On Hegel’s ‘Philosophy of Nature’ : A Free Reflex of Spirit — part twelve.
‘Poem’
by Gottfried Benn (1886–1956)
And what means this force,
half picture, half word and half guess’d,
what do you intend,
wherefore the need
for quiet anguished feeling?
It spills out of you from nothingness
from the singular, from the diverse,
here, you take ash, there the flame,
you scatter and would delete and protect them.
You blanch, you cannot grasp it all,
bound it, contain it,
about this and that,
you remain lost,
entranced but also mistrusting.
By day and by night
you are drawn,
also on Sundays, you chip away at it
and wear the stylus to a nub,
then, you leave it — it is: the Essence.
‘Gedicht’
Und was bedeuten diese Zwänge,
halb Bild, halb Wort und halb Kalkül,
was ist in dir,
woher die Dränge
aus stillem traürnden Gefühl?
Es strömt dir aus dem Nichts zusammen
aus Einzelnem, aus Potpourri,
dort nimmst du Asche, dort die Flamme,
du streust und löschst und hütest sie.
Du weißt, du kannst nicht alles fassen,
umgrenze es, den grünen Zaun
um dies und das,
du bleibst gelassen,
doch auch gebannt in Missvertraun.
So Tag und Nacht
bist du am Zuge,
auch sonntags meisselst du dich ein
und klopfst das Silber in die Fuge,
dann lässt du es — es ist: das Sein.
Georg Wilhelm Friedrich Hegel, (1770–1831). ‘The Philosophy of Nature’
Michael John Petry, translator of the ‘Philosophy of Nature’ edition that I am consulting, said this of the troublesome relation between Hegel and Sir Isaac Newton, (1642–1726/27):
‘At first sight, what we seem to have here [i.e. in the relation between Hegel and Newton] is little more than the contrast between the tested accomplishments of the founding father of modern science, and the random remarks of a confused and somewhat disgruntled philosopher; and if we are persuaded to concede that it may perhaps be something more than this — between the work of a clearsighted mathematician and experimentalist, and the blind assertions of some sort of Kantian logician, blundering about among the facts of the real world’.
- ‘Hegel and Newtonianism’
Writing in 1992 these words reflect a general attitude towards the relationship between Newton’s and Hegel’s work which Petry faced in the late 1960s an attitude which he tried to call into question in his own and in a joint international effort of research, an attitude which thereby became questionable among philosophers and yet which still persists among scientists and indeed almost any scientist more or less independent of his or her epistemological and philosophical concept will still ask whether Hegel’s objections to Newton’s mechanics and optics far from being justified are the product of a post-scholastic approach at all and even a physicist who has for some reason studied the original text of Newton’s ‘Philosophiæ Naturalis Principia Mathematica’ and who has hence realized that there do exist inconsistencies in the Newtonian concept of force will still have grave doubts about whether Hegel’s fundamental scepticism towards Newton’s concept of dynamical laws is at all warranted.
The persisting conception of Hegel’s criticism of Newton’s physics as an irrational or at least hopelessly exaggerated one partly has its roots mainly in Hegel’s terminology and in his style which of course does not mean that a simple translation of Hegel’s arguments into any contemporary philosophical language be sufficient to immediately convince every Newtonian scientist nonetheless a non-Hegelian way of rephrasing the core of Hegel’s anti-Newtonian philosophy of nature can help to understand to which extent the latter does satisfy any scientist’s criteria for a rational and self-consistent theory.
One must bring to the fore the basic features of Hegel’s criticism of Newton’s optics and celestial mechanics and focus in on his concept of a sense of nature and to highlight the fundamental difference between Newton’s and Hegel’s ideas of natural laws and of the relation between mathematics and physics and subject the metaphysical background of this difference to analysis. There is a wide range of topics upon which Hegel disagrees with Newton while there is only one subject which Newton has according to Hegel treated adequately from a philosophical point of view which is to say the foundations of analysis. Newton’s way of unifying terrestrial and celestial mechanics and his method of investigating the nature of light and his allegedly empiristic epistemology have been severely criticised by Hegel a criticism traceable back to his earliest writings indicating that already the way in which Newtonian physics was taught in Tübingen in the 1790s gave Hegel the impression that Newton’s fame as founding father of modern physics be doubtful at best.
Had Hegel been educated in England or France then his attitude towards this question would have probably been somewhat different since he would have had to perceive Newtonianism as a widely accepted and solid basis of scientific research, a basis which it became in Germany only some decades after Hegel’s death, when mathematical physics began to flourish especially in Berlin, which does not imply that Hegel if educated in England or in Germany around 1850 would not have criticised Newtonian physics at all. He considers many of Newton’s optical experiments as moot and questions several aspects of Newton’s way of calculating planetary motions which may seem to e exaggerated even were we to take into account the possibility of errors both in the Principia and in the Opticks. ‘If the natural science of the day is questioned’, said Petry, ‘this is usually because Hegel thinks that it is overlooking qualitative differences. He never quarrels with it simply in order to make striking observations or indicate novel connections’. Hegel does not question Newton’s optical experiments or his calculations in celestial mechanics merely to make striking observations and there is a metaphysical background of these Hegelian critical remarks that appear to concern mere empirical questions yet Hegel does attack Newton the physicist at some points and not only Newton the philosopher and in the ‘Philosophy of Nature’ he stresses that Newton erroneously claimed the impossibility of constructing a fully colour-corrected refracting telescope, that the Colour Wheel does in fact not look white when rotating, that it is unnecessary to completely darken the room when studying the sun’s spectrum using a prism, and so on, thereby getting lost in details that do not contribute substantially to the respective main points of interest such as the nature of gravity or the nature of light.
Does Hegel have a point? For instance Hegel discovered inconsistencies in Newton’s use of the concept of centrifugal force, inconsistencies that independently led post-Newtonian physicists to the clarification or even to the refutation of this concept and furthermore Hegel had a prominent example in his stance against the physicist Newton which is to say Johann Wolfgang von Goethe, (1749–1832), who had done the same in his Farbenlehre and whom he repeatedly praises for his great sense of nature. Sense of nature is a central expression in Hegel’s natural philosophy and even though he does certainly not reduce his method of natural philosophy to this sense he appears to be of the opinion that it is a necessary opponent of understanding (Verstand) and especially of the Newtonian understanding.
What is this sense of nature? A method of contemplating nature that conserves natural phenomena as totalities instead of decomposing them into parts which are then made sort of atoms of the phenomena and this can be illustrated by the example of planetary motion as well as by the example of the spectrum of the sun for in the case of planetary motion Hegel opposes its decomposition according to the parallelogram of forces arguing that the concrete totality is thereby artificially dissected although as Samuel Alexander, (1859–1938), notes: ‘Hegel does not deny the convenience of the distinction, but he accuses Newton of mistaking the directions into which the motion is resolved for real and actual forces, independent of each other’. In the case of Newton’s theory of colour, Hegel argues similarly in stating that considering colours as the components or elements of light reverses the real order of the things which is according to him that light is the primordial phenomenon and colours only emerge if light interacts with matter and so sense of nature is conceived as a synthetic way of grasping the essence of phenomena, as a way of experience which does not introduce any distinctions of which it then forgets that they are extrinsic, and a question arises concerning the extent to which Hegel has worked out a definition of this method of experience and recognition, besides which some stress has to be laid upon the fact that the sense of nature which should grasp a phenomenon as a whole is not necessarily in opposition to mathematical recognition of nature for in an analysis of Hegel’s concept of natural laws we observe that he very much appreciates the laws of the phenomena as opposed to laws of forces and these so-called laws of the phenomena are characterized by a consideration of natural phenomena in their totality that does not exclude the derivation of mathematical relations between moments of these phenomena such as space and time.
Hegel’s view of the relation between physics and mathematics. There is another motive in Hegel’s criticism of Newton’s physics which is even more fundamental than the epistemology of the sense of nature which is to say the totally different way in which Newton and Hegel conceive the relationship between mathematics and physics and this difference reflects two entirely different methods of conceiving the essence of nature and the method of science. Let us briefly consider the Newtonian way first. Newton made several paramount statements on his view of the relation between mathematics and physics or mechanics or natural philosophy in a prominent passages of his Principia. and already the first sentence of his Foreword refers to this problem. There can be no doubt that Hegel carefully studied this first sentence, and little doubt that it embarrassed him given that it reads: Cum veteres mechanicam […] in rerum naturalium investigatione maximi fecerint; et recentiores, missis formis substantialibus et qualitatibus occultis, phaenomena naturae ad leges mathematicas revocare agressi sint: Visum est in hoc tractatu mathesim excolere, quatenus ea ad philosophiam spectat. This can be rephrased thus: ‘Now that (since Bacon) the substantial forms (of the Aristotelians) have been abandoned from natural philosophy, mathematics should replace them to the maximum possible extent’. Having in mind the development of physics in the second half of the 19th century, this seem a reasonable and well-defined programme and yet during Newton’s lifetime it was not as well-defined, for it was still unclear: What means mathematics in the context of science? Is it geometry, algebra, analysis, or the sum of all these disciplines? And furthermore, can the mathematical description of nature replace the Aristotelian ontological framework without introducing a new aleit implicit and unwanted ontology into the history of human thought?
Concerning this question Petry has stressed Newton apparently underestimated the metaphysical content of his Principia and Newton himself commented on the relation between mathematics and philosophy in the beginning of the third book of his Principia: ‘In the preceding books I have laid down the principles of philosophy; principles not philosophical but mathematical: such, namely, as we may build our reasonings upon in mathematical inquiries. These principles are the laws and conditions of certain motions, and powers or forces, which chiefly have respect to philosophy; but, lest they should have appeared of themselves as dry and barren, I have illustrated them here and there with some philosophical scholiums, giving an account of such things as are of more general nature, and which philosophy seems chiefly to be founded on; such as the density and the resistance of bodies, spaces void of all bodies, and the motion of light and sounds. It remains that, from the same principles, I now demonstrate the frame of the System of the World’. Petry as it happens did not explicitly trace back this metaphysical content to the application of mathematics. The passage from Newton reflects a quasi-Cartesian understanding of mathematics which has been left behind at the latest in the 19th century. For Newton and his contemporaries, mathematics is by no means identical with what we call pure mathematics. It was C.F. Gauss who at the beginning of the 19th century, laid stress on the importance and the development of pure mathematics. Newton considered equations describing the trajectories of particles in space as mathematical equations not as elements of what we would call theoretical physics and it is evident that this is not only a terminological problem since it is one of the basic features of the mechanistic wordview to be grounded upon an immediate that is to say unreflected application of mathematics to scientific inquiry. It appears that Newton’s application of mathematics is unreflected and he finds it more or less self-evident that the phenomena described by the sciences have a mathematical structure. The concept of mass even though introduced into physics by Newton is an interesting example in this regard in that Newton seems to have missed the point that is was a nontrivial abstraction to define mass in the way he did on the basis of an atomistic theory of matter, Newton’s direct unreflected application of mathematics in his physical investigations probably has its roots in Descartes.
And so he leaves aside the question why quantitative categories of thought can be applied to the description of nature at all and which implications this description has while what Newton calls philosophy or natural philosophy is supposed to be little more than applied mathematics in order not to involve any hypotheses if possible. Hegel’s view on the relation between mathematics and physics is in extreme opposition to Newton’s as he goes so far as to call the ambition to mathematically prove theorems of physics ridiculous. ‘The physical’ (Physisches), says Hegel in his lecture on natural philosophy from 1823/24,’cannot be proved mathematically’. Similarly, he writes in the Logic of Measure that the attempt to prove natural laws mathematically ‘in the strict sense of the word, i.e. neither empirically nor conceptually, is absurd’. And in the manuscript by H.W. Dove recording Hegel’s lecture from 1825/26 he says: ‘If nothing ought to be determined physically [as Newton pretends], then the term ‘force’ should be totally omitted’. It is true that the terms ‘physics’, ‘the physical’ and ‘physically are not exactly identical with their present-day counterparts but they do not refer to the second part of the natural philosophy either since from a Hegelian standpoint it would be trivial to say that philosophical theorems cannot be proved mathematically. Hegel when blaming Newton for pretending to have proved his physical theorems mathematically seems to have an archetype of modern physics in mind which exists in parallel to natural philosophy.
‘What is now called physics, was formerly called natural philosophy. It is, what is more, a theoretical and thinking consideration of nature, and while on the one hand it does not concern itself with determinations such as these purposes, which are external to nature, on the other hand it does aim at comprehending that which is universal in nature as it presents itself in a determinate form, i.e. forces, laws, genera. Here the content is not a simple aggregate, but is distributed through orders and classes, and must be regarded as an organic whole. In that the philosophy s of nature is a comprehending consideration, its object is the same universal; it is however the universal for itself, which it regards in its own immanent necessity, according to the self-determination of the Notion’.
- ‘The Philosophy of Nature’
Which conception of the relation between physics and mathematics do the above cited sentences reflect? It is a conception that can be traced back to the time when Hegel lectured in Jena and published his ‘Dissertation on the Orbits of the Planets’ and the ‘Phenomenology of Spirit’. In his Dissertation from 1801 Hegel emphasises the difference between the domain of mathematics and the domain of physics: ‘De qua [i.e. Newton’s] cum Mathesi Physices conjuctione praecipue monendum est, ut caveamus, ne rationes pure mathematicas cum rationibus physicis confundamus […]’. That is to say beware of assigning any ontological value to mathematical concepts like vector components of the motion of a body, and in the Foreword to the Phenomenology where Newton is not mentioned explicitly Hegel contends that it is impossible to construct mathematical proofs of theorems of statics and mechanics like the laws of the lever or the law of free fall for such proofs do not prove any more than the necessity of real proofs which is to say philosophy alone, provided that it makes use of the dialectical method can in the strict sense of the word prove the laws of the motion of natural bodies.
The so-called proofs that applied mathematics which Hegel correctly distinguishes from pure mathematics (pure mathematics for Hegel, does not use the concept of time it deals exclusively with space (geometry) and with numbers (arithmetics, algebra)) is able to deliver do not grasp the genuine relation between the moments of natural laws, for instance space and time, which is the essential content of these laws, and like pure mathematics applied mathematics is unable to seize the qualitative immanent, self-determined motion (Selbstbewegung) of the concept, a motion that includes non-quantitative transitions like that from the point to the line or from space to time. But what should the scientist do with natural laws, if not try to prove them in some sense?Hegel distinguishes the empirical (das Empirische) on the one hand and the Notion that is to say the philosophical way of reasoning on the other hand and given that the scientist is not a philosopher should he pretend to derive natural laws merely from experimental research? Recall Hegel’s comment in a footnote in the Encyclopaedia on Joseph-Louis Lagrange, (1736–1813):
‘Lagrange, in his own way, employs the straightforward and perfectly valid procedure in his ‘Theorie des fonctions’: see pt. III ch. i ‘Application de la Theorie a la Mecanique’. He takes the mathematical treatment of functions as given, and in his application of the same to mechanics, discovers that the fi and bt2 involved in s=fi occur in nature; s=ct3 does not occur there. At this juncture it is quite right that there should be no attempt to prove that s=bt2, but that this relationship should simply be accepted as occurring in nature. In the development of the function; 1 becomes 1=8, and as the series expressing the space traversed in 8 time can only make use of the first two terms, the others are omitted. As is usual with Lagrange, this circumstance is dealt with in an analytical manner. It is however only because the first two terms have a determination of a real nature, that they are treated as being of significance to the object, ‘on voit que les fonctions primes et secondes se presentent naturellement’ (Hegel’s emphasis) ‘dans la mecanique, ou elles ont une value et une signification determinees.’ (ibid. 4.5). It is true that at this point Lagrange falls into Newtonian expressions, abstract or simply uniform velocity derived from the force of inertia, and an accelerative force, and so also introduces the mental fabrications of an infinitely small space of time having a beginning and an end yet this does not prejudice the legitimacy of his procedure which instead of these determinations being used to prove the law, the relevant aspect of the law is taken up as it is presented in experience, and then submitted to mathematical treatment.’
- ‘The Philosophy of Nature’
Hegel is commenting on Lagrange’s remark on the relation of the Taylor series to the motion of point masses and he praises Lagrange for not pretending to prove the law of free fall by the expansion of such a series. Lagrange says Hegel rightly refrains from any alleged proof of this kind but restricts himself to adopting the acceleration term (a t²) from empirical research and comparing the mathematical (i.e. analytical) theory with it. A similar judgement can be found in Hegel’s treatise on the calculus in the first volume of his Science of Logic even though this judgement is more focussed on the danger of assigning a physical meaning to the terms of the Taylor series. From this praise for Lagrange it can be concluded that Hegel far from opposing the application of mathematics more specifically of analysis to mechanics did have a certain idea of this application which is to say experimental physics should examine the motions and other changes of state of bodies under certain idealized conditions and Hegel does not stress the aspect of idealization much rather he stresses the necessity of making experiments without doing too much violence to nature and this is emphasised in the discussion of Newton’s theory of colour.
The motions thereby examined by experimental physics should not be explained by any comprehensive theory least of all should forces be introduced into the scientific description as explanatory principles such that different phenomena would be derived from one basic set of concepts, for instance, space, time, mass, force or for instance space — time — mass — energy and the latter task should be reserved to philosophy, since there is nothing between the empirical on the one hand and philosophical theory on the other hand and if it is not reserved to philosophy and more specifically to a dialectical system of philosophy some sort of a mechanistic worldview will inevitably result.
We must delve into the architecture of the encyclopaedic system further, the metaphysical background of Hegel’s view of the relation between mathematics and physics and his repeated contention that theorems of physics cannot be proved mathematically. What motivates such a contention? Did Hegel view Newton’s use of mathematics as an epistemologically naïve one? A methodological criticism that is a part of Hegel’s fundamental disapproval with Newton? There is something else connected to the relation between physics and mathematics, Hegel’s anti-reductionism and its influence on the conception of the relation between mathematics and physics. Reductionism is a tendency of human understanding „to put everything on the same level such as on the level of mechanics or chemistry.
‘The attempt is made to put everything on the same level. Everything can of course be treated from a chemical point of view, but everything can also be treated from a mechanical point of view […]. When bodies are treated at one stage, these does not exhaust the nature of other bodies however, as for example when vegetable or animal bodies are treated chemically’.
- ‘The Philosophy of Nature’
Hegel does not deny the possibility of applying mechanical models or the category of mechanism even to subject matters of psychology. The conception of the Encyclopaedia even demands mechanism to realize itself in a logical, natural and spiritual (psychological) form hence it is a misunderstanding to conceive of Hegel’s anti-reductionism as a tendency to forbid the application of thought-categories to realms of reality which are apparently alien to these categories, on the contrary it is the encyclopaedic system which makes it understandable why thought-categories designed to comprehend apparently primitive realms of reality can re-gain significance as moments but only as moments of higher realms of reality. Mechanical memory is a good example thereof.
However the encyclopaedic system still conserves an important feature of the concept of the chain of beings in that it conserves the contention that philosophy should comprehend reality as having a hierarchical structure, that thought should not nivellate it in spite of recognizing the usefulness of analogies and mechanical models and anti-reductionism in this sense can be defined as sticking to ontological hierarchies in a way that is compatible with Kant’s critique of traditional metaphysics. Kant was not an anti-reductionist for his thinking is too much concentrated upon his critique of ancient naive ontology and he is largely unable to highlight the merits of ontological hierarchies like the concept of the chain of being.
How and to which degree post-Kantian philosophy can stick to ontological hierarchies is not something to go into here rather the so defined anti-reductionism connection to the relation between physics and mathematics can be albeit there is seemingly little interrelation between both topics. For why should a given concept of applying mathematics in science result in a reductionist or anti-reductionist worldview? There is no necessary connection between one and the other although coming back to the idea that any unreflected use of mathematics in science is likely to favour the mechanistic worldview and having in mind that the latter is certainly a kind of reductionism the question arises as to which extent Hegel’s opposition to Newton is ultimately motivated by the impression that the author of the Principia does unintentionally favour reductionism by his very understanding of ‘mathesim excolere, quatenus ea ad philosophiam spectat’.
Newton’s way of ‘mathesim excolere’ depends upon a new type of law that he introduced to science albeit he did not formalize it in the way in which it has been formalized and greatly generalized in the 18th and 19th centuries, the dynamical law which has the structure of a differential equation, and the law of universal gravitation is an example of such a law. Hegel’s idea of Newton’s being a reductionist is intimately connected to this new type of dynamical law, the dynamical law takes the place of the type of laws established by Johannes Kepler, (1571–1630), Kepler and Galileo Galilei, (1564–1642), a type which is known to have been thoroughly analysed by Hegel, the laws of the Kepler-Galileo-type are phenomenological laws for as Hegel observed Newton ‘set the laws of forces in the place of the laws of phenomena’. (‘Lectures on the History of Philosophy’). The phenomenological laws are not universal natural laws rather they refer to particular classes of phenomena which occur under certain circumstances, for instance under terrestrial gravitation in vacuum or under interplanetary conditions, furthermore in ideal gases and so on. The dynamical laws due to their formal structure can describe motions or changes of state only after the specification of boundary conditions and after analytical or numerical integration and phenomenological laws also can in many cases be derived from dynamical laws by the process of specifying boundary conditions and performing an integration. Galileo’s law for instance can be derived from Newton’s law of universal gravitation in such a way.
And so even though not directly describing motions or changes of state dynamical laws are in general considered as more fundamental than phenomenological laws and in this perspective many phenomenological laws are considered as no more than rules for particular classes of motions governed by an underlying fundamental dynamical law and Newton did not yet use the terms dynamical laws, boundary conditions and so on these terms as such are the result of a later formalization of Newton’s predominantly geometrical understanding of forces. However the basic concept of dynamical laws and of the dynameis (forces) governing them and being the very scope of scientific research — can be found in Newton’s work and so it is the introduction of dynamical laws that Hegel refuses to accept as a progress of science. Hegel’s words on Newton’s alleged intermingling of mathematics and physics as well as his general anti-reductionism are related to apology of the phenomenological against the dynamical law and his praise for Kepler and Lagrange implies he would want the scientists to discover and deal with phenomenological laws of motions and of changes of state while he would not want them to construct whole theories deriving several classes of motions from unified dynamical laws.
Hegel is convinced that only phenomenological laws like Kepler’s laws, Galileo’s law of free fall or Snell’s law of refraction can be integrated into a philosophical theory of natural phenomena that does really deserve this name and unified dynamical laws by contrast like Newton’s law of universal gravitation together with his axioms of mechanical motion appear to Hegel as a sort of a semi-philosophy which on the one hand has to use de facto metaphysical categories and on the other hand cannot justify the use of these categories nor construct a hierarchical system of them.
Hegel’s apology of the phenomenological law is furthermore related to his distinction between physics and natural philosophy as thinking and “comprehending consideration of nature (denkende and begreifende Naturbetrachtung). Physics and philosophy are related to each other in the same way as thinking consideration of nature and comprehending consideration. This distinction is progressive compared to any sensualistic approach to physics which would deny even the status of thinking consideration of nature insisting for example on the idea that physics is just a method of economically dealing with perceptions. Recall Ernst Mach’s, (1838–1916), conception of science. Hegel’s distinction reserves the status of comprehending consideration of nature to philosophy and ultimately this implies an unwillingness to concede the status of a theory(with its own epistemological status to physics, in any case, stating that physics and science in general is not comprehending consideration of nature leads Hegel to insist on the scientist’s task being the discovery and mathematical formulation of phenomenological laws and these laws are indeed not sufficient for the foundation of a theory of nature for they do not relate different classes of motions or more generally speaking different classes of phenomena to each other for example they do not relate magnetism to electricity or acoustical to mechanical phenomena while dynamical laws aim precisely at that for example Maxwell’s equations or the equations of wave mechanics.
But the way in which dynamical laws relate apparently different realms of (phenomenal) reality to each other appears to Hegel as a dangerous mechanistic way. True, dynamical laws suspects Hegel would probably make it possible for physics to become a theory of nature on its own, but a reductionistic theory which does harm to the ambitions of philosophy. Phenomenological laws are not likely to do harm to a dialectical concept of nature because they can be integrated into it as moments, thereby gaining their place in the hierarchy of an increasingly concrete system of the real and this is Hegel’s view of science as cooperating with philosophy.
‘Physics must […] work together with philosophy so that the universalized understanding which it provides may be translated into the Notion’.
- ‘The Philosophy of Nature’
It is possible to give a still more precise description of the kind of natural laws Hegel approves from a philosophical point of view and the kind of laws he disapproves and Hegel greatly appreciates power laws relating to each other what he would consider as phenomenological quantities such as orbital periods and distances from the sun and so on and he is convinced that at least in many important cases it is possible to develop sort of an a priori deduction of such power laws from the concepts of the respective related entities even though he concedes that this is a most difficult task. What Hegel disapproves of on the other hand are non-phenomenological natural laws especially if they are supposed to establish a link between different branches of physics and if they accomplish this by highly abstract concepts such as force, energy, entropy, probability and so on.
Admittedly most of these concepts have been introduced to science only after Hegel’s death but Hegel’s resistance to this type of concepts is evident enough from the way in which he treats atomism and Newton’s concept of force an example to illustrate the point being the principle of conservation of energy albeit it is neither a principle established by Newton nor a dynamical law in the strict sense of the word since it is not formulated as a differential equation and does not refer to forces, but to energies yet the energetic approach is equivalent to the Newtonian approach of founding mechanics upon the concept of force the energetic approach being an integrated version of the dynamical approach and of course Hegel would have criticised the principle of conservation of energy in a very similar way as he criticised Newton’s law of gravitation, like the latter the energy conservation principle represents a partial unification of hitherto distinct theories like mechanics and thermodynamics.
Insofar as it is formulated in sentences like ‘heat is a kind of mechanical energy’, this was the version of the energy conservation principle which Robert Mayer, (1814–1878), had in 1842, this principle threatens to nivellate the difference between mechanical motions and phenomena related to heat. In his Jenaer Systementwürfe Hegel uses himself terms which he borrows from mechanics like lever, throw and so on for the description of phenomena related to heat. ion principle which Robert Mayer had in 1842. 42 NB: In his Jenaer Systementwürfe, Hegel uses himself terms which he borrows from mechanics (like lever, throw etc.) for the description of phenomena related to heat. To claim that the energy conservation principle will necessarily reduce the essence of heat to the essence of mechanical motion would be as naïve as certain uncritical attempts to understand the concept of energy as the basis of physics par excellence, rather the claim is that we can better understand Hegel’s view of natural laws by hypothetically constructing his assessment of the law of energy conservation and so a Hegelian assessment of the energy conservation principle would very much like the Hegelian assessment of Newton’s law of gravitation not involve the statement that the concept of energy is totally useless in physics, on the contrary, Hegel would find it highly significant, for instance, that the radiation energy emitted by a star can be related by a power law to its surface temperature if the star is considered as representing the case of a blackbody, he would endeavour to find a reason immanent in the very concept of temperature which makes this law, the Stefan-Boltzmann law, understandable from a philosophical point of view, especially with respect to the occurrence of the fourth power, which is, by the way rather rare in natural laws and at the same time Hegel point out that there is an issue in setting up equations relating different kinds of energy to each other following the principle of understanding which is looking for quantitative identity (das Verstandesdenken, welches an der Linie der Gleichheit fortgeht) and in this perceptive the energy conservation principle too entails the danger of overlooking essential differences between the kinds of energy which it equates numerically and the general rule behind this hypothetical assessment of energy conservation is the following, not only Newton is of the opinion that physics should beware from metaphysics but Hegel is of this opinion as well just that he defines the use of metaphysics in physics quite differently.
While in Newton’s view the introduction of the concept of force helps physics to surmount the status of a scholastic doctrine Hegel maintains that forces energies and other highly abstract concepts of physics if used for a unification of natural laws without the guidance of philosophy accidentally render science a new variety of metaphysics. Does the reconstruction of the metaphysical background of Hegel’s criticism of Newton’s method render the former in its basic structure fully justified? Well, Hegel’s criticism of the type of natural laws introduced by Newton has some things going for it, by being for Kepler and against Newton Hegel proposes to make a fundamental difference between what he considers as phenomenological laws on the one hand and dynamical laws on the other hand, and furthermore he correctly points out that the establishment of dynamical laws is more than a self-evident application of mathematical equations to physics and in this sense he demonstrates that Newton has maybe a somewhat naïve concept of the relation between mathematics and physics, and even further Hegel foresees that scientific theories based upon the unification of dynamical laws may abet the mechanistic worldview if uncritically understood as theories of everything which is to say Hegel’s criticism of Newton’s aiming at unified dynamical laws is justified if re-interpreted as a criticism of the damage which the mechanistic worldview can do to philosophy.
On the downside the anti-Newtonian attitude can be considered as a widely accepted result of the research on Newton and Hegel that Newtonianism and the mechanistic worldview are not exactly one and the same thing and if so then Hegel by identifying both has partly failed to correctly assess Newton’s achievements and insofar as the latter laid the foundation of modern physics Hegel has in addition failed to correctly situate physics from an epistemological point of view and in this regard it might have been an option 200 years ago to restrict physics to the quest for phenomenological laws and to state that natural philosophy alone will be able to construct a comprehensive theory of nature based on the self-determination of the Notion however the development of physics in the 19th century compels us to conceive the relation between physics and philosophy in a different way and the starting point of this way should be the recognition of physics as well as chemistry and so on as a separate theory of nature which is to say the recognition that science does not need to wait for a philosophical interpretation in order to become something more complex and more consistent than what Hegel calls the empirical which does not mean however that a philosophical interpretation of scientific theories be superfluous it rather means that it has to be an interpretation of scientific theories in the strict sense of the word, not an interpretation of isolated laws and phenomena.
Today as well as at Hegel’s time it does make sense to give a philosophical answer to the question for the difference between the chemical and the mechanical object while it probably makes less sense to prove laws of mechanical motion or chemical interaction in a philosophical manner and it does make sense to ask how the status of objectivity has changed with the transition from classical to quantum mechanics while it would be myopic to aim at an a priori deduction of Werner Karl Heisenberg’s, (1901–1976), uncertainty principle, and Hegel’s philosophy of nature while avoiding isolated allegedly philosophical considerations of natural phenomena in its best parts is not free of the temptation of philosophizing about individual scientific theorems and equations and it is the case that Hegel makes plenty of astonishing and elucidating observations when philosophizing about Galileo’s and Kepler’s laws yet it is to be doubted whether he thereby gives a good example to his acolytes from a methodological point of view, which is to say in brief that Hegel’s justified insistence on qualitative differences within the realm of nature is not contrary to his own conviction necessarily coupled to the refutation of the Newtonian quest for unified dynamical laws even though the latter seem to automatically endanger the former at first sight but it is certainly true however that unified dynamical laws are much more difficult to integrate into a philosophy of nature of the Hegelian type the reason being that the philosopher in contemplating these laws can by no means rely upon his or her sense of nature but has to analyse the epistemological status of the scientific disciplines that have worked out the respective laws, the formal structure of them, and their phenomenal content, until eventually arriving at a refined concept of nature as a system of stages, stages about which the scientist may shrug his or her shoulders with the question isn’t it all the same anyway?
Kepler’s laws of planetary motion following the Copernican revolution in cosmology according to Gottfried Wilhelm (von) Leibniz, (1646–1716), and Hegel for the first-time in history discovered the keys to what Hegel designated the absolute mechanics mediated by dialectical laws which drives the celestial bodies in opposition to finite mechanics in terrestrial Nature developed by mathematical and empirical sciences but that are of very limited scope. Newton mistakenly extended and imposed finite mechanics on the absolute mechanics of the cosmic bodies in the form of his Law of one-sided Universal Gravitational Attraction by distorting and misrepresenting Kepler’s laws and in opposition to Leibniz’s ‘Radial Planetary Orbital Equation’. The still-prevailing Newtonian error demonstrates the limitation of mathematical idealism and dare one say prejudicially driven modern cosmology in the form of Einstein’s theories of relativity have rendered gaining positive knowledge of the cosmos an impossibility and has impeded social/historical development of humanity through the imposition of such moribund ruling notions.
Hegel’s ‘Philosophy of Nature’ is a complaint against the misrepresentation of Kepler’s Laws and his Encyclopaedia is the negation and the direct refutation of Newtonian physics and the Principia something which contemporary science should regard seriously for Kepler’s phenomenological laws of planetary motion and the dialectical insights of Leibnitz and Hegel clear the way for gaining positive knowledge of the dynamics, structure and the evolution of the cosmic bodies and other cosmic phenomena and without invoking mysteries and dark/black cosmic entities that standard astrophysics and cosmology like to entertain themselves with. Recall however Petry’s words about the founding father of modern science and the confused and somewhat disgruntled philosopher, a reflection of the general attitude towards the relationship between Newton’s and Hegel’s work prevailing among physicists in particular and philosophers in general yet if truth be told Kepler’s laws of the planetary motion in the solar system came following the observations without the aid of a telescope by Tycho Brahe, (1546–1601), at the advent of Copernican revolution in cosmology against Ptolemaic Epicycles that had formed the ruling idea of medieval feudal Europe until that time and the great upheaval that followed led to one of history’s greatest social and scientific revolution propelled by the scientific works of Galileo, Kepler et al., among others culminating in Newtonian mechanics.
The social, scientific and technological revolution following on from that is all well and good yet what is overlooked is that a Newtonian crude mechanistic and mathematical approach to natural science seemingly successful in terrestrial Nature actually poses a threat to the Copernican revolution itself for Newton’s unlimited and one-sided extension and transference of his dynamical laws developed in terrestrial Nature and the related mathematization of physics to the realm of the cosmos in the form of his law of universal gravitational attraction albeit unwittingly, distorted and undermined Kepler’s phenomenological laws of the heavens thereby clouding the vision of the cosmos.
The misrepresentation of Kepler’s discovery did damage to the Copernican/Galilean revolution against the ruling metaphysics, theology and the God of feudalism and also led to the latter’s reinforcement in the form of Einsteinian cosmology based upon general relativity and the Newtonian mathematization of physics and cosmology was extended further with Albert Einstein, (1879–1955), Einsteinian cosmology solidifying the ancient outlook concerning the absolute immutability of Nature for howsoever Nature came into existence it remained the same and the universe and the cosmic bodies once set in motion by the first impulse or Big Bang kept on moving in their predestined orbits in an ever-expanding universe.
Such came as a reaction to the radical developments in biology in the form of Charles Darwin’s, (1809–1882), theory of evolution of the species and more importantly to one of history’s most revolutionary developments in physics, namely quantum physics that unveiled an aspect of objective reality that was totally unknown or even unthought of before and only very dimly anticipated by Hegel’s dialectics yet resistance to this fate of physics and cosmology came in the form of the conflict in epistemology between British Empiricism epitomised by Newtonianism on the one hand and the German philosophy of Leibniz, Kant and Hegel on the other. Leibniz’s alternative formulation of planetary motion, Kant’s nebular hypothesis of the cosmos, Hegel’s dialectical method of Hegel, points of departure for cosmology, and based upon the discovery of Kepler, Leibniz came up with the radial orbital equation of planetary motion of the solar system in terms of the contradiction of centrifugal and centripetal forces.
But Leibniz was muted by Newtonian manipulations and the authoritative ruling through Commercium Epistolicum of The Royal Society including his claim of priority as the inventor of calculus yet also his radial orbital equation that potentially could have corrected Newton’s error concerning the law of universal gravitational attraction that got in the way of understanding the cosmos, the universe and objective reality. Kant’s nebular hypothesis was a point of departure for physics and cosmology a hypothesis for the first time in the history of natural science pointing to the fact that things and processes in Nature are not given at one stroke and perfect in themselves as was thought before but comes into being and evolves in the course of time, that Nature and the cosmic bodies not only have existence and extension in space but also have a history of evolution in time.
And yet this revolutionary and dialectical world view like Leibniz’s work on planetary motion had little chance of seeing daylight and remained without any consequence and the prevailing static world view of Aristotelian formal logic, British empiricism, common-sense of everyday life experience that came as the natural evolutionary legacy of human beings that Hegel collectively termed as the view of understanding and popularly known as causality and personified by Newtonian mechanics was too strong and reactionary social force to allow Leibniz’s work to have any positive impact and Leibniz’s conflict with Newton was not confined to the issues involving calculus and the interpretation of Kepler’s Laws it also entailed a difference in world view of which philosophy and physics were the primary elements. It was not only physics that languished within the confines of British empiricism, practical, useful for ordinary life, but inherently impotent as a tool for positive knowledge of Nature, philosophy in the form of Kantian subjective idealism was even more so, and Kant, following David Hume, (1711–1776), declared that objective reality is an unknowable thing-in-itself and warned philosophy to abate its claim to any knowledge of the world beyond sense perception.
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Hegel took up the challenge of confronting this world view, the view of understanding, that infected for philosophy, and physics and cosmology represented by Kant and Newton respectively. Hegel’s Encyclopaedia albeit only an outline embraces the ideas of conceptual evolution and contradictions and so on which the view of understanding rebels against placing them at the centre of his new philosophical system, the dialectical method. Under scrutiny now is the law of non-contradiction of theology, old idealism, rationalism and classical materialism, the excluded middle of Aristotle and the thing-in-itself of Kant. Rather, everything consists of the identity of identity and non-identity and opposites reside together in the very element of a thing or a process in simultaneous unity and opposition to each other and a resolution of this logical contradiction and conflict provides the dynamics for change, motion, evolution, development and so on. There is no absolute being or absolute nothing by themselves they always implicitly contain each other and hence one can issue out of the other without the necessity of any act of creation and without breaking the rules of formal logic and the view of understanding is unable to do this without resorting to the intervention from Providence or God, that is to say without breaching the fallacy of illicit process or the principle ex nihilo nihil fit of formal logic which forbids the derivation of a conclusion that is not present in the premise or a consequent not contained in the antecedent.
From an encyclopaedic comprehension of the history of humanity and Nature, Hegel developed his speculative philosophy and the dialectical method for epistemology through incorporating the ideas of Heraclitus, (fl. c. 500 BC), and the later development of dialectics by other thinkers of history from Epicurus, (341–270 BC), to Kant and it is called speculative or the view of reason to distinguish it from the traditional and merely mechanical philosophy or the view of understanding intensified through Newtonian natural science. Hegel for the first time in the history of thought united the perennial division between idealism and materialism or the separation of the ideal and the real into one of a dialectical contradiction of the unity of the opposites a contradiction that is at the root of all change, motion, evolution, development and so on in the manifestation of the universe as a never-ending process. In this view any existence at all is a process in contradiction eternally resolving through the negation of the negation quantitative change giving rise to qualitative leap and vice versa, the universe is an infinite, eternal and ever-changing organic being and an integrated whole self-evolving due to inner contradiction and mediated by chance and necessity without any outside intervention, a view directly opposed to the view of understanding that posits a finite universe and all its contents created in the finite past, perfect in themselves a confining view whereby knowledge is limited to sense perception, the whole is reduced to the sum of its parts, and it loses its way in the minor details of complexity in crude empiricism, mechanism and determinism and rejects the role of dialectical chance and necessity from playing its essential role both in the manifestation of Nature and its reflection in humanity’s cognitive thought, the view of understanding (Verstandeserkenntnis) is conservative in its outlook, creating without good reason an artificial gulf between the Ideal and the Real, Thought and Matter, Spirit and Nature and then finds itself in need of an arbitrary mysterious external power or force to bridge the gaps.
Hegelian dialectics are posited at the very heart of reality and ontology itself and everything in the universe implicitly contains everything else and evolves in stages through discrete leaps of the negation of the negation in the chain of the resolution of the contradictions mediated by blind chance and an iron necessity that is inherent in chance and the role of epistemology is to subjectively grasp and comprehend this objective dialectical process occurring in the manifestation of the universe, Nature, Life, Thought. Hegelian dialectics are capable of perceiving the evolution of the universe from the quantum microcosm to the macrocosm of the galaxies and their clusters, of organic life, humanity and his or her thought as an interconnected whole in a hierarchical order that provide necessity and universality for everything that was lacking in pre- Hegelian epistemology. Hegelian dialectics is not only a negation and a rejection of the old and prevailing system of thought and a refusal of its rehabilitation through Kantian subjective idealism, a revolutionary epistemology of the cosmos, which like Hericlitean epistemology rebuffs any dominating established order.
Contradictions and the Dialectical Method. An understanding of Hegelian dialectical method is needed to appreciate the position taken on Kepler’s laws and planetary dynamics vis-à-vis that of Newton for contradiction may seem unintuitive with regard to the sensibility of formal logic but it is the spirit of the dialectical method lack of appreciation of which has led to misunderstandings of Hegel’s philosophy and science.
‘But it is one of the fundamental prejudices of logic as hitherto understood and of ordinary thinking that contradiction is not so characteristically essential and immanent a determination as identity; but in fact, if it were a question of grading the two determinations and they had to be kept separate, then contradiction would have to be taken as the profounder determination and more characteristic of essence. For, as against contradiction, identity is merely the determination of the of the simple immediate, of dead being; but contradiction is the root of all movement and vitality; it is only in so far as something has a contradiction within it that it moves, has an urge and activity’.
- ‘The Science of Logic’
Dialectical thought is unintuitive to ordinary reflection in particular to formally trained scientists who are totally engrossed and conformed to formal logic and take a mechanical, deterministic and reductionist mathematical approach to physical phenomena, dialectical thought requires deep reflection, introspection and retrospection, the thought of thoughts.
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Contradictions lie at the very fundamental level of ontology and objective reality and the spontaneous and successive resolution of the contradictions form the dynamics for the manifestation of the material universe, the contradiction of abstract and infinite space and time resolves to the virtual particles of the quantum reality and the contradiction of the real and virtual resolves to the formation of matter/antimatter particles in free motion and so on and new fundamental matter and antimatter particles are spontaneously created from the quantum virtual particles preferably at the core of the galaxies leading to their extension and proliferation as a dialectical process mediated by chance and necessity and in this view the galaxies and other cosmic bodies grow and proliferate from within rather then through the universal and one-directional condensation of diffuse matter created from a single event in the past such as the Big Bang. Material bodies are endowed with the contradiction of the unity of the opposites of absolute free motion expressed as repulsion the tendency to fly away from itself and attraction the tendency of free fall mediated by dialectical chance and necessity.
And gravity is the moment of these two opposite tendencies and a distinction has to be made between the finite or ordinary mechanics of dead or selfless bodies on the surface of the earth or of any large cosmic body whose absolute motion is suppressed by earth’s dominant and one-sided gravitational attraction that Newton was concerned with, from the absolute free motion of the cosmic bodies in any group formation like the solar system where the contradiction is active. Hence the Hegelian critique of Newtonian physics and cosmology or anything else of pre-Hegelian scholasticism has to be seen from his overall dialectical world outlook and for any septics I mean sceptics out there who might entertain doubts regarding Hegel’s scientific competence recall his shot across the bows given in a letter the rationalist theologian Paulus in 1843: ‘You know that I have had too much to do not merely with ancient literature, but even with mathematics, latterly with the higher analysis, differential calculus, chemistry, to let myself be taken in by the humbug of Naturphilosophie, philosophising without knowledge of fact and by mere force of imagination, and treating mere fancies, even imbecile fancies, as Ideas’. J. N. Findlay has observed: ‘There is no case in Hegel where a philosophical interpretation of Nature is not scientifically documented’.
Hegel, sided with Leibniz view in opposition to that of Newton’s interpretation of Kepler’s Laws though in a more systematic way objected to the misrepresentation by Newton of Kepler’s laws and in particular and the mis-redirection of Newtonian orientation of physics and cosmology in general towards the unreflected view of understanding as opposed to the view of reason or dialectics, a distinction between unreflected thinking (denkende) and comprehending consideration of Nature (begreifende Naturbetrachtung) yet Newtonian physics and British empiricism won out in natural science and yet developments in quantum phenomena are nudging theoretical physics further into the domain of metaphysics, mathematical idealism and theology. Not my area of expertise but Peter J. Lewis in ‘Quantum Ontology: A Guide to the Metaphysics of Quantum Mechanics’ writes: Quantum mechanics ‘is a theory in which we have no idea what we are talking about, because we have no idea what (if anything) the basic mathematical structures of the theory represent’ and if quantum mechanics is a field in which they don’t know what they are talking about I can certainly find a home for myself there.
Hegel was dismissed by the ensuing developments in physics but through bringing the Newtonian programme of mathematization of physics to its logical conclusion which is to say to its epitome of a metaphysics which Newton himself warned against by the turn of 20th century Albert Einstein with his theories of relativity demonstrated conceptual physics to be reflecting Hegelian dialectic for indeed any truth extended beyond certain limit either turns to its opposite or becomes an absurdity and the theory of biological evolution and the discovery of quantum phenomena subverts further the mathematical idealism that began with Newton thereby vindicating Hegel’s view of reason or dialectics.
There is renewed interest in Hegel not merely for his criticism of Newton’s misstep in misrepresenting Kepler’s laws of the heavens, also in Hegel’s philosophy in general, and in England too, aided by myself, albeit this philosophical interest in Hegel’s works is a consequence of the revolutionary nature of Hegel’s ‘Philosophy of Nature’ forcing the hand of contemporary epistemology and of the jejune nature of official theoretical physics and cosmology on the other brought about by Einsteinian mathematical idealism the very thing that Hegel foresaw and warned against. Endeavours are always afoot to undermine it, however, Hegelian science that is, and to put some life back into Newtonian metaphysics in the form of Einsteinian metaphysics in natural science. This renewed interest in Hegel according to Henry Paulucci is only ‘to review Hegel’s criticism of Newton’s ‘system of the world’ and then to examine critically the many aspects of it that seem to anticipate the approach to mathematical physics, which is today associated with the name of Einstein’. This stems from a lack of understanding of dialectical mode of thought if I may be so bold as to suggest so.
So, signalling the danger of mathematical idealism to the integrity of physics, undoing Newtonian metaphysics in natural science and replacing it with a revolutionary dialectical approach, expunging all forms of metaphysics and mysticism from natural science, taking on board an ontology of space, time and objective reality that was ahead in time anticipating quantum phenomena in Nature with the being-nothing-becoming triad. Well let’s not get ahead of ourselves. The well-known dialectical materialists Karl Marx, (1818–1883), Friedrich Engels, (1820–1895), and Vladimir Lenin, (1870–1924), did not appreciate the revolutionary significance of Hegel’s views on ontology and cosmology for natural science by their time did not progress far enough yet to put the questions of ontology in its agenda and the developments in science and technology made Newtonian science appear unassailable, though Lenin lived long enough too long in my opinion to see the early development of quantum physics though yet to disclose its ontological significance, and Lenin fought against the positivist and anti-materialist orientation of physics brought on as a reaction against the revolutionary quantum phenomena of objective reality while at the same time denouncing Hegel’s speculations on the ontological questions as purblind idealism.
The nature and the significance of Hegel’s antagonism of Newtonian physics. Hegel’s criticism of Newton, his world view, understanding, and physics pulled no punches, comparing Newton with Moliere’s bourgeois gentilhomme who like Monsieur Jourdain’s prose seemed never to have realized that he thought in and had to deal with notions of the understanding, while he imagined he was dealing with physical facts. Hegel rejected the Principia’s proofs of Kepler’s laws, proofs which he characterized as demonstrational jugglery and counterfeiting and even a modern critic of Hegel concedes he has a point. Paulucci says: ‘One must emphasize that Hegel’s criticism was well informed. Certainly, he knew the Philosophiae naturalis principia mathematica and Opticks first hand and had the requisite training in mathematics to comprehend what he read. Through hundreds of well-documented pages of his Science of Logic (large and small) and Philosophy of Nature, Hegel explores the meaning of Newton’s fluxional calculus, his concepts of space, time, mass, inertia, centripetal and centrifugal forces, his laws of motion, his gravitational world-system, and, finally, his theory of light and colors. Particularly under the headings ‘Quantity’ and ‘Measure’ in the Logic and ‘Mechanics’ in the Philosophy of Nature, Newton’s doctrine provides much of the empirical datum upon which the Hegelian philosophical dialectic operates”.
Newtonian metaphysics and the mathematization of physics is seen as impairing further positive knowledge of the cosmos in particular and of natural science in general and Newtonian metaphysics is a counter-revolution to undo the revolutionary developments brought on by Copernicus, Kepler and Galileo et al., resulting in the rise of the impotent mathematical idealism of Einstein. Why Hegel made a challenge to Newtonian physics and cosmology the central issue of his philosophy and science in particular and a challenge to all pre-Hegelian epistemology and world view in general, well, we get the picture:
‘Newton gave physics an express warning to beware of metaphysics, it is true; but to his own honour, be it said, he did not obey his own warning’
- ‘The Encyclopaedia Logic’
The ‘Encyclopedia of Philosophical Sciences’ is in its three parts, ‘The Science of Logic’ (the short version), ‘The Philosophy of Nature’, ‘The Philosophy of Mind/Spirit’, with Newton as a principal adversary in the clash of a new revolutionary world outlook and Hegel himself is a principal inheritor of the scientific revolution brought forth by Copernicus, Kepler and Galileo. If ‘Philosophiæ Naturalis Principia Mathematica’ is the magnus opus of Newton the ‘Enzyklopädie der Philosophischem Wissenschaften’ rings it down to size, a veritable dialectical negation of Newton, differing with Newton on a wide range of fundamental concepts of epistemology and ontology, on the criteria of positive knowledge, the notions of space, time, matter, motion, force and so on, the relation between mathematics and physics and so on, with a completely different world views in general. For Hegel, reason and comprehending of the notions is the most essential element for any knowledge of Nature in contrast to any sensualistic and crude empirical approach which deny even the status of ‘thinking consideration of Nature’ on the contrary insisting on the arbitrary and random approach of economically dealing with sensual perception and a mathematical approach that is considered as the most economical, quantitative and exact determination of Nature and this view of understanding is what Hegel calls metaphysics because understanding.
Hegel’s view on the relation between mathematics and physics is in opposition to Newton’s seeing the ambition to mathematically prove theorems of physics ridiculous a reaction to be understood in the light of the opening sentence of the Foreword of Newton’s Principia: ‘Now that (since Bacon) the substantial forms (of the Aristotelians) have been abandoned from natural philosophy, mathematics should replace them to the maximum possible extent’. Newton evidently rejected materialist and conceptual (Begrieff) methods of philosophical enquiry of Aristotle in favour of the mathematical idealism of Plato that posits that mathematical forms define the phenomenology of objective reality or at least the phenomena described by the sciences have a mathematical structure a point of view that Einstein brought to its extreme stating it thus: ‘Our experience hitherto justifies us in believing that nature is the realization of the simplest conceivable mathematical ideas. I am convinced that we can discover by means of purely mathematical constructions the concepts and the laws connecting them with each other, which furnish the key to the understanding of natural phenomena. … In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed’.
Einstein inspired modern theoretical physicists and mathematics is not merely a tool of scientific enquiry but the very element of ontology, an a priori determinant of the universe and a proposition that Hegel’s dialectics rejects, as Frederick Engels said:
‘Like all other sciences, mathematics arose out of the need of man; from measurement of land and of the content of vessels, from computation of time & mechanics. But, as in every department of thought, at a certain stage of development the laws abstracted from the real world become divorced from the real world and are set over against it as something independent, as laws coming fr om outside to which the world has to conform. This took place in society and in the state, and in this way, and not otherwise, pure mathematics is subsequently applied to the world, although it is borrowed from this same world and only represents one section of its forms of interconnection — and it is only just precisely because of this that it can be applied at all’.
- ‘Anti-Dühring’
Schrei ‚Verwüstung! Lasst die Hunde des Krieges schlüpfen!
Gustav Holst — ‘Mars’:
Interpretations of Kepler’s Laws. Leibniz and Hegel against Newton. Kepler’s three laws working from the data on the planetary motions of the solar system by Tycho Brahe are as follows:
1. The orbit of a planet about the Sun is an ellipse with the Sun at one focus.
2. A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.
3. The squares of the sidereal periods of the planets are proportional to the cubes of their semi-major axes. Or:
… where G is the gravitational constant and M is the mass of the sun.
Newton constructed an idealistic interpretation of Kepler’s laws through ignoring the first and second law and assuming a perfect circle of Ptolemy as the orbit of the planets and employed his theory of unidirectional universal gravitational attraction using a perfectly fitting centrifugal force perfectly balancing the gravitational pull inwards such that there is zero outward force producing a perfect equilibrium.
And so here merely compared the motion of a planet going around the sun with a stone tied to a string and rotated in a circle manually and the centrifugal motion of the stone being balanced by the tension of the string, so the gravitational alleged pull of the sun then is equal to the centripetal force of the planet in the following manner:
…. unlike Kepler’s elliptical one
This presupposes an ideal condition where the planet has to circle the sun at uniform speed at a constant distance from the sun with an outward tangential force exactly balancing the inward gravitational force at each point of the orbit and a planet from distance must approach the sun at an optimum velocity and direction to fulfil the perfect equilibrium which is to say without contradiction condition for eternity a condition to possibly be fulfilled only by the hand of God while the anomalies discovered in the actual solar system dictated by Brahe’s precise observational data and by Kepler’s laws is merely attributed in retrospect without any evidence to the effect of other planets by Newton and his followers till this very day. Kepler from the observational data of Brahe presupposed an elliptical orbit a priori and never considered the effect from other planets on a particular one and in an elliptical orbit where the velocity of the planet goes through a cycle of maximum and minimum the hand of God’s must be there to steer the planet in its course a point Hegel refers to in his comment quoted above and yet what we observe in reality and the latest data from NASA agrees more closely with Kepler and Hegelian contradictions in the solar system.
E.J. Aiton (1920 — still alive as far as I know) sheds some new light on the history of the theories of celestial motion and on the conflict between Newton and Leibniz not merely on the authorship of calculus but also on the interpretation of Kepler’s laws of planetary motion:
‘In an early notebook known as the Waste Book, Newton wrote: ‘All bodies moved circularly have an endeavour from centre about which they move’. As late as 1681, in describing the orbit of a comet, he wrote of vis centrifuga overpowering the attraction and forcing the comet, notwithstanding the attraction, to begin to recede from the sun. There is no mention of centrifugal force in Newton’s Principia (1687), but in one of his attacks on Leibniz in 1711, Newton says that centrifugal force is always equal and opposite to the force of gravity by the Third Law of motion’.
- ‘ An Episode in the History of Celestial Mechanics’
Aiton further notes that Leibniz took into account both the centrifugal and centripetal forces and derived the radial acceleration expressed as:
Where a and b are constants and r is the radial distance from the centre of attraction, the first and the second terms on the righthand side are centrifugal and centripetal forces respectively. According to Aiton, ‘Newton objected that since centrifugal force was equal and opposite to attraction by his Third Law of motion, Leibniz’s reasoning implied that ∂²r/∂t² = 0. Leibniz’s formula in fact gives a correct measure of the radial acceleration and is a notable contribution, which his contemporaries failed to appreciate, Quite clearly, Newton and Leibniz are using the term ‘centrifugal force’ in different senses. Newton should have recognized this, as he had for nearly twenty years himself. His intention, however, was not to understand Leibniz, but to denigrate his work’. The rest is history. It is evident enough that unlike Newton’s view the contention of Leibniz and also of Hegel’s dialectics is that the centrifugal and the centripetal are two different and independent forces acting upon the planets and the comets. F. D. Tombe has deduced Leibniz’s radial planetary orbital equation from a consideration of the elliptical orbit of planetary motion and Kepler’s Laws.
What Hegel had to say about this:
‘The motion of bodies of relative centrality, in relation to bodies of abstract, general centrality, is absolutely free motion, and the conclusion of this system is that the general central body is brought together through relative centrality with dependent corporeality. As is well−known, the laws of absolutely free motion were discovered by Kepler, a discovery of immortal fame. Kepler proved them, too, in the sense that he found the general expression for the empirical data (cf § 145). Since then it has become a commonplace that Newton first found the proofs of these laws. Not often has fame been more unjustly transferred from the first discoverer to another. Here I only want to point out what has basically already been admitted by mathematicians, namely: (1) that the Newtonian formulas can be derived from Keplerian laws; (2) that the Newtonian proof of the proposition that a body governed by the law of gravitation moves in an ellipse around the central body proceeds in general in a conic section, whereas the main point that was to be proven consists precisely in this, that the course of such a body is neither a circle nor any other conic section, but solely the ellipse. The conditions which make the course of the body into a specific conic section are referred back to an empirical condition, namely, a particular situation of the body at a specific point in time, and to the contingent strength of an impulse which it is supposed to have received at the beginning. (3) Newton’s ‘law” of the force of gravity has likewise only been demonstrated inductively from experience. On closer inspection it appears that what Kepler, in a simple and sublime manner, articulated in the form of laws of celestial motion, Newton converted into the nonconceptual, reflective form of the force of gravity. The whole manner of this ‘proof’ presents in general a confused tissue of lines of merely geometrical construction to which a physical meaning of independent forces is given, of the empty concepts of the understanding of a force of acceleration, of particles of time, at whose beginning those forces always play a renewed role, and of a force of inertia, which presumably continues its previous effect, and so on. A rational proof of the quantitative determinations of free motion can only rest on the determinations of the concepts of space and time, the moments whose relation is motion’.
- ‘The Philosophy of Nature’
Kepler’s Third Law does not refer to any mysterious force but only in terms of that which Hegel designates the absolute dynamics of absolute free motions of the cosmic bodies which are mediated by the contradiction of attraction of free fall and the repulsion of the tendency to fly away which contrasts with a material body for instance a piece of stone on the surface of a large cosmic body like the earth for example, where the piece of stone, a dead body, has lost absolute free motion but it is held under the overwhelming gravitational force of the larger body free of contradictory forces acting on the stone. What Hegel refers to as Newton’s jugglery is that Newton eliminated the difference between the two cases above, by incorporating a mysterious first impulse in the case the cosmic bodies, because Newton cannot explain the origin neither of motion nor of matter, these come from God.
On gravity. Where gravity is the one-sided universal attractive force for Newton, for Hegel it is the dialectical contradiction of the unity of the opposites of attraction and repulsion. Hegel deduces gravity in the following way:
‘Matter in itself holds itself apart from itself through the moment of its negativity, diversity, or abstract separation into parts; it has repulsion. Its being apart from itself is just as essential, however, because these differences are one and the same: the negative unity of this existence apart from itself as being for itself, and thus continuous. Matter therefore has attraction. The unity of these moments is gravity’.
- ‘The Philosophy of Nature’
On finite and absolute dynamics. Based upon his philosophical notions of space, time, matter and motion Hegel makes a fundamental distinction between finite mechanics on terrestrial earth and the absolute mechanics of free motion of the heavenly bodies a distinction that Newton eliminated with his mystical force and the magic of mathematics and the above two fundamental conceptual and methodological differences define the reasons why the dialectical view of Hegel rejects Newton’s interpretation of Kepler’s laws in particular and Newton’s cosmology in general and by extension Einstein’s theories of relativity based cosmology in addition. In a dissertation on planetary motion, ‘Dissertatio Philosophica de Orbitis Planetarum — Philosophische Erörterung über die Planetenbahnen’ Hegel discusses the logical contradictions of Newton’s interpretation of Kepler’s laws based upon infinitesimal calculus, a point also made by Aiton.
To take into account the dialectical contradiction in the planetary motion as Hegel suggested one can consider a latent force pushing the planets outward like a repulsive force and according to Newton,where G is the gravitational constant the force F on a body m by the central body M at a distance r is given by,
(1)
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(2)
If we consider that the centrifugal force of Leibniz and the free motion of Hegel are jointly pushing m outwards, then we can add some additional terms in Newton’s equation, reflecting this force (and the contradiction), which is independent of the central body but is a function only of m and r as shown below:
The first and the third terms in equation [3] correspond to an outward force on mass m, but independent of mass M at the centre. The potential energy function is strongly negative both at very small r and at very large r. For small r only the potential energy term (GMm)/r representing Newtonian gravitational attraction is significant and the other two terms are negligible. For large r, only the Cmr(to the power n) term is significant, where the body m would have absolute free motion. The potential energy E(subscript p) would have a maximum value at some intermediate value of r, which represents the optimum condition for the contradiction of a pseudo-stable orbit of mass m, representing all the factors of a particular planetary orbit. The WTF-1 below shows a simplified plot of the equation [3] for n = 2. If the Leibniz’s term, 𝑚(𝑎𝑟3) in equation [3] is replaced by the escape velocity √2𝐺𝑀𝑟 then the plot becomes a continuous parabola as shown in WTF — 2.
WTF — 1
WTF — 2
A particular planet will remain in pseudo-stable orbit if these conditions are satisfied and multiplying (5) by m on both sides gives Newton’s gravitational force GMm/r2 on the left hand side [6] which implies that unlike Newton’s single and unidirectional force of universal gravitational attraction the contradiction of the opposite centrifugal force suggested by Leibniz and the inferred free motion term of Hegel remains active on any orbiting cosmic bodies around a centre and probably can explain for instance the advance of the perihelion of the planets, the orbital eccentricity, the high escape velocity and the high orbital motion of the stars at the periphery of the galaxies and of galaxies at the periphery of the clusters etc. and other cosmic phenomena without the necessity of fantastic spacetime warping or hypothetical dark matter, dark energy, black holes and so on.
In conclusion the anti-dialectical Newtonian concept of gravity as an unidirectional universal attractive force and later Einsteinian esoteric theories of astrophysics grounded solely upon mathematical idealism have only assisted in the proliferation of mysteries and unknowable dark/black cosmic objects but no positive knowledge of the cosmos an approach that has undermined the discovery of the phenomenological laws like those of Kepler that are the primary basis to gain knowledge of the universe and only a dialectical approach as initiated by Leibniz and Hegel can help humankind to gain progressively better knowledge of the dynamics, transformation and the evolution of the cosmic bodies and other phenomena from the macrocosm of the galaxies to the microcosm of the quantum world.
Vangelis, Beautiful Planet Earth:
Note: Physics is not my area of expertise, I got a ‘D’ in ‘Physics’ at High School, well I couldn’t engage with it, and all I remember of it is one interminably boring lesson after another watching pendulums swinging, so on the matter on Kepler, Newton etc I have drawn in part from Abdul Malik, PhD, who is described as an ‘independent thinker’ (always a warning signal for me, independent thinker, like Rupert Sheldrake, (1942 — ), do you know about morphic resonances?), researcher in Physics and Astrophysics (ok that’s good), but I ignored his political extrapolations (I suspect he is left leaning) nor did I pay too much attention to the ‘quantum’ references (another warning signal, makes me think of Deepak Chopra, (1946 — ) another ‘independent thinker’).
But as always my real inspiration is my Muse who is my World, my Universe 🌌
You (you), you are (you are) my universe
And I (I) just want (just want) to put you first
And you (you), you are (you are) my universe, and I
In the night, I lie and look up at you
When the morning comes, I watch you rise
There’s a paradise they couldn’t capture
That bright infinity inside your eyes
매일 밤 네게 날아가 (가)
꿈이란 것도 잊은 채
나 웃으며 너를 만나 (나)
Never-ending forever, baby
You (you), you are (you are) my universe
And I (I) just want (just want) to put you first
And you (you), you are (you are) my universe
And you make my world light up inside
어둠이 내겐 더 편했었지
길어진 그림자 속에서 (eyes)
And they said that we can’t be together
Because, because we come from different sides
You (you), you are (you are) my universe
And I (I) just want (just want) to put you first
And you (you), you are (you are) my universe
And you make my world light up inside
My universe (doo-doo, doo-doo)
My universe (doo-doo, doo-doo)
My universe (doo-doo, doo-doo)
(You make my world)
You make my world light up inside
You make my world light up inside
나를 밝혀주는 건
너란 사랑으로 수 놓아진 별
내 우주의 넌
또 다른 세상을 만들어 주는 걸
너는 내 별이자 나의 우주니까
지금 이 시련도 결국엔 잠시니까
너는 언제까지나 지금처럼 밝게만 빛나줘
우리는 너를 따라 이 긴 밤을 수놓을 거야
너와 함께 날아가 (가)
When I’m without you, I’m crazy
자 어서 내 손을 잡아 (아)
We are made of each other, baby
You (you), you are (you are) my universe
And I (I) just want (just want) to put you first
And you (you), you are (you are) my universe
And you make my world light up inside
My universe (you, you are)
My universe (I just want)
My universe (you, you are my universe, and I)
Coldplay X BTS — My Universe
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Coming up next:
The rationality of nature.
To be continued …
