B. The Judgment of Reflection

A singular as such is what the subject is in the judgment that has by now emerged; likewise the universal is no longer abstract universality, or a single property, but stands posited as a universal that has drawn itself into one through the reference of things distinguished, or, taken with respect to the content of diverse determinations at large, as that which is the taking together of manifold properties and concrete existences. – Should examples of predicates belonging to judgments of reflection be called for, they must be of a different cast from those serving judgments of existence. Properly speaking, it is only in the judgment of reflection that a determinate content, that is, a content at all, is at hand; for the content is the form-determination reflected into identity, marked off from form insofar as form is differentiated determinateness, – which is what form still amounts to as judgment. Within the judgment of existence, the content is merely something immediate, or something abstract and undetermined. – Judgments of reflection may accordingly be exemplified thus: the human being is mortal, things are transient, this thing is useful, harmful; hardness, elasticity in bodies, happiness and so forth are predicates of that peculiar sort. What they [express] is an essentiality, one that is nevertheless a determination within a relation, or a gathering universality. This universality, which will go on determining itself in the course of the judgment of reflection's movement, still stands apart from the universality of the concept as such; granted, it is no longer the abstract universality of the qualitative judgment, yet it keeps a reference to the immediate out of which it comes, and has that immediate lying at its base for its negativity. – In the first instance the concept determines existence into relational determinations, into continuities of themselves within the diverse manifoldness of concrete existence, – so that, while the truly universal is indeed their inner essence, still, in appearance, this relative nature, or their mark, is not yet what they are in and for themselves.

It might well look like the obvious course to determine the judgment of reflection as the judgment of quantity, in the way that the judgment of existence was also determined as the qualitative judgment. Yet just as the immediacy there was not only the immediacy which is but essentially the mediated, abstract one besides, so here too the sublated immediacy in question is not simply sublated quality, hence not simply quantity; quantity is rather, in the same manner in which quality is the most external immediacy, the most external determination belonging to mediation.

A remark remains to be made about the determination as it shows itself in its movement within the judgment of reflection: in the judgment of existence the movement of that determination displayed itself at the predicate, this judgment standing in the determination of immediacy, so that the subject appeared as what lies at the base. On the same grounds, in the judgment of reflection the onward course of determining runs off at the subject, since it is reflected being-in-itself that this judgment has for its determination. Here, then, what is essential is the universal, or the predicate; it therefore makes up what lies at the base, whereby the subject is to be measured and in conformity with which it is to be determined. – The predicate does, all the same, acquire a further determination through the ongoing formation of the subject's form, only indirectly so, whereas the latter formation, on the grounds just given, shows itself as direct onward determining.

Turning to the objective significance of the judgment: through its universality the singular steps into existence, yet as within an essential relational determination, an essentiality that holds itself intact throughout the manifoldness of appearance; the subject ought to be what is determined in and for itself; this determinateness it possesses in its predicate. On the other side, the singular is reflected into this predicate of its own, which is its universal essence; to that extent the subject is what concretely exists and what appears. The predicate in this judgment does not any longer inhere in the subject; it is rather what is in itself, under which the singular in question stands subsumed as something accidental. Whereas the judgments of existence may also be determined as judgments of inherence, those of reflection count rather as judgments of subsumption.

a. The Singular Judgment

The immediate judgment of reflection now reads once more: the singular is universal; only that subject and predicate now bear the sense indicated; put more closely, therefore, it may be worded thus: this is an essentially universal.

But a this is not an essentially universal. Positive though that judgment at large is by its universal form, it has to be taken negatively. But inasmuch as a merely positive judgment is not all that the judgment of reflection amounts to, the negation fails to touch the predicate directly, this being no inhering predicate but rather what is in itself. Rather it is the subject that is alterable and awaits determining. The negative judgment must accordingly be caught here in this shape: not a this is a universal of reflection; an in-itself such as this has a concrete existence of wider universality than what lies in one single this. The singular judgment thus has its next truth in the particular one.

b. The Particular Judgment

That non-singularity of the subject which must be posited in place of its singularity in the first judgment of reflection is particularity. Singularity, however, stands determined in the judgment of reflection as essential singularity; particularity therefore cannot be some simple, abstract determination wherein the singular would stand sublated and whatever concretely exists would have foundered, but only an expansion of that singular in external reflection; hence the subject reads: some thises, or a particular multitude of singulars.

The judgment some singulars are a universal of reflection looks at first like a positive judgment, and yet is negative every bit as much; for some harbours universality; on that score it may be regarded as comprehensive; but so far as it is particularity, it fails just as much to match universality. As was shown above, the negative determination which the subject has acquired through the singular judgment's transition is a determination of the reference too, of the copula. – Lodged in the judgment some human beings are happy is the immediate consequence: some human beings are not happy. Granted that some things are useful, then for that very reason some things are not useful. Positive and negative judgment no longer fall asunder; the particular judgment holds both together at once, immediately, precisely on account of its being a judgment of reflection. – But for that reason the particular judgment is indeterminate.

Take the subject further, in the example of such a judgment, as some human beings, animals and so forth: besides the particular form-determination some, it holds within it the content-determination human being and so forth. For the singular judgment the subject could read this human being, a singularity that belongs properly to outward showing; better, then, that it should run, say, Cajus. Yet some Caji can no longer serve as the subject of the particular judgment; for Cajus is meant to be a singular as such. To the some, therefore, a more universal content gets attached, say human beings, animals and so forth. Such a content is not merely empirical but one determined through the judgment's form; namely, it is a universal, since some harbours universality, and this universality must at the same time stand apart from the singulars, reflected singularity lying at the base. More precisely, it is also the universal nature, or the genus human being, animal; – thus anticipating that universality which is the outcome of the judgment of reflection, much as the positive judgment, having the singular for its subject, anticipated the determination that is the outcome of the judgment of existence.

To that extent the subject, holding within it the singulars, their reference to particularity, and the universal nature, already stands posited as the totality of the determinations of the concept. Such a consideration, however, is properly an external one. What its form posits in the subject, in the first instance and in reference of the terms to one another, is the expansion of the this into particularity; only, this universalizing does not match the this; this is something perfectly determinate, whereas some this is undetermined. The expansion is meant to attach to the this, hence to be perfectly determinate in conformity with it; and such is totality, or in the first instance universality at large.

Underlying this universality is the this, for the singular is here what is reflected into itself; the further determinations of the singular therefore run their course upon it externally, and just as particularity for that reason determined itself as some, so the universality the subject has gained is allness, and with that the particular judgment has passed over into the universal one.

c. The Universal Judgment

Universality, as it is met with at the subject of the universal judgment, is that external universality belonging to reflection, allness; all are all the singulars; the singular remains unaltered within it. Such universality is therefore no more than a gathering together of singulars that subsist on their own; it is a commonality accruing to them only upon comparison. – Where universality comes up for discussion, it is commonality of this kind that habitually presents itself first to subjective representation. When a ground is wanted, closest to hand, for why some determination should count as a universal one, what gets alleged is that it belongs to several. – In analysis chiefly, too, this concept of universality is what hovers before one, seeing that, for instance, developing a function by a polynomial passes for the more universal procedure over against developing the same function by a binomial; because the polynomial exhibits more singularities than the binomial does. Strictly, the requirement that the function be exhibited in its universality calls for a pantonomial, for infinity run through to the end; but at this point the restriction upon that requirement sets in of its own accord, and the exhibition of the infinite multitude has to rest content with the ought of such exhibition, and hence with a polynomial after all. In point of fact, however, the binomial already is the pantonomial in every case where the method or rule concerns nothing beyond the dependence of one term upon one other, and where the dependence of the several terms upon those preceding them does not particularize itself, one and the same function staying at the base. It is the method or rule that has to be looked upon as the truly universal; carrying the development onward, or developing a polynomial, merely repeats it; through the enlarged multiplicity of terms it accordingly gains nothing in universality. Bad infinity and the deception belonging to it have been discussed earlier already; the universality of the concept is the beyond attained; that infinity, though, stays saddled with the beyond as with something unattainable, so far as it stays the mere progress into infinity. Should nothing but allness hover before one in the case of universality, a universality supposed to be exhausted in the singulars taken as singulars, then here is a relapse into that bad infinity; or else plurality is simply passed off for allness. Plurality, be it ever so vast, stays sheer particularity all the same, and is not allness. – Dimly, however, there hovers along with all this the universality of the concept, which is in and for itself; it is the concept that drives forcibly out beyond the stubborn singularity to which representation clings, and out beyond the externality of representation's reflection, slipping allness as totality in its place, or rather the categorical being-in-and-for-itself.

The same shows itself elsewhere in allness, which at large is the empirical universality. So far as the singular is presupposed as something immediate, and hence come upon and taken up externally, the reflection that gathers it into allness is external to it in just the same measure. But since the singular as this is utterly indifferent toward such reflection, universality and a singular of that sort cannot close into one unity. Empirical allness therefore remains a task; an ought which, so taken, admits of no exhibition as being. An empirically universal proposition, for such are put forward all the same, rests, then, upon the tacit agreement that, so long as no instance to the contrary can be adduced, the multiplicity of cases is to hold as allness; or that the subjective allness, namely that of the cases which have come to knowledge, may be taken for an objective allness.

Looking now more closely at the universal judgment where we stand: the subject, which, as was noted just now, holds within it the universality that is in and for itself as presupposed, now carries [that same universality] at itself as posited too. All human beings expresses first the genus human being, second this genus in its singularization, though in such wise that the singulars are simultaneously widened out into the universality of the genus; conversely, through this linkage with singularity universality is determined every bit as perfectly as singularity is; hereby the posited universality has become EQUAL to the presupposed one.

Properly, however, no advance account is to be taken of what is presupposed; the outcome is rather to be considered on its own at the form-determination. – Singularity, in having widened itself out to allness, is posited, as negativity that is identical reference to itself. It has thereby not stayed that first singularity, such as, for instance, the singularity of a Cajus, but is the determination identical with universality, or the universal's absolute being-determined. – The first singularity belonging to the singular judgment was no immediate one such as the positive judgment has, but had arisen out of the dialectical movement of the judgment of existence taken as a whole; already it stood determined as the negative identity of that judgment's determinations. Here is the genuine presupposition within the judgment of reflection; over against the positing that runs its course in the latter, that first determinateness of singularity was singularity's in-itself; what singularity accordingly is in itself now stands posited through the movement of the judgment of reflection, namely singularity as the identical reference of what is determinate to its own self. Hence that reflection which widens singularity out to allness is none that would be external to it; what singularity already is in itself merely comes thereby to be for itself. – So the outcome is in truth objective universality. To that extent the subject has stripped off the form-determination of the judgment of reflection, which travelled from this by way of some to allness; in place of all human beings one has henceforth to say: the human being.

Universality thus arisen is the genus; the universality that is concrete at its own self. The genus does not inhere in the subject, nor is it a single property, and at large not a property of the subject at all; every singularized determinateness it holds dissolved within its substantial solidity. – Precisely because it stands posited as this negative identity with itself, the genus is essentially subject; but it is no longer subsumed under its predicate. Herewith the nature of the judgment of reflection alters altogether.

That judgment was essentially one of subsumption. Its predicate stood determined over against its subject as the universal that is in itself; on the side of content it admitted of being taken as an essential relational determination, or else as a mark; – a determination whereby the subject is nothing but an essential appearance. Determined as objective universality, however, the subject ceases to be subsumed under any such relational determination, or gathering reflection; a predicate of that sort is rather, measured against this universality, a particular one. The relation of subject and predicate has thus turned itself about, and to that extent the judgment has for the time being sublated itself.

This sublation of the judgment coincides with what turns into the determination of the copula, still awaiting our consideration; the sublating of the judgment's determinations and their transition into the copula are one and the same. – For so far as the subject has raised itself into universality, in this determination it has become equal to the predicate, which as the reflected universality comprises particularity too within itself; subject and predicate are accordingly identical, that is, they have run together into the copula. Such identity is the genus, or the nature of a thing as it is in and for itself. So far, then, as this identity sunders itself once more into a judgment, it is the inner nature by which subject and predicate refer to each other; – a reference of necessity, wherein those determinations of the judgment are unessential differences merely. – What belongs to all the singulars of a genus, belongs by their nature, to the genus, – this is an immediate consequence, and the expression of what came out just now, that the subject, for instance all human beings, strips off its form-determination, and the human being is to be said instead. – Such interconnection, which is in and for itself, makes up the groundwork of a new judgment; – the judgment of necessity.

C. The Judgment of Necessity

The determination into which universality has developed is, as has come out, universality in and for itself, or objective universality, answering to which in the sphere of essence stands substantiality. What sets it apart from substantiality is that it belongs to the concept, and thereby is not the inner necessity of its determinations only but the posited necessity as well, or that difference is immanent to it, whereas substance harbours its own difference only in its accidents and not as a principle within its own self.

In the judgment this objective universality is now posited; hence first along with this its essential determinateness, as immanent to it, second as distinct from it as particularity, for which that universality makes up the substantial groundwork. Determined in this manner, it is genus and species.

a. The Categorical Judgment

The genus divides itself, or repels itself essentially into species; genus it is only so far as it comprises species beneath it; and the species is species only so far as, on the one side, it concretely exists in singulars, and, on the other, possesses in the genus a universality higher than itself. – As its predicate the categorical judgment now has a universality of that kind, wherein the subject possesses its immanent nature. It is itself, however, the first, immediate judgment of necessity; hence the determinateness of the subject, whereby the subject is a particular or a singular over against genus or species, belongs so far to the immediacy that external concrete existence has. – Objective universality, however, likewise has here as yet only its immediate particularization; on one side it is on that account itself something determinate, over against which higher genera stand; – on the other side it is not exactly the nearest genus, that is, one whose determinateness is not precisely what constitutes the principle of the subject's specific particularity. What is necessary about it, though, is the substantial identity of the subject with the predicate, over against which whatever is peculiar to the former, marking it off from the latter, counts only as an unessential positedness, – or indeed as a mere name; in its predicate the subject is reflected back into its being-in-and-for-itself. – A predicate of this sort ought not to be lumped in with the predicates of the judgments treated so far; if the judgments, say: the rose is red, the rose is a plant, or else: this ring is yellow, it is gold, get flung together into a single class, and a property as external as the colour of a flower is taken for a predicate on a par with the flower's vegetable nature, then a difference is passed over that must strike even the crudest apprehension. – Sharply, therefore, must the categorical judgment be marked off from positive and negative judgment; in the latter two, what the subject gets credited with is a single contingent content, while in the former it is that totality of the form which is reflected into itself. In it, accordingly, the copula carries the meaning of necessity, in those others only that of abstract, immediate being.

At first the determinateness of the subject whereby the subject is a particular over against the predicate is still something contingent; subject and predicate stand in no necessary reference through form or determinateness; necessity therefore still stands as something inner. – Subject, however, the subject is only as a particular, and so far as it has objective universality, it is to have that universality essentially in accordance with the determinateness which is as yet only immediate. In determining itself, that is, in setting itself into the judgment, the objectively universal stands essentially in identical reference with this determinateness as such repelled out of it, that is, the determinateness is essentially not to be posited as something merely contingent. Only through such necessity of its immediate being does the categorical judgment answer to its objective universality, and in this manner has passed over into the hypothetical judgment.

b. The Hypothetical Judgment

If A is, then B is; or, A's being is not a being of its own, but the being of an other, of B. – What this judgment posits is the necessary interconnection of immediate determinatenesses, something the categorical judgment does not yet posit. – Two immediate concrete existences are present here, or externally contingent ones, of which the categorical judgment at first has only the one, the subject; but since the one stands externally over against the other, this other likewise stands, immediately, externally over against the first. – Given such immediacy the content of the two sides remains indifferent, each towards the other; hence this judgment is at first a proposition of empty form. Now immediacy is, first, admittedly a self-subsistent, concrete being as such; but, second, it is the reference of this being that is essential; hence that being counts equally as mere possibility; what the hypothetical judgment contains is not that A is, nor that B is, but only this: if one of them is, then so is the other; the interconnection of the extremes alone is posited, as being, and not the extremes themselves. On the contrary, within this necessity each is posited as being equally the being of an other. – The proposition of identity declares: A is A only, not B; and B is B only, not A; whereas in the hypothetical judgment the concept posits the being of finite things according to their formal truth, namely this: that the finite is a being of its own and yet equally not its own, but the being of an other. Within the sphere of being the finite alters itself, it turns into an other; within the sphere of essence it is appearance, and it is posited that its being consists in an other's shining in it, while necessity is the inner reference, not yet posited as such. But the concept is precisely this: that such identity is posited, and that whatever has being is not abstract identity with itself but concrete identity, and, immediately in its own self, the being of an other.

The hypothetical judgment may be taken in a closer determinateness by way of the relations of reflection, as the relation of ground and consequence, of condition and conditioned, of causality, and so forth. What substantiality is in the categorical judgment, the interconnection of causality is in the hypothetical, in its form as concept. This relation and the rest all fall under it, but here they are no longer relations between self-subsistent sides; these sides essentially are only moments of one and the selfsame identity. – Within it, however, they are not yet opposed following the determinations of the concept, as singular or particular and universal, but only as moments in general. So far, then, the hypothetical judgment has rather the shape of a proposition; as the particular judgment is indeterminate in content, so the hypothetical is indeterminate in form, since its content does not stand in the determination of subject and predicate. – Yet in itself being, being as it is the being of the other, is precisely thereby unity of itself and of the other, and so universality; therewith it is at the same time properly only a particular, since it is determinate and, in its determinateness, does not refer merely to itself. What is posited, however, is not the simple abstract particularity; through the immediacy which the determinatenesses have, the moments of that particularity are as differentiated; through their unity, which constitutes their reference, particularity is at the same time also their totality. – Accordingly, what this judgment in truth posits is universality, the concept's concrete identity, whose determinations possess no subsistence on their own account and are merely particularities posited within it. So it is the disjunctive judgment.

c. The Disjunctive Judgment

The concept in the categorical judgment is as objective universality, and an external singularity. Upon this externality, in the hypothetical, the concept comes forward in its negative identity; through that identity they obtain the determinateness now posited in the disjunctive judgment, the determinateness which in the former they have immediately. The disjunctive judgment is accordingly objective universality posited at once together with the form. What it holds is therefore, first, the concrete universality or the genus, under simple form, as the subject; second, however, that same universality as totality of the determinations differentiated within it. A is either B or C. Herein lies the necessity of the concept, wherein, first, there is the selfsameness of the two extremes, one and the same extension, content and universality; second, they stand differentiated following the form of the determination of the concept, though so that, for the sake of that identity, this form is as mere form. Third, the identical objective universality appears on that account as what is reflected into itself over against the unessential form, as content, which nonetheless carries the determinateness of form in its own self; the one time as the simple determinateness of the genus; the other time just this determinateness as developed into its difference, – in which manner it constitutes the particularity of the species, and the totality of these, the genus's universality. – Particularity in its development makes up the predicate, because it is to that extent the more universal, in that it contains the whole universal sphere of the subject, yet contains it also in the laying-out of particularization.

Looking at this particularization more closely, then in the first place the substantial universality of the species is constituted by the genus; the subject is accordingly both B and C; this both and marks the positive identity of particular with universal; this objective universal maintains itself completely in its particularity. The species, second, shut each other out; A is either B or C; for they constitute the determinate difference of the universal sphere. This either-or is the negative reference of them. In the latter, however, they are just as identical as in the former; the genus is their unity as determinate particulars. – Were the genus abstract universality, as in the judgments of existence, then the species too would have to be taken merely as diverse ones, indifferent towards each other; but the genus is not that external universality arising only through comparison and omission, but rather their immanent and concrete one. – Necessity is lacking in an empirical disjunctive judgment; A is either B or C or D and so forth, because the species B, C, D and so forth have simply turned up; strictly speaking no either-or can be pronounced by such a judgment; for species of that kind make up at best a subjective completeness; the one species does indeed exclude the other; but either-or excludes every further one, and closes off a total sphere within itself. The necessity of this totality lies in the negative unity of the objectively universal, which has dissolved singularity within itself and carries it immanently within itself as the simple principle of difference, whereby the species stand determined and referred to one another. The empirical species, by contrast, have their differences in some contingency or other, one that is an external principle and hence not their principle, and so also not the immanent determinateness of the genus; for that reason they are not referred to one another according to their determinateness either. – It is through the reference of their determinateness, though, that the species make up the universality of the predicate. – The so-called contrary and contradictory concepts ought strictly to find their place only here; for in the disjunctive judgment the essential difference of the concept is posited; but therein they at the same time also have their truth, namely that the contrary and the contradictory are themselves differentiated just as much contrarily as contradictorily. The species are contrary insofar as they are only diverse, namely, through the genus as their objective nature they have a subsistence in and for itself; contradictory, insofar as they exclude each other. Each of these determinations taken on its own is, however, one-sided and lacking in truth; within the either-or of the disjunctive judgment there is posited their unity as their truth, according to which that self-subsistent subsistence, as concrete universality, is itself likewise the principle of the negative unity through which they shut each other out.

Through the identity of subject and predicate just now exhibited, an identity following negative unity, the disjunctive judgment determines the genus as the nearest one. This expression points at first to a bare quantitative difference of more or fewer determinations that a universal may contain over against a particularity standing beneath it. On such a reckoning it remains contingent what the nearest genus properly is. But insofar as one takes the genus for a universal formed merely by leaving determinations out, it cannot properly form any disjunctive judgment; for it is contingent whether the determinateness making up the principle of the either-or has happened to remain in it; the genus would not be exhibited in the species according to its determinateness at all, and these could have only a contingent completeness. In the categorical judgment the genus stands over against the subject at first only in this abstract form, hence not necessarily as the genus nearest to it, and to that extent externally. But since the genus, as concrete, is essentially determinate universality, as the simple determinateness it is the unity of those moments of the concept which in that simplicity are merely sublated but have their real difference in the species. The genus is therefore the nearest one of a species insofar as that species has its specific differentiation in the essential determinateness of the genus, and insofar as the species in general have their differentiated determination, as principle, in the nature of the genus.

The side just considered makes up the identity of subject and predicate on the side of being-determined in general; a side that has been posited through the hypothetical judgment, whose necessity is an identity of immediates and of diverse things, and is therefore essentially as negative unity. This negative unity is what in general separates subject and predicate, though it is now itself posited as differentiated, in the subject as simple determinateness, and in the predicate as totality. That separating of the subject from the predicate is the difference of the concept; but the totality of the species in the predicate can just as little be any other difference. – The determination of the disjunctive members over against each other thus issues from this. It reduces itself to the difference of the concept, for the concept alone disjoins itself and manifests its negative unity in its determination. For the rest, the species comes into consideration here only according to its simple determinateness of the concept, not according to the shape in which it has stepped out of the idea into a further self-subsistent reality; that shape does indeed fall away where the genus's simple principle is concerned; but the essential differentiation has to be a moment of the concept. In the judgment considered here it is properly through the concept's own further determining that its disjunction is now itself posited, that which emerged in the case of the concept as its determination existing in and for itself, as its differentiation into determinate concepts. – Since the concept is now the universal, the positive just as much as the negative totality of the particulars, precisely thereby it itself is also immediately one of its disjunctive members; the other, though, is this universality resolved into its particularity, that is, the concept's determinateness as determinateness; and in that determinateness universality just so presents itself as the totality. – If a genus's disjunction into species has not yet attained this form, that is proof that it has not risen to the concept's determinateness and has not issued out of it. – Colour is either violet, indigo, light blue, green, yellow, orange, or red; – in a disjunction of that sort its mixedness and impurity, empirical as well, can be seen at once; regarded on this side on its own, it already deserves to be called barbaric. If colour has been grasped as the concrete unity of bright and dark, then this genus carries the determinateness in it which makes up the principle by which it is particularized into species. Among these, however, one has to be the absolutely simple colour, which holds the opposition in even balance and enclosed and negated within its intensity; over against it the opposition of the relation of the bright and the dark must present itself, to which, since a phenomenon of nature is at issue, the indifferent neutrality of the opposition must further be added. – Taking mixtures like violet and orange, and gradations like indigo and light blue, for species can have its ground only in a wholly unconsidered procedure, one showing too little reflection even for empiricism. – What differentiated and still more closely determined forms the disjunction may have, according as it takes place in the element of nature or of spirit, does not belong here to be worked out.

The disjunctive judgment has the members of the disjunction at first in its predicate; but it is just as much itself disjoined; the members of the disjunction are its subject and its predicate; these are the concept's moments, posited in their determinateness and yet at once as identical, as identical α) in objective universality, this being the simple genus in the subject, and in the predicate the universal sphere together with the totality of the concept's moments, and β) in the negative unity, the developed interconnection of necessity, according to which the simple determinateness in the subject has gone apart into the difference of the species, and precisely therein is their essential reference and what is identical with itself.

The copula of this judgment, this unity into which the extremes have gone together through their identity, is thus the concept itself, and indeed as posited; with this the mere judgment of necessity has raised itself to the judgment of the concept.

D. The Judgment of the Concept

Knowing how to pass judgments of existence: the rose is red, snow is white, and so forth, will hardly count as evidence of a great power of judgment. The judgments of reflection come closer to being propositions; the object in the judgment of necessity stands, admittedly, in its objective universality, yet only in the judgment now to be considered is its reference to the concept at hand. Therein the concept is laid down as ground, and since it stands in reference to the object, it is there as an ought to which reality may correspond or may fail to. – Hence only a judgment of this sort holds a genuine appraisal; the predicates good, bad, true, beautiful, correct, and so forth express that the fact, measured against its universal concept as against the simply presupposed ought, either stands in agreement with it or does not.

The judgment of the concept has been called judgment of modality, and is looked upon as containing the form in which the reference of subject and predicate stands within an external understanding, and as concerning the value of the copula only in reference to thinking. On this account the problematic judgment is said to consist in one's taking the affirming or denying as optional or as possible; – the assertoric, in one's taking it as true, that is, actual; and the apodictic, in one's taking it as necessary. – It is easy to see why, with this judgment, it lies so near to hand to step outside the judgment itself and to view its determination as something merely subjective. For what steps forward once more in the judgment here is the concept, the subjective, and it comports itself towards an immediate actuality. Only, this subjective is not to be confounded with external reflection, which is admittedly also something subjective, but in another sense than the concept itself; the concept, stepping forward again out of the disjunctive judgment, is on the contrary the very reverse of a mere manner and mode. In this sense the earlier judgments are only something subjective, since they rest upon an abstraction and one-sidedness wherein the concept has gone lost. As against them, the judgment of the concept is rather the objective one and the truth, precisely because what lies at its ground is the concept in its determinateness as concept, and not the concept in external reflection or in reference to a subjective, that is, contingent thinking.

In the disjunctive judgment the concept had been posited as identity of the universal nature with its particularization; therewith the relation of the judgment had sublated itself. This concrete unity of universality and particularization is at the outset a simple result; it has now to build itself out further into totality, seeing that the moments it holds have at first gone under within it and do not yet confront one another in determinate self-subsistence. – The deficiency of the result may also be put more determinately thus: that in the disjunctive judgment the objective universality has indeed become complete in its particularization, but that the negative unity of the latter goes back only into the former and has not yet determined itself into the third, into singularity. – Insofar, however, as the result is itself the negative unity, it already is this singularity; but so taken it is only this one determinateness, which now has to posit its own negativity, to sunder itself into the extremes, and thus to develop itself fully into the syllogism.

The next diremption of this unity is the judgment, wherein it is posited the one time as subject, as an immediately singular, and then as predicate, as the determinate reference of its moments.

a. The Assertoric Judgment

At first the judgment of the concept is immediate; so taken it is the assertoric judgment. Its subject is a concrete singular in general, while the predicate expresses that same singular as the reference of its actuality, determinateness or constitution, to its own concept. (This house is bad, this action is good.) More closely, then, what it holds is a) that the subject ought to be something or other; its universal nature has posited itself as self-subsistent concept; b) the particularity, which is as constitution and external concrete existence not merely on account of its immediacy but because it is expressly differentiated from its self-subsistent universal nature; owing to the self-subsistence of the concept, this particularity is for its part likewise indifferent towards the universal, and may prove adequate to it or fail to. – Such constitution is the singularity that lies outside the universal's necessary determination in the disjunctive judgment, a determination which is only as the particularizing of the species and as the genus's negative principle. To that extent the concrete universality issuing from the disjunctive judgment is, in the assertoric judgment, torn in two into the form of extremes, and these still lack the concept itself as the posited unity referring them to each other.

For that reason the judgment is as yet only assertoric; its verification is a subjective assurance. That something is good or bad, correct, fitting or not, and so forth, has its interconnection in an external third. But that this interconnection is externally posited amounts to the same as its being as yet only in itself or inwardly. – If something is good or bad and so forth, hardly anyone will therefore suppose that it is good only in subjective consciousness while in itself perhaps bad, or that good and bad, correct, fitting, and so forth are not predicates of the objects themselves. What is merely subjective in the assertion of this judgment thus lies in this, that the interconnection of subject and predicate which is in itself is not yet posited, or, what comes to the same, that it is merely external; the copula remains an immediate, abstract being.

The assurance of the assertoric judgment is therefore met, with just as much right, by the opposite one. Should the assurance run: this action is good; then the opposite, this action is bad, still has warrant just as good. – Or, considered in itself: since the subject of this judgment is an immediate singular, it has in this abstraction not yet posited in it that determinateness which would hold its reference to the universal concept; it is thus still something contingent, as apt to answer to the concept as to fail of it. The judgment is therefore essentially problematic.

b. The Problematic Judgment

The problematic judgment is nothing but the assertoric one, insofar as the latter has to be taken positively just as much as negatively. – On this qualitative side the particular judgment is a problematic one as well, for it holds positively just as much as negatively; – in like manner the being of subject and predicate is problematic in the hypothetical judgment; – through these judgments too it is posited that the singular and the categorical judgment are as yet something merely subjective. Within the problematic judgment as such, though, this positing is more immanent than it is in the judgments mentioned above, since in the latter the content of the predicate is the reference of the subject to the concept, and here therewith the determination of the immediate as a contingent thing is itself at hand.

At the outset it appears merely problematic whether the predicate is to be joined with some given subject or not, and to that extent the indeterminateness falls within the copula. Nothing determinate can issue from this for the predicate, for the predicate already is objective, concrete universality. What is problematic concerns, then, the immediacy of the subject, an immediacy thereby determined as contingency. – Yet the singularity of the subject is not on that account to be abstracted from; cleansed of singularity altogether, the subject would be a universal merely; the predicate holds precisely this, that the subject's concept is to be posited in reference to its singularity. – There is no saying: the house or a house is good; the answer runs rather: according to how it is constituted. – What is problematic about the subject in its own self makes up its contingency as a moment: the subjectivity of the fact set over against its objective nature or its concept, the bare manner and mode, or the constitution.

The subject is thus itself differentiated into its universality or objective nature, its ought, and into the particular constitution of existence. Therewith it holds the ground of whether it is as it ought to be. In this way it has been brought into balance with the predicate. – The negativity of what is problematic, insofar as it is turned against the immediacy of the subject, accordingly signifies nothing but this original dividing of the subject, which in itself already is as unity of universal and particular, into these its moments; – a dividing which is the judgment itself.

One may further remark that each of the subject's two sides, its concept and its constitution, might be called that subject's subjectivity. The concept is a fact's universal essence gone into itself, the fact's negative unity with itself; and this unity constitutes its subjectivity. But a fact is also essentially contingent and carries an external constitution; this too is called its bare subjectivity, over against the objectivity just named. The fact itself is precisely this, that its concept, as the negative unity of itself, negates its universality and puts itself forth into the externality of singularity. – It is as this doubled thing that the subject of the judgment is posited here; those conflicting significations of subjectivity are, according to their truth, in one. – The signification of the subjective has itself turned problematic through this, that it has lost the immediate determinateness which belonged to it in the immediate judgment, together with its determinate opposition to the predicate. – That conflicting signification of the subjective, occurring as it does in the reasoning of ordinary reflection as well, might at least on its own draw notice to the point that the subjective has no truth in one of the two alone. The doubled signification is the appearance of this, that each on its own, taken singly, is one-sided.

Once what is problematic is posited in this way as the problematic of the fact, as the fact along with its constitution, then the judgment is itself no longer problematic but apodictic.

c. The Apodictic Judgment

The apodictic judgment's subject (a house of such and such a make is good, an action so and so constituted is right,) carries about it first the universal, what it ought to be, secondly its constitution; the second of these holds the ground for why a predicate belonging to the judgment of the concept does or does not attach to the subject entire, that is, whether or not the subject measures up to its concept. – With this the judgment is genuinely objective; or rather, it is the truth of judgment generally. Subject and predicate answer to each other, their content is one and the same, and this content is itself concrete universality as posited; for within it lie a pair of moments — the objectively universal element, or the genus, together with the singularized. So what we have here is the universal which is itself, which carries itself on through its opposite, and which counts as universal only in being unity with that opposite. – A universal of this kind — such predicates as good, fitting, correct, and so on — rests upon an ought, and at once takes in the answering of existence to that ought; not that ought, nor the genus for itself, but precisely this answering is the universality that constitutes what is predicated in the apodictic judgment.

These two moments are contained in the subject likewise, in immediate unity, as the fact. But the truth about the fact is that it stands broken within itself into its ought and its being; such is the absolute judgment upon all actuality. – That this original division, the very omnipotence of the concept, is equally a return into the concept's unity and an absolute reference of ought and being to one another — this is what makes the actual into one fact; and the inner reference between them, this concrete identity, makes up the soul of the fact.

The transition from the fact's immediate simplicity over to the answering that is the determinate reference between its ought and its being, – or the copula, now proves on closer inspection to have its seat in the fact's particular determinateness. The genus is the universal that is in and for itself, which to that extent shows up as standing in no reference at all; the determinateness, by contrast, is what reflects itself within that universality into itself and yet at the same time into an other. Hence the judgment has its ground in how the subject is constituted, and for that reason is apodictic. So there is now present the determinate and fulfilled copula, the one that formerly consisted in the abstract is but has by now grown out into ground as such. To begin with it sits at the subject as an immediate determinateness, yet it is every bit as much the reference to the predicate, whose content is nothing but this answering itself, or the subject's reference to universality.

So the judgment's form has gone under: first, because in themselves subject and predicate are one and the same content; but secondly, because through its determinateness the subject points out beyond itself and refers itself to the predicate, while thirdly this referring has equally passed over into the predicate, makes up the predicate's whole content, and is thus the posited reference, or the judgment itself. – In this way the concrete identity of the concept — which was the result of the disjunctive judgment and which makes up the inner groundwork of the judgment of the concept — is established throughout the whole, whereas at first it was posited only in the predicate.

Looked at more closely, the positive side of this result, the side that makes for the judgment's transition into another form, shows subject and predicate in the apodictic judgment, as we have seen, each of them as the concept entire. – Yet the unity of the concept, being the determinateness that makes up the copula which sets them in reference to each other, is at the same time distinguished from the two. To begin with, it stands only over on the subject's side, as that subject's immediate constitution. But since it is essentially the referring factor, it is not just such an immediate constitution but rather what runs through subject and predicate alike, and is universal. – Given that subject and predicate have the same content, what that determinateness posits, by contrast, is the form-reference; the determinateness as a universal, or particularity. – Thus it holds both form-determinations of the extremes within itself; and is the determinate reference of subject and predicate; it is the fulfilled or content-laden copula of the judgment, the concept's unity stepped forth again out of the judgment in which it had been lost in the extremes. – Through this fulfilment of the copula the judgment has turned into the syllogism.

Chapter 3. The Syllogism

The syllogism has emerged as the reinstatement of the concept within the judgment, and hence as the unity and truth of the two. The concept as such keeps its moments sublated in unity; in the judgment this unity is something inner, or, what comes to the same, something outer, and though the moments do stand in reference, they are posited as self-subsistent extremes. In the syllogism the determinations of the concept are just as the extremes of the judgment are, and along with that their determinate unity is posited.

The syllogism is thus the concept posited in full; on that account it is the rational. – Understanding counts as the faculty of the determinate concept, the concept being held fast for itself by way of abstraction and of the form of universality. Within reason, by contrast, the determinate concepts stand posited in their totality and unity. Hence the syllogism is not merely something rational; rather, whatever is rational is a syllogism. Syllogizing has long since been ascribed to reason; yet on the other side people speak of reason in and for itself, of rational principles and laws, in a manner that leaves it obscure how the reason which draws a syllogism and this reason which is the wellspring of laws and of further eternal verities and absolute thoughts are connected at all. Should the former be merely formal reason while the latter is to bring forth content, then by that very difference the form of reason — the syllogism — would be precisely what the latter could not do without. For all that, the two are customarily held so far apart, neither being mentioned where the other is discussed, that the reason of absolute thoughts appears as if ashamed of the reason of the syllogism, while the syllogism appears to be counted a doing of reason almost solely by inherited usage. Yet, as has just been noted, logical reason, taken as the formal kind, must plainly be discernible in essence within that reason too which deals with a content; indeed, no content whatever can be rational except through the rational form. For guidance here one cannot turn to the very common chatter about reason, since it abstains from saying what is to be understood by reason at all; the cognition that purports to be rational is for the most part so taken up with its subject matters that it neglects to cognize reason itself, marking reason off and naming it merely by the subject matters it is said to possess. Suppose reason is to be the cognition which knows of God, of freedom, of right and of duty, of the infinite, the unconditioned, the supersensible, or which at least yields representations and feelings of these; then partly these latter are only negative subject matters, and partly there still remains the very first question, namely what it is in all those subject matters for the sake of which they are rational? – This is what it is: that the infinite in them is no empty abstraction from the finite, no universality bare of content and of determination, but rather fulfilled universality, the concept, which is determinate and which has its determinateness at itself in that genuine way of drawing distinctions within itself and of being the unity of these its own distinctions, distinctions belonging to the understanding and themselves determinate. Only thus does reason lift itself above the finite, the conditioned, the sensible, or however else that may be determined, and in this negativity it is essentially content-laden, for it is unity precisely as unity of determinate extremes; taken so, however, the rational is nothing other than the syllogism.

At first, then, the syllogism is immediate, as the judgment was; its determinations (termini) are thus simple, abstract determinatenesses, and it is on that account a syllogism of the understanding. Where one halts at this shape of it, the rationality within it, though certainly present and posited, remains inconspicuous. Its essential moment is the extremes in their unity, the middle term conjoining them and the ground upholding them. In that abstraction holds fast to the self-subsistence of the extremes, it confronts them with this unity as with a determinateness just as rigid, just as much for itself, and in that manner takes it to be non-unity rather than unity. The designation: middle term (medius terminus) is borrowed from spatial representation, and does its part in keeping us fixed upon the determinations' being-outside-one-another. If now the syllogism consists in this, that the unity of the extremes is posited within it, while that unity is nonetheless taken flatly, on the one hand as a particular for itself, on the other as a merely external reference, and non-unity is turned into the syllogism's essential relation, then the reason which the syllogism is contributes nothing to rationality.

The syllogism of existence, first, in which the determinations are determined thus immediately and abstractly, exhibits at its own self — seeing that, like the judgment, it is the reference of those determinations — the fact that they are no such abstract determinations, but each of them is rather the reference to the other, and that the middle term holds not merely particularity over against the determinations of the extremes, but holds these posited at itself.

By this dialectic of its own it makes itself into the syllogism of reflection, the second syllogism, – one with determinations of such a sort that in each of them the other essentially shines, or that stand posited as mediated, which is what they are meant to be according to the syllogism as such.

Thirdly, once this shining or being-mediated has reflected itself into its own self, the syllogism stands determined as syllogism of necessity, where the mediating factor is the objective nature of the fact. Inasmuch as this syllogism determines the extremes of the concept just as much as totalities, the syllogism has attained the answering of its concept, or the middle term, to its existence, or the extreme differences, and so has reached its truth, and with that has stepped over out of subjectivity into objectivity.

A. The Syllogism of Existence

1. In the way it is immediate, the syllogism has for its moments the concept's determinations as immediate ones. These are thus form's abstract determinatenesses, not yet worked up through mediation into concretion, but only the determinatenesses taken singly. The first syllogism is on that account the strictly formal one. Syllogizing's formalism lies in halting at what determines this first syllogism. Sundered into its abstract moments, the concept has for its extremes singularity and universality, while the concept itself shows up as the particularity that stands between them. Owing to their immediacy, as determinatenesses referring solely to themselves, they amount taken together to one single content. Particularity makes up the middle term, to begin with, only to this extent, that it holds the two moments — singularity and universality — united immediately within itself. Owing to its determinateness, it falls on one side under the universal as subsumed, and on the other side the singular, in relation to which it counts as universality, falls as subsumed under it. Yet this concretion is at first no more than a two-sidedness; owing to the immediacy in which the Medius Terminus stands within the immediate syllogism, it is there only as simple determinateness, and the mediation that it constitutes is not yet posited. The dialectical movement belonging to the syllogism of existence now consists in this: that the mediation which alone constitutes the syllogism should come to be posited at the syllogism's moments.

a. First Figure of the Syllogism

S–P–U is the universal schema of the determinate syllogism. By way of particularity singularity closes with universality into one; not immediately is the singular universal, but through particularity; and inversely the universal is not immediately singular either, but lets itself down to singularity by way of particularity. – These determinations face one another as extremes, and in a diverse third they are one. Determinateness is what both of them are, and in that they are identical; particularity is this universal determinateness of theirs. Yet against this particularity, no less than against each other, they are extremes, since each holds to a determinateness of its own that is immediate.

What this syllogism means in general is that the singular, which as such is infinite reference to itself and would on that account be merely something inward, comes forth through particularity into existence, as into universality, where it belongs no longer to itself alone but stands in outer connection; inversely, once the singular parts itself off into its determinateness as particularity, it is in that severance a concrete, and, as reference of determinateness to itself, a universal that refers to itself, and hence a truly singular as well; within the extreme of universality it has withdrawn out of externality into itself. – Only superficially is the objective meaning of the syllogism present in this first one, for its determinations are not yet posited as that unity which makes up the essence of the syllogism. So far it is still something subjective, seeing that the abstract meaning carried by its Termini stands isolated in this way not in and for itself but only within subjective consciousness. – For the rest, how singularity, particularity and universality are related is, as has come out, the necessary and essential form-relation borne by the determinations of the syllogism; the deficiency is not to be sought in this determinateness of form, but in this, that under this form no single determination is at the same time richer. – Aristotle attached himself rather to the bare relation of inherence, since he states the nature of the syllogism thus: when three determinations stand so related to one another that the one extreme is in the whole of the middle determination, and this middle determination in the whole of the other extreme, then these two extremes are of necessity joined together. What gets expressed here is rather the repeating of one and the same relation of inherence, first of the one extreme in the middle term, then of that middle term in the other extreme, than the determinateness which the three Terminorum have toward one another. – Since the syllogism now rests on the determinateness of these just indicated over against each other, it becomes plain straightaway that other relations of the Terminorum, those which the other figures supply, can count as valid syllogisms of the understanding only so far as they admit of being traced back to that original relation; they are not diverse species of figure ranged alongside the first, but, on the one hand, so far as they are meant to be correct syllogisms, what they rest on is nothing but the essential form of the syllogism as such, and that form is the first figure; on the other hand, so far as they depart from it, they are reshapings, and that first abstract form passes over into them of necessity, determining itself thereby further and up to totality. Just how matters stand with this will emerge more closely in a moment.

S–P–U, then, is the syllogism's universal schema in its determinateness. Under the particular the singular is subsumed, and the particular under the universal; hence the universal subsumes the singular too. Or again, in the singular the particular inheres, and in the particular the universal; hence the universal inheres in the singular as well. Looked at from the one side, namely toward the universal, the particular is subject; toward the singular it is predicate; or toward the former it counts as singular, toward the latter as universal. Since both determinatenesses are united within it, the extremes stand joined together by this unity of theirs. The hence shows up as a consequence drawn within the subject, one that is supposed to follow from subjective insight into how the two immediate premises are related. When subjective reflection pronounces the middle term's two references to the extremes as particular judgments or propositions, and immediate ones at that, then the conclusion too, being the mediated reference, is admittedly a particular proposition, and the hence or therefore voices its being the mediated one. This hence, however, must not be taken for a determination lying outside this proposition, one whose ground and seat would be nothing but subjective reflection; it is rather grounded in the very nature of the extremes, whose reference only for the purposes of abstracting reflection, and through it, gets pronounced once again as a mere judgment or proposition, while their true reference stands posited as the Terminus Medius. – Therefore S is U: that this should be a judgment is a merely subjective circumstance; the syllogism consists precisely in its not being a mere judgment, that is, not a reference brought about by the bare copula or by the empty is, but one brought about by the determinate middle term filled with content.

If the syllogism is on that account looked at as consisting merely of three judgments, this is a formal view, one that says nothing of the relation among the determinations, on which alone everything in the syllogism turns. Throughout, it is a merely subjective reflection that tears the reference of the Terminorum apart into separated premises and a conclusion diverse from them: All human beings are mortal,

Cajus is a human being

Therefore he is mortal.

Boredom overtakes one the moment such a syllogism is heard trotted out; – this comes of that useless form, which through the separated propositions lends a shine of diversity, one that dissolves straightaway in the fact itself. Chiefly through this subjective shaping, syllogizing looks like a subjective makeshift to which reason or the understanding takes refuge wherever it cannot cognize immediately. – The nature of things, the rational, certainly does not go about its work by first setting up a major premise, the reference of a particularity to a subsisting universal, then finding, secondly, a separated reference of a singularity to that particularity, out of which at last, thirdly, a new proposition would come to light. – Syllogizing that advances by way of separated propositions is a subjective form and nothing besides; what the fact is, is that the distinguished conceptual determinations of the fact stand united in the essential unity. Such rationality is no makeshift; against the immediacy of the reference that still obtains in the judgment it is rather the objective, and that immediacy of cognizing is rather the merely subjective, while the syllogism is the truth of the judgment. – All things are the syllogism, a universal that through particularity stands joined together with singularity; but wholes consisting of three propositions they are of course not.

2. In the immediate syllogism of the understanding the Termini carry the form of immediate determinations; it is from this side, the side on which they are content, that it must now be considered. It can to that extent [be] taken as the qualitative syllogism, in the way the judgment of existence exhibits this same side of qualitative determination. Like the Termini of that judgment, the Termini of this syllogism are thereby singular determinatenesses, determinateness being posited, by its reference to itself, as indifferent toward the form and so as content. The singular is some immediate concrete object or other; particularity is a single one among its determinatenesses, properties or relations; universality is once more a determinateness at the particular that is more abstract and more singular still. – Because the subject, as something immediately determined, is not yet posited in its concept, its concretion has not been led back to the essential conceptual determinations; the determinateness that refers to itself is on that account indeterminate, infinite manifoldness. Within this immediacy the singular carries an infinite multitude of determinatenesses belonging to its particularity, and any one of them may accordingly serve it as a Medius Terminus in a syllogism. Through each other Medius Terminus, however, it joins itself together with another universal; by each of its properties it stands in a different contact and connection of existence. – Then too the Medius Terminus is itself a concrete when compared with the universal; several predicates are contained in it, and by one and the same Medius Terminus the singular can be joined together again with several universals. Which among a thing's many properties gets seized upon, and from which of them it is bound up with a predicate, is on the whole wholly contingent and arbitrary; other Medii Termini are the passages to other predicates, and even the same Medius Terminus may of itself be a passage to diverse predicates, containing as it does, qua particular over against the universal, several determinations.

Not merely, however, is an indeterminate multitude of syllogisms equally possible for one subject, with any single syllogism contingent so far as its content goes; these syllogisms, all bearing on the same subject, must also pass over into contradiction. Difference in general, after all, which at first is indifferent diversity, is quite as essentially opposition. The concrete is no longer something merely appearing; within the concept it is concrete through the unity of the opposed terms, which have determined themselves into moments of the concept. Now when, in the formal syllogism, the qualitative nature of the Terminorum leads the concrete to be seized upon by way of a single one of the determinations that belong to it, the syllogism assigns to it the predicate answering to this Medius Terminus; but when from another side the inference runs to the opposed determinateness, that conclusion is thereby shown up as false, however correct its premises taken singly, and its consequence along with them, may be. – Infer from the Medius Terminus that a wall has been given a coat of blue that the wall is thereby blue, and the inference is correct; yet for all this syllogism the wall may be green, should it have been coated with yellow paint besides, a circumstance from which it would follow on its own account that the wall is yellow. – Infer from the Medius Terminus of sensuousness that the human being is neither good nor evil, on the ground that of the sensuous neither may be predicated, and the syllogism is correct while the conclusion is false, since of the human being as the concrete the Medius Terminus of spirituality holds quite as much. – From the Medius Terminus of the gravity of planets, satellites and comets toward the sun it correctly follows that these bodies fall into it; yet fall into it they do not, being just as much, each for itself, a centre of gravity of their own, or, as the phrase goes, driven by centrifugal force. Just so, from the Medius Terminus of sociality one may conclude to community of goods among the citizens, while from the Medius Terminus of individuality, pursued just as abstractly, there follows the dissolution of the state, such as came about for instance in the German Empire, where this latter Medius Terminus was clung to. – Nothing is with better right counted so inadequate as a formal syllogism of this sort, resting as it does on chance, or on the arbitrary choice of which Medius Terminus is used. Let such a deduction have wound its way through syllogisms ever so handsomely, and let its correctness be granted entirely, this still leads to nothing whatever, since it always remains that further Medii Termini are to be found from which the very reverse may be derived with equal correctness. – The Kantian antinomies of reason amount to nothing else than that out of one concept the one determination of it is laid at the base at one time, and at another, with just the same necessity, the other. – This inadequacy and contingency of a syllogism must not, in that connection, be pushed off onto the content alone, as if it were independent of the form and the form alone were logic's business. It lies rather in the form of the formal syllogism that the content should be a quality so one-sided; to this one-sidedness the content is determined by that abstract form. It is, namely, one single quality among the many qualities or determinations of a concrete object or of a concept, since according to the form nothing more is asked of it than to be such an immediate, single determinateness. The extreme of singularity, as abstract singularity, is the immediate concrete, hence the infinitely or indeterminably manifold; the middle term is particularity that is abstract in like measure, hence one single quality out of that manifold; and just so the other extreme is the abstract universal. For the sake of its form, then, the formal syllogism is essentially something wholly contingent so far as its content goes; not in the sense that it should be contingent for the syllogism whether this or another object is put under it, for logic abstracts from such content, but in the sense that, a subject being laid at the base, what determinations of content the syllogism infers of it is contingent.

3. On this side the determinations of the syllogism are determinations of content, so far as they are immediate, abstract determinations reflected into themselves. What is essential to them, however, is rather that they should not be such self-reflected determinations, indifferent toward one another, but form-determinations; to that extent they are essentially references. These references are, first, those of the extremes to the middle term, – references which are immediate: the propositiones praemissae, in part that of the particular to the universal, propositio major, in part that of the singular to the particular, propositio minor. Secondly, there is at hand the reference of the extremes to each other, the one that is the mediated reference, conclusio. The premises, those immediate references, are propositions or judgments as such, and they contradict the syllogism's nature, by which the distinguished conceptual determinations are not to be referred immediately, their unity being what is to be posited just as much; the syllogism is the truth of the judgment. All the less can the premises remain immediate references, in that their content is made of immediately distinguished determinations, so that they are not immediately identical in and for themselves; unless they be purely identical propositions, that is, empty tautologies that lead nowhere.

The demand laid on the premises accordingly runs, as a rule, that they are to be proved, that is, that they too are to be set out as conclusions. So the two premises hand us two further syllogisms. But these two new syllogisms again furnish four premises between them, calling for four new syllogisms; those have eight premises, whose eight syllogisms in turn furnish sixteen syllogisms for their sixteen premises, and so on in a geometrical progression into infinity.

So here the progress into infinity comes forward once more, which had turned up earlier in the lower sphere of being, and which in the field of the concept, of absolute reflection out of the finite into itself, in the region of free infinity and truth, was no longer to be looked for. In the sphere of being it was shown that wherever the bad infinity that runs out into the progress comes forward, there is at hand the contradiction of a qualitative being and of a powerless ought reaching out beyond it; the progress is itself the repeating of the demand for unity raised against the qualitative, and of the constant relapse into a restriction that does not answer to the demand. Now in the formal syllogism the immediate reference, or the qualitative judgment, is the groundwork, and the mediation of the syllogism is what gets set against it as the higher truth. Proving the premises on into infinity does not resolve that contradiction; it only renews it again and again, repeating one and the same original defect. – Rather, the truth of the infinite progress lies in this, that the progress itself, together with the form it has already marked out as defective, gets sublated. – That form is the form of mediation as S–P–U. The two references S–P and P–U are supposed to be mediated ones; if this is done in the same fashion, the defective form S–P–U is merely doubled, and so on into infinity. P carries toward S the form-determination of a universal as well, and toward U that of a singular, these references being judgments throughout. Mediation is therefore what they require, yet through that shape of mediation only the relation which is to be sublated comes on the scene again.

The mediation must accordingly come about in another fashion. For mediating P–U, S is at hand; it is therefore the shape

P–S–U

that the mediation must receive. To mediate S–P, U is at hand; this mediation therefore becomes the syllogism:

S–U–P.

Taking this transition more closely in terms of its concept: firstly, the mediation of the formal syllogism is, as regards its content, contingent, as was shown just now. In its determinatenesses the immediate singular has an indeterminable multitude of Mediis Terminis, and these again have just as many determinatenesses of their own; so that with what sort of universal the subject of the syllogism is to be joined together lies wholly in an external arbitrariness, or generally in an external circumstance and contingent determination. As to content, then, the mediation is nothing necessary, nor anything universal; it has no ground in the concept of the fact; the ground of the syllogism is rather what is external to it, that is, the immediate; and among the conceptual determinations the immediate is the singular.

In respect of the form, likewise, the mediation has for its presupposition the immediacy of the reference; the mediation is therefore itself mediated, and mediated by the immediate, that is, by the singular. – More closely, it is through the conclusion of the first syllogism that the singular has become what mediates. The conclusion is S–U; by it the singular stands posited as universal. In the one premise, the minor premise S–P, it already stands as particular; it is thus posited as that in which these two determinations are united. – Or the conclusion in and for itself gives voice to the singular as universal, and this not in an immediate way but through the mediation, hence as a necessary reference. The simple particularity was Medius Terminus; in the conclusion this particularity comes developed, posited as the reference of the singular and universality. But the universal is still a qualitative determinateness, the singular's predicate; determined as universal, the singular gets posited as universality of the extremes, that is, as middle term; taken for itself it is the extreme of singularity, yet since it now stands determined as universal it is at once the unity of both extremes.

b. The Second Figure: P-S-U

1. What the first qualitative syllogism comes to in truth is that something stands joined together with a qualitative determinateness, taken as a universal one, not in and for itself but through a contingency, or within a singularity. The subject of the syllogism, in a quality of that kind, has not gone back into its concept; it is grasped only in its externality; immediacy is what makes up the ground of the reference, and so the mediation; to that extent the middle term is in truth the singular.

Further, though, the syllogistic reference is the sublation of immediacy; not an immediate reference is the conclusion, but one holding by way of a third; a negative unity is therefore contained in it; and so the mediation is now determined to hold a negative moment within itself.

The premises in this second syllogism are P–S and S–U; of the two, only the former is still immediate, whereas S–U is a mediated one already, namely through the first syllogism; so the second syllogism has the first for its presupposition, and inversely the first the second. – The two extremes are in this determined against one another as particular and universal; the latter so far keeps its place, being predicate; but the particular has swapped its own, being now subject, or posited under the determination of the extreme of singularity, while the singular, for its part, has been posited with the determination of the middle term, namely of particularity. Both of them, therefore, are no longer those abstract immediacies that they were in the first syllogism. As concretes, however, they are not yet posited; each standing in the place of the other, each finds itself posited in its own determination and, though only externally, in the other determination at the same time.

The determinate, objective sense this syllogism carries is that the universal is not in and for itself some determinate particular; for it is rather the totality of its particulars; rather, its being thus one of its species comes about through singularity; the rest of its species are shut out from it by immediate externality. The particular, on the other side, is likewise not the universal immediately and in and for itself; the negative unity strips the determinateness off it and raises it thereby into universality. – Singularity bears itself negatively toward the particular so far as it is supposed to be the latter's predicate; predicate of the particular it is not.

2. At first, though, the Termini are still immediate determinatenesses; by themselves they have grown into no objective meaning; the altered position two of them receive is a form that so far attaches to them only externally; as in the first syllogism generally, they are therefore still a content indifferent toward one another, two qualities knit together not in and for their own selves but through a contingent singularity.

The syllogism of the first figure was the immediate one, or just as much the syllogism so far as it stands in its concept as abstract form, a form not yet realized in its determinations. That this pure form has passed over into another figure is, on the one side, the realization of the concept begun, since the negative moment of mediation, and with it a further form-determinateness, gets posited on the at first immediate, qualitative determinateness of the Terminorum. – At the same time, though, this is a becoming-other of the pure form of the syllogism; the syllogism no longer answers to it completely, and the determinateness posited on its Terminis is diverse from that original form-determination. – So far as it is regarded merely as a subjective syllogism running its course in an external reflection, it passes for a species of syllogism, one that ought to answer to the genus, that is, to S–P–U, the universal schema of the syllogism. At first, though, it does not answer to it; the two premises it has are P–S, or S–P, and S–U; the Medius Terminus is accordingly subsumed both times, or is both times subject, so that the two other Termini inhere in it; hence not a middle term which is to be at one time subsuming, or predicate, and at another subsumed, or subject, in which the one Terminus is to inhere while it itself inheres in the other. – That this syllogism fails to answer to the universal form of the syllogism has the genuine sense that this form has passed over into it, its truth consisting in being a subjective, contingent joining-together. Should the conclusion in the second figure be correct, (leaving aside, that is, the limitation soon to be mentioned, which turns it into something indeterminate,) it is so because it is correct for itself, and not on the strength of being this syllogism's conclusion. With the conclusion of the first figure, however, matters stand the same; it is just this truth of the first that the second figure posits. – On the view that the second figure is merely a species, one overlooks how the first passes over of necessity into this second form, and stays put at the first as the genuine form. So far, then, as in the second figure (which out of old habit, and with no further ground, is listed as the third) a syllogism that is correct in this subjective sense is likewise supposed to have place, it would have to be adequate to the first; hence, the one premise S–U having the relation of subsumption of the Medius Terminus under the one extreme, the other premise S–P would have to acquire the relation opposite to the one it has, so that S would be what P is subsumed under. Such a relation, though, would sublate the determinate judgment: S is P, and could have place only within an indeterminate judgment, – within a particular one; whence in this figure the conclusion can only be a particular one. The particular judgment, though, is, as noted above, positive as much as negative; – a conclusion, therefore, that can hardly be credited with much worth. – So far as the particular and the universal are also the extremes, and immediate determinatenesses indifferent toward one another, their relation is itself indifferent; the one or the other may be taken at pleasure as Terminus Major or Minor, and hence the one or the other premise as major or as minor premise.

3. Being positive as much as negative, the conclusion is thus a reference indifferent toward these determinatenesses, and so a universal one. Looked at more closely, the first syllogism's mediation was in itself contingent; in the second this contingency stands posited. The mediation is thus one that sublates itself; it carries the determination of singularity and of immediacy; what gets joined together by this syllogism must rather be identical in itself and immediately, for that middle term, the immediate singularity, is the infinitely manifold and external being-determined. What is posited in it, then, is rather the mediation that is external to itself. But singularity's externality is universality; that mediation by way of the immediate singular points out past itself to the mediation other to it, which comes about accordingly through the universal. – Or: whatever the second syllogism is supposed to unite must be joined together immediately; out of the immediacy lying at its base no determinate joining-together comes to pass. The immediacy it points on to is the other over against its own, – the sublated first immediacy of being, – hence the immediacy reflected into itself, or what is in itself, the abstract universal.

On the side considered, this syllogism's transition was a becoming-other, like the passing over of being, since what lies at its base is the qualitative, namely immediate singularity. In terms of the concept, however, singularity joins particular and universal together so far as it sublates the determinateness of the particular; which is what shows itself as this syllogism's contingency; the extremes do not get joined together through the determinate reference in which they stand to the Medius Terminus; the Medius Terminus is therefore not their determinate unity, and the positive unity still accruing to it is only the abstract universality. Yet once the middle term is posited in this determination, its truth, what we have is another form of the syllogism.

c. The Third Figure: S-U-P

1. Of immediate premises this third syllogism retains not a single one; the reference S–U came to be mediated through the first syllogism, the reference P–U through the second. It has the two earlier syllogisms, therefore, for its presupposition; but they in turn presuppose it, as indeed each of the three presupposes the remaining two. With it, accordingly, the determining of the syllogism reaches completion on the whole. – What this mutual mediating contains is just this, that each syllogism, though for itself it be the mediation, is at the same time not in its own self the totality of that mediation, but carries about it an immediacy whose mediating is to be found outside it.

Taken in its own self, the syllogism S–U–P is the truth of the formal syllogism; what it enunciates is that the mediation belonging to the latter is the abstractly universal one, and that of the extremes their essential determinateness [is] not held in the middle term, which holds them only as regards their universality, so that just what ought to have been mediated is precisely what fails to be conjoined there. Posited here, accordingly, is that wherein the formalism of the syllogism lies: its terms carry an immediate content that stands indifferent to the form, or, which says the same, they are form determinations that have not yet reflected themselves into determinations of content.

2. True, the middle term of this syllogism is the unity of the extremes, but a unity that has abstracted from their determinateness, the indeterminate universal. Yet so far as this universal, being the abstract one, stands at the same time distinguished from the extremes as the determinate, it too remains a determinate as against them, and the whole is a syllogism whose bearing upon its own concept calls for examination. Being the universal, the middle term is towards both of its extremes the subsuming one, or predicate, and on no occasion the subsumed one, or subject. If, then, this syllogism as one species of syllogism is to answer to what a syllogism is, that can come about only thus: while the one reference S–U already stands in the fitting relation, the other, P–U, must come to stand in it as well. Such is the case with a judgment where subject and predicate are related indifferently, with the negative judgment. So the syllogism turns out legitimate; its conclusion, however, of necessity negative.

Herewith it also makes no difference which of the two determinations of this proposition should count as predicate and which as subject, and, within the syllogism, whether as the extreme of singularity or as that of particularity, hence whether as minor or as major term. Since on the received supposition it is by this that the major or the minor premise gets decided, the point has here lost all weight. – Herein lies the ground of that customary fourth figure of the syllogism, unknown to Aristotle, which moreover has to do with an utterly empty distinction void of all interest. The unmediated placing of the terms in it inverts the placing of the first figure; for since, on the formal view of the judgment, subject and predicate of a negative conclusion do not stand in the determinate relation of subject and predicate but either may occupy the position of the other, nothing turns on which of the terms is made subject and which predicate, and just as little on which premise is made major or minor. – Such indifference, helped along by the determination of particularity as well (above all where the remark is made that it may be taken in the comprehensive sense), reduces that fourth figure to something wholly idle.

3. What the syllogism having the universal for its middle term means objectively is that the mediating factor, being the unity of the extremes, is essentially universal. Since, however, universality is at the outset only the qualitative or abstract sort, it does not harbour the determinateness of the extremes within it; should a conjoining of these come about, its ground must equally lie in a mediation situated outside this syllogism, and so far as this syllogism goes it is every bit as contingent as with the earlier forms of syllogism. Now since it is the universal that gets determined as middle term, and the determinateness of the extremes finds no place there, that determinateness stands posited as something altogether indifferent and external. – Thus by way of this bare abstraction a fourth figure of the syllogism does indeed come about, that of the relationless syllogism, U–U–U: it abstracts from whatever qualitative difference the terms have, and so takes for its determination their merely external unity, namely their equality.

d. The Fourth Figure: U-U-U, or the Mathematical Syllogism

1. Thus runs the mathematical syllogism: when two things or determinations are equal to some third, they are equal to one another. – The relation of inherence or of subsumption among the terms is extinguished in it.

A third in general is what does the mediating; yet it carries no determination whatever over against its extremes. Any one of the three, therefore, may just as well serve as the mediating third. Which of them is employed for the purpose, and hence which of the three references count as the immediate ones and which as the mediated one, hangs upon outward circumstances and other conditions; – namely upon which two of them happen to be the immediately given ones. This determination, however, in no way concerns the syllogism itself and is wholly external.

2. In mathematics the mathematical syllogism passes for an axiom; – as something evident in and for itself, a first proposition neither capable of nor in need of proof, that is, of mediation, presupposing nothing further, nor derivable from anything. – Look more closely at the merit it has of being immediately evident, and this shows itself to lie in the formalism of this syllogism, which abstracts from every qualitative diversity among the determinations and takes up only their quantitative equality or inequality. Yet for that very reason it is not free of presupposition or unmediated; the quantitative determination, the sole one that comes into view in it, exists only through the abstraction from qualitative difference and from the determinations of the concept. – Lines and figures set equal to one another are grasped solely as regards their magnitude; a triangle is set equal to a square, yet not as triangle to square, but in point of magnitude alone and so forth. The concept and its determinations likewise gain no entry into this inferring; nothing whatever gets comprehended by it; indeed the understanding does not so much as have before it the formal, abstract determinations of the concept; what is evident in this syllogism therefore rests on nothing but its poverty and abstractness in point of thought-determination.

3. But what the syllogism of existence results in is not merely this abstracting from every determinateness of the concept; the negativity of the immediate, abstract determinations that came forth from it has a further, positive side as well, namely that into the abstract determinateness its other has been posited, whereby it has become concrete.

In the first place, the syllogisms of existence taken all together have one another for their presupposition, and the extremes conjoined in the conclusion are conjoined truly and in and for themselves only insofar as they are otherwise held together by an identity grounded elsewhere; the middle term, constituted as it is in the syllogisms we have examined, is to be their unity of concept, yet it is only a formal determinateness and not posited as the concrete unity of the two. But that which is presupposed by each of those mediations is not merely a given immediacy as such, as in the mathematical syllogism; it is itself a mediation, namely, for each, the other two syllogisms. What is truly at hand, then, is a mediation founded not upon a given immediacy but upon mediation. It is thus not the quantitative mediation that abstracts from the form of mediating, but rather the mediation that refers itself to mediation, or the mediation of reflection. The circle of mutual presupposing which these syllogisms close with one another is the turning back of this presupposing into its own self, whereby it forms a totality and holds the other to which each single syllogism points not outside itself by force of abstraction, but rather encloses it within the circle.

Furthermore, as regards the single form determinations, it has shown itself that within this whole of formal syllogisms every one of them has come to the place of the middle term . At first the middle term stood determined as particularity; thereupon it determined itself, through the dialectical movement, as singularity and universality. Each of these determinations ran through the places of the two extremes as well. The bare negative result lies in the extinguishing of the qualitative form determinations within the merely quantitative, mathematical syllogism. But what is truly at hand is the positive result that mediation takes place not through a single qualitative form determinateness, but through the concrete identity of these determinacies. Just here lies the defect and the formalism of the three figures of syllogism we have examined, that in them one such single determinateness was to make up the middle term. – Mediation has determined itself, then, as the indifference belonging to the immediate or abstract form determinations and as the positive reflection of the one into the other. With this the immediate syllogism of existence has passed over into the syllogism of reflection.

Remark

In the account given here of the syllogism's nature and of its various forms, notice has also been taken in passing of what makes up the chief interest in the customary consideration and treatment of syllogisms, namely how a correct inference can be drawn in each figure; in doing so, however, only the principal moment has been indicated, and those cases and entanglements have been passed over which arise once the difference between positive and negative judgments is drawn in along with the quantitative determination, particularity above all. – A few remarks upon the customary view of the syllogism in logic, and upon the manner of dealing with it, will not be out of place here. – As is well known, this doctrine was elaborated into such minute detail that its so-called subtleties became a general vexation and disgust. As natural understanding asserted itself against substanceless forms of reflection on every side of intellectual culture, it turned against that artificial acquaintance with the forms of reason as well, and supposed that such a science could be done without, for the reason that by nature, and with no special learning, it already performs of itself the individual operations of thought recorded there. Where rational thinking is concerned, the human being would in fact be as badly off, were the condition of it the toilsome study of the formulae of the syllogism, as he would be, (as was already remarked in the preface) if he could not walk and digest without having studied anatomy and physiology. Just as the study of those sciences may not be without profit for one's dietetic conduct, so too an influence more important still upon the correctness of thinking will doubtless have to be ascribed to the study of the forms of reason; but without entering here upon this side of the matter, which concerns the cultivation of subjective thinking and hence really belongs to pedagogy, it will have to be granted that a study whose object is how reason operates and what its laws are must in and for itself be of the very greatest interest, – of one at least no smaller than the knowledge of the laws of nature and of their particular shapes. If it is held to be no small thing to have discovered some sixty odd species of parrot, a hundred and thirty-seven kinds of veronica and so forth, then finding out the forms of reason must be held to be a far less trifling matter; is a figure of the syllogism not something infinitely higher than a parrot species or a veronica species?

Much as it is therefore to be reckoned nothing but crudity to despise acquaintance with the forms of reason altogether, just as much must one grant that the customary exposition of the syllogism and of its particular shapes yields no rational cognition, no exhibition of these as forms of reason, and that the wisdom of syllogistic, through its own worthlessness, drew upon itself the low esteem that fell to it. Its defect consists in this, that it stops short absolutely at the understanding's form of the syllogism, according to which the determinations of the concept get taken for abstract determinations of form. Holding fast to them as abstract qualities is all the more inconsequent in that in the syllogism it is the references among them that make up the essential thing, and inherence and subsumption already contain this, that the singular, having the universal inhere in it, is itself something universal, and the universal, subsuming the singular as it does, is itself something singular, while more precisely the syllogism expressly posits just this unity as middle term and its determination is mediation precisely, that is, that the determinations of the concept no longer have for their basis, as they do in the judgment, their externality towards one another, but rather their unity. – Through the concept of the syllogism, then, the imperfection of the formal syllogism is pronounced, the syllogism in which the middle term, instead of being the unity of the extremes, is to be held fast as an abstract determination of form, qualitatively diverse from them. – The consideration is rendered still emptier of content by the fact that even such references or judgments as those in which the formal determinations themselves become indifferent, as in the negative and the particular judgment, and which therefore come close to being mere propositions, are still accepted as perfect relations. – Since now the qualitative form S–P–U counts quite generally as the last and absolute one, the dialectical consideration of the syllogism drops away entirely, and the remaining syllogisms are accordingly regarded as species rather than as necessary alterations of that form. – Here it makes no difference whether the first formal syllogism is itself regarded merely as one species alongside the rest, or else as genus and species at once; the latter happens when the remaining syllogisms are led back to the first. Where this reduction is not carried out expressly, the same formal relation of external subsumption which the first figure expresses always lies at the basis.

The formal syllogism just described is the contradiction of a middle term that is to be the determinate unity of the extremes and yet is not that unity, but a determination qualitatively diverse from the very terms whose unity it is to be. Being this contradiction, the syllogism is dialectical in its own self. Its dialectical movement exhibits it in the complete moments of the concept, so that not merely the relation of subsumption, that is, particularity, but just as essentially the negative unity, along with universality, are moments of the conjoining. So far as each of them, taken for itself, is again only a one-sided moment of particularity, they too are imperfect middle terms, though they constitute at the same time the developed determinations of that middle term; the whole course through the three figures displays the middle term in one after another of these determinations, and what truly results from this is that the middle term is not a single one of them but their totality.

The formal syllogism's defect lies, therefore, not in the form of the syllogism, – this form is rather the very form of rationality, – but in its being there only as an abstract and hence conceptless form. It has been shown of the abstract determination that, by virtue of its abstract reference to itself, it may just as well be regarded as content; to that extent the formal syllogism accomplishes nothing beyond this, that a subject's reference to a predicate does or does not follow merely from this middle term. Nothing is gained by having proved a proposition through a syllogism of that sort; because the middle term has an abstract determinateness, being a conceptless quality, there may equally well be other middle terms yielding the opposite, and indeed from the same middle term opposed predicates can in turn be derived by further syllogisms. – Apart from accomplishing little, the formal syllogism is besides a very simple affair; the many rules people have devised are burdensome already because they stand in such contrast with the simple nature of the fact, but then also because they bear upon those cases in which the formal content of the syllogism is diminished altogether by the external form determination, particularity especially, and chiefly insofar as it must for this purpose be taken in the comprehensive sense, and in which results are brought out that are wholly void of content even as regards form. – The most just and the most important side of the disfavour into which syllogistic has fallen, however, is that it is so long-drawn-out and conceptless a business with an object whose one and only content is the concept itself. – The many syllogistic rules call to mind the procedure of reckoning masters, who likewise give a multitude of rules about the arithmetical operations, all of which presuppose that one does not have the concept of the operation. – But numbers are a conceptless material, the operation of reckoning an external gathering or separating, a mechanical procedure, as witness the calculating machines that have been invented to carry these operations out; the harshest and most glaring thing, by contrast, is that the form determinations of the syllogism, which are concepts, should be handled as a conceptless material.

The uttermost point of this conceptless way of taking the conceptual determinations of the syllogism is surely that Leibniz (Opp. Tom. II. P. I.) subjected the syllogism to the combinatorial calculus and by its means computed how many positions of the syllogism are possible; – with reference, namely, to the differences between positive and negative judgments, and then between universal, particular, indeterminate and singular ones; of such combinations 2048 turn out to be possible, and after exclusion of the unusable ones 24 usable figures are left over. – Leibniz makes a great deal of the usefulness of combinatorial analysis for finding not only the forms of the syllogism but the combinations of other concepts as well. The operation by which this is found is the same as the one by which it is computed what combinations of letters an alphabet permits, how many kinds of throw a game of dice affords, how many games are possible with a hand of L’hombre cards and so forth. What one finds here, then, is that the determinations of the syllogism are set in one class with the pips of the die and of the L’hombre card, that the rational is taken as something dead and conceptless, and that what is peculiar to the concept and its determinations, namely to refer themselves as spiritual essences and through this referring to sublate their immediate determination, is left on one side. – This Leibnizian application of combinatorial calculus to the syllogism, and to how other concepts combine, differed in nothing from the notorious Lullian art save that on the side of amount it was more methodical, matching it for the rest in senselessness. – Bound up with this was a favourite thought of Leibniz's, conceived by him in his youth and, for all its immaturity and shallowness, not given up in later years either, of a universal characteristic of concepts, – a written language in which every concept would be exhibited as being a reference out of others, or as referring itself to others – as though in the rational combination, which is essentially dialectical, a content still kept the same determinations that it has when it is fixed for itself.

Ploucquet's calculus has without doubt seized upon the most consistent procedure by which the relation of the syllogism becomes fit to be subjected to a calculus. This rests on abstracting from the difference of relation, from the difference of singularity, particularity and universality in the judgment, and on holding fast the abstract identity of subject and predicate, whereby these stand in mathematical equality; – a reference which turns inferring into a formation of propositions wholly empty of content and tautological. – In the proposition: the rose is red, what the predicate signifies is supposed to be not red in its universality but only the determinate red of the rose; again, in the proposition: all Christians are human beings, only those human beings who are Christians are what the predicate is supposed to signify; from this together with the proposition: the Jews are not Christians, there then follows the conclusion that did this syllogistic calculus no good service with Mendelssohn: therefore the Jews are not human beings, (namely not those human beings who are the Christians). – Ploucquet states, as something his invention brings with it, posse etiam rudes mechanice totam logicam doceri, uti pueri arithmeticam docentur, ita quidem, ut nulla formidine in ratiociniis suis errandi torqueri, vel fallaciis circumveniri possint, si in calculo non errant. – This recommendation, that the whole of logic could be imparted mechanically to the uneducated by way of the calculus, is assuredly the worst that could be said of an invention regarding the exposition of logical science.

B. The Syllogism of Reflection

What the qualitative syllogism ran through has sublated the abstract character of its determinations; the term has thereby posited itself as such a determinateness that the other shines within it too. Over and above the abstract terms, there is present in the syllogism their reference as well, and the conclusion posits this as mediated and necessary; in truth, then, no determinateness is posited as a single one on its own account, but each as a referring of the others, as concrete determinateness.

As abstract particularity, the middle term was for itself a simple determinateness, and a middle only in an external, relative way as against extremes that subsist on their own. Now it stands posited as the totality of determinations, and so is the posited unity of the extremes, though to begin with the unity of reflection embracing them; – an embracing which, as a first sublating of immediacy and a first referring of determinations, falls short still of the concept's absolute identity.

The extremes here are determinations belonging to the judgment of reflection; singularity in the proper sense, and universality as determination of relation, or a reflection drawing a manifold together in itself. Yet the singular subject, as the judgment of reflection showed, harbours besides the bare singularity that pertains to form the determinateness as well, as a universality reflected simply into itself, as a genus presupposed, that is, one here still taken up immediately.

Out of this determinateness of the extremes, belonging as it does to the course taken by the determining of judgment, there issues the closer content of the middle term, on which everything in the syllogism essentially turns, since it is what sets the syllogism apart from the judgment. What it contains is 1) singularity, 2) singularity widened, however, to universality, as all, 3) the universality that underlies these and unites singularity and abstract universality outright within itself, the genus. – Not until now, with the middle term posited as the totality of the determinations, does the syllogism of reflection possess the proper determinateness of form; measured against it the immediate syllogism is for that very reason the indeterminate one, its middle term being as yet no more than the abstract particularity, wherein the moments of its concept remain unposited. – One may call this first syllogism of reflection the syllogism of allness.