On Hegel’s ‘Science of Logic’ : A Realm of Shadows — part twenty five.
‘Widerspruch’
Wenn ich durch Busch und Zweig
Brech’ auf beschränktem Steig:
Wird mir so weit, so frei,
Will mir das Herz entzwei.
Rings dann im Waldeshaus
Rücken die Wänd’ hinaus,
Wölbt sich das Laubgemach
Hoch mir zum Schwindeldach,
Webt sich der Blätter schier
Jedes zur Schwinge mir,
Daß sich mein Herz, so weit,
Sehnt nach Unendlichkeit!
Doch wann in weitem Raum
Hoch am Gebirgessaum,
Ueber dem Thal’ ich steh’,
Nieder zum Thale seh’
Ach! wie beschränkt, wie eng
Wird mir’s im Luftgedräng;
Rings auf mein Haupt, so schwer,
Nicken die Wolken her,
Niederzustürzen droht
Rings mir das Abendroth,
Und in ein Kämmerlein
Sehnt sich mein Herz hinein!
‘Contradiction’
When through bush and branch
I strike out for the narrow climb,
it becomes so wide for me — so free -
that my heart nearly bursts in two.
Around this forest house then
the walls recede
and a leafy chamber arches
high above me, a roof of dizzying height.
Nearly every leaf is interwoven
into a wing for me,
so that my heart
yearns deeply for infinity.
Yet when in wide spaces
high on the mountain edge,
over the valley I stand
and gaze toward it.
Oh, how restricted, how narrow,
it becomes for me in the oppressive air;
Around my head so heavy
the clouds nod down;
Threatening to crash down,
the sunset surrounds me;
and in a little chamber
does my heart long to be.
- Johann Gabriel Seidl (1804–1875)
Georg Wilhelm Friedrich Hegel’s, (1778–1831), ‘Science of Logic’. Opposite Magnitudes in Arithmetic and Ethics. Hegel’s general critique of mathematics is that it doesn’t sufficiently grasp the speculative content of its subject matter. As was the case throughout the interminable calculus commentaries of chapter five, mathematics does not discern in the Positive and Negative the qualitative nature of its quantitative concepts.
Hegel states that there are two real determinations of the positive and negative.
‘Mention must be made here of the concept of the positive and negative as it occurs in arithmetic. The concept is presupposed there as known, but, since it is not grasped in its specific difference, it is not immune to insoluble difficulties and complications. We have just seen how the two real determinations of the positive and negative, outside the simple concept of their opposition, come to be. Namely, only a differentiated immediate existence stands in a first instance as ground, the simple immanent reflection of which is distinguished from its positedness, from the opposition itself. This opposition, therefore, does not count as anything which is in and for itself, and, although it does apply to its diverse sides so that each is an opposite in general, the sides remain nonetheless indifferent to it and it is a matter of indifference which of the two is regarded as positive or negative. — In a second instance, the positive is however the positive in itself, and the negative is the negative in itself, so that the two diverse sides are not indifferent to their respective determination but each is that determination in and for itself. — We see these two forms of the positive and the negative occur in arithmetic in the very first applications of them’.
- ‘The Science of Logic’
Positive and Negative are pure opposition. Opposition is found in the notion that negative cancels positive, and vice versa. Thus, +y — y =0. An hour’s journey to the east and the same distance travelled back to the west, cancels the first journey.
‘According to the first sense, +y and −y = 0; or, in −8 + 3, the positive 3 are negatives in the 8. The opposites cancel themselves in combination. A one-hour march is made to the East, and an equal march back to the West undoes it; so many are the debts pending, that many less assets are available; so many are the assets available, that many debts are absolved. The one-hour march to the East is not in itself a positive march; nor is the march to the West a negative march; the directions are rather indifferent to this determinateness of opposition; only a third standpoint external to both makes a positive of the one and a negative of the other. So also debts are not a negative in and for themselves but are such only with reference to the one in debt; for the creditor, they are a positive asset; they are a sum of money, or anything else of a given value, which, in accordance with standpoints external to it, is either debt or asset’.
- ‘The Science of Logic’
A debtor’s negative liabilities cancels out her positive assets.
Each sends its being into a third. In Self-Subsistence, this third is b. Each is an immediate reflection-into-self, standing over against a positedness. Hegel calls b the base. With regard to +a and -a, between these two opposites is a common base which is indifferent to the signs (+, -). That base is a (taken as neither positive nor negative), which is indifferent to the opposition itself and serves here as a dead base (inert foundation in the translation I am using).
‘In a first sense, the +a and –a are simply opposite magnitudes; the a is the unit that stands by itself at the base of both — itself indifferent towards the opposition and serving here as an inert foundation, without further conceptual consideration. The –a is indeed designated as the negative, the +a as the positive; but the one is just as much an opposite as the other. In yet another sense, the a is not only the simple unit serving as the foundation but, as +a and –a, it is the reflection of these opposites into themselves; there are two different as at hand, and it is indifferent which of the two is designated as the positive or the negative; each has a particular self-subsistence and is positive’.
- ‘The Science of Logic’
This base in effect announces that it is not opposition and from this perspective, the base is indifferent which of its extremes is deemed negative and which positive. Each side exists indifferently on its own. That +a and -a are different from a has been said to capture the entirety of peculative Reason. As Michael Kosok explains : ‘Reflection, in attempting to determine or assert [a], produces a self-negation of [a], involving a coupling of contraries: the original pre-formal non-positive and non-negative [a] becomes transformed into a formed self-relation as a whole is written [+-a], i.e. something which is neither +[a] nor -[a] . . . ‘. Michael Wolff claims that Hegel’s remarks led directly to the invention of [a] by Hermann Graßmann, (1809–1877), a student of the Logic.
The dead base is present in the travel example whereby travelling east is not inherently positive nor is westerly travel inherently negative and east and west are indifferent to positivity or negativity. If I walk one mile east and then one mile west, I have walked two miles, not zero miles and it is a third point of view outside them that makes one positive and the other negative.
In debtor-creditor terms, liabilities, negatives for a debtor, are not inherently so. To a creditor, the debtor’s liability is an asset. In economics, the money supply is largely defined by countervailing bank credits. But this does not mean the money supply is always zero. The liabilities of one bank are counted as the positive wealth of another bank. In calculating the money supply, +a — a = a.
‘The opposites do indeed cancel themselves in reference to each other, the result being equal to zero; but there is also present in them their identical reference3 which is itself indifferent to the opposition; so the two constitute a one. The same goes for the sum of money just mentioned, which is only one sum; or for the a, which is only one a whether in +a or –a; and for the one-hour march as well, which covers one stretch of road, whether in the direction of East or West. And the same applies to an ordinate y, which is the same whether taken on one side or the other of the axis; hence, +y − y = y; it is only one ordinate with only one determination and law for it’.
- ‘The Science of Logic’
Should Hegel should have written +a — a = 2a? It a is defined as the infinite set of cardinal numbers, Hegel’s formulation is perfectly correct. Michael Potter describing transfinite arithmetic.
This second moment of non-opposition is a qualitative moment. To illustrate, Hegel points out that “an ordinate y is the same on which ever side of the axis it is taken; so far +y-y=y; it is only the one ordinate and it has only one determination and law. In other words, -y is positively on the y ordinate. As such, it is qualitative. So it is correct, in a sense, to write +y -y = y. In -8 + 3, eleven units (not five) are implicated.
‘Thus in −8 +3 there are eleven units altogether; +y ,−y , are ordinates on opposite sides of the axis, where each is an existence indifferent to this limit and to their opposition; in this sense, +y − y = 2y. — Also the road covered from East to West and back is the sum of a twofold effort or the sum of two time periods. Likewise in the economy of a state, a quantum of money or of assets is not just this one quantum as a means of subsistence but is rather doubled; it is a means of subsistence for both creditor and debtor. The capital of a state is calculated not merely as the sum of cash and of other real or liquid assets available to it; even less so as the sum of what is left over after subtracting passive from active assets; for the capital rather, even if its active and passive accounts nullify each other, remains, first, positive capital, as +a − a = a; and, second, since it is passive in a variety of ways, by being lent many times over, it is thereby a resource many times over’.
- ‘The Science of Logic’
Arithmetic thinks opposite magnitudes are merely opposite and sees the net result as zero. But the intrinsically positive or negative are qualitative moments. When a bears no sign, it is meant to be taken as +a. T]he positive sign is given to it immediately, because the positive on its own has the peculiar meaning of the immediate, as self-identical, in contrast to opposition.
‘But not only are opposite magnitudes, on the one hand, just merely opposed, and, on the other hand, real or indifferent. For although quantum itself is being indifferent to limit, the positive in itself and the negative in itself do also occur in it. Take the a, for instance, with no sign designation. If a sign is required, the presumption is that the a is positive. If opposition is required, though only in general, then it can just as well be taken as –a. But the positive sign is the one given to it immediately, for the positive carries as such the particular meaning of the immediate, as self-identical, in contrast to the opposition’.
- ‘The Science of Logic’
When positive and negative magnitudes are added/subtracted, they are counted as positive and negative in their own right and not as becoming positive or negative in an external manner through the relation of addition and subtraction. That is, the signs (+, -) signal an arithmetic operation, but they also have a separate meaning in relation to their dead base. In 8-(-3) the first minus means opposite to 8, but the second minus (-3), counts as opposite in itself, apart from this relation.
‘Further, inasmuch as positive and negative magnitudes are added or subtracted, they count as positive or negative for themselves, not as acquiring this value externally, merely through the connective of addition or subtraction. In 8 − (−3), the first minus means ‘opposite to 8’, but the second, the (−3), has the value of something opposed in itself, outside the reference to 8'.
- ‘The Science of Logic’
In other words, the first minus is relational. It indicates that 8 is to be reduced by the integer that follows the minus sign. The second minus is not this pure opposition. Yet the function of the second minus sign is still partly oppositional. It works in reversing the prior minus sign, so that 8 enjoys an increase to 11 instead of a reduction to 5.
The qualitative nature of plus and minus becomes more apparent in multiplication and division. Here the positive must essentially be taken as the not-opposite, and the negative, on the other hand, as the opposite.
‘This is even more apparent in multiplication and division. Here we must take the positive as essentially the not-opposite and the negative, on the contrary, as the opposite, not both determinations equally as just opposites in general. In the textbooks of arithmetic, the demonstrations of how the signs function in these two types of reckoning do not go past the concept of opposite magnitudes in general, and for this reason they remain incomplete and land themselves in contradictions. — In multiplication and division the plus and the minus obtain the more specific meaning of the positive and the negative in itself, because the relation of ‘unit’ and ‘amount’ in which the factors stand to each other is not a mere relation of the more and less, as in addition and subtraction, but is a qualitative relation, and for this reason the plus and minus also obtain the qualitative meaning of the positive and the negative. — Without this determination and merely from the concept of opposite magnitudes, the false conclusion can easily be drawn that, if −a · +a = −a2, then contrariwise +a · −a = +a2. Since one factor indicates the “amount” and the other the ‘unit’, and the ‘amount’ is usually indicated by the factor that comes first, the two expressions, −a · +a and +a · −a, are distinguished by the fact that in the first the +a is the unit and –a the amount, and the contrary is the case in the other. Now it is common to say with respect to the first expression that if I am to take +a (the unit) –a times, then I take it not merely a times but also in the manner opposite to it, +a times –a; therefore, since the a is plus, I have to take it negatively, and the product is –a to the power of 2. But if, in the second case, –a is to be taken +a times, then –a should equally be taken not –a times but in the determination opposite to it, namely +a times. Therefore, on the argument of the first case the product would have to be +a to the power of 2. — The same goes for division’.
- ‘The Science of Logic’
They are not to be taken as merely the opposite of each other. Rather, each has a qualitative integrity against the other. In multiplication, the relation of the factors is not a mere relation of increasing and decreasing as in the case of addition and subtraction. That is, in addition +8 -3 implies that +8 is to be decreased in magnitude to 5. In multiplication, the minus sign in +8 (-3) indicates that the product has the quality of being opposite to +24. If plus and minus were to be taken as mere opposites of each other, with no qualitative integrity, the false conclusion can easily be drawn that if -a times + a = -a2, conversely +a times — a = +a2. This would violate the commutative nature of multiplication.
Why does the minus tyrannize the plus in multiplication? Because the plus is qualitatively determined against the minus!
‘This is the conclusion that necessarily follows when we take plus and minus as opposite magnitudes in general; in the first case, to the minus is attributed the power of altering the plus; yet in the second case the plus is supposed not to have the same power over the minus, despite the fact that it is as good an opposite determination of magnitude as the minus. In point of fact, the plus does not have this power, for it is to be taken here according to its qualitative determination as against the minus, since the factors stand in qualitative relation to each other. For this reason, the negative here is therefore the inherently opposite as such, but the positive is the indeterminate, the indifferent in general; it, too, is indeed the negative, but the negative of the other, not a negative within it. — A determination of negation thus derives solely by virtue of the negative at hand, not by virtue of the positive’.
- ‘The Science of Logic’
The plus has a non-oppositional quality. The negative is also qualitative — it is the intrinsically opposite as such. It is in the very nature of the negative to reverse. The positive is something different — an indeterminate, indifferent sign in general. It has no power to reverse anything. Only the negative has power. When -a times -a produces +a to the power of 2, each minus sign orders us to take the other minus negatively. Here the mathematicians at last agree with Hegelian speculative philosophy — the negation of the negation is something positive.
Hegel gives some examples of the qualitative nature of Positive and Negative in ethical thought. These examples show that even superficial thinking recognizes both the qualitative and oppositional nature of Positive and Negative.
‘Superficial thought that does not consider the positive and the negative as they are in themselves can of course be made aware of the instability of these distinct terms, which it assumes to be fixed in their opposition to each other, by being referred to the act of comparing. The most cursory experiment in reflective thought will demonstrate that, if something is determined as a positive and is then taken as the starting point, this same something will have immediately turned in the process into a negative and, vice versa, anything negatively determined will have turned into a positive; it will demonstrate that reflective thinking gets confused and runs into contradictions in these determinations. Ignorance of their nature will interpret this confusion as a misstep that should not occur, and will ascribe it to a subjective failure. Indeed, the shifting back and forth from one determination to the other will remain mere confusion as long as there is no awareness of the necessity of the alternation. — But even to external reflection it will be a matter of simple consideration that the positive, to start with, is not a simple identity but is rather, on the one hand, opposed to the negative — has meaning only in this reference to it and therefore entails the negative in its very concept — and, on the other hand, is inherently the self-referring negation of mere positedness or of the negative and therefore is itself implicitly the absolute negation. — Similarly, the negative that stands over against the positive has meaning only in thus referring to its other; it contains it, therefore, in its concept. But the negative has a self-subsistence of its own also without the reference to the positive; it is self-identical; thus it is itself what the positive was supposed to be’.
- ‘The Science of Logic’
Virtue is taken as qualitative. It is not merely the lack of vice. But virtue is also negative — it has already negated vice. Vice is not merely the lack of virtue. Vice is positively evil.
‘The opposition of positive and negative is normally taken in the sense that the former (even though its name conveys positedness) is to be supposed as objective; the latter, instead, as something subjective that only belongs to an external reflection and has nothing to do with what exists objectively in and for itself, even is for the latter nothing at all. And in fact, if the negative only expressed a subjectively arbitrary abstraction or a determination of external comparison, then it would indeed be for the positive nothing at all, that is, there would be no reference in the positive to such an empty abstraction; but then its determination, that it is a positive, would equally be only external to it. — As an example of the fixed opposition of these determinations of reflection, take light in general to be the solely positive, and darkness the solely negative. But light has, in its unending expansion and power to suscitate and vivify, the nature of absolute negativity. Darkness, on the other hand, as a non-manifold or as the non-self-differentiating womb of generation, is simple self-identity, the positive. In the way it is taken, it is only a negative, in the sense that it is the mere absence of light, nothing at all for itself, so that light, in referring to it, would not be referring to another but purely to itself, would therefore simply disappear before it. But surely light is dimmed to gray by darkness; and, besides this merely quantitative alteration, it also suffers the qualitative one of being determined as color by referring to darkness. — So also virtue, for example, is not without struggle; it is rather the highest, the perfect struggle, and thus not only a positive but rather absolute negativity; virtue is virtue, not just by comparison to vice, but for the opposition and the combat in it. Or again, vice is not only the lack of virtue — innocence too is such a lack — and distinct from virtue not just in the eyes of an external reflection, but is opposed to virtue in itself; it is evil. Evil consists in maintaining one’s own ground as against the good; it is positive negativity. Innocence, on the other hand, as the lack of both good and evil, is indifferent to these determinations — is neither positive nor negative. But at the same time this lack must be taken also as a determinateness and, as such, on the one hand it is to be considered as the positive nature of something just as, on the other, as referring to an opposite. And thus all natures fall from innocence, from their indifferent self-identity; because of what they are in themselves they refer to their other, and therefore they cause themselves to founder, or, positively expressed, they return to their ground. — Truth also is the positive as the knowledge that agrees with the object, but it is this likeness to itself only in so far as knowledge has related itself negatively to the other, has penetrated the object and sublated the negation which the latter is. Error is something positive as the self-aware and deliberate assertion of something which has no existence in and for itself. Ignorance, for its part, is either something indifferent to truth and error — hence neither positively nor negatively determined, its determination a lack and thus the domain of external reflection — or, objectively taken as the defining determination of a nature, an instinct that is directed against itself, a negative containing a positive direction within it. — To perceive and to be mindful of this nature of the determinations of reflection is among the most important steps in cognition: that their truth consists only in their reference to one another, and hence that each contains the other within its very concept. Without this recognition, no proper step in philosophy can be made’.
- ‘The Science of Logic’
Innocence is a qualitative concept, but it is related to its opposite as well 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 Thought its ground and this last remark about innocence perhaps refers to Kantian radical evil or in Christian terms, original sin. Per Immanuel Kant, (1724–1804), pure morality and pure (diabolical) evil are impossible, instead because we cannot discern our own motives, we are constantly in doubt as to whether pure acts were moral or motivated by inclination. See Jeanne L. Schroeder and David Gray Carlson, here, Hegel refers to the soul emerging from innocence and falling to the ground. Since ground is the unity of opposites, the innocent person falls into a state of radical evil. They are analysing the beautiful soul in the ‘Phenomenology of Spirit’, the beautiful soul that projects its own disorder onto the world and attempts to cure this disorder by imposing the law of the heart upon everyone else. See my article Intermission: On the Threshold of the System.
Truth is also qualitative. In the accompanying diagram, truth is knowing b that agrees with the object c. b becomes perfectly coincident with c, thereby sublating the negative subject a. This operation Hegel would view as impossible. It is nevertheless the view of truth that ordinary thinking has. In fact, the subject a survives this operation as not the object. Hence truth is qualitative but also refers to negative relation. Like truth, error is qualitative. It is opinion asserting what is not in and for itself. Ignorance is viewed as standing over against either truth or error and is indifferent to it. Or, it is objective — an impulse that is directed against itself, a negative that contains a positive direction within it. Perhaps this means that ignorance must strive to preserve itself. Otherwise, it cannot help but turn into its opposite.
Thought
Contradiction. In common parlance, contradiction cannot be. It is impossible that A should be and not be. For Hegel, A is and is not. So Hegel has a rather different view of contradiction. It is precisely what endures — not an impossibility that passes away. Contradiction is ‘not a defect associated with certain statements; on the contrary, it is an unavoidable … feature without which we would be left with the barren and sterile abstract identity’, explains Hartnack. ‘The function of contradiction is not to cancel but to demonstrate the impossibility of coherent partiality or apartness’, says Rosen. It is the self-subsistent determination of Reflection that contains the opposite determination, and is self-subsistent in virtue of this inclusion.
‘Since the self-subsisting determination of reflection excludes the other in the same respect as it contains it and is self-subsisting for precisely this reason, in its self-subsistence the determination excludes its own self-subsistence from itself. For this self-subsistence consists in that it contains the determination which is other than it in itself and does not refer to anything external for just this reason; but no less immediately in that it is itself and excludes from itself the determination that negates it. And so it is contradiction’.
- ‘The Science of Logic’
Contradiction is the “relation between one of two opposed determinations [i.e., positive or negative] and the substrate of logical reflection Contradiction with regard to which the determinations are mutually opposed’ explains Wolff. It is the unity between Positive/Negative (which cannot endure) and the self-subsistence of opposition. It is ‘the application of opposite categories to the same reality that cannot be maintained and requires the search for a ground or explanation’ explains Burbidge.
To review, in Diversity, Difference fell indifferently apart.
‘Difference in general contains both its sides as moments; in diversity, these sides fall apart as indifferent to each other; and in opposition as such, they are the moments of difference, each determined by the other and hence only moments. But in opposition these moments are equally determined within, indifferent to each other and mutually exclusive, self-subsisting determinations of reflection’.
- ‘The Science of Logic’
Opposition united the two sides. There, each side opposes and so determines the other — though each side was equally mutually indifferent. On the law of sublation, the sides are diverse. They are the self-subsistent determinations of reflection. They are not merely opposition. But each was also the whole — a self-contained opposition.
‘One is the positive and the other the negative, but the former as a positive which is such within, and the latter as a negative which is such within. Each has indifferent self-subsistence for itself by virtue of having the reference to its other moment within it; each moment is thus the whole self-contained opposition. — As this whole, each moment is self-mediated through its other and contains this other. But it is also self-mediated through the non-being of its other and is, therefore, a unity existing for itself and excluding the other from itself’.
- ‘The Science of Logic’
These attributes add up to Contradiction. Contradiction endures because Self-Subsistence f is a Diversity that is not self-subsistent. It endures only when it joins with the non-self-subsistent Opposites. But while Opposition is included in Contradiction, it is also excluded, since Reflection always announces what it is not. Its negative being is sent forth and retained — the hallmark of True Infinity. A middle term, Contradiction is the name of an act.
Contradiction resolves itself Hegel promises. Positive and Negative self-erase. Each is the self-transposition of itself into its opposite. Hegel names this ceaseless vanishing of the opposites into themselves, this first unity resulting from the contradiction, the Null (die Null).
‘Contradiction resolves itself. In the self-excluding reflection we have just considered, the positive and the negative, each in its self-subsistence, sublates itself; each is simply the passing over, or rather the self-translating of itself into its opposite. This internal ceaseless vanishing of the opposites is the first unity that arises by virtue of contradiction; it is the null. But contradiction does not contain merely the negative; it also contains the positive; or the self-excluding reflection is at the same time positing reflection; the result of contradiction is not only the null. — The positive and the negative constitute the positedness of the self-subsistence; their own self-negation sublates it. It is this positedness which in truth founders to the ground in contradiction’.
- ‘The Science of Logic’
Contradiction
Contradiction is not merely Null. Dialectical Reason intervenes to remind the Understanding that the Null is also positive; the self-excluding reflection is at the same time positing reflection. Positing Reflection was Reflection’s immediate moment. It announced what it was not, and this affirmatively proved what it was. Contradiction, then, is Null but also something positive. ‘The null is only one side of the concept of contradiction wherein positive and negative are superseded’, says Andrew Haas. ‘To stop at the null would be to hold on to exclusion rather than releasing it into its self-demise’, says Wendell Howard Kisner. Hegel describes this positive selfsubsistent moment as follows. Positive and Negative constitute the positedness of self-subsistence. This can be seen in Self-Subsistence, where Self-Subsistence stood over against Positive and Negative. There, Self-Subsistence said, I am not that and so Positive/Negative was its presupposition. As presupposed they were posited by Self-Subsistence and hence were its positedness. Positive and Negative, however, erase themselves. They are Null. When they exhibit their Nullity, they leave Self-Subsistence b standing alone. This activity of the Null in which Positive and Negative engage is the Positive Moment of Contradiction. In other words, what self-subsists is self-erasure — the very selfhood of essence. ‘Through this demise a genuine, non-exclusive self-subsistence is attained’, says Haas. The subsistence of self-erasure is Ground tout court.
Null
What is the difference between Self-Subsistence and The Positive Moment of Contradiction? In Self-Subsistence, the sides were still opposites; they were only implicitly selfsubsistent, still positednesses. Each side referred to its other. In The Positive Moment of Contradiction, the sides have explicitly excluded themselves from themselves in an act Hegel calls excluding reflection.
‘The immanent reflection by virtue of which the sides of opposition are turned into self-subsistent self-references is, first of all, their self-subsistence as distinct moments; thus they are this self-subsistence only in themselves, for they are still opposites, and that they are in themselves self-subsistent constitutes their positedness. But their excluding reflection sublates this positedness, turns them into self-subsistent beings existing in and for themselves, such as are self-subsistent not only in themselves but by virtue of their negative reference to their other; in this way, their self-subsistence is also posited. But, further, by thus being posited as self-subsistent, they make themselves into a positedness. They fate themselves to founder, since they determine themselves as self-identical, yet in their self-identity they are rather the negative, a self-identity which is reference-to-other’.
‘However, on closer examination, this excluding reflection is not only this formal determination. It is self-subsistence existing in itself, and the sublating of this positedness — is only through this sublating a unity that exists for itself and is in fact self-subsistent. Of course, through the sublating of otherness or positedness, positedness or the negative of an other is indeed present again. But in fact, this negation is not just a return to the first immediate reference to the other, is not positedness as sublated immediacy, but positedness as sublated positedness. The excluding reflection of selfsubsistence, since it is excluding, makes itself a positedness but is just as much the sublation of its positedness. It is sublating reference to itself; in that reference, it first sublates the negative and it secondly posits itself as a negative, and it is only this posited negative that it sublates; in sublating the negative, it both posits and sublates it at the same time. In this way the exclusive determination is itself that other of itself of which it is the negation; the sublation of this positedness is not, therefore, once more positedness as the negative of an other, but is self-withdrawal, positive self-unity. Selfsubsistence is thus unity that turns back into itself by virtue of its own negation, for it turns into itself through the negation of its positedness. It is the unity of essence — to be identical with itself through the negation not of an other, but of itself’.
- ‘The Science of Logic’
The Positive Moment of Contradiction
At this point the sides have a negative relation — that is, no relation — to their opposite. Self-subsistence is nevertheless posited by Opposition. Hence, these non-positednesses are positednesses by virtue of their reference to other. They are both self-identical and related to other. Here on display is the ordinary workings of sublation. Positedness is erased and preserved. Self-subsistence is “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 itself. So Essence preserves itself and returns to itself by negating itself. It announces what it is not and thereby announces what it is. What we witness in The Positive Moment of Contradiction is self-erasure of the sides. Speculative Reason now names this activity: the contradictory sides withdraw into their Ground.
Contradiction is ‘self-liquifaction’ as Rodolphe Gasché, (1938 — ), puts it. It self-erases and sends its being elsewhere. The place to which its being is sent is Ground. As Hegel says later, the significance of every becoming is that it is the reflection of the transient into its ground and that the other into which the transient has passed constitutes its truth.
‘Hence the objective logic, which treats of being and essence, constitutes in truth the genetic exposition of the concept. More precisely, substance already is real essence, or essence in so far as it is united with being and has stepped into actuality. Consequently, the concept has substance for its immediate presupposition; substance is implicitly what the concept is explicitly. The dialectical movement of substance through causality and reciprocal affection is thus the immediate genesis of the concept by virtue of which its becoming is displayed. But the meaning of its becoming, like that of all becoming, is that it is the reflection of something which passes over into its ground, and that the at first apparent other into which this something has passed over constitutes the truth of the latter. Thus the concept is the truth of substance, and since necessity is the determining relational mode of substance, freedom reveals itself to be the truth of necessity and the relational mode of the concept’.
- ‘The Science of Logic’
Ground is negative. It is simply not the sides it Ground opposes. It is essence determined as undetermined.
‘The determination of reflection, inasmuch as this determination returns into ground, is a first immediate existence in general from which the beginning is made. But existence still has only the meaning of positedness and essentially presupposes a ground, in the sense that it does not really posit a ground; that the positing is a sublating of itself; that it is rather the immediate that is posited, and the ground the non-posited. As we have seen, this presupposing is the positing that rebounds on that which posits; as sublated determinate being, the ground is not an indeterminate but is rather essence determined through itself, but determined as indeterminate or as sublated positedness. It is essence that in its negativity is identical with itself’.
- ‘The Science of Logic’
For this reason, Contradiction is ‘the structure of the absence of essence’ explains Rosen It was posited by excluding reflection and is now the truer being of the self-erasing sides. Compared to Ground, the opposite sides — Positive and Negative — are reduced to the status of mere determinations. Each of these positednesses has simply returned into its unity with itself. Ground is thus simple essence. In fact, since essence is properly self-erasure, it is posited as essence for the first time in Ground.
‘According to this positive side, since self-subsistence in opposition, as excluding reflection, makes itself into a positedness and equally sublates this positedness, not only has opposition foundered but in foundering it has gone back to its foundation, to its ground. — The excluding reflection of the self-subsisting opposition turns it into a negative, something only posited; it thereby reduces its formerly self-subsisting determinations, the positive and the negative, to determinations which are only determinations; and the positedness, since it is now made into positedness, has simply gone back to its unity with itself; it is simple essence, but essence as ground. Through the sublating of the determinations of essence, which are in themselves self-contradictory, essence is restored, but restored in the determination of an exclusive, reflective unity — a simple unity which determines itself as negation, but in this positedness is immediately like itself and withdrawn into itself’.
- ‘The Science of Logic’
Ground, Hegel says, 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. It should be clear by now what this means. In Ground the extremes excluded themselves from themselves. Self-exclusion was their unity.
Ground
This unity is negative to the extremes: g is a beyond, from the perspective of d, e, f. In its negativity, g is nevertheless a self-identity. Yet, as negative, it is supposed to have an other. It is therefore in a state of contradiction — an immediate entity that implies relation-to-other. It is Essence determined as undetermined.
In chapter two we had such a contradiction — Limit. When point was taken as Limit to line the line sprang forth automatically. In other words, Limit is a relation, so if a point is Limit, there must be a line; otherwise there is no Limit. Limit was therefore implicitly Ground. Ground’s function is to bring forth the Grounded, as we shall see in the next chapter. Because of this function, Hegel calls ground the prius, the immediate, that forms the starting point.
In the first place, therefore, because of its contradiction, the self-subsisting opposition goes back into a ground; this opposition is what comes first, the immediate from which the beginning is made, while the sublated opposition or the sublated positedness is itself a positedness. Accordingly, essence is as ground a positedness, something that has become. But conversely, only this has been posited, namely that the opposition or the positedness is something sublated, only is as positedness. As ground, therefore, essence is excluding reflection because it makes itself into a positedness; because the opposition from which the start was just now made and was the immediate is the merely posited determinate self-subsistence of essence; because opposition only sublates itself within, whereas essence is in its determinateness reflected into itself. As ground, therefore, essence 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 the negative, something self-contradictory which, consequently, remains in the essence as in its ground’.
- ‘The Science of Logic’
Obviously, it is not the starting point that Pure Being was. Rather, Ground is a positedness, something that has become. Ground is completed self-subsistence.
‘The resolved contradiction is therefore ground, essence as unity of the positive and the negative. In opposition, determinateness has progressed to self-subsistence; but ground is this self-subsistence as completed; in it, the negative is self-subsistent essence, but as negative; and, as self-identical in this negativity, ground is thus equally the positive. In ground, therefore, opposition and its contradiction are just as much removed as preserved. Ground is essence as positive self-identity which, however, at the same time refers itself to itself as negativity and therefore determines itself, making itself into an excluded positedness; but this positedness is the whole selfsubsisting essence, and essence is ground, self-identical in its negation and positive. The self-contradictory self-subsistent opposition was itself, therefore, already ground; all that was added to it was the determination of self-unity which emerges as each of the self-subsisting opposites sublates itself and makes itself into its other, thereby founders and sinks to the ground but therein also reunites itself with itself; thus in this foundering, that is, in its positedness or in the negation, it rather is for the first time the essence that is reflected into itself and self-identical’.
- ‘The Science of Logic’
What endures is self-erasure. We now have the durability of things that Charles Taylor found wanting in Hegel’s analysis of Being. Taylor was too impatient in demanding that it be produced in the super-simple realm of Being. Ironically, what subsists is non-subsistence. What makes Ground self-subsistent is that it is self-identical and hence positive as well as negative. In Ground, Opposition and Contradiction are as much abolished as preserved. These earlier unities were only implicitly Ground. All that was added to Ground 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 but in this process the opposite only unites with itself; therefore, it is only in falling to the ground that is, in its positedness or negation, that the opposite is really the essence that is reflected into and identical with itself.
Essence is now the act of self-erasure and falling to the ground (zugrunde geht). Gasché thinks the lesson of contradiction is that the Romantic dissolution of contradiction [was] within the realm of truth. [W]hat the Romantics aimed at was not so nihilistic after all. [T]he romantic idea of the medium of reflexivity, as well as that of the text as a medium of neutralization and annulment of concepts and strata, fails to achieve what it seeks: a unitary ground or essence in which all self-subsistent opposites dissolve in order to ground themselves. Were they to achieve this goal, Romantic self-reflection and deconstructive criticism would represent a fulfillment of the telos of metaphysics. But Hegel’s speculative critique of the movement of contradiction … shows that this movement produces only the simple or abstract idea of such a ground. As Hegel shows, such a unity cannot be achieved in a logically satisfactory manner within a logic of essence or reflection but only in the logic of the Concept or Notion, since only here can the determination of interdetermination by self-determination be completed’.
- ‘The Tain of the Mirror: Derrida and the Philosophy of Reflection’
The Law of the Excluded Middle.
The law of the excluded middle (Satze des ausgeschlossenen Dritten) says, something is either A or not A; there is no third.
‘The principle of the excluded middle is further distinguished from the previously examined principles of identity or contradiction that said, ‘Nothing is A and not-A at the same time’. What this implies is that there is nothing which is not either A or not-A; that there is no third that would be indifferent to that opposition. But in fact a third indifferent to it is given in the principle itself, for the A itself is there. This A is neither +A nor –A and just as much also +A and –A. — The something which ought to have been either +A or –A is here attached to the +A as well as the –A; and again, inasmuch as it is attached to the A, it ought not to be attached to the –A, just as it ought not to be attached to the A inasmuch as it is to the not-A. The something itself is therefore the third which ought to have been excluded. Since in this something the opposite determinations are equally posited and sublated, that third which is here in the shape of an inert something, when taken more profoundly, is the unity of the reflection into which the opposition returns as into ground’.
- ‘The Science of Logic’
One need only look at any of the propositions of Dialectical Reason to see that Hegel disagrees with the validity of such a law. The excluded middle is b. If b is excluded, we would be left with the diverse entities A and not-A. These, Hegel says, cannot even be thought — they are mere Beings-for-self. ‘The logic of the excluded middle … insofar as it thinks only two ways of being/not-being or having/not-having, makes all things into dead things’, says Haas. The law of the excluded middle should be understood as follows: everything is an opposite. Everything should be determined as a positive or negative. This proposition is proven by the fact that identity passes over into difference, and this into opposition.
‘This principle contains, first, that everything is an opposite, determined either as positive or as negative. — It is an important principle, necessary because identity passes over into diversity and diversity into opposition. But this is not the sense in which it is normally understood, for its ordinary meaning amounts rather to just this, that of all predicates, either this one here or its non-being comes to a thing. Here the opposite of the predicate signifies a mere lack or rather indeterminateness; and the principle is so insignificant that it is hardly worth the effort of enunciating it. If the predicates ‘green’, ‘sweet’, ‘square’, are taken — and it is assumed that they are all taken — and then it is said of spirit that it is either sweet or not sweet, green or not-green, and so on, this is a triviality that leads nowhere. Determinateness, the predicate, is referred to something; ‘this something is determined’, the principle says. Now what the principle ought essentially to imply is that the determinateness should further determine itself, that it become determinateness in itself, opposition. Instead of this, however, it only goes, in the trivial sense just mentioned, from determinateness over to its non-being in general, goes back to indeterminateness’.
- ‘The Science of Logic’
Unreflective thinking does not understand the law in this sense. The law usually means nothing more than that, of all predicates, either this particular predicate or its non-being belongs to a thing. Things are either sweet or not sweet, green or not green. The Law of the Excluded Middle stands for completeness, whereas the Law of Contradiction stands for consistency: ‘the notion of consistency demands that an elements and its negation cannot both be present, while the notion of completeness demands that an element and its negation cannot both be absent’, says Kosok. According to Kosok, Reflection represents the non-presence of two opposites, which is not inconsistent. Thus not A and not not A are equally not present, which is not contradictory. However, the Law of the Excluded Middle is offended, because either A or not A must be present, which is not the case in Hegel’s Reflection.
Hegel compares the law of the excluded middle to the law of contradiction, which states that A cannot be +A and -A at the same time. The law of contradiction implies the law of the excluded middle. Both claim that there is no third that is neither +A nor -A (even though these laws overtly refer to A with no plus or minus sign in it). This third becomes the excluded middle for purposes of the law now under consideration. This third, when taken more profoundly, is the unity of reflection into which the opposition withdraws as into ground.
The Law of Contradiction. After criticizing the laws of identity, difference and opposition, Hegel proposes a real law to which he can subscribe his name. The true law of contradiction is everything is inherently contradictory. Here is a law that in contrast to the others expresses rather the truth and the essential nature of things. Ordinary thinking abhors contradiction, as nature abhors a vacuum.
‘We have already remarked concerning the ontological proof of God’s existence that the determination on which it is based is that of the sum-total of all realities. It is customary regarding this determination first to demonstrate that it is possible because it entails no contradiction, since reality is taken here only as reality without restrictions. We pointed out that this concept, the sum-total of all realities, is thereby reduced to simple, indeterminate being, or, if the realities are in fact taken as severally determinate, to the sum-total of all negations. And if the distinction differentiating them is then taken with greater precision, the difference turns into opposition and consequently into contradiction, and the sum-total of all realities in general into absolute internal contradiction. The usual horror which ordinary (not speculative) thought has of contradiction (as nature has of the vacuum) rejects this consequence, for it remains at the one-sided consideration that contradiction resolves into nothing without recognizing its positive side where it becomes absolute activity and absolute ground’.
- ‘The Science of Logic’
It privileges Identity over Contradiction. This very preference distinguishes ordinary from speculative thinking. Speculative thinking is precisely thinking that holds fast contradiction, and in it, its own self.
‘Internal self-movement, self-movement proper, drive in general (the appetite or nisus of the monad, the entelechy of the absolutely simple essence) is likewise nothing else than that something is, in itself, itself and the lack of itself (the negative), in one and the same respect. Abstract self-identity is not yet vitality; but the positive, since implicitly it is negativity, goes out of itself and sets its alteration in motion. Something is alive, therefore, only to the extent that it contains contradiction within itself: indeed, force is this, to hold and endure contradiction within. If, on the contrary, a concrete existent were not capable of overreaching its positive determination and grasping the negative one at the same time, holding the two firmly together; if it were not capable of harboring contradiction within it, it would not then be a living unity as such, not a ground, and in contradiction it would founder and sink to the ground. — Speculative thought consists only in this, in holding firm to contradiction and to itself in the contradiction, but not in the sense that, as it happens in ordinary thought, it would let itself be ruled by it and allow it to dissolve its determinations into just other determinations or into nothing’.
Ordinary thinking, in contrast, resolves contradiction into other non-contradictory determinations or into nothing.
In fact, Hegel remarks, 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. Identity is merely the determination of the simple immediate, of dead being. But Contradiction, Hegel says, 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.
‘It is, however, one of the basic prejudices of previous logic and of ordinary thought that contradiction is not as essential and immanent a determination as identity. But in fact, if order of precedence were an issue, and the two determinations were to be held separate, it would be the principle of contradiction that should be taken as the more profound and the more essential. For in contrast to it, identity is only the determination of simple immediacy, of inert being, whereas contradiction is the root of all movement and life; it is only in so far as something has a contradiction within it that it moves, is possessed of instinct and activity’.
- ‘The Science of Logic’
For this reason, contradiction 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.
‘The upshot of this examination of the nature of contradiction is that, if a contradiction can be pointed out in something, by itself this is still not, as it were, a blemish, not a defect or failure. On the contrary, every determination, anything concrete, every concept, is essentially a unity of distinguished and distinguishable elements which, by virtue of the determinate, essential difference, pass over into elements which are contradictory. This contradictoriness of course resolves itself into nothing: it goes back into its negative unity. A thing, a subject, a concept, is then precisely this negative unity; it is something inherently self-contradictory, but it is no less the resolved contradiction; it is the ground which contains the determinations it bears. The thing, the subject or the concept, each as reflected into itself within its sphere, is their contradiction as resolved; but the whole sphere of each is in turn determinate, diverse, and therefore finite, and this means contradictory. This sphere is not itself the resolution of its higher contradiction but has yet a higher sphere for its negative unity, for its ground. Finite things, in their indifferent variety, are therefore just this: to be contradictory, internally fractured and bound to return to their ground. — As we shall see in due course, the true inference from the finite and accidental to an absolutely necessary being does not consist in inferring the latter from that finite and accidental as a being which is and remains the ground of the inference, but from it as a being which is only ‘falling’ [as accidentality, from the Latin cadere, immediately conveys], a being inherently self-contradictory; or rather, the inference consists in demonstrating that accidental being makes in itself its return to its ground and is there sublated — in addition, that in this return to the ground it posits the latter in such a manner that it makes itself rather into a positedness. In customary inference, the being of the finite appears to be the ground of the absolute; because the finite is, the absolute is. But the truth is that the absolute is because the finite is the immanently self-contradictory opposition, because it is not. In the former meaning, the conclusion is that ‘the being of the finite is the being of the absolute’; but in the latter, that ‘the non-being of the finite is the being of the absolute’.
- ‘The Science of Logic’
Hegel has already emphasized how unreflective thinkers like to keep Contradiction aloof from things, from the sphere of being and of truth generally. Michael Inwood wreaks revenge on behalf of unreflective thinking claiming that Hegel ‘lacked the formal training to handle [contradiction] effectively’ For a rigorous counter demonstration, see Wolff. Contradiction is removed from the objective world and made a subjective fault. But even in this reflection, it does not really exist, for it is said that the contradictory cannot be imagined or thought. Contradiction ranks in general as a contingency, a kind of abnormality and a passing paroxysm of sickness.
‘Contradiction is ordinarily the first to be kept away from things, away from any existent and from the true; as the saying goes, there is nothing contradictory. For the rest, it is relegated to subjective reflection which allegedly first posits it by way of reference and comparison. And even within this reflection it is not really there, for the contradictory cannot supposedly be represented or thought. Whether it occurs in actuality or in the reflection of thought, it is universally reckoned as an accident, an abnormality as it were, a momentary fit of sickness’.
- ‘The Science of Logic’
All this is wrong, Hegel thinks. Contradiction is the negative as determined in the sphere of essence, the principle of all self-movement.
‘Now as regards the claim that there is no contradiction, that none is to be found, we need not worry on account of such protestations; an absolute determination of essence must be found in every experience, in anything actual just as in every concept. We have already remarked this much earlier on in connection with the infinite, which is contradiction as displayed in the sphere of being. But ordinary experience itself testifies that there do exist at least a great many contradictory things, contradictory dispositions etc., of which the contradiction is present not in any external reflection but right in them. Nor is contradiction to be taken as an abnormality which happens only here and there, but it is rather the negative in its essential determination, the principle of all self-movement which consists in nothing else than in the display of contradiction. External, sensuous motion is itself contradiction’s immediate existence. Something moves, not because now it is here and there at another now, but because in one and the same now it is here and not here; because in this here it is and is not at the same time. One must concede to the dialecticians of old the contradictions which they pointed to in motion; but what follows from them is not that motion is not but that it is rather contradiction as existent’.
- ‘The Science of Logic’
External movement of a thing is “contradiction’s immediate existence. Something moves, not because at one moment it is here and another there, but because in this ‘here’, it at once is and is not. Recall that, in Hegel’s Logic, there is no time. Everything unfolds instantaneously. If this is true, then movement is indeed problematic. The thing that moves is in two (or more) places at once. Contradiction solves the problem, because things are always present and absent simultaneously. In fact, historicization can be viewed as mankind’s effort to remove contradiction from the world and make sense of it. Self-movement is nothing else but the fact that something is self-contained and deficient, the negative of itself. 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.
‘Internal self-movement, self-movement proper, drive in general (the appetite or nisus of the monad, the entelechy of the absolutely simple essence) is likewise nothing else than that something is, in itself, itself and the lack of itself (the negative), in one and the same respect. Abstract selfidentity is not yet vitality; but the positive, since implicitly it is negativity, goes out of itself and sets its alteration in motion. Something is alive, therefore, only to the extent that it contains contradiction within itself: indeed, force is this, to hold and endure contradiction within. If, on the contrary, a concrete existent were not capable of overreaching its positive determination and grasping the negative one at the same time, holding the two firmly together; if it were not capable of harboring contradiction within it, it would not then be a living unity as such, not a ground, and in contradiction it would founder and sink to the ground. — Speculative thought consists only in this, in holding firm to contradiction and to itself in the contradiction, but not in the sense that, as it happens in ordinary thought, it would let itself be ruled by it and allow it to dissolve its determinations into just other determinations or into nothing’.
- ‘The Science of Logic’
On the other hand, if the thing is insufficiently strong to contain Contradiction, it falls to the Ground and ceases to be. In Opposition, even ordinary thinking must acknowledge the self-subsistence of Contradiction. The relationship between left and right, for example, contains both right and not-right, left and not-left, but even here, ordinary thinking suppresses the speculative content of Opposition. It looks at left and right and forgets their negative unity and so retains them merely as differents in general. Yet it cannot be denied that left and right are incapable of being isolated. The very notion of left refers to right and vice versa. Ordinary thinking everywhere has contradiction for its content, but it does not become aware of it. It remains an external reflection which passes from likeness to unlikeness. Or it focuses at one moment on the self-identity of opposites and then forgets in order to focus on the negative relation between the two terms. It refuses to think both moments at once.
‘If to ordinary thought the contradiction which is in motion, in a drive and the like, remains concealed in the simplicity of such determinations, contradiction is, on the other hand, immediately displayed in the determinations of relation. The most trivial of examples — ‘above and under’, ‘right and left’, ‘father and son’, and so on ad infinitum — all contain opposition within one and the same term. ‘Above’ is what ‘under’ is not; ‘above’ is determined by just this, ‘not to be under’, and is only to the extent that an ‘under’ is, and contrariwise. ‘Father’ is the other of ‘son’ and ‘son’ the other of ‘father’, and each is only as this other of the other; and the one determination is at the same time only with reference to the other; their being is one subsisting. The father is indeed something for itself outside this reference to the son, but then he is not ‘father’ but a ‘man’ in general. The same applies to ‘above’ and ‘under’, ‘right’ and ‘left’: they too are something outside the reference when reflected into themselves, but just ‘places’ in general. — Opposites entail contradiction inasmuch as, in negatively referring to each other, they sublate each other reciprocally and are indifferent to each other. Ordinary thought, when it passes over to the moment of indifference, forgets there the negative unity of the opposites and therefore holds on to them only as ‘different’ in general. And, of course, in this general determination ‘right’ is no longer ‘right’, ‘left’ no longer ‘left’, and so on. But if ‘right’ and ‘left’ are in fact there, present to the thought, then they are present to it in determinations which are self-negating, each negating itself in the other, and yet, in this unity, also not negating itself but each existing indifferently for itself’.
- ‘The Science of Logic’
Ordinary thought supposes that contradictions must dissolve into nothing. It fails to recognize the positive side of contradiction where it becomes absolute activity and absolute ground. Hegel, in contrast, has isolated this positive moment in The Positive Moment of Contradiction where it stands against the Null — the one-sided view of ordinary thinkers. The Null is nevertheless a genuine moment. Contradictory things erase themselves and withdraw into a negative Ground. This negative unity is precisely what a thing is. It is the ground that contains and supports the determinations of the thing. The thing is nothing but resolved contradiction, but any such resolution is merely finite and therefore itself contradictory. Finite things are simply this, to be contradictory and disrupted within themselves and to return into their ground.
Hegel’s eventual goal is to derive the Absolute from the finite realm of Being. The truth is that absolute necessity arises from the very collapse of the finite thing. The true inference consists in showing that contingent being in its own self withdraws into its ground. Hegel puts this point in different words: the absolute is, because the finite is not. The non-being of the finite is the being of the absolute. Vladimir Ilyich Ulyanov Lenin, (1870–1924), apparently misinterpreted this passage from the Logic as Lucio Colletti explains:
‘It is a fact that Lenin, as well as Engels, sees in this page of the Logic the ‘kernel’ worth saving from Hegel’s philosophy, the breaking through of a genuine realism in contradiction to the system’s ‘shell’ and to the ‘mystique of the Idea.’ The ‘reading’ given by Lenin of these pages rests … on a basic misinterpretation. He tried to read Hegel ‘materialistically’ precisely at the place where the latter was negating matter’.
- ‘Marxism and Hegel’
Colletti sees this ‘dialectic of matter’ as religious in character — not the anti-spiritual materialism of the Marxists. Yet, as chapter twelve will show, Colletti supports the interpretation that matter transports itself into form, so that there is a materialist aspect to Hegel’s thought, contrary to what Karl Marx, (1818–1883), thought.
When the contradictory thing collapses, it returns to the Ground. By this withdrawal it posits the ground only in such a manner that it rather makes itself into a positedness. That is to say, Ground is not the Absolute. Being a positedness, it refers to something else and for this very reason is not the last destination of the Logic.
‘With Whom is no Variableness, Neither Shadow of Turning’
by Arthur Hugh Clough, (1819–1861)
It fortifies my soul to know
That, though I perish, Truth is so:
That, howsoe’er I stray and range,
Whate’er I do, Thou dost not change.
I steadier step when I recall
That, if I slip, Thou dost not fall.
______________________
Some further thoughts on contradiction:
The verb widersprechen (literally to speak against) and the noun Widerspruch are exact equivalents of to contradict (a person or a thing) and contradiction. In logic, contradiction has two senses. First, a narrower sense in which two propositions or concepts contradict each other if, and only if, one is the negation of the other, for instance red and not red. Second, a wider sense in which two propositions or concepts contradict each other if they are logically incompatible, for instance square and circle, or red and blue. The law (in German, the Satz, proposition) of contradiction was regarded, since its first formulation by Aristotle, (384–322 BC), as the supreme law of thought (Denkgesetz). It was formulated in various ways. ‘It is impossible for the same thing both to belong and not to belong to something at the same time’, said Aristotle. ‘A is not non-A’, said Gottfried Wilhelm Leibniz, (1646–1716). ‘A predicate belongs to no thing that it contradicts’, said Kant. Kant saw contradiction as a negative criterion of truth whereby no two contradictory propositions are both true and no single self-contradictory proposition is true but both of two propositions that do not contradict each other or a proposition that is not self-contradictory may yet be false.
From the earliest times some philosophers claimed that not only our thought but the world itself involves oppositions or contradictions. Aristotle’s paradigm of this was Heraclitus who though he had no word for contradiction describes the world in oppositional or contradictory ways and furthermore the world is governed by the logos, (word, reason, and so on), so that no sharp distinction is drawn between the contradictions involved in his own thought or discourse and those in the world itself. Jakob Böhme, (1575–1624), also, though not using the word Widerspruch saw Gegenwurf or opposition in the world. Evil as well as good is in everything and without it there would be no life or movement all things are a Yes and No the No is the Gegenwurf of the Yes or of the truth. Novalis who was largely responsible for Böhme’s revival in this period wrote: ‘It is perhaps the highest task of the higher logic to annihilate the law of contradiction’.
Early on, Hegel saw a conflict between the law of contradiction and the truths of religion. In ‘The Spirit of Christianity and its Fate’ he argues with reference to the opening of John’s Gospel ‘In the beginning was the Logos; the Logos was with God; and God was the Logos; in him was life’ that ‘everything expressed about the divine in the language of reflection is eo ipso contradictory’ and concludes that ‘what is a contradiction in the realm of the dead is not one in the realm of life’. From the early 1800s he attempted to devise a logic that could accommodate religion and life as well as the insights of traditional logic.
The view of contradiction that Hegel eventually reached is this: We can, provisionally, distinguish between subjective contradictions, contradictions in our thoughts, and objective contradictions, contradictions in things. Traditional logic acknowledges the occurrence of subjective contradictions. Kant held that in reasoning about the world as a whole we inevitably fall into contradictions or antinomies. But Hegel argued such contradictions are far more widespread and significant than Kant believed. Any finite thought or conception taken in isolation involves a contradiction. Such a contradiction lies primarily in a concept such as causality but it also infects propositions, such as ‘The world is a causal order’. Thinking, or the thought itself, has an impulse (Trieb) to overcome the contradiction. It often attempts to do so, initially, by resorting to an infinite regress (for instance of causes and effects), but the appropriate solution is to move to a new, higher concept, which is intrinsically related to the first and removes the contradiction in it. The new concept usually involves a contradiction of its own, and so thought proceeds by successively revealing and overcoming contradictions, until it arrives at the (infinite) absolute Idea which is free of the sort of contradiction that generates further movement. The absolute idea is appropriate for the conceptualization of entities, such as God, that elude the rigid conceptions of the understanding. It, and the claims licensed by it (for instance that God is both a ground and a consequence, that he is mediated but sublates his mediation into immediacy), seem contradictory to the understanding, but this is because the understanding isolates aspects of the absolute idea in ways that have been shown to be illegitimate.
Traditional logicians, notably Kant, excluded the possibility of objective contradictions. But Hegel argued that finite things, like finite thoughts, involve contradictions. Just as finite thoughts have an impulse to overcome contradiction, and thus move on to other thoughts, so finite things have such an impulse that leads them to move and change. But finite things, unlike the Mind, cannot sustain contradictions: they ultimately perish. The world as a whole, by contrast, does not perish, since it is free of the contradictory finitude of the entities that it embraces.
Hence the law of contradiction is a ‘law of thought’ neither in the sense that contradictions are unthinkable (or unintelligible) nor in the sense that contradictions cannot occur in the world. Hegel accepts it only in so far as he holds that contradictions, both objective and subjective, must be overcome, and that a contradictory thought or entity is not true (in Hegel’s sense of ‘true’). Hegel saw the contradictions that he postulated in thoughts and in things as contradictions in the traditional sense. But there is room for doubt whether this is so. He occasionally flatly rejects notions, such as that of a ‘composite concept’, by describing them not as contradictory, but as ‘wooden iron’ (viz. a ‘square circle’ or a contradiction in terms). In the Logic, his account of contradiction follows those of Difference and of Opposition, suggesting that he sees a contradiction as an intense opposition: no formal logician need deny that the world contains intense oppositions. Moreover, his examples, especially of objective contradictions, often bear little resemblance to formal logical contradictions. Objective contradictions are, for the most part, inner conflicts produced by a thing’s entanglements with other things. Subjective contradictions are often the result of an attempt to keep distinct concepts, such as those of cause and of effect, that are conceptually interdependent. But occasionally a finite, truncated conceptual system gives rise to a more interesting ‘contradiction’: if I deploy only terms for determinate qualities belonging to ranges whose members are mutually exclusive (for instance red, green, etc.; flat, round, etc.), then, since I am aware, both simultaneously and successively, of several such qualities, I can describe myself or my own consciousness in such terms only contradictorily (for instance ‘I am both red and green (and neither red nor green’); to avoid this, I must introduce, as Hegel does in the Logic, the concept of being for itself which transcends the determinacy of Dasein (‘Determinate Being’).
Subjective contradictions are thus more palatable than objective ones. But for Hegel both are intrinsically interdependent. There is, on his view, no sharp distinction between thought and the world. Thoughts and concepts are embedded in the world, and many of the concepts reserved by traditional logic for the description of our thought and discourse ‘Negation’, ‘Truth’, ‘Judgement’, ‘Inference, and so on, have, for Hegel, an objective sense in which they are applicable to things. That finite things embody finite concepts and their contradictions is thus a central feature of Hegel’s Idealism. The traditional view that a contradictory proposition entails any proposition whatsoever, (which I was taught when a philosophy undergraduate), often put forward as a critique of Hegel is now rejected by relevance logic whereby the antecedent and consequent of implications are required to be relevantly related.
Contradiction is the driving force of movement and change.
Contradiction is the root of all movement and life, it is only so far as something has contradiction within it that it moves, is possessed of instinct and activity.
Outside the realm of mathematical objects, within which there is perfection for all is timeless abstraction, change is constant and perfection thereby self-contradictory, and yet here it is, my muse and lady, to whom my article is dedicated, is perfect for me, the driving force behind all my activities.
I can’t help it you’re perfect for me
I couldn’t care less you’re perfect for me
I’ve been waiting
You’re perfect for me right now
In the moment you’re perfect for me
I’ve been waiting you’re perfect for me
I’m not perfect
But you’re perfect for me right now
I’ve been waiting for the moment
I’m not perfect but you’re perfect for me
I couldn’t care less you’re perfect for me
From a distance
You’re perfect for me right now
And I’m sitting next to you
In a corner of a room getting writers block
From calling you is all I want to do
I can’t help it but you’re perfect for me
I’m not perfect but you’re perfect for me
From a distance
You’re perfect for me right now
Its a different kind of love
I’m not perfect but you’re perfect for me
From a distance you’re perfect for me
In pyjamas you’re perfect for me right now
Its a different kind of love
Perfect for me
John Cale, ‘Perfect’:
Coming up next:
Ground
To be continued …
