines have been invented which effect these operations. It is the severest and most violent contradiction if the form-determinations of the Syllogism, which are Notions, are treated as a notionless material.

The extreme example of this notionless treatment of the Notion-determinations of the Syllogism is probably Leibniz’s subjection of the Syllogism (Opp. Tom. II. P. I) to the calculus of combinations, by which he calculated how many formations of the Syllogism are possible—regard being had to the distinctions between positive and negative, and between universal, particular, indeterminate, and singular Judgments: 2,048 such combinations are found to be possible, of which, after exclusion of the useless figures, 24 useful figures remain.—Leibniz makes much of the utility of combinatory analysis in helping to find not only the forms of the Syllogism, but also combinations of other Notions. The operation by means of which this is discovered is the same as that by which it is calculated how many combinations of letters are possible in an alphabet, how many casts in a game of dice, how many games in a hand of ombre, and so forth. Thus here the determinations of the Syllogism are placed in one class with the points of dice and of a card of ombre; what is reasonable is taken as dead and notionless, and the peculiarity of the Notion and its determinations (namely that, as spiritual essences, they relate themselves and through this relating transcend their immediate determination) are left on one side.—Leibniz’s application of the calculus of combinations to the Syllogism and to the connexion of other Notions differed in nothing from the notorious art of Lullus except that it was more methodical in regard to amount; in senselessness they were equal.—This procedure is associated with a favourite idea of Leibniz, conceived in his youth and never surrendered in spite of its immaturity and shallowness, the idea of a general characteristic of Notions,—a set of symbols in which each Notion is represented as a relation derived from others or as related to others;—as though in that reasonable connexion which is essentially dialectic a content retained those determinations which it had while it was fixed by itself.

Undoubtedly Ploucquet’s calculus adopted the most consistent method by which the relation of the Syllogism admits of being subjected to a calculus. Its basis is this, that abstraction is made from the relation-distinction (the distinction of individuality, particularity, and universality) in the Judgment, and the abstract identity of subject and predicate is retained; they are thus mathematically equal,—which relation makes the process of syllogizing a wholly empty and tautological casting of propositions.—In the proposition “the rose is red,” the predicate is not to denote red in general, but only the particular red of the rose; in the proposition “all Christians are men,” the predicate is to denote those men only who are Christians. From this proposition and the proposition “the Jews are not Christians” follows the conclusion (which Mendelssohn found so poor a recommendation of this syllogistic calculus) “therefore the Jews are not men” (namely not those men that the Christians are).—Ploucquet states that it follows from his discovery posse etiam rudes mechanice totam logicam doceri, uti pueri arithmeticam docentur, ita quidem, ut nulla formidine in ratiociniis suis errandi torqueri, vel fallaciis circumveniri possint, si in calculo non errant,—This recommendation—that by means of the calculus the whole of logic can mechanically be inculcated into the ignorant—is perhaps the worst thing that could be said about an invention touching the presentation of the science of logic.

In the course of the Qualitative Syllogism the abstract element of its determinations was transcended; thus each term has posited itself as such a determinateness as has the other determinateness showing within it. Apart from the abstract terms the Syllogism also contains their relation, which, in the conclusion, is posited as mediated and necessary; thus every determinateness in truth is posited not as individual for itself, but as relation of the others, or as concrete determinateness.

The middle was abstract particularity: it was for itself a simple determinateness, and was middle only externally and relatively to the independent extremes. It is now posited as the totality of the determinations: it is thus the posited unity of the extremes; but so far it is the unity of Reflection, which it includes within itself—an inclusion which, as first transcendence of immediacy and first relating of the determinations, is not yet the absolute identity of the Notion.

The extremes are the determinations of the Judgment of Reflection—individuality and universality, properly so called, as determination of relation, or a Reflection comprehending a manifold within itself. But also—as was shown in the Judgment of Reflection—the individual subject contains determinateness as utterly intro-reflected universality and apart from mere individuality (which belongs to form),—determinateness which is genus presupposed or here still taken as immediate.

From this determinateness of the extremes, which belongs to the course of the determination of the Judgment, the further content of the middle term results: the middle distinguishes the Syllogism from the Judgment, and is therefore of capital importance in the Syllogism. The middle contains (1) individuality, (2) the same, but extended into universality as All, (3) the fundamental universality which unites utterly within itself individuality and abstract universality, that is, the genus.—It is now only in this manner that the Syllogism of Reflection has the proper determinateness of form, the middle being posited as totality of the determinations; the immediate Syllogism is, as against it, the indeterminate Syllogism, since the middle still is abstract particularity in which the moments of its Notion are not yet posited.—This first Syllogism of Reflection may be called the Syllogism of Allness.

1. The Syllogism of Allness is the syllogism of understanding in its completeness, but as yet no more. It is indeed an essential requirement for the Notion that the middle is not abstract particularity in it, but is developed into its moments and is therefore concrete; but, at first at least, the form of Allness comprehends the individual into universality only externally, and, conversely, it still preserves the individual as something which persists immediately for itself, in universality. The negation of the immediacy of the determinations which was the result of the Qualitative Syllogism is only first negation, and not yet the negation of negation or absolute intro-Reflection. They are still therefore the foundation of that universality of Reflection which comprehends the individual determinations within itself,—in other words, Allness is not yet the universality of the Notion, but the external universality of Reflection.

The Qualitative Syllogism was contingent because its middle term is a single determinateness of the concrete subject, and as such admits an indeterminable number of other such middle terms, so that it was possible for the subject to be bound together with predicates indeterminably other, or opposite. But now the middle contains individuality and thereby is concrete itself, so that it can serve to connect only one predicate with the subject, which belongs to the latter as concrete.—For example, from the middle term “green” it might be concluded that a picture is pleasant because green is pleasant to the eye, or it might be inferred that a poem or a building, and so forth, is beautiful because it possesses regularity; but nevertheless the picture (and the other things) might be ugly, because of other determinations from which one might conclude to this latter predicate. But now the middle term has the determination of Allness, and therefore contains green or regularity as concrete, which for this very reason is not the abstraction of something merely green or regular and so forth; and with this concrete term only such predicates can be connected as are adequate to the totality of the concrete.—In the judgment “the green (or regular) is pleasant,” the subject is only the abstraction of green, or regularity; but in the proposition “whatever is green (or regular) is pleasant,” the subject is all actual, concrete objects which are green or regular,—which consequently are taken as concrete with all their properties which they have besides greenness or regularity.

2. But the very perfection of Reflection in this Syllogism now makes it a mere delusion. The middle term has the determinateness of “all”; to these latter the predicate which is bound together with the subject belongs immediately in the major premiss. But all are all individuals; and thus each individual subject already contains the predicate immediately, and does not wait to receive it through the Syllogism.—Or again the subject obtains a predicate as a consequence in the conclusion; but the major premiss already contains this conclusion; thus the major premiss is not valid for itself; it is not an immediate, presupposed judgment, but already presupposes the conclusion of which it was supposed to be the ground.—In the favourite complete Syllogism;—

All men are mortal,

Gaius is a man, therefore Gaius is mortal, the major premiss is correct only because and in so far as the conclusion is correct; if Gaius happened not to be mortal, the major premiss would be incorrect. The proposition destined to be conclusion must be correct immediately for itself, because otherwise the major premiss cannot comprehend all the individuals; before the major premiss can be pronounced correct, the question exists whether the conclusion itself may not testify against it.

3. In the Qualitative Syllogism it resulted from the Notion of the Syllogism that the premisses, as immediate, contradicted the conclusion, which is the mediation demanded by the Notion of the Syllogism; so that the first Syllogism presupposed others, and conversely these others presupposed it. And it is posited in the Syllogism of Reflection itself that the major premiss presupposes its conclusion, since the former contains a connexion of the individual with a predicate, which connexion precisely is itself to be the conclusion.

The position which has been reached may then be thus expressed, that the Syllogism of Reflection is no more than an external and empty show of syllogizing, and that consequently the essence of this syllogizing rests upon subjective individuality, which latter therefore constitutes the middle and is to be posited as such,—the individuality which exists as such and has universality only in an external manner.—Or again, it appeared from the content of the Syllogism of Reflection, more precisely examined, that the individual stands in an immediate and not in an inferred relation to its predicate; and that the major premiss (the connexion of a particular with a universal, or, better, of a formally universal term with one which is universal in itself) is mediated by the relation of individuality which exists in the former—individuality as Allness. Now this is the Syllogism of Induction.

1. The Syllogism of Allness stands under the scheme of the first figure I—P—U, the Syllogism of Induction under that of the second—P, since it once more has individuality for middle,—not abstract individuality, but individuality posited as complete, that is, posited with the determination opposite to itself, namely universality.—The one extreme is just any predicate which is common to all these individuals; its relation to these constitutes the immediate premisses, which are such that one of them, in the previous Syllogism, was to be conclusion.—The other extreme can be the immediate genus as it is found in the middle of the previous Syllogism or in the subject of the Universal Judgment, which genus is exhausted in the collected individuals (or species) of the middle. Consequently the Syllogism has this shape:— i i U — — P i i to infinity.

2. The second figure of the formal Syllogism U—I—P did not correspond to the scheme, because in one of the premisses /, which constitutes the middle, did not exist as subsuming, or as predicate. This fault is removed in Induction: here the middle is “all the individuals”; the proposition U—I, which contains the objective universal or the genus as segregated into an extreme, as subject, has a predicate which at least is co-extensive with it, and therefore, for external reflection, identical. Lion, elephant, and so on, constitute the genus of quadruped; the distinction that the same content is first posited in individuality and next in universality is thus a merely indifferent form-determination—an indifference which is the result of the formal Syllogism posited in the Syllogism of Reflection: here it is posited through the equality of extent.

Consequently Induction is not the Syllogism of mere perception or of contingent Existence, like the second figure which corresponds to it, but it is the Syllogism of Experience—of the subjective comprehension of the individual in the genus and the binding together of the genus with a universal determinateness because it is found in all the individuals. This Syllogism has the further objective meaning that the immediate genus determines itself through the totality of individuality into a universal property—that it has its existence in a universal relation or characteristic.—However, the objective meaning of this Syllogism, as of the others, is as yet only their inner Notion, and is not yet here posited.

3. Rather, Induction is still essentially a subjective Syllogism. The middle consists of the individuals in their immediacy; their comprehension into the genus by means of allness is an external reflection. Because of the persistent immediacy of the individuals and the externality which follows thence, universality is no more than completeness, or rather remains a problem to be solved.—Consequently the progress to bad infinity once more emerges in universality: individuality is to be posited as identical with universality; but, the individuals being equally posited as immediate, this unity remains no more than an enduring Ought; it is a unity of equality; the terms which are to be identical at the same time are not to be identical, a, b, c, d, but only to infinity, constitute the genus and give perfected experience. In so far, the conclusion of Induction remains problematical.

But, while it expresses that perception, in order to become experience, ought to be continued into infinity, it presupposes that the genus is bound together in and for itself with its determinateness. Thus really it presupposes its conclusion as immediate, just as the Syllogism of Allness presupposes the conclusion for one of its premisses.—An experience which rests upon induction is taken as valid although admittedly the perception is not completed; but no more can be assumed than that no example can be produced contrary to this experience, in so far as the latter is true in and for itself. Thus the Syllogism through Induction grounds itself upon an immediacy, but not upon that upon which it ought to ground itself, upon the existent immediacy of individuality; it grounds itself upon that only which is in and for itself, or universal immediacy.—The fundamental determination of Induction is that it is a Syllogism; if individuality is taken as the essential determination of the middle, and universality only as its external determination, the middle falls apart into two unconnected parts, and no Syllogism would be there: this externality belongs rather to the extremes. Individuality can be middle only as immediately identical with universality; such universality is really objective—it is the genus.—This may also be considered in the following manner: universality is external, but essential, to the determination of individuality, which is the foundation of the middle of Induction; but such an external entity is equally immediately its opposite, the internal.—The truth of the Syllogism of Induction is therefore such a Syllogism as has an individuality for middle which is universality immediately in itself—the Syllogism of Analogy.

1. This Syllogism has for its abstract scheme the third figure of the immediate Syllogism, I—U—P. But its middle no longer is any individual quality, but a universality which is the intro-Reflection of some concrete entity, and therefore its nature;—and conversely, because it is universality as universality of a concrete, it also is this concrete in itself.—Thus here an individual is the middle, but is so according to its general nature; further some other individual is the extreme, which has the same general nature as the former. For example:—

The earth has inhabitants, the moon is an earth, therefore the moon has inhabitants.

2. The analogy is the more superficial, the more the universal (in which the two individuals are one, and according to which one individual becomes predicate of the other) is a mere quality or (since quality here is taken subjectively) some characteristic or other, when the identity of the two in it is taken as a mere similarity. But there should be no place in logic for such a superficiality as that to which a form of understanding or reason is reduced by being degraded to the sphere of mere sensuous representation.—It is also improper to represent the major premiss of this Syllogism as running thus: “whatever resembles an object in some characteristics also resembles it in others.” In this manner the form of the Syllogism is expressed as a content, and its empirical content (which really deserves that name) is altogether localized in the minor premiss. Thus also the whole form of, for example, the first Syllogism might be expressed as its major premiss:—“if A is subsumed under another term in which a third term inheres, then this third term too inheres in A; now.. and so forth. But its empirical content is irrelevant to the Syllogism itself, and it is as indifferent to make its own form the content of a major premiss as if any other empirical content were taken for it. But, in so far as this content were irrelevant in the Syllogism of Analogy (which content contains nothing but the peculiar form of the Syllogism), so far also it would be irrelevant in the first Syllogism; that is, that is irrelevant which makes the Syllogism a syllogism.—What matters is always the form of the Syllogism, whether it has for empirical content this form itself or something else. Thus the Syllogism of Analogy is a peculiar form, and it is quite invalid to refuse to regard it as such because its form might be made the content or matter of a major premiss and matter does not concern logic.—This idea may be fostered in the Syllogism of Analogy, and possibly in the Syllogism of Induction, by the fact that in these the middle and the extremes are determined further than in the merely formal Syllogism, so that the form-determination, because it is no longer simple and abstract, must also appear as content-determination. But the fact that the form does in this manner determine itself as content is, first, a necessary progress of the formal element, and thus touches essentially the nature of the Syllogism; consequently, secondly, such a content-determination cannot be looked upon in the same light as any other empirical content, nor can abstraction be made from it.

The form of the Syllogism of Analogy may also be considered in that expression of its major premiss which states that if two objects agree in one or more properties, then the one has still a further property which belongs to the other; and if this is done it might seem as though this Syllogism contained four determinations, a quaternio terminorum—which circumstance made it so difficult to reduce Analogy into the form of a formal Syllogism.—There are two individuals, thirdly there is a property which is immediately assumed to be common to them, and fourthly the other property, which the one individual has immediately, while the other obtains it only through the Syllogism.—The reason for this is that in the Syllogism of Analogy (as was seen) the middle is posited as individuality, but also and immediately as the latter’s true universality.—In Induction, apart from the two extremes, the middle is an indeterminable number of individuals; hence in this Syllogism an infinite number of terms ought to be enumerated.—In the Syllogism of Allness, universality is in the middle only as external form-determination of allness, but in the Syllogism of Analogy as essential universality. In the above example the middle term (the earth) is taken as a concrete which in its truth is a universal nature or genus as much as an individual.

From this side the quaternio terminorum does not make Analogy into an imperfect Syllogism. But the Syllogism does suffer this from another side; for although one subject has the same general nature as the other, it is not determined whether the one subject has that determinateness which is also inferred for the other by virtue of its nature or of its particularity; whether, for example, the earth has inhabitants as heavenly body in general or as this heavenly body in particular.—Analogy is still a Syllogism of Reflection in so far as individuality and universality are immediately united in its middle. Because of this immediacy the externality of the unity of Reflection is preserved; the individual is genus only in itself it is not posited in that negativity through which its determinateness would be the peculiar determinateness of the genus. For this reason the predicate which belongs to the individual of the middle is not, for that reason, also predicate of the other individual, although both belong to the same genus.

3. I—P (“the moon has inhabitants”) is the conclusion; but one of the premisses (“the earth has inhabitants”) is likewise I—P; and in so far as I—P is to be a conclusion, this includes the demand that that premiss too shall be one. This Syllogism thus is its own postulation as against the immediacy which it contains: it presupposes its own conclusion. A Qualitative Syllogism has its presupposition in the other Qualitative Syllogisms: in the Syllogisms which have just been considered the presupposition has been planted within them, since they are Syllogisms of Reflection. Accordingly, since the Syllogism of Analogy is the postulation of its mediation as against the immediacy with which its mediation is infected, it is the moment of individuality of which this Syllogism demands that it shall be transcended. Thus the objective universal remains for the middle, purged of immediacy—the genus.—In the Syllogism of Analogy the genus was moment of the middle only as immediate presupposition; since the Syllogism itself demands the transcendence of the presupposed immediacy, the negation of individuality, and hence the universal, is no longer immediate, but posited.—The Syllogism of Reflection contained only the first negation of immediacy: now the second has appeared, and has determined the external universality of Reflection as one which is in and for itself—Considered from the positive side, the conclusion shows itself to be identical with the premiss, and the mediation as having coincided with its presupposition; thus there is an identity of the universality of Reflection by virtue of which it has become a higher universality.

If we contemplate the course of the Syllogisms of Reflection, mediation in general is the posited or concrete unity of the form-determinations of the extremes; Reflection consists of this positing of one determination in the other; Allness is thus the mediating entity. But individuality shows itself as the essential ground, and universality as a merely external determination in it—as completeness. But universality is essential to the individual: the individual must be middle, and must bind together; consequently it must be taken as universal which is in itself. But it is not united with universality in this merely positive manner: it is transcended in it, and is negative moment; and thus the universal (that which is in and for itself) is posited genus, and the individual as immediate is rather its externality, or is extreme.—Taken generally, the Syllogism of Reflection falls under the scheme P—I—U the individual is still here, as such, essential determination of the middle. But its immediacy has transcended itself, and the middle has determined itself as universality which is in and for itself: the Syllogism then has entered into the formal scheme I—U—P, and the Syllogism of Reflection has passed over into the Syllogism of Necessity.

The mediating element has now determined itself (1) as simple determinate universality, like particularity in the Qualitative Syllogism; but (2) as objective universality, which contains (that is) the whole determinateness of the extremes in their distinctness, like the allness of the Syllogism of Reflection, a completed but simple universality,—the general nature of the Thing, the genus.

This Syllogism is full of content because the abstract middle of the Qualitative Syllogism has posited itself as determinate distinction (as it is as middle of the Syllogism of Reflection), while further this distinction has reflected itself into simple identity.—Consequently this Syllogism is Syllogism of Necessity, since its middle is not some alien and immediate content, but is the intro-Reflection of the determinateness of the extremes. These have their inner identity in the middle, whose content-determinations are the form-determinations of the extremes.—So now that by means of which the terms are distinct from one another exists as external and unessential form, while they themselves exist as the moments of a necessary Existence.

At this point this Syllogism is immediate, and in so far formal in such a way that the connexion of the terms is the essential nature, as content; the latter is in the distinct terms in only a various form, while the extremes for themselves are only as an unessential persistence.—This Syllogism must, by the process of its realization, be determined in such a manner that the extremes too are posited as this totality (which the middle is at first); while the necessity of the relation—which at first is only the substantial content—is a relation of the posited form.

1. The Categorical Syllogism has the Categorical Judgment for one or both of its premisses.—Here this more determinate significance is connected with this Syllogism (as with the Judgment), that its middle is objective universality. Superficially the Categorical Syllogism too is taken for nothing more than a mere syllogism of inherence.

According to the significance of its content the Categorical Syllogism is the first Syllogism of Necessity, in which a subject is bound together with a predicate through its substance. But substance, raised to the sphere of Notion, is the universal, posited as being in and for itself in such a way that it has for form and for the manner of its being not accidentality (which it had in its peculiar relation) but the Notion-determination. Its distinctions therefore are the extremes of the Syllogism, or (determinately) universality and individuality. The former, as against the genus (which now is the closer determination of the middle) is abstract universality or universal determinateness—the accidentality of substance comprehended into simple determinateness, which however is its essential distinction or specific difference.—Individuality on the other hand is the actual; in itself it is the concrete unity of genus and determinateness, while here (as in the immediate Syllogism) it is as yet immediate individuality, accidentality which is comprehended into the form of persistence which is for itself.—The relation of this extreme to the middle constitutes a Categorical Judgment; but the other extreme too expresses the specific difference of the genus or its determinate principle, according to the determination which has been mentioned; and, in so far, this other premiss too is categorical.

2. At first this Syllogism, as being first and therefore immediate Syllogism of Necessity, stands under the scheme of the first formal Syllogism /—P—U.—But the middle is the essential nature of the individual, and not just any determinateness or property of it; and similarly the extreme of universality is not just any abstract universal, or any individual quality, but the universal determinateness, the specific part of the distinction of the genus; and therefore that contingency vanishes which would cause the subject to be bound together by just any middle term with just any quality.—And thus the relations of the extremes to the middle have not that external immediacy which they have in the Qualitative Syllogism, and consequently the necessity of a proof does not arise as it did there, leading to the infinite progress.

Further this Syllogism, unlike a Syllogism of Reflection, does not presuppose its conclusion for its premisses. The terms, according to their substantial content, stand to one another in an identical relation which is in and for itself: there is one essence pervading the three terms, in which the determinations of individuality, particularity, and universality are only formal moments.

Consequently the Categorical Syllogism is in so far no longer subjective; in this identity, objectivity commences; the middle is the identity (which is full of content) of its extremes, and these are contained in it according to their independence; for their independence is that substantial universality, the genus. The subjective element of the Syllogism consists in the indifferent persistence of the extremes against the Notion (or the middle).

3. But there remains something subjective in this Syllogism: the identity exists still as substantial (or as content), and not at the same time as identity of form. Consequently the identity of the Notion is still an internal bond, whence, as relation, it is still Necessity; the universality of the middle is solid and positive identity, and does not equally exist as the negativity of its extremes.

More closely considered, in this Syllogism the immediacy, which is not yet posited as that which it is in itself is present in the following manner. The properly immediate element of the Syllogism is the individual. This is subsumed under its genus as middle; but below it there stand other individuals of indeterminate number; it is therefore contingent that only this one individual is posited under it as subsumed.—But further this contingency does not belong merely to external reflection, which discovers the individual posited in the syllogism to be contingent through comparison with others; rather, it is posited as contingent (as a subjective actuality) because it is itself related to the middle as to its objective universality. On the other side the subject, since it is an immediate individual, contains determinations which are not contained in the middle as in the universal nature; consequently it has also an existence which is indifferent to it and is determined for itself, having a peculiar content. And hence this other term too, conversely, has an indifferent immediacy and an existence different from the former.—The same relation subsists also between the middle and the other extreme; for the latter too has the determination of immediacy, and hence of a contingent being as against its middle.

The following then are the positings of the Categorical Syllogism:—(a) extremes having such a relation to the middle that they have objective universality or independent nature in themselves and at the same time exist as immediate terms, that is, as actualities indifferent to each other; (b) they exist equally as contingent, that is, their immediacy is determined as transcended in their identity. But, by reason of this independence, and totality of actuality, this identity is only formal and inner; thus the Syllogism of Necessity has determined itself as the Hypothetical Syllogism.

1. The Hypothetical Judgment contains only the necessary relation without the immediacy of the related terms. If A, then B; in other words, the being of A is also and equally the being of an Other, namely B; but this implies neither that A is nor that B is. The Hypothetical Syllogism adds this immediacy of being:—

If A is, then B is, but A is, therefore B is. The minor premiss by itself expresses the immediate being of A.

But not this alone has been added to the Judgment. The Syllogism contains the relation of subject and predicate not as abstract copula but as completed mediating unity. Consequently the being of A must be taken not as mere immediacy but essentially as middle of the Syllogism. This must be further considered.

2. First the relation of the Hypothetical Judgment is necessity or inner substantial identity combined with external variety of existence or mutual indifference of the being which appears—an identical content which forms an internal foundation. Consequently the two sides of the Judgment are not an immediate being, but a being which is held suspended in Necessity: that is, they are at the same time transcended, or merely apparent, being. Further they are related as sides of the Judgment, as universality and individuality; consequently the one is this content as totality of conditions, the other as actuality. It is however indifferent which side is taken as universality and which as individuality. For in so far as the conditions still are the inner or abstract element of an actuality, they are the universal; and they have entered into actuality by virtue of the fact that they are comprehended into one individuality. Conversely the conditions are an isolated and scattered appearance which acquires unity, significance, and a universally valid Determinate Being only in actuality.

But the closer relation which has been here assumed between the two sides as being the relation between condition and conditioned, can also be taken as that of cause and effect, or ground and consequence. Here this is indifferent; but the relation of condition corresponds more closely to the relation which is present in the Hypothetical Judgment and Syllogism, in so far as condition essentially is as an indifferent existence, while ground and cause pass over into Other through themselves; and also condition is a more universal determination, for it comprehends both sides of these relations, since effect, consequence, and the like, are as much condition of cause, or ground, as these latter are of the former.—

Now A is mediating being, first, in so far as it is an immediate being, an indifferent actuality; but also, secondly, in so far as it is a being contingent in itself and self-transcending. What translates the conditions into the actuality of the new shape of which they are the conditions, is this, that they are not being as the abstract immediate, but Being in its Notion and, at first, Becoming; but, since the Notion no longer is the process of passing over, they are (being more closely determined) individuality as self-relating negative unity.—The conditions are a scattered material awaiting and demanding employment; this negativity is the mediating entity, the free unity of the Notion. It determines itself as activity, since this middle is the contradiction between objective universality (or the totality of the identical content) and indifferent immediacy.—This middle consequently is no longer necessity which is merely inner, but existent necessity; objective universality contains self-relation as simple immediacy, as Being;—in the Categorical Syllogism this moment is at first determination of the extremes, but it determines itself as contingency against the objective universality of the middle, and hence as something merely posited or also as transcended, that is, as something which has passed back into the Notion or into the middle as unity, which middle itself now in its objectivity is Being.

The conclusion “therefore B is” expresses the same contradiction, that B is immediately but equally is through an Other, or is mediated. Formally therefore it is the same Notion which the middle also is; only it is distinguished from Necessity as the Necessary,—in the form (which is quite superficial) of individuality as against universality. The absolute content of A and of B is the same; they are only two different names of the same foundation for imagination, in so far as it holds fast the appearance of the diversified shape of Determinate Being and distinguishes its necessity from the necessary; but in so far as this necessity were supposed to be separated from B, it would not be the necessary. There is thus here the identity of mediator and mediated.

3. The Hypothetical Syllogism at first represents the necessary relation as connexion through form, or as negative unity, just as the Categorical Syllogism represented, through positive unity, the solid content, or objective universality. But necessity collapses into the necessary; the formal activity of the translation of conditioning into conditioned actuality is in itself the unity in which the determinatenesses of the opposition (which had before achieved the licence of indifferent existence) are transcended, and the distinction between A and B is an empty name. Consequently it is intro-reflected unity,—and therefore also an identical content; and this not only in itself—it is also posited through this Syllogism, since the being of A is not its own but also that of B, and, conversely and in general, the being of the one is the being of the other, and in the conclusion immediate being or indifferent determinateness exists definitely as mediated—since, that is, externality has transcended itself, and its unity which has passed into itself is now posited.

The mediation of the Syllogism has thus determined itself as individuality, immediacy, and self-relating negativity, or as identity which distinguishes itself and, out of this distinction, collects itself into itself;—that is, as absolute form, and for this very reason as objective universality or self-identical content. In this determination the Syllogism is the Disjunctive Syllogism.

The Hypothetical Syllogism in general stands under the scheme of the second figure, U—I—P: the Disjunctive Syllogism stands under the scheme of the third figure of the formal syllogism, I—U—P. But the middle is universality filled with form; it has determined itself as totality, as developed objective universality. Consequently the middle term is as well universality as particularity and individuality. As the former it is, first, the substantial identity of the genus; but secondly it exists as one which has absorbed particularity, as being equal with itself, that is, as general sphere which contains its total particularization—as the genus divided into its species, or A which is B as much as C or D. But particularization is distinction, and therefore is equally the alternativeness of B, C, and D, or negative unity, or reciprocal exclusiveness of the determinations.—This exclusiveness further is not only reciprocal, and the determination is not merely relative, but is equally and essentially self-relating determination,—the particular as individuality to the exclusion of the others.

A is either B or C or D, but A is B, therefore A is neither C nor D; or again

A is either B or C or D, but A is neither C nor D, therefore A is B.

A is subject not only in the two premisses, but also in the conclusion. In the first premiss it is universal, and in its predicate it is the universal sphere particularized into the totality of its species; in the second it exists as determinate or as one species; in the conclusion it is posited as the exclusive individual determinateness.—Or again the subject is already posited in the minor premiss as exclusive individuality, and in the conclusion, positively, as that determinate entity which it is.

The term which here appears as mediated is the universality of A, which is mediated with individuality. But the mediating term is this A, which is the universal sphere of its particularizations and is an entity determined as individual. Thus the truth of the Hypothetical Syllogism—the unity of mediator and mediated—is posited in the Disjunctive Syllogism, which for this reason has also ceased to be a Syllogism. For the middle, which in it is posited as the totality of the Notion, contains itself the two extremes in their complete determinateness. The extremes, in distinction from this middle, exist only as a positedness no longer having a peculiar determinateness as against the middle.

If this is considered with more particular respect to the Hypothetical Syllogism, it appears that the latter contained (1) a substantial identity as the inner bond of necessity, and (2) a negative unity distinct therefrom—namely activity, or the form which translated one existence into another. The Disjunctive Syllogism in general is in the determination of universality; its middle is the A as genus and as perfectly determinate entity; by virtue of this unity this content (which was inner before) is also posited; and conversely positedness or form is not external negative unity as against an indifferent existence, but is identical with that solid content. The whole form-determination of the Notion is posited in its determinate distinction and at the same time in the simple identity of the Notion.

Hereby the formalism of the syllogizing process, and hence the subjectivity of the Syllogism and the Notion, have transcended themselves. This formal or subjective element consisted in this, that that which mediates the extremes is the Notion as abstract determination, so that this latter is thereby distinct from them while it is their unity. But in the perfection of the Syllogism, where objective universality is equally posited as totality of the form-determinations, the distinction between mediator and mediated has disappeared. What is mediated is itself an essential moment of its mediator, and each moment exists as the totality of the mediated.

The figures of the Syllogism represent each determinateness of the Notion separately as the middle, which at the same time is the Notion as Ought, as a demand that the mediating term shall be its totality. But the various genera of Syllogisms represent the stages of the completion or concretion of the middle. In the formal Syllogism the middle is posited as totality only by virtue of the fact that all the determinatenesses (but each separately) run through the function of mediation. In the Syllogisms of Reflection the middle is the unity which externally comprehends the determinations of the extremes. In the Syllogism of Necessity it has determined itself to be a unity equally developed and total, and simple; and the form of the Syllogism, which consisted in the distinction of the middle as against its extremes, has thereby transcended itself.

And now the Notion altogether has become realized, or, more exactly, it has achieved a reality which is Objectivity. The last reality was that the Notion (as internally negative unity) sunders itself and, as Judgment, posits its determinations in a determinate and indifferent distinction, while in the Syllogism it opposes itself to these. Thus it is still the internality of this its externality; and so in the course of the Syllogisms this externality is equalized with the internal unity. The various determinations return into this unity through the mediation which, while it unites them, is still a third term. Thus externality in itself represents the Notion, which now is no longer an internal unity and, as such, distinct from it.

But that determination of the Notion which had been considered as reality is, conversely, equally a positedness. For in this result the truth of the Notion has turned out to be the identity of its internality and externality; and not only this: already the moments of the Notion, in the Judgment, remain, in their indifference to each other, determinations which have their significance only in their relation. The Syllogism is mediation—the complete Notion in its positedness. Its movement is the transcendence of this mediation, in which nothing is in and for itself, but each term is only through the mediation of another. Consequently the result is an immediacy which has emerged through the transcendence of mediation, a Being which is equally identical with mediation, and is the Notion which has constructed itself out of and in its otherness. Hence this Being is a Thing which is in and for itself, or Objectivity.