The Doctrine of the Notion
Section One: Subjectivity
The Notion is, in the first instance, formal, the Notion in its beginning or the immediate Notion. In the immediate unity, its difference or positedness is itself at first simple and only an illusory being [Schein], so that the moments of the difference are immediately the totality of the Notion and are simply the Notion as such.
Secondly, however, because it is absolute negativity, it sunders itself and posits itself as the negative or as the other of itself; and further, because as yet it is only the immediate Notion, this positing or differentiation is characterised by the fact that the moments become indifferent to one another and each becomes for itself; in this partition, its unity is still only an external connection. As such connection of its moments, which are posited as self-subsistent and indifferent, it is Judgment.
Thirdly, though the judgment does contain the unity of the Notion that has vanished into its self-subsistent moments, yet this unity is not posited. It becomes so through the dialectical movement of the judgment, through which it has become the Syllogism, the Notion posited in its completeness; for in the syllogism there is posited not only the moments of the Notion as self-subsistent extremes, but also their mediating unity.
But since this unity itself as the unifying middle, and the moments as self-subsistent extremes, are in the first instance immediately opposed to one another, this contradictory relationship that occurs in the formal syllogism sublates itself, and the completeness of the Notion passes over into the unity of the totality, the subjectivity of the Notion into its Objectivity.
Chapter 1 The Notion
Understanding is the term usually employed to express the faculty of notions; as so used, it is distinguished from the faculty of judgment and the faculty of syllogisms, of the formal reason But it is with reason that it is especially contrasted; in that case, however, it does not signify the faculty of the notion in general, but of determinate notions, and the idea prevails that the notion is only a determinate notion. When the understanding in this signification is distinguished from the formal faculty of judgment and from the formal reason, it is to be taken as the faculty of the single determinate notion. For the judgment and the syllogism or reason are, as formal, only a product of the understanding since they stand under the form of the abstract determinateness of the Notion. Here, however, the Notion emphatically does not rank as something merely abstractly determinate; consequently, the understanding is to be distinguished from reason only in the sense that the former is merely the faculty of the notion in general.
This universal Notion, which we have now to consider here, contains the three moments: universality, particularity and individuality. The difference and the determinations which the Notion gives itself in its distinguishing, constitute the side which was previously called positedness. As this is identical in the Notion with being-in-and-for-self, each of these moments is no less the whole Notion than it is a determinate Notion and a determination of the Notion.
In the first instance, it is the pure Notion or the determination of universality. But the pure or universal Notion is also only a determinate or particular Notion, which takes its place alongside other Notions. Because the Notion is a totality, and therefore in its universality or pure identical self-relation is essentially a determining and a distinguishing, it therefore contains within itself the standard by which this form of its self-identity, in pervading and embracing all the moments, no less immediately determines itself to be only the universal over against the distinguishedness of the moments.
Secondly, the Notion is thereby posited as this particular or determinate Notion, distinct from others.
Thirdly, individuality is the Notion reflecting itself out of the difference into absolute negativity. This is, at the same time, the moment in which it has passed out of its identity into its otherness, and becomes the judgment.
A.The Universal Notion
The pure Notion is the absolutely infinite, unconditioned and free. It is here, at the outset of the discussion which has the Notion for its content, that we must look back once more at its genesis. Essence is the outcome of being, and the Notion, the outcome of essence, therefore also of being. But this becoming has the significance of a self-repulsion, so that it is rather the outcome which is the unconditioned and original. Being, in its transition into essence, has become an illusory being or a positedness, and becoming or transition into an other has become a positing; and conversely, the positing or reflection of essence has sublated itself and has restored itself as a being that is not posited, that is original. The Notion is the interfusion of these moments, namely, qualitative and original being is such only as a positing, only as a return-into-self, and this pure reflection-into-self is a sheer becoming-other or determinateness which, consequently, is no less an infinite, self-relating determinateness.
Thus the Notion is, in the first instance, the absolute self-identity that is such only as the negation of negation or as the infinite unity of the negativity with itself. This pure relation of the Notion to itself, which is this relation by positing itself through the negativity, is the universality of the Notion.
As universality is the utterly simple determination, it does not seem capable of any explanation; for an explanation must concern itself with definitions and distinctions and must apply predicates to its object, and to do this to what is simple, would alter rather than explain it. But the simplicity which constitutes the very nature of the universal is such that, through absolute negativity, it contains within itself difference and determinateness in the highest degree. Being is simple as immediate being; for that reason it is only something meant or intended and we cannot say of it what it is; therefore, it is one with its other, with non-being. Its Notion is just this, to be a simplicity that immediately vanishes in its opposite; it is becoming. The universal, on the contrary, is that simplicity which, because it is the Notion, no less possesses within itself the richest content.
First, therefore, it is the simple relation to itself; it is only within itself. Secondly, however, this identity is within itself absolute mediation, but it is not something mediated. The universal that is mediated, namely, the abstract universal that is opposed to the particular and the individual, this will be discussed later when we are dealing with the specific notion. Yet even the abstract universal involves this, that in order to obtain it we are required to leave out other determinations of the concrete. These determinations, simply as such, are negations; equally, too, the omitting of them is a negating. So that even with the abstraction, we have the negation of the negation. But this double negation is conceived of as though it were external to the abstraction, as though not only were the other omitted properties of the concrete distinct from the one retained, which is the content of the abstract universal, but also as though this operation of omitting the other properties and retaining the one were a process outside the properties themselves. To such an externality in face of that movement, the universal has not yet determined itself; it is still within itself that absolute mediation which is, precisely, the negation of the negation or absolute negativity.
By virtue of this original unity it follows, in the first place, that the first negative, or the determination, is not a limitation for the universal which, on the contrary, maintains itself therein and is positively identical with itself. The categories of being were, as Notions, essentially these identities of the determinations with themselves in their limitation or otherness; but this identity was only in itself the Notion; it was not yet manifested. Consequently, the qualitative determination as such was lost in its other and had for its truth a determination distinct from itself. The universal, on the contrary, even when it posits itself in a determination, remains therein what it is. It is the soul [Seele] of the concrete which it indwells, unimpeded and equal to itself in the manifoldness and diversity of the concrete. It is not dragged into the process of becoming, but continues itself through that process undisturbed and possesses the power of unalterable, undying self-preservation.
But even so, it does not merely show, or have an illusory being, in its other, like the determination of reflection; this, as a correlate, is not merely self-related but is a positive relating of itself to its other in which it manifests itself; but, in the first instance, it only shows in it, and this illusory being of each in the other, or their reciprocal determining, along with their self-dependence, has the form of an external act. The universal, on the contrary, is posited as the essential being of its determination, as the latter's own positive nature. For the determination that constitutes its negative is, in the Notion, simply and solely a positedness; in other words, it is, at the same time, essentially only the negative of the negative, and is only as this identity of the negative with itself, which is the universal. Thus the universal is also the substance of its determinations; but in such wise that what was a contingency for substance, is the Notion's own self-mediation, its own immanent reflection. But this mediation which, in the first instance, raises contingency to necessity, is the manifested relation; the Notion is not the abyss of formless substance, or necessity as the inner identity of things or states distinct from, and limiting, one another; on the contrary, as absolute negativity, it is the shaper and creator, and because the determination is not a limitation but is just as much utterly sublated, or posited, the illusory being is now manifestation, the manifestation of the identical.
The universal is therefore free power; it is itself and takes its other within its embrace, but without doing violence to it; on the contrary, the universal is, in its other, in peaceful communion with itself. We have called it free power, but it could also be called free love and boundless blessedness, for it bears itself towards its other as towards its own self; in it, it has returned to itself.
We have just mentioned determinateness, although the Notion, being as yet only the universal and only self-identical, has not yet advanced to that stage. However, we cannot speak of the universal apart from determinateness which to be more precise is particularity and individuality, for the universal, in its absolute negativity, contains determinateness in and for itself. The determinateness, therefore, is not introduced from outside when we speak of it in connection with the universal. As negativity in general or in accordance with the first, immediate negation, the universal contains determinateness generally as particularity; as the second negation, that is, as negation of the negation, it is absolute determinateness or individuality and concreteness. The universal is thus the totality of the Notion; it is a concrete, and far from being empty, it has through its Notion a content, and a content in which it not only maintains itself but one which is its own and immanent in it. We can, indeed, abstract from the content: but in that case we do not obtain the universal of the Notion but only the abstract universal, which is an isolated, imperfect moment of the Notion and has no truth.
More precisely, the universal shows itself as this totality as follows. In so far as it contains determinateness, it is not merely the first negation, but also the reflection of this negation into itself. Taken expressly with this first negation, it is a particular, and it is as such that we are soon to consider it; but in this determinateness it is essentially still a universal; this side we have here still to consider. For determinateness, being in the Notion, is the total reflection, the two-fold illusory being which on the one hand has an illusory reference outwards, the reflection-into-other, and on the other hand has an illusory reference inwards, the reflection-into-self. The former reflection involves distinction from an other; from this standpoint, the universal possesses a particularity which has its resolution in a higher universal. Now even though it is merely a relative universal, it does not lose its character of universal; it preserves itself in its determinateness, not merely as though in its connection with the determinateness it remained indifferent to it — for then it would be merely compounded with it but so that it is what we have just called the illusory reference inwards. The determinateness, as determinate Notion, is bent back into itself out of the externality; it is the Notion's own immanent character, which is an essential character by virtue of the fact that, in being taken up into the universality and pervaded by it, it equally pervades the universality, being of like compass and identical with it; it is the character that belongs to the genus as the determinateness that is not separated from the universal. Accordingly, the limitation is not outward-going but positive, for the Notion, through its universality, stands in free relation to itself. Thus even the determinate Notion remains within itself infinitely free Notion.
But in regard to the other side, in which the genus is limited by its specific character, it has been observed that this, as a lower genus, has its resolution in a higher universal. The latter, in its turn, can also be grasped as genus but as a more abstract one; but it always pertains only to that side of the determinate Notion which has a reference outwards. The truly higher universal is that in which this outward-going side is taken back into the universal, the second negation, in which the determinateness is present simply as posited or as illusory being. Life, ego, spirit, absolute Notion, are not universals merely in the sense of higher genera, but are concretes whose determinatenesses, too, are not species or lower genera but genera which, in their reality, are absolutely self-contained and self-fulfilled. In so far as life, ego, finite spirit are, as they certainly are, also only determinate Notions, their absolute resolution is in that universal which as truly absolute Notion is to be grasped as the Idea of infinite spirit, whose posited being is infinite, transparent reality wherein it contemplates its creation, and in this creation its own self.
The true, infinite universal which, in itself, is as much particularity as individuality, we have next to consider as particularity. It determines itself freely; the process by which it makes itself finite is not a transition, for this occurs only in the sphere of being; it is creative power as the absolute negativity which relates itself to its own self. As such, it differentiates itself internally, and this is a determining, because the differentiation is one with the universality. Accordingly, the universal is a process in which it posits the differences themselves as universal and self-related. They thereby become fixed, isolated differences. The isolated subsistence of the finite which earlier was determined as its being-for-self, and also as thinghood, as substance, is, in its truth universality, the form with which the infinite Notion clothes its differences — a form that is, in fact, one of its own differences. Herein consists the creative power of the Notion, a power which is to be comprehended only in this, the Notion's innermost core.
B.The Particular Notion
Determinateness as such belongs to being and the qualitative sphere; as determinateness of the Notion it is particularity. It is not a limit, as though it were related to an other beyond it; on the contrary, as we have just seen, it is the native, immanent moment of the universal; in particularity, therefore, the universal is not in the presence of an other, but simply of itself.
The particular contains universality, which constitutes its substance; the genus is unaltered in its species, and the species are not different from the universal but only from one another. The particular has one and the same universality as the other particulars to which it is related. At the same time, by virtue of the identity of the particulars with the universal, their diversity is, as such, universal; it is totality. The particular, therefore, not only contains the universal but through its determinateness also exhibits it; consequently, the universal constitutes a sphere that must exhaust the particular. This totality appears, in so far as the determinateness of the particular is taken as mere diversity, as completeness. In this respect, species are complete simply because there are no more of them. There is no inner standard or principle that could apply to them, simply because diversity is the difference without unity in which the universality, which in its own self is absolute unity, is a merely external reflection and an unrestricted, contingent completeness. But diversity passes over into opposition, into an immanent relation of the diverse moments. Particularity, however, because it is universality, is this immanent relation, not through a transition, but in and for itself; it is in its own self totality and simple determinateness, essentially a principle. It has no other determinateness than that posited by the universal itself and resulting from the universal in the following manner.
The particular is the universal itself, but it is its difference or relation to an other, its illusory reference outwards [sein Scheinen nach aussen]; but there is no other present from which the particular could be distinguished, except the universal itself. The universal determines itself, and so is itself the particular; the determinateness is its difference; it is distinguished only from its own self. Therefore its species are only (a) the universal itself, and (b) the particular. The universal as the Notion is itself and its opposite, and this again is the universal itself as its posited determinateness; it embraces its opposite and in it is in union with itself. Thus it is the totality and principle of its diversity, which is determined wholly and solely by the universal itself.
Therefore there is no other true logical classification than this, that the Notion sets itself on one side as immediate indeterminate universality; this very indeterminateness constitutes its determinateness or makes it a particular. Each of them is the particular and is therefore co-ordinate with the other. Each of them as a particular is also determinate as against the universal, and in so far can be said to be subordinate to it. But even this universal, as against which the particular is determined, is for that reason itself merely one of the opposed sides. For if we speak of two opposed sides, we must supplement this by saying that it is not merely together that they constitute the particular – as if they were alike in being particulars only for external reflection – but rather that their determinateness over against one another is at the same time essentially only one determinateness, the negativity, which in the universal is simple.
Difference, as it shows itself here, is in its Notion and therefore in its truth. All previous difference has this unity in principle (im Begriffe). As immediate difference in the sphere of being, it is limit of an other; in reflection it is relative and posited as essentially relating itself to its other; here therefore the unity of the Notion begins to be posited, but at first it is only illusory being in an other. The true meaning and resolution of these determinations is just this, that they attain to their Notion, their truth; being, determinate being, something, or whole and parts, etc. substance and accidents, cause and effect, are by themselves [merely] thought-determinations; but they are grasped as determinate Notions when each is cognized in unity with its other or opposite determination. Whole and parts, cause and effect, for example, are not as yet different terms determined as particulars relatively to each other, because although in themselves they constitute one Notion, their unity has not yet reached the form of universality; thus the difference, too, which is in these relationships, has not as yet the form of being one determinateness. Cause and effect, for example, are not two different Notions, but only one determinate Notion, and causality, like every Notion, is a simple Notion.
With respect to completeness, we have seen that the determinate side of particularity is complete in the difference of the universal and the particular, and that these two alone constitute the particular species. In nature, of course, there are to be found more than two species in a genus, just as between these many species there cannot exist the relationship we have just indicated. This is the impotence of nature, that it cannot adhere to and exhibit the strictness of the Notion and runs wild in this blind irrational [begrifflos] multiplicity. We can wonder at nature’s manifold genera and species and the endless diversity of her formations, for wonderment is unreasoning and its object the irrational. Nature, because it is the self-externality of the Notion, is free to indulge itself in this variety, just as spirit, too, even though it possesses the Notion in the shape of the Notion, engages in pictorial thinking and runs riot in its endless variety. The manifold natural genera or species must not be esteemed as anything more than the capricious fancies of spirit in its representations. Both indeed show traces and inklings of the Notion on all sides, but do not present a faithful copy of it because they are the side of its free self-externality. The Notion is absolute power just because it can freely abandon its difference to the shape of self-subsistent diversity, outer necessity, contingency, caprice, opinion, which however must not be taken for more than the abstract aspect of nothingness.
We have seen that the determinateness of the particular is simple as principle, but it is also simple as moment of the totality — as a determinateness opposed to the other determinateness. The Notion, in determining or distinguishing itself, is negatively directed against its unity and gives itself the form of one of its ideal moments, that of being: as a determinate Notion, it has a determinate Being in general. But this Being no longer signifies bare immediacy but Universality — immediacy which through absolute mediation is equal to itself and equally contains the other moment, essential being or reflection. This Universality with which the determinate moment is clothed is abstract Universality. The particular has Universality within it as its essential being; but, in so far as the determinateness of the difference is posited, and thereby has Being, Universality is a form assumed by the difference, and the determinateness as such is the content. The Universality becomes form in so far as the difference is present as the essential moment, just as, on the contrary, in the purely universal it is present only as absolute negativity, not as difference which posited as such.
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Now determinateness, it is true, is the abstract, as against the other, determinateness; but this other is only universality itself which is, therefore, also abstract, and the determinateness of the Notion, or particularity, is again nothing more than a determinate universality. In this, the Notion is outside itself; since it is the Notion that is here outside itself, the abstract universal contains all the moments of the Notion. It is (a) universality, (b) determinateness, (c) the simple unity of both; but this unity is immediate, and therefore particularity is not present as totality. In itself it is also this totality and mediation; it is essentially an exclusive relation to an other, or sublation of the negation, namely, of the other determinateness – an other, however, that exists only in imagination, for it vanishes immediately and shows itself to be the same as its supposed other. Therefore, what makes this universality abstract is that the mediation is only a condition or is not posited in the universality itself. Because it is not posited, the unity of the abstract universality has the form of immediacy, and the content has the form of indifference to its universality, for the content is not present as the totality which is the universality of absolute negativity. Hence the abstract universal is, indeed, the Notion, yet it is without the Notion; it is the Notion that is not posited as such.
When people talk of the determinate Notion, what is usually meant is merely such an abstract universal. Even by notion as such, what is generally understood is only this notion that is no Notion, and the understanding denotes the faculty of such notions. Demonstration appertains to this understanding in so far as it progresses by notions, that is to say, merely by determinations. Such a progression by notions, therefore, does not get beyond finitude and necessity; for it, the highest is the negative infinite, the abstraction of the supreme being [des h chsten Wesen], which is itself the determinateness of indeterminateness. Absolute substance, too, though it is not this empty abstraction – from the point of view of its content it is rather the totality – is nevertheless abstract because it lacks the absolute form; its inmost truth is not constituted by the Notion; true, it is the identity of universality and particularity, or of thought and asunderness, yet this identity is not the determinateness of the Notion; on the contrary, outside substance there is an understanding – and just because it is outside it, a contingent understanding – in which and for which substance is present in various attributes and modes.
Moreover, abstraction is not empty as it is usually said to be; it is the determinate Notion and has some determinateness or other for its content. Even the supreme being, the pure abstraction, has, as already remarked, the determinateness of indeterminateness; but indeterminateness is a determinateness, because it is supposed to stand opposed to the determinate. But the enunciation of what it is, itself sublates what it is supposed to be; it is enunciated as one with determinateness, and in this way, out of the abstraction is established its truth and the Notion. But every determinate Notion is, of course, empty in so far as it does not contain the totality, but only a one-sided determinateness. Even when it has some other concrete content, for example man, the state, animal, etc., it still remains an empty Notion, since its determinateness is not the principle of its differences; a principle contains the beginning and the essential nature of its development and realization; any other determinateness of the notion, however, is sterile. To reproach the Notion generally with being empty, is to misjudge that absolute determinateness of the Notion which is the difference of the Notion and the only true content in the element of the Notion.
Connected with the above is the reason why latterly the Understanding has been so lightly esteemed and ranked as inferior to Reason; it is the fixity which it imparts to the determinatenesses, and hence to finite determinations. This fixity consists in the form of abstract Universality which has just been considered: through it they become immutable. For qualitative determinateness, and also determinations of reflection, are essentially limited, and, through their limitation, have a relation to their other; hence the necessity of transition and passing away. But universality which they possess in the understanding gives them the form of reflection-into-self by which they are freed from the relation-to-other and have become imperishable. Now though in the pure Notion this eternity belongs to its nature, yet its abstract determinations are eternal essentialities only in respect of their form; but their content is at variance with this form; therefore they are not truth, or imperishable. Their content is at variance with the form, because it is not determinateness itself as universal; that is, it is not totality of the Notion's difference, or not itself the whole form; but the form of the limited understanding is itself the imperfect form, namely, abstract universality. But further, we must recognise the infinite force of the understanding in splitting the concrete into abstract determinatenesses and plumbing the depth of difference, the force that at the same time is alone the power that effects their transition.
The concrete of intuition is a totality, but a sensuous one – a real material which has an indifferent, sundered existence in space and time; but surely this absence of unity in the manifold, where it is the content of intuition, ought not to be counted to it for merit and superiority over intellectual existence. The mutability that it exhibits in intuition already points to the universal; yet all that it brings to view is merely another, equally mutable, material; therefore, only the same thing again, not the universal which should appear and take its place. But least of all in sciences such as geometry and arithmetic, should we count it as a merit that their material involves an intuitive element, or imagine that their propositions are established on it. On the contrary, it is on account of that element that the material of such sciences is of an inferior nature; the intuition of figures or numbers does not procure a scientific knowledge of them; only thinking about them can do this. But if by intuition we are to understand not merely the element of sense but the objective totality, then it is an intellectual intuition; that is to say, intuition has for its object not the external side of existence, but what existence holds of imperishable reality and truth-reality, only in so far as it is essentially in the Notion and determined by it, the Idea, whose more precise nature has to reveal itself at a later stage. The advantage which intuition as such is supposed to have over the Notion is external reality, the Notionless element, which first receives a value through the Notion.
Since, therefore, understanding exhibits the infinite force which determines the universal, or conversely, imparts through the form of Universality a fixity and subsistence to the determinateness that is in and for itself transitory; then it is not the fault of understanding if no further progress is made beyond this point. It is a subjective impotence of reason which adopts these determinatenesses in their fixity, and which is unable to bring them back to their unity through the dialectical force opposed to this abstract universality, in other words, through their own peculiar nature or through their Notion. The understanding does indeed give them, so to speak, a rigidity of being such as they do not possess in the sphere of quality and the sphere of reflection; but at the same time it spiritually impregnates them and so sharpens them, that just at this extreme point alone they acquire the capability to dissolve themselves and pass over into their opposite. The highest maturity, the highest stage, which anything can attain is that in which its downfall begins. The fixity of the determinateness into which the understanding seems to run, the form of the imperishable, is that of self-relating universality. But this belongs properly to the Notion; and consequently in this universality is to be found expressed, and infinitely close at hand, the dissolution of the finite. This Universality directly refutes the determinateness of the finite and expresses its incongruity with the universality. Or rather, the adequacy of the finite is already to hand; the abstract determinate is posited as one with the universality, and for that very reason is posited as not for itself — for then it would only be a determinate — but only as unity of itself and the universal, that is, as Notion.
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Therefore the usual practice of separating understanding and reason is, from every point of view, to be rejected. When the Notion is regarded as irrational, this should be interpreted rather as an incapacity of reason to recognize itself in the Notion. The determinate and abstract Notion is the condition, or rather an essential moment of reason; it is form spiritually impregnated, in which the finite, through the universality in which it relates itself to itself, spontaneously catches fire, posits itself as dialectical and thereby is the beginning of the manifestation of reason.
In the foregoing, the determinate Notion has been presented in its truth, and therefore it only remains to indicate what it is as already posited therein. Difference, which is an essential moment of the Notion though not yet posited as such in the pure universal, receives its due in the determinate Notion. Determinateness in the form of universality is linked with the universal to form a simple determination; this determinate universal is the self-related determinateness; it is the determinate determinateness or absolute negativity posited for itself. But the self-related determinateness is individuality. Just as universality is immediately in and for itself already particularity, so too particularity is immediately in and for itself also individuality; this individuality is, in the first instance, to be regarded as the third moment of the Notion, in so far as we hold on to its opposition to the two other moments, but it is also to be considered as the absolute return of the Notion into itself, and at the same time as the posited loss of itself.
Remark. Universality, particularity, and individuality are, according to the foregoing exposition, the three determinate Notions, that is, if one insists on counting them. We have already shown that number is an unsuitable form in which to hold Notional determinations; but for the determinations of the Notion itself it is unsuitable in the highest degree; number, since it has the unit [das Eins] for its principle, converts them as counted into completely isolated and mutually indifferent determinations. We have seen from the foregoing that the truth is that the different determinate Notions, far from falling apart into number, are simply only one and the same Notion.
In the customary treatment of logic hitherto, various classifications and species of notions occur. We are at once struck by the inconsequential way in which the species of notions are introduced: there are, in respect of quantity, quality, etc., the following notions. There are, expresses no other justification than that we find such species already to hand and they present themselves empirically. In this way, we obtain an empirical logic – an odd science this, an irrational cognition of the rational. In proceeding thus, logic sets a very bad example of obedience to its own precepts; it permits itself for its own purpose to do the opposite of what it prescribes as a rule, namely that notions should be deduced, and scientific propositions (therefore also the proposition: there are such and such species of notions) should be proved. In this matter, the Kantian philosophy commits a further inconsequence: it borrows the categories, as so-called root notions, for the transcendental logic, from the subjective logic in which they were adopted empirically. Since it admits the latter fact, it is hard to see why transcendental logic resolves to borrow from such a science instead of directly resorting to experience.
To cite some details of this, notions are mainly classified according to their clearness, into clear and obscure, distinct and indistinct, adequate and inadequate. To these we can also add complete, profuse, [ berfliessend] notions and suchlike superfluities. As regards the classification by clearness, it is readily seen that this standpoint and its related distinctions are taken from psychological, not from logical, determinations. The so-called clear notion is supposed to suffice for distinguishing one object from another; but this is not yet a notion, it is nothing more than a subjective representation. What an obscure notion is must be left to itself, for otherwise it would not be an obscure but a distinct notion. The distinct notion is supposed to be one whose marks can be indicated. As such it is, strictly speaking, the determinate notion. The mark, if it is taken in its correct meaning, is none other than the determinateness or the simple content of the notion, in so far as it is distinguished from the form of universality. But the mark, in the first instance, does not have quite this preciser meaning but is in general merely a determination whereby a third something takes note of an object, or the notion; it can therefore be a very contingent circumstance. In general it expresses not so much the immanence and essential nature of the determination as its relation to an understanding external to it. If this is really an understanding, it has the notion before it and distinguishes this only and solely by what is in the notion. But if the mark is supposed to be distinct from the notion, then it is a sign or some other determination which belongs to the representation of the thing, not to its notion. What the indistinct notion may be, can be passed over as superfluous.
But the adequate notion is something higher; what it really implies is the agreement of the Notion with reality, which is not the Notion as such but the Idea.
If the mark of the distinct notion were really supposed to be the determination of the notion itself, logic would find itself in difficulty over the simple notions which, according to another classification, are opposed to compound. For if a true, that is an immanent, mark of the simple notion were to be indicated, we should not be regarding it as simple; but in so far as no mark was given, it would not be a distinct notion. But here, now, the clear notion helps out, Unity, reality, and suchlike determinations are supposed to be simple notions, probably only because logicians were unable to discover their specific nature and contented themselves with having merely a clear notion of them, that is, no notion at all. Definition, that is, the statement of the notion, in general demands the statement of the genus and the specific difference. Therefore it presents the notion, not as something simple, but in two countable components. Yet surely no one will for that reason suppose such notion to be a compound. The simple notion seems to suggest abstract simplicity, a unity which does not contain within itself difference and determinateness and which therefore, too, is not the unity that belongs to the Notion. In so far as an object is present in ordinary thinking, especially in memory, or even as an abstract thought determination, it can be quite simple. Even the object that is richest in content, such as, for example, spirit, nature, the world, even God, when uncomprehendingly taken up into the simple representation of the equally simple expression: spirit, nature, the world, God, is doubtless something simple at which consciousness can stop short without going on to pick out its peculiar determination or its mark. But the objects of consciousness should not remain simple, should not remain such representations or abstract thought determinations; on the contrary, they should be comprehended, that is to say, their simplicity should be determined with their inner difference. The compound notion, however, is a contradiction in terms. We can, of course, have a notion of something composite; but a compound notion would be something worse than materialism, which assumes only the substance of the soul to be composite, yet none the less takes thought to be simple. Uneducated reflection first stumbles on the idea of composition, because it is the completely external relation, the worst form in which anything can be considered; even the lowest natures must be an inner unity. That the form of the untruest existence should be assigned, above all, to the ego, to the Notion, that is something we should not have expected and that can only be described as inept and barbarous.
Further, notions are divided mainly into contrary and contradictory. If, in our treatment of the notion, we are supposed to state what determinate notions there are, then we must adduce all possible determinations – for all determinations are notions, consequently determinate notions – and all the categories of being as well as all determinations of essence, would have to be adduced under the species of notions. Just as in the text-books of logic – to a greater or lesser degree, according to the whim of the author – it is related that there are affirmative, negative, identical, conditional, necessary notions, and so on. As the nature of the Notion itself has progressed beyond all such determinations and therefore these, if adduced in connexion with the Notion, occur out of their proper place, they only admit of superficial definitions and appear at this stage devoid of all interest. At the basis of contrary and contradictory notions – a distinction to which particular attention is paid here – lies the reflective determination of diversity and opposition. They are regarded as two particular species, that is, each as firmly fixed on its own account and indifferent to the other, without any thought of the dialectic and the inner nullity of these differences – as though what is contrary must not equally be determined as contradictory. The nature and the essential transition of the forms of reflection which they express have been considered in their proper place. In the Notion, identity has developed into universality, difference into particularity, opposition, which withdraws into the ground, into individuality. In these forms, those categories of reflection are present as they are in their Notion. The universal has proved itself to be not only the identical, but at the same time the different or contrary as against the particular and individual, and in addition, also to be opposed to them or contradictory; in this opposition, however, it is identical with them and is their true ground in which they are sublated. The same holds good of particularity and individuality which are likewise the totality of the determinations of reflection.
A further classification of notions is into subordinate and coordinate – a distinction which approaches more closely to the determination of the Notion, namely, the relationship of universality and particularity, where these terms, too, have been mentioned in passing. Only it is customary to regard them likewise as completely rigid relationships and from this point of view to put forward a number of sterile propositions about them. The most prolix discussion on this point concerns again the relation of contrariety and contradiction to subordination and co-ordination. Since the judgment is the relation of determinate Notions, it is only at that stage that the true relationship will come to view. That fashion of comparing these determinations without a thought for their dialectic or for the progressive alteration of their determination, or rather for the conjunction of opposed determinations present in them, makes the whole consideration of what is concordant or not concordant in them – as though the concord or discord were something separate and permanent – into something merely sterile and meaningless.
The great Euler, who displayed an infinitely fertile and acute mind in seizing and combining the deeper relations of algebraic magnitudes, the dry, prosaic Lambert in particular, and others, have attempted to construct a notation for this class of relation between determinations of the Notion by lines, figures and the like, the general intention being to elevate, or rather in fact to degrade, the logical modes of relation to a calculus. The utter futility of even attempting a notation is at once apparent when one compares the nature of the sign and what it is supposed to signify. The determinations of the Notion, universality, particularity and individuality, are certainly diverse, as are lines, or the letters of algebra; further, they are also opposed, and to this extent would also admit of the signs plus and minus. But they themselves, and above all their relations – even if one stops at subsumption and inherence – are in their essential nature entirely different from letters and lines and their relationships, the equality or difference of magnitude, the plus and minus, or a superimposition of lines, or their joining to form angles and the dispositions of spaces enclosed by them. It is characteristic of such objects that, in contrast to determinations of the Notion, they are mutually external, and have a fixed character. Now when Notions are so taken that they correspond to such signs, they cease to be Notions. Their determinations are not inert entities like numbers and lines whose relation does not itself belong to them; they are living movements; the distinguished determinateness of the one side is immediately internal to the other side too. What would be a complete contradiction in the case of numbers and lines is essential to the nature of the Notion. Higher mathematics, which also goes on to the infinite and allows itself contradictions, can no longer employ its usual signs for representing such determinations. To denote the conception – which is still very far from being a Notion – of the infinite approximation of two ordinates, or in equating a curve with an infinite number of infinitesimal straight lines, all it does is to draw two straight lines apart from each other and to make the straight lines approach the curve but remain distinct from it; for the infinite, which is here the point of interest, it refers us to pictorial thinking.
What has misled logicians into this attempt is primarily the quantitative relationship in which universality, particularity and individuality are supposed to stand to one another; the universal means, more extensive than the particular and the individual, and the particular means, more extensive than the individual. The Notion is the most concrete and richest determination because it is the ground and the totality of the preceding determinations, of the categories of being and of the determinations of reflection; these, therefore, are certainly also present in it. But its nature is completely misunderstood when they are retained in it in their former abstraction, when the wider extent of the universal is taken to mean that it is something more or a greater quantum than the particular and the individual. As absolute ground, it is the possibility of quantity, but equally so of quality, that is, its determinations are just as much qualitatively distinct; therefore they are taken in direct opposition to their truth when they are posited under the form of quantity alone. Thus, too, the determination of reflection is a correlate in which its opposite has an illusory being [scheint]; it is not in an external relationship like a quantum. But the Notion is more than all this; its determinations are determinate Notions, are themselves essentially the totality of all determinations. It is therefore quite inappropriate for the purpose of grasping such an inner totality, to seek to apply numerical and spatial relationships in which all determinations fall asunder; on the contrary, they are the last and worst medium which could be employed. Natural relationships such as magnetism, or colour relations, would be infinitely higher and truer symbols for the purpose. Since man has in language a means of designation peculiar to Reason, it is an idle fancy to search for a less perfect mode of representation to plague oneself with. It is essentially only spirit that can comprehend the Notion as Notion; for this is not merely the property of spirit but spirit’s pure self. It is futile to seek to fix it by spatial figures and algebraic signs for the purpose of the outer eye and an uncomprehending, mechanical mode of treatment such as a calculus. In fact, anything else which might be supposed to serve as a symbol can at most, like symbols for the nature of God, evoke intimations and echoes of the Notion; if, however, one should seriously propose to employ them for expressing and cognizing the Notion, then the external nature of all symbols is inadequate to the task; the truth about the relationship is rather the converse, namely, that what in symbols is an echo of a higher determination, is only truly known through the Notion and can be approximated to the Notion only by separating off the sensuous, unessential part that was meant to express it.
C.The Individual
Individuality, as we have seen, is already posited by particularity; this is determinate universality and therefore self-related determinateness, the determinate determinate.
1. In the first instance, therefore, individuality appears as the reflection of the Notion out of its determinateness into itself. It is the self-mediation of the Notion in so far as its otherness has made itself into an other again, whereby the Notion has reinstated itself as self-identical, but in the determination of absolute negativity. The negative in the universal whereby this is a particular, was defined above as a two-fold illusory being: in so far as the negative is an illusory being within the universal, the particular remains a universal; through the reference of the illusory being outwards it is a determinate; the return of this side into the universal is two-fold: either through abstraction which lets drop the particular and rises to the higher and the highest genus, or else through the individuality to which the universal in the determinateness itself descends. Here is where the false path branches off and abstraction strays from the highway of the Notion and forsakes the truth. Its higher and highest universal to which it raises itself is only the surface, which becomes ever more destitute of content; the individuality it despises is the profundity in which the Notion seizes itself and is posited as Notion. ©
Universality and particularity appeared, on the one hand, as moments of the becoming of individuality. But it has already been shown that they are in themselves the total Notion, and consequently in individuality do not pass over into an other, but that in individuality there is only posited that they are in and for themselves. The universal is in and for itself because it is in its own self absolute mediation, self-reference only as absolute negativity. It is an abstract universal in so far as this sublating is an external act and so a dropping of the determinateness.
Life, Spirit, God — the pure Notion itself, are beyond the grasp of abstraction, because it deprives its products of singularity, of the principle of individuality and personality, and so arrives at nothing but universalities devoid of life and spirit, colour and content.
Yet the unity of the Notion is so indissoluble that even these products of abstraction, though they are supposed to drop individuality are, on the contrary, individuals themselves. Abstraction raises the concrete into universality in which, however, the universal is grasped only as a determinate universality; and this is precisely the individuality that has shown itself to be self-related determinateness. Abstraction, therefore, is a sundering of the concrete and an isolating of its determinations; through it only single properties and moments are seized; for its product must contain what it is itself. But the difference between this individuality of its products and the Notion's individuality is that, in the former, the individual as content and the universal as form are distinct from one another — just because the former is not present as absolute form, as the Notion itself, or the latter is not present as the totality of form. However this more detailed consideration shows that the abstract product itself is a unity of the individual content and abstract universality, and is, therefore, a concrete — and the opposite of what it aims to be.
For the same reason the particular, because it is only the determinate universal, is also an individual, and conversely the individual, because it is the determinate universal, is just as much a particular. If we stick to this abstract determinateness, then the Notion has the three particular determinations, the universal, the particular, and the individual; whereas previously we had given only the universal and the particular as the species of the particular. Since individuality is the return of the Notion, as negative, into itself, this very return from the abstraction which, strictly speaking, is sublated in the return, can be placed along with the others as an indifferent moment and counted with them.
If individuality is reckoned as one of the particular determinations of the Notion, then particularity is the totality which embraces them all; precisely in being this totality it is the concretion of them or individuality itself. But it is also the concrete in accordance with its aspect, noted above, of determinate universality; as such it is the immediate unity in which none of these moments is posited as distinct or as the determinant, and in this form it will constitute the middle term of the formal syllogism.
It is self-evident that each determination made in the preceding exposition of the Notion has immediately dissolved itself and lost itself in its other. Each distinction is confounded in the very attempt to isolate and fix it. Only mere representational thinking, for which abstraction has isolated them, is capable of holding the universal, particular and individual rigidly apart; in this way they can be counted, and for a further distinction such thinking holds to the completely external one of being, namely, quantity, which is nowhere less appropriate than here. In individuality, the true relationship mentioned above, the inseparability of the Notion’s determinations is posited; for as negation of the negation it contains their opposition and at the same time contains it in its ground or unity, the effected coincidence of each with its other. As this reflection is in its very own nature universality, it is essentially the negativity of the Notion’s determinations, but not merely as if it were a third something distinct from them; on the contrary, it is now posited that posited being [Gesetztsein] is being-in-and-for-itself; that is, that each of the determinations pertaining to the difference is itself the totality. The return of the determinate Notion into itself means that it has the determination of being, in its determinateness, the whole Notion.
2. But Individuality is not only the return of the Notion into itself; but immediately its loss. Through individuality, where the Notion is internal to itself, it becomes external to itself and enters into actuality. Abstraction which, as the soul of individuality is the relation of the negative to the negative; and, as we have shown not external to the universal and the particular but immanent in them; and through it they are concrete, content, an individual. But as this negativity, individuality is the determinate determinateness, is differentiation as such; through this reflection of the difference into itself, the difference becomes fixed; it is only through individuality that the determining of the particular takes place, for individuality is that abstraction which simply as individuality, is now posited abstraction.
The individual, therefore, as self-related negativity, is immediate identity of the negative with itself; it is a being-for-self. Or it is the abstraction that determines the Notion, according to its ideal moment of being, as an immediate. In this way, the individual is a qualitative one or this. With this quality it is, first, repulsion of itself from itself, whereby the many other ones are presupposed; secondly, it is now a negative relation towards these presupposed others; and, the individual is in so far exclusive.
Universality, when related to these individuals as indifferent ones – and related to them it must be because it is a moment of the Notion of individuality – is merely their common element. When one understands by the universal, that which is common to several individuals, one is starting from the indifferent subsistence of these individuals and confounding the immediacy of being with the determination of the Notion. The lowest possible conception of the universal in its connection with the individual is this external relation of it as merely a common element. ©
The individual, which in the sphere of reflection exists as a this, does not have the exclusive relation to another one which belongs to qualitative being-for-self. This, as the one reflected into itself, is for itself and without repulsion; or repulsion in this reflection is one with abstraction and is the reflecting mediation which attaches to the this in such wise that the this is a posited immediacy pointed out by someone external to it. The this is; it is immediate; but it is only this in so far as it is pointed out. The ‘pointing out’ is the reflecting movement which collects itself inwardly and posits immediacy, but as a self-external immediacy. Now the individual is certainly a this, as the immediate restored out of mediation; but it does not have the mediation outside it – it is itself a repelling separation, posited abstraction, yet in its very act of separating, it is a positive relation.
This act of abstraction by the individual, being the reflection of the difference into itself, is first a positing of the differentiated moments as self-subsistent and reflected-into-self. They immediately are; but further, this sundering is reflection as such, the illusory being of the one in the other; thus they stand in essential relation. Further, the individuals are not merely inertly present in relation to one another; such plurality belongs to being; the individuality, in positing itself as determinate, posits itself not in an external difference but in the difference of the Notion. It therefore excludes the universal from itself; yet since this is a moment of individuality, the universal is equally essentially related to it.
The Notion, as this relation of its self-subsistent determinations, has lost itself; for as such it is no longer their posited unity, and they are no longer present as moments, as the illusory being, of the Notion, but as subsistent in and for themselves. As individuality, the Notion in its determinateness returns into itself, and therewith the determinate moment has itself become a totality. Its return into itself is therefore the absolute, original partition of itself, or, in other words, it is posited as judgment.
Chapter 2 The Judgment
The judgment is the determinateness of the Notion posited in the Notion itself. The Notion's determinations, or what we have seen to be the same thing, the determinate Notions, have already been considered on their own; but this consideration was more a subjective reflection or subjective abstraction. But the Notion is itself this abstractive process, the opposing of its determinations is its own determining activity. The judgment is this positing of the determinate Notions by the Notion itself. Judging is thus another function than comprehension, or rather it is the other function of the Notion as the determining of the Notion by itself, and the further progress of the judgment into the diversity of judgments is the progressive determination of the Notion. What kinds of determinate Notions there are, and how these determinations of the Notion are arrived at, has to reveal itself in the judgment.
The judgment can therefore be called the proximate realisation of the Notion, inasmuch as reality denotes in general entry into existence as a determinate being. More precisely, the nature of this realisation has presented itself in such a manner that, on the one hand, the moments of the Notion through its reflection-into-self or its individuality are self-subsistent totalities, while on the other hand the unity of the Notion is their relation. The determinations reflected into themselves are determinate totalities, no less essentially in their indifferent and disconnected subsistence as through their reciprocal mediation with one another. The determining itself is only totality in that it contains these totalities and their connection. This totality is the judgment. It contains, therefore, first, the two self-subsistents which are called subject and predicate. What each is cannot yet really be said; they are still indeterminate, for it is only through the judgment that they are to be determined. The judgment, being the Notion as determinate, the only distinction present is the general one that the judgment contains the determinate Notion over against the still indeterminate Notion. The subject can therefore, in the first instance, be taken in relation to the predicate as the individual over against the universal, or even as the particular over against the universal, or as the individual over against the particular; so far, they confront each other only in general, as the more determinate and the more universal.
It is therefore appropriate and necessary to have these names, subject and predicate for the determinations of the judgment; as names, they are something indeterminate that still awaits its determination, and are, therefore, no more than names. It is partly for this reason that the Notion determinations themselves could not be used for the two sides of the judgment; but a stronger reason is because the nature of the Notion determination is emphatically to be, not something abstract and fixed, but to have and to posit its opposite within it; since the sides of the judgment are themselves Notions and therefore the totality of its determinations, each side must run through all these determinations and exhibit them within itself, whether in abstract or concrete form. Now in order to fix the sides of the judgment in a general way when their determination is altered, those names are most serviceable which remain the same throughout the alteration. The name however stands over against the matter in hand or the Notion; this distinction presents itself in the judgment as such; now the subject is in general the determinate, and is therefore more that which immediately is, whereas the predicate expresses the universal, the essential nature or the Notion; therefore the subject as such is, in the first instance, only a kind of name; for what it is is first enunciated by the predicate which contains being in the sense of the Notion. In the question: what is this? or: what kind of a plant is this? what is often understood by the being enquired after, is merely the name, and when this is learned one is satisfied and now knows what the thing is. This is being in the sense of the subject. But the Notion, or at least the essence and the universal in general, is first given by the predicate, and it is this that is asked for in the sense of the judgment. Consequently, God, spirit, nature, or whatever it may be, is as the subject of a judgment at first only the name; what such a subject is as regards its Notion is first enunciated in the predicate. When enquiry is made as to the kind of predicate belonging to such subject, the act of judgment necessarily implies an underlying Notion. But this Notion is first enunciated by the predicate itself. Properly speaking, therefore, it is the mere general idea that constitutes the presupposed meaning of the subject and that leads to the naming of it; and in doing this it is contingent and a historical fact, what is, or is not, to be understood by a name. So many disputes about whether a predicate does or does not belong to a certain subject are therefore nothing more than verbal disputes, because they start from the form above mentioned; what lies at the base is so far nothing more than the name.
We have now to examine, secondly, how the relation of subject and predicate in the judgment is determined and how subject and predicate themselves are at first determined through this very relation. The judgment has in general for its sides totalities which to begin with are essentially self-subsistent. The unity of the Notion is, therefore, at first only a relation of self-subsistents; not as yet the concrete and pregnant unity that has returned into itself from this reality, but only a unity outside which the self-subsistent sides persist as extremes that are not sublated in it. Now consideration of the judgment can begin from the original unity of the Notion, or from the self-subsistence of the extremes. The judgment is the self-diremption of the Notion; this unity is, therefore, the ground from which the consideration of the judgment in accordance with its true objectivity begins. It is thus the original division [Teilung] of what is originally one; thus the word Urteil refers to what judgment is in and for itself. But regarded from the side of externality, the Notion is present in the judgment as Appearance, since its moments therein attain self-subsistence, and it is on this external side that ordinary thinking tends to fasten.
From this subjective standpoint, then, subject and predicate are considered to be complete, each on its own account, apart from the other: the subject as an object that would exist even if it did not possess this predicate; the predicate as a universal determination that would exist even if it did not belong to this subject. From this standpoint, the act of judgment involves the reflection, whether this or that predicate which is in someone's head can and should be attached to the object which exists on its own account outside; the very act of judging consists in this, that only through it is a predicate combined with a subject, so that, if this combination did not take place, each on its own would still remain what it is, the latter an existent object, the former an idea in someone's head. The predicate which is attached to the subject should, however, also belong to it, that is, be in and for itself identical with it. Through this significance of attachment, the subjective meaning of judgment and the indifferent, outer subsistence of subject and predicate are sublated again: this action is good; the copula indicates that the predicate belongs to the being of the subject and is not merely externally combined with it. In the grammatical sense, that subjective relationship in which one starts from the indifferent externality of the subject and predicate has its complete validity; for it is words that are here externally combined. We may take this opportunity of remarking, too, that though a proposition has a subject and predicate in the grammatical sense, this does not make it a judgment. The latter requires that the predicate be related to the subject as one Notion determination to another, and therefore as a universal to a particular or individual. If a statement about a particular subject only enunciates something individual, then this is a mere proposition. For example, 'Aristotle died at the age of 73, in the fourth year of the 115th Olympiad,' is a mere proposition, not a judgment. It would partake of the nature of a judgment only if doubt had been thrown on one of the circumstances, the date of the death, or the age of that philosopher, and the given figures had been asserted on the strength of some reason or other. In that case, these figures would be taken as something universal, as time that still subsists apart from this particular content of the death of Aristotle, whether as time filled with some other content, or even as empty time. Similarly, the news that my friend N. has died is a proposition; and it would be a judgment only if there were a question whether he was really dead or only in a state of catalepsy.
In the usual way of defining the judgment we may indeed accept the indeterminate expression connection for the external copula, as also that the connected terms are at least supposed to be notions. But in other respects this definition is superficial in the extreme: not only, for example, that in the disjunctive judgment more than two so-called notions are connected, but rather that the definition is far better than its subject matter; for it is not notions at all that are meant, hardly determinations of the Notion, but really only determinations of representational thought; it was remarked in connection with the Notion in general and the determinate Notion, that what is usually so named by no means deserves the name of Notion; where then should Notions come from in the case of the judgment? Above all, in this definition the essential feature of the judgment, namely, the difference of its determinations, is passed over; still less does it take into account the relationship of the judgment to the Notion.
As regards the further determination of the subject and predicate, we have remarked that it is really in the judgment first that they have to receive their determination. Since the judgment is the posited determinateness of the Notion, this determinateness possesses the said differences immediately and abstractly as individuality and universality. But in so far as the judgment is in general the determinate being or otherness of the Notion which has not yet restored itself to the unity whereby it is as Notion, there emerges also-the determinateness which is notionless, the opposition of being and reflection or the in-itself. But since the Notion constitutes the essential ground of the judgment, these determinations are at least indifferent to the extent that when one belongs to the subject and the other to the predicate, the converse relationship equally holds good. The subject as the individual appears, in the first instance, as that which simply is or is for itself in accordance with the specific determinateness of the individual — as an actual object, even though it be only an object in representational thought — as for example bravery, right, agreement, etc. — on which judgment is being made. The predicate, on the other hand, as the universal, appears as this reflection on the object, or rather as the object's reflection into itself, which goes beyond that immediacy and sublates the determinatenesses in their form of mere being; that is, it is the object's in-itself. In this way, one starts from the individual as the first, the immediate, and it is raised by the judgment into universality, just as, conversely, the universal that is only in itself descends in the individual into determinate being or becomes a being that is for itself.
This signification of the judgment is to be taken as its objective meaning, and at the same time as the truth of the earlier forms of the transition. In the sphere of being, the object becomes and others itself, the finite perishes or goes under in the infinite; in the sphere of Existence, the object issues from its ground into Appearance and falls to the ground, the accident manifests the wealth of substance as well as its power; in being, there is transition into an other, in essence, reflected being in an other by which the necessary relation is revealed. This movement of transition and reflection has now passed over into the original partition of the Notion which, while bringing back the individual to the in-itself of its universality, equally determines the universal as something actual. These two acts are one and the same process in which individuality is posited in its reflection-into-self, and the universal as determinate.
But now this objective signification equally implies that the said differences, in reappearing in the determinateness of the Notion, are at the same time posited only as Appearances, that is, that they are not anything fixed, but apply just as much to the one Notion determination as to the other. The subject is, therefore, just as much to be taken as the in-itself, and the predicate, on the other hand, as determinate being. The subject without predicate is what the thing without qualities, the thing-in-itself is in the sphere of Appearance — an empty, indeterminate ground; as such, it is the Notion enclosed within itself, which only receives a differentiation and determinateness in the predicate; the predicate therefore constitutes the side of the determinate being of the subject. Through this determinate universality the subject stands in relation to an externality, is open to the influence of other things and thereby becomes actively opposed to them. What is there comes forth from its being-within-self and enters into the universal element of connection and relationship, into the negative connections and the interplay of actuality, which is a continuation of the individual into other individuals and therefore universality.
The identity just demonstrated, namely, that the determination of the subject equally applies to the predicate and vice versa, is not, however, something only for us; it is not merely in itself, but is also posited in the judgment; for the judgment is the connection of the two; the copula expresses that the subject is the predicate. The subject is the specific determinateness, and the predicate is this posited determinateness of the subject; the subject is determined only in its predicate, or, only in the predicate is it a subject; in the predicate it has returned into itself and is therein the universal. Now in so far as the subject is the self-subsistent, this identity has the relationship that the predicate does not possess a self-subsistence of its own, but has its subsistence only in the subject; it inheres in the subject. Since the predicate is thus distinct from the subject, it is only an isolated determinateness of the latter, only one of its properties; while the subject itself is the concrete, the totality of manifold determinatenesses, just as the predicate contains one; it is the universal.
But on the other hand the predicate, too, is a self-subsistent universality and the subject, conversely, only a determination of it. Looked at this way, the predicate subsumes the subject; individuality and particularity are not for themselves, but have their essence and substance in the universal. The predicate expresses the subject in its Notion; the individual and the particular are contingent determinations in the subject; it is their absolute possibility. When in the case of subsumption one thinks of an external connection of subject and predicate and the subject is conceived of as a self-subsistent something, the subsumption refers to the subjective act of judgment above-mentioned in which one starts from the self-subsistence of both subject and predicate. From this standpoint subsumption is only the application of the universal to a particular or an individual, which is placed under the universal in accordance with a vague idea that it is of inferior quality.
When the identity of subject and predicate are so taken that at one time one Notion determination applies to the former and the other to the latter, and at another time the converse equally holds good, then the identity is as yet still only an implicit one; on account of the self-subsistent diversity of the two sides of the judgment, their posited unity also has these two sides, in the first instance as different. But differenceless identity really constitutes the true relation of the subject to the predicate. The Notion determination is itself essentially relation for it is a universal; therefore the same determinations possessed by the subject and predicate are also possessed by their relation itself. The relation is universal, for it is the positive identity of the two, of subject and predicate; but it is also determinate, for the determinateness of the predicate is that of the subject; further, it is also individual, for in it the self-subsistent extremes are sublated as in their negative unity. However, in the judgment this identity is not as yet posited; the copula is present as the still indeterminate relation of being as such: A is B; for in the judgment, the self-subsistence of the Notion determinatenesses or the extremes, is the reality which the Notion has within it. If the is of the copula were already posited as the above determinate and pregnant unity of subject and predicate, as their Notion, it would already be the syllogism.
To restore this identity of the Notion, or rather to posit it, is the goal of the movement of the judgment. What is already present in the judgment is, on the one hand, the self-subsistence of subject and predicate, but also their mutually opposed determinateness, and on the other hand their none the less abstract relation. What the judgment enunciates to start with is that the subject is the predicate; but since the predicate is supposed not to be what the subject is, we are faced with a contradiction which must resolve itself, pass over into a result. Or rather, since subject and predicate are in and for themselves the totality of the Notion, and the judgment is the reality of the Notion, its forward movement is only a development; there is already present in it what comes forth from it, so that proof is merely an exposition, a reflection as a positing of that which is already present in the extremes of the judgment; but even this positing itself is already present; it is the relation of the extremes.
The judgment in its immediacy is in the first instance the judgment of existence; its subject is immediately an abstract individual which simply is, and the predicate is an immediate determinateness or property of the subject, an abstract universal.
This qualitative character of subject and predicate being sublated, the determination of the one is reflected, to begin with, in the other; the judgment is now, secondly, the judgment of reflection.
But this more external conjunction passes over into the essential identity of a substantial, necessary connection; as such it is, thirdly, the judgment of necessity.
Fourthly, since in this essential identity the difference of subject and predicate has become a form, the judgment becomes subjective; it contains the opposition of the Notion and its reality and the equation of the two; it is the judgment of the Notion.
This emergence of the Notion establishes the transition of the Judgment into the syllogism.
A. THE JUDGMENT OF EXISTENCE
In the subjective judgment we want to see one and the same object double, first in its individual actuality, and then in its essential identity or in its Notion: the individual raised into its universality, or, what is the same thing, the universal individualised into its actuality. In this way the judgment is truth: for it is the agreement of the Notion and reality. But this is not the nature of the judgment at first; for at first it is immediate, since as yet no reflection and movement of the determinations has appeared in it. This immediacy makes the first judgment a judgment of existence; it can also be called the qualitative judgment, but only in so far as quality does not apply only to the determinateness of being but also includes the abstract universality which, on account of its simplicity, likewise has the form of immediacy.
The judgment of existence is also the judgment of inherence; because it is in the form of immediacy, and because the subject as distinguished from the predicate is the immediate, and consequently the primary and essential feature in a judgment of this kind, the predicate has the form of a non-self-subsistent determination that has its foundation in the subject.
(a) The Positive Judgment
1. The subject and predicate as we have remarked, are in the first instance names, which only receive their actual determination through the course of the judgment. However, as sides of the judgment, which is the posited determinate Notion, they have the determination of moments of the Notion, but by virtue of their immediacy, the determination is still quite simple: for it is not enriched by mediation, and also, in accordance with the abstract opposition, it is determined as abstract individuality and universality. The predicate, to speak of this first, is the abstract universal; since this abstract is conditioned by the mediation in which the individual or particular is sublated, this mediation is so far only presupposition. In the sphere of the Notion there can be no other immediacy than one in which mediation is essentially and explicitly a moment and which has come to be only through the sublating of that mediation, that is, the immediacy of the universal. Thus even qualitative being, too, is in its Notion a universal; but as being, the immediacy is not yet so posited; it is only as universality that it is the Notion determination in which is posited the fact that negativity essentially belongs to it. This relation is given in the judgment in which it is the predicate of a subject. Similarly, the subject is an abstract individual, or the immediate that is supposed to be as such, and therefore the individual as a something in general. Thus the subject constitutes the abstract side of the judgment according to which the Notion has in it passed over into externality. As the two Notion determinations are determined, so also is their relation, the is or copula; it too can only have the significance of an immediate, abstract being. On account of the relation which as yet contains no mediation or negation, this judgment is called the positive.
2. The immediate pure enunciation of the positive judgment is, therefore, the proposition: the individual is universal.
This enunciation must not be put in the form: A is B; for A and B are entirely formless and consequently meaningless names; the judgment as such, however, and therefore even the judgment of existence, has Notion determinations for its extremes. A is B can represent any mere proposition just as well as a judgment. But in every judgment, even in those with a more richly determined form, there is asserted the proposition having this specific content: the individual is universal; inasmuch, namely, as every judgment is also in general an abstract judgment. With the negative judgment, how far it likewise comes under this expression, we shall deal presently. If no heed is given to the fact that in every judgment-at least, to begin with, every positive judgment, the assertion is made that the individual is a universal, this is partly because the determinate form whereby subject and predicate are distinguished is overlooked-the judgment being supposed to be nothing but the relation of two notions-and partly, probably, because the rest of the content of the judgment, Gaius is learned, or the rose is red, floats before the mind which is busy with the representation of Gaius, etc., and does not reflect on the form although such content at least as the logical Gaius who has usually to be dragged in as an example, is a much less interesting content and, indeed, is expressly chosen as uninteresting in order not to divert attention from the form to itself.
In its objective signification, the proposition that the individual is universal connotes, as we previously had occasion to remark, on the one hand the perishableness of individual things, and on the other hand their positive subsistence in the Notion as such. The Notion itself is imperishable, but that which comes forth from it in its partition is subject to alteration and to return into its universal nature. But conversely, the universal gives itself a determinate being. Just as essence issues into a reflected being [Schein] in its determinations, ground into the manifestation of Existence, and substance into the revelation of itself, into its accidents, so the universal resolves itself into the individual; and the judgment is this explication of the universal, the development of the negativity which it already is in itself. The latter fact is enunciated by the converse proposition, the universal is individual, which is equally enunciated in the positive judgment. The subject, which in the first instance is the immediate individual, is related in the judgment itself to its other, namely, the universal; consequently it is posited as the concrete; in the sphere of being as a something of many qualities, or as the concrete of reflection, a thing of manifold properties, an actuality of manifold possibilities, a substance of such and such accidents. Since these manifold determinations here belong to the subject, the something or the thing, etc., is reflected into itself in its qualities, properties or accidents; or it continues itself through them, maintaining itself in them and equally them in itself. The positedness or determinateness belongs to the being-in-and-for-self. The subject is, therefore, in its own self the universal. The predicate, on the other hand, as this universality which is not real or concrete but abstract, is, in contrast to the subject, the determinateness and contains only one moment of the subject's totality to the exclusion of the others. By virtue of this negativity which, as an extreme of the judgment, is at the same time self-related, the predicate is an abstract individual. For example, in the proposition: the rose is fragrant, the predicate enunciates only one of the many properties of the rose; it singles out this particular one which, in the subject, is a concrescence with the others; just as in the dissolution of the thing, the manifold properties which inhere in it, in acquiring self-subsistence as matters, become individualised. From this side, then, the proposition of the judgment runs thus: the universal is individual
In bringing together this reciprocal determination of subject and predicate in the judgment, we get a twofold result. First that immediately the subject is, indeed, something that simply is, an individual, while the predicate is the universal. But because the judgment is the relation of the two, and the subject is determined by the predicate as a universal, the subject is the universal. Secondly, the predicate is determined in the subject; for it is not a determination in general, but of the subject; in the proposition: the rose is fragrant, this fragrance is not any indeterminate fragrance, but that of the rose; the predicate is therefore an individual. Now since subject and predicate stand in the relationship of the judgment, they have to remain mutually opposed as determinations of the Notion; just as in the reciprocity of causality, before it attains its truth, the two sides have to retain their self-subsistence and mutual opposition in face of the sameness of their determination. When, therefore, the subject is determined as a universal, we must not take the predicate also in its determination of universality-else we should not have a judgment--but only in its determination of individuality; similarly, when the subject is determined as an individual, the predicate is to be taken as a universal.
Reflection on the above mere identity yields the two identical propositions:
The individual is individual,
The universal is universal,
in which the sides of the judgment would have fallen completely asunder and only their self-relation would be expressed, while their relation to one another would be dissolved and the judgment consequently sublated. Of the two original propositions, one, the universal is individual, enunciates the judgment in respect of its content, which in the predicate is a singled out determination, while in the subject it is the totality of them; the other, the individual is universal, enunciates the form which is stated immediately by the proposition itself. In the immediate positive judgment the extremes are still simple: form and content are, therefore, still united. In other words, it does not consist of two propositions; the twofold relation which we found in it directly constitutes the one positive judgment. For its extremes appear as (a) self-subsistent, abstract sides of the judgment, and (b) each side is determined by the other, by virtue of the copula connecting them. But for that very reason, the difference of form and content is implicit in it, as we have seen; to wit, what is implied in the first proposition: the individual is universal, pertains to the form, because it expresses the immediate determinateness of the judgment. On the other hand, the relationship expressed by the other proposition: the universal is individual, that is to say, that the subject is determined as universal, but the predicate as particular or individual concerns the content; for the sides of the judgment arise only through the reflection-into-self whereby the immediate determinatenesses are sublated, with the result that the form converts itself into an identity that has withdrawn into itself and persists in opposition to the distinction of form: that is, it converts itself into content.
3. Now if the two propositions, the one of form and the other of content:
Subject - Predicate
The individual is universal
The universal is individual,
were, because they are contained in the one positive judgment, to be united, so that both subject and predicate alike were determined as unity of individuality and universality, then both subject and predicate would be the particular; and this must be recognised as implicitly their inner determination. Only, on the one hand, this combination would only have been effected by an external reflection, and, on the other hand, the resultant proposition, the particular is the particular, would no longer be a judgment, but an empty identical proposition like those already derived from the positive judgment, namely, the individual is individual, and the universal is universal. Individuality and universality cannot yet be united into particularity, because in the positive judgment they are still posited as immediate. In other words, the judgment must still be distinguished in respect of its form and content, just because subject and predicate are still distinguished as immediacy and something mediated, or because the judgment, according to its relation, is both self-subsistence of the related sides and also their reciprocal determination or mediation.
First, then, the judgment considered in respect of its form asserts that the individual is universal. But the truth is that such an immediate individual is not universal; its predicate is of wider scope and therefore does not correspond to it. The subject is an immediate being-for-self and therefore the opposite of that abstraction, of that universality posited through mediation, which was supposed to be predicated of it.
Secondly, when the judgment is considered in respect of its content, or as the proposition, the universal is individual, the subject is a universal of qualities, a concrete that is infinitely determined; and since its determinatenesses are as yet only qualities, properties or accidents, its totality is the spuriously infinite plurality of them. Such a subject therefore is, on the contrary, not a single property such as its predicate enunciates. Both propositions, therefore, must be denied and the positive judgment must be posited rather as negative.
(b) The Negative Judgment
1. We have already referred above to the prevalent idea that it depends merely on the content of the judgment whether it be true or not, since logical truth concerns only the form and demands only that the said content shall not contradict itself. The form of the judgment is taken to be nothing more than the relation of two notions. But we have seen that these two notions do not have merely the relationless character of a sum, but are related to one another as individual and universal. These determinations constitute the truly logical content, and, be it noted, constitute in this abstraction the content of the positive judgment; all other content that appears in a judgment (the sun is round, Cicero was a great orator in Rome, it is day now, etc.) does not concern the judgment as such; the judgment merely enunciates that the subject is predicate, or, more definitely, since these are only names, that the individual is universal and vice versa. By virtue of this purely logical content, the positive judgment is not true, but has its truth in the negative judgment. All that is demanded of the content is that it shall not contradict itself in the judgment; but as has been shown it does contradict itself in the above judgment. It is, however, a matter of complete indifference if the above logical content is also called form, and by content is understood merely the remaining empirical filling; in that case, the form does not imply merely an empty identity, the determinate content lying outside it. The positive judgment has, then, through its form as positive judgment no truth; whoever gives the name of truth to the correctness of an intuition or perception, or to the agreement of the picture-thought with the object, at any rate has no expression left for that which is the subject matter and aim of philosophy. We should at least have to call the latter the truth of reason; and it will surely be granted that judgments such as: Cicero was a great orator, and: it is day now, and so on, are not truths of reason. But they are not such not because they have, as it were contingently, an empirical content, but because they are merely positive judgments that can have and are supposed to have no other content than an immediate individual and an abstract determination.
The positive judgment has its proximate truth in the negative: the individual is not abstractly universal - but on the contrary, the predicate of the individual, because it is such a predicate or taking it by itself apart from its relation to the subject-because it is an abstract universal, is itself determinate; the individual is, therefore, in the first instance a particular. Further, in accordance with the other proposition contained in the positive judgment, the negative judgment asserts that the universal is not abstractly individual, but on the contrary, this predicate, just because it is a predicate, or because it stands in relation to a universal subject, is something wider than a mere individuality, and the universal is therefore likewise in the first instance a particular. Since this universal, as subject, is itself in the judgment determination of individuality, the two propositions reduce to one: the individual is a particular.
We may remark (a) that here the predicate proves to be in the determination of particularity of which we have already made mention; but here it is not posited by external reflection, but has arisen by means of the negative relation exhibited by the judgment. (b) This determination here results only for the predicate. In the immediate judgment, the judgment of existence, the subject is the underlying basis; the determination seems therefore to run its course at first in the predicate. But as a matter of fact this first negation cannot as yet be a determination, or strictly speaking a positing of the individual, for the individual is the second negation, the negative of the negative.
The individual is a particular, is the positive expression of the negative judgment. This expression is not itself a positive judgment, for the latter, by reason of its immediacy, has only abstractions for its extremes, while the particular, precisely through the positing of the relation of the judgment presents itself as the first mediated determination. But this determination is not to be taken only as moment of the extreme, but also-as it really is in the first instance-as determination of the relation; in other words, the judgment is to be regarded also as negative.
This transition is based on the relationship of the extremes and their connection generally in the judgment. The positive judgment is the relation of the immediately individual and universal, therefore the relation of things, one of which at the same time is not what the other is; the relation is, therefore, no less essentially separation or negative; that is why the positive judgment had to be posited as negative. It was, therefore, unnecessary for logicians to make such a fuss over the not of the negative judgment being attached to the copula. In the judgment, what is determination of the extreme is no less a determinate relation. The judgment's determination, or the extreme, is not the purely qualitative determination of immediate being which is supposed to confront only an other outside it. Nor is it determination of reflection, which, in accordance with its general form, has a positive and negative bearing, each being posited as exclusive, and only implicitly identical with the other. The judgment's determination, as determination of the Notion, is in its own self a universal, posited as continuing itself into its other determinations. Conversely, the relation of the judgment is the same determination as that possessed by the extremes; for it is just this universality and continuation of them into one another; in so far as these are distinguished, the relation also has negativity in it.
The above-stated transition from the form of the relation to the form of the determination has for its immediate consequence that the not of the copula must no less be attached to the predicate and the predicate determined as the not-universal. But by an equally immediate consequence the not-universal is the particular. If we stick to the negative in the completely abstract determination of immediate not-being, then the predicate is only the completely indeterminate not-universal. This determination is commonly treated in logic in connection with contradictory notions and it is inculcated as a matter of importance that in the negative of a notion one is to stick to the negative only and it is to be regarded as the merely indeterminate extent of the other of the positive notion. Thus the mere not-white would be just as much red, yellow, blue, etc., as black. But white as such is a notionless determination of intuition; the not of white is then equally notionless not-being, an abstraction that has been considered at the very beginning of the logic, where we learned that its proximate truth is becoming. To employ as examples, when treating of the terms of the judgment, such notionless contents drawn from intuition and pictorial thinking, and to take determinations of being and reflection for terms of the judgment, is the same uncritical procedure as the Kantian application of the notions of the understanding to the infinite Idea of reason or the so-called thing-in-itself; the Notion, which also includes the judgment that proceeds from it, is the veritable thing-in-itself or the rational; those other determinations, however, are proper to being or essence and have not yet been developed into forms which exhibit them as they are in their truth, in the Notion. If we stop at white and red as sensuous images, we are giving, as is commonly done, the name of Notion to what is only a determination of pictorial thinking; in that case the not-white and not-red are of course not positive predicates, just as also the not-triangular is something completely indeterminate, for a determination based on number and quantum is essentially indifferent and notionless. But this kind of sensuous content, like not-being itself, must be conceptually grasped and must lose that indifference and abstract immediacy which it has in blind, static, pictorial thinking. Already in determinate being, the meaningless nothing becomes the limit, through which something does, after all, relate to an other outside it. But in reflection, it is the negative that essentially relates to a positive and hence is determinate; a negative is already no longer that indeterminate not-being; it is posited as existing only in so far as the positive is its counterpart, the third member of the triad being their ground; the negative is thus confined within an enclosed sphere in which, what the one is not, is something determinate. But more than this, in the absolutely fluid continuity of the Notion and its determinations the not is immediately a positive, and the negation is not merely a determinateness but is taken up into the universality and posited as identical with it. The not-universal is therefore immediately the particular.
2. Since the negation affects the relation of the judgment, and we are dealing with the negative judgment still as such, it is in the first place still a judgment; consequently we have here the relationship of subject and predicate, or of individuality and universality, and their relation, the form of the judgment. The subject as the immediate which forms the basis remains unaffected by the negation; it therefore retains its determination of having a predicate, or its relation to the universality. What is negated, therefore, is not the universality as such in the predicate, but the abstraction or determinateness of the latter which appeared as content in contrast to that universality. Thus the negative judgment is not total negation; the universal sphere which contains the predicate still subsists, and therefore the relation of the subject to the predicate is essentially still positive; the still remaining determination of the predicate is just as much a relation. If, for example, it is said that the rose is not red, it is only the determinateness of the predicate that is negated and separated from the universality which likewise belongs to it; the universal sphere, colour, is preserved; in saying that the rose is not red, it is assumed that it has a colour, but a different one. In respect of this universal sphere the judgment is still positive.
The individual is a particular - this positive form of the negative judgment enunciates immediately that the particular contains universality. But in addition it also expresses that the predicate is not merely a universal but also a determinate universal. The negative form implies the same; for though for example the rose is not red, it must not merely retain the universal sphere of colour for predicate but must also have some other specific colour; thus it is only the single determinateness of red that is negated; and not only is the universal sphere left but determinateness, too, is preserved, though converted into an indeterminate or general determinateness, that is, into particularity.
3. The particularity which we have found to be the positive determination of the negative judgment is the mediating term between individuality and universality; thus the negative judgment is now, in general, the mediating term leading to the third step, to the reflection of the judgment of existence into itself. It is, in its objective significance, merely the moment of alteration of the accidents-or, in the sphere of existence, of the isolated properties of the concrete. Through this alteration the complete determinateness of the predicate, or the concrete, emerges as posited.
The individual is particular, according to the positive enunciation of the negative judgment. But the individual is also not a particular, for particularity is of wider extent than individuality; it is therefore a predicate that does not correspond to the subject, and in which, therefore, it does not yet possess its truth. The individual is only an individual, the negativity that relates not to an other whether positive or negative, but only to itself. The rose is not a thing of some colour or other, but has only the specific colour that is rose-colour. The individual is not an undetermined determinate, but the determined determinate.
Starting from this positive form of the negative judgment, this negation of it appears again as only a first negation. But it is not so. On the contrary, the negative judgment is already in and for itself the second negation or the negation of the negation, and what it is in and for itself must be posited. That is to say, it negates the determinateness of the predicate of the positive judgment, the predicate's abstract universality, or, regarded as content, the single quality which the predicate contains of the subject. But the negation of the determinateness is already the second negation, and therefore the infinite return of individuality into itself. With this, therefore, the restoration of the concrete totality has been achieved, or rather, the subject is now for the first time posited as an individual, for through negation and the sublating of the negation it is mediated with itself. The predicate, too, on its side, has herewith passed over from the first universality to absolute determinateness and has equated itself with the subject. Thus the judgment runs: the individual is individual. From the other side, inasmuch as the subject was equally to be taken as universal, and as the predicate (which in contrast to that determination of the subject is the individual) widened itself in the negative judgment into particularity, and as now, further, the negation of this determinateness is no less the purification of the universality contained in the predicate, this judgment also runs: the universal is the universal.
In these two judgments, which we had previously reached by external reflection, the predicate is already expressed in its positivity. But first, the negation of the negative judgment must itself appear in the form of a negative judgment. We saw that in it there still remained a positive relation of the subject to the predicate, and the universal sphere of the latter. From this side, therefore, the negative contained a universality more purged of limitation than the positive judgment, and for that reason must be all the more negated of the subject as an individual. In this manner, the whole extent of the predicate is negated and there is no longer any positive relation between it and the subject. This is the infinite judgment.
(c) The Infinite Judgment
The negative judgment is as little a true judgment as the positive. But the infinite judgment which is supposed to be its truth is, according to its negative expression, negatively infinite, a judgment in which even the form of judgment is set aside. But this is a nonsensical judgment. It is supposed to be a judgment, and consequently to contain a relation of subject and predicate; yet at the same time such a relation is supposed not to be in it. Though the name of the infinite judgment usually appears in the ordinary logics, it is not altogether clear what its nature really is. Examples of negatively infinite judgments are easily obtained: determinations are negatively connected as subject and predicate, one of which not only does not include the determinateness of the other but does not even contain its universal sphere; thus for example spirit is not red, yellow, etc., is not acid, not alkaline, etc., the rose is not an elephant, the understanding is not a table, and the like. These judgments are correct or true, as the expression goes, but in spite of such truth they are nonsensical and absurd. Or rather, they are not judgments at all. A more realistic example of the infinite judgment is the evil action. In civil litigation, something is negated only as the property of the other party, it being conceded that it should be theirs if they had the right to it; and it is only the title of right that is in dispute; the universal sphere of right is therefore recognised and maintained in that negative judgment. But crime is the infinite judgment which negates not merely the particular right, but the universal sphere as well, negates right as right. This infinite judgment does indeed possess correctness, since it is an actual deed, but it is nonsensical because it is related purely negatively to morality which constitutes its universal sphere.
The positive moment of the infinite judgment, of the negation of the negation, is the reflection of individuality into itself, whereby it is posited for the first time as a determinate determinateness. According to that reflection, the expression of the judgment was: the individual is individual. In the judgment of existence, the subject appears as an immediate individual and consequently rather as a mere something in general. It is through the mediation of the negative and infinite judgments that it is for the first time posited as an individual.
The individual is hereby posited as continuing itself into its predicate, which is identical with it; consequently, too, the universality no longer appears as immediate but as a comprehension of distinct terms. The positively infinite judgment equally runs: the universal is universal, and as such is equally posited as the return into itself.
Now through this reflection of the terms of the judgment into themselves the judgment has sublated itself; in the negatively infinite judgment the difference is, so to speak, too great for it to remain a judgment; the subject and predicate have no positive relation whatever to each other; in the positively infinite judgment, on the contrary, only identity is present and owing to the complete lack of difference it is no longer a judgment.
More precisely, it is the judgment of existence that has sublated itself; hereby there is posited what the copula of the judgment contains, namely, that the qualitative extremes are sublated in this their identity. Since however this unity is the Notion, it is immediately sundered again into its extremes and appears as a judgment, whose terms however are no longer immediate but reflected into themselves. The judgment of existence has passed over into the judgment of reflection.
B. THE JUDGMENT OF REFLECTION
In the judgment that has now arisen, the subject is an individual as such; and similarly the universal is no longer an abstract universality or a single property, but is posited as a universal that has gathered itself together into a unity through the relation of distinct terms; or, regarding it from the point of view of the content of various determinations in general, as the taking together of various properties and existences. If examples are to be given of predicates of judgments of reflection, they must be of another kind than for judgments of existence. It is in the judgment of reflection that we first have, strictly speaking, a determinate content, that is, a content as such; for the content is the form determination which is reflected into identity as distinct from the form in so far as this is a distinct determinateness — as it still is in the judgment. In the judgment of existence the content is merely an immediate, or abstract, indeterminate content. The following may therefore serve as examples of judgments of reflection: man is mortal, things are perishable, this thing is useful, harmful; hardness, elasticity of bodies, happiness, etc. are predicates of this peculiar kind. They express an essential determination, but one which is in a relationship or is a unifying universality.
This universality, which will further determine itself in the movement of the judgment of reflection, is still distinct from the universality of the Notion as such; true, it is no longer the abstract universality of the qualitative judgment, but it still possesses a relation to the immediate from which it proceeds and has the latter as the basis of its negativity. The Notion determines the existent, in the first instance, to determinations of relation, to self-continuities in the diverse multiplicity of concrete existence-yet in such a manner that the genuine universal, though it is the inner essence of that multiplicity, is still in the sphere of Appearance, and this relative nature-or even the mark-of this multiplicity is still not the moment of being-in-and-for-self of the latter.
It may suggest itself to define the judgment of reflection as a judgment of quantity, just as the judgment of existence was also defined as qualitative judgment. But just as immediacy in the latter was not merely an immediacy which simply is, but one which was essentially also mediated and abstract, so here, too, that sublated immediacy is not merely sublated quality, and therefore not merely quantity; on the contrary, just as quality is the most external immediacy, so is quantity, in the same way, the most external determination belonging to mediation.
Further, as regards the determination as it appears in its movement in the judgment of reflection, it should be remarked that in the judgment of existence the movement of the determination showed itself in the predicate, because this judgment was in the determination of immediacy and the subject consequently appeared as the basis. For a similar reason, in the judgment of reflection, the onward movement of determining runs its course in the subject, because this judgment has for its determination the reflected in-itself. Here therefore the essential element is the universal or the predicate; hence it constitutes the basis by which, and in accordance with which, the subject is to be measured and determined. However, the predicate also receives a further determination through the further development of the form of the subject; but this occurs indirectly, whereas the development of the subject is, for the reason stated, a direct advance.
As regards the objective signification of the judgment, the individual, through its universality, enters into existence, but in an essential determination of relationship, in an essentiality which maintains itself throughout the multiplicity of the world of Appearance; the subject is supposed to be determinate in and for itself; this determinateness it possesses in its predicate. The individual, on the other hand, is reflected into this its predicate which is its universal essence; the subject is in so far a concrete existence in the world of Appearance. The predicate in this judgment no longer inheres in the subject; it is rather the implicit being under which this individual is subsumed as an accidental. If the judgments of existence may also be defined as judgments of inherence, judgments of reflection are, on the contrary, judgments of subsumption.
(a) The Singular Judgment
Now the immediate judgment of reflection is again, the individual is universal — but with subject and predicate in the stated signification; it can therefore be more precisely expressed as this is an essential universal.
But a 'this' is not an essential universal. This judgment which, as regards its general form, is simply positive, must be taken negatively. But since the judgment of reflection is not merely a positive one, the negation does not directly affect the predicate, which does not inhere but is the in itself. It is the subject rather that is alterable and awaits determination. Here, therefore, the negative judgment must be understood as asserting not a 'this' is a universal of reflection — an in-itself of this kind has a more universal existence than merely in a 'this'. Accordingly, the singular judgment has its proximate truth in the particular judgment.
(b) The Particular Judgment
The non-individuality of the subject, which must be posited instead of its individuality in the first judgment of reflection, is particularity. But individuality is determined in the judgment of reflection as essential individuality; particularity cannot therefore be a simple, abstract determination, in which the individual would be sublated and the concrete existent destroyed, but must be merely an extension of the individual in external reflection. The subject is, therefore, these or a particular number of individuals.
This judgment, that some individuals are a universal of reflection, appears at first as a positive judgment, but it is negative as well; for some contains universality. In this respect it may be regarded as comprehensive; but in so far as it is particularity, it is no less inadequate to that universality. The negative determination which the subject has received through the transition of the singular judgment is, as we have shown above, also a determination of the relation, of the copula. The judgment: some men are happy, involves the immediate consequence that some men are not happy. If some things are useful, then for this very reason some things are not useful. The positive and negative judgments no longer fall apart, but the particular judgment immediately contains both at the same time, just because it is a judgment of reflection. But the particular judgment is, for this reason, indeterminate.
If, in the example of such a judgment, we examine further the subject, some men, animals, etc., we find that it contains besides the particular form-determination some, the content-determination man, etc. The subject of the singular judgment could be expressed by this man, a single individual, which really pertains to an external pointing; it might therefore be better expressed, say, by Gaius. But the subject of the particular judgment can no longer be, some Gaii; for Gaius is supposed to be an individual as such. To the some is therefore added a more universal content, say, men, animals, etc. This is not merely an empirical content, but one determined by the form of the judgment; that is to say, it is a universal, because some contains universality and this must at the same time be separated from the individuals, since reflected individuality forms the basis. More precisely, this universality is also the universal nature or genus man, animal — that universality which is the result of the judgment of reflection, anticipated; just as the positive judgment, in having the individual for subject, anticipated the determination which is the result of the judgment of existence. Thus the subject that contains the individuals, their relation to particularity and the universal nature, is already posited as the totality of the determinations of the Notion. But this is really an external reflection. What is, in the first instance, already posited in the subject by its form, in respect of the mutual relation of these determinations, is the extension of the 'this' to particularity; but this generalisation is not adequate to the 'this'; 'this' is something completely determined, but 'some' is indeterminate. The extension must be appropriate to the 'this' and therefore, in conformity with it, be completely determined; such an extension is totality, or, in the first instance, universality.
This universality has the 'this' as its basis, for the individual here is the individual reflected into itself; its further determinations, therefore, run their course in it externally; and just as particularity for this reason determined itself as some, so the universality which the subject has attained is allness, and the particular judgment has passed over into the universal.
(c) The Universal Judgment
Universality, as it appears in the subject of the universal judgment, is the external universality of reflection, allness; 'all' means all individuals, and in it the individual remains unchanged. This universality is, therefore, only a taking together of independently existing individuals; it is the community of a property which only belongs to them in comparison. It is this community that is usually the first thing that occurs to subjective, unphilosophical thinking when universality is mentioned. It is given as the obvious reason why a determination is to be regarded as universal that it belongs to a number of things. It is mainly this concept of universality, too, that analysis has in mind when, for example, it takes the development of a function in a polynomial to be more universal than its development in a binomial, because the polynomial presents more individual terms than the binomial. The demand that the function should be presented in its universality requires, strictly speaking, a pantonomial, the exhausted infinity; but here the limitation of this demand becomes apparent, and the representation of the infinite number of terms has to content itself with its ought, and therefore also with a polynomial. But in fact the binomial is already the pantonomial in those cases where the method or rule affects only the dependence of one term on another, and the dependence of several terms on their predecessors does not particularise itself, but one and the same function remains the base. The method or rule is to be regarded as the genuine universal; in the progress of the development or in the development of a polynomial the rule is merely repeated; so that it gains nothing in universality through the increased number of the terms. We have already in an earlier chapter spoken of the spurious infinity and its illusory nature; the universality of the Notion is the reached beyond; the spurious infinity remains afflicted with the beyond as an unattainable goal, for it remains the mere progress to infinity. When universality is pictured merely as allness, a universality which is supposed to be exhausted in the individuals as individuals, then this is a relapse into that spurious infinity; or else mere plurality is taken for allness. Plurality, however, no matter how great, remains unalterably mere plurality, and is not allness. But there is, here, a vague awareness of the true universality of the Notion; it is the Notion that forces its way beyond the stubborn individuality to which unphilosophical thinking clings and beyond the externality of its reflection, substituting allness as totality, or rather that being which is categorically in and for itself.
This is apparent, too, in allness which is in general the empirical universality. Inasmuch as the individual as an immediate is presupposed and therefore already given and externally adopted, the reflection which gathers it into allness is equally external. But because the individual as 'this', is absolutely indifferent to this reflection, the universality and an individual of this kind cannot combine to form a unity. For this reason, this empirical allness remains a task, something which ought to be done and which cannot therefore be represented as being. Now an empirically universal proposition — for nevertheless such are advanced — rests on the tacit agreement that if only no contrary instance can be adduced, the plurality of cases shall count as allness; or, that subjective allness, namely, those cases which have come to our knowledge, may be taken for an objective allness.
Now a closer examination of the universal judgment now before us, reveals that the subject, which, as previously remarked, contains the true universality as presupposed, now also contains it as posited in it. All men expresses first, the genus man, secondly this genus as sundered into individuals, but so that the individuals are at the same time extended to the universality of the genus; conversely, the universality through this connection with individuality is just as completely determined as the individuality; thus the posited universality has been equated with the presupposed.
Strictly speaking, however, we should not anticipate what is presupposed, but should consider the result in the form determination on its own. Individuality, through this extension of itself to allness, is posited as negativity, which is identical self-relation. It has not therefore remained that first individuality, that for example of Gaius, but is the determination that is identical with universality, or is the absolutely determined being of the universal. That first individuality of the individual judgment was not the immediate one of the positive judgment, but came into being through the dialectical movement of the judgment of existence as such; it was already determined as the negative identity of the terms of that judgment. This is the true presupposition in the judgment of reflection; in contrast to the positing which runs its course in that judgment, that first determinateness of individuality was the latter's in-itself; thus, what individuality is in itself, is now, through the movement of the judgment of reflection, posited, namely, individuality as identical self-relation of the determinate. Therefore this reflection, which extends individuality to allness, is not external to it; on the contrary, this reflection merely makes explicit what it already is in itself. Hence the result is in truth objective universality. The subject has thus stripped off the form determination of the judgment of reflection which passed from this through some to allness; instead of all men we have now to say man.
The universality which has hereby come into being is the genus — the universality which is in its own self a concrete. The genus does not inhere in the subject; it is not a single property, or a property at all, of the subject; it contains all the single determinatenesses dissolved in its substantial solidity. In virtue of the fact that it is posited as this negative identity with itself, it is essentially a subject, but it is no longer subsumed in its predicate. In consequence, the nature of the judgment of reflection is altogether changed.
That judgment was essentially a judgment of subsumption. The predicate was determined, in contrast to its subject, as the implicit universal; according to its content, it could be taken as an essential determination of relation, or also as a mark — a determination which makes the subject merely an essential Appearance. But when the predicate is determined to objective universality, it ceases to be subsumed under such a determination of relation, or comprehensive reflection; on the contrary, such a predicate in contrast to this universality is a particular. The relationship of subject and predicate has therefore become inverted and hence the judgment has, first of all, sublated itself.
This sublation of the judgment coincides with the advance in the determination of the copula, which we have still to consider; the sublation of the terms of the judgment is the same thing as their transition into the copula. In other words, the subject, in raising itself to universality has, in this determination become equated with the predicate, which as reflected universality also contains particularity within itself; subject and predicate are therefore identical, that is they have coalesced into the copula. This identity is the genus or absolute nature of a thing. In so far, therefore, as this identity again sunders itself into a judgment it is the inner nature through which subject and predicate are related to one another — a relation of necessity in which these terms of the judgment are only unessential differences. What belongs to all the individuals of a genus belongs to the genus by its nature, is an immediate consequence and the expression of what we have seen, that the subject, for example all men, strips off its form determination, and man is to take its place. This intrinsic and explicit connection constitutes the basis of a new judgment, the judgment of necessity.
C. THE JUDGMENT OF NECESSITY
The determination to which universality has advanced is, as we have seen, the universality which is in and for itself or objective, to which in the sphere of essence substantiality corresponds. It is distinguished from the latter in that it belongs to the Notion and is therefore not merely the inner but also the posited necessity of its determinations; or, in other words, the difference is immanent in it, whereas substance has its difference only in its accidents, but not as principle within itself.
Now in the judgment, this objective universality is posited; first, therefore, with this its essential determinateness as immanent in it, secondly, with its determinateness distinguished from it as particularity, of which this universality constitutes the substantial basis. In this way it is determined as genus and species.
(a) The Categorical Judgment
The genus essentially sunders itself, or repels itself into species; it is genus only in so far as it comprehends species under itself; the species is species only in so far as on the one hand it exists in the individuals, and on the other hand is in the genus a higher universality. Now the categorical judgment has such a universality for its predicate, a predicate in which the subject possesses its immanent nature. But the categorical judgment is itself the first or immediate judgment of necessity; accordingly the determinateness of the subject whereby it is a particular or individual over against the genus or species, so far belongs to the immediacy of external existence. But objective universality, too, has here as yet only its immediate particularisation; hence it is on the one hand itself a determinate universality in contrast to which there are higher genera; on the other hand, it is not exactly the proximate genus, that is, its determinateness is not exactly the principle of the specific particularity of the subject. But what is necessary in it is the substantial identity of the subject and predicate, contrasted with which that property of the subject which distinguishes it from the predicate is only an unessential positedness, or even merely a name; the subject is reflected in its predicate into its being-in-and-for-self. A predicate of this kind should not be classed with the predicates of the preceding judgments; to throw, for example, the judgments
The rose is red,
The rose is a plant, or
This ring is yellow,
It is gold,
into the one class, and to regard such an external property as the colour of a flower as a predicate on the same level as its vegetable nature, is to overlook a difference which must strike the meanest intelligence. The categorical judgment must therefore be definitely distinguished from the positive and negative judgments; in the latter, what is predicated of the subject is a single contingent content; in the former, the content is the totality of the form reflected into itself. Here therefore the copula has the meaning of necessity, whereas in the others it merely signifies abstract, immediate being.
The determinateness of the subject, which makes it a particular in contrast to the predicate, is in the first instance something contingent; subject and predicate are not necessarily related by the form or determinateness; the necessity is, therefore, still an inner necessity. But the subject is subject only as a particular, and in so far as it possesses objective universality it must possess it essentially in accordance with that primarily immediate determinateness. The objective universal in determining itself, that is in positing itself in the judgment, is essentially in an identical relation with this expelled determinateness as such, that is, it is essential that the determinateness is not posited as a mere contingency. It is only through this necessity of its immediate being that the categorical judgment conforms to its objective universality and in this way it has passed over into the hypothetical judgment.
(b) The Hypothetical Judgment
If A is, then B is; or, the being of A is not its own being, but the being of another, of B. What is posited in this judgment is the necessary connection of immediate determinatenesses, a connection which is not yet posited in the categorical judgment. There are here two immediate Existences or external contingencies, of which in the categorical judgment there is at first only one, the subject; but since one is external to the other, this other is also external to the first. In accordance with this immediacy, the content of the two sides is still mutually indifferent; hence this judgment is in the first instance a proposition of empty form. Now in the first place the immediacy is indeed as such a self-subsistent, concrete being; but secondly, the relation of this being is the essential point; therefore this being is just as much a mere possibility; the hypothetical judgment involves, not that A is or that B is, but only that if one is, then the other is; only the connection of the extremes is posited as being, not the extremes themselves. On the contrary, in this necessity each extreme is posited as equally the being of an other. The principle of identity affirms that A is only A, not B; and that B is only B, not A; in the hypothetical judgment, on the contrary, the being of finite things is posited by the Notion in accordance with their formal truth, namely that the finite is its own being, but equally is not its own being, but that of an other. In the sphere of being, the finite alters and becomes an other; in the sphere of essence it is Appearance, and being is posited as consisting in the reflection of an other in it, and necessity is the inner relation, not yet posited as such. But the Notion is the positing of this identity so that what is, is not an abstract self-identity but a concrete identity and is immediately in its own self the being of an other.
By employing reflective relationships, the hypothetical judgment can be more precisely characterised as a relationship of ground and consequent, condition and conditioned, causality, etc.
Just as in the categorical judgment substantiality appeared in the form of its Notion, so, too, does the nexus of causality in the hypothetical judgment. This and the other relationships all come under the hypothetical judgment; but here they are no longer relationships of self-subsistent sides, but these sides are essentially only moments of one and the same identity. However, in the hypothetical judgment they are not yet opposed as Notion determinations, as individual or particular to universal, but at first only as moments in general. Thus the hypothetical judgment has rather the shape of a proposition; just as the particular judgment has an indeterminate content, so the hypothetical is indeterminate in form, since its content is not determined as a relationship of subject to predicate. Yet since the being is the being of an other, for that very reason it is in itself a unity of itself and its other, and consequently universality; at the same time it is, strictly speaking, only a particular, for it is a determinate and in its determinateness is not purely self-related. But it is not the simple, abstract particularity that is posited; on the contrary, through the immediacy which the determinatenesses possess, the moments of the particularity are distinguished; at the same time, through the unity of the moments which constitutes their relation, the particularity is also their totality. What therefore is truly posited in this judgment is universality as the concrete identity of the Notion, whose determinations have no subsistence of their own but are only particularities posited in that identity. As such, it is the disjunctive judgment.
(c) The Disjunctive Judgment
In the categorical judgment, the Notion is objective universality and an external individuality. In the hypothetical judgment, the Notion in its negative identity emerges in this externality. Through this identity, its moments receive the same determinateness, now posited in the disjunctive judgment, that they possess immediately in the hypothetical judgment. Hence the disjunctive judgment is objective universality posited at the same time in union with the form. It therefore contains first concrete universality or the genus in simple form as the subject, and secondly the same universality but as totality of its distinct determinations. A is either B or C. This is the necessity of the Notion, in which first the identity of the two extremes is one and the same extent, content and universality; secondly they are distinguished according to the form of the Notion-determinations, but in such a manner that, by reason of that identity, this distinction is a mere form. Thirdly, the identical objective universality appears for that reason as the determination that is reflected into itself in contrast to the unessential form, that is, as the content, but a content which possesses within itself the determinateness of form, once as the simple determinateness of the genus, and again, this same determinateness developed into its difference-in which way it is the particularity of the species and their totality, the universality of the genus. The particularity in its development constitutes the predicate, for it is the more universal in so far as it embraces the entire universal sphere of the subject, and this too in its detailed particularisation.
A closer examination of this particularisation shows first of all that the genus constitutes the substantial universality of the species; the subject is therefore both B and C; this both-and denotes the positive identity of the particular with the universal; this objective universal completely maintains itself in its particularity. Secondly, the species mutually exclude one another; A is either B or C; for they are the specific difference of the universal sphere. This either-or is their negative relation. Yet in this they are just as identical as in their positive relation; the genus is their unity as determinate particulars. If the genus were an abstract universality as in the judgments of existence, the species would also have to be taken as only diverse and mutually indifferent; but it is not that external universality which results merely from comparison and omission but is the immanent and concrete universality of the species. An empirical disjunctive judgment lacks necessity; A is either B or C or D, etc., because the species B, C and D, etc., have already been given; strictly speaking, this cannot give us an either-or, for species of this kind constitute, as it were, a merely subjective completeness; true, one species excludes the other; but either-or excludes every further species and shuts off within itself a total sphere. This totality has its necessity in the negative unity of the objective universal, which dissolves individuality within itself and possesses it as a simple principle of difference immanent in it by which the species are determined and related. Empirical species, on the contrary, have their differences in some contingency or other which is an external principle and therefore not their principle, and consequently also not the immanent determinateness of the genus; for this reason they are also not related to one another according to their determinateness. But it is through the relation of their determinateness that the species constitute the universality of the predicate. It is here really that the so-called contrary and contradictory notions should first find their place; for in the disjunctive judgment is posited the essential difference of the Notion; but in it they at the same time also possess their truth, namely, that the contrary and contradictory themselves are each distinguished as contrary and contradictory. Species are contrary in so far as they are merely diverse, that is to say in so far as they possess through the genus as their objective nature an existence that is in and for itself; they are contradictory in so far as they exclude one another. But each of these determinations by itself is one-sided and lacks truth; in the either-or of the disjunctive judgment their unity is posited as their truth, in accordance with which the species' self-subsistent existence as concrete universality is itself also the principle of the negative unity whereby they mutually exclude one another.
By the just demonstrated identity of subject and predicate in accordance with the negative unity, the genus in the disjunctive judgment is determined as the proximate genus. This expression indicates in the first place, a mere quantitative difference of more or less-determinations possessed by a universal in relation to a particularity coming under it. From this point of view, it remains contingent what is properly the proximate genus. In so far, however, as the genus is taken as a universal formed merely by the omission of determinations, it cannot really form a disjunctive judgment; for it is contingent whether it has retained the determinateness which constitutes the principle of the either-or; the genus would not be exhibited at all in the species according to its determinateness, and the species could only possess a contingent completeness. In the categorical judgment, the genus is at first only in this abstract form over against the subject, and therefore not necessarily the proximate genus to it and is so far external. But when the genus is a concrete, essentially determinate universality, then it is, as a simple determinateness, the unity of the moments of the Notion, which in this simplicity are only sublated, but have their real difference in the species. Accordingly, a genus is the proximate genus of a species in so far as the latter has its specific difference in the essential determinateness of the genus, and the species as a whole are differentiated by a principle that lies in the nature of the genus.
The aspect just considered constitutes the identity of subject and predicate from the aspect of their determinedness in general, an aspect which has been posited by the hypothetical judgment, whose necessity is an identity of immediate and diverse things and therefore essentially a negative unity. It is this negative unity in general that separates subject and predicate, but now it is itself posited as differentiated-in the subject as a simple determinateness, in the predicate as totality. This separation of subject and predicate is the difference of the Notion; and thus the totality of the species in the predicate cannot be any other difference. The reciprocal determination of the disjunctive terms is therefore given by this. It reduces to the difference of the Notion, for it is this alone that disjoins itself and in its determination reveals its negative unity. However, the species is considered here only in respect of its simple Notion determinateness, not in respect of the shape in which it has come forth from the Idea into a further self-subsistent reality; this latter is indeed dropped in the simple principle of the genus; but the essential distinction must be a moment of the Notion. In the judgment here considered, it is really the Notion's own progressive determination that now posits its disjunction; the same thing that we found, when considering the Notion, to be its essential and explicit determination, its differentiation into determinate Notions. Now because the Notion is the universal, both the positive and the negative totality of the particulars, it is itself for that very reason also immediately one of its disjunctive members; the other, however, is this universality resolved into its particularity, or the determinateness of the Notion as determinateness, that determinateness in which the universality exhibits itself as totality. If the disjunction of a genus into species has not yet attained this form, this is a proof that it has not risen to the determinateness of the Notion and has not proceeded from the Notion. Colour is either violet, indigo, blue, green, yellow, orange or red; even the empirical confusion and impurity of such a disjunction is at once apparent; just from this aspect alone it must be termed barbarous. When colour has been grasped as the concrete unity of light and dark, then this genus contains within it the determinateness which constitutes the principle of its particularisation into species. But of these species, one must be the utterly simple colour which contains the opposition in equipoise and confined and negated in the colour's intensity; over against this there must be presented the opposition of the relationship between light and dark, to which must be added, since a natural phenomenon is involved, the indifferent neutrality of the opposition. When mixtures such as violet and orange, and differences of degree, such as blue and light blue, are taken for species, this can only result from a completely thoughtless procedure that shows too little reflection even for empiricism. But this is not the place to discuss what further distinct and more precisely determined forms disjunction may have, according as they occur in the element of Nature or of spirit.
In the first instance, the disjunctive judgment has the members of the disjunction in its predicate; but it is itself no less disjoined; its subject and predicate are the members of the disjunction. They are the moments of the Notion, posited in their determinateness but at the same time as identical; identical (a) in the objective universality which, in the subject is the simple genus, and in the predicate is the universal sphere and the totality of the moments of the Notion, and (b) in the negative unity, in the developed connection of necessity, in accordance with which the simple determinateness in the subject is sundered into the difference of the species, and in this very difference is their essential relation and self-identity.
This unity, the copula of this judgment into which the extremes have coalesced through their identity, is therefore the Notion itself, and the Notion, too, as posited; the mere judgment of necessity has thereby risen into the judgment of the Notion.
D. THE JUDGMENT OF THE NOTION
The ability to form judgments of existence such as 'the rose is red', 'snow is white', and so forth, will hardly count as evidence of great powers of judgment. The judgments of reflection are rather propositions; in the judgment of necessity the object appears, it is true, in its objective universality, but it is only in the judgment now to be considered that its relation to the Notion is found. In this judgment the Notion is laid down as the basis, and since it is in relation to the object, it is an ought-to-be to which the reality may or may not be adequate. Therefore it is only a judgment of this kind that contains a true appreciation; the predicates good, bad, true, beautiful, correct, etc. express that the thing is measured against its universal Notion as the simply presupposed ought-to-be and is, or is not, in agreement with it.
The judgment of the Notion has been called the judgment of modality and it has been regarded as containing that form of the relationship between subject and predicate which is found in an external understanding, and to be concerned with the value of the copula only in relation to thinking.
According to this view, the problematical judgment is one where the affirmation or denial is taken as optional or possible; the assertoric, where it is taken as true, that is as actual; and the apodeictic, where it is taken as necessary. It is easy to see why it is so natural in the case of this judgment to step out of the sphere of judgment itself and to regard its determination as something merely subjective. For here it is the Notion, or the subjective, that reappears in the judgment and stands in relationship to an external actuality. But this subjectivity is not to be confused with external reflection, which of course is also something subjective, but in a different sense from the Notion itself; on the contrary, the Notion that re-emerges from the disjunctive judgment is the opposite of a mere contingent mode. The earlier judgments are in this sense merely subjective, for they are based on an abstraction and one-sidedness in which the Notion is lost. The judgment of the Notion, on the contrary, is objective and the truth as against those earlier judgments, just because it has for its basis the Notion, not the Notion in external reflection or in relation to a subjective, that is contingent, thinking, but the Notion in its determinateness as Notion.
In the disjunctive judgment the Notion was posited as identity of the universal nature with its particularisation; consequently the relation of the judgment was cancelled. This concretion of universality and particularisation is, at first, a simple result; it has now to develop itself further into totality, since the moments which it contains are at first swallowed up in it and as yet do not confront one another in determinate self-subsistence. The defect of the result may also be more definitely expressed by saying that in the disjunctive judgment, although objective universality has completed itself in its particularisation, yet the negative unity of the latter merely returns into the former and has not yet determined itself to the third moment, that of individuality. Yet in so far as the result itself is negative unity, it is indeed already this individuality; but as such it is only this one determinateness, which has now to posit its negativity, sunder itself into the extremes and in this way finally develop into the syllogism.
The proximate diremption of this unity is the judgment in which it is posited first as subject, as an immediate individual, and then as predicate, as the determinate relation of its moments.
(a) The Assertoric Judgment
The judgment of the Notion is at first immediate; as such it is the assertoric judgment. The subject is a concrete individual in general, and the predicate expresses this same as the relation of its actuality, determinateness, or constitution to its Notion. (This house is bad, this action is good.) More precisely, therefore, it involves (a) that the subject ought to be something; its universal nature has posited itself as the self-subsistent Notion; and (b) particularity which, not only on account of its immediacy but also on account of its express differentiation from its self-subsistent universal nature, appears as an external existence with such and such a constitution; this, on its side, because of the Notion's self-subsistence, is also indifferent to the universal and may or may not conform to it. This constitution is the individuality, which lies beyond the necessary determination of the universal in the disjunctive judgment, a determination which only appears as the particularisation of the species and as the negative principle of the genus. Thus the concrete universality which has emerged from the disjunctive judgment is sundered in the assertoric judgment into the form of extremes, to which the Notion itself as the posited unity that relates them is still lacking.
For this reason the judgment is so far merely assertoric; the verification is a subjective assurance. The fact that something is good or bad, correct, suitable or not, is connected with an external third factor. But the fact that the connection is externally posited means that it is, at first, only implicit or internal. When therefore something is good or bad, etc. no one will suppose that it is, say, good only in subjective consciousness but perhaps bad in itself, or that good and bad, correct, suitable, etc., are not predicates of the objects themselves. The merely subjective element in the assertion of this judgment consists therefore in the fact that the implicit connection of subject and predicate is not yet posited, or, what is the same thing, that it is only external; the copula is still an immediate, abstract being.
Accordingly, the assurance of the assertoric judgment is confronted with equal right by its contradictory. When one is assured that 'this action is good', then the opposite assurance that 'this action is bad', is equally justified. Or, considering the judgment in itself, because the subject of the judgment is an immediate individual, in this abstraction it does not as yet possess posited within it the determinateness that should contain its relation to the universal Notion; thus the subject is still something contingent which may or may not conform to the Notion. The judgment is therefore essentially problematic.
(b) The Problematic Judgment
The problematic judgment is the assertoric in so far as the latter must be taken both positively and negatively. From this qualitative side, the particular judgment is likewise a problematic one, for it is equally valid positively and negatively; similarly, in the hypothetical judgment, the being of the subject and predicate is problematic; also, it is posited by the particular and hypothetical judgments that the individual and the categorical judgments are as yet merely subjective. But in the problematic judgment as such this positing is more immanent than in the judgments just mentioned, because in it the content of the predicate is the relation of the subject to the Notion, and here, therefore, the determination of the immediate as something contingent is itself given.
At first, it appears only problematic whether the predicate is to be coupled with a certain subject or not, and so far the indeterminateness falls in the copula. From this, no determination can emerge for the predicate, for this is already the objective, concrete universality. The problematic element, therefore, concerns the immediacy of the subject which is hereby determined as a contingency. But further, we must not for that reason abstract from the individuality of the subject; if this latter were purged of its individuality altogether, it would be merely a universal; the predicate contains just this, that the Notion of the subject is to be posited in relation to its individuality. We cannot say: the house or a house is good, but: according to its constitution. The problematic element in the subject itself constitutes its moment of contingency, the subjectivity of the thing over against its objective nature or its Notion, its merely contingent mode or its constitution.
Hence the subject itself is differentiated into its universality or objective nature, what it ought to be, and the particular constitution of its existence. Thus it contains the ground of its being or not being what it ought to be. In this way, it is equated with the predicate. The negativity of the problematic element, in so far as it is directed against the immediacy of the subject, accordingly means only this original partition of the subject which is already in itself the unity of the universal and particular, into these its moments-a partition which is the judgment itself.
It may further be remarked that each of the two sides of the subject, its Notion and its constitution, could be called its subjectivity. The Notion is the universal essence of a thing or a fact [Sache] withdrawn into itself, its negative unity with itself; this constitutes its subjectivity. But a thing is also essentially contingent and has an external constitution; this may equally be called the mere subjectivity of the thing in contrast to the other side, its objectivity. The thing itself is just this, that its Notion, as the negative of itself, negates its universality and projects itself into the externality of individuality. The subject of the judgment is here posited as this duality; those opposite significations of subjectivity are, in accordance with their truth, brought into a unity. The signification of the subjective element has itself become problematic by reason of its having lost the immediate determinateness which it possessed in the immediate judgment, and its determinate opposition to the predicate. This opposite signification of subjective which occurs even in the ratiocination of ordinary reflection might of itself at least draw attention to the fact that subjectivity in one of these significations alone, has no truth. The twofold signification is the manifestation of this truth that each by itself is one-sided.
When the problematic element is thus posited as the problematic element of the thing, as the thing with its constitution, then the judgment itself is no longer problematic, but apodeictic.
(c) The Apodeictic Judgment
The subject of the apodeictic judgment (the house constituted so and so is good, the action constituted so and so is right) has within it, first, the universal, what it ought to be, and secondly, its constitution; this latter contains the ground why a predicate of the Notion judgement applies or does not apply to the whole subject, that is, whether the subject corresponds to its Notion or not.
This judgment, then, is truly objective; or it is the truth of the judgment in general. Subject and predicate correspond to each other and have the same content, and this content is itself the posited concrete universality; it contains, namely, the two moments, the objective universal or the genus, and the individualised universal. Here, therefore, we have the universal which is itself and continues itself through its opposite and is a universal only as unity with this opposite. A universal of this kind, such as the predicate good, suitable, correct, etc., is based on an ought-to-be and at the same time contains the correspondence of existence to that ought-to-be; it is not this ought-to-be or the genus by itself, but this correspondence that is the universality which constitutes the predicate of the apodeictic judgment.
The subject likewise contains these two moments in immediate unity as the fact. But it is the truth of the fact that it is internally split into what it ought-to-be and what it is; this is the absolute judgment on all actuality. It is because this original partition, which is the omnipotence of the Notion, is just as much a return into its unity and an absolute relation of the ought-to-be and being to each other that makes what is actual into a fact; its inner relation, this concrete identity, constitutes the soul of the fact.
The transition from the immediate simplicity of the fact to the correspondence which is the determinate relation of its ought-to-be and its being — or the copula — is now seen, on closer examination, to lie in the particular determinateness of the fact. The genus is the universal in and for itself, which as such appears as the unrelated; while the determinateness is that which in that universal is reflected into itself, yet at the same time is reflected into an other. The judgment therefore has its ground in the constitution of the subject and thereby is apodeictic. Hence we now have before us the determinate and fulfilled copula, which formerly consisted in the abstract 'is', but has now further developed itself into ground in general. It appears at first as an immediate determinateness in the subject, but it is no less the relation to the predicate which has no other content than this very correspondence, or the relation of the subject to the universality.
Thus the form of the judgment has perished; first because subject and predicate are in themselves the same content; secondly because the subject through its determinateness points beyond itself and relates itself to the predicate; but also, thirdly, this relating has passed over into the predicate, alone. constitutes its content, and is thus the posited relation, or the judgment itself. Thus the concrete identity of the Notion which was the result of the disjunctive judgment and which constitutes the inner basis of the Notion judgment — which identity was at first posited only in the predicate — is now restored in the whole.
If we examine the positive element of this result which effects the transition of the judgment into another form, we find, as we have seen, that subject and predicate in the apodeictic judgment are each the whole Notion. The unity of the Notion as the determinateness constituting the copula that relates them, is at the same time distinct from them. At first, it stands only on the other side of the subject as the latter's immediate constitution. But since it is essentially that which relates subject and predicate, it is not merely such immediate constitution but the universal that permeates both subject and predicate. While subject and predicate have the same content, the form relation, on the other hand, is posited through this determinateness, determinateness as a universal or particularity. Thus it contains within itself the two form determinations of the extremes and is the determinate relation of subject and predicate; it is the fulfilled copula of the judgment, the copula pregnant with content, the unity of the Notion that has re-emerged from the judgment in which it was lost in the extremes. Through this impregnation of the copula the judgment has become the syllogism.
Chapter 3 The Syllogism
We have found the syllogism to be the restoration of the Notion in the judgment, and consequently the unity and truth of both. The Notion as such holds its moments sublated in unity; in the judgment this unity is internal or, what is the same thing, external; and the moments, although related, are posited as self-subsistent extremes. In the syllogism the Notion determinations are like the extremes of the judgment, and at the same time their determinate unity is posited.
Thus the syllogism is the completely posited Notion; it is therefore the rational. The understanding is regarded as the faculty of the determinate Notion which is held fast in isolation by abstraction and the form of universality. But in reason the determinate Notions are posited in their totality and unity. Therefore, not only is the syllogism rational, but everything rational is a syllogism. The syllogistic process has for a long time been ascribed to reason; yet on the other hand reason in and for itself, rational principles and laws, are spoken of in such a way that it is not clear what is the connection between the former reason which syllogises and the latter reason which is the source of laws and other eternal truths and absolute thoughts. If the former is supposed to be merely formal reason, while the latter is supposed to be creative of content, then according to this distinction it is precisely the form of reason, the syllogism, that must not be lacking in the latter. Nevertheless, to such a degree are the two commonly held apart, and not mentioned together, that it seems as though the reason of absolute thoughts was ashamed of the reason of the syllogism and as though it was only in deference to tradition that the syllogism was also adduced as an activity of reason. Yet it is obvious, as we have just remarked, that the logical reason, if it is regarded as formal reason, must essentially be recognisable also in the reason that is concerned with a content; the fact is that no content can be rational except through the rational form. In this matter we cannot look for any help in the common chatter about reason; for this refrains from stating what is to be understood by reason; this supposedly rational cognition is mostly so busy with its objects that it forgets to cognise reason itself and only distinguishes and characterises it by the objects that it possesses. If reason is supposed to be the cognition that knows about God, freedom, right and duty, the infinite, unconditioned, supersensuous, or even gives only ideas and feelings of these objects, then for one thing these latter are only negative objects, and for another thing the first question still remains, what it is in all these objects that makes them rational. It is this, that the infinitude of these objects is not the empty abstraction from the finite, not the universality that lacks content and determinateness, but the universality that is fulfilled or realised, the Notion that is determinate and possesses its determinateness in this true way, namely, that it differentiates itself within itself and is the unity of these fixed and determinate differences. It is only thus that reason rises above the finite, conditioned, sensuous, call it what you will, and in this negativity is essentially pregnant with content, for it is the unity of determinate extremes; as such, however, the rational is nothing but the syllogism.
Now the syllogism, like the judgment, is in the first instance immediate; hence its determinations are simple, abstract determinatenesses; in this form it is the syllogism of the understanding. If we stop short at this form of the syllogism, then the rationality in it, although undoubtedly present and posited, is not apparent. The essential feature of the syllogism is the unity of the extremes, the middle term which unites them, and the ground which supports them. Abstraction, in holding rigidly to the self-subsistence of the extremes, opposes this unity to them as a determinateness which likewise is fixed and self-subsistent, and in this way apprehends it rather as non-unity than as unity. The expression middle term is taken from spatial representation and contributes its share to the stopping short at the mutual externality of the terms. Now if the syllogism consists in the unity of the extremes being posited in it, and if, all the same, this unity is simply taken on the one hand as a particular on its own, and on the other hand as a merely external relation, and non-unity is made the essential relationship of the syllogism, then the reason which constitutes the syllogism contributes nothing to rationality.
First, the syllogism of existence in which the terms are thus immediately and abstractly determined, demonstrates in itself (since, like the judgment, it is their relation) that they are not in fact such abstract terms, but that each contains the relation to the other and that the middle term is not particularity as opposed to the determinations of the extremes but contains these terms posited in it.
Through this its dialectic it is converted into the syllogism of reflection, into the second syllogism. The terms of this are such that each essentially shows in, or is reflected into, the other; in other words they are posited as mediated, which they are supposed to be in accordance with the nature of the syllogism in general.
Thirdly, in that this reflecting or mediatedness of the extremes is reflected into itself, the syllogism is determined as the syllogism of necessity, in which the mediating element is the objective nature of the thing. As this syllogism determines the extremes of the Notion equally as totalities, the syllogism has attained to the correspondence of its Notion or the middle term, and its existence of the difference of its extremes; that is, it has attained to its truth and in doing so has passed out of subjectivity into objectivity.
A.The Syllogism of Existence
1. The syllogism in its immediate form has for its moments the determinations of the Notion as immediate. Hence they are the abstract determinatenesses of form, which are not yet developed by mediation into concretion, but are only single determinatenesses. The first syllogism is, therefore, strictly the formal syllogism. The formalism of the syllogising process consists in stopping short at the determination of this first syllogism. The Notion, differentiated into its abstract moments, has individuality and universality for its extremes, and appears itself as the particularity standing between them. On account of their immediacy they are merely self-related determinatenesses, and one and all a single content. Particularity constitutes the middle term in the first instance since it unites immediately within itself the two moments of individuality and universality. On account of its determinateness it is on the one hand subsumed under the universal, while on the other hand the individual, as against which it possesses universality, is subsumed under it. But this concretion is in the first instance merely a duality of aspect; on account of the immediacy in which the middle term presents itself in the immediate syllogism. it appears as a simple determinateness, and the mediation which it constitutes is not yet posited. Now the dialectical movement of the syllogism of existence consists in the positing in its moments of the mediation that alone constitutes the syllogism.
(a) First Figure of the Syllogism
1. I-P-U is the general schema of the determinate syllogism. Individuality unites with universality through particularity; the individual is not universal immediately, but through the medium of particularity; and conversely the universal similarly is not immediately individual but descends to individuality through particularity. These determinations confront each other as extremes and are united in a different third term. Each is determinateness; in this they are identical; this their general determinateness is particularity. But they are no less extremes against this particularity than against each other, because each is present in its immediate determinateness.
The general significance of this syllogism is that the individual, which as such is infinite self-relation and therefore would be merely inward, emerges by means of particularity into existence as into universality, in which it no longer belongs merely to itself but stands in an external relationship; conversely the individual, in separating itself into its determinateness as a particularity, is in this separation a concrete individual and, as the relation of the determinateness to itself, a universal, self-related individual, and consequently is also truly an individual; in the extreme of universality it has withdrawn from externality into itself. In the first syllogism, the syllogism's objective significance is only superficially present, since in it the determinations are not yet posited as the unity which constitutes the essence of the syllogism. It is still subjective in so far as the abstract significance possessed by its terms is not thus isolated in and for itself but only in subjective consciousness. Moreover, the relationship of individuality, particularity and universality is as we have seen the necessary and essential form-relationship of the determinations of the syllogism; the defect consists not in this determinateness of the form, but in the fact that under this form each single determination is not at the same time richer. Aristotle has confined himself rather to the mere relationship of inherence, in stating the nature of the syllogism as follows: When three terms are related to one another in such a manner that one extreme is in the whole of the middle term and this middle term is in the whole of the other extreme, then these two extremes are necessarily united in a conclusion. What is expressed here is more the mere repetition of the like relationship of inherence between one extreme to the middle term, and again between the middle term and the other extreme, than the determinateness of the three terms to one another. Now since the syllogism rests on the stated relative determinateness of the terms, it is immediately evident that other relationships of the terms which are given by the other figures can only have validity as syllogisms of the understanding [Verstandesschlusse] in so far as they can be reduced to that original relationship; they are not different species of figures which stand alongside the first; on the contrary, on the one hand, in so far as they purport to be correct syllogisms, they rest solely on the essential form of the syllogism in general, which is the first figure; on the other hand, in so far as they deviate from it they are transformations into which that first abstract form necessarily passes, thereby further determining itself and advancing to totality. We shall presently see what this process is.
I-P-U is thus the general schema of the syllogism in its determinateness. The individual is subsumed under the particular, and the latter under the universal; therefore the individual too is subsumed under the universal. Or the particular inheres in the individual and the universal in the particular; therefore the universal also inheres in the individual. From one aspect, namely, in relation to the universal, the particular is subject; in relation to the individual it is predicate; or, in relation to the former it is an individual, in relation to the latter it is a universal. Because the two determinatenesses are united in it, the extremes are linked together by this their unity. The therefore appears as the conclusion that has taken place in the subject, a conclusion deduced from subjective insight into the relationship between the two immediate premises. As subjective reflection enunciates the two relations of the middle term to the extremes as particular and indeed immediate judgments or propositions, the conclusion as the mediated relation is also, of course, a particular proposition, and the consequently or therefore is the expression of the fact that it is the mediated one. But this therefore is not to be regarded as an external determination in this proposition, as if it had its ground and seat only in subjective reflection; on the contrary, it is grounded in the nature of the extremes themselves whose relation again is expressed as a mere judgment or proposition only for the purpose of, and by means of, abstractive reflection, but whose true relation is posited as the middle term. That therefore I is U is a judgment, is a merely subjective circumstance; the very meaning of the syllogism is that this is not merely a judgment, that is, not a relation effected by the mere copula or the empty is, but one effected by the determinate middle term which is pregnant with content.
Consequently, to regard the syllogism merely as consisting of three judgments, is a formal view that ignores the relationship of the terms on which hinges the sole interest of the syllogism. It is altogether a merely subjective reflection that splits the relation of the terms into separate premises and a conclusion distinct from them:
All men are mortal,
Gaius is a man,
Therefore he is mortal.
At the approach of this kind of syllogism we are at once seized with a feeling of boredom; this stems from that unprofitable form which by means of the separate propositions presents a semblance of difference that immediately dissolves in the fact itself. It is mainly this subjective shape that gives the syllogistic process the appearance of a subjective makeshift, to which reason or understanding resorts when it cannot cognise immediately. The nature of things, the rational element, certainly does not set to work by first framing for itself a major premise, the relation of a particularity to a subsistent universal, and then secondly, picking up a separate relation of an individuality to the particular, out of which thirdly and lastly a new proposition comes to light. This syllogistic process that advances by means of separate propositions is nothing but a subjective form; the nature of the fact is that the differentiated Notion determinations of the fact are united in the essential unity.
This rationality is not a makeshift; on the contrary, in contrast to the immediacy of relation that still obtains in the judgment, it is the objective element; and the former immediacy of cognition is rather the merely subjective element, whereas the syllogism is the truth of the judgment. Everything is a syllogism, a Universal that through particularity is united with individuality; but it is certainly not a whole consisting of three propositions.
2. In the immediate syllogism of the understanding the terms have the form of immediate determinations; it is now to be considered from this aspect according to which they are a content. It may thus be regarded as the qualitative syllogism, just as the judgment of existence has the same aspect of qualitative determination. Accordingly the terms of this syllogism, like the terms of that judgment, are individual determinatenesses, the determinateness through its self-relation being posited as indifferent to the form and hence as content. The individual is any immediate concrete object; particularity a single one of its determinatenesses, properties or relationships; universality again a still more abstract, more individual determinateness in the particular' Since the subject as immediately determined is not yet posited in its Notion, its concretion is not reduced to the essential Notion determinations; its self-related determinateness is, therefore, an indeterminate, infinite multiplicity. In this immediacy the individual possesses an infinite number of determinatenesses which belong to its particularity, each of which therefore may constitute a middle term for it in a syllogism. But through any other middle term it is united with another universal; through each of its properties it stands in a different connection and context of existence. Further, the middle term is also a concrete in comparison with the universal; it contains several predicates itself, and the individual in turn can be united through the same middle term with several universals. In general, therefore, it is completely contingent and arbitrary which of the many properties is adopted for the purpose of connecting it with a predicate; other middle terms are transitions to other predicates, and even the same middle term may by itself be a transition to various predicates, for as a particular against the universal it contains several determinations.
But not only is an indefinite number of syllogisms equally possible for one subject and not only is any single syllogism contingent in respect of its content, but these syllogisms that concern the same subject must also pass over into contradiction. For difference in general, which in the first instance is an indifferent diversity, is no less essentially opposition. The concrete is no longer something belonging merely to the sphere of Appearance, but is concrete through the unity in the Notion of the opposites that have become determined as moments of the Notion. Now when, in accordance with the qualitative nature of the terms in the formal syllogism, the concrete is grasped in respect of a single one of the determinations belonging to it, the syllogism assigns to it the predicate corresponding to this middle term; but as from another side the opposite determinateness is inferred, this shows the former conclusion to be false, although its premises by themselves and equally its inference are quite correct. If from the middle term, that a wall has been painted blue, it is inferred that therefore the wall is blue, this is a correct inference; yet in spite of this syllogism the wall can be green if it has also been painted over yellow, from which latter circumstance taken by itself it would follow that it was yellow. If from the middle term of sense-nature it is inferred that man is neither good nor evil, because neither the one nor the other can be predicated of sense, the syllogism is correct but the conclusion is false; because as man is a concrete being, the middle term of spirituality is equally valid. From the middle term of the gravitation of the planets, satellites and comets towards the sun, it correctly follows that these bodies fall into the sun; but they do not fall into it, because each is no less its own centre of gravity, or, as it is said, they are impelled by centrifugal force. Similarly, from the middle term of sociality we can deduce the community of goods among citizens, but from the middle term of individuality, if it is pursued with equal abstractness, there follows the dissolution of the state, as has happened for example in the Holy Roman Empire from holding to the latter middle term. It is justly held that there is nothing so inadequate as a formal syllogism of this kind, since it is a matter of chance or caprice which middle term is employed. No matter how elegantly a deduction of this kind has run its course through syllogisms, however fully its correctness may be conceded it still leads to nothing of the slightest consequence, for the fact always remains that there are still other middle terms from which the exact opposite can be deduced with equal correctness.
The Kantian antinomies of reason amount to nothing more than that from a notion first one of its determinations is laid down as basis, and then with equal necessity, the other. In these cases this inadequacy and contingency of a syllogism must not merely be shifted on to the content, as though these defects were independent of the form and the latter alone were the concern of logic. On the contrary, it lies in the form of the formal syllogism that the content is such a one-sided quality; it is determined to this one-sidedness by the said abstract form.
It is, namely, one single quality of the many qualities or determinations of a concrete object or Notion because according to the form it is not supposed to be anything more than such an immediate, single determinateness. The extreme of individuality, as abstract individuality, is the immediate concrete, consequently the infinite or indeterminable manifold; the middle term is the equally abstract particularity, consequently a single one of these manifold qualities, and similarly the other extreme is the abstract universal. Therefore it is essentially on account of its form that the formal syllogism is wholly contingent as regards its content; and contingent, not in the sense that it is contingent for the syllogism whether this or another object be submitted to itlogic abstracts from this content-but in so far as a subject forms the basis it is contingent what kind of content determinations the syllogism shall infer from it.
3. The determinations of the syllogism are determinations of content in so far as they are immediate, abstract, and reflected into themselves. But their essential nature, on the contrary, is that they are not such mutually indifferent, intro-reflected determinations, but determinations of form; as such they are essentially relations. These relations are first, those of the extremes to the middle term-relations that are immediate, the propositiones praemissae, and, to name them, the propositio major, the relation of the particular to the universal, and the propositio minor, the relation of the individual to the particular. Secondly we have the relation of the extremes to one another, which is the mediated relation, conclusio. The immediate relations, the premises, are propositions or judgments in general, and contradict the nature Of the syllogism according to which the different Notion determinations are not related immediately, but their unity should also be posited; the truth of the judgment is the syllogism. All the less can the premises remain immediate relations, since their content consists of immediately distinguished determinations and they are therefore not immediately identical in and for themselves-unless they are pure, identical propositions, that is empty tautologies that lead to nothing.
Accordingly, it is commonly demanded of the premises that they shall be proved, that is, that they likewise shall be presented as conclusions. Consequently, the two premises yield two further syllogisms. But these two new syllogisms in turn yield between them four premises which demand four new syllogisms; these have eight premises whose eight syllogisms in turn yield for their sixteen premises sixteen syllogisms, and so on in a geometrical progression to infinity.
Thus there here comes to view again the progress to infinity which appeared before in the lowlier sphere of being, but which was no longer to be expected in the domain of the Notion, of the absolute reflection-into-self out of the finite, in the region of free infinitude and truth. It was shown in the sphere of being that whenever we find the spurious infinite that runs away into a progression, we are faced with the contradiction of a qualitative being and an impotent ought-to-be that goes out and away beyond it; the progression itself is the repetition of the demand for unity in opposition to the qualitative, and of the persistent relapse into the limitation which is inadequate to that demand. Now in the formal syllogism the immediate relation or the qualitative judgment is the basis, and the mediation of the syllogism that which is posited as the higher truth over against it. The unending process of proving the premises does not resolve this contradiction but only perpetually renews it and is the repetition of one and the same original defect. The truth of the infinite progression consists, on the contrary, in the sublation of the progression itself and the form which is already determined by it as defective. This form is that of mediation as I-P-U. The two relations I-P and P-U are to be mediated relations; if this is effected in the same way the defective form I-P-U will merely be duplicated, and so on to infinity. P has to I also the form determination of a universal, and to U the form determination of an individual, because these relations are, in general, judgments. Therefore they require mediation; but mediation in the form just mentioned only results in the re-appearance of the relationship that was to have been sublated.
The mediation must therefore be effected in another manner. For the mediation of P-U, we have I; accordingly the mediation must take the form P-I-U. To mediate I-P, we have U; this mediation therefore becomes the syllogism I-U-P.
When we examine this transition in the light of its Notion, we find in the first place that the mediation of the formal syllogism is, as has been shown, contingent in respect of its content. The immediate individual has in its determinatenesses an indeterminable number of middle terms, and these in turn have a similar number of determinatenesses in general; so that it depends entirely on an external caprice or simply on some external circumstance and contingent determination, with what kind of a universal the subject of the syllogism shall be united. As regards content, therefore, the mediation is not anything necessary or universal; it is not grounded in the Notion of the fact; on the contrary, the ground of the syllogism is something external to it, that is, something immediate; but among the Notion-determinations the immediate is the individual. As regards the form, the mediation likewise has for its presupposition the immediacy of the relation; therefore the mediation is itself mediated, and mediated by the immediate, that is, the individual. More precisely, through the conclusion of the first syllogism, the individual has become the mediating factor. The conclusion is I-U; the individual is thereby posited as a universal In one premise, the minor I-P, it is already present as a particular; hence it is that in which these two determinations are united. Or we may say that the conclusion in and for itself enunciates the individual as a universal, and that too not in an immediate manner but through mediation; consequently as a necessary relation. The simple particularity was the middle term; in the conclusion this particularity is posited in its developed form as the relation of the individual and universality. But the universal is still a qualitative determinateness, a predicate of the individual; the individual in being determined as a universal is posited as the universality of the extremes or as the middle term; by itself it is the extreme of individuality, but because it is now determined as a universal it is at the same time the unity of the two extremes.
(b) The Second Figure: P-I-U
1. The truth of the first qualitative syllogism is that something is united with a qualitative determinateness as a universal, not in and for itself but through a contingency or in an individuality. In such a quality, the subject of the syllogism has not returned into its Notion, but is apprehended only in its externality; immediacy constitutes the ground of the relation and consequently the mediation; thus the individual is in truth the middle term.
But further, the syllogistic relation is the sublation of the immediacy; the conclusion is not an immediate relation but relation by means of a third term; it contains therefore a negative unity; consequently the mediation is now determined as possessing within itself a negative moment.
In this second syllogism the premises are: P-I and I-U; only the first of these premises is still immediate; the second, I-U, is already mediated, namely by the first syllogism. The second syllogism therefore presupposes the first, just as conversely the first presupposes the second. Here the two extremes are distinguished as particular and universal; thus the latter still keeps its place; it is predicate. But the particular has changed places; it is subject, or posited in the determination of the extreme of individuality, just as the individual is posited in the determination of middle term, or of particularity. Both are therefore no longer the abstract immediacies that they were in the first syllogism. However, they are not yet posited as concretes; in standing in the place of the other, each is posited in its own determination and at the same time, though only externally, in the determination of the other.
The specific and objective meaning of this syllogism is that the universal is not in and for itself a determinate particular — for on the contrary it is the totality of its particulars — but is one such of its species through the medium of individuality; the rest of its species are excluded from it by the immediate externality. On the other hand the particular likewise is not immediately and in and for itself the universal, but the negative unity strips it of its determinateness and thereby raises it into universality. The individuality stands in a negative relationship to the particular in so far as it is supposed to be its predicate; it is not predicate of the particular.
2. But in the first instance the terms are still immediate determinatenesses; they have not of themselves developed into any objective significance; the altered position which two of them occupy is the form, which is as yet only external to them. Therefore they are still, as in the first syllogism, simply a mutually indifferent content-two qualities that are connected, not in and for themselves, but by means of a contingent individuality.
The syllogism of the first figure was the immediate syllogism or, otherwise expressed, the syllogism in its Notion as abstract form which has not yet realised itself in its determinations. The transition of this pure form into another figure is on the one hand the beginning of the realisation of the Notion, in that the negative moment of mediation, and thereby a further determinateness of form, is posited in the initially immediate qualitative determinateness of the terms. But this is at the same time an alteration of the pure form of the syllogism; the latter no longer completely corresponds to its pure form, and the determinateness posited in its terms differs from the original form determination. Regarded merely as a subjective syllogism proceeding in an external reflection, it counts as a species of syllogism which ought to correspond to the genus, namely to the general schema I-P-U. But to begin with it does not correspond to this; its two premises are P-I, or I-P, and I-U; hence the middle term is in both cases subsumed or in both cases the subject, in which accordingly the two other terms inhere. It is therefore not a middle term, for this should on the one hand subsume or be predicate, and on the other hand be subsumed or be subject, or one of the terms should inhere in it while it itself inheres in the other. The true meaning of the fact that this syllogism does not correspond to the general form of the syllogism, is that the general form has passed over into this syllogism since the truth of that form consists in its being a subjective and contingent connecting of the terms. If the conclusion in the second figure (that is, without taking advantage of the restriction about to be mentioned, which converts it into something indeterminate) is correct, then it is so because it is so on its own account, not because it is the conclusion of this syllogism. But the same is the case with the conclusion of the first figure; it is this, its truth, that is posited by the second figure. In the view that holds the second figure to be merely one species, the necessary transition of the first into this second form is overlooked and the former is adhered to as the true form. Consequently, if in the second figure (which from ancient custom is quoted without further reasons as the third) we are likewise supposed to have a syllogism correct in this subjective sense, then it would have to be conformable to the first; hence, since one premise I-U has the relationship of the subsumption of the middle term under one extreme, then it would have to be possible to give the other premise, P-I, the opposite relation to that which it has and to subsume P under I. But such a relation would be the sublation of the determinate judgment I is P, and could only occur in an indeterminate, in a particular judgment; consequently the conclusion in this figure can only be particular. The particular judgment, however, as remarked above, is both positive and negative — a conclusion to which for that very reason no great value can be attached. Since too the particular and universal are the extremes, and are immediate, mutually indifferent determinatenesses, their relationship is itself indifferent; either can be taken at choice as major or minor term and therefore, too, either premise can be taken as major or minor.
3. The conclusion, being positive as well as negative, is thus a relation indifferent to these determinatenesses and hence a universal relation. More precisely, the mediation of the first syllogism was in itself a contingent one; in the second syllogism this contingency is posited. Hence it is the self-sublating mediation; the mediation has the determination of individuality and immediacy; what is united by this syllogism must on the contrary be in itself and immediately identical; for this middle term, immediate individuality, is determined in an infinitely manifold and external manner. In it, therefore, is rather posited the self-external mediation. But the externality of the individuality is universality; the above mediation by means of the immediate individual points beyond itself to its other form, and the mediation s therefore effected by the universal. In other words, what is to be united by the second syllogism must be conjoined immediately; the immediacy on which this syllogism is based cannot bring about a definite conclusion. The immediacy to which it points is the opposite to its own-the sublated first immediacy of being-therefore the universal that is reflected into itself, or the implicit, abstract universal.
From the point of view we have just considered, the transition of this syllogism was an alteration like transition in the sphere of being, because the qualitative element, that of immediate individuality, lies at its base. But according to the Notion, individuality unites the particular and universal in so far as it sublates the determinateness of the particular, and this presents itself as the contingency of this syllogism; the extremes are not united by their determinate relation which they have for a middle term; this term is therefore not their determinate unity, and the positive unity which still attaches to the middle term is only abstract universality. But with the positing of the middle term in this determination, which is its truth, we have another form of the syllogism.
(c) The Third Figure: I- U-P
1. This third syllogism no longer has any immediate premise; the relation I-U has been mediated by the first syllogism, the relation P-U by the second. Hence it presupposes the first two syllogisms; but conversely, they both presuppose it, and in general each presupposes the other two. In this figure, therefore, the determination of the syllogism is in general completed. What this reciprocal mediation precisely contains is this, that each syllogism, although by itself mediation, is none the less not in its own self the totality of the mediation but contains an immediacy whose mediation lies outside it.
The syllogism I-U-P, regarded in itself, is the truth of the formal syllogism; it expresses that the mediation of the formal syllogism is the abstractly universal mediation, and that the extremes are not contained in the middle term according to their essential determinateness but only according to their universality; and that therefore what was supposed to be mediated in it is precisely what is not brought into unity. Here then is made explicit in what the formalism of the syllogism consists; its terms have an immediate content which is indifferent to the form, or, what is the same thing, they are determinations of form which have not yet reflected themselves into determinations of content.
2. The middle term of this syllogism is indeed the unity of the extremes, but a unity in which abstraction is made from their determinateness; it is the indeterminate universal. But since this universal is at the same time distinguished as abstract from the extremes as determinate, it is itself still a determinate relatively to them, and the whole is a syllogism whose relation to its Notion has now to be considered. The middle term, as the universal, is the subsuming term or predicate to both its extremes, and does not occur once as subsumed or as subject. In so far, therefore, as it is supposed to correspond, as a species of syllogism, to the syllogism, it can do so only on condition that when one relation I-U, already possesses the proper relationship, the other relation U-P also possesses it. This occurs in a judgment in which the relationship of subject and predicate is indifferent, in a negative judgment. In this way the syllogism becomes legitimate, but the conclusion necessarily negative.
Thus it is now also indifferent which of the two determinations of this proposition is taken as predicate and which as subject; and in the syllogism, whether it is taken as extreme of individuality or of particularity, therefore as minor or major term. Since on the common assumption it depends on this which of the premises is to be major and which minor, this too has become a matter of indifference. This is the ground of the ordinary fourth figure of the syllogism, a figure unknown to Aristotle and which in any case is concerned with a wholly empty and pointless distinction. In it the immediate position of the terms is the reverse of their position in the first figure. Since subject and predicate of the negative conclusion in the formal treatment of the judgment do not have the definite relationship of subject and predicate, but either can take the place of the other, it is indifferent which term is taken as subject and which as predicate; therefore equally indifferent which premise is taken as major and which as minor. This indifference, aided as it is by the determination of particularity (especially when it is observed that this can be taken in the comprehensive sense) makes this fourth figure a sheer futility.
3. The objective significance of the syllogism in which the universal is the middle term, is that the mediating element, as unity of the extremes, is essentially a universal. But since the universality is in the first instance only qualitative or abstract universality, it does not contain the determinateness of the extremes; their conjunction, if it is to be effected, must similarly have its ground in a mediation lying outside this syllogism and is in respect of this latter just as contingent as in the case of the preceding forms of the syllogism. But now since the universal is determined as the middle term, and the determinateness of the extremes is not contained in it, this middle term is posited as a wholly indifferent and external one.
As the immediate result of this bare abstraction, we obtain, of course, a fourth figure of the syllogism, namely that of the relationless syllogism U-U-U, which abstracts from the qualitative difference of the terms and consequently has for its determination their merely external unity, namely their equality.
(d) The Fourth Figure: U-U-U, or the Mathematical Syllogism
1. The mathematical syllogism runs: if two things or determinations are equal to a third, they are equal to each other. Here the relationship of inherence or subsumption of the terms is extinguished.
The mediating factor is a third in general, but it has absolutely no determination whatever as against its extremes. Each of the three can therefore equally well be the third, mediating term. Which one is to be used for this purpose, and which of the three relations, therefore, are to be taken as immediate and which as mediated, depends on external circumstances and other conditions, namely on which two of them are the immediately given terms. But this determination does not concern the syllogism itself and is completely external.
2. The mathematical syllogism ranks as an axiom in mathematics, as an absolutely self-evident, primitive proposition, that neither admits nor requires any proof, that is any mediation, and neither presupposes anything else nor can be deduced from anything else. If its prerogative of being immediately self-evident is looked at more closely, it will be seen that it lies in the formalism of this syllogism which abstracts from all qualitative distinction of the terms and only takes up their quantitative equality or inequality. But for this very reason it is not without presupposition or unmediated; the quantitative determination, which is the only thing in it taken into account, is only through abstraction from qualitative difference and from the determinations of the Notion. Lines, figures, posited as equal to one another, are understood only in terms of their magnitude; a triangle is affirmed to be equal to a square, but not as triangle to square, but only in regard to magnitude, etc. Similarly, the Notion and its determinations do not enter into this syllogising; there is no comprehending at all [that is, in terms of the Notion] in this process; and understanding too has not even the formal, abstract determinations of the Notion before it. The self-evidence of this syllogism, therefore, rests merely on the fact that its thought content is so meagre and abstract.
3. But the result of the syllogism of existence is not merely this abstraction from all Notional determinateness; the negativity of the immediate, abstract determinations which emerged from it has yet another positive side, namely that the abstract determinateness has had its other posited in it and thereby has become concrete.
In the first place, the syllogisms of existence all mutually presuppose one another and the extremes united in the conclusion are only genuinely and in and for themselves united in so far as they are otherwise united by an identity that has its ground elsewhere; the middle term, as it is constituted in the syllogisms we have considered, is supposed to be their Notion unity, but is only a formal determinateness that is not posited as their concrete unity. But this presupposed element of each of those mediations is not merely a given immediacy in general, as in the mathematical syllogism, but is itself a mediation, namely, for each of the two other syllogisms. Therefore what we truly have before us is not mediation based on a given immediacy, but mediation based on mediation. Hence this is not the quantitative mediation that abstracts from the form of mediation, but rather the mediation that relates itself to mediation, or the mediation of reflection. The circle of reciprocal presupposing that these syllogisms unite to form with one another is the return of this act of presupposition into itself, which herein forms a totality, and thus the other to which each individual syllogism points is not placed through abstraction outside the circle but embraced within it.
Further, from the side of the individual determinations of the form it has been seen that in this entirety of the formal syllogisms each individual term has in turn taken the place of middle term. This was determined as particularity; subsequently, through the dialectical movement it determined itself as individuality and universality. Similarly, each of these determinations occupied in turn the places of the two extremes. The merely negative result is the extinction of the qualitative form determinations in the merely quantitative, mathematical syllogism. But what we truly have here is the positive result, that mediation is not effected through an individual qualitative determinateness of form, but through the concrete identity of the determinations. The defect and formalism of the three syllogistic figures considered above consists just in this, that an individual determinateness of this kind was supposed to constitute their middle term. Mediation has thus determined itself as the indifference of the immediate or abstract form determinations and as positive reflection of one into the other. The immediate syllogism of existence has thereby passed over into the syllogism of reflection.
Remark: The Common View of the Syllogism
In the account here given of the nature of the syllogism and its various forms, passing reference has also been made to what in the usual consideration and treatment of syllogisms constitutes the main interest, namely, how a correct conclusion may be obtained in each figure; however, in those references only the main point has been indicated, and those cases and complexities which arise when the distinction of positive and negative judgments, together with the quantitative determination — especially particularity — is also dragged in, have been passed over. Some remarks on the ordinary view and mode of treatment of the syllogism in logic will be in place here. It is a familiar fact that this doctrine was elaborated into such finely drawn distinctions that its so-called subtleties have been the object of universal aversion and disgust. The natural understanding in asserting itself in every department of mental and spiritual culture against the unsubstantial forms of reflection, also turned against this artificial knowledge of the form of reason and supposed itself able to dispense with such a science on the ground that it performed the individual operations of thought specified therein naturally and spontaneously without any special instruction. In point of fact, if a precondition of rational thinking were the laborious study of syllogistic formulae, mankind would in that respect be in the same sorry plight as they would be, as already remarked in the Preface in another respect, if they could not walk or digest without having studied anatomy and physiology. Granting that the study of these sciences may not be without profit for the regulation of one's diet, we must undoubtedly credit the study of the forms of reason with an even more important influence on the correctness of thinking. But without going into this aspect of the matter which concerns the education of subjective thinking and therefore, strictly speaking, pedagogics, it must be admitted that the study which has for its subject matter the modes and laws of operation of reason, must in its own self be of the greatest interest-of an interest at least not inferior to an acquaintance with the laws of nature and of her particular forms. If it is not thought a small matter to have discovered some sixty species of parrots, one hundred and thirty-seven species of veronica, etc., much less ought it to be thought a small matter to discover the forms of reason; is not a figure of the syllogism something infinitely superior to a species of parrot or veronica?
Therefore, though contempt for the knowledge of the forms of reason must be regarded as sheer barbarism, equally we must admit that the ordinary presentation of the syllogism and its particular formations is not a rational cognition, not an exposition of them as forms of reason, and that syllogistic wisdom by its own worthlessness has brought upon itself the contempt which has been its lot. Its defect consists in its simply stopping short at the understanding's form of the syllogism in which the Notion determinations are taken as abstract, formal terms. It is all the more inconsequent to cling to these determinations as abstract qualities, since in the syllogism it is their relations that constitute the essential feature, and inherence and subsumption already imply that the individual, because the universal inhe.-es in it, is itself a universal, and the universal, because it subsumes the individual, is itself an individual; more exactly, the syllogism expressly posits this very unity as middle term, and its determination is precisely mediation, that is, the Notion determinations no longer, as in the judgment, have for basis their mutual externality, but rather their unity. It is thus the Notion of the syllogism that declares the imperfection of the formal syllogism in which the middle term is fixedly held, not as unity of the extremes but as a formal, abstract determination qualitatively distinct from them. The treatment is rendered still less meaningful by the fact that also relations or judgments in which even formal determinations become indifferent, as in negative and particular judgments, and which therefore approximate to propositions, are still regarded as perfect relationships. Now since the qualitative form I-P- U is generally accepted as the ultimate and absolute, the dialectical treatment of the syllogism no longer operates; the remaining syllogisms are consequently regarded not as necessary alterations of that first form but as species. In this case, it is indifferent whether the first formal syllogism itself is regarded only as a kind of species alongside the rest, or as genus and species at the same time; the latter occurs when the other syllogisms are reduced to the first. If this reduction is not expressly effected, yet the basis is always the same formal relationship of external subsumption expressed by the first figure.
This formal syllogism is the contradiction that the middle term which is supposed to be the determinate unity of the extremes does not appear as this unity but as a determination qualitatively distinct from those extremes whose unity it is supposed to be. Because the syllogism is this contradiction, it is in its own nature dialectical. Its dialectical movement exhibits it in each of the moments of the Notion, so that not only the above relationship of subsumption or particularity, but equally essentially negative unity and universality are moments in the union of the extremes. In so far as each of these by itself is equally only a one-sided moment of particularity, they are likewise imperfect middle terms, but at the same time they constitute the developed determinations of the middle term; the entire course through the three figures presents the middle term in each of these determinations, and the true result that emerges from it is that the middle is not an individual Notion determination but the totality of them all.
The defect of the formal syllogism, therefore, does not lie in the form of the syllogism — on the contrary, this is the form of rationality — but in the fact that the form appears only as an abstract and therefore notionless form. It has been shown that the abstract determination, on account of its abstract relation-to-self, can equally be regarded as content; this being so, the formal syllogism merely serves to show that a relation of a subject to a predicate follows or does not follow only from this middle term. Nothing is gained in having proved a proposition by a syllogism of this kind; on account of the abstract determinateness of the middle term, which is a Notionless quality, other middle terms can just as well be given from which the opposite follows; in fact, from the same middle term opposite predicates may in turn be deduced by further syllogisms. Besides being of little service, the formal syllogism is also a very simple affair; the numerous rules which have been invented are tiresome not only because they contrast so strongly with the simple nature of the fact but also because they relate to cases where the formal worth of the syllogism is furthermore diminished by the external form determination, above all, particularity (especially as for this purpose it must be taken in a comprehensive sense), and where even in respect of form nothing but completely worthless results are deduced. However, the most merited and most important aspect of the disfavour into which syllogistic doctrine has fallen is that this doctrine is such a long-drawn out, notionless occupation with a subject matter whose sole content is the Notion itself. The numerous syllogistic rules remind one of the procedure of arithmeticians who similarly give a host of rules about arithmetical operations, all of which rules presuppose that one has not the Notion of the operation. But numbers are a notionless material and the operations of arithmetic are an external combining or separating of them, a mechanical procedure-indeed, calculating machines have been invented which perform these operations; whereas it is the harshest and most glaring of contradictions when the form determinations of the syllogism, which are Notions, are treated as a notionless material.
The extreme example of this irrational treatment of the Notion determinations of the syllogism is surely Leibniz's subjection of the syllogism to the calculus of combinations and permutations and has reckoned thereby how many positions of the syllogism are possible — that is, with respect to the distinctions of positive and negative, of universal, particular indeterminate and singular judgments; 2,048 such combinations are found to be possible of which, after the exclusion of the useless figures, twenty-four useful figures remain. Leibniz makes much of the usefulness of the analysis of combinations for ascertaining not only the forms of the syllogism but also the combinations of other concepts. The operation by which this is ascertained is the same as that by which it is calculated how many combinations of letters are possible in an alphabet, how many throws are possible in a game of dice, how many kinds of play with an ombre card, etc. Here therefore we find the determinations of the syllogism put in the same class with the points of the die and the ombre card, the rational is taken as a dead and non-rational thing, and the characteristic feature of the Notion and its determinations as spiritual essences to relate themselves and through this relating to sublate their immediate determination, is ignored. This Leibnizian application of the calculus of combinations and permutations to the syllogism and to the combination of other notions, differed from the notorious Art of Lully solely in being more methodical on the arithmetical side, but for the rest, they were both equally meaningless. Connected with this was a pet idea of Leibniz, embraced by him in his youth, and in spite of its immaturity and shallowness not relinquished by him even in later life, the idea of a characteristica universalis of notions-a language of symbols in which each notion would be represented as a relation proceeding from others or in its relation to others as though in rational combinations, which is essentially dialectical, a content still retained the same determinations that it possesses when fixed in isolation.
Ploucquet's calculus has undoubtedly got hold of the most consistent method by which the relationship of the syllogism is made capable of being subjected to a calculus. It rests upon the abstraction from the difference of relationship, from the difference of individuality, particularity and universality in the judgment and upon strict adherence to the abstract identity of subject and predicate whereby they are in a mathematical equality — in a relation which converts the syllogising process into a completely meaningless and tautological formulation of propositions. In the proposition: the rose is red, the predicate is not to denote red in general but only the specific red of the rose; in the proposition: all Christians are men, the predicate is to denote only those men who are Christians; from this proposition and the proposition: the Jews are not Christians, there follows the conclusion (which did not particularly commend this syllogistic calculus to Mendelssohn) therefore the Jews are not men (namely, not those men that the Christians are). Ploucquet states as a consequence of his discovery: 'posse etiam rudes mechanics totam logicam doceri, uti pueri arithmeticam docentur, ita quidem, ut nulla formidine in ratiociniis suis errands torqueri, vel fallaciis circumveniri possint, si in calculo non errant.' This recommendation, that by means of the calculus the whole of logic can be mechanically brought within reach of the uneducated, is surely the worst thing that can be said of a discovery bearing on the presentation of the science of logic.
B.The Syllogism of Reflection
The course of the qualitative syllogism has sublated what was abstract in its terms with the result that the term has posited itself as a determinateness in which the other determinateness is also reflected. Besides the abstract terms, the syllogism also contains their relation, and in the conclusion this relation is posited as mediated and necessary; therefore each determinateness is in truth posited not as an individual, separate one, but as a relation to the other, as a concrete determinateness.
The middle term was abstract particularity, by itself a simple determinateness, and was a middle term only externally and relatively to the self-subsistent extremes. Now it is posited as the totality of the terms; as such it is the posited unity of the extremes, but in the first instance it is the unity of reflection which embraces them within itself — an inclusion which, as the first sublating of immediacy and the first relating of the terms, is not yet the absolute identity of the Notion.
The extremes are the determinations of the judgment of reflection, individuality proper and universality as a connective determination or a reflection embracing a manifold within itself. But the individual subject also contains, as we have seen in the case of the judgment of reflection, besides the bare individuality which belongs to form, determinateness as universality absolutely reflected into itself, as presupposed, that is here still immediately assumed, genus.
From this determinateness of the extremes which belongs to the progressive determination of the judgment, there results the precise content of the middle term, which is essentially the point of interest in the syllogism since it distinguishes syllogism from judgment. It contains (1) individuality, but (2) individuality extended to universality as all, (3) universality which forms the basis and absolutely unites within itself individuality and abstract universality — that is, the genus. It is in this way that the syllogism of reflection is the first to possess genuine determinateness of form, in that the middle term is posited as the totality of the terms; the immediate syllogism is by contrast indeterminate, because the middle term is still only 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.
(a) The Syllogism of Allness
1. The syllogism of allness is the syllogism of understanding in its perfection, but is as yet no more than that. That the middle term in it is not abstract particularity but is developed into its moments and is therefore concrete, is indeed an essential requirement for the Notion; but the form of allness so far only gathers the individual externally into universality, and conversely still preserves the individual in the universality as something possessing immediately a separate self-subsistence. The negation of the immediacy of the determinations which was the result of the syllogism of existence, is only the first negation, not yet the negation of the negation or absolute reflection into self. Therefore the single determinations still form the basis of the universality of reflection that embraces them within itself; in other words, allness is still not the universality of the Notion but the external universality of reflection.
The syllogism of existence was contingent because its middle term, as a single determinateness of the concrete subject, admits of an indeterminable number of other such middle terms, and therefore the subject could be united in the syllogism within determinably different and even contradictory predicates. But since the middle term now contains individuality and is thereby itself concrete, it can only serve to connect the subject with a predicate which belongs to the subject as concrete. If for example from the middle term green it should be inferred that a picture was pleasing because green is pleasing to the eye, or that a poem or building was beautiful because it possessed regularity, the picture, etc., might all the same be ugly on account of other qualities from which this latter predicate could be inferred. On the other hand, since the middle term has the determination of allness, it contains the greenness or regularity as a concrete, which just for that reason is not the abstraction of something merely green or merely regular; with this concrete then only those predicates can be connected which conform to the totality of the concrete thing. In the judgment: what is green or regular is pleasing, the subject is only the abstraction of green or regularity; in the proposition: all green or regular things are pleasing, the subject is, on the contrary: all actual concrete objects that are green or regular —objects, therefore, which are taken as concrete with all their properties that they possess besides greenness or regularity.
2. But this very perfection of the syllogism of reflection makes it a mere delusion. The middle term has the determinateness 'all'; to this is immediately attached in the major premise the predicate that is united with the subject in the conclusion. But 'all' are 'all individuals'; therefore in the major premise the individual subject already immediately possesses this predicate and does not obtain it first through the syllogism. Or to put it otherwise the subject obtains through the conclusion a predicate as a consequence; but the major premise already contains this conclusion within it; therefore the major premise is not correct on its own account, or is not an immediate, presupposed judgment, but already presupposes the conclusion whose ground it was supposed to be. In the favourite perfect syllogism:
All men are mortal
Now Gaius is a man
Therefore Gaius is mortal,
the major premise is correct only because and in so far as the conclusion is correct; if Gaius should chance to be not mortal, the major premise would not be correct. The proposition which was supposed to be the conclusion must already be immediately correct on its own account, because otherwise the major premise could not embrace all individuals; before the major premise can pass as correct, there is the prior question whether the conclusion itself may not be an instance against it.
3. In the case of the syllogism of existence we found from the Notion of the syllogism that the premises, as immediate, contradicted the conclusion, that is to say the mediation demanded by the Notion of the syllogism, and that the first syllogism therefore presupposed others and conversely these others presupposed it. In the syllogism of reflection, this is posited in the syllogism itself, namely, that the major premise presupposes its conclusion, in that the former contains that connection of the individual with a predicate which is supposed to appear only as conclusion.
What, then, we really have here may be expressed in the first instance by saying that the syllogism of reflection is only an external, empty show of syllogising — hence that the essence of this syllogising rests on subjective individuality and that therefore this latter constitutes the middle term and is to be posited as such the individuality that is individuality as such and possesses universality only externally. We may also say that the precise content of the syllogism of reflection showed that the relation in which the individual stands to its predicate is immediate, not inferred, and that the major premise, the connection of a particular with a universal, or, more precisely, of a formal universal with an intrinsic universal, is mediated by the relation of individuality which is present in the former — of individuality as allness. But this is the syllogism of induction.
(b) The Syllogism of Induction
1. The syllogism of allness comes under the schema of the first figure, I-P-U; the syllogism of induction under that of the second, U-1-P, as it again has individuality for middle term, not abstract individuality but individuality as complete, namely, posited with its opposite determination, universality. One extreme is some predicate or other that is common to all these individuals; its relation to them constitutes the immediate premises, of which one, in the preceding syllogism was supposed to be the conclusion. The other extreme may be the immediate genus as it is found in the middle term of the preceding syllogism or in the subject of the universal judgment and which is exhausted in all the individuals or species collectively of the middle term. Accordingly the syllogism has the shape:
i
i
U- -P
i
i
ad infinitum
2. The second figure of the formal syllogism U-I-P did not correspond to the schema, because I which constitutes the middle term was not the subsuming term or predicate. In induction this defect is eliminated; here the middle term is all the individuals; the proposition: U-I, which contains as subject the objective universal or genus separated off to form an extreme, has a predicate that is at least coextensive with the subject, and consequently for external reflection is identical with it. Lion, elephant, and so on constitute the genus of quadruped; the difference, that the same content is posited once in individuality and again in universality, is accordingly a mere indifferent determination of form-an indifference which is the result of the formal syllogism posited in the syllogism of reflection, and here is posited through the equality of extension.
Induction, therefore, is not the syllogism of mere perception or of contingent existence, like the corresponding second figure, but the syllogism of experience — of the subjective taking together of the individuals into the genus and of the conjoining of the genus with a universal determinateness because this latter is found in all the individuals. It has also the objective significance that the immediate genus determines itself through the totality of individuality to a universal property, has its existence in a universal relationship or mark. But the objective significance of this, as of the other syllogisms, is at first only its inner Notion, and is not yet posited here.
3. On the contrary, induction is still essentially a subjective syllogism. The middle terms are the individuals in their immediacy; the subjective taking together of them into the genus by means of allness is an external reflection. On account of the persistent immediacy of the individuals and their consequent externality, the universality is only completeness, or rather remains a problem. In induction, therefore, the progress into the spurious infinite once more makes its appearance; individuality is supposed to be posited as identical with universality, but since the individuals are no less posited as immediate, that unity remains only a perennial ought-to-be; it is a unity of likeness; those which are supposed to be identical are, at the same time, supposed not to be so. It is only when the a, b, c, d, e are carried on to infinity that they constitute the genus and give the completed experience. The conclusion of induction thus remains problematical.
But induction, in expressing that perception in order to become experience ought to be carried on to infinity, presupposes that the genus [Kind] is in and for itself united with its determinateness. Therefore, strictly speaking, it rather presupposes its conclusion as something immediate, just as the syllogism of allness presupposes the conclusion for one of its premises. An experience that rests on induction is accepted as valid although the perception is admittedly incomplete; but the assumption that no contradictory instance of that experience can arise is only possible if the experience is true in and for itself. Thus the syllogism by induction, though indeed based on an immediacy, is not based on that immediacy on which it is supposed to be based, on the merely affirmative immediacy of individuality, but on the immediacy which is in and for itself, the universal immediacy. The fundamental character of induction is that it is a syllogism; if individuality is taken as the essential, but universality as only the external, determination of the middle term, then the middle term would fall asunder into two unconnected parts and we should not have a syllogism; this externality belongs rather to the extremes. It is only as immediately identical with universality that individuality can be the middle term; such universality is properly objective universality, the genus [Kind]. This may also be looked at in this way: universality is external but essential in the determination of individuality that forms the basis of the middle term of induction; but such an external is no less immediately its opposite, the internal. The truth of the syllogism of induction is, therefore, a syllogism that has for its middle term an individuality that is immediately in its own self universality; this is the syllogism of analogy.
(c) The Syllogism of Analogy
1. This syllogism has for its abstract schema the third figure of the immediate syllogism I-U-P. But its middle term is no longer just any single quality, but universality that is the reflection-into-self of a concrete, and hence its nature; and conversely, because it is thus the universality of a concrete, it is at the same time in its own self this concrete. Here, then, the middle term is an individual but an individual taken in its universal nature; further, another individual forms an extreme possessing the same universal nature with the former. For example:
The earth is inhabited,
The moon is an earth,
Therefore the moon is inhabited.
2. Analogy is the more superficial, the more the universal in which the two individuals are one, and according to which one individual becomes the predicate of the other, is a mere quality, or (quality being taken subjectively) some mark or other, when the identity of the two therein is taken as a mere similarity. Superficiality of this kind, however, to which a form of understanding or reason is reduced by being degraded to the sphere of mere representation, should not find a place in logic at all. Also it is improper to represent the major premise of this syllogism as though it should run: that which resembles an object in some characteristics resembles it in others also. By so doing, the form of the syllogism is expressed in the shape of a content, while the empirical content, the content properly so called, is relegated to the minor premise. In this way the whole form, for example, of the first syllogism, could be expressed as its major premise: That which is subsumed under some other thing in which a third inheres, has also that third inherent in it: now .... and so forth. But the importance of the syllogism itself does not depend on the empirical content, and to convert its own form into the content of a major premise is no less a matter of indifference than to take any other empirical content for that purpose. But in so far as the importance of the syllogism of analogy does not depend on the former content which contains nothing but the form peculiar to the syllogism, then the importance of the first syllogism would not depend on it either, that is to say, would not depend on that which makes the syllogism a syllogism. The main point always is the form of the syllogism, whether it have the form itself or something else for its empirical content. Thus the syllogism of analogy is a peculiar form, and it is quite futile not to regard it as such on the ground that its form can be converted into the content or matter of a major premise, whereas logic is not concerned with the matter. What may lead to this misunderstanding in the case of the syllogism of analogy and perhaps also in the case of the syllogism of induction, is that in them the middle term and the extremes, too, are further determined than in the merely formal syllogism, and therefore the form determination, because it is no longer simple and abstract, must appear also as a determination of content. But the fact that the form determines itself to content in this way is in the first place a necessary advance of the formal element and therefore essentially concerns the nature of the syllogism; and therefore, secondly, a content determination of this kind cannot be regarded in the same way as any other empirical content, nor can abstraction be made from it.
When we consider the form of the syllogism of analogy in the above expression of its major premise, which states that if two objects agree in one or more properties, then a property which one possesses also belongs to the other, it may seem that this syllogism contains four terms, the quaternio terminorum — a circumstance which entails the difficulty of bringing analogy into the form of a formal syllogism. There are two individuals, thirdly, a property immediately assumed as common, and fourthly the other property which one individual immediately possesses but which the other first obtains through the syllogism. This arises from the fact that, as we have seen, in the analogical syllogism the middle term is posited as individuality, but immediately also as the true universality of the latter. In induction, the middle term is, apart from the two extremes, an indeterminable number of individuals; in this syllogism therefore an infinite number of terms ought to be enumerated. In the syllogism of allness the universality in the middle term is so far merely the external form determination of allness; in the syllogism of analogy, on the contrary, it is essential universality. In the above example the middle term, the earth, is taken as a concrete that in its truth is as much a universal nature or genus as an individual.
From this aspect, the quaternio terminorum would not render analogy an imperfect syllogism. Yet it does so from another aspect; for although one subject has the same universal nature as the other, it is undetermined whether the determinateness which is inferred for the second subject belongs to the first by virtue of its nature or by virtue of its particularity; whether for example the earth is inhabited as a heavenly body in general, or only as this particular heavenly body. Analogy is still a syllogism of reflection inasmuch as individuality and universality are immediately united in its middle term. On account of this immediacy, the externality of the unity of reflection is still with us; the individual is only implicitly the genus, it is not posited in that negativity by which its determinateness would be the determinateness proper to the genus itself. For this reason the predicate which belongs to the individual of the middle term is not already predicate of the other individual although both belong to the one genus.
3. I-P (the moon is inhabited) is the conclusion; but one premise (the earth is inhabited) is likewise I-P; inasmuch as I-P is supposed to be a conclusion it involves the demand that the said premise shall be one also. Hence this syllogism is in its own self the demand for itself to counter the immediacy which it contains, in other words it presupposes its conclusion. A syllogism of existence has its presupposition in the other syllogisms of existence; in the case of the syllogisms just considered the presupposition has been placed within them, because they are syllogisms of reflection. Since then the syllogism of analogy is the demand for its own mediation against the immediacy with which its mediation is burdened, it is the moment of individuality whose sublation it demands. Thus there remains for middle term the objective universal, the genus, purged of immediacy. In the syllogism of analogy the genus was a moment of the middle term only as an immediate presupposition; since the syllogism itself demands the sublation of the presupposed immediacy, the negation of the individuality, and consequently 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 with it the external universality of reflection is determined into universality in and for itself. Regarded from the positive side the conclusion shows itself to be identical with the premise, the mediation as having coincided with its presupposition; thus there is an identity of the universality of reflection by which it has become a higher universality.
Looking over the course of the syllogisms of reflection, we see that the mediation is in general the posited or concrete unity of the form determinations of the extremes; the reflection consists in this positing of one determination in the other; thus the mediating element is allness. But individuality appears as the essential ground of allness and universality only as an external determination in it, as completeness. But universality is essential to the individual if it is to be a middle term that unites; the individual is therefore to be taken as in itself a universal. But the individual is not united with universality in this merely positive manner but is sublated in it and a negative moment; thus the universal is that whose essential being has become actual, the posited genus, and the individual as immediate is rather the externality of the genus, or it is an extreme. The syllogism of reflection taken in general comes under the schema P-I-U, in which the individual is still as such the essential determination of the middle term; but in that its immediacy has sublated itself, and the middle term has determined itself as the universality that is in and for itself, the syllogism has entered under the formal schema I-U-P, and the syllogism of reflection has passed over into the syllogism of necessity.
C.The Syllogism of Necessity
The mediating element has now determined itself (1) as simple determinate universality, like the particularity in the syllogism of existence, but (2) as objective universality, that is to say, universality which contains the entire determinateness of the distinguished extremes like the allness of the syllogism of reflection, a fulfilled yet simple universality-the universal nature of the fact, the genus.
This syllogism is pregnant with content, because the abstract middle term of the syllogism of existence posited itself as determinate difference to become the middle term of the syllogism of reflection, while this difference has reflected itself into simple identity again. This syllogism is therefore the syllogism of necessity, for its middle term is not some alien immediate content, but the reflection-into-self of the determinateness of the extremes.
These possess in the middle term their inner identity, the determinations of whose content are the form determinations of the extremes. Consequently, that which differentiates the terms appears as an external and unessential form, and the terms themselves as moments of a necessary existence.
In the first instance this syllogism is immediate, and thus formal in so far as the connection of the terms is the essential nature as content, and this content is present in the distinguished terms in only a diverse form, and the extremes by themselves are merely an unessential subsistence. The realisation of this syllogism has so to determine it that the extremes also shall be posited as this totality which initially the middle term is, and that the necessity of the relation which is at first only the substantial content, shall be a relation of the posited form.
(a) The Categorical Syllogism
1. The categorical syllogism has the categorical judgment for one or both of its premises. Here, with this syllogism, as with the judgment, is associated the more specific significance that its middle term is objective universality. Superficially the categorical syllogism too is taken for nothing more than a mere syllogism of inherence.
The categorical syllogism in its substantial significance is the first syllogism of necessity, in which a subject is united with a predicate through its substance. But substance raised into the sphere of the Notion is the universal, posited as being in and for itself in such a manner that it has for the form or mode of its being, not accidentality, which is the relationship peculiar to substance, but the Notion-determination. Its differences are therefore the extremes of the syllogism and, precisely, universality and individuality. The former, in contrast to the genus, which is the precise determination of the middle term, is abstract universality or universal determinateness — the accidentality of substance gathered into simple determinateness which however is its essential difference, specific difference. But individuality is the actual, in itself the concrete unity of genus and determinateness; here, however, in the immediate syllogism it appears at first as immediate individuality, accidentally gathered into the form of a subsistence on its own. The relation of this extreme to the middle term constitutes a categorical judgment; but since the other extreme, too, according to the above-stated determination, expresses the specific difference of the genus or its determinate principle, this other premise is also categorical.
2. This syllogism, as the first and therefore immediate syllogism of necessity, comes in the first instance under the schema of the first formal syllogism I-P-U. But as the middle term is the essential nature of the individual and not just any of its determinatenesses or properties, and as, similarly, the extreme of universality is not just any abstract universal nor again merely a single quality, but the universal determinateness, the specific principle of difference, the subject is no longer contingently united through the syllogism with any quality through any middle term. Consequently, as the relations too of the extremes to the middle term have not that external immediacy which they had in the syllogism of existence, the demand for proof, which occurred in the latter and led to the infinite progress, does not arise.
Further, this syllogism does not, as does a syllogism of reflection, presuppose its conclusion for its premises. The terms, in keeping with their substantial content, stand in a relation to one another which is in and for itself identical; we have here one essential nature pervading the three terms, a nature in which the determinations of individuality, particularity and universality are merely formal moments.
To this extent therefore the categorical syllogism is no longer subjective; in the above identity, objectivity begins; the middle term is the pregnant identity of its extremes which are contained therein in their self-subsistence, for their self-subsistence is the above substantial universality, the genus. The subjective element of the syllogism consists in the indifferent subsistence of the extremes relatively to the Notion or middle term.
3. But this syllogism still continues to be subjective, in that the said identity is still the substantial identity or content, but is still not at the same time identity of form. Consequently, the identity of the Notion is still an inner bond of union, and therefore as relation is still necessity; the universality of the middle term is substantial, positive identity, but is not equally the negativity of its extremes.
More precisely, the immediacy of this syllogism, which immediacy is not yet posited as that which it is in itself, is present in the following manner. What is really immediate in the syllogism is the individual. This is subsumed under its genus as middle term; but under the same genus come also an indefinite number of other individuals; it is therefore contingent that only this individual is posited as subsumed under it. But further, this contingency does not merely belong to the external reflection which finds the individual posited in the syllogism to be contingent by comparison with others; on the contrary, it is because the individual itself is related to the middle term as to its objective universality that it is posited as contingent, as a subjective actuality. On the other hand, in that the subject is an immediate individual, it contains determinations which are not contained in the middle term as the universal nature; therefore it also has a specific nature of its own indifferent to the middle term and possessing a content peculiar to itself. Hence, conversely, this other term also has an indifferent immediacy and an Existence distinct from the former. The same relationship also obtains between the middle term and the other extreme; for this likewise has the determination of immediacy and hence of a being that is contingent relatively to its middle term.
Accordingly, what is posited in the categorical syllogism is on the one hand extremes standing in such a relationship to the middle term that they possess in themselves objective universality or a self-subsistent nature, and at the same time appear as immediate terms and therefore as mutually indifferent actualities. But on the other hand they are equally determined as contingent, that is to say, their immediacy is sublated in their identity. But by reason of the said self-subsistence and totality of the actuality, this identity is only formal and inner; the syllogism of necessity has hereby determined itself to the hypothetical syllogism.
(b) The Hypothetical Syllogism
1. The hypothetical judgment contains only the necessary relation without the immediacy of the related terms. 'If A is, then B is'; or, the being of A is equally the being of another, of B; so far, it is not stated either that A is, or 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 premise by itself enunciates the immediate being of A.
But it is not only this that is added to the judgment. The syllogism contains the relation of subject and predicate, not as the abstract copula, but as the pregnant mediating unity. Accordingly, the being of A is to be taken not as a mere immediacy, but essentially as the middle term of the syllogism. This is to be examined more closely.
2. In the first place, the relation of the hypothetical judgment is necessity or inner substantial identity associated with external diversity of Existence, or mutual indifference of being in the sphere of Appearance — an identical content which forms the internal basis. The two sides of the judgment therefore do not appear as an immediate being but as a being held within the necessity and thus at the same time as sublated being or being only in the sphere of Appearance. Further, as sides of the judgment they stand to one another as universality and individuality; one of them, therefore, is the above content as totality Of conditions, the other as actuality. It is, however, indifferent which side is taken as universality and which as individuality. That is to say, in so far as the conditions are still the inner, abstract side of an actuality, they are the universal, and it is through their being gathered together into an individuality that they enter into actuality. Conversely, the conditions are a separated, scattered Appearance which only in actuality obtains unity and significance and a universally valid existence.
The precise relation between the two sides that has here been assumed as the relation of condition and conditioned, may however also be taken as that of cause and effect, of ground and consequent — here this is indifferent; but the relation of condition corresponds more closely to the relation that obtains in the hypothetical judgment and syllogism, inasmuch as condition appears essentially as an indifferent Existence, whereas ground and cause are spontaneously transitive [ubergehend]; also condition is a more universal determination in that it comprehends both sides of the above relations, since effect, consequent, etc., is just as much condition of the cause, ground, etc., as the latter are of the former.
Now A is the mediating being in so far as first it is an immediate being, an indifferent actuality, and secondly, in so far as it is no less an intrinsically contingent, self-sublating being. What translates the conditions into the actuality of the new shape whose conditions they are is the fact that they are not being in its abstract immediacy, but being in its Notion, in the first instance, becoming; but as the Notion is no longer transition they are more specifically individuality as self-related negative unity. The conditions are a scattered material that waits and demands to be used; this negativity is the mediating element, the free unity of the Notion. It determines itself as activity, since this middle term is the contradiction of the objective universality or the totality of the identical content, and the indifferent immediacy. This middle term is therefore no longer merely an inner necessity, but a necessity that is; the objective universality contains self-relation as a simple immediacy, as being; in the categorical syllogism this moment is in the first instance a determination of the extremes, but as against the objective universality of the middle term it determines itself as contingency, consequently, as something only posited and also sublated, that is, as something withdrawn into the Notion or into the middle term as unity, which middle term itself in its objectivity is now also being.
The conclusion, 'therefore B is', expresses the same contradiction, that B is in the form of immediate being, but equally has its being through an other, or is mediated. In respect of its form, therefore, it is the same Notion that the middle term is, distinguished from necessity only as the necessary — in the wholly superficial form of individuality as against universality. The absolute content of A and B is the same; they are only two different names for the same underlying fact for ordinary thinking [Vorstellung] which clings to the appearance of the diversified shape of determinate being and distinguishes between the necessary and its necessity; but in so far as this necessity were to be separated from B, B would not be the necessary. Thus we have here the identity of the mediating and the mediated.
3. The hypothetical syllogism in the first instance exhibits necessary relation as connection through the form or negative unity, just as the categorical syllogism exhibits through the positive unity, substantial content, objective universality. But necessity collapses into the necessary; the form-activity of translating the conditioning into the conditioned actuality is in itself the unity in which the determinatenesses of the opposition, that previously were liberated into an indifferent determinate existence, are sublated, and the difference of A and B is an empty name. Thus it is a unity reflected into itself — hence an identical content; and it is so not merely implicitly but it is also posited as such through this syllogism, in that the being of A is also not its own but B's, and vice versa, and in general the being of one is the being of the other, and in the conclusion the immediate being or indifferent determinateness appears specifically as mediated; the externality of the determinatenesses has therefore sublated itself and their unity into which they have withdrawn is posited.
The mediation of the syllogism has hereby determined itself as individuality, immediacy, and as self-related negativity, or as an identity that differentiates itself and gathers itself into itself out of that difference — as absolute form, and for that very reason as objective universality, a content that is identical with itself. The syllogism in this determination is the disjunctive syllogism.
(c) The Disjunctive Syllogism
As the hypothetical syllogism in general comes under the schema of the second figure of the formal syllogism, U-I-P, so the disjunctive syllogism comes under the schema of the third figure, I-U-P. But the middle term is the universality that is pregnant with form; it has determined itself as totality, as developed objective universality. Consequently the middle term is not only universality but also particularity and individuality. As universality it is first the substantial identity of the genus; but secondly an identity that embraces within itself particularity, but a particularity co-extensive with this identity of the genus; it is therefore the universal sphere that contains its total particularisation — the genus disjoined into its species: A that is B and C and D.
But particularisation is differentiation and as such is just as much the either-or of B, C and D, the negative unity, the reciprocal exclusion of the terms. Further, this exclusion is not merely a reciprocal exclusion, or the determination merely a relative one, but it is just as essentially a self-related 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 premises but also in the conclusion. In the first premise it is a universal, and in its predicate, the universal sphere particularised into the totality of its species; in the second premise it appears as determinate or as a species; in the conclusion it is posited as the exclusive, individual determinateness. Or again, it already appears in the minor premise as exclusive individuality and is positively posited in the conclusion as the determinate which it is.
Hence what appears in general as mediated is the universality of A with individuality. But the mediating factor is this A, which is the universal sphere of its particularisations and is determined as an individual. Consequently the truth of the hypothetical syllogism, namely the unity of the mediating and the mediated, is posited in the disjunctive syllogism, which for this reason is equally no longer a syllogism at all. For the middle term, which is posited in it as the totality of the Notion, contains itself the two extremes in their complete determinateness. The extremes, in distinction from this middle term, appear only as a positedness which no longer possesses any determinateness peculiar to itself as against the middle term.
Considering this point further with more particular reference to the hypothetical syllogism, we see that in the latter we had a substantial identity as the inner bond of necessity, and a negative unity distinguished therefrom — namely, the activity or form which translated one existence into another. The disjunctive syllogism is in general in the determination of universality; its middle term is the A as genus and as perfectly determinate; through this unity, that content which previously was inner is also posited and, conversely, the positedness or form is not the external, negative unity over against an indifferent existence, but is identical with the said substantial content. The whole form determination of the Notion is posited in its determinate difference and at the same time in the simple identity of the Notion.
In this way then the formalism of the syllogistic process, and with it the subjectivity of the syllogism and of the Notion in general, has sublated itself. This formal or subjective side consisted in the fact that the mediating factor of the extremes is the Notion as an abstract determination, and this latter is distinct from the extremes whose unity it is. In the consummation of the syllogism, on the other hand, where objective universality is no less posited as totality of the form determinations, the distinction of mediating and mediated has disappeared. That which is mediated is itself an essential moment of what mediates it, and each moment appears as the totality of what is mediated.
The figures of the syllogism exhibit each determinateness of the Notion individually as the middle term, which at the same time is the Notion as an ought-to-be, a demand that the mediating factor shall be the Notion's totality. But the different genera of the syllogism exhibit the stages of impregnation or concretion of the middle term. In the formal syllogism the middle term is only posited as totality by all the determinatenesses, though each singly, functioning as the mediating factor. In the syllogisms of reflection the middle term appears as the unity that gathers together externally the determinations of the extremes. In the syllogism of necessity it has likewise determined itself to the unity that is no less developed and total than simple, and the form of the syllogism which consisted in the difference of the middle term from its extremes has thereby sublated itself.
Thus the Notion as such has been realised; more exactly, it has obtained a reality that is objectivity. The first reality was that the Notion, as within itself negative unity, sunders itself, and as judgment posits its determinations in a determinate and indifferent difference, and in the syllogism sets itself in opposition to them. In this way it is still the inwardness of this its externality, but the outcome of the course of the syllogisms is that this externality is equated with the inner unity; the various determinations return into this unity through the mediation in which at first they are united only in a third term, and thus the externality exhibits in its own self the Notion, which therefore is no longer distinguished from it as an inner unity.
However, this determination of the Notion which has been considered as reality, is, conversely, equally a positedness. For it is not only in this result that the truth of the Notion has exhibited itself as the identity of its inwardness and externality; already in the judgment the moments of the Notion remain, even in their mutual indifference, determinations that have their significance only in their relation. The syllogism is mediation, the complete Notion in its positedness. Its movement is the sublating of this mediation, in which nothing is in and for itself, but each term is only by means of an other. The result is therefore an immediacy which has issued from the sublating of the mediation, a being which is no less identical with the mediation, and which is the Notion that has restored itself out of, and in, its otherness. This being is therefore a fact that is in and for itself objectivity.