Hegel’s Science of Logic
Now the immediate judgment of reflection is again, the individual is universal — but with subject and predicate in the stated signification; it can therefore be more precisely expressed as this is an essential universal.
But a 'this' is not an essential universal. This judgment which, as regards its general form, is simply positive, must be taken negatively. But since the judgment of reflection is not merely a positive one, the negation does not directly affect the predicate, which does not inhere but is the in itself. It is the subject rather that is alterable and awaits determination. Here, therefore, the negative judgment must be understood as asserting not a 'this' is a universal of reflection — an in-itself of this kind has a more universal existence than merely in a 'this'. Accordingly, the singular judgment has its proximate truth in the particular judgment.
The non-individuality of the subject, which must be posited instead of its individuality in the first judgment of reflection, is particularity. But individuality is determined in the judgment of reflection as essential individuality; particularity cannot therefore be a simple, abstract determination, in which the individual would be sublated and the concrete existent destroyed, but must be merely an extension of the individual in external reflection. The subject is, therefore, these or a particular number of individuals.
This judgment, that some individuals are a universal of reflection, appears at first as a positive judgment, but it is negative as well; for some contains universality. In this respect it may be regarded as comprehensive; but in so far as it is particularity, it is no less inadequate to that universality. The negative determination which the subject has received through the transition of the singular judgment is, as we have shown above, also a determination of the relation, of the copula. The judgment: some men are happy, involves the immediate consequence that some men are not happy. If some things are useful, then for this very reason some things are not useful. The positive and negative judgments no longer fall apart, but the particular judgment immediately contains both at the same time, just because it is a judgment of reflection. But the particular judgment is, for this reason, indeterminate.
If, in the example of such a judgment, we examine further the subject, some men, animals, etc., we find that it contains besides the particular form-determination some, the content-determination man, etc. The subject of the singular judgment could be expressed by this man, a single individual, which really pertains to an external pointing; it might therefore be better expressed, say, by Gaius. But the subject of the particular judgment can no longer be, some Gaii; for Gaius is supposed to be an individual as such. To the some is therefore added a more universal content, say, men, animals, etc. This is not merely an empirical content, but one determined by the form of the judgment; that is to say, it is a universal, because some contains universality and this must at the same time be separated from the individuals, since reflected individuality forms the basis. More precisely, this universality is also the universal nature or genus man, animal — that universality which is the result of the judgment of reflection, anticipated; just as the positive judgment, in having the individual for subject, anticipated the determination which is the result of the judgment of existence. Thus the subject that contains the individuals, their relation to particularity and the universal nature, is already posited as the totality of the determinations of the Notion. But this is really an external reflection. What is, in the first instance, already posited in the subject by its form, in respect of the mutual relation of these determinations, is the extension of the 'this' to particularity; but this generalisation is not adequate to the 'this'; 'this' is something completely determined, but 'some' is indeterminate. The extension must be appropriate to the 'this' and therefore, in conformity with it, be completely determined; such an extension is totality, or, in the first instance, universality.
This universality has the 'this' as its basis, for the individual here is the individual reflected into itself; its further determinations, therefore, run their course in it externally; and just as particularity for this reason determined itself as some, so the universality which the subject has attained is allness, and the particular judgment has passed over into the universal.
Universality, as it appears in the subject of the universal judgment, is the external universality of reflection, allness; 'all' means all individuals, and in it the individual remains unchanged. This universality is, therefore, only a taking together of independently existing individuals; it is the community of a property which only belongs to them in comparison. It is this community that is usually the first thing that occurs to subjective, unphilosophical thinking when universality is mentioned. It is given as the obvious reason why a determination is to be regarded as universal that it belongs to a number of things. It is mainly this concept of universality, too, that analysis has in mind when, for example, it takes the development of a function in a polynomial to be more universal than its development in a binomial, because the polynomial presents more individual terms than the binomial. The demand that the function should be presented in its universality requires, strictly speaking, a pantonomial, the exhausted infinity; but here the limitation of this demand becomes apparent, and the representation of the infinite number of terms has to content itself with its ought, and therefore also with a polynomial. But in fact the binomial is already the pantonomial in those cases where the method or rule affects only the dependence of one term on another, and the dependence of several terms on their predecessors does not particularise itself, but one and the same function remains the base. The method or rule is to be regarded as the genuine universal; in the progress of the development or in the development of a polynomial the rule is merely repeated; so that it gains nothing in universality through the increased number of the terms. We have already in an earlier chapter spoken of the spurious infinity and its illusory nature; the universality of the Notion is the reached beyond; the spurious infinity remains afflicted with the beyond as an unattainable goal, for it remains the mere progress to infinity. When universality is pictured merely as allness, a universality which is supposed to be exhausted in the individuals as individuals, then this is a relapse into that spurious infinity; or else mere plurality is taken for allness. Plurality, however, no matter how great, remains unalterably mere plurality, and is not allness. But there is, here, a vague awareness of the true universality of the Notion; it is the Notion that forces its way beyond the stubborn individuality to which unphilosophical thinking clings and beyond the externality of its reflection, substituting allness as totality, or rather that being which is categorically in and for itself.
This is apparent, too, in allness which is in general the empirical universality. Inasmuch as the individual as an immediate is presupposed and therefore already given and externally adopted, the reflection which gathers it into allness is equally external. But because the individual as 'this', is absolutely indifferent to this reflection, the universality and an individual of this kind cannot combine to form a unity. For this reason, this empirical allness remains a task, something which ought to be done and which cannot therefore be represented as being. Now an empirically universal proposition — for nevertheless such are advanced — rests on the tacit agreement that if only no contrary instance can be adduced, the plurality of cases shall count as allness; or, that subjective allness, namely, those cases which have come to our knowledge, may be taken for an objective allness.
Now a closer examination of the universal judgment now before us, reveals that the subject, which, as previously remarked, contains the true universality as presupposed, now also contains it as posited in it. All men expresses first, the genus man, secondly this genus as sundered into individuals, but so that the individuals are at the same time extended to the universality of the genus; conversely, the universality through this connection with individuality is just as completely determined as the individuality; thus the posited universality has been equated with the presupposed.
Strictly speaking, however, we should not anticipate what is presupposed, but should consider the result in the form determination on its own. Individuality, through this extension of itself to allness, is posited as negativity, which is identical self-relation. It has not therefore remained that first individuality, that for example of Gaius, but is the determination that is identical with universality, or is the absolutely determined being of the universal. That first individuality of the individual judgment was not the immediate one of the positive judgment, but came into being through the dialectical movement of the judgment of existence as such; it was already determined as the negative identity of the terms of that judgment. This is the true presupposition in the judgment of reflection; in contrast to the positing which runs its course in that judgment, that first determinateness of individuality was the latter's in-itself; thus, what individuality is in itself, is now, through the movement of the judgment of reflection, posited, namely, individuality as identical self-relation of the determinate. Therefore this reflection, which extends individuality to allness, is not external to it; on the contrary, this reflection merely makes explicit what it already is in itself. Hence the result is in truth objective universality. The subject has thus stripped off the form determination of the judgment of reflection which passed from this through some to allness; instead of all men we have now to say man.
The universality which has hereby come into being is the genus — the universality which is in its own self a concrete. The genus does not inhere in the subject; it is not a single property, or a property at all, of the subject; it contains all the single determinatenesses dissolved in its substantial solidity. In virtue of the fact that it is posited as this negative identity with itself, it is essentially a subject, but it is no longer subsumed in its predicate. In consequence, the nature of the judgment of reflection is altogether changed.
That judgment was essentially a judgment of subsumption. The predicate was determined, in contrast to its subject, as the implicit universal; according to its content, it could be taken as an essential determination of relation, or also as a mark — a determination which makes the subject merely an essential Appearance. But when the predicate is determined to objective universality, it ceases to be subsumed under such a determination of relation, or comprehensive reflection; on the contrary, such a predicate in contrast to this universality is a particular. The relationship of subject and predicate has therefore become inverted and hence the judgment has, first of all, sublated itself.
This sublation of the judgment coincides with the advance in the determination of the copula, which we have still to consider; the sublation of the terms of the judgment is the same thing as their transition into the copula. In other words, the subject, in raising itself to universality has, in this determination become equated with the predicate, which as reflected universality also contains particularity within itself; subject and predicate are therefore identical, that is they have coalesced into the copula. This identity is the genus or absolute nature of a thing. In so far, therefore, as this identity again sunders itself into a judgment it is the inner nature through which subject and predicate are related to one another — a relation of necessity in which these terms of the judgment are only unessential differences. What belongs to all the individuals of a genus belongs to the genus by its nature, is an immediate consequence and the expression of what we have seen, that the subject, for example all men, strips off its form determination, and man is to take its place. This intrinsic and explicit connection constitutes the basis of a new judgment, the judgment of necessity.
C. The Judgment of Necessity
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