On Hegel’s ‘Philosophy of Nature’ : A Free Reflex of Spirit — part sixteen.

David Proud

35 min readJun 21, 2023

‘Free fall’

by Johann Baptist Mayrhofer (1787–1836)

Which way, O Helios? To sink my fire

Under the waves for coolness I desire,

Sure at the core I thus renew my might

To fuel earth again with warmth and light.

I never take, my skill is but to give;

And yet though wholly spendthrift while I live,

I store up splendor to release when going,

Flaunt it just as night brings my undoing.

The stars unseen, the moon a watery gray,

While on the track I make my violent way;

Not till on those far hills I lay my crown

Do they gain strength, find fire that is their own.

‘Freiwilliges Versinken’

Wohin, o Helios? in Fluthen

Will ich den Flammenleib versenken,

Gewiß im Innern, neue Gluthen

Der Erde nach Bedarf zu schenken.

Ich nehme nichts, gewohnt zu geben;

Und wie verschwenderisch mein Leben,

Umhüllt mein Scheiden goldne Pracht,

Ich scheide herrlich, naht die Nacht.

Wie bleich der Mond, wie matt die Sterne!

So lang ich kräftig mich bewege,

Erst wenn ich ab die Krone lege,

Wird ihnen Muth und Glanz in ihrer Ferne.

Georg Wilhelm Friedrich Hegel, (1770–1831). ‘Philosophy of Nature’.

In case you have lost track of where I am up to I am still in the ‘Mechanics’ section, the first part of the three part ‘Philosophy of Nature’. My sixty part series on the three part ‘Science of Logic’ consisted on twenty articles for each of the three parts and so I am doing the same thing with the three parts of the ‘Philosophy of Nature’.

Finite mechanics: Inertia.

‘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 being-for-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’

In the ‘Science of Logic’ and the ‘Philosophy of Nature’ Hegel is very critical of the concept of inertia as expressed in Isaac Newton’s, (1642–1726/27), first law of motion. An object not moving remains still. And one that is moving continues to move at an unchanging speed, so long as no outside force influences it. Objects in space continue to move because nothing exists in space to stop them. So what is the problem? Hegel is very critical of Newton in the ‘Philosophy of Nature’ and in particular he criticizes the law of inertia for being an empty abstraction.

‘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. (…dies Aufheben beginnt schon am selbstlosen Körper gesetzt zu sein). 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’.

Is not the concept of inertia critical in the decentring of the physical world view that took place from Nicolaus Copernicus, (1473–1543), to Johannes Kepler, (1571–1630), Galileo di Vincenzo Bonaiuti de’ Galilei, (1564–1642), and through to Albert Einstein, (1879–1955). in fact Hegel went further than Newton such a process of decentring and in order for a deeper understanding of his philosophy of nature one must take note of it in relation to his systematic project, as opposed to discerning putative connections between Hegel and Einsteinian relativity as has been done by Henry Paolucci and Edward C. Halper.

Galileo was the first to discover the so-called law of inertia by considering a body falling down an inclined plane and then ascending a second plane with the velocity so acquired, he observed that the nearer the second plane approaches the horizontal the less will be the retardation of the body and that if it is horizontal the body would continue to move indefinitely with a constant velocity if air resistance and friction could be removed. This law resurfaces in Newton’s ‘Mathematical Principles’: ‘The vis insita, or innate force of matter, is a power of resisting, by which every body, as much as in it lies, continues in its present state, whether it be of rest, or of moving uniformly forwards in a right line’. Ernst Mach, (1838–1916), in ‘The Science of Mechanics’, points out that it was Galileo’s successors who developed a theory of inertia out of his description of this situation and that Newton’s third definition (if an object A exerts a force on object B, then object B must exert a force of equal magnitude and opposite direction back on object A) is made superfluous by his subsequent definitions of force, inertia being included and given in the fact that forces are accelerative. Hegel avoids this fault in the traditional treatment of inertia by taking it to involve a body’s having motion external to it so he would therefore have denied that a body’s moving uniformly forwards in a right line is an example of inertia and he may have been influenced by Immanuel Kant, (1724–1804), and Leonhard Euler’s, (1707–1783), questioning of the concept.

Kant’s Second Law of Mechanics states that every change in matter has an external cause, though at once following on from this statement a claim is parenthetically made that is a version of the law of inertia much nearer to Newton’s: ‘every body persists in its state of rest or motion, in the same direction, and with the same speed, if it is not compelled by an external cause to leave this state’. In virtue of the fact that Kant’s Second Law of Mechanics is not identical to Newton’s law of inertia an argument is needed to demonstrate that and by means of what additional assumptions the former entails the latter. The proof of the main principle depends upon his Second Analogy of Experience whereby all changes occur in accordance with the law of cause and effect and hence entails that every change in matter has a cause in addition to the further assumption that matter has no internal grounds of determinations such as thinking and desiring but rather only external relations in space, and in his remark to this proposition which clarifies this law of inertia Kant explains that inertia is to be contrasted with life or the ability of a substance to determine itself to act from an internal principle hence a body’s inertia ‘does not mean a positive striving to conserve its state’ , but rather what it does not do, its lifelessness.

And furthermore Kant contends that the very possibility of natural science proper depends upon the law of inertia in virtue of the fact that rejection of it would be hylozoism, ‘the death of all natural philosophy’. (Hylozoism, the doctrine that all matter has life). Kant explicitly objects that ‘the terminology of inertial force (vis inertiae) must be entirely banished from natural science, not only because it carries with it a contradiction in terms, nor even because the law of inertia (lifelessness) might thereby be easily confused with the law of reaction in every communicated motion, but primarily because the mistaken idea of those who are not properly acquainted with the mechanical laws is thereby maintained and even strengthened’, and he continues by pointing out that if inertia were to entail an active force of resistance then it would be possible that when one moving body hits another the moving body has to apply part of its motion solely to overcome the inertia of the one at rest and might not have any motion left over so to speak to set the body at rest into motion which is contrary to experience.

Kant’s Third Law of Mechanics asserts the equality of action and reaction in the communication of motion and Kant formulates a version of the Third Analogy of Experience according to which all external action in the world is interaction and suggests that the main point at issue in mechanics is establishing that mutual action is necessarily reaction, and his argument for this law is based upon the following line of reasoning:

1. If all changes of matter are changes of motion

2. If all changes of motion are reciprocal and equal since one body cannot move closer to/farther away from another body without the second body moving closer to/farther away from the first body and by exactly the same amount)

3. If every change of matter has an external cause a proposition that was established as the Second Law of Mechanics

4. Then the cause of the change of motion of the one body entails an equal and opposite cause of a change of motion of the other body or, in brief, action must be equal to reaction.

Kant then proceeds to demonstrate how his position differs from that of others. Newton ‘by no means dared to prove this law a priori, and therefore appealed rather to experience’ and similarly Kepler likewise derived it from experience though he went further conceiving of it in terms of a special force of inertia. Certain unnamed transfusionists, we suppose John Locke, (1632–1704), and perhaps René Descartes, (1596–1650), or Jacques Rohault, (1618–1672), are referred to, endeavoured to deny the law altogether by suggesting that motion could merely be transferred from one body to another in the communication of motion, a view Kant rejects on the grounds that explaining the communication of motion in terms of the transfer of motion is no explanation at all and in addition amounts to admitting that accidents (properties) could be literally transferred from one substance (self-standing entity) to another.

Kepler understood inertia as resistance to motion and this is very much how one still tends to think of it today, for imagine a large ship with a broken rudder that is moving towards a drowning witch with the objective of saving her and is moving towards spew infestations in the waters. This is not Kepler’s example, though his mother was accused of being a witch (but what about the swimming test of less enlightened times whereby accused witches were dragged to the nearest body of water stripped to their undergarments bound and then tossed in to to see if they would sink or float? Since witches were said to have spurned the sacrament of baptism it was believed that the water would reject their body and prevent them from submerging and so an innocent person would sink like a stone whereas a witch would simply bob on the surface. The ‘drowning’ witch wouldn’t need saving then would she? Or perhaps she was pretending). Suppose a small tow-boat endeavours to push it back or to the side it will achieve very little and so it appears as though the ship contains a force or impetus which makes it keep moving despite a force being applied to it in a different direction.

=====

There’s a ship arriving too late

To save a drowning witch

She was swimmin’ along

Tryna keep a date

With a merchant marine who told her he was really rich

But it doesn’t matter no more

She’s on the ocean floor

And the water’s all green down there

And it’s not very clean down there

And water snakes and rusty wrecks

Is all that she can see

As the light goes dim

And she’s tryin’ to swim

Will she make it?

Boy, we sure hope so

Not even a witch oughta be caught

On the bottom of America’s spew-infested waterways

Hey, hey

She could get radiation all over her

She could mutate insanely

That’s right

She could mutate insanely

She could grow up to be 15 feet tall and scary looking

And it would be really ugly

Did you know that cars could crash all over the place?

As a result of people with Hawaiian shirts on

Looking up to see her face

Sardines in her eyebrows

Lobsters up and down her forehead

All of them horribly large from radiation

And smelling very bad

And dangerous

Maybe a submarine could save her

And take her home to the Navy

For some kind of ritual

Sacrifice ….

Frank Vincent Zappa, (1940–1993), ‘Drowning Witch’:

But in fact this is a mistaken view of inertia for inertia is not a force, the ship just is moving and it does not resist change at all and the applied force has exactly the effect which it should have according to its magnitude relative to the mass of the ship, and so the notion that it resists change rests purely in our judgement relative to our desire that the ship should avoid the spew infestations, and yet if inertia is neither a force nor a property of an object, that it resists change, the question arises as to what it is. In classical physics the principle of inertia does not denote any quantifiable law it is merely supposed to effect a shift in our perspective of what motion is, and the common sense way to think about motion is that things are naturally at rest and a force needs to be applied to them to make them move and this led Aristotle, (384–322 BC), to suppose that things have a natural place to which they tend in the absence of forces moving them away from it and that rest at their natural place is the default state of all objects.

Kepler was the first to propose the term inertia in relation to the movement of heavenly bodies and yet he still took it to be the case that the natural state of these bodies was rest and that they resisted being put into motion while the significance of the Galilean/Newtonian concept of inertia is that it totally inverts such a common sense view, something that science has a habit of doing, for according to Newton motion is not secondary to rest, rather rest is a special case of motion, rest is a constant motion with a velocity of 0. The Galilean/Newtonian concept of inertia takes the Copernican decentring of the universe one step further in that motion is no longer relative to a natural state of rest or a natural place, the earth and the sun are just inert objects moving like all others and all motion is relative not to some absolute centre but to an inertial frame, a system of coordinates that might itself be moving. The notion of an inertial frame can be more clearly understood if we consider that for Newton an inertial frame is a physical coordinate system within which the law of inertia holds, which is to say within which an object at rest remains at rest and an object moving at a constant velocity continues to move at a constant velocity. For instance the earth is relatively close to being an inertial frame yet it is not actually an inertial frame because of its rotation and variations in its orbiting velocity yet such accelerations are small enough not to have a noticeable effect most of the time and so for practical purposes we can accept Newton’s laws to hold on earth.

An object that appears at rest on the surface of the earth relative to the reference frame of the earth is actually moving relatively to the reference frame of the sun and the significance of the law of inertia is that this does not actually make any difference as long as the movement is at a constant velocity but for Newton on the other hand there is still a difference between movement and rest in that the distant stars were fixed and that inertial frames are at motion or rest relative to absolute space defined by the fixed stars hence there is still a difference between motion and rest in virtue of things moving in absolute space and thus having an absolute velocity, and it was problems with this view that led to a series of redefinitions of the notion of an inertial frame which eventually culminated in Einstein’s theory of general relativity.

**‘Studio di ballerini per il Bal Tic Tac, 1921, Giacomo Balla**

And so, what was Hegel’s concept of physical inertia? This is what Hegel says about inertia in the section on ‘Mechanism’ in the Science of Logic that it is an empty abstraction when it is assumed in the field of mechanics that a body which has been set in motion would continue to move in a straight line to infinity if it did not lose its motion because of external resistance.

‘In the material world it is the central body which is the genus or rather the individualized universality of the single objects and their mechanical process. The unessential single bodies relate to one another by impact and pressure; this kind of relation does not hold between the central body and the objects of which it is the essence; for their externality no longer constitutes their fundamental determination. Hence their identity with the central body is rather rest, namely the being at their centre; this unity is their concept existing in and for itself. It nevertheless remains only an ought, since the objects’ externality, still posited at the same time, does not conform to that unity. The striving which the objects consequently have towards the centre is their absolute universality, one which is not posited through communication; it constitutes the true rest, itself concrete and not posited from the outside, into which the process of instability must find its way back. — It is for this reason an empty abstraction to assume in mechanics that a body set in motion would go on moving in a straight line to infinity if it did not lose movement because of external resistance. Friction, or whatever other form resistance takes, is only a phenomenon of centrality; it is the latter that in principle brings the body back to itself, since that against which the body rubs and incurs friction has its power of resistance only because it is united with the centre. — In things spiritual the centre, and the union with it, assume higher forms; but the unity of the concept and the reality of that unity, which is here in a first instance mechanical centrality, must there too constitute the fundamental determination’.

- ‘The Science of Logic’

The concept of inertia as defined by Newton being an empty abstraction can be understood in relation to Hegel’s views on matter, inertia and movement for there are a number of different theoretical issues in operation in the rejection of Newton’s concept of inertia. In the ‘Philosophy of Nature’ there is a similar comment about inertia (see above). It is an axiom of physical mechanics that a body as such is set into motion or equally into rest as if motion and rest are conditions of the body only as a result of an external cause and one thinks in this case only of the selfless bodies of the earth of which these determinations are indeed valid yet this is only immediate and for that reason abstract and finite corporality. It might appear that Hegel wants to oppose bodies that have a self such as living bodies to the selfless dead bodies of merely inert matter a reading that would appeal to those subscribing to the traditional picture of Hegel wishing to subordinate nature to spirit, history and life but it is rather more complex for the criticism of inertial motion remains for the most part within the basic categories of physics, and nature itself is already the transition from this selfless form of corporeal existence to what he calls free necessity.

‘Dead mechanism was the mechanical process of objects above considered that immediately appeared as self-subsisting, but precisely for that reason are in truth nonself-subsistent and have their centre outside them; this process that passes over into rest exhibits either contingency and indeterminate difference or formal uniformity. This uniformity is indeed a rule, but not law. Only free mechanism has a law, the determination proper to pure individuality or to the concept existing for itself. As difference, the law is in itself the inexhaustible source of a self-igniting fire and, since in the ideality of its difference it refers only to itself, it is free necessity’.

- ‘The Science of Logic’

The law of inertia may well provide a valuable insight but according to Hegel it is one-sided. Matter is inert in itself, that is, as its concept, which is opposed to its reality.

‘Mass, posited immediately, contains motion as resistance; for this immediacy is being-for-other. The real moment of difference is external to mass, which has motion either as this Notion, or as sublated within it. Mass is inert when it is fixed in this way, yet it does not express rest. Duration is rest in that as the Notion of its realization, it is opposed to motion. Mass is the unity of the moments of rest and motion; both are sublated within it, for it is indifferent to both of them; it is as capable of motion as it is of rest, and in itself is confined to neither of them. In itself it 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. In so far as it rests, it remains quiescent, and does not, of its own accord, pass over into motion. Similarly, when in motion, it is in fact in motion, and does not pass over of its own accord into rest. Matter is implicitly inert, i.e. it is inert in so far as its Notion is opposed to its reality. Its reality has therefore separated itself and gone into opposition to it, and it is this that first constitutes its sublated reality, or that in which it exists merely as abstraction; it is this abstraction which is always regarded as the implicit nature and essence of matter by those for whom sensuous actuality is what is real, and the form of abstraction constitutes implicitness. While finite matter is moved from without therefore, free matter moves itself; within its sphere it is therefore infinite, for within the whole, matter belongs to the stage of finitude. The just man is free, although he is bound by the laws which limit the unjust man. In nature each sphere exists not only in its infinitude, but as a finite relationship in itself. Finite relationships such as pressure and impact have the advantage of being known to us through reflection and being drawn from experience. They are defective merely because other relationships are subsumed under a rule constituted in this way. People think that things should happen in heaven as they do at home, but these finite relationships cannot show forth the infinitude of a sphere of nature.

- ‘The Philosophy of Nature’.

In-itself, an sich, matter is inert but this is only one aspect of matter, the other aspect is that it is subject to gravity (Schwere or fall) and the essence that is to say self-expression of matter is falling motion or gravitational attraction, not rectilinear inertial motion. Halpert explains Hegel’s criticism of Newton in such a manner whereby Newton has two different concepts of matter. In relation to the laws of motion matter is inert, it only moves when it is affected externally by something else. In relation to gravity however matter has its principle of motion within itself and heavy bodies are attracted to other heavy bodies because of this inner principle and in virtue of Hegel being interested in giving a conceptual account of matter rather than a mathematical description of movement he believes this duality entails a contradiction. Halpert regards this is a valid criticism of Newton because even though Newton is interested in a mathematical description of empirical motion and from that point of view it matters not that the account of gravity cannot be squared with the one of inertial motion, nevertheless Newton also wants to give a theoretical account of material reality. As it happens Hegel would in such a case have a more developed view of matter and motion yet of more interest is the notion of inertia and a kind of continuity that is traceable from Newton to Hegel to Einstein in relation to the decentring of the material world view hence part of Hegel’s criticism is that matter is in its very concept heavy, that is to say subject to gravitational attraction.

**‘Linee forza di mare’ (‘Motivo per arazzo’), 1929, Giacomo Balla**

As Hegel points out elsewhere freedom inheres in the will as gravity inheres in matter.

‘The I is solitude and absolute negation. The indefinite will is thus quite as much one-sided as the will, which continues merely in the definite. The will is the unity of these two elements. It is particularity turned back within itself and thus led back to universality; it is individuality; it is the self-direction of the I. Thus at one and the same time it establishes itself as its own negation, that is to say, as definite and limited, and it also abides by itself, in its self-identity and universality, and in this position remains purely self-enclosed. The I determines itself in so far as it is the reference of negativity to itself ; and yet in this self-reference it is indifferent to its own definite character. This it knows as its own, that is, as an ideal or a mere possibility, by which it is not bound, but rather exists in it merely because it establishes itself there. This is the freedom of the will, constituting its conception or substantive reality. It is its gravity, as it were, just as gravity is the substantive reality of a body’.

- ‘The Philosophy of Right’

A heavy body for instance a planet has a centre of gravity and it holds together because its parts or particles are attracted to this centre while at the same time gravity is also its relation to other bodies and as such two bodies have a common centre of gravity outside themselves, or to put it another way in order to understand matter at all as self-subsisting, as the existence of material entities, we need to think of it as self-cohering, as offering resistance to impulse, and hence as inert and yet in this relation-to-self it is also related to another. And considered in terms of gravity matter is self-moving, it is attracted to another body because of its inner heaviness, while at the same time it is attracted by the mass of the other body and this body is other but only other as the same which is to say as matter so they have a common centre to which they attract each other.

Considered as inert matter is affected only from the outside and considered as falling, that is to say, subject to gravity, matter is self-moving, but this self-motion is at the same time the idealization of matter because with respect to gravity it is not an individual body but it is universally attracted to all other matter. Any true account of motion will have to take into account both gravity and inertia and this kind of motion is expressed in the orbital motion of heavenly bodies which Hegel describes in the section on absolute mechanics which I will get on to in the next article. The orbit of one body around a much heavier body such as a planet around the sun is indeed a combination of inertial and gravitational motion, the planet falls towards the sun but in virtue of it being at the same time moving in a direction perpendicular to the surface of the sun it always misses the sun’s surface and moves around it in an elliptical orbit.

The concept of inertia is absorbed into this fuller form of motion for inertia has here disappeared in as far as we have attained the concept of matter and because every mass, insofar as it is heavy, strives towards the centre of gravity common to both bodies and so exerts pressure, the movement is only an attempted movement, which manifests itself in the other mass and posits it ideally, as that one equally posits the first one ideally, in as far as it offers resistance and maintains itself. In finite Mechanics, both kinds of rest and movement are thought to be the same. Everything is reduced to forces, which stand in relation and have different directions and velocities; and the main thing is then the result, that is, the net force.

‘Each individual mass is then such a body, which strives towards its centre, i.e. the absolute centre of gravity. In so far as matter determines a centre towards which it strives, and this centre is a point of unity while matter remains a multiplicity, matter is determined as proceeding out if itself and out of its place. By proceeding out of itself, it also proceeds out of its self-externality, and as sublation of externality, this is the first true inwardness. All mass belongs to such a centre, and each particular mass is dependent and contingent as against this truth. It is because of this contingency, that an individual mass can be separated from this central body. In so far as the specific mass which intervenes offers no resistance, the body will not be prevented from moving towards the centre; it will then move on account of there being no impediment, or rather fall on account of there being no support. The rest into which external motion is brought by fall is certainly still a tendency, but unlike the first kind of rest, it is not contingent, nor is it a mere condition, or posited externally. The rest we have now is posited through the Notion, like fall, the motion which is posited through the Notion and sublates external and contingent motion. Here inertia has disappeared, for we have reached the Notion of matter. In that each mass, through its weight, has a tendency towards the centre, and therefore exerts pressure, its motion is only an attempted motion, which makes itself effectual within another mass, and so posits its ideal nature. Similarly, by offering resistance and maintaining itself, this second mass posits the ideal nature of the first. In finite mechanics both kinds of rest and motion are placed on the same level. Everything is reduced to interrelated forces differing only in direction and velocity; consequently the result becomes all-important. Thus, the motion of fall, which is posited by the force of gravity, is placed on the same level as the force of projection’.

- ‘The Philosophy of Nature’

What we see here is Hegel’s criticism of the concept of force which is inherent in the understanding of motion as inertial, that, as he says, “everything is reduced to forces.” Both in the Logic and the Philosophy of Nature, Hegel has long diatribes against the idea that physical events can be explained by reducing them to the interaction of opposing forces. With regard to the orbit of planets, his criticism focuses on the assumption of a ‘centrifugal force’ which is opposed to the gravitational force pulling the planet towards the sun. In his article Hegel’s Criticism of Newton, Petry argues that the target of Hegel’s attack is not so much Newton himself, but the popular understanding of Newton which was widespread in Hegel’s time. This understanding led to a strange kind of formalism which tried to explain everything, including psychology, aesthetics and god, as an equilibrium of opposing forces. Petry gives the example of the Scotsman John Brown, who devised a mathematical medicine, according to which health consists of an equilibrium between over- and under-stimulation. Brown’s method, which was very popular in Germany, apparently led to more deaths than the Napoleonic wars.

The criticism of the law of inertia as abstract is therefore connected to the dialectic of force which is described in the ‘Phenomenology of Spirit’ as well as in the Logic, Hegel is endeavouring to demonstrate that force is nothing else than the expression of force and this is part of a general anti-Cartesian and anti-essentialist argument developed in the book of Essence of the Logic. There are material objects and in causal interaction one object acts upon another by exercising a force, a distinction is made between cause and effect, active and passive yet if one thing exercises a force upon another the other thing also exercises a force upon the first. For instance if one billiard ball hits another billiard ball we may suppose that the one which was moving first, that is to say, was moved by the player, causes the other to move, yet in fact and from a purely neutral standpoint there is no reason why we should privilege the moving ball as being a cause, for in the impact of one ball upon the other the particular state, that is, momentum, direction, mass, of the second ball just as much determines what happens to the first ball as the other way around and just as the concept of inertia makes us see the movement of objects as it is for the objects rather than for us such a revised concept of force demonstrates that activity, movement and force are posited by us as really existing things while for the objects they are relative determinations.

Hence Hegel posits at the end of the book on Essence a system of reciprocal action whereby whatever is supposed to be active can only be active by the specific kind of passivity of the thing it acts upon hence a thing’s action is determined by its object and the relation can just as much be inversed. What is passive is equally active and vice-versa and this reducibility of the active-passive distinction has firstly a material dimension in the sense of the example given above, material things mutually determine one another, or, to go back to the case of gravity, heavy bodies attract one another, so that their centre of gravity lies between the two. And further, in the Logic, it also has a logical and ontological dimension which i discuss in a previous article.

Inertia is an abstraction in virtue of the sort of external impulse or external cause of motion which it presupposes always and only takes place in a system of reciprocal action and looking at objects in isolation and attributing forces to them amounts to a privileging of our point of view, and on a more developed account motion does not consist of isolated events, which is to say, impact, throw, fall, but rather of a system of motion in which bodies are mutually determining according to laws. The model for this kind of motion is the solar system hence as I have discussed previously Kepler’s laws of planetary motion are a more original insight then Newton’s laws, in such a system the motion of any particular body is not external to it in virtue of it depending upon its place in the lawful regularity of the system, and this is free necessity.

The concept of inertia Hegel is criticizing is the standard view whereby things are at rest or moving uniformly and then something external pushes it into action, yet such a view rests upon an undue distinction between active and passive bodies, a result of the finite point of view which leads us to see, for instance, a ship on an expedition to save a drowning witch as resisting change yet considered in its own sphere matter is free since from the point of view of material reality as a system, that is to say, not from the perspective of a situated observer, there is never an active object acting upon a passive object externally, interaction is always reciprocal. And such a systematic understanding grates against common sense that would like to understand things in terms of directly observable phenomena. Finite relations such as pressure and impact have the advantage that they are familiar to our reflection and that they are accounted for by experience and the defect here is just that other relations are subsumed under this stipulated rule. See above, I like this line: people think that the way it is with us at home should also be how it is in the heavens but finite relations are just unable to present a sphere in its infinity.

Hegel may have too much downplayed the significance of the concept of inertia for it is indeed an abstraction, an idealization, yet a profound shift in thinking was occasioned by this abstract law albeit he himself worked out the consequences implicit in it. We must separate inertial movement, that is, external movement, and gravitational movement, or essential movement, in order to treat them mathematically, but they should not be treated as physically independent existences and in such a conceptual unification of inertial and gravitational movement Hegel’s thinking is moving in the direction of Einstein’s equivalence principle whereby there is no difference between gravitational and inertial movement since it is impossible to distinguish experimentally between being in a gravitational field with force G or being in a uniformly accelerated spaceship with acceleration equal to G.

Thoughts? Paolucci contendss that Hegel presages Einstein’s curvature of space since he believes that curved that is orbital motion is more essential than rectilinear motion, however, and this is not my area of expertise, for Einstein orbital motion is exactly not curved but a fall in a straight line which only appears curved to us because of the curvature of spacetime. Similarly Halpert contends Hegel’s notion that matter is active can be fruitfully compared with Einstein’s identification of matter and energy or our contemporary understanding of the nature of the atom which is rather stretching things a bit due to its anachronism and recourse to analogy, rather the value of Hegel’s great insight rests in the shift in point of view which it establishes which is a philosophical elaboration of the anti-foundationalism correlative to the decentring of the physical world view and thus ontological consequences can be drawn from the shift implicit in the concept of inertia. Indeed Hegel outdoes Newton in common sense in that he extracts the consequences of the principle of inertia for a theory of matter and motion as well as problematizing the notion of an absolute frame of reference since the limits of the system are always already necessarily engaged in the system.

**‘Vortex, Space, Form’, Giacomo Balla**

To recap, Hegel provides definitions of nature and space in the ‘Philosophy of Nature’ and focuses upon the progressive subordination of mere spatial juxtapositions within the philosophy of nature’s system of degrees, from quantitative to qualitative stages, that is, from mechanical and external relations to the configuration of the regions of the earth. There is an immanent progressive transition from nature to spirit through forms of subjective appropriations of externality and in the ‘Philosophy of Spirit’ that follows the ‘Philosophy of Nature’ within subjective spirit geography aims to conceive the necessity involved in the determinate articulations of continental masses and seas, and in relation to geography Hegel treats corresponding physical and spiritual human differences as the life of spirit still immersed in its natural world which prepares for including geography within the philosophy of history. But all that is to come, it is an exciting journey.

Relative mechanics: Impact.

Inertia, impact, pressure, draw, fall and so on, these are the determinations of ordinary mechanics and belong to the sphere of finite corporeality.

‘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-for-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 (see § r03 Rem.). 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 (c£ § 26r Rem.)’.

- ‘The Philosophy of Nature’

Some views on impact that Hegel knew about. Lazare Nicholas Marguerite Carnot (1753–1823), (‘Essai sur les machines en general’, 1783, ‘Principes fondamentaux de l’equilibre et du mouvement’, 1803), regarded the action of a continuous force such as gravity as a series of infinitely small impacts and in his studies on the mechanics of systems he introduces the concept of geometrical motions which is to say motions that have no effect upon the actions which are exerted between the bodies of a system but depend only upon the conditions of constraint between the parts of the system and this led him to establish his theorem of the impact of hard bodies: ‘In the impact of hard bodies, the sum of living forces before the impact is always equal to the sum of the living forces after the impact together with the sum of the living forces that each of these bodies would have if it moved freely with only the velocity which it lost in the impact’.

John Wallis, (1616–1703), (‘Mechanica sive de Motu’, 1670–1671), observed that if a body is rotating about an axis and its motion is suddenly checked by the retention of one of its points the force of the percussion will vary with the distance of this point from the axis and this observation led him into investigations of what he called the centre of percussion, that is to say, the point at which the intensity of impact is greatest. In 1666 the Royal Society set certain of its members, including Christiaan Huygens, (1629–1695), John Wallis, (1616–1703), and Sir Christopher Wren, (1632–1723), the problem of investigating the laws of impact. Their papers were communicated between November 26, 1668 and January 4, 1669, and constituted the first systematic treatment of the subject, see Newton ‘Mathematical Principles’, (I am sure you have it on your book shelf) the scholium to the initial axioms. According to Wallis the decisive factor in impact is momentum or the product of the mass (pondus) into velocity and all his theorems may be brought together in the formula u= (mv+m’v’)j(m+m’) in which m,m’ denote the masses, v,v’ the velocities before impact, and u the velocity after impact. ( ‘Mechanica sive de Motu’, 1670–1671). Hard bodies certainly have their significance in the history of scientific thought.

In the section on Mechanics Hegel discusses three kinds of movement, uniform motion resulting from external thrust (impact), which is expressed by the simple relation of space to time, relatively free motion in which motion accelerates uniformly due to gravity, and absolutely free motion, the movement of planets orbiting in the solar system, a stable mechanical occilator. These three stages of Mechanics demonstrate how a relatively homogeneous matter passes from passivity to activity, from being set in motion by external thrust to having the principle of motion within itself. And the speculative debt to the sublated inherence of relations between the abstract self-indifference of continuity (space) and the dividing punctuality of discreteness (points or moments: time), is rendered clear enough upon defining matter as essentially composite consisting entirely of discrete parts all of which tend toward a centre. Matter is always divisible though not divided (immer teilbar aber nicht geteilt), matter allows self-differentiation only as a possibility, because division (Trennung) by empty space is impossible, what is concrete is the different masses within the universality of gravity, their mutual gravitational attraction. Matter is still characterized above all by essential externality, governed by gravity, it has thus not yet become properly self-determining.

‘… 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 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’

In the 1825/26 Lectures Hegel emphasised that self-motion (Selbstbewegung) is the key to reassessing the significance of indifferent spatial externality within animal life, for self-motion is a singular Mittelpunkt, free from gravity and this feature belongs to the in itself, in sich, of the animal for the animal spontaneously determines its place. Later in the ‘Philosophy of Nature’ Hegel will highlights that the significance of moving at will is to have a time freed from real externality, animals move at their own initiative, not merely in reaction to external impact.

‘The animal is able to move itself to a certain extent, because like light, which is ideality severed from gravity, its subjectivity is a liberated time, which as it is removed from the real nature of externality, spontaneously determines its place. The animal’s vocal faculty is bound up with this, for as the actual ideality of soul, animal subjectivity dominates the abstract ideality of time and space, and displays its autonomous movement as a free vibration within itself. It has animal heat as a permanent process of the dissolution of cohesion, and of the independent subsistence of parts in the permanent preservation of its shape. What is more, it has interrupted intussusception, as a self-individualizing relation with an individual and inorganic nature. Above all it has feeling however, for as the existent ideality of determinate bejng, it is the individuality which is immediately universal in determinateness, and abides by itself and preserves itself in its simplicity’.

- ‘The Philosophy of Nature’

Together with possessing voice which allows expressing oneself as the self-motion of vocal cords which freely vibrate from within the animal can exhibit mastery (Herrschaft) over the abstract ideality of space and time and in this way systematic Nature reaches its highest point as well as the boundary of its proper sphere, yet at the same time in so far as Life exists only as natural Idea, throughout its existence, the individual vitality is entangled (befangen) with what is external to it as an alien singularity, and consigned (hingeben) to the unreason of externality.

‘Nature is what it is through its determinate existence, and it should not therefore be deified. It is wrong to regard and treat the sun, the moon, animals, plants etc. as works of God superior to the deeds and events of humanity. Nature is implicitly divine in that it is in the Idea; but in reality its being does not correspond to its Notion, and it is rather the unresolved contradiction. Its distinctive characteristic is its positedness, its negativity. The ancients grasped matter in general as non-ens, and nature has also been regarded as the Idea’s falling short of itself, for in this external shape the Idea is inadequate to itself. It is only to the external and immediate stage of sensuous consciousness that nature appears as that which is primary, immediate, as mere being. Even in such an element of externality, nature is, nevertheless, the representation of the Idea, and consequently one may and should admire the wisdom of God within it. Vanini said that a piece of straw was enough to prove the being of God, but every product of the spirit, the very worst of its imaginings, the capriciousness of its most arbitrary moods, a mere word, are all better evidence of God’s being than any single object. It is not only that in nature the play of forms has unbounded and unbridled contingency, but that each shape by itself is devoid of its Notion. Life is the highest to which nature drives in its determinate being, but as merely natural Idea, life is submerged in the irrationality of externality, and the living individual is bound with another individuality in every moment of its existence, while spiritual manifestation contains the moment of a free and universal relation of spirit to itself’.

- ‘The Philosophy of Nature’

The living being confronts an inorganic nature to which it relates as the power (Macht) over it which it assimilates though it may disrupt the life of the organism, and the process of nutrition (assimilation) is a continuing struggle of a subjective individual to preserve itself by first mechanically taking away elements of its environment which it subjectively needs and secon, by chemically digesting and assimilating its external objectivity, positing its immediate self-identity and reproducing itself in this self-preservation.

‘The process begins with the mechanical seizure of the external object. Assimilation itself is the enveloping of the externality within the unity of the subject. Since the animal is a subject, a simple negativity, the nature of this assimilation can be neither mechanical nor chemical, for in these processes, the substances, as well as the conditions and the activity, remain external to one another, and lack an absolute and living unity’.

- ‘The Philosophy of Nature’

In this way the animal is a living point of unity that in positing itself in determinate opposition to a material nature which externally conditions its life acquires feeling and sentience of itself, the sense of being an exclusive singularity in tension with an inorganic nature which stands over against it.

‘In this external relation, the animal organism is immediately intro-reflected, and consequently the ideal nature of this relatedness is the theoretical process, sensibility as outward process, and indeed as determinate feeling which differentiates itself into its multifarious perceptions of inorganic nature’.

- ‘The Philosophy of Nature’