Hegel’s Science of Logic
1. Difference as such contains its two sides as moments; in diversity they fall indifferently apart; in opposition as such, they are sides of the difference, one being determined only by the other, and therefore only moments; but they are no less determined within themselves, mutually indifferent and mutually exclusive: the self-subsistent determinations of reflection.
One is the positive, the other the negative, but the former as the intrinsically positive, the latter as the intrinsically negative. Each has an indifferent self-subsistence of its own through the fact that it has within itself the relation to its other moment; it is thus the whole, self-contained opposition. As this whole, each is mediated with itself by its other and contains it. But further, it is mediated with itself by the non-being of its other; thus it is a unity existing on its own and it excludes the other from itself.
The self-subsistent determination of reflection that contains the opposite determination, and is self-subsistent in virtue of this inclusion, at the same time also excludes it; in its self-subsistence, therefore, it excludes from itself its own self-subsistence. For this consists in containing within itself its opposite determination — through which alone it is not a relation to something external — but no less immediately in the fact that it is itself, and also excludes from itself the determination that is negative to it. It is thus contradiction.
Difference as such is already implicitly contradiction; for it is the unity of sides which are, only in so far as they are not one-and it is the separation of sides which are, only as separated in the same relation. But the positive and negative are the posited contradiction because, as negative unities, they are themselves the positing of themselves, and in this positing each is the sublating of itself and the positing of its opposite. They constitute the determining reflection as exclusive; and because the excluding of the sides is a single act of distinguishing and each of the distinguished sides in excluding the other is itself the whole act of exclusion, each side in its own self excludes itself.
If we consider the two determinations of reflection on their own, then the positive is positedness as reflected into likeness to itself, positedness that is not a relation to an other, a subsistence, therefore, in so far as positedness is sublated and excluded. But with this, the positive makes itself into the relation of a non-being — into a positedness. It is thus the contradiction that, in positing identity with itself by excluding the negative, it makes itself into the negative of what it excludes from itself, that is, makes itself into its opposite. This, as excluded, is posited as free from that which excludes it, and therefore as reflected into itself and as itself exclusive. The exclusive reflection is thus a positing of the positive as excluding its opposite, so that this positing is immediately the positing of its opposite which it excludes.
This is the absolute contradiction of the positive, but it is immediately the absolute contradiction of the negative; the positing of each is a single reflection. The negative, considered on its own over against the positive, is positedness as reflected into unlikeness to itself, the negative as negative. But the negative is itself the unlike, the non-being of an opposite; therefore its reflection into its unlikeness is rather its relation to itself. Negation in general is the negative as quality, or immediate determinateness; but the negative as negative, is related to the negative of itself, to its opposite. If this negative is only taken as identical with the first, then it, too, like the first, is merely immediate; and so they are not taken as mutual opposites and therefore not as negatives; the negative is not an immediate at all. But now, since it is also just as much a fact that each is the same as its opposite, this relation of the unlike is just as much their identical relation.
This is therefore the same contradiction that the positive is, namely, positedness or negation as self-relation. But the positive is only implicitly this contradiction, whereas the negative is the contradiction posited; for the latter, in virtue of its reflection-into-self which makes it a negative in and for itself or a negative that is identical with itself, is accordingly determined as a non-identical, as excluding identity. The negative is this, to be identical with itself in opposition to identity, and consequently, through its excluding reflection to exclude itself from itself.
The negative is, therefore, the whole opposition based, as opposition, on itself, absolute difference that is not related to an other; as opposition, it excludes identity from itself — but in doing so excludes itself; for as self-relation it is determined as the very identity that it excludes.
2. Contradiction resolves itself. In the self-excluding reflection we have just considered, positive and negative, each in its self-subsistence, sublates itself; each is simply the transition or rather the self-transposition of itself into its opposite. This ceaseless vanishing of the opposites into themselves is the first unity resulting from contradiction; it is the null.
But contradiction contains not merely the negative, but also the positive; or, the self-excluding reflection is at the same time positing reflection; the result of contradiction is not merely a nullity. The positive and negative constitute the positedness of the self-subsistence. Their own negation of themselves sublates the positedness of the self-subsistence. It is this which in truth perishes in contradiction.
The reflection-into-self. whereby the sides of opposition are converted into self-subsistent self-relations is, in the first instance, their self-subsistence as distinct moments; as such they are only implicitly this self-subsistence, for they are still opposites, and the fact that they are implicitly self-subsistent constitutes their positedness. But their excluding reflection sublates this positedness, converts them into explicitly self-subsistent sides, into sides which are self-subsistent not merely implicitly or in themselves but through their negative relation to their opposite; in this way, their self-subsistence is also posited. But further, through this their positing, they make themselves into a positedness. They destroy themselves in that they determine themselves as self-identical, yet in this determination are rather the negative, an identity-with-self that is a relation-to-other.
However, this excluding reflection, looked at more closely, is not merely this formal determination. It is an implicit self-subsistence and is the sublating of this positedness, and it is only through this sublating that it becomes explicitly and in fact a self-subsistent unity. True, through the sublating of otherness or positedness, we are again presented with positedness, the negative of an other. But in point of fact, this negation is not merely the first, immediate relation-to-other again, not positedness as a sublated immediacy, but as a sublated positedness. The excluding reflection of self-subsistence, being exclusive, converts itself into a positedness, but is just as much a sublating of its positedness. It is a sublating self-relation; in this, it first sublates the negative, and secondly, posits itself as a negative, and it is only this negative that it sublates; in sublating the negative, it posits and sublates itself at the same time. In this way, the exclusive determination itself is that other of itself whose negation it is; consequently, the sublating of this positedness is not again a positedness as the negative of an other, but is a uniting with itself, the positive unity with itself. Self-subsistence is thus through its own negation a unity returned into itself, since it returns into itself through the negation of its own positedness. It is the unity of essence, being identical with itself through the negation, not of an other, but of itself.
3. According to this positive side, in which the self-subsistence in opposition, as the excluding reflection, converts itself into a positedness which it no less sublates, opposition is not only destroyed [zugrunde gegangen] but has withdrawn into its ground. The excluding reflection of the self-subsistent opposition converts this into a negative, into something posited; it thereby reduces its primarily self-subsistent determinations, the positive and negative, to the status of mere determinations; and the positedness, being thus made into a positedness, has simply returned into its unity with itself; it is simple essence, but essence as ground. Through the sublating of its inherently self-contradictory determinations, essence has been restored, but with this determination, that it is the excluding unity of reflection-a simple unity that determines itself as a negative, but in this positedness is immediately like itself and united with itself.
In the first place, therefore, the self-subsistent opposition through its contradiction withdraws into ground; this opposition is the prius, the immediate, that forms the starting point, and the sublated opposition or the sublated positedness is itself a positedness. Thus essence as ground is a positedness, something that has become. But conversely, what has been posited is only this, that opposition or positedness is a sublated positedness, only is as positedness. Therefore essence as ground is the excluding reflection in such wise that it makes its own self into a positedness, that the opposition from which we started and which was the immediate, is the merely posited, determinate self-subsistence of essence, and that opposition is merely that which sublates itself within itself, whereas essence is that which, in its determinateness, is reflected into itself. Essence as ground excludes itself from itself, it posits itself; its positedness — which is what is excluded — is only as positedness, as identity, of the negative with itself. This self-subsistent is the negative posited as negative; it is self-contradictory and therefore remains immediately in essence as-init ground.
The resolved contradiction is therefore ground, essence as unity of the positive and negative. In opposition, the determination has attained to self-subsistence; but ground is this completed self-subsistence; in it, the negative is self-subsistent essence, but as a negative; as self-identical in this negativity, ground is just as much the positive. Opposition and its contradiction is, therefore, in ground as much abolished as preserved. Ground is essence as positive identity-with-self, which, however, at the same time relates itself to itself as negativity, and therefore determines itself and converts itself into an excluded positedness; but this positedness is the whole self-subsistent essence, and essence is ground, as self-identical and positive in this its negation. The self-contradictory, self-subsistent opposition was therefore already itself ground; all that was added to it was the determination of unity-with-self, which results from the fact that each of the self-subsistent opposites sublates itself and makes itself into its opposite, thus falling to the ground [zugrunde geht]; but in this process it at the same time only unites with itself; therefore, it is only in falling to the ground [in seinem Untergange], that is, in its positedness or negation, that the opposite is really the essence that is reflected into and identical with itself.
Remark 1: Unity of Positive and Negative
The positive and negative are the same. This expression stems from external reflection in so far as this draws a comparison between these two determinations. But it is not an external comparison that should be drawn between them any more than between any other categories; rather must they be considered in themselves, that is, we have to consider what their own reflection is. But we have found that each is essentially the mere show or illusory being of itself in the other and is itself the positing of itself as the other.
But the superficial thinking that does not consider the positive and negative as they are in and for themselves, can, of course, be referred to comparison in order to bring to its notice the untenability of these distinguished sides which it assumes to be fixed in their opposition to one another.
Even a slight experience in reflective thinking will make it apparent that if something has been defined as positive and one moves forward from this basis, then straightway the positive has secretly turned into a negative, and conversely, the negatively determined into a positive, and that reflective thinking gets confused and contradicts itself in these determinations. Unfamiliarity with their nature imagines this confusion to be an error that ought not to happen, and ascribes it to a subjective mistake. This transition also, in fact, remains a mere confusion when there is no awareness of the necessity of the transformation.
But even for external reflection, it is a simple first place, the positive is not an immediately identical, but on the one hand is an opposite to a negative, having meaning only in this relation, so that the negative itself is contained in its notion; on the other hand, that it is in its own self the self-related negation of mere positedness or the negative, is therefore itself absolute negation within itself. Similarly, the negative which stands over against the positive, has meaning only in this relation to its other; it therefore contains this in its notion. But the negative also has a subsistence of its own apart from this relation to the positive; it is self-identical; but as such it is itself that which the positive was supposed to be.
The opposition between the positive and negative is taken chiefly in the sense that the former (although etymologically it expresses positedness) is supposed to be an objective, and the latter a subjective that stems only from an external reflection and is no concern of the objective, which exists in and for itself and for which the subjective does not exist at all. Indeed, if the negative expresses nothing else but the abstraction of a subjective caprice or a determination of an external comparison, than of course it does not exist for the objective positive, that is, this is not related in its own self to such empty abstraction; that case the determination that it is a positive is likewise merely external to it. Thus, to take an example of the fixed opposition of these reflective determinations, light as such is reckoned as the pure positive and darkness as the pure negative. But light essentially possesses in its infinite expansion and in its power to promote growth and to animate, the nature of absolute negativity. Darkness, on the other hand, as a non-manifold or as the non-self-differentiating womb of generation, is the simply self-identical, the positive. It is taken as the pure negative in the sense that, as the mere absence of light, it simply does not exist for it, so that light, in its relation with darkness, is supposed to be in relation, not with an other but purely with itself, darkness therefore simply vanishing before it. But it is a familiar fact that light is dimmed to grey by darkness; and besides this merely quantitative alteration it suffers also the qualitative change of being determined to colour by its relation to darkness. Thus, for example virtue too is not without conflict; rather is it the supreme, finished conflict; as such it is not merely the positive, but is absolute negativity; also it is virtue not only in comparison with vice, but is in its own self opposition and conflict. Or again, vice is not merely the lack of virtue-innocence, too, is this lack-nor is it distinct from virtue only for an external reflection; on the contrary, it is in its own self opposed to it, it is evil. Evil consists in being self-poised in opposition to the good; it is a positive negativity. But innocence, being neither good nor evil, is indifferent to both determinations, is neither positive nor negative. But at the same time this lack must also be taken as a determinateness: on the one hand, it is to be considered as the positive nature of something; on the other, it is related to an opposite, and every nature emerging from its innocency, from its indifferent self-identity, spontaneously relates itself to its other and thereby falls to the ground or, in the positive sense, withdraws into its ground.
Truth also is the positive as the knowing that agrees with the object; but it is only this likeness to itself in so far as the knower had put himself into a negative relation with the other, has penetrated the object and sublated the negation which it is. Error is a positive, as an opinion asserting what is not in and for itself, an opinion that is aware of itself and asserts itself. But ignorance is either indifferent to truth and error, and therefore neither positively not negatively determined, its determination stemming from external reflection; or else as objective, as a nature's own determination, it is the impulse that is directed against itself, a negative that contains a positive direction within it. It is of the greatest importance to perceive and to bear in mind this nature of the reflective determinations we have just here considered, namely, that their truth consists only in their relation to one another, that therefore each in its very Notion contains the other; without this knowledge, not a single step can really be taken in philosophy. ©
Remark 2: The Law of the Excluded Middle
The determination of opposition has also been made into a law, the so-called law of the excluded middle: something is either A or not-A; there is no third.
This law implies first, that everything is an opposite, is determined as either positive or negative. An important proposition, which has its necessity in the fact that identity passes over into difference, and this into opposition. Only it is usually not understood in this sense, but usually means nothing more than that, of all predicates, either this particular predicate or its non-being belongs to a thing. ®
The opposite means here merely the lack lot a predicate or rather indeterminateness; and the proposition is so trivial that it is not worth the trouble of saying it. When the determinations sweet, green, square are taken-and all predicates are meant to be taken-and then it is said that spirit is either sweet or not sweet, green or not green, and so on, this is a triviality leading nowhere. The determinateness, the predicate, is referred to something; the proposition asserts that the something is determined; now it ought essentially to imply this: that the determinateness further determine itself, become an intrinsic determinateness, become opposition. Instead of this, however, it merely passes over, in the trivial sense just mentioned, from the determinateness into its non-being in general, back to indeterminateness.
The law of the excluded middle is also distinguished from the laws of identity and contradiction considered above; the latter of these asserted that there is nothing that is at once A and not-A. It implies that there is nothing that is neither A nor not-A, that there is not a third that is indifferent to the opposition. But in fact the third that is indifferent to the opposition is given in the law itself, namely, A itself is present in it. This A is neither +A nor -A, and is equally well +A as -A. The something that was supposed to be either -A or not A is therefore related to both +A and not-A; and again, in being related to A, it is supposed not to be related to not-A, nor to A, if it is related to not-A. The something itself, therefore, is the third which was supposed to be excluded. Since the opposite determinations in the something are just as much posited as sublated in this positing, the third which has here the form of a dead something, when taken more profoundly, is the unity of reflection into which the opposition withdraws as into ground.
Remark 3: The Law of Contradiction
If, now, the first determinations of reflection, namely, identity, difference and opposition, have been put in the form of a law, still more should the determination into which they pass as their truth, namely, contradiction, be grasped and enunciated as a law: everything is inherently contradictory, and in the sense that this law in contrast to the others expresses rather the truth and the essential nature of things. The contradiction which makes its appearance in opposition, is only the developed nothing that is contained in identity and that appears in the expression that the law of identity says nothing. This negation further determines itself into difference and opposition, which now is the posited contradiction.
But it is one of the fundamental prejudices of logic as hitherto understood and of ordinary thinking that contradiction is not so characteristically essential and immanent a determination as identity; but in fact, if it were a question of grading the two determinations and they had to be kept separate, then contradiction would have to be taken as the profounder determination and more characteristic of essence. For as against contradiction, identity is merely the determination of the simple immediate, of dead being; but contradiction is the root of all movement and vitality; it is only in so far as something has a contradiction within it that it moves, has an urge and activity.
In the first place, contradiction is usually kept aloof from things, from the sphere of being and of truth generally; it is asserted that there is nothing that is contradictory. Secondly, it is shifted into subjective reflection by which it is first posited in the process of relating and comparing. But even in this reflection, it does not really exist, for it is said that the contradictory cannot be imagined or thought. Whether it occurs in actual things or in reflective thinking, it ranks in general as a contingency, a kind of abnormality and a passing paroxysm or sickness.
Now as regards the assertion that there is no contradiction, that it does not exist, this statement need not cause us any concern; an absolute determination of essence must be present in every experience, in everything actual, as in every notion. We made the same remark above in connection with the infinite, which is the contradiction as displayed in the sphere of being. But common experience itself enunciates it when it says that at least there is a host of contradictory things, contradictory arrangements, whose contradiction exists not merely in an external reflection but in themselves. Further, it is not to be taken merely as an abnormality which occurs only here and there, but is rather the negative as determined in the sphere of essence, the principle of all self-movement, which consists solely in an exhibition of it. External, sensuous movement itself is contradiction's immediate existence. Something moves, not because at one moment it is here and at another there, but because at one and the same moment it is here and not here, because in this 'here', it at once is and is not. The ancient dialecticians must be granted the contradictions that they pointed out in motion; but it does not follow that therefore there is no motion, but on the contrary, that motion is existent contradiction itself.
Similarly, internal self-movement proper, instinctive urge in general, (the appetite or nisus of the monad, the entelechy of absolutely simple essence), is nothing else but the fact that something is, in one and the same respect, self-contained and deficient, the negative of itself. Abstract self-identity has no vitality, but the positive, being in its own self a negativity, goes outside itself and undergoes alteration. Something is therefore alive only in so far as it contains contradiction within it, and moreover is this power to hold and endure the contradiction within it. But if an existent in its positive determination is at the same time incapable of reaching beyond its negative determination and holding the one firmly in the other, is incapable of containing contradiction within it, then it is not the living unity itself, not ground, but in the contradiction falls to the ground. Speculative thinking consists solely in the fact that thought holds fast contradiction, and in it, its own self, but does not allow itself to be dominated by it as in ordinary thinking, where its determinations are resolved by contradiction only into other determinations or into nothing. ® ©
If the contradiction in motion, instinctive urge, and the like, is masked for ordinary thinking, in the simplicity of these determinations, contradiction is, on the other hand, immediately represented in the determinations of relationship. The most trivial examples of above and below, right and left, father and son, and so on ad infinitum, all contain opposition in each term. That is above, which is not below; 'above' is specifically just this, not to be 'below', and only is, in so far as there is a 'below'; and conversely, each determination implies its opposite. Father is the other of son, and the son the other of father, and each only is as this other of the other; and at the same time, the one determination only is, in relation to the other; their being is a single subsistence. The father also has an existence of his own apart from the son-relationship; but then he is not father but simply man; just as above and below, right and left, are each also a reflection-into-self and are something apart from their relationship, but then only places in general. Opposites, therefore, contain contradiction in so far as they are, in the same respect, negatively related to one another or sublate each other and are indifferent to one another. Ordinary thinking when it passes over to the moment of the indifference of the determinations, forgets their negative unity and so retains them merely as 'differents' in general, in which determination right is no longer right, nor left left, etc. But since it has, in fact, right and left before it, these determinations are before it as self-negating, the one being in the other, and each in this unity being not self-negating but indifferently for itself.
Therefore though ordinary thinking everywhere has contradiction for its content, it does not become aware of it, but remains an external reflection which passes from likeness to unlikeness, or from the negative relation to the reflection-into-self, of the distinct sides. It holds these two determinations over against one another and has in mind only them, but not their transition, which is the essential point and which contains the contradiction. ©
Intelligent reflection, to mention this here, consists, on the contrary, in grasping and asserting contradiction. Even though it does not express the Notion of things and their relationships and has for its material and content only the determinations of ordinary thinking, it does bring these into a relation that contains their contradiction and allows their Notion to show or shine through the contradiction. Thinking reason, however, sharpens, so to say, the blunt difference of diverse terms, the mere manifoldness of pictorial thinking, into essential difference, into opposition. Only when the manifold terms have been driven to the point of contradiction to they become active and lively towards one another, receiving in contradiction the negativity which is the indwelling pulsation of self-movement and spontaneous activity. ®
We have already remarked that the basic determination in the ontological proof of the existence of God is the sum total of all realities. It is usually shown, first of all, that this determination is possible because it is free from contradiction, reality being taken only as reality without any limitation. We remarked that this sum total thus becomes simple indeterminate being, or if the realities are, in fact, taken as a plurality of determinate beings, into the sum-total of all negations. More precisely, when the difference of reality is taken into account, it develops from difference into opposition, and from this into contradiction, so that in the end the sum total of all realities simply becomes absolute contradiction within itself. Ordinary — but not speculative — thinking, which abhors contradiction, as nature abhors a vacuum, rejects this conclusion; for in considering contradiction, it stops short at the one-sided resolution of it into nothing, and fails to recognise the positive side of contradiction where it becomes absolute activity and absolute ground.
In general, our consciousness of the nature of contradiction has shown that it is not, so to speak, a blemish, an imperfection or a defect in something if a contradiction can be pointed out in it. On the contrary, every determination, every concrete thing, every Notion, is essentially a unity of distinguished and distinguishable moments, which, by virtue of the determinate, essential difference, pass over into contradictory moments. This contradictory side of course resolves itself into nothing — it withdraws into its negative unity. Now the thing, the subject, the Notion is just this negative unity itself: it is inherently self-contradictory, but it is no less contradiction resolved; it is the ground which contains and supports its determinations. The thing, subject, or Notion, as reflected into itself in its sphere, is its resolved Contradiction; but its entire sphere again is also determinate, different; it is therefore finite, and this means a contradictory one. Itself it is not the resolution of this higher Contradiction; but it has a higher sphere for its negative unity, for its Ground. Accordingly, finite things in the indifferent multiplicity are simply this, to be contradictory in themselves, to be contradictory and disrupted within themselves and to return into their Ground. As will be demonstrated later, the true inference from a finite and contingent being to an absolutely necessary Being does not consist in inferring the latter from the former as from a Being which is and remains Ground, on the contrary, the inference is from a being that, as is also implied immediately in contingency, is only in a state of collapse and is inherently self-contradictory; or rather, the true inference consists in showing that contingent Being in its own self withdraws into its Ground, in which it is sublated — and, further, that by this withdrawal it posits Ground in such a manner only that it makes itself into the posited element. In an ordinary inference the being of the finite appears as the Ground of the absolute: because the finite is the inherently self-contradictory opposition, because it is not. In the former meaning an inference runs thus: The Being of the finite is the Being of the absolute; but in the latter: The non-being of the finite is the being of the absolute. ©
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