On Hegel’s ‘Science of Logic’ : A Realm of Shadows — part sixteen.
‘Measure the weight of your love’
by Vinceno Grimani (1655–1710)
Measure the true weight of your love
against your hopes and your pleasure.
You may hope to enjoy,
and to do so well
if your heart is indeed faithful.
‘Col peso del tuo amor’
Col peso del tuo amor
misura il tuo piacer,
e la tua spene.
S’è fedele il tuo cor,
spera pur di goder,
e speri bene.
Well here we are at Measure in Georg Wilhelm Friedrich Hegel’s, (1770–1831), ‘Science of Logic’, the final part of the Section on Being after which we will move on to Essence. Hegel proclaims the development of Measure extremely difficult.
‘The development of measure, which we have attempted in what follows, is among the most difficult of subject matters. Starting with immediate, external measure, it would have to proceed, on the one hand, to the further abstract determination of the quantitative aspect of natural things (of a mathematics of nature); on the other side, it would have to indicate the link between this determination of measure and the qualitative aspect of those things — at least in general, for the detailed demonstration of the link between the qualitative and the quantitative aspects as they originate in the concept of a concrete object belongs to the particular science of the concrete (examples of which, concerning the law of falling bodies and the free movement of the heavens, will be found in the Encyclopedia of the Philosophical Sciences)’.
- ‘The Science of Logic’
This has been found ‘a particularly significant observation, since such modesty is not often encountered in his writings’, said Louis Fleischhacker, (1936 — ). Cinzia Ferrini finds in this remark, added to the 1831 version of the Logic, a complex story involving Hegel’s renunciation of his controversial early dissertation, De Orbitis Planetarum, where he logically deduced the ratio of the distances between planets. Ferrini notes that Hegel simply renounced this conclusion in the 1817 Heidelberg Encyclopedia, but omitted the renunciation in the later Berlin editions. The Heidelberg version was based on a single transition from Quality to Quantity, and a single transition back. In this single transition, only vanishing was emphasized. Hence, Hegel could flatly renounce De Orbitis. But in the 1827 and 1830 Berlin editions of the Encyclopedia, Hegel realized that there was the double transition described at the end of chapter six. In the double transition, each side of the syllogism vanishes and sustains itself. This leads Hegel to withdraw his renunciation of his earlier work, since empirical quanta are not entirely unrelated to Logic.
Errol Harris, (1908–2009) judges Measure to be ‘extraordinarily difficult… so obscure as to be, for the most part, hardly intelligible, and, while it contains some astonishingly prescient scientific comments, it also indulges in what, to us in the twentieth century, must appear ill-informed and perverse polemic against sound scientific insights’.
We can nevertheless describe the theme of Measure easily enough: change, more precisely, an exploration of the difference between qualitative and quantitative change. Change has itself changed over our logical journey. At first, change was transition. Being became Nothing. Determinate Being became Negation. The Finite ceased to be. Starting with the True Infinite, however, change itself changed. The True Infinite did not cease to be. It stayed what it was even while it became something different. This was the beginning of ideality. In True Infinity, immediate Being ceased to be and preserved itself in an idealized form.
When Being ceased to be and survived as an ideal memory of immediacy, we entered the realm of Quantity — Being with all its content outside of itself. Quantity is determined by outside intellect. Quantitative change is change imposed from the outside. The very quality of Quantum was that it was open (and therefore indifferent) to change imposed upon it from the outside. Qualitative change is self-imposed change from the inside. We willlearn, however, that genuine qualitative change depends on quantitative change. Nature does make great leaps, but only after indifferently undergoing incremental quantitative change. For this reason, a seemingly innocent change of quantity acts as a kind of snare, to catch hold of the quality:
‘The identity of quality and quantity present in measure is only implicit at first, and not yet posited. This implies that each of the two determinations, whose unity is measure, also claims validity on its own account. In this way, on the one hand, quantitative determinations of what is there can be altered, without its quality being affected thereby, but, on the other, this indifferent increase and decrease also has a limit, the transgression of which alters the quality. Thus, for instance, the temperature of water is, up to a point, indifferent in relation to its liquid state; but there comes a point in the increasing or decreasing of the temperature of liquid water where this state of cohesion changes qualitatively, and the water is transformed into steam, on the one hand, and ice, on the other. When a quantitative alteration takes place it appears, to start with, to be something quite innocent; but something quite different lurks behind it, and this seemingly innocent alteration of the quantitative is like a ruse with which to catch the qualitative’.
- ‘The Encyclopedia Logic’
Liquid water, as it gets colder due to outside force, indifferently stays liquid, but, at 0° centigrade, liquid, radically and all at once, turns solid.
Measure emerged in the Ratio of Powers (x2 = y), which showed itself to be self-related externality. In x2 = y, the identity of the first (internal) x is determined by the second (external) x. The first x is in the thrall of externality. Nevertheless, x = JC, and so it is selfrelated, not just externally determined. As self-related, the Ratio of Powers (which we now call Measure) is a sublated externality. Under the law of sublation, externality is canceled and preserved; Measure has within itself the difference from itself. Because this is so, Measure will sublate itself in favor of its measureless beyond.
‘Abstractly expressed, quality and quantity are in measure united. Being as such is the immediate equality of determinateness with itself. This immediacy of determinateness has sublated itself. Quantity is being that has returned to itself in such a way that it is a simple self-equality indifferent to determinateness. But this indifference is only the externality of having the determinateness not in itself but in an other. As third, we now have the externality that refers itself to itself; as self-reference, it is at the same time sublated externality and carries the difference from itself in it — a difference which, as externality, is the quantitative moment, and, as taken back into itself, the qualitative’.
- ‘The Science of Logic’
When difference was simply external, we had before us quantitative difference. But now, having been captured by Measure, this difference is a qualitative moment. The quantitative report of a Measure is the thing’s own authentic report of itself. When the mode is external but essential, Measure is before us. ‘In the Hegelian system, the quantities involved in measurement, which from an epistemological point of view are a means to cognition, are ontologized and treated as natural objects, that is to say as the objects of an overriding analytical cognition. What is more, the equalities in behaviour constituting the substance or content of the quantities measured are interpreted as being things. As a result, the natural world as determined by Hegel corresponds to the view of nature developed by mechanicism, the world-view of the mechanistically-minded popularizers of natural science’, explains Renate Wahsner, (1938 — ).
As John Burbidge remarks:
‘Measuring … introduces an explicit act of relating. It brings together two realities, indifferent to each other. This conjunction is recognized as valid, however, only if each term allows for, and indeed encourages, the association. Since mutual reference is now an inherent characteristic of the concept, one passes beyond simple immediacy.
- ‘On Hegel’s Logic: Fragment of a Commentary’
In his later book on chemistry, however, Burbidge less plausibly remarks: ‘Measuring uses a quantity to specify a quality. That definition sets the logical task’. This formulation threatens to obscure the fact that, for Hegel, a Measure’s quality is its quantity — accurate reportage of what the thing is.
Essence. Measures are brought together by an external measurer. Nevertheless, they are ready to be brought together. Measure therefore is the immanent quantitative relationship of two qualities to each other.
‘The qualitative side of the quantum, in itself determined, exists only as a reference to the external quantitative side; as specifying the latter, it is a sublating of its externality through which quantum as such is. This qualitative side thus has a quantum for the presupposition from which it starts. But this quantum is also qualitatively distinguished from quality, and this difference between the two must now be posited in the immediacy of being in general which still characterizes measure. The two sides thus stand to each other in a qualitative respect, each a qualitative existence for itself, and the one side that was at first only an internally indeterminate formal quantum is the quantum of a something and of its quality, and, just as their reciprocal reference is now determined as measure in general, so too is the specific magnitude of these qualities. These qualities stand in relation to each other according to a determination of measure. This determination is their exponent, but they are already implicitly connected to each other in the being-for-itself of measure: the quantum is in its double being external quantum and specific quantum, so that each of the distinct quantities has this double determination in it and is at the same time inextricably interwoven with the other; it is in this way alone that the qualities are determined. They are not, therefore, a determinate being in general existing for each other but are rather posited as indivisible, and the specific magnitude tied to them is a qualitative unity — one determination of measure in which they are implicitly bound together in accordance with Specific quantity their concept. Measure is thus the immanent quantitative relating of two qualities to each other’.
- ‘The Science of Logic’
Each Measure, however, imposes quantitative change on the other. Each Measure has a qualitative resilience against the change imposed upon it from the outside. If this resilience is isolated and considered on its own, we have the Measureless — or Essence. So Hegel provides his first definition of Essence to be self-identical in the immediacy of its determined being.
‘Already present in measure is the idea of essence, namely of being selfidentical in the immediacy of being determined, so that this immediacy is reduced through the self-identity to something mediated, just as the selfidentity is equally mediated only through this externality, but the mediation is one with itself: this is reflection, the moments of which indeed are, but in this being are absolutely nothing but moments of their negative unity. In measure, the qualitative element is quantitative; the determinateness or the difference is indifferent and therefore a difference which is none; it is sublated and this quantitativeness, as an immanent turning back in which it is qualitative, constitutes the being-in-and-for-itself which is essence. But measure is essence only implicitly in itself or in its concept; this concept of measure is not yet posited. Measure is as such still the existent unity of the qualitative and the quantitative element; its moments are an existence, a quality and some quanta of this quality which, in themselves, are indeed only indivisible, but do not yet have the meaning of this reflected determination. In the development of measure, these moments are differentiated but at the same time referred to each other, so that the identity which they are in themselves becomes their connection explicitly, that is, is posited. The meaning of this development is the realization of measure in which the latter posits itself in relation to itself and consequently as moment as well; through this mediation, measure is determined as sublated; its immediacy as well as that of its moments disappears; these moments are reflected and thus measure, having disclosed what it is according to its concept, has passed over into essence’.
- ‘The Science of Logic’
In the realm of Essence, things mediate themselves. They are not mediated by outside forces. The Determinations of Reflection are destined to enjoy a selfsubsistence and independence from the qualitative and the quantitative.Later, Hegel will criticize such naive descriptions as I have provided for assuming the existence of atoms without metaphysical proof. I am undoubtedly guilty as charged. My point simply is that solid objects are made up mostly of empty space.
‘It is Berzelius especially who should be heard further on this subject. But in his Textbook of Chemistry he fails to present anything original or more determinate on the matter. Berthollet’s views are taken up and repeated word by word, only outfitted with a metaphysics typical of uncritical reflection, and all that we are thus offered for closer inspection is just the categories of this metaphysics. The theory departs from experience and does both, fabricates sense-representations such as are not given in experience itself and applies thought determinations, in either case exposing itself to logical criticism. On this score, we want to take a look at what it says about the theory in the Textbook itself (Vol. III, Section I, Wohler’s translation, pp. 82ff.). We now read there “that one must imagine that in a uniformly mixed liquid each atom of the dissolved body is surrounded by an equal number of atoms of the solvent; and if several substances are jointly dissolved, they must share among them the intervening spaces between the atoms of the solvent, so that, granted a uniform mixture of the liquid, a symmetry is produced in the disposition of the atoms in such a way that all the atoms of each individual body find themselves uniformly disposed with reference to the atoms of the other bodies; it could therefore be said that the solution is characterized by the symmetry in the position of the atoms, and the combination by the fixed proportions.” The claim is then elucidated by the example of the compounds precipitated from a solution of copper chloride when sulphuric acid is added to it. But surely the example does not demonstrate that atoms exist; or that a number of atoms of the dissolved bodies surround the atoms of the fluid, the free atoms of both acids positioning themselves around those that remain in combination (with copper oxide); or that there is actually a symmetry in their position and disposition or, for that matter, that there are intervening spaces between atoms — least of all, that the dissolved substances share among them these intervening spaces between the atoms of the solvent. This would mean that the loose atoms take up their position where the solvent is not — for the intervening spaces in the solvent are spaces void of it — consequently that the dissolved substances are not in the solvent but outside it — even though they surround and besiege it or are surrounded and besieged by it — and of course that they are not dissolved by it. One fails to see, therefore, why one would have to entertain such representations which are not evident in experience, are essentially contradictory on the face of it, and remain uncorroborated otherwise. Corroboration could come only by a consideration of these representations themselves, that is, by metaphysics, which is logic; but logic does not confirm them any more than experience does — on the contrary!’
- ‘The Science of Logic’
[Jöns Jakob Berzelius, (1779–1848), Swedish chemist responsible for the introduction of modern chemical notation. After being appointed professor at the Karolinska Institute in Stockholm, (1807), he published a three-volume Textbook of Chemistry (1808–1828)]
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‘The Measure of a Man’
by Anonymous
Not — ‘How did he die?’ But — ‘How did he live?’
Not — ‘What did he gain?’ But — ‘What did he give?’
These are the units to measure the worth
Of a man as a man, regardless of birth.
Not — ‘What was his station?’ But — ‘Had he a heart?’
And — ‘How did he play his God-given part?
Was he ever ready with a word of good cheer,
To bring back a smile, to banish a tear?’
Not — ‘What was his church?’ Nor — ‘What was his creed?’
But — ‘Had he befriended those really in need?’
Not — ‘What did the sketch in the newspaper say?’
But — ‘How many were sorry when he passed away?’
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For the moment, Quality and Quantity are still with us, but in mediated form. Each of these extremes in the syllogism of Measure is equally the one and the other. This was not so before. In Quality, the Understanding grasped Being as an affirmative immediacy. In Quantity, the Understanding learned that the negative, quantitative moment of Continuity was the truth of Being. Now the Understanding sees that the qualitative and the quantitative are two houses both alike in dignity. The difference between them is indifferent and so is no difference. The difference between Quality and Quantity has been sublated. In Ratio, Quantity showed itself to be a return-into-self, an indifference to mere quantitative change. This reflection-into-self is Quality. It is not mere Being-for-self (which self-destructed and became nothing). Rather, this form of Being- reflection-into-self — is being-inand-for-self- the attribute of Essence. Thus, Hegel introduces in Measure the portentous new brand of substance — being-in-and-for-self.
‘Already present in measure is the idea of essence, namely of being selfidentical in the immediacy of being determined, so that this immediacy is reduced through the self-identity to something mediated, just as the selfidentity is equally mediated only through this externality, but the mediation is one with itself: this is reflection, the moments of which indeed are, but in this being are absolutely nothing but moments of their negative unity. In measure, the qualitative element is quantitative; the determinateness or the difference is indifferent and therefore a difference which is none; it is sublated and this quantitativeness, as an immanent turning back in which it is qualitative, constitutes the being-in-and-for-itself which is essence. But measure is essence only implicitly in itself or in its concept; this concept of measure is not yet posited. Measure is as such still the existent unity of the qualitative and the quantitative element; its moments are an existence, a quality and some quanta of this quality which, in themselves, are indeed only indivisible, but do not yet have the meaning of this reflected determination. In the development of measure, these moments are differentiated but at the same time referred to each other, so that the identity which they are in themselves becomes their connection explicitly, that is, is posited. The meaning of this development is the realization of measure in which the latter posits itself in relation to itself and consequently as moment as well; through this mediation, measure is determined as sublated; its immediacy as well as that of its moments disappears; these moments are reflected and thus measure, having disclosed what it is according to its concept, has passed over into essence’.
- ‘The Science of Logic’
Being-in-and-for-self, however, is so far merely implicit. Measure is still the immediate [seiende] unity of quality and quantity; its moments are determinately present as a quality, and quanta thereof. Immediate Measure is a mediation of qualitative and quantitative moments. But soon Measure will turn out to be always a ratio of Measures. Within the ratio, each side will further reveal itself to be a ratio of specific quanta having the form of self-subsistent measures, yielding an infinite regression or bad infinity. The sides of every ratio have mere quantitative difference from each other. This implies that each measure continues into the other and so beyond itself entirely. The name of this beyond is the Measureless.
‘Measure is at first the immediate unity of the qualitative and the quantitative element, so that it is, first, a quantum that has qualitative meaning and is as measure. As so implicitly determined in itself, its further determination is that the difference of its moments, of its qualitatively and quantitatively determined being, is disclosed in it. These moments further determine themselves into wholes of measure which as such are self-subsistent, and, inasmuch as they refer to each other essentially, measure becomes, second, a ratio of specific quanta, each an independent measure. But their self-subsistence also rests essentially on a quantitative relation and a difference of magnitude, and so the self-subsistence becomes a transition of one measure into another. The result is that measure collapses into the measureless. — But this beyond of measure is the negativity of measure only in itself; thus, third, the indifference of the determinations of measure is thereby posited, and measure (real measure because of the negativity contained within it) is posited as an inverse ratio of measures which, as self-subsistent qualities, essentially rest on only their quantity and their negative reference to each other, and consequently prove to be only moments of their truly selfsubsistent unity. This unity is the reflection-into-itself of each and the positing of them; it is essence’.
- ‘The Science of Logic’
The Measureless is Measure’s negativity. The indifference of the Measureless to determinations of Measure is the final result of Real Measure. Real for Hegel, tends to be a dialectical word, denoting a determinateness. ‘Reality is the determinacy something in virtue of its contrast to something else’, explains Burbidge. Here, Real Measure is the second, dialectical chapter of Measure. Measure becomes an inverse ratio of measures. In this Ratio, which must remain largely mysterious until chapter nine, the Measureless is shown to be continuous with its Measures — quantitatively related but qualitatively distinct. Qualitative Measures are superfluous to the Measureless. They sublate themselves and yield their being to Essence, which is their reflection-into-self. At this point, externality sublates itself, and Being’s journey draws to a close.
Measure and the social sciences. Because Measure entails external imposition upon a phenomenon that is partly free and immune from outside oppression, Hegel is able to set forth a hierarchy in the natural sciences in terms of conduciveness to Measure. The complete, abstract indifference of developed measure can only be manifested in the sphere of mechanics wherein matter is abstract.
‘The complete, abstract indifference of developed measure, that is, of its laws, can only be found in the sphere of mechanism where concrete corporeity is only abstract matter itself; the qualitative differences of this matter are of an essentially quantitative nature; space and time are nothing but pure externalities, and the aggregates of matters, the masses, the intensity of weight, are determinations which are just as external and have their proper determinateness in the quantitative element. On the other hand, in physical things but even more so in the organic, this quantitative determinateness of abstract materiality is already disturbed by the multiplicity and consequently the conflict of qualities. And the thus ensuing conflict is not just one of qualities as such, but measure itself is subordinated here to higher relations and its immanent development is reduced rather to the simple form of immediate measure. The limbs of the animal organism have a measure which, as a simple quantum, stands in a ratio to the other quanta of the other limbs; the proportions of the human body are the fixed ratios of such quanta, and the science of nature still has far to go in discovering anything about the link that connects these magnitudes with the organic functions on which they are entirely dependent. But the closest example of the reduction of an immanent measure to a merely externally determined magnitude is motion. In the heavenly bodies, motion is free motion, one which is only determined by the concept from which alone, consequently, its magnitudes equally depend (see above); but in the organic body this free motion is reduced to one which is arbitrary or mechanically regular, that is, to one which is totally abstract and formal’.
- ‘The Science of Logic’
In the inorganic and even more in the organic spheres, Measure is subordinated to higher relationships. Cinia Ferrini suggests that these observations were designed to answer Johann Wolfgang von Goethe, (1749–1832), who questioned the propriety of measuring organic processes. She reads Hegel as not entirely rejecting measures of organic life, in the nature of Goethe, but conceding the limitations of doing so. The free development of Measure according to logic is still less to be found in politics or constitutional law — the realm of spirit. It may be that the Athenian constitution is suited only to city-states, but all this yields neither laws of measure nor characteristic forms of it.
‘And in the realm of spirit there is even less of a characteristic, free development of measure to be found. For instance, it is obvious that a republican constitution like the Athenian, or an aristocratic constitution mixed with democracy, is possible only in a state of a certain size; it is also obvious that in civil society the multitudes of individuals who belong to the different occupations stand in a certain ratio to each other. But none of this yields either laws of measures or typical forms of it. In the spiritual realm as such there are indeed distinctions of intensity of character, strength of imagination, sensations, representations, and so on; but in determining them one cannot go past this indefinite duo of ‘strength’ and ‘weakness’. To see how lame and totally empty ultimately turn out to be the so called laws which have been established for the relation of strength and weakness in sensations, representations, and so on, one need only look at the psychologies that busy themselves with just such matters’.
- ‘The Science of Logic’
In this sphere there occur differences of intensity of character, strength of imagination, sensations, general ideas, and so on. The measure of such phenomena never goes beyond the indefiniteness of strength or weakness Ordinal, not cardinal measures are the most political science can expect to achieve.
‘On the other hand, in physical things but even more so in the organic, this quantitative determinateness of abstract materiality is already disturbed by the multiplicity and consequently the conflict of qualities. And the thus ensuing conflict is not just one of qualities as such, but measure itself is subordinated here to higher relations and its immanent development is reduced rather to the simple form of immediate measure. The limbs of the animal organism have a measure which, as a simple quantum, stands in a ratio to the other quanta of the other limbs; the proportions of the human body are the fixed ratios of such quanta, and the science of nature still has far to go in discovering anything about the link that connects these magnitudes with the organic functions on which they are entirely dependent. But the closest example of the reduction of an immanent measure to a merely externally determined magnitude is motion. In the heavenly bodies, motion is free motion, one which is only determined by the concept from which alone, consequently, its magnitudes equally depend (see above); but in the organic body this free motion is reduced to one which is arbitrary or mechanically regular, that is, to one which is totally abstract and formal’.
- ‘The Science of Logic’
Hegel terminates his introduction to Measure with a blast against empirical psychology — of late passing under the name of behavioralism. How insipid and completely empty the so-called laws turn but to be which have been laid down about the relation of strength and weakness of sensations, general ideas and so on, comes home to one on reading the psychologies which occupy themselves with such laws. Immanuel Kant, (1724–1804), agrees: ‘If we took principles from psychology, i.e. from observations about our understanding … this would therefore lead to the cognition of merely contingent laws. In logic, however, the question is not one of contingent but of necessary laws’, he says. Hegel, I think, objects to empirical psychology because it proposes to reduce human freedom to a set of inviolable laws. ‘Modern science yields necessary or certain knowledge of the body, but if that knowledge is applied to the mind or soul, the result is a loss of freedom, and even further, of Syllogism of Necessity or subjectivity’, explains Stanley Rosen, (1929–2014). Any such attempt to measure freedom is what Hegel attacks elsewhere as mere phrenology in the ‘Phenomenology of Spirit’. On social science’s hatred of freedom see Jeanne L. Schroeder.
Modality, Early in his treatment of Measure, Hegel addresses a topic seemingly unrelated to physical measurement — Kant’s notion of modality. At the beginning of the Logic, Hegel wrote Measure can also, if one wishes, be regarded as a modality; but since with Kant modality is supposed no longer to constitute a determination of the content, but to concern only the relation of the content to thought, to the element, it is a quite heterogeneous relation.
‘Measure is a relation, not relation in general but specifically of quality and quantity to each other; the categories dealt with by Kant under relation will come up elsewhere in their proper place.16 Measure, if one so wishes, can be considered also a modality; but since with Kant modality is no longer supposed to make up a determination of content, but only concerns the reference of the content to thought, to the subjective, the result is a totally heterogeneous reference that does not belong here’.
- ‘The Science of Logic’
This passage in effect accuses Kant of believing that thought has no effect on the object measured. ‘The categories of modality … do not augment the concept to which they are ascribed in the least, but rather express only the relation to the faculty of cognition’, said Kant. Hegel now elaborates upon this criticism. Ferrini suggests that Hegel’s identification of modality as a form of measure constitutes ‘the essence of Hegel’s response to the challenge of the way in which transcendental idealism treated determinate being’. According to Ferrini, most commentators wrongly view the discussion of modality to be a digression that has nothing to do with Measure. Modality — where thought meets object — is the sphere of coming-to-be and ceasing-to-be.
‘The principle of the mode and of alteration does not, of course, exclude unity altogether. In Spinozism, for instance, precisely the mode is as such untrue while substance alone is what truly is; everything is supposed to be reduced to substance, and this is then a sinking of all content into an only formal unity void of content. As for Shiva, it too is again the great whole, not distinct from Brahma, from Brahma itself, that is, the distinction and the determinateness just disappear without being preserved, without being sublated, and the unity does not become concrete unity, nor is the diremption reconciled. The supreme goal of the human being, relegated as he is to the sphere of coming-to-be and passing-away, of modality in general, is to sink into unconsciousness, into unity with Brahma, annihilation; the Buddhist Nirvana, Nibbana, etc., is the same’.
- ‘The ‘Science of Logic’
By this, Hegel means to comment on Kant’s claim that the gap between subject and object is unbridgeable. Hence, subjectivity ceases to be in the thing-in-itself. And the thing-in-itself ceases to be in subjective experience. In Hegel’s view, objects come to be in the measure of thought. Kantian modality is faulted for not being Measure to the extent thought leaves the object unaffected. For Kant, modality, fourth in his table of categories,is the choice of possibility or impossibility, existence or non-existence, necessity or contingency.
Kant’s categories are as follows:
(I) Of Quantity _______________________(II) Of Quality
Unity _________________________________Reality
Plurality _______________________________Negation
Totality _______________________________Limitation
(III) Of Relation
Of Inherence and Subsistence (substantia et accidens)
Of Causality and Dependence (cause and effect)
Of Community (reciprocity between the agent and patient)
(IV) Of Modality
Possibility-Impossibility
Existence-Non-existence
Necessity-Contingence
- ‘Critique of Pure Reason’
In his table, Kant leads with quantity and quality — a priority Hegel reverses. For Kant, quantity comes first. Within quantity, unity stands over against plurality. The unity of unity and plurality is totality. Quality is second. Within Quality, Kant opposes reality to negation; their unity is limitation. The triplicity that Hegel so much favors is confined by Kant within a given category. No triplicity inheres between the concepts themselves. For this very reason, Hegel writes, Kant was unable to hit on the third to quality and quantity.
‘Since among the categories of transcendental idealism modality comes after quantity and quality, with relation inserted in between, this is an appropriate place to say something about it. In transcendental idealism, this category has the meaning that it is the connection of the subject matter to thought. As understood by that idealism, thought is as such essentially external to the thing-in-itself. Hence, inasmuch as the other categories have the transcendental determination of belonging only to consciousness, but as its objective moment, so modality, which is the category of the connection to the subject, possesses the determination of reflection in itself in a relative sense, that is to say, the objectivity which is granted to the other categories is lacking in those of modality; these, according to Kant’s words, do not add in the least to the concept as a determination of the object but only express its relation to the faculty of cognition (Cr. of Pure R., 2nd edn, pp. 99, 266).3 — The categories which Kant groups under modality — possibility, actuality, and necessity — will come up later in their proper place. Kant did not apply the form of triplicity — an infinitely important form even though with him it occurred only as a formal spark of light — to the genera of his categories (to quantity, quality, etc.), but only to their species to which he also gave the name of genera.He was therefore unable to hit upon the third to quality and quantity’.
- The Science of Logic’
Hegel implies that modality was Kant’s true third. If so, then we can see why Hegel equates modality with Measure. Relation — Kant’s nominal third — is dismissed as an insertion. Hans-Georg Gadamer, (1900–2002), suggests that Relation in Kant corresponds to Essence in Hegel’s Logic. Kantian modality, Hegel says, is the relation of the object to thought. Ferrini said ‘for Kant, modality was concerned solely with the meaning of the verb ‘to be’, as is used in order to indicate or establish a connection between an object and a proposition, and this use had to be based upon the faculty of cognition in that the modality is understood as de re and not de dicto’.
Kant perceived thought as entirely external to the thing-in-itself. The first three categories belong to thought alone — though to the objective element of it. Modality involves the relation of thought to object. It contains the determination of reflection-into-self, meaning that, by encountering objects, modality renders the objects into thoughts and brings them under the jurisdiction of the mind. This signifies that the objectivity common to the other categories is lacking in modality. The modalities — possibility, existence and necessity — do not add to the determination of the object. They only express the relation of the object to the faculty of cognition. In short, for Kant, thought leaves the object unaffected.
For Spinoza, mode was third after substance and attribute. Mode was the affectations of substance: that element which is in an other through which it is comprehended. Accordingly, mode for Spinoza is externality as such. Because external, mode is untrue.
‘With Spinoza, the mode is likewise the third after substance and attribute; Spinoza defines it as the affections of substance, or as that which is in another through which it is also comprehended. In this way of conceiving it, this third is externality as such; as has already been mentioned, with Spinoza generally, the rigidity of substance lacks the turning back into itself’.
It is the non-substantial generally, which can only be grasped through an other.
‘The remark just made extends to any of the systems of pantheism which thought has in one way or other produced. Being, the one, substance, the infinite, essence, is the first; opposite this abstraction is the second which can be mustered in an equally abstract form, as is habitually done as the next step in any purely formalistic thinking, namely all determinateness generally taken as the mere finite, the mere accidental, the transitory, the extraneous and unessential, etc. But the bond connecting this second with the first is too invasive for the second not to be not equally grasped with the first; thus with Spinoza the attribute is the whole of substance, though as comprehended by the understanding, which is itself a restriction of substance or mode; and so the mode, the insubstantial as such which can be grasped only through an other, constitutes the opposite extreme of substance, the third’.
- ‘The Science of Logic’
On Hegel’s personal history with Spinozism, see Hans-Christian Lucas, (1942–1997). Modal being for Spinoza is precisely what does not endure. Yet when the modal thought of substance disappears (back into substance), nothing of mode remains. Spinoza thus failed to see that if every determination is a negation, that negation is genuinely expressed (for-itself and no longer only in-itself) only in the mode. The Hindus had a similar triune system, leading to comparisons with Christianity, but, Hegel insists, the comparison is misleading. In Hinduism, the unity of Brahma disperses but does not return. The supreme goal is submergence in unconsciousness, unity with Brahma, annihilation. In Christianity, there is not only unity but union [nicht nur Einheit, sondern Einigkeit], the conclusion of the syllogism which is a unity possessing content and actuality, a unity which in its wholly concrete determination is spirit.
‘Also Indian pantheism, taken abstractly, has attained in its monstrous fantasies this refinement which runs like a moderating thread across its excesses as its one point of interest — namely that Brahma, the one of abstract thought, progresses through the shape of Vishnu, particularly in the form of Krishna, to the third, Shiva. The determination of this third is that of mode, alteration, coming-to-be and passing-away; it is the field of externality in general. This Indian trinity has tempted a comparison with the Christian, and one must indeed acknowledge a common element in them. But it is essential to be aware of the difference that separates them. It is not just that this difference is infinite but that the true infinity makes the difference. The determination of the Indian third principle is that it is the dispersal of the substantial unity into its opposite, not its turning back to itself — a spiritual void rather, not spirit. In the true trinity, there is not only unity but unification; the syllogism is brought to a unity which is full of content and actual, a unity which in its totally concrete determination is spirit. The principle of the mode and of alteration does not, of course, exclude unity altogether’.
- ‘The Science of Logic’
Like the Brahmans, Spinoza does not manage return-into-self. Mode is external and untrue. Truth lies only in substance. But this is only to submerge all content in the void, in a merely formal unity lacking all content, Hegel says. In Spinozism, mode is abstract externality, indifferent to qualitative and quantitative determinations. These unessential elements are not supposed to count, but, nevertheless, everything depends on the kind and manner of the mode. This dependence shows that the mode belongs to the essential nature of a thing — a very indefinite connection but one which at least implies that this external element is not so abstractly an externality.
‘Now although the mode is as such abstract externality, indifference to qualitative as well as quantitative determinations, and nothing in the essence should depend on the external, the unessential, it is nevertheless conceded that in the many all depends on the how; but this is to concede that the mode itself essentially belongs to the substance of a thing, a very indefinite connection but one which at least implies that the externality of the mode is not all that abstract an externality after all’.
- ‘The Science of Logic’
[This paragraph does not appear in the 1812 edition. It is part of the much enlarged 1832 text. It is especially important because it signals a clarification in Hegel’s own mind regarding the new objective meaning that the modal categories assume when measure is understood as a yet undeveloped form of mode.]
The Specific Quantum. At the end of chapter six, Quantity had recaptured its Quality — its immunity from outside manipulation. Measure is the unity of Quality and Quantity. Our first step, then, is Immediate Measure. Immediate Measure is an immediate quantum, hence just some specific quantum or other, but it is equally an immediate quality, some specific quality or other.
‘Measure is the simple self-reference of quantum, its own determinateness in itself; quantum is thus qualitative. At first, as an immediate measure it is an immediate quantum and hence some specific quantum; equally immediate is the quality that belongs to it; it is some specific quality or other. — Thus quantum, as this no longer indifferent limit but as selfreferring externality, is itself quality and, although distinguished from it, it does not extend past it, just as quality does not extend past quantum. Quantum is thus the determinateness that has returned into simple selfequality — which is at one with determinate existence just as determinate existence is at one with it’.
- ‘The Science of Logic’
It is therefore appropriate to represent mediatedness within Immediate Measure. The Understanding therefore presents Measure as a mediated immediacy. a, b. Immediate Measure is brittle. The slightest quantitative change yields qualitative change. In Measure, Quantum is no longer a limit which is no limit; it is now the determination of the thing, which is destroyed if it is increased or diminished beyond this quantum.
‘If a proposition is to be made of the determination just obtained, it could be expressed thus: ‘Whatever is, has a measure’. Every existence has a magnitude, and this magnitude belongs to the very nature of a something; it constitutes its determinate nature and its in-itself. The something is not indifferent to this magnitude, as if, were the latter to alter, it would remain the same; rather the alteration of the magnitude alters its quality. As measure the quantum has ceased to be a limit which is none; it is from now on the determination of a thing, so that, were the latter to exceed or fall short of this quantum, it would perish. –’
- ‘The Science of Logic’
Quantitative change is externally imposed change. Yet Quality is supposed to be immunity from quantitative change. Dialectic Reason therefore brings forth the qualitative moment that Immediate Measure suppresses. The Quality of a measure is the extent it can withstand quantitative change without succumbing to qualitative change. Quantum, Hegel says, is a self-related externality and thus itself quality. Why Immediate Measure is a self-relation should by now be apparent. b represents the mediation between a and b and is the very being-within-self of the concept of Measure. But why is this self-relation an externality? The answer lies in the True Infinite nature of Measure. True Infinitude requires that a go out of itself and into b, which, as always, instantly implies that a is an externality — represented by c. Hence, the externality of Immediate Measure is both inside and outside — b and c. Accordingly, Hegel says of the Quantum a that it is distinguished from Quality, but does not transcend it, neither does the quality transcend the quantum. Measure is thus the determinateness which has returned into simple identity with itself.
‘Measure is the simple self-reference of quantum, its own determinateness in itself; quantum is thus qualitative. At first, as an immediate measure it is an immediate quantum and hence some specific quantum; equally immediate is the quality that belongs to it; it is some specific quality or other. — Thus quantum, as this no longer indifferent limit but as self-referring externality, is itself quality and, although distinguished from it, it does not extend past it, just as quality does not extend past quantum. Quantum is thus the determinateness that has returned into simple self-equality — which is at one with determinate existence just as determinate existence is at one with it’.
- ‘The Science of Logic’
‘These last two steps represent the claim that all that exists has a measure. If a proposition is to be made of the determination just obtained, it could be expressed thus: ‘Whatever is, has a measure’. Every existence has a magnitude, and this magnitude belongs to the very nature of a something; it constitutes its determinate nature and its in-itself. The something is not indifferent to this magnitude, as if, were the latter to alter, it would remain the same; rather the alteration of the magnitude alters its quality. As measure the quantum has ceased to be a limit which is none; it is from now on the determination of a thing, so that, were the latter to exceed or fall short of this quantum, it would perish’.
- ‘The Science of Logic’
‘Whatever is, has a measure’. The proposition of the Pythagoreans as Clark Butler points out. Quantum belongs to the nature of the something itself. It is inherent in Being — its being-within-self b. Accordingly, Being is not indifferent to its magnitude. If its magnitude is altered, the quality of the thing in question alters as well: Quantum, as measure, has ceased to be a limit which is not limit; it is now the determination of the thing, which is destroyed if it is increased or diminished beyond this quantum.
Immediate Measure
A measured thing is supposed to exhibit a degree of resilience. It remains what it is even though its quantum changes. Eventually there comes a dramatic moment when the measured thing becomes qualitatively different. The example of water has already been given. Water has a liquid quality over a range of temperatures. But if we lower the quantitative side of water’s Measure to below zero degrees centigrade, water undergoes a sudden cataclysmic change. It turns into ice, which is qualitatively different from liquid water.
Mediated Immediate Measure
A measured thing is supposed to exhibit a degree of resilience. It remains what it is even though its quantum changes. Eventually there comes a dramatic moment when the measured thing becomes qualitatively different. The example of water has already been given. Water has a liquid quality over a range of temperatures. But if we lower the quantitative side of water’s Measure to below zero degrees centigrade, water undergoes a sudden cataclysmic change. It turns into ice, which is qualitatively different from liquid water.
Quantitative determinateness, then, has a double nature. It is that to which the quality is tied and also that which can be varied without affecting the quality.
‘Since in the existence of anything the quantitative determinateness is thus twofold, in the sense that quality is tied to it and yet the quantity can fluctuate without prejudice to quality — so the demise of anything that has a measure occurs through the alteration of its quantum. On the one hand, the demise appears unexpected, inasmuch as there can be alteration in the quantum without the measure and the quality being altered; but, on the other hand, it is made into something quite simple to grasp by means namely of the concept of gradualness. It is easy to turn to this category for visualizing or ‘explaining’ the disappearance of a quality or of a something, for it gives the impression that one can witness this disappearance as if before one’s eyes: since the quantum is posited as the external limit which is by nature alterable, the alteration (of quantum only) then follows by itself. But in fact nothing is thereby explained, for the alteration is at the same time essentially the transition of one quality into another, or the more abstract transition of one existence into a non-existence, and therein lies another determination than just gradualness, which is only a decrease or increase, and the one-sided holding fast to magnitude’.
- ‘The Science of Logic’
Immediate Measure brings forth both moments — the idea that quantitative change destroys quality and the idea that quality is indifference to quantitative change. The first point states that the destruction of anything which has a measure takes place through the alteration of its quantum. The second point states that not every quantitative change is a qualitative change. The idea of quantitative change resulting in qualitative change is captured by the common sense notion of gradualness. Suppose we lower the temperature of water with a view of destroying its quality as liquid (i.e., we make some ice cubes).
On the one hand this destruction appears as unexpected, in so far as the quantum can be changed without altering the measure and the quality of the thing; but on the other hand, it is made into something quite easy to understand through the idea of gradualness. The reason why such ready use is made of this category to render conceivable or to explain the disappearance of a quality or of something, is that it seems to make it possible almost to watch the disappearing with one’s eyes, because quantum is posited as the external limit which is by its nature alterable, and so alteration of (quantum only) requires no explanation. But in fact nothing is explained thereby; the alteration is essentially the transition of one quality into another, or the more abstract transition of an existence into a negation of the existence; this implies another determination than that of gradualness which is only a decrease or an increase and is a one-sided holding fast to quantity.
‘The ancients had already taken notice of this coincidence, that an alteration which appears to be only quantitative suddenly changes into a qualitative one, and they used popular examples to illustrate the inconsistencies that arise when such a coincidence is not understood. Two such examples go under the familiar names of ‘the bald’ and ‘the heap’. They are elenchi, that is, according to Aristotle’s explanation, two ways in which one is compelled to say the opposite of what one has previously asserted. The question was put: does the plucking of one hair from someone’s head or from a horse’s tail produce baldness, or does a heap cease to be a heap if one grain is removed? The expected answer can safely be conceded, for the removal amounts to a merely quantitative difference, and an insignificant one at that. And so one hair is removed, one grain, and this is repeated with only one hair and one grain being removed each time the answer is conceded. At last the qualitative alteration is revealed: the head or the tail is bald; the heap has vanished. In conceding the answer, it was not only the repetition that was each time forgotten, but also that the individually insignificant quantities (like the individually insignificant disbursements from a patrimony) add up, and the sum constitutes the qualitative whole, so that at the end this whole has vanished: the head is bald, the purse is empty’.
- ‘The Science of Logic’
In short, incremental change is simply easier to accept as a psychological matter, compared to radical qualitative change. Behind every incrementalist strategy, however, lies the radical program of obliterating what exists and installing something new. Hegel asks does the pulling out of a single hair from the head . . . produce baldness, or does a heap cease to be a heap if a grain is removed? An answer in the negative can be given without hesitation since such a removal constitutes only a quantitative difference, a difference moreover which is itself quite insignificant; thus a hair, a grain, is removed and this is repeated, only one of them being removed each time in accordance with the answer given. At last the qualitative change is revealed; the head is bald, the heap has disappeared. In giving the said answer, what was forgotten was not only the repetition, but the fact that the individually insignificant quantities (like the individually insignificant disbursements from a fortune) add up and the total constitutes the qualitative whole, so that finally this whole has vanished; the head is bald, the purse is empty.
[Note: The sorites paradox originated in an ancient puzzle that appears to be generated by vague terms, which is to say, terms with unclear blurred or fuzzy boundaries of application. Bald, heap, tall, old, and blue are prime examples of vague terms: no clear line divides people who are bald from people who are not, or blue objects from green hence not blue, or old people from middle-aged hence not old. Because the predicate heap has unclear boundaries, it seems that no single grain of wheat can make the difference between a number of grains that does, and a number that does not, make a heap. Therefore, since one grain of wheat does not make a heap, it follows that two grains do not; and if two do not, then three do not; and so on. This reasoning leads to the absurd conclusion that no number of grains of wheat make a heap.]
In the next chapter, Hegel suggests that the gradual, quantitative side of change is external to the thing, On the qualitative side the gradual, merely quantitative progress is absolutely interrupted; the new quality in its merely quantitative relationship is, relatively to the vanishing quality, an indifferent, indeterminate other, and the transition is therefore a leap. People fondly try to make an alteration comprehensible by means of the gradualness of the transition; but the truth is that gradualness is an alteration which is merely indifferent, the opposite of qualitative change.
‘Inasmuch as the advance from a quality proceeds in the steady continuity of quantity, the ratios approaching the one qualifying point are distinguished, quantitatively considered, by a more or less. In this respect, the alteration is a gradual one. But the gradualness concerns merely the externality of the alteration, not its qualitative moment; the preceding quantitative relation, though infinitely near to the succeeding one, is still another qualitative existence. From the qualitative side, therefore, the gradual, merely quantitative progression which has no limits in itself, is absolutely interrupted; and since in its merely quantitative connection the newly emerging quality is with respect to the vanishing one an indeterminate other, one which is indifferent to it, the transition is a leap; the two are posited as wholly external to each other. — It is a favorite practice to try to make an alteration conceptually comprehensible by the gradualness of the transition leading up to it; but gradualness is rather alteration precisely as merely indifferent, the opposite of a qualitative alteration. Rather, in gradualness the connecting link between two realities — be they states or self-subsistent things — is sublated, what is posited is that neither reality is the limit of the other, but that each is absolutely external to the other. Thus, the very point necessary for the conceptual comprehension of the alteration is missed, although little enough is required for that purpose’.
- ‘The Science of Logic’
Hegel goes on to complain that gradualism quantifies and therefore externalizes qualitative change, thereby robbing it of its immanence. Gradualness subjectifies what should be an objective process. For example, in an attempt to save the American legal system from the nihilism of Critical Legal Studies, Andrew Altman announces that we more or less live under a rule of law. David Gray Carlson, ‘Liberal Philosophy’s Troubled Relation to the Rule of Law’, 1993, (a particular pertinent issue when we see what is happening in America today) had occasion to suggest that the invocation more or less is designed to lend the American system some give, so that counter-examples of lawlessness cannot blow apart the argument. Common sense errs, then, when it thinks that removal of a single hair does not produce baldness. The mistake is assuming a quantity to be only an indifferent limit, that is to say of assuming that it is just a quantity in the specific sense of quantity.
‘The embarrassment, the contradiction, produced by the result, is not anything sophistic in the usual sense of the word, as if the contradiction were a pretense. The mistake is committed by the assumed interlocutor (that is, our ordinary consciousness), and that is of assuming a quantity to be only an indifferent limit, that is, of taking it in the narrowly defined sense of a quantity. But this assumption is confounded by the truth to which it is brought, namely that quantity is a moment of measure and is linked to quality; refuted is the one-sided stubborn adherence to the abstract determinateness of quantum. — Also those elenchi are, therefore, not anything frivolous or pedantic but basically correct: they attest to a mind which has an interest in the phenomena that come with thinking’.
- ‘The Science of Logic’
Quantitative change is thought to have no bite. What common sense misses is that quantity is a moment of measure and is connected with quality. When Quantum is taken as an indifferent limit of a thing, it leaves the thing open to unsuspected attack and destruction. Gradual quantitative change can lead to a catastrophic coupure. Accordingly, Hegel writes, it is the cunning of the Notion to seize on this aspect of a reality where its quality does not seem to come into play; and such is its cunning that the aggrandizement of a State or of a fortune, etc., which leads finally to disaster for the State or for the owner, even appears at first to be their good fortune.
‘Quantum, when it is taken as indifferent limit, is the side from which an existence is unsuspectedly attacked and laid low. It is the cunning of the concept that it would seize on an existence from this side where its quality does not seem to come into play — and it does it so well that the aggrandizement of a State or of a patrimony, etc., which will bring about the misfortune of the State or the owner, even appears at first to be their good fortune’.
- ‘The Science of Logic’
We can leave it to the cunning of the concept to sort it all out …
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‘Whatever is, has a measure’.
Solomon
Sweep, sweep the string, to soothe the royal fair,
And rouse each passion with th’alternate air.
Solomon & Israelites
Music, spread thy voice around,
Sweetly flow the lulling sound.
Solomon & Israelites
Now a diff’rent measure try,
Shake the dome, and pierce the sky.
Rouse us next to martial deeds;
Clanking arms, and neighing steeds,
Seem in fury to oppose —
Now the hard-fought battle glows.
Solomon
Then at once from rage remove;
Draw the tear from hopeless love;
Lengthen out the solemn air,
Full of death and wild despair.
Chorus of Israelites
Draw the tear from hopeless love,
Lengthen out the solemn air,
Full of death and wild despair.
Solomon
Next the tortur’d soul release,
And the mind restore to peace.
Solomon & Israelites
Thus rolling surges rise,
And plough the troubled main;
But soon the tempest dies,
And all is calm again.
Queen of Sheba
Thy harmony’s divine, great king,
All, all obey the artist’s string.
And now, illustrious prince, receive
Such tribute as my realm can give.
Here, purest gold, from earth’s dark entrails torn;
And gems resplendent, that outshine the morn;
There balsam breathes a grateful smell,
With thee the fragrant strangers wish to dwell.
Yet of ev’ry object I behold,
Amid the glare of gems and gold,
The temple most attracts my eye,
Where, with unwearied zeal, you serve the Lord on high.
‘Whatever is, has a measure’.
With the exception of the love and adoration I have for my muse to whom I dedicate this article. That is beyond all measure.
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Behold, thou art fair, my love; behold, thou art fair; thou hast doves’ eyes within thy locks: thy hair is as a flock of goats, that appear from mount Gilead.
Thy teeth are like a flock of sheep that are even shorn, which came up from the washing; whereof every one bear twins, and none is barren among them.
Thy lips are like a thread of scarlet, and thy speech is comely: thy temples are like a piece of a pomegranate within thy locks.
Thy neck is like the tower of David builded for an armoury, whereon there hang a thousand bucklers, all shields of mighty men.
Thy two breasts are like two young roes that are twins, which feed among the lilies.
Until the day break, and the shadows flee away, I will get me to the mountain of myrrh, and to the hill of frankincense.
Thou art all fair, my love; there is no spot in thee.
- ‘The Song of Solomon’
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Coming up Next:
Specifying Measure
To be continued ….
