On Hegel’s ‘Philosophy of Nature’ : A Free Reflex of Spirit — part seven.
‘A mighty matter I rehearse’
by Alfred Tennyson, 1st Baron Tennyson (1809–1892)
A mighty matter I rehearse,
A mighty matter undescried;
Come listen all who can.
I am the spirit of a man,
I weave the universe,
And indivisible divide,
Creating all I hear and see.
All souls are centers: I am one,
I am the earth, the stars, the sun,
I am the clouds, the sea.
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Georg Wilhelm Friedrich Hegel, (1770–1831). ‘The Philosophy of Nature’.
Continuing with ‘Mechanics’.
Space and Time,
In keeping with Hegel’s conception of Nature as the otherness (Andersseyn) of the Idea the ‘Philosophy of Nature’ begins as we saw with pure separateness, that is to say, with what is completely unstructured and contains no determinate difference.
‘The primary or immediate determination of nature is the abstract universality of its self-externality, its unmediated indifference, i.e. space. It is on account of its being self-externality, that space constitutes collaterality of a completely ideal nature; as this extrinsicality is still completely abstract, space is simply continuous, and is devoid of any determinate difference’.
‘To ask whether space by itself is real, or whether it is only a property of things, is to ask one of the most well-worn of all metaphysical questions. If one says that it is something inherently substantial, then it must resemble a box, which, even if there is nothing in it, is still something subsisting within itself Space is absolutely yielding and utterly devoid of opposition however; and if something is real, it is necessary that it should be incompatible with something else. One cannot point to a part of space which is space for itself, for space is always filled, and no part of it is separated from that which fills it. It is therefore a non-sensuous sensibility and a sensuous insensibility. The things of nature are in space, and as nature is subject to the condition of externality, space remains the foundation of nature. If one says, as Leibnitz did, that space is an order of things which does not concern the noumena, and which has its substrata in things, we assume that if one removes the things which fill space, the spatial relationships between them still persist independently. It may certainly be said that space is an order, for it is of course an external determination, but it is much more than a merely external determination, it is externality itself’.
- ‘The Philosophy of Nature’
Nevertheless something comes out of this separateness despite its lack of structural differentiation and the argument concerning this result proceeds as follows. Merely in virtue of it lacking all differences pure separateness is actually no separateness because things must be distinct if they are separate from one another, and in a dialectical sense the concept of pure separateness collapses into that of non-separateness, which is to say, the concept of a point, and both belong together and they exclude one another and This dialectically contradictory state of affairs therefore is in need of a new structure in which both separateness and punctuality are compatible, and this becomes possible in the form of a line. Considered lengthwise or longitudinally a line is extension characterized by separateness while considered crosswise or transversely on the other hand it is non-extension characterized by non-separateness in which case its transverse direction at the same time brings into play a new spatial dimension. Hegel’s procedure of conceptual development thus leads to an explanation of the three-dimensional character of intuitional space and his interpretation of space’s tri-dimensionality is somewhat unique in philosophy as even for Immanuel Kant, (1724–1804), spatial tri-dimensionality is not proved but is rather declared to be a fact of our a priori intuition of space.
The concept of pure separateness has hence been demonstrated to contain an internal dialectic the explication of which gives rise to new categorical structures which is to say, at this initial juncture, the concepts of point, line and further spatial determinations. Limit (Grenze) is in this way shown to be essential to spatial structures, a limit is that which separates parts of space albeit it belongs to none of them and therefore a limit is itself non-spatial inasmuch as it is, in a manner of speaking, thin as a point But if this is so, what exactly is it? As a limit, it is essentially a negating — the excluding or, respectively, the leaving of a part of space. In the concept of space, then, negation (in the sense of change) and hence the concept of time are always implied. For the non-spatial character of the limiting function rests on its point-related character: The negativity which relates itself to space as a point and is thus posited for itself is time.
‘The negativity which relates itself to space as point and develops its determinations within it as line and plane, is however also a being-for-self within the sphere of self-externality; it posits its determinations within space, but at the same time, in conformity with the sphere of self-externality, and is therefore apparently indifferent to the immobile collaterality of space. Thus posited for itself, this negativity is time’.
‘Addition. Space is the immediate determinate being of quantity, in which everything remains subsistent, and even limit has the form of a subsistence. This is its deficiency. Space is a contradiction, for the negation within it disintegrates into indifferent subsistence. As space is merely this inner negation of itself, its truth is the self-transcendence of its moments. It is precisely the existence of this perpetual self-transcendence which constitutes time. In time therefore the point has actuality. Through the generation of difference within it, space ceases to be mere indifference, and through all its changes, is no longer paralysed, but is for itself. This pure quantity, as: difference existing for itself, is that which is implicitly negative, i.e. time; it is the negation of the negation, or self-relating negation. Negation in space is negation relative to another; in space therefore the negative does not yet come into its own. In space the plane is certainly negation of the negation, but in its truth it is different from space. The truth of space is time, so that space becomes time; our transition to time is not subjective, space itself makes the transition. Space and time are generally taken to be poles apart: space is there, and then we also have time. Philosophy calls this ‘also’ in question’.
- ‘The Philosophy of Nature’
Contrary to spatial being, which as such just is what it is, time is the being which, in that it is, is not, and in that it is not, is.
‘Time, as the negative unity of self-externality, is also purely abstract and of an ideal nature. It is the being which, in that it is, is not, and in that it is not, is. It is intuited becoming; admittedly, its differences are therefore determined as being simply momentary; in that they immediately sublate themselves in their externality however, they are self-external’.
‘Remark: Time, like space, is a pure form of sensibility or intuition; it is the insensible factor in sensibility. Like space however, time does not involve the difference between objectivity and a distinct subjective consciousness. If these determinations were to be applied to space and time, the first would be abstract objectivity, and the second abstract subjectivity. Time is the same principle as the ego=ego of pure self-consciousness, but as time, this principle, or the simple Notion, is still completely external and abstract as mere intuited becoming; it is pure being-in-self, as a plain self-production. Time is as continuous as space is, for it is abstract negativity relating itself to itself, and in this abstraction there is as yet no difference of a real nature. It is said that everything arises and passes away in time, and that if one abstracts from everything, that is to say from the content of time and space, then empty time and empty space will be left, i.e. time and space are posited as abstractions of externality, and represented as if they were for themselves. But everything does not appear and pass in time; time itself is this becoming, arising, and passing away, it is the abstraction which has being, the Cronos which engenders all and destroys that to which it gives birth. That which is of a real nature is certainly distinguished from time, but is just as essentially identical with time. It is limited, and the other involved in this negation is outside it. Consequently, the determinateness is implicitly external to itself, and is therefore the contradiction of its being. Time itself consists of the abstraction and contradiction of this externality and of the restlessness of this contradiction. That which is finite is transitory and temporal because unlike the Notion, it is not in itself total negativity. It certainly contains negativity as its universal essence, but as it is not adequate to this essence and is one-sided, it relates itself to negativity as to its power. The Notion however, in its freely existing identity with itself, as ego=ego, is in and for itself absolute negativity and freedom, and is consequently, not only free from the power of time, but is neither within time, nor something temporal. It can be said on the contrary that it is the Notion which constitutes the power of time, for time is nothing but this negation as externality. Only that which is natural, in that it is finite, is subject to time; that which is true however, the Idea, spirit, is eternal. The Notion of eternity should not however be grasped negatively as the abstraction of time, and as if it existed outside time; nor should it be grasped in the sense of its coming after time, for by placing eternity in the future, one turns it into a moment of time’.
- ‘The Philosophy of Nature’
Hegel continues by determining time as intuited becoming. He does this because ‘becoming’ signifies the now occurring transition from a past to a future that is about to be realized. Hegel calls past, present and future the dimensions of time which, on account of their differing ontological modalities, are nowadays designated as the modes of time. The triadic overarching structure of time, however, can become tangible only by representing the modes of time in the form of simultaneous juxtaposition.
‘The present, future, and past, the dimensions of time, constitute the becoming of externality as such, and its dissolution into the differences of being as passing over into nothing, and of nothing as passing over into being. The immediate disappearance of these differences into individuality is the present as now, which, as it excludes individuality and is at the same time simply continuous in the other moments, is itself merely this disappearance of its being into nothing, and of nothing into its being’.
- ‘The Philosophy of Nature’
But this is to represent time in a spatial form since the past and the future of time, in so far as they have being in nature, is space.
‘The finite present is the now fixed as being, and as the concrete unity, distinguished from the negative, the abstract moments of the past and the future, it is therefore the affirmative factor; yet in itself this being is merely abstract, and disappears into nothing. Incidentally, these dimensions do not occur in nature, where time is now as separately subsistent differences, for they are only necessary in subjective representation, in memory, and in fear or hope. The past and the future of time are space in so far as they have being in nature, for space is negated time; just as sublated space is initially the point, which developed for itself is time. There is no science of time corresponding to geometry, the science of space. Temporal differences do not have this indifference of self-externality which constitutes the immediate determinability of space, and unlike this determinability, do not therefore give rise to figurations. Time first becomes capable of such figurations when the understanding paralyzes it and reduces its negativity to a unit. This dead unity, which is thought’s highest externality, gives rise to external combinations; these are the figures of arithmetic, which may be applied by the understanding to equality and inequality, identity and difference’.
— — — — -
‘If we refer back to the exposition of the Notion of duration, we see that this immediate unity of space and time is already the ground of their being. The negative of space is time, and the positive, or the being of the differences of time, is space. In this analysis however, they are posited as of unequal import, or their unity is merely presented as the movement of the transition from one into the other. Consequently the beginning, and the realization, the result, fall apart. The result is the precise expression of their ground and truth however. The durable element is the self-equality into which time has returned; this is space, the determinability of which is indifferent existence in general. Here the point is that which it is in its truth as a universal; it is in fact the whole of space, as a totality of all dimensions. This here is to the same extent time, and is now an immediately self-sublating present, or a now which has been. As it is the point of duration, the here is at the same time a now. This unity of here and now is place’.
- ‘The Philosophy of Nature’
A temporal structure is therefore one that is only spatially — that is, intuitively — representable. Moreover, only spatial representation allows for time to be ‘fixed’, which is a basic requirement of scientific method. Consider, for example, what occurs in the determination of time by means of a clock. Earlier temporal states have in a sense left their traces behind in space. It is only in this way that they can be confronted with the later temporal states by which they are determined as earlier . While Hegel does not develop this point in detail, it is by building on his analysis that time’s property of irreversibility becomes intelligible. Time must appear as anisotropic and unidirectional since what is later is ascertainable only by recourse to what is earlier. A new occurrence appears in view of an earlier one, and the progression of time is thereby univocally defined by additive augmentation. But a well-defined direction of temporal progression can only be drawn in a uni-dimensional manifold which is what likely provides the simplest argument for the one-dimensional character of time.
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Tangerine Dream, ‘Raum’:
Motion and matter. The spatialization of time has widely been regarded as a falsification of the concept of time. By Henri Bergson, (1859–1941) for instance, who distinguished between time as we actually experience it, lived time, which he called ‘real duration’ (durée réelle) — and the mechanistic time of science. This, he contended, is based upon a misperception, it consists of superimposing spatial concepts onto time, which then becomes a distorted version of the real thing, so time is perceived via a succession of separate, discrete, spatial constructs, just like seeing a film. We think we’re seeing a continuous flow of movement, but in reality what we’re seeing is a succession of fixed frames or stills and claim that one can measure real duration by counting separate spatial constructs is an illusion:
‘We give a mechanical explanation of a fact and then substitute the explanation for the fact itself’.
- ‘Time and Free Will: An Essay on the Immediate Data of Consciousness’
Opposing this view is the consideration that Hegel’s explication of spatial limit , and thus his explication of the negativity latently contained in space, makes evident the intrinsic connectedness of space and time.
‘Space is the immediate determinate being of quantity, in which everything remains subsistent, and even limit has the form of a subsistence. This is its deficiency. Space is a contradiction, for the negation within it disintegrates into indifferent subsistence. As space is merely this inner negation of itself, its truth is the self-transcendence of its moments. It is precisely the existence of this perpetual self-transcendence which constitutes time. In time therefore the point has actuality. Through the generation of difference within it, space ceases to be mere indifference, and through all its changes, is no longer paralysed, but is for itself. This pure quantity, as: difference existing for itself, is that which is implicitly negative, i.e. time; it is the negation of the negation, or self-relating negation. Negation in space is negation relative to another; in space therefore the negative does not yet come into its own. In space the plane is certainly negation of the negation, but in its truth it is different from space. The truth of space is time, so that space becomes time; our transition to time is not subjective, space itself makes the transition. Space and time are generally taken to be poles apart: space is there, and then we also have time. Philosophy calls this ‘also’ in question’.
- ‘The Philosophy of Nature’
The truth of both is thus a synthetic determination: spatial limit — or more accurately, the spatial point — is now also expressly determined as a temporal point. This sort of point, which intrinsically connects space and time, is what Hegel calls (in a linguistically unusual manner) place.
‘Space in itself is the contradiction of indifferent juxtaposition and of continuity devoid of difference; it is the pure negativity of itself, and the initial transition into time. Time is similar, for as its opposed moments, held together in unity, immediately sublate themselves, it constitutes an immediate collapse into undifferentiation, into the undifferentiated extrinsicality of space. Consequently, the negative determination here, which is the exclusive point, is no longer merely implicit in its conformity to the Notion, but is posited, and is in itself concrete on account of the total negativity of time. This concrete point is place.
- ‘The Philosophy of Nature’
Whoever schedules a meeting, for example, at a certain place must provide a temporal specification in addition to a spatial identification.
A place is a spatial now.
‘Initially, the place which is thus the posited identity of space and time is also the posited contradiction set up by the mutual exclusiveness of space and time. place is spatial and therefore indifferent singularity, and is this only as the spatial now, or time. As this place, it is therefore in a condition of immediate indifference to itself; it is external to itself, the negation of itself, and constitutes another place. This passing away and self-regeneration of space in time and time in space, in which time posits itself spatially as place, while this indifferent spatiality is likewise posited immediately in a temporal manner, constitutes motion. To an equal extent however, this becoming is itself the internal collapse of its contradiction, it is therefore the immediately identical and existent unity of place and motion, i.e. matter’.
- ‘The Philosophy of Nature’
As such, however, a place is also essentially determined by change on account of its intrinsic temporality. As one place in space and time, it continually becomes another place. In other words, place in Hegel’s sense is in principle motion. Since even a spatially fixed place changes temporally, it is fundamentally a movement — in this case, a motion with zero velocity. Now motion takes place not only in time but also in space. A place changes its spatial and temporal position while remaining a moving place. As such, it maintains itself in motion and thus has a sort of a substantial character. It is a something that moves — a something that Hegel identifies as matter. Hegel grants that this transition to the reality that appears as matter is incomprehensible for the understanding.
‘The transition from ideality to reality, from abstraction to concrete existence, in this case from space and time to the reality which makes its appearance as matter, is incom20 prehensible to the understanding, for which it therefore always remains as something externally presented. Space and time are usually imagined as being empty and indifferent to that which fills them, and yet as always to be regarded as full. They are thought to be empty until they have been filled with matter from without. On the one hand material things are therefore taken to be indifferent to space and time, and yet at the same time they are accepted as essentially spatial and temporal’.
‘It is said of matter that: (a) it is composite, which is a property it derives from its abstract extrinsicality, space. In so far as an abstraction is made of time and all form, matter is said to be eternal and immutable, which is in fact the immediate result of this; but matter in such a state is merely an untrue abstraction. (b) It is impenetrable and offers resistance, it can be felt, seen etc. These predicates merely indicate that matter has two determinations, according to which it exists partly for determinate perception, or more generally for another, and partly and equally, for itself. It has these two determinations as the identity of space and time, and of immediate extrinsicality and negativity, or as the being-for-self of singularity. The transition of ideality into reality also expresses itself in the familiar mechanical phenomenon of reality being replaceable by ideality and vice versa, and it is only the thoughtlessness of popular conception and of the understanding which prevents the identity of both from being recognized in this interchangeability. In the case of the lever for example, the mass may be replaced by the distance and vice versa, and a certain quantum of moments of an ideal nature produces the same effect as the corresponding moments of a real nature. Similarly, in the magnitude of motion, velocity, which is a quantitative relationship, simply between space and time, replaces mass; and conversely, the real nature of the same effect is obtained by augmenting the mass and correspondingly diminishing space and time. A tile does not strike a man dead by itself, it only has this effect by virtue of the velocity it has acquired, i.e. the man is struck dead by space and time. Here the understanding gets no further than the reflectional determination of force, which it regards as fundamental, and is not therefore tempted to look further into the relationship of its determinations. Even this thought implies vaguely that the effect of force is a sensuous event of a real nature however, that there is no difference between the content and expression of force, and that precisely this force has the real nature of its expression in the relationship between the ideal nature of the moments of space and time. This sort of notionless reflection also thinks of what it calls forces, as being implanted in matter, and therefore as originally external to it. The very identity of time and space which hovers vaguely before this reflectional determination of force, and which constitutes the true essence of matter, is consequently posited as something alien and contingent to it, and as brought into it from without’.
- ‘The Philosophy of Nature’
But this is only because the understanding regards matter as something ‘indifferent towards space and time’ (i.e. as something completely different from space and time) and at the same time regards material things as essentially spatial and temporal. This internally contradictory conception of matter has to be overcome. It has to be recognized that the logic of the concept of motion contains the determination of something moved. that is, the determination of something that in its motion preserves its identity as ‘a singularity that is for itself ’ and that therefore possesses substantial character.
According to Hegel, this something is matter. At this juncture, of course, it is matter without any properties apart from those required by its determination purely as mass. As Hegel puts this point where there is motion there is something that moves; and this durable something is matter. Just as there is no motion without matter, so there is no matter without motion.
A passage from Hegel’s Jena period puts the point similarly: ‘Just as there is no motion without matter, there is no matter without motion. Motion is process, the transition from space to time and the reverse; matter, however, is the relation of space and time as resting identity’. Friedrich Engels, (1820–1895), later adapted the relation in question to his view of materialism.
‘One place does not merely imply another, it sublates itself into becoming another; the difference is also a sublatedness however. Each place is for itself only this place, so that all places are the same, and place is the simply mediated here. Something occupies one place, and then changes its place, passing thereby into another place; but both before and after this, it does not leave, but occupies its place. Zeno enunciated this dialectic within place, when he demonstrated immobility by saying that to move was to change place, but that the arrow never leaves its place. This dialectic is precisely the infinite Notion, or the here, for time is posited as being implicit. There are three different places, the present, that which is to be occupied, and the vacated. The disappearance of the dimensions of time is paralysed, but at the same time there is only one place which is common to these places, and invariable throughout all change, and this is the duration which is in immediate accordance with its Notion, i.e. motion. This demonstration of motion is self-evident, for the intuition of it coincides with its Notion. Its essence is its being as the immediate unity of space and time; it is time realizing itself and subsisting in space, or space first truly differentiated through time. We know therefore that space and time belong to motion. Velocity, which is quantum of motion, is space in relationship to a specific time elapsed. Motion is also said to be a relation of space and time; it was necessary however to grasp the more exact definition of this relation. Space and time first attain actuality in motion. Just as time is the simply formal soul of nature, and according to Newton, space is the sensorium of God, so motion is the Notion of the true soul of the world. We habitually regard it as a predicate or state, but it is in fact the self, the subject as subject, and the persistence, even of disappearance. It is precisely because of its immediate necessity to dissolve itself that it appears as predicate. Rectilinear motion is not motion in and for itself, but motion subordinated to another term, of which, in that it has become a predicate, or sublated, it is a moment. The re-establishment of the duration of the point in opposition to its motion, is the re-establishment of the immobility of place. This re-established place is not immediate, but the return from alteration, and is the result and ground of motion. In that it is dimension, and so opposed to the other moments, it is the centre. This return as line is the circular line; it is the now, before, and after, joining itself with itself; it is the indifference of these dimensions, in which the before is just as much an after as the after is a before. This is the first necessary paralysis of these dimensions posited in space. Circular motion is the spatial or subsistent unity of the dimensions of time. The point tends towards a place which is its future, and vacates one which is the past; but that which it has behind it, is at the same time that at which it will arrive; and it has already been at the after towards which it tends. Its goal is the point which is its past. The truth of time is that its goal is the past and not the future. The motion which relates itself to the centre is itself the plane, that is to say the motion which, in that it forms a synthetic whole, itself contains its moments or its dissolution in the centre, as well as the radii of the circle, which relate it to the dissolution. This plane itself moves however, and so becomes its otherness, an entirety of space, i.e. the motion returns into itself, and the immobile centre becomes a universal point, in which the whole sinks into quiescence. It is in fact the essence of motion which has here sublated the now, the past, and the future, or the different dimensions which constitute its Notion. In the circle these dimensions are precisely one, and constitute the re-established Notion of duration, or of motion extinguishing itself within itself This is posited mass, durability, that which has condensed itself through itself, and displays motion as its possibility’.
‘We have now reached the following position: Where there is motion, there is something which moves, and this durable something is matter. Space and time are filled with matter. Space is not adequate to its Notion, and it is consequently the Notion of space itself which creates its existence in matter. People have often begun with matter, and then regarded space and time as its forms. This is a valid procedure in so far as matter is the reality of space and time, but for us space and time must come first because of their abstraction, and matter must then show itself to be their truth. Just as there is no motion without matter, so there is no matter without motion. Motion is the process; it is the passage of time into space, and of space into time. Matter on the contrary is the relation of time and space as a quiescent identity. Matter is the primary reality, existent being for-self; it is not merely abstract being, it is the positive subsistence of space as exclusive of other space. The point should also exclude other points, but it does not yet do so, for it is merely an abstract negation. Matter is exclusive relation to self, and consequently the first real limit in space. That which is said to fill time and space, which can be grasped and felt, which offers resistance, and which is for itself in its being-for-other, is simply reached in the general unity of time and space’.
- ‘The Philosophy of Nature’
And so, by enduring, that is, by preserving itself in its motion as something identical — matter is something that occupies one place, and then changes its place, passing thereby into another place, but both before and after this, it does not leave, but occupies, its place. Zeno, (c. 495 — c. 430 BC), expresses this dialectic by demonstrating immobility, by showing that to move would be to change place, but the arrow never leaves its place. As Aristotle, (384–322 BC), explains:
‘If everything when it occupies an equal space is at rest at that instant of time, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless at that instant of time and at the next instant of time but if both instants of time are taken as the same instant or continuous instant of time then it is in motion’.
- ‘Physics’
In the arrow paradox, Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that at any one (duration-less) instant of time, the arrow is neither moving to where it is, nor to where it is not. It cannot move to where it is not, because no time elapses for it to move there; it cannot move to where it is, because it is already there. In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible. Whereas the first two paradoxes divide space, this paradox starts by dividing time and not into segments, but into points.
Thus, what is moved so to speak defines its own place. This is a place that does not change for what is moved, which means that something moved is there at rest. The determination of rest, then, is always contained in the concept of motion. That, however, is precisely the core of Zeno’s paradox of the arrow, that is, the paradox according to which a flying arrow remains at rest. Motion is determined only in relation to something that, in its motion, rests. This means that motion is determined only in relation to a place that is likewise a material place, that is, a mass. Therefore if both of these instances of place are masses, then the relation of motion is symmetrical in the sense that each mass is at rest in relation to itself while it is moved in relation to the other. This is the principle of the relativity of motion, which can be abbreviated as follows: the motion of a mass is equivalent to a relative motion. As we will see later to the motion of light, an Einsteinian perspective is already in evidence with this principle.
Jean-Michel Jarre & Tangerine Dream , ‘Zero Gravity’:
Gravity. The concept of matter or mass has been determined first of all as singularity that is for itself. According to this concept, masses are basically many singular entities that in an ‘abstract’ sense are characterized by repulsion . Since all of them are in equal measure separate and isolated, however, they are all alike; and insofar as they are alike, they show themselves to be (in the same abstract sense) attraction.
‘Matter maintains itself against its self-identity and in a state of extrinsicality, through its moment of negativity, its abstract singularization, and it is this that constitutes the repulsion of matter. As these different singularities are one 5 and the same however, the negative unity of the juxtaposed being of this being-for-self is just as essential, and constitutes their attraction, or the continuity of matter. Matter is inseparable from both these moments, and constitutes their negative unity, i.e. singularity. This is however still distinct from the immediate extrinsicality of matter, and is therefore not yet posited as being a centre, a material singularity of an ideal nature, i.e. gravity’.
- ‘The Philosophy of Nature’
Repulsion and attraction are here not to be understood as natural forces, but rather as conceptual determinations of singularity.
In keeping with this understanding, Hegel seeks to establish argumentatively the construction of the concept of matter in terms of opposing forces of repulsion and attraction, which Kant undertook in ‘Metaphysical Foundations of Natural Science. Hegel’s decisive point in this regard is that singularization is the ground of both the difference and the sameness of singularities. These exist so to speak in the stress field of a contradiction that drives towards its sublation. At issue, fundamentally, is the concept of field that is indispensable for the modern understanding of nature.
In this context, Hegel discerns the origin of gravity as something that is, as it were, an ought, a yearning, the most unhappy striving to which matter is eternally damned; for its unity does not come into its own — it does not fulfill itself precisely because singularization (as repulsion) is just as much an essential moment of matter as attraction
‘Matter is spatial separation. By offering resistance it repels itself from itself, and so constitutes repulsion, through which it posits its reality and fills space. The singularities, which are repelled from another, all merely constitute a unit of many units; they are identical with each other. The unit only repels itself from itself, and it is this which constitutes the sublation of the separation of being-for-self, or attraction. Together, attraction and repulsion constitute gravity, which is the Notion of matter. Gravity is the predicate of matter, which constitutes the substance of this subject. Its unity is a mere should, a yearning; this is the most afflicted of efforts, and matter is damned to it eternally, for the unity does not fulfil itself, and is never reached. If matter reached what it aspires to in gravity, it would fuse together into a single point. It is because repulsion is as essential a moment as attraction, that unity is not attained here. This subdued, crepuscular unity does not become free; yet since matter has as its determination the positing of the many within a unit, it is not so thick as those would-be philosophers who separate the one from the many, and are therefore refuted by matter. Although the two unities of repulsion and attraction are the inseparable moments of gravity, they do not unite themselves in a single unity of an ideal nature. As we shall see later, this unity reaches the first being-for-self of its existence in light. Matter searches for a place outside the many, and since there is no difference between the factors which do this, there is no reason for regarding one as nearer than the other. They are at the same distance on the periphery, and the point sought is the centre; this extends to all dimensions, so that the next determination we reach is the sphere. Gravity is not the dead externality of matter, but a mode of its inwardness. At this juncture, this inwardness has no place here however, for matter, as the Notion of that which is Notionless, is still lacking in inwardness’.
‘The second sphere which we now have to consider is therefore finite mechanics, in which matter is not yet adequate to its Notion. This finitude of matter is the differentiated being of motion and of matter as such; matter is therefore ftnite in so far as the motion which is its life, is external to it. Either the body is at rest, or motion is imparted to it from without. This is the primary difference within matter as such, which is subsequently sublated through its nature, or gravity. Here therefore we have the three determinations of finite mechanics: firstly inert matter, secondly impact, and thirdly fall; this constitutes the transition to absolute mechanics, in which the existence of matter is also adequate to its Notion. Gravity does not occur within matter in a merely implicit manner, but in so far as the implicitness already makes its appearance; in that it does this it constitutes fall, which is therefore the first occurrence of gravity’.
- The Philosophy of Nature’
Repulsion is as essential as attraction since matter would fuse together in a single point if it reached what it aspires to in gravity. Such is Hegel’s visionary intuition of physical singularity. Hegel treats the property of gravity, which is constitutive for mass, in three steps that concern corporeal inertia, the impact of bodies, and falling motion.
The single body is indifferent towards motion. Motion is external to the body in the same way as its negation of motion, or rest — the body is in fact inert.
‘Initially, in its mere universality and immediacy, matter has only a quantitative difference, and is particularized into different quanta or masses, which in the superficial determination of a whole or unit, are bodies. The body is also immediately distinguished from its ideality; it is however within space and time that it is essentially spatial and temporal, and it appears as their content, indifferent to this form. Addition. Matter fills space merely because it is exclusive in its beingfor-self, and so posits a real limit in space. Space as such lacks this exclusiveness. The determination of plurality necessarily accompanies being-for-self, but is as yet completely indeterminate difference, and not yet a difference implicit within matter itself; matters are mutually exclusive’.
‘In accordance with the spatial determination in which time is sublated; the body is durable; in accordance with the temporal determination in which indifferent spatial subsistence is sublated, it is transitory; in general, it is a wholly contingent unit. It is indeed the unity which binds both moments in their opposition, i.e. motion; but in its indifferent opposition to space and time (prev. §), and so to the relation of space and time in motion (§ 261), the body has motion external to it in the same way as its negation of motion, or rest. It is in fact inert’.
- ‘The Philosophy of Nature’
Given its indifference to motion and rest, the single mass is something that in itself neither rests nor moves, but merely passes from one state to the other through external impulse, i.e., rest and motion are posited within it by means of another. A motion makes its appearance in the single, isolated mass — but not yet explicitly as the proper essence of the latter.
‘In this sphere the body is inadequate to its Notion or finite, because as matter it is only posited as the immediate abstract unity of time and space, and not as a single developed restless unity with motion immanent within it. Ordinary physical mechanics accepts the body in this determination, so that it is one of its axioms that a body can only be set in motion or come to rest through an external cause, motion or rest being merely a state of the body. Determinations such as this are vaguely envisaged as applying to selfless terrestrial bodies, as of course they do. This is merely finite corporeality in its immediacy and abstraction however. The body as body means this abstraction of body. The imperfection of this abstract existence is sublated in concretely existent bodies however, and the positing of this sublation begins already in the selfless body. Inertia, impact, pressure, draw, fall etc., the determinations of ordinary mechanics, belong to the sphere of finite corporeality and so to finite motion, and should not therefore be transferred to absolute mechanics, where it is rather in the freedom of their Notion that corporeality and motion have their existence’.
- ‘The Philosophy of Nature’
‘Fall is relatively free motion: free, in that it is posited through the Notion of the body and is the manifestation of the body’s own gravity; within the body it is therefore immanent. At the same time, it is however only the primary negation of externality, and is therefore conditioned. Separation from the connection with the centre is therefore still a contingent determination, posited externally’.
- ‘The Philosophy of Nature’
Hawklords, ‘Free Fall’:
According to Hegel, the indifference of inert matter is negated in impact . In the interaction of any two bodies that are party to impact, motion is one movement of both bodies though they also resist one another inasmuch as each of them is likewise presupposed as an immediate unity.
‘When movement which is external to an inert body and therefore finite, sets this body in motion and so relates it to another, the two form the momentary unit of a single body, for they are both masses, and only differ quantitatively. It is thus that both bodies are united by movement through the imparting of motion, but as each is to an equal extent presupposed as an immediate unit, they also resist one another. In the relationship between them, their being-f or-self, which is further particularized by the quantum of mass, constitutes their relative gravity. This is weight as the gravity of a quantitatively distinct mass; it is extensive as a number of weighted parts, and intensive as a specific pressure. As the real determinateness, together with velocity, or the ideal nature of the quantitative determinateness of motion, it constitutes a single determinability (quantitas motus), within which weight and velocity can reciprocally replace one another’.
- ‘The Philosophy of Nature’
This inertial effect occurring in the impact of bodies is what Hegel calls their relative gravity. The isolation of inert masses is in principle overcome in falling motion , that is, in bodies’ free striving towards one another. The movement of these bodies has thus become their ‘essential’ motion; it is no longer only the ‘accidental’ motion of impacted inertial masses.
‘This weight, concentrated as an intensive amount into one point within a body, is the body’s centre of gravity; in that it is weighted, the body has its centre where it posits it however, i.e. outside itself. Consequently, impact and resistance, as well as the motion posited through them, have a substantial foundation in a centre which, while lying outside each particular body, is common to them all. This explains why each contingent motion imposed on them from without, passes into rest in this centre. As the centre is outside matter, this rest is at the same time merely a tendency towards the centre, and as the result of the relationship of the particular bodies, and of this tendency towards the centre in the matter which is common to them, they exert pressure on 5 one another. In relationships where bodies are separated from their centre of gravity by relatively empty space, this tendency constitutes fall, i.e. essential motion, in which contingent motion conforms to the Notion and its existence, by passing over into rest’.
- ‘The Philosophy of Nature’
The essential gravity by which falling masses are inseparably combined is the striving by which bodies seek to posit and have their centre outside themselves. This is a figurative formulation for the idea that each mass tends of itself to move towards other masses that, taken together, virtually constitute a common centre. It is not the centre, but the tendency towards the centre, which is immanent in matter. Gravity is so to speak matter’s acknowledgment of the nullity of the self-externality of matter in its being-for-self, of its lack of independence, of its contraction. Such is matter’s tendency to sublate its externality. But as long as matter is taken as a singular body, this tendency is only an inner disposition. As such, it does not manifest itself in an external form. Matter is still indeterminate, undeveloped, occludent since its form itself is not yet material.
‘It is to be regarded as one of the many merits of Kant, that in his ‘Metaphysical foundations of Natural Science’, he made an attempt at a so-called construction of matter, and by establishing a notion of matter, revived the concept of a philosophy of nature. In so doing however, he postulated the reflective determinations of the forces of attraction and repulsion as being firmly opposed to and independent of one another, and although matter had to be derived from them, assumed it to be complete in itself, and therefore that that which is to be attracted and repelled is already fully constituted matter. I have dealt more fully with the fundamental flaw in this Kantian exposition in my ‘Science of Logic’. It should be noted moreover that weighted matter is the first totality and real nature in which attraction and repulsion can occur; it has the ideal nature of the moments of the Notion, of singularity or subjectivity. Consequendy they are not to be regarded as independent, or as self-contained forces. It is only as moments of the Notion that they result in matter, although matter is however the presupposition of their appearance’.
‘It is essential to distinguish gravity from mere attraction, which is simply the general sublation of juxtaposition, and yields nothing but continuity. Gravity on the other hand is the reduction of juxtaposed and yet continuous particularity into unity, into negative relation to self, singularity, a single subjectivity which is however still quite abstract. In the sphere of the primary immediacy of nature, the self-external being of continuity is still posited as subsistent however. Material introflection first occurs in physics, and although singularity is therefore certainly present here as a determination of the Idea, it is external to material being. Consequently the primary essence of matter is that it has weight. This is not an external property which may be separated from it. Gravity constitutes the substantiality of matter, which itself consists of a tendency towards a centre which falls outside it. It is however this externality of its centre which constitutes the other essential determination of matter. As it negates its juxtaposed and continuous subsistence, one can say that matter is attracted to the centre, but if the centre itself is thought of as material, the attraction is merely reciprocal, and is at the same time a being attracted, so that the centre is again different from them both. The centre should not be thought of as material however, for the precise nature of material being is that it posits its centre as external to itself. It is therefore not the centre, but the tendency towards the centre, which is immanent in matter. Gravity is so to speak the acknowledgement by matter of its lack of independence, its state of contradiction, of the nullity of the self-externality involved in its being-for-self. It can also be said that gravity is the being-in-self of matter in so far as it is not yet in its own self a centre or subjectivity, but is still indeterminate, undeveloped, occludent, and lacking as yet in material form. Where the centre lies is determined by means of the weighted matter of which it is the centre; in so far as it is mass, it is determined, and is therefore its tendency, which is consequently a determinate positing of the centre’.
- ‘The Philosophy of Nature’
It is only at the highest stage of mechanics that form becomes material. At this stage, which Hegel titles ‘Absolute Mechanics’, matter’s form becomes material in the totality of the solar system . Hegel characterizes the solar system as ‘absolute’, and consequently as un-conditioned (un-bedingt), because as a whole it appears as something self-contained.
‘Gravitation is the true and determinate Notion of material corporeality realized as the Idea. Universal corporeality divides itself essentially into particular bodies, and links itself together in the moment of individuality or subjectivity, as determinate being appearing in motion; this, in its immediacy, is thus a system of many bodies’.
‘In bodies in which the full freedom of the Notion of gravity is realized, the determinations of their distinctive nature are contained as the moments of their Notion. Thus, one of the moments is the universal centre of abstract relation to self. Opposed to this extreme is immediate singularity, which is self-external and centreless, and which also appears as an independent corporeality. The particular bodies are however those which simultaneously stand as much in the determination of self-externality, as they do in that of being-in-self; they are in themselves centres and find their essential unity through relating themselves to the universal centre’.
‘Gravity, which is the substance of matter, no longer has the self-externality of matter external to it when it is developed into totality of form. The form appears first in its differences in the ideal determinations of space, time, and motion, and in accordance with its being-for-self, as a determinate centre outside self-external matter. In developed totality however, this extrinsicality is posited as determined solely by the totality; this is the juxtaposition of matter, outside of which it has no existence. It is in this way that form is materialized. Looked at in the opposite way, matter has itself attained implicit determinateness of form in this negation of its self-externality in the totality, which was formerly merely the centre which it sought. Its abstract and subdued being-in-self, general weightedness, has been resolved into form; it is qualified matter, or physics’.
- ‘The Philosophy of Nature’
It requires no external impulse, but is rather supported and preserved by itself. In the solar system as a whole, then, the externality of matter is no longer external to itself. With this system of many bodies Hegel has in mind a system of masses that maintains itself through gravitation and that is completely determined internally by Kepler’s laws . According to Hegel, it is in this Keplerian system that everything implicitly contained in the concept of matter is explicitly developed: thus developed into the totality of form, the merely sought centre that is virtually posited by singular masses is now realized in the shape of the central body, namely, the sun.
‘We shall pursue the solar, planetary, lunar, and cometary spheres through all the subsequent stages of nature. The deepening of nature is merely the progressive transformation of these four. It is because planetary nature is the totality, the unity of opposites, while the other spheres, being its inorganic nature, merely exhibit its particular moments, that it is the most perfect to come under consideration here; and this is also true of it as a motion. It is for this reason that living being occurs only on the planets. Ancient peoples have glorified the sun and worshipped it; we do the same when we recognize the final supremacy of the abstract understanding, and so determine God for example, as the supreme essence’.
- ‘The Philosophy of Nature’
Hegel is fascinated by Kepler’s laws. They embody for him a discovery of immortal fame — of fame wrongly conferred upon Newton and his law of gravity. Hegel recognizes that the law of gravitation embodies the most comprehensive generalization the science of his day could make about simply material bodies. He also realizes however, that subordinate to it are several fields of specific enquiry in which the law itself is not fully apparent. This leads him to treat geometry, arithmetic, motion, matter, gravity, fall etc. as involving disciplines and studies less complex in subject matter and limited in scope than enquiry into the nature of universal gravitation itself. He takes the solar system to involve still more comprehensive generalizations (Kepler’s laws) on account of the particularity of its component bodies and the complexity of their motions.
‘It was not Newton but Kepler who first thought of the planets as standing in immanent relation to the sun, and it is therefore absurd to regard their being drawn as a new idea originating with Newton. What is more, ‘attraction’ is not the right word here, for it is the planets rather than the sun, which take initiative. Everything depends upon the proof that they move in an ellipse. This is the crux of Kepler’s law, but the proof of it was never attempted by Newton. Laplace (‘Exposition du 20 systeme du monde’, vol. II p. 12–13.) admits that, ‘Infinitesimal analysis, which on account of its generality embraces everything that may be deduced from a given law, makes it clear that not only the ellipse, but every conic section, may be described by means of the force which maintains the planets in their orbits’. It is in this essential fact that the complete inadequacy of the Newtonian proof becomes apparent. In the geometrical proof Newton employs the infinitely small; it is not a rigorous proof, and modern analysis has therefore abandoned it. Instead of proving the laws of Kepler, Newton did the opposite. An explanation of the matter was called for, and Newton was content with a bad one. The idea of the infinitely small stands out in this proof, which depends upon Newton’s having posited all triangles in the infinitely small as equal. The sine and the cosine are unequal however, and if one then says that they are equal when posited as infinitely small quanta, the proposition will certainly enable one to do anything. When it is dark, all cows are black. The quantum has to disappear, but if qualitative difference is also eliminated in the process, there is no end to what can be proved. It is upon such propositions that the Newtonian proof is based, and that is why it is such an utterly bad one. Analysis goes on to deduce the other two laws from the ellipse; it has found a non-Newtonian way of doing this, but it is precisely the first law, the foundation of the deduction, which remains unproved’.
- ‘The Philosophy of Nature’
According to Hegel, what ‘Kepler expressed in a simple and sublime manner in the form of laws of celestial motion is changed by Newton ‘into the reflectional form of the force of gravity. The concepts of independent forces such as those of centripetal and centrifugal force, etc., are likewise but empty reflectional determinations in the sense of being fictions of the understanding. Hegel has in mind here the ideal of a rational proof (Vernunftbeweis) of Kepler’s laws as the foundation of absolute mechanics. In his extensive considerations on this topic Hegel demonstrates his competency in contemporaneous physics (even if he does hold that the force effective in capillary action is a form of gravitation). His invective against Newton, though, shows him to be something of a errant figure as far as this aspect of his natural philosophy is concerned.
‘Universal gravitation must be recognized as a profound thought in its own right. It has already attracted attention and inspired confidence, particularly through the quantitative determination bound up within it, and its verification has been pursued from the experience of the solar system down to that of the phenomenon of the miniature capillary tube. When it is seized upon in this way in the sphere of reflection however, it has a merely general abstract significance, which in its more concrete form is merely gravity in the quantitative determination of fall, and it therefore lacks the significance of the Idea developed into its reality, which is given to it in this paragraph. Gravitation is the immediate contradiction of the law of inertia, and it is because of this that matter strives out of itself towards another’.
- ‘The Philosophy of Nature’
Transition to qualified matter. The determinateness of form of matter as such , and hence that of unqualified mass, is completed and finalized in the solar system. Matter has therefore been disclosed to form [zur Form entschlossen]. In other words, the concept of matter has been developed to the stage at which it is prepared to feature forms of matter that are of greater specificity. At issue, then, is qualified matter, and thus the thematic content of what Hegel calls physics.
With regard to the argumentative structure of Hegel’s natural philosophy, it is not readily apparent why the treatment of matter’s qualified determinations should occur at this point. It will therefore be helpful to have recourse to Hegel’s science of logic since this is what is supposed to furnish the structural basis of the ‘Philosophy of Nature’. The Logic of Being is the part of logical science to which Hegel’s ‘Mechanics’ corresponds; and the transition to ‘Physics’, which is here the point in question, corresponds to the transition in logic from the sphere of being to that of essence . The logical transition between these spheres is mediated by the category of ‘measure [Maß]’. For the sake of illustrative brevity, let us consider how this category relates to the phase change between water and steam. Regarding this physical phase, the quantitative increase in temperature makes evident intrinsic relations of measure by which continual change in quantity — as governed by these relations — is transformed into qualitative change in the sense that there is the emergence of new qualitative determinations.
Ice, water and steam figure here as forms of appearance of an underlying substrate (designated by the chemical formula H 2 O) that represents the essence of what appears. The relation of planets in the solar system is also defined by fixed relations of measure, which is what Hegel finds so highly fascinating in Kepler’s laws of planetary motion. It is in view of that relation that Hegel seeks to get closer to the essence of matter: that which the solar system is as a whole, matter should be in particular the complete form of the solar system is the concept of matter in general the determinations of form which constitute the solar system are the determinations of matter itself, and these determinations constitute the being of matter.
‘In this way we conclude the first part; mechanics now constitutes a distinct whole. When Descartes said, ‘Give me matter and motion and I will construct the world’, he took the standpoint of mechanics as his ftrst principle, and in these words he shows a greatness of spirit which we should not deny, despite the inadequacy of this standpoint. In motion, bodies are mere points, and gravity only determines the spatial relations between points. The unity of matter is simply the unity of place which matter seeks, it is not a single concrete unit. It is in the nature of this sphere that this externality of determinedness should constitute the peculiar determinateness of matter. Matter is weighted being-for-self seeking its being-in-self; in this infinity the point is merely a place, so that the being-for-self is not yet real. It is only in the whole solar system that the totality of being-for-self is posited, so that what the solar system is as a whole, matter should be in particular. The complete form of the solar system is the Notion of matter in general; its self-externality should now be present in each determinate existence of the completely developed Notion. Matter should find its unity by being for itself in the whole of its determinate being, which is the being for self of being-for-self. Put in another way, the self-motivation of the solar system is the sublation of the merely ideal nature of being-for-self, of mere spatiality of determination, of not-being-for-self. In the Notion, the negation of place does not merely give rise to its re-instatement; the negation of not-being-for-self is a negation of the negation, i.e. an affirmation, so that what comes forth is real being-for-self. This is the abstractly logical determination of the transition. It is precisely the total development of being-for-self which is real being-for-self; this might be expressed as the freeing of the form of matter. The determinations of form which constitute the solar system are the determinations of matter itself, and these determinations constitute the being of matter, so that determination and being are essentially identical. This is of the nature of quality, for if the determination is removed here, being also disappears. This is the transition from mechanics to physics’.
- ‘The Philosophy of Nature’
In a certain sense, this sounds quite modern since Niels Bohr’s, (1885–1962), pictorial model of the atom is also orientated towards that of the solar system. Hegel is so to speak intuitively correct even if the example of the solar system is misleading when taken literally. As we hold today, the intrinsic structure of measure of a material’s electronic configuration is indeed the actual basis for the emergence of qualitative determinations of matter. And matter is thereby no longer mere mass. It has become something that is determined in itself — something that determines by the immanent form’ which constitutes its inner essence and that enters into appearance as qualitatively determinate individuality.
‘Matter has individuality to the extent that it is determined within itself by having being-for-self developed within it. It is through this determination that matter breaks away from gravity and manifests itself as implicitly self-determining. This is its s immanent form, by which it determines spatiality in the face of a gravity which formerly received this determination as something opposed to matter, and as a centre to which matter merely aspired’.
- ‘The Philosophy of Nature’
The transition to the sphere of essence, as it is understood in the context of Hegel’s science of logic, is hereby completed. It is characteristic of this sphere that determinations are only relational, that is, are essentially referred to one another, as is the case with essence and appearance, identity and difference, content and form, etc.
‘Essence is the Concept as posited Concept. In Essence the determinations are only relational, not yet as reflected strictly within themselves; that is why the Concept is not yet for-itself. Essence-as Being that mediates itself with itself through its own negativity-is relation to itself only by being relation to another; but this other is immediately, not as what is but as something-posited and mediated.-Being has not vanished; but, in the first place, essence as simple relation to itself is being; while on the other hand, being, according to its one-sided determination of being something immediate, is degraded to something merely negative, to a shine [or semblance] . — — As a result, essence is being as shining within itself’.
- ‘The Encyclopaedia Logic’
Dedicated to my lovely One. Falling in love every day.
And in your eyes I see ribbons of color
I see us inside of each other
I feel my unconscious merge with yours
And I hear a voice say, “What’s his is hers”
I’m falling into you (Falling into you)
This dream could come true
And it feels so good (Falling into you)
Falling into you
I was afraid (I was afraid)
To let you in here
Now I have learned
Love can’t be made in fear
The walls begin to tumble down
And I can’t even see the ground
I’m falling into you (Falling into you)
This dream could come true
And it feels so good (Falling into you)
Falling into you
Falling like a leaf
Falling like a star
Finding a belief
Falling where you are
Catch me, don’t let me drop
Love me, don’t ever stop
So close your eyes
And let me kiss you
And while you sleep
I will miss you
Oh, I’m falling into you (Falling into you)
This dream could come true
And it feels so good (Falling into you)
Falling into you
Falling like a leaf
Falling like a star, oh-oh
Finding a belief
Falling where you are
Falling into you
Falling into you
Falling into you
Céline Dion, ‘Falling Into You’:
Coming up next:
Matter and thought.
To be continued…
