Hegel’s Science of Logic
1. The syllogism of allness is the syllogism of understanding in its perfection, but is as yet no more than that. That the middle term in it is not abstract particularity but is developed into its moments and is therefore concrete, is indeed an essential requirement for the Notion; but the form of allness so far only gathers the individual externally into universality, and conversely still preserves the individual in the universality as something possessing immediately a separate self-subsistence. The negation of the immediacy of the determinations which was the result of the syllogism of existence, is only the first negation, not yet the negation of the negation or absolute reflection into self. Therefore the single determinations still form the basis of the universality of reflection that embraces them within itself; in other words, allness is still not the universality of the Notion but the external universality of reflection.
The syllogism of existence was contingent because its middle term, as a single determinateness of the concrete subject, admits of an indeterminable number of other such middle terms, and therefore the subject could be united in the syllogism within determinably different and even contradictory predicates. But since the middle term now contains individuality and is thereby itself concrete, it can only serve to connect the subject with a predicate which belongs to the subject as concrete. If for example from the middle term green it should be inferred that a picture was pleasing because green is pleasing to the eye, or that a poem or building was beautiful because it possessed regularity, the picture, etc., might all the same be ugly on account of other qualities from which this latter predicate could be inferred. On the other hand, since the middle term has the determination of allness, it contains the greenness or regularity as a concrete, which just for that reason is not the abstraction of something merely green or merely regular; with this concrete then only those predicates can be connected which conform to the totality of the concrete thing. In the judgment: what is green or regular is pleasing, the subject is only the abstraction of green or regularity; in the proposition: all green or regular things are pleasing, the subject is, on the contrary: all actual concrete objects that are green or regular —objects, therefore, which are taken as concrete with all their properties that they possess besides greenness or regularity.
2. But this very perfection of the syllogism of reflection makes it a mere delusion. The middle term has the determinateness 'all'; to this is immediately attached in the major premise the predicate that is united with the subject in the conclusion. But 'all' are 'all individuals'; therefore in the major premise the individual subject already immediately possesses this predicate and does not obtain it first through the syllogism. Or to put it otherwise the subject obtains through the conclusion a predicate as a consequence; but the major premise already contains this conclusion within it; therefore the major premise is not correct on its own account, or is not an immediate, presupposed judgment, but already presupposes the conclusion whose ground it was supposed to be. In the favourite perfect syllogism:
All men are mortal
Now Gaius is a man
Therefore Gaius is mortal,
the major premise is correct only because and in so far as the conclusion is correct; if Gaius should chance to be not mortal, the major premise would not be correct. The proposition which was supposed to be the conclusion must already be immediately correct on its own account, because otherwise the major premise could not embrace all individuals; before the major premise can pass as correct, there is the prior question whether the conclusion itself may not be an instance against it.
3. In the case of the syllogism of existence we found from the Notion of the syllogism that the premises, as immediate, contradicted the conclusion, that is to say the mediation demanded by the Notion of the syllogism, and that the first syllogism therefore presupposed others and conversely these others presupposed it. In the syllogism of reflection, this is posited in the syllogism itself, namely, that the major premise presupposes its conclusion, in that the former contains that connection of the individual with a predicate which is supposed to appear only as conclusion.
What, then, we really have here may be expressed in the first instance by saying that the syllogism of reflection is only an external, empty show of syllogising — hence that the essence of this syllogising rests on subjective individuality and that therefore this latter constitutes the middle term and is to be posited as such the individuality that is individuality as such and possesses universality only externally. We may also say that the precise content of the syllogism of reflection showed that the relation in which the individual stands to its predicate is immediate, not inferred, and that the major premise, the connection of a particular with a universal, or, more precisely, of a formal universal with an intrinsic universal, is mediated by the relation of individuality which is present in the former — of individuality as allness. But this is the syllogism of induction.
1. The syllogism of allness comes under the schema of the first figure, I-P-U; the syllogism of induction under that of the second, U-1-P, as it again has individuality for middle term, not abstract individuality but individuality as complete, namely, posited with its opposite determination, universality. One extreme is some predicate or other that is common to all these individuals; its relation to them constitutes the immediate premises, of which one, in the preceding syllogism was supposed to be the conclusion. The other extreme may be the immediate genus as it is found in the middle term of the preceding syllogism or in the subject of the universal judgment and which is exhausted in all the individuals or species collectively of the middle term. Accordingly the syllogism has the shape:
2. The second figure of the formal syllogism U-I-P did not correspond to the schema, because I which constitutes the middle term was not the subsuming term or predicate. In induction this defect is eliminated; here the middle term is all the individuals; the proposition: U-I, which contains as subject the objective universal or genus separated off to form an extreme, has a predicate that is at least coextensive with the subject, and consequently for external reflection is identical with it. Lion, elephant, and so on constitute the genus of quadruped; the difference, that the same content is posited once in individuality and again in universality, is accordingly a mere indifferent determination of form-an indifference which is the result of the formal syllogism posited in the syllogism of reflection, and here is posited through the equality of extension.
Induction, therefore, is not the syllogism of mere perception or of contingent existence, like the corresponding second figure, but the syllogism of experience — of the subjective taking together of the individuals into the genus and of the conjoining of the genus with a universal determinateness because this latter is found in all the individuals. It has also the objective significance that the immediate genus determines itself through the totality of individuality to a universal property, has its existence in a universal relationship or mark. But the objective significance of this, as of the other syllogisms, is at first only its inner Notion, and is not yet posited here.
3. On the contrary, induction is still essentially a subjective syllogism. The middle terms are the individuals in their immediacy; the subjective taking together of them into the genus by means of allness is an external reflection. On account of the persistent immediacy of the individuals and their consequent externality, the universality is only completeness, or rather remains a problem. In induction, therefore, the progress into the spurious infinite once more makes its appearance; individuality is supposed to be posited as identical with universality, but since the individuals are no less posited as immediate, that unity remains only a perennial ought-to-be; it is a unity of likeness; those which are supposed to be identical are, at the same time, supposed not to be so. It is only when the a, b, c, d, e are carried on to infinity that they constitute the genus and give the completed experience. The conclusion of induction thus remains problematical.
But induction, in expressing that perception in order to become experience ought to be carried on to infinity, presupposes that the genus [Kind] is in and for itself united with its determinateness. Therefore, strictly speaking, it rather presupposes its conclusion as something immediate, just as the syllogism of allness presupposes the conclusion for one of its premises. An experience that rests on induction is accepted as valid although the perception is admittedly incomplete; but the assumption that no contradictory instance of that experience can arise is only possible if the experience is true in and for itself. Thus the syllogism by induction, though indeed based on an immediacy, is not based on that immediacy on which it is supposed to be based, on the merely affirmative immediacy of individuality, but on the immediacy which is in and for itself, the universal immediacy. The fundamental character of induction is that it is a syllogism; if individuality is taken as the essential, but universality as only the external, determination of the middle term, then the middle term would fall asunder into two unconnected parts and we should not have a syllogism; this externality belongs rather to the extremes. It is only as immediately identical with universality that individuality can be the middle term; such universality is properly objective universality, the genus [Kind]. This may also be looked at in this way: universality is external but essential in the determination of individuality that forms the basis of the middle term of induction; but such an external is no less immediately its opposite, the internal. The truth of the syllogism of induction is, therefore, a syllogism that has for its middle term an individuality that is immediately in its own self universality; this is the syllogism of analogy. ®
1. This syllogism has for its abstract schema the third figure of the immediate syllogism I-U-P. But its middle term is no longer just any single quality, but universality that is the reflection-into-self of a concrete, and hence its nature; and conversely, because it is thus the universality of a concrete, it is at the same time in its own self this concrete. Here, then, the middle term is an individual but an individual taken in its universal nature; further, another individual forms an extreme possessing the same universal nature with the former. For example:
The earth is inhabited,
The moon is an earth,
Therefore the moon is inhabited.
2. Analogy is the more superficial, the more the universal in which the two individuals are one, and according to which one individual becomes the predicate of the other, is a mere quality, or (quality being taken subjectively) some mark or other, when the identity of the two therein is taken as a mere similarity. Superficiality of this kind, however, to which a form of understanding or reason is reduced by being degraded to the sphere of mere representation, should not find a place in logic at all. Also it is improper to represent the major premise of this syllogism as though it should run: that which resembles an object in some characteristics resembles it in others also. By so doing, the form of the syllogism is expressed in the shape of a content, while the empirical content, the content properly so called, is relegated to the minor premise. In this way the whole form, for example, of the first syllogism, could be expressed as its major premise: That which is subsumed under some other thing in which a third inheres, has also that third inherent in it: now .... and so forth. But the importance of the syllogism itself does not depend on the empirical content, and to convert its own form into the content of a major premise is no less a matter of indifference than to take any other empirical content for that purpose. But in so far as the importance of the syllogism of analogy does not depend on the former content which contains nothing but the form peculiar to the syllogism, then the importance of the first syllogism would not depend on it either, that is to say, would not depend on that which makes the syllogism a syllogism. The main point always is the form of the syllogism, whether it have the form itself or something else for its empirical content. Thus the syllogism of analogy is a peculiar form, and it is quite futile not to regard it as such on the ground that its form can be converted into the content or matter of a major premise, whereas logic is not concerned with the matter. What may lead to this misunderstanding in the case of the syllogism of analogy and perhaps also in the case of the syllogism of induction, is that in them the middle term and the extremes, too, are further determined than in the merely formal syllogism, and therefore the form determination, because it is no longer simple and abstract, must appear also as a determination of content. But the fact that the form determines itself to content in this way is in the first place a necessary advance of the formal element and therefore essentially concerns the nature of the syllogism; and therefore, secondly, a content determination of this kind cannot be regarded in the same way as any other empirical content, nor can abstraction be made from it.
When we consider the form of the syllogism of analogy in the above expression of its major premise, which states that if two objects agree in one or more properties, then a property which one possesses also belongs to the other, it may seem that this syllogism contains four terms, the quaternio terminorum — a circumstance which entails the difficulty of bringing analogy into the form of a formal syllogism. There are two individuals, thirdly, a property immediately assumed as common, and fourthly the other property which one individual immediately possesses but which the other first obtains through the syllogism. This arises from the fact that, as we have seen, in the analogical syllogism the middle term is posited as individuality, but immediately also as the true universality of the latter. In induction, the middle term is, apart from the two extremes, an indeterminable number of individuals; in this syllogism therefore an infinite number of terms ought to be enumerated. In the syllogism of allness the universality in the middle term is so far merely the external form determination of allness; in the syllogism of analogy, on the contrary, it is essential universality. In the above example the middle term, the earth, is taken as a concrete that in its truth is as much a universal nature or genus as an individual.
From this aspect, the quaternio terminorum would not render analogy an imperfect syllogism. Yet it does so from another aspect; for although one subject has the same universal nature as the other, it is undetermined whether the determinateness which is inferred for the second subject belongs to the first by virtue of its nature or by virtue of its particularity; whether for example the earth is inhabited as a heavenly body in general, or only as this particular heavenly body. Analogy is still a syllogism of reflection inasmuch as individuality and universality are immediately united in its middle term. On account of this immediacy, the externality of the unity of reflection is still with us; the individual is only implicitly the genus, it is not posited in that negativity by which its determinateness would be the determinateness proper to the genus itself. For this reason the predicate which belongs to the individual of the middle term is not already predicate of the other individual although both belong to the one genus.
3. I-P (the moon is inhabited) is the conclusion; but one premise (the earth is inhabited) is likewise I-P; inasmuch as I-P is supposed to be a conclusion it involves the demand that the said premise shall be one also. Hence this syllogism is in its own self the demand for itself to counter the immediacy which it contains, in other words it presupposes its conclusion. A syllogism of existence has its presupposition in the other syllogisms of existence; in the case of the syllogisms just considered the presupposition has been placed within them, because they are syllogisms of reflection. Since then the syllogism of analogy is the demand for its own mediation against the immediacy with which its mediation is burdened, it is the moment of individuality whose sublation it demands. Thus there remains for middle term the objective universal, the genus, purged of immediacy. In the syllogism of analogy the genus was a moment of the middle term only as an immediate presupposition; since the syllogism itself demands the sublation of the presupposed immediacy, the negation of the individuality, and consequently the universal, is no longer immediate, but posited. The syllogism of reflection contained only the first negation of immediacy; now the second has appeared, and with it the external universality of reflection is determined into universality in and for itself. Regarded from the positive side the conclusion shows itself to be identical with the premise, the mediation as having coincided with its presupposition; thus there is an identity of the universality of reflection by which it has become a higher universality.
Looking over the course of the syllogisms of reflection, we see that the mediation is in general the posited or concrete unity of the form determinations of the extremes; the reflection consists in this positing of one determination in the other; thus the mediating element is allness. But individuality appears as the essential ground of allness and universality only as an external determination in it, as completeness. But universality is essential to the individual if it is to be a middle term that unites; the individual is therefore to be taken as in itself a universal. But the individual is not united with universality in this merely positive manner but is sublated in it and a negative moment; thus the universal is that whose essential being has become actual, the posited genus, and the individual as immediate is rather the externality of the genus, or it is an extreme. The syllogism of reflection taken in general comes under the schema P-I-U, in which the individual is still as such the essential determination of the middle term; but in that its immediacy has sublated itself, and the middle term has determined itself as the universality that is in and for itself, the syllogism has entered under the formal schema I-U-P, and the syllogism of reflection has passed over into the syllogism of necessity.
C. The Syllogism of Necessity
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