On Hegel’s ‘Science of Logic’ : A Realm of Shadows — part nineteen.
‘A dried up river is like the soul’
by Malcolm Lowry (1909–1957)
A dried up river is like the soul
Of a poet who can’t write, yet perceives
With imperfect clarity his theme and grieves
To parched death over the drought. But his goal
Once a wholesome sea of clearest crystal
Recedes, grows grey in Hartseye, like old love leaves,
Leaves the mind altogether. He conceives
Nothing to replace it: only at the pole
Of memory flickers some senseless compass
So the river, by her grey pitying trees
Is agony of stones, horrors which sank
But are now declared, bleached.For it is these,
These stones and nothingnesses wich possess
When river is a road and mind a blank.
Georg Wilhelm Friedrich Hegel’s ‘Science of Logic’. The Measureless.
There is one thing I should point out before continuing though. Vorstellung, representation, often translated as picture-thinking, in Hegel is a mode of knowing that renders the immaterial and the abstract as sensuous, material and concrete. Picture-thinking is the mode of knowing of both religion and global popular thinking, and is inferior to philosophical thinking which does away with representations (that’s the plan anyway). In picture-thinking reality becomes inverted through its sensuous, particular, imagining, like Mills and Boon romance novels not that I have read any though I have seen movies about doctors and nurses emphasize the sensual concrete and cancel the abstract. And yet these articles of mine are peppered with diagrams (I take my cue from an illustrated commentary on Hegel, though not Lloyd Spencer and Andrzej Krauze’s ‘Introducing Hegel: a Graphic Guide’, Hegel the comic book version!) to illustrate what is going on in a philosophical discourse that is conducted at a high level of abstraction. Not to mention the paintings I include because I think they touch upon whatever theme or themes at that moment I am engaging with. Hegel would not have approved. Which is worth bearing in mind. I hope if the diagrams are of no help in understanding what is going on they at least do not mislead.
And so, the Measureless. The Nodal Line is a sequence of Rules within which Quality is indifferent to quantitative change. Yet quantitative change is potentially lethal. Magnitude is Abstract Measureless that side of determinate being through which it can be caught up in a seemingly harmless entanglement which can destroy it.
‘The exclusive measure, even in its realized being-for-itself, remains affected by the moment of quantitative existence and is therefore susceptible to the movement up and down the quantum scale of varying ratios. Something, or a quality, based on such a ratio is driven beyond itself into the measureless, collapsing under the mere mutation of its magnitude. Magnitude is that constitutional aspect where an existence can be caught up in an apparently harmless entanglement and be destroyed by it’.
- ‘The Science of Logic’
Nne of this concerns the Substrate however and hence the Understanding proposes that travel up and down the Nodal Line is a Spurious or Bad Infinity d, e, f to which the Substrate is indifferent. Thus there is posited the alternation of specific existences with one another and of these equally with relations remaining merely quantitative -and so on ad infinitum. This Spurious Infinity cannot teach us what the substrate g is, the Substrate is therefore Measureless, and Quality is impelled beyond itself into the measureless and is destroyed by the mere alteration of its magnitude. This follows because if the temperature of water is lowered from 1° to -1° C the liquid quality is impelled beyond itself but this does not result in a new quality, solid ice, for that represents the Spurious Infinity of the Nodal Line but liquid quality is discontinuous with the solid quality. Both these qualities are, however, continuous with the Abstract Measureless Substrate so when the liquid quality erases itself its being is sent to the Substrate, not to the new, discontinuous solid quality. The Abstract Measureless therefore represents the Continuity between the Substrate and the Nodal Line. It is tthe quantum as such which lacks an inner significance and is only an indifferent determinateness which does not alter the measure.
Abstract Measureless
‘The abstract measureless is the quantum in general inasmuch as it lacks internal order and is only indifferent determinateness which does not alter measure. In the nodal lines of measures this determinateness is at the same time posited as specifying; the abstract measureless sublates itself into qualitative determinateness; the new measure-relation into which the original passes over is measureless with respect to the latter but, in it, it equally is a quality that exists for itself; what is thus posited is the alternation of specific existences with one another and equally of them with relations that still remain merely quantitative — an alternation ad infinitum. Therefore, present in this transition is both the negation of the specific relations and the negation of the quantitative progression; this is the infinite existing for itself. — In the sphere of existence, the qualitative infinite was the irruption of the infinite into the finite, the immediate transition and vanishing of the ‘this here’ into its ‘beyond there’. In contrast to it, the quantitative infinite is in its very determinateness the continuity of quantum, its continuing beyond itself. The qualitatively finite becomes infinite; the quantitatively finite is its beyond in it: it points beyond itself. But this infinite of the specification of measure posits both the qualitative and the quantitative as each sublating itself into the other, and it thereby posits their first immediate unity, which is measure in general, as returned into itself and consequently as itself posited. The transition of the qualitative, of one specific concrete existence into another, is such that what happens is only an alteration of magnitude determinateness; the alteration of the qualitative as such into the qualitative is thus posited as an external and indifferent alteration, as a coming together with itself; the quantitative, for its part, sublates itself by suddenly turning into the qualitative, that is, a being which is determined in-and-for-itself. This unity which thus continues in itself in its alternating measures is the self-subsistent matter that truly persists, the fact’.
- ‘The Science of Logic’
Quality of the Abstract Measureless
By this Hegel means that the Abstract Measureless Substrate cannot determine its own state on the Nodal Line and an external measurer is in charge of Quantum and for this reason the Abstract Measureless is itself a Quantum — open to Quality of the Abstract outside determination and lacking inner Measureless significance. It depends on the measurer for its appearance in the Nodal Line of Measures.
The Measureless is quantitative. Michael Baur takes the Measureless as an illusion. ‘But any Measurelessness merely provides the grounds for the generation of a new set of Measure-relations. This new set persists until its Quantities once again change beyond a certain point to produce yet another apparent Measurelessness. This process repeats itself indefinitely, and so Measure, too, has developed a bad infinite oscillation, only this time between Measure and the Measureless’, he explains. And yet this supposes that the Measureless is just another Measure in disguise but the Measureless describes the essence of Substrate that which underlies the Nodal Line and in accordance with this the Measureless is a beyond and the modulation in question is between syllogistic extremes which each deny the influence of quantitative change. It is this negation which places the Infinite for Itself beyond the realm of Measure proper.
Yet dialectical Reason counters the Abstract Measureless is equally a quality on its own account and ts quality is that it has no quality, if quality is what changes via quantitative pressure. Hegel gives this new step no name other than the qualitative aspect of the Abstract Measureless. ‘Hegel is hard put to find names for his categories which will distinguish them satisfactorily’, contends Errol Eustace Harris, (1908–2009).
Once again Quality appears on the rightward side of the diagram (see my comment on picture thinking above) which is the side of nothingness. In this alternation, a proclaims itself not qualitative and it sees the Substrate as immune from quantitative pressure while c proclaims itself not quantitative and both of them export what they are not to b. Speculative Reason agrees that b is neither quality nor quantity and this concrete version of the Measureless is beyond Quality and Quantity. The name Hegel gives to this speculative step is the Infinite For Itself.
Infinite For Itself
John Burbidge the past president of the Hegel Society of America gives a somewhat different account whereby he views the Nodal Line as giving rise to absolutely discontinuous qualities, conceived as distinct neutral compounds. But this omits the whole notion of Substrate which is the very point of the Nodal Line. Burbidge explains: ‘Since there is no qualitative boundary the two [neutral compounds] share — at least to the extent that thought can anticipate it — they are simply external to each other. So we are far removed from even a minimal account that would enable us to understand the relation. From this perspective no explanation is possible. We cannot conceive what is involved; it is immeasurable’. Hence for Burbidge what is immeasurable is qualitative change. ‘The transformation of one quality into another is defined as immeasurable’. But this misses the point that there is nothing inconceivable about the Measureless as it represents the substantial Substrate which is immune from qualitative change through quantitative manipulation and it does not represent a property of qualitative transformations.
Hegel compares this new Infinite to earlier versions. Most primitive was the Qualitative (Spurious) Infinite. This was the eruption of the infinite in the finite as an immediate transition and vanishing of the latter in its beyond. What the Spurious Infinite lacked was continuity. In Spurious Infinity and Its Other the Spurious Infinite went out of existence and became Another Finite. The True Infinite, in infinite For itself contrast, stayed what it was and became something different.
Quantitative Infinity was more advanced, it had continuity, it expelled itself from itself, as did the Spurious Infinite but as a True Infinite the Quantitative Infinite also remained what it was. The Quantitative Infinite was already in its own self its beyond and points beyond itself. A True Infinite is both inside and outside of itself. The Infinite For Itself, in contrast, posits both the qualitative and quantitative as sublating themselves in each other. In short, the Infinite For Itself represents Measure returned to itself, and, in this reflection-into-self, the Infinite For Itself shows itself to be outside the scope of the realm of Being.
The Infinite For Itself is beyond the concept of qualitative change. So long as Measure is open to quantitative change, it is slave to something external — not yet free. Yet in the Abstract Measureless, externality sublated itself, converting itself into that which is determined in and for itself. Here we have for the first time the concept of in and for self, the very essence of Essence. Being-in-itself is mere implicitness. Its task is to become for itself. Being-for-self expelled its content and became Quantity. Quantity had to recapture its Quality in order to subsist. But openness to qualitative change still portended an inability to subsist. ‘The precise nature of ‘measure’ is shown to be that of superseded externality which constitutes totality in that it reinstates the sublated being-for-self. Measure has still to be regarded as an externality, a more or less, the determination of the concrete truth of finite being’, explains Cinzia Ferrini.
Only when Quality and Quantity are both sublated can a thing subsist and the state that is beyond quantitative and qualitative transition is being-in-and-for-self. This unity which thus continues itself into itself in its alternating measures is the truly persisting self-subsistent material substance or thing.
‘What we have here is (a) one and the same substantial matter which is posited as the perennial substrate of its differentiations. This detaching of being from its determinateness already begins in quantum in general; something is great indifferently as against the determinateness it has. In measure, the persisting matter is itself already in itself the unity of the qualitative and the quantitative — the two moments into which the general sphere of being is distinguished, each as the beyond of the other; in this way the perennial substrate begins to possess in it the determination of an existent infinity. (b) This self-sameness of the substrate is posited in that the qualitative independent measures into which the determining unit is dispersed consist of only quantitative differences, so that the substrate persists while being internally distinguished. © In the infinite progression of the nodal series there is posited the continuation of the qualitative into the quantitative advance as into an indifferent alteration, but equally too, there is posited the negation of the qualitative contained in the progression and consequently, at the same time, of the merely quantitative externality. The quantitative pointing beyond itself to an other which is itself quantitative perishes with the emergence of a measure-relation, of a quality, and the qualitative transition is sublated in the very fact that the new quality is itself only a quantitative relation. This reciprocal transition into the other of the qualitative and the quantitative moments occurs on the basis of their unity, and the meaning of this process is only the existence which is the demonstration or the positing that such a substrate does underlie the process and is the unity of its moments.
[Note: This is a reminder, at the end of the dialectic of being, that the task we have been performing all along, and are still engaged in at the moment, is to bring stability to the fluidity of becoming. We first did this with the category of existence or the being this or that (Dasein). That first determination has now developed into an objective structure with an internal distinction between a permanent substrate and all the other determinations introduced so far under the rubrics of quality and quantity. This distinction will next develop into the distinction between Essence and Being].
‘In the series of independent measure-relations the one-sided members of the series are immediate qualitative somethings (specific gravities or chemical materials, bases or alkalis, acids, for instance), and their neutralizations (by which we must understand here also the combinations of materials of different specific gravities) are in turn self-subsistent and themselves exclusive measure-relations, mutually indifferent totalities existing for themselves. Such relations are now determined only as nodes of one and the same substrate. The measures and the self-subsistent forms posited with them are consequently demoted to states. Alteration is only the mutation of a state, and that which passes over is posited as remaining the same in the mutation’.
- ‘The Science of Logic’
An important consideration must not be overlooked is that Quality and Quantity have a beyond in a Measureless Infinite For Itself, but the Infinite For Itself has no beyond. It is a totality that ‘has an identity that is more than then the sum of its parts’, explains Robert M. Wallace. A non-reflexive relation adheres between Measure and the Infinite For Itself and Measure has its beyond in the Infinite For Itself, but the latter has no beyond. It runs like this When Determinate Being was negated, negation was Limitation to determinate Being but Negation was not ultimately Limitation to Determinate Being on the contrary Negation was immanent within Determinate Being. At first, Negation the product of dialectical Reason was reified and opposed abstractly to determinate Being and Negation was a Determinate Being and accordingly had Limitation but now the true nature of Negation has been revealed. It is Determinate Being’s interior material so the Infinite For Itself is no determinate Being limited by Measure but on the contrary it is unlimited, Infinite and for-itself, and Measure has a beyond but the Infinite For Itself does not.
Hegel concludes with three propositions about the Infinite For Itself. The first is qualitative, the second quantitative, the third the beyond of these concepts. There is now posited a perennial substrate underlying all quantitative and qualitative change and this is a severance of being from its determinateness. The Measures which manifest the Substrate are qualitative self-subsistent measures separate and apart from the Substrate, nonetheless the difference between Substrate and Measure is quantitative and the Substrate is continuous with them, if qualitative change is merely quantitative that is to say it has no teeth then quality itself is negated and since quantity requires quality, quantity goes also .
The Substrate negates both its qualitative and its quantitative moments and there is now a distinction between Measure and the Substrate that underwrites it and the meaning of the infinite progress up and down the Nodal Line is only to show or to posit the determinate being of the Substrate, consequently, the measures and the self-subsistent things posited with them are reduced to states. The alteration is only change of a state, and the subject of the transition is posited as remaining the same in the process.
Hegel now recommends we review the story so far.
‘In reviewing the progressive determination which measure has gone through, the moments of the progression can be summed up as follows. Measure is at first itself the immediate unity of quality and quantity in the form of a common quantum which is, however, specific. As a determinateness of quantity which does not refer to an other but refers to itself, measure is thus essentially a ratio. Consequently, it also holds its moments as sublated and unseparated in itself; as is always the case in a concept, the difference in the ratio is such that each of its moments is itself the unity of the qualitative and the quantitative moment. The difference is thus real, and it yields a multitude of measure-relations which, as formal totalities, are each self-subsistent in themselves. The series which form the two sides of these ratios are for each single member the same constant ordering by which the member, as belonging to the one side, relates itself to the whole series standing opposite it. This ordering, although a mere order, a still wholly external unity, demonstrates itself to be, as the immanently specifying unity of a measure which has a determinate being-for-itself, distinguished from its specifications; but this specifying principle is not yet the free concept, which alone gives its differences an immanent determination; the principle is at first, rather, only a substrate, a matter, for whose differences, in order that they be totalities, that is, that they should have in themselves the nature of their stable, self-equal substrate, there is only available the external quantitative determination which shows itself at the same time to be a qualitative differentiation. In this self-unity of the substrate the determination of measure is a sublated determination, its quality an external state determined by quantum. — This course is equally the progressive determination of measure and its demotion to a moment’.
- ‘The Science of Logic’
To summarize the progress to begin with in chapter seven ‘Specific Quantity’ the extremes were not self-sufficient Measures, only the middle term was, and in ‘Ratio of Measures’ the extremes became Measures in themselves. In ‘Elective Affinity’ Measure was revealed to be a series of Measures and the metonymic thing shows itself to be an immanent specifying unity of a self-subsistent measure distinguished from its specifications yet it is still in thrall to externality it is not yet the free Notion which alone gives its differences an immanent determination, it is as yet only a substrate, a material, and for its differentiation into totalities, that is into difference embodying the nature of the unchanged substrate, it is dependent solely on the external, quantitative determination which shows itself at the same time as a difference of quality and what the Measureless must now do is escape this dependence on externality altogether.
Coming up next:
The Becoming of Essence.
The ‘Science of Logic’ divides into three parts, the logic of Being, the logic of Essence, and the logic of the Concept. Before delving into Essence I will do for the second time something I do not normally do and direct you to someone giving an excellent scholarly exposition on Hegel, here he is talking about Hegelian Essence, and I do so knowing full well they make my own poor efforts seem like, well, poor efforts. But at least I offer a condensed version, without dumbing down, hopefully, anyway you will have noticed my expositions have large chunks in which I let the man speak for himself directly, through quoted passages. I wouldn’t want to be charged with robbing Hegelian philosophy of its Spirit, as introductory books on the master philosopher tend to do. As introductory books on any great philosopher tend to do in fact.
My poor efforts are not nearly so poor as they would be without my muse, however, to whom I dedicate this slight article. I am keeping it brief for now and in the next article as I prepare for my excursion into the realm of dark shadows that is Essence somewhat like Gandalf (though I am wiser than he because I cannot abide Hobbits) preparing to ender Mordor.
For you my silver lining :
I don’t want to wait anymore I’m tired of looking for answers
Take me some place where there’s music and there’s laughter
I don’t know if I’m scared of dying but I’m scared of living too fast, too slow
Regret, remorse, hold on, oh no I’ve got to go
There’s no starting over, no new beginnings, time races on
And you’ve just gotta keep on keeping on
Gotta keep on going, looking straight out on the road
Can’t worry ‘bout what’s behind you or what’s coming for you further up the road
I try not to hold on to what is gone, I try to do right what is wrong
I try to keep on keeping on
Yeah I just keep on keeping on
I hear a voice calling
Calling out for me
These shackles I’ve made in an attempt to be free
Be it for reason, be it for love
I won’t take the easy road …
To be continued …
