Hegel’s Science of Logic
1. The categorical syllogism has the categorical judgment for one or both of its premises. Here, with this syllogism, as with the judgment, is associated the more specific significance that its middle term is objective universality. Superficially the categorical syllogism too is taken for nothing more than a mere syllogism of inherence.
The categorical syllogism in its substantial significance is the first syllogism of necessity, in which a subject is united with a predicate through its substance. But substance raised into the sphere of the Notion is the universal, posited as being in and for itself in such a manner that it has for the form or mode of its being, not accidentality, which is the relationship peculiar to substance, but the Notion-determination. Its differences are therefore the extremes of the syllogism and, precisely, universality and individuality. The former, in contrast to the genus, which is the precise determination of the middle term, is abstract universality or universal determinateness — the accidentality of substance gathered into simple determinateness which however is its essential difference, specific difference. But individuality is the actual, in itself the concrete unity of genus and determinateness; here, however, in the immediate syllogism it appears at first as immediate individuality, accidentally gathered into the form of a subsistence on its own. The relation of this extreme to the middle term constitutes a categorical judgment; but since the other extreme, too, according to the above-stated determination, expresses the specific difference of the genus or its determinate principle, this other premise is also categorical.
2. This syllogism, as the first and therefore immediate syllogism of necessity, comes in the first instance under the schema of the first formal syllogism I-P-U. But as the middle term is the essential nature of the individual and not just any of its determinatenesses or properties, and as, similarly, the extreme of universality is not just any abstract universal nor again merely a single quality, but the universal determinateness, the specific principle of difference, the subject is no longer contingently united through the syllogism with any quality through any middle term. Consequently, as the relations too of the extremes to the middle term have not that external immediacy which they had in the syllogism of existence, the demand for proof, which occurred in the latter and led to the infinite progress, does not arise.
Further, this syllogism does not, as does a syllogism of reflection, presuppose its conclusion for its premises. The terms, in keeping with their substantial content, stand in a relation to one another which is in and for itself identical; we have here one essential nature pervading the three terms, a nature in which the determinations of individuality, particularity and universality are merely formal moments.
To this extent therefore the categorical syllogism is no longer subjective; in the above identity, objectivity begins; the middle term is the pregnant identity of its extremes which are contained therein in their self-subsistence, for their self-subsistence is the above substantial universality, the genus. The subjective element of the syllogism consists in the indifferent subsistence of the extremes relatively to the Notion or middle term.
3. But this syllogism still continues to be subjective, in that the said identity is still the substantial identity or content, but is still not at the same time identity of form. Consequently, the identity of the Notion is still an inner bond of union, and therefore as relation is still necessity; the universality of the middle term is substantial, positive identity, but is not equally the negativity of its extremes.
More precisely, the immediacy of this syllogism, which immediacy is not yet posited as that which it is in itself, is present in the following manner. What is really immediate in the syllogism is the individual. This is subsumed under its genus as middle term; but under the same genus come also an indefinite number of other individuals; it is therefore contingent that only this individual is posited as subsumed under it. But further, this contingency does not merely belong to the external reflection which finds the individual posited in the syllogism to be contingent by comparison with others; on the contrary, it is because the individual itself is related to the middle term as to its objective universality that it is posited as contingent, as a subjective actuality. On the other hand, in that the subject is an immediate individual, it contains determinations which are not contained in the middle term as the universal nature; therefore it also has a specific nature of its own indifferent to the middle term and possessing a content peculiar to itself. Hence, conversely, this other term also has an indifferent immediacy and an Existence distinct from the former. The same relationship also obtains between the middle term and the other extreme; for this likewise has the determination of immediacy and hence of a being that is contingent relatively to its middle term.
Accordingly, what is posited in the categorical syllogism is on the one hand extremes standing in such a relationship to the middle term that they possess in themselves objective universality or a self-subsistent nature, and at the same time appear as immediate terms and therefore as mutually indifferent actualities. But on the other hand they are equally determined as contingent, that is to say, their immediacy is sublated in their identity. But by reason of the said self-subsistence and totality of the actuality, this identity is only formal and inner; the syllogism of necessity has hereby determined itself to the hypothetical syllogism.
1. The hypothetical judgment contains only the necessary relation without the immediacy of the related terms. 'If A is, then B is'; or, the being of A is equally the being of another, of B; so far, it is not stated either that A is, or that B is. The hypothetical syllogism adds this immediacy of being:
If A is, then B is,
But A is,
Therefore B is.
The minor premise by itself enunciates the immediate being of A.
But it is not only this that is added to the judgment. The syllogism contains the relation of subject and predicate, not as the abstract copula, but as the pregnant mediating unity. Accordingly, the being of A is to be taken not as a mere immediacy, but essentially as the middle term of the syllogism. This is to be examined more closely.
2. In the first place, the relation of the hypothetical judgment is necessity or inner substantial identity associated with external diversity of Existence, or mutual indifference of being in the sphere of Appearance — an identical content which forms the internal basis. The two sides of the judgment therefore do not appear as an immediate being but as a being held within the necessity and thus at the same time as sublated being or being only in the sphere of Appearance. Further, as sides of the judgment they stand to one another as universality and individuality; one of them, therefore, is the above content as totality Of conditions, the other as actuality. It is, however, indifferent which side is taken as universality and which as individuality. That is to say, in so far as the conditions are still the inner, abstract side of an actuality, they are the universal, and it is through their being gathered together into an individuality that they enter into actuality. Conversely, the conditions are a separated, scattered Appearance which only in actuality obtains unity and significance and a universally valid existence.
The precise relation between the two sides that has here been assumed as the relation of condition and conditioned, may however also be taken as that of cause and effect, of ground and consequent — here this is indifferent; but the relation of condition corresponds more closely to the relation that obtains in the hypothetical judgment and syllogism, inasmuch as condition appears essentially as an indifferent Existence, whereas ground and cause are spontaneously transitive [ubergehend]; also condition is a more universal determination in that it comprehends both sides of the above relations, since effect, consequent, etc., is just as much condition of the cause, ground, etc., as the latter are of the former.
Now A is the mediating being in so far as first it is an immediate being, an indifferent actuality, and secondly, in so far as it is no less an intrinsically contingent, self-sublating being. What translates the conditions into the actuality of the new shape whose conditions they are is the fact that they are not being in its abstract immediacy, but being in its Notion, in the first instance, becoming; but as the Notion is no longer transition they are more specifically individuality as self-related negative unity. The conditions are a scattered material that waits and demands to be used; this negativity is the mediating element, the free unity of the Notion. It determines itself as activity, since this middle term is the contradiction of the objective universality or the totality of the identical content, and the indifferent immediacy. This middle term is therefore no longer merely an inner necessity, but a necessity that is; the objective universality contains self-relation as a simple immediacy, as being; in the categorical syllogism this moment is in the first instance a determination of the extremes, but as against the objective universality of the middle term it determines itself as contingency, consequently, as something only posited and also sublated, that is, as something withdrawn into the Notion or into the middle term as unity, which middle term itself in its objectivity is now also being.
The conclusion, 'therefore B is', expresses the same contradiction, that B is in the form of immediate being, but equally has its being through an other, or is mediated. In respect of its form, therefore, it is the same Notion that the middle term is, distinguished from necessity only as the necessary — in the wholly superficial form of individuality as against universality. The absolute content of A and B is the same; they are only two different names for the same underlying fact for ordinary thinking [Vorstellung] which clings to the appearance of the diversified shape of determinate being and distinguishes between the necessary and its necessity; but in so far as this necessity were to be separated from B, B would not be the necessary. Thus we have here the identity of the mediating and the mediated.
3. The hypothetical syllogism in the first instance exhibits necessary relation as connection through the form or negative unity, just as the categorical syllogism exhibits through the positive unity, substantial content, objective universality. But necessity collapses into the necessary; the form-activity of translating the conditioning into the conditioned actuality is in itself the unity in which the determinatenesses of the opposition, that previously were liberated into an indifferent determinate existence, are sublated, and the difference of A and B is an empty name. Thus it is a unity reflected into itself — hence an identical content; and it is so not merely implicitly but it is also posited as such through this syllogism, in that the being of A is also not its own but B's, and vice versa, and in general the being of one is the being of the other, and in the conclusion the immediate being or indifferent determinateness appears specifically as mediated; the externality of the determinatenesses has therefore sublated itself and their unity into which they have withdrawn is posited.
The mediation of the syllogism has hereby determined itself as individuality, immediacy, and as self-related negativity, or as an identity that differentiates itself and gathers itself into itself out of that difference — as absolute form, and for that very reason as objective universality, a content that is identical with itself. The syllogism in this determination is the disjunctive syllogism.
As the hypothetical syllogism in general comes under the schema of the second figure of the formal syllogism, U-I-P, so the disjunctive syllogism comes under the schema of the third figure, I-U-P. But the middle term is the universality that is pregnant with form; it has determined itself as totality, as developed objective universality. Consequently the middle term is not only universality but also particularity and individuality. As universality it is first the substantial identity of the genus; but secondly an identity that embraces within itself particularity, but a particularity co-extensive with this identity of the genus; it is therefore the universal sphere that contains its total particularisation — the genus disjoined into its species: A that is B and C and D.
But particularisation is differentiation and as such is just as much the either-or of B, C and D, the negative unity, the reciprocal exclusion of the terms. Further, this exclusion is not merely a reciprocal exclusion, or the determination merely a relative one, but it is just as essentially a self-related determination, the particular as individuality to the exclusion of the others.
A is either B or C or D,
But A is B,
Therefore A is neither C nor D.
A is either B or C or D,
But A is neither C nor D,
Therefore A is B.
A is subject not only in the two premises but also in the conclusion. In the first premise it is a universal, and in its predicate, the universal sphere particularised into the totality of its species; in the second premise it appears as determinate or as a species; in the conclusion it is posited as the exclusive, individual determinateness. Or again, it already appears in the minor premise as exclusive individuality and is positively posited in the conclusion as the determinate which it is.
Hence what appears in general as mediated is the universality of A with individuality. But the mediating factor is this A, which is the universal sphere of its particularisations and is determined as an individual. Consequently the truth of the hypothetical syllogism, namely the unity of the mediating and the mediated, is posited in the disjunctive syllogism, which for this reason is equally no longer a syllogism at all. For the middle term, which is posited in it as the totality of the Notion, contains itself the two extremes in their complete determinateness. The extremes, in distinction from this middle term, appear only as a positedness which no longer possesses any determinateness peculiar to itself as against the middle term.
Considering this point further with more particular reference to the hypothetical syllogism, we see that in the latter we had a substantial identity as the inner bond of necessity, and a negative unity distinguished therefrom — namely, the activity or form which translated one existence into another. The disjunctive syllogism is in general in the determination of universality; its middle term is the A as genus and as perfectly determinate; through this unity, that content which previously was inner is also posited and, conversely, the positedness or form is not the external, negative unity over against an indifferent existence, but is identical with the said substantial content. The whole form determination of the Notion is posited in its determinate difference and at the same time in the simple identity of the Notion.
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