Copernican Multilateral Revolution: Gradual Reconciliation of Aristotelean Terrestrial Physics and Ptolemaic Celestial Mathematics

The Rise and Extinction of Ptolemaic Sophisticated Research Program

Lakatos and Zahar carefully described how Ptolemy and Copernicus had coherently advanced the diverse research programs. In particular, both rival designs branched off from the same Pythagorean – Platonic ‘protoprogram’. Its dominating principle constituted that, since heavenly bodies are immaculately perfect, all the astronomical appearances should be deftly ‘saved’ by the artful combinations of as few uniform circular motions as possible. The resolute principle was installed as the firm cornerstone of the powerful heuristic of both programs; wherein the ‘heuristic’ was principal, while the ‘hard core’ only subordinate. The hard core of Ptolemy’s program was made up from the geocentric solid hypothesis in conjunction with the Aristotelian natural philosophy, with its paraphernalia of natural and violent motions and the impenetrable and stout demarcation line between the shabby terrestrial (sublunary) and sublime celestial realms. Though Aristotelian physics was an empirical science par excellence that imbibed common experience much more naturally and fully than the rigid, strict, elevated, and abstract science of Galileo, Descartes, and Newton. Everyone knows too well that hard bodies quite naturally and often unexpectedly fall down, while fire cheerfully and lightly soars up.

Regrettably, inertial motion is not an experimental fact at all: common experience apparently contradicts it. Furthermore, everyone knows quite well that in Nature ‘there is no void existing separately’ [23]. The Sun and the Moon relentlessly rise and set, while the thrown bodies do not conserve their rectilinear motion.

Due to common human experience, masterly fixed by the flexible notions of Aristotelian natural philosophy, the distinctive ‘lebenswelt’ (Husserl) in which one lives and acts mercifully is not a mathematical one nor can it be successfully ‘mathematized’. This volatile kind of reality is the wonted realm of uncertainty, unsteadiness, inaccuracy, in an appropriate manner described by the vague terms ‘almost’, ‘a kind of’, ‘more or less’, etc. Whereupon the Greek sober thought could hardly concede that exactness can successfully survive in the wry world around us and that the ponderous matter of stale sublunary world with its inextricable medley of four basic elements (earth, water, air, and fire) can adequately ‘represent mathematical entities’ [24] similar to the ideal objects of Euclidean geometry. For obvious reasons, thanks to Stagiritul, ‘the [immaculate] mathematical exactness should be demanded only for the [peculiar] objects lacking matter’ [25].

On the contrary, the heavens are erected from an entirely different, odd, and immutable substance, the mysterious ‘aether’ (or the renowned ‘fifth element’). Heavenly bodies are inextricable components of queer ether spherical shells that fit tightly around each other in a strict order that begins with the Moon, and extends to the sphere of distant fixed stars. Each heavenly shell is characterized by its specific rotation, which accounts for the peculiar motion of the heavenly body contained in it. At the same time, outside the utmost sphere of the fixed stars, the powerful prime mover is solidly situated. This one diligently imports motion from the outside sphere inward. Eventually, the natural motions of all the heavenly bodies are unforced, perfectly circular, and neither speeding nor slowing down. Clearly, the perfect motions of the stars take their place in accordance with strict geometrical laws. Thus, thanks to Stagiritul’s discreet doctrine, mathematical astronomy is apparently possible while mathematical physics is certainly not. Whereupon the masterful Greek astronomers not only applied sophisticated mathematics but with amazing patience and magnificent skill observed the skies. Though they had not even dared to mathematize inextricable terrestrial motions.

Claudius Ptolemy (87-150) famously reached the acme of ancient science not least because he was a Нellenistic astronomer, astrologer, mathematician, geographer, and even poet. His chef-d-oeuvre – the celebrated ‘Almagest’ [26] - stiffly dominated the European thought for more than fourteen centuries. The social-cultural context of the Ptolemaic intricate research program was determined by the eloquent fact that the author of ‘Almagest’ was a successful resident of Alexandria, the splendid capital of Hellenized Egypt. Hellenistic conspicuous civilization was a distinctive blend of stunning Greek culture with the most ancient civilizations of Egypt and Babylon and a substantial departure from the earlier arrogant Greek attitudes towards the dubious ‘barbarian’ cultures. The extent to which genuinely hybrid Greco-Asian cultures emerged is rather contentious, but it is indisputable that the relentless encounter of the three cultures captured even the elevated domain of theoretical astronomy [27].

Unlike the ‘antediluvian’ Babylonians and Egyptians, who sedulously studied the heavens merely to keep track of their shabby seasons, the sophisticated Greeks considered astronomy from a sublime theoretical standpoint: they strived to comprehend the basic nature and makeup of the whole Universe. Claudius Ptolemy, as a typical Hellenist, craved (not without success) for balancing himself discreetly between the three distinctive cultures in all the basic domains of research activity but first and foremost in ontology and epistemology. In natural philosophy, he deftly oscillated between sophisticated mathematical models and blunt, empirically-grounded qualitative physics, while in epistemology – between the condo realism and quasi- Duhemian crude instrumentalism.

On the one hand, he was certainly aware yet decidedly skeptical of Aristarchus’ quirk heliocentric hypothesis due to quite rational arguments grounded on the stout and well- grounded empirically principles of Aristotelian physics On the other hand, since Aristotle turned to be the only philosopher to whom Ptolemy referred explicitly, the notorious author of the ‘Almagest’ was hastily accused of slavish adherence to the blunt principles of Aristotelian natural philosophy. However, the perfunctory dictum is an obvious oversimplification. One should never forget that, according to Aristotle (De Caelo, ch. V), the rest is nobler than the motion and the Sky is much more perfect and nobler than the Earth. Further, the ‘Almagest’ immaculate model of the solar system did substantially deviate from orthodox Aristotelianism at least in the two crucial respects. i. Aristotle persistently maintained that heavenly bodies should move around the Earth in single uniform circles. Yet, in the Ptolemaic inextricable models, the odd motion of the planets is an intricate combination of two circular motions; moreover, at least one of them is non-uniform. ii. Aristotle also asserted – alas, again from the elevated and abstract ontological grounds – that the Earth should be located at the exact center of the Universe. But in the Ptolemaic feasible distinctive system, the Earth is decidedly displaced from the center of the Universe. Moreover, in Ptolemy’s inextricable cosmology there is no unique center of the Universe; the central orbit of the Sun and the planetary local deferents all have slightly different geometric centers, none of which coincides with the Earth. Incidentally, in the ‘Almagest’ Ptolemy had frequently shown off that the non-orthodox (concerning the Aristotelian natural philosophy) aspects of his subtle models all were directly dictated by stubborn facts of observations.

Whereupon, Ptolemy’s most controversial contrivance was the famous ‘equant’: a planet revolves around the Sun at a non-uniform rate. Nevertheless, it can facilely be exhibited that the non-uniform rotation of the radius-vector connecting the planet to the Sun implies a uniform rotation of the radius- vector connecting the planet to the so-called ‘equant’. The latter is the peculiar point directly opposite the Sun relative to the geometric center of the orbit [28].

It is merely from the modern historically one-sided standpoint that Ptolemy’s notorious equant appears a precursor of the textbook Kepler ellipses. Yet for such caustic yet objective critics as the Islamic /Arabic astronomers and subsequently Copernicus (since the works of the Maragha school might be known to the author of ‘De Revolutionibus’) [29] and his associates, the compelled insertion of the equant was a typical Lakatosian ‘ad hoc3 hypothesis’. It obviously contradicted the respectable spirit of the Aristotle - Ptolemy program – the pivotal tenet of uniformity of motion in respect to the center of the Universe. Let us recall that, according to Lakatos & Zahar’s alluring stance, the ‘ad-hocness’ should be taken, within the flexible frames of the SRP methodology, not as a narrow property of an isolated hypothesis but as a multilateral relation between two consecutive theories. Incidentally, it had been Ibn al-Haytham (965-1040) who initiated the first critique of Ptolemy’s physics for the violation of the basic principle of uniform circular motion.

It is no coincidence that after Eudoxus’ primitive model (made up of the system of concentric rotating spheres) was decidedly abandoned, any actual progress in the realization of geostatic program ran counter to the powerful heuristic of Platonic protoprogram [30]. The eccentric stiffly displaced the Earth from the center of the circle; the Apollonian and Hipparchan deft epicycles provided that the actual path of the planets about the Earth was not circular; and, eventually, the Ptolemaic notorious equants entailed that even the motion of the epicycle’s empty center was not simultaneously uniform and circular. The perfidious insertion of the equant was the heaviest blow upon the stale heuristic of the Platonic protoprogram: it was almost equal to its full wreck. Thus, within the Ptolemaic intricate program mathematical exactness that insisted on the insertion of noncircular orbits and the centers of rotation not coinciding with the earth center began to diverge increasingly and irreversibly from the stout and empirically sound principles of Aristotelian physics. Hence in the long run one can take Ptolemaic inextricable cosmology as a substantially dual fundamental theoretical scheme waywardly mixing the principles of ‘Platonic immaculate mathematics’ with those of ‘Aristotelian sober physics’.

To retain the indubitable advances of the Aristotelian dazzling doctrine and the conspicuous achievements of the mathematical astronomy, Ptolemy in the ‘Planetary Hypotheses’ had to advance further and at the same time soften the blatant rupture between the mundane and celestial phenomena. Since the ‘Almagest’ confined itself to subtle mathematical models, Ptolemy had to proffer preliminary physical models for the same constructions, yet in vain. One of the apparent examples of his numerous failures is represented by the attempt to construct the ingenious ‘tambourine-like’, ‘sawn-off’ mechanism able to transform motion from outer spheres of his cosmos to inner ones [31].

Alas, after the ‘Planetary Hypotheses’ the deep abyss between the physical and mathematical facets became even deeper [32]. So, Ptolemy’s inextricable cosmology could not help but be exposed to severe repeated attacks during the European Middle Ages [33]. It obviously confronted the strict principles of monotheism not admitting the stiff demarcation line between the celestial and mundane worlds; all seemingly different worlds nevertheless should have one and the same Creator.

The Copernican Abstruse Breakthrough: An Origin and Advancement

It was Alexander Koyré who turned to the asset of the pivotal cross-contradiction necessary to comprehend the subtle intertheoretic context of the Copernican revolution again. Koyré was a thought-provoking French / Russian epistemologist, philosopher and historian of science, renowned for neo-Hegelian standpoint, as well as for his profound influence on Thomas Kuhn’s celebrated concept of structure of scientific revolutions.

Not by chance it was an ‘internalist’ Alexander Koyré who in the middle of the XX-th century became increasingly aware of the ‘tremendous gap’ between mathematical astronomy and Aristotelian qualitative physics inherent to ancient cosmology. Respectively, the ultimate motive of contrivance of the heliocentric program consisted not at all in sedulous elimination of the wonted discrepancies between the Ptolemaic ‘wry’ cosmology and stout observational ‘hard facts’. (Forsooth, according to Imre Lakatos, experimental anomalies are inherent in all stages of development of a scientific theory).

Accordingly, in part III of his punctilious monograph , André Goddu contended that Copernicus can rightfully be called a ‘principled thinker’ [16], for he broached and resolved first and foremost principal questions while ignoring secondary ones. Though he was not a systematic philosophical thinker; philosophy in due course taught at his alma mater - Cracow University – in the last quarter of the 15th century can be characterized as ‘eclecticism’. Yet he strived to maintain a clear sense of his principal goal, and to distinguish properly between the questions that he had to address and ones he could leave aside.

Moreover, in my humble view, Copernicus was invigorated predominantly by aesthetic and metaphysical (and, I insist, essentially theological) considerations aimed at effectively eliminating the profound rupture between refined mathematical astronomy and Aristotelian blunt qualitative physics. However, it did not prevent him from applying standard Aristotelian ‘argumentative technique’ to demonstrate the greater probability of his assumptions over those of his geocentric opponents.

For instance, “all these arguments make it more likely [more probabilior] that the earth moves than that it is at rest. This is especially true of the daily rotation, as particularly appropriate to the earth” (De Revolutionibus, book I, ch.8, p.17).

But certainly it was his Christian Weltanschauung that made the rupture especially bigoted. Namely this Weltanschauung moulded the staff provided by the three basic sources: the cosmological views of Pythagoreans, Aristotle’s fine cosmology [34] and (last but not least!) the inexorable its critique provided by the Buridan’s school embracing John Buridan, Nicole Oresme, and Albert of Saxony. “Copernicus developed a critical approach to natural philosophy but one that enabled him to modify Aristotelianism while remaining a participant in a broadly conceived Aristotelean tradition […] He developed his own version of Aristotelianism, very much influenced by Renaissance Platonism, Neoplatonism, Stoicism […] It was also a version of Aristotelianism that was anti-Averroistic and more flexible in its approach to mathematics” (pp. xxii, xxiv) [16].

In that respect Copernicus can be regarded as a scholar which belonged to a respectable ancient tradition of reconciling Ptolemy’s mathematical models with the concentric cosmology of Aristotle [34] though in favorable socio-cultural context of Christian Weltanschauung enforcement.

Whereupon, the celebrated introduction to his opus Magnus - ‘De revolutionibus orbium coelestium’ (1543) - was by right dedicated to ‘his holiness Pope Paul III’. The honorable canon at Frombork Cathedral, Doctor of Theology, whose maternal uncle (and powerful promoter) was Lucas Watzenrode, the honorable bishop of Warnia, openly admits that he had been relentlessly “impelled to consider a different [from Ptolemy] system of deducing the motions of the universe’s spheres for no other reason than the realization that astronomers do not agree among themselves in their investigations of this subject”.

Furthermore, “those who devised the eccentrics seem thereby in large measure to have solved the problem of the apparent motions with appropriate calculations. But meanwhile, they introduced a good many ideas which contradict the first principles of uniform motion. Nor could they elicit or deduce from the eccentrics the principal consideration, that is, the structure of the universe and the true symmetry of its parts”.

On the contrary, “we discover a marvelous symmetry of the universe, and an established harmonious linkage between the motion of the spheres and their size, such as can be found in no other way” (p.22) [35].

Note that Copernicus’ Christian Weltanschauung determined his especially discreet attitude towards the sober arguments of the pagan Aristotle. Therefore, he is not limited to referring to the authority of Aristotle to justify the unacceptability of uneven movement. Instead, he works out a stout metaphysical argument of his own: variable speed can only be caused by variable force. But God, as the Primordial Cause of all the movements, is Always Constant. Consequently, “I began to be annoyed that the movements of the world machine, created for our sake by the best and most systematic Artisan of all, were not understood with greater certainty by the philosophers, who otherwise examined so precisely the most insignificant trifles of this world” [35].

Not by chance one of the pivotal chapters in Rheticus’ ‘Narration prima’ wore the meaningful headline “The Principal Reason Why We Must Abandon the Hypotheses of the Ancient Astronomers”.

Secondly, while for Stagiritus gravitation constitutes the tendency of heavier bodies to long to the center of Universe, for Copernicus it is merely the tendency of heavier bodies to get to the centers of any spherical masses of matter.

The true origin of the inextricable paradoxes, due to Copernicus’s sublime standpoint, consists in the non-ideal odd movement of the planets. However, according to the Aristotle - Ptolemy sober doctrine, resolutely buttressed by the Christian faith, the planets necessarily belong to ideal spheres and should be engaged in uniform motions along with the perfect circles or along with their artful combinations. Following not so much Stagiritul as his own theological arguments, Copernicus was convinced that the supposed perfection of the heavens requires celestial bodies to execute uniform circular motion only. Whereupon he was spurred to decisively reject first and foremost the dubious equant model.

The drastic rejection of the equant was connected with that Copernicus not only employed a great deal of observational data from Arabic astronomical sources, but also many subtle theoretical components as well. The latter first and foremost included the famous ‘Tusi couple’, used by Copernicus to exchange Ptolemy’s geometrical construction of the equant model. Thus he willingly agreed with the sharp criticism of Ptolemy’s model by Ibn al-Haytham, Ibn Rushd, Nur as-Din al-Betrugi and other Moslem astronomers [36].

In ‘De Revolutionibus’ Copernicus realizes the task targeted already in the ‘Commentariolus’.The motivation for creating the heliocentric system consisted in the assertion, that if the planetary orbs are ordered around a single center according to a strict principle, then the Earth cannot be that center. Eventually, ultimately inspired by the ‘best intentions to layout the Divine Order of the Heavens’ Copernicus craves to return to Aristarchus’s queer proposal to place the center of the Universe on the Sun. But namely this generated the profound paradoxes within the Aristotelian physics inextricably connected with the stale notions of ‘natural’ and ‘violent’ movements. As a result, Copernicus had gradually constructed merely a sophisticated crossbred theory that incepted to pave the way to divine immaculate mathematics and mundane qualitative physics profound interpenetration. As modern French historian punctuated, “Copernicus in an insinuating manner and probably unconsciously had inserted into the stout Aristotelian fortress two innocent premises through which Kepler, Galileo, and Descartes vigorously blew it up” (p.430) [9].

In the stupendous Introduction to ‘De Revolutionibus’, Copernicus passionately appeals to a refined, influential coterie of respectable clergy including Pope Paul III (to whom the Opus Magnus was dedicated), Pope Clement VII (who not only adopted the ‘De Revolutionibus’ but even insisted on its publication), Nicholas Schonberg, cardinal of Capua, Lucas Watzenrode, bishop of Warmia, Tiedemann Giese, bishop of Chelmno, et al. Throughout the whole book the author of ‘De Revolutionibus’ consistently condemns the author of ‘Almagest’ for inherent paganism. In short, his scathing criticism of Ptolemy’s stale system is grounded on the weighty argument, according to which the Pagan’s inextricable medley system (deftly embracing tens and hundreds of epicycles, abstruse epicyclets, and quirk equants) is nevertheless lacking strict, monotheistic Order, pre-established by the Lord, ‘the best and most systematic Artisan’. Incidentally, sometimes the instrumentalism of the notorious ‘Almagest’ went so far that one and the same movement of the same planet was described by two substantially different mathematical models (see, for instance, Ptolemy’s queer math models of Mars’s odd motion). Whereupon, the multifarious components of the Ptolemaic motley system vividly epitomize the various plans of different pagan ‘artisans’, of warring Hellenistic gods, densely inhabiting both dazzling Olympus and the dismal tombs of the pharaohs.

Incidentally, “their [the Ptolemy partisans’] experience was just like someone taking from various places hands, feet, a head, and other pieces, very well depicted, it may be, but not for the representation of a single person; since these fragments would not belong to one another at all, a monster rather than a man would be put together from them” [35].

Similarly, Copernicus – probably paved the broad way for Galileo’s and Newton’s mighty mathematical physics. If the strict and robust demarcation line between divine and mundane worlds is lacking since the Earth is just an ordinary planet of the Solar system, the mathematical subtle notions and elevated principles should apply both to its rotations around its axis and the Sun, as well as to all the bodies moving along its surface. It is no coincidence that in subsequent Galileo’s works, the graphical Aristotelian ‘natural’ movements had to be decidedly transformed into abstract and sublime ‘inertial’ ones.

For obvious reasons, the quirk heliocentric picture of the world seemed incredible to most sane people of that time. For instance, if the Earth actually revolves around its axis and even around the Sun, how are celestial bodies held on the planet’s surface? - Copernicus himself cleverly, though unfoundedly tried to get out of the stumbling block using a typical ad hoc2 hypothesis: each celestial body can have its own, local, (of incomprehensible origin) gravity. Therefore, all heavy objects should gravitate towards the local centre.

Galileo commenced with descending mathematics from the Skies to the Earth, being inspirited not so much by ‘De Revolutionibus’ as by Plato’s ‘Timaeus’ (and the corresponding renowned yet controversial discoveries provided by the new-fangled telescope). Indeed, if the Earth is just one of the ordinary planets, then the laws of mathematics, previously applied to describe the motion of everything that happens in the supra-lunar world, now apply to its movement as a whole, and to what happens on its surface as well. As a true Copernican, Salviati points out in the ‘Dialogues’ in his dispute with the stubborn Aristotelian Simplicio, “and [as] to the Earth, we try to ennoble it and make it more perfect, striving to liken it to celestial bodies and, in a sense, to place it in heaven, from where your philosophers expelled it” [38].

In path-breaking ‘The Assayer’ [37] Galileo famously asserts that “philosophy is written in that great book which ever lies before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles, and other geometrical figures, without whose help it is impossible to comprehend a single word of it” (p.75, [39]; see also Drake’s distinctive translation pp.237-238, [40]).

And to calm down the reader by whom the magnificent Book was written, in his renowned introduction to the ‘Dialogue Concerning the Two Chief Systems – Ptolemaic and Copernican’ Galileo points out that “he who looks the higher is the more highly distinguished, and turning over the Great Book of Nature (which is the proper object of philosophy) is the way to elevate one’s gaze. And though whatever we read in that book is the creation of the omnipotent Craftsman, and is accordingly excellently proportioned, nevertheless that part is most suitable and most worthy which makes His work and His craftsmanship most evident to our view” [38]. Eventually (for faithful Galileo) immaculate and dazzling “mathematics is the language with which God has written the Universe “(p.2) [41].

Koyré insisted that Galileo’s alluring interpretation of Christian theology was inspired by Plato’s ‘Timaeus’; especially by the whimsical myth of the creation of the Universe. The key figure of the renowned dialogue – the almighty Demiurge, a divine Craftsman – punctiliously constructs the stout mathematical order out of the preexistent chaos to put up the Universe (the ‘cosmos’). For that grand purpose he punctiliously cuts out small triangles to erect four regular solids; and then he artfully applies them to construct real bodies, plants, and even animals out of them [42]. Moreover, it was in ‘Timaeus’ where the notion of a divine Craftsman was enriched by the notion of pre- established harmony devised by him.

Thus, Nature transpires to be empty and ordered: in the process of its creation God discreetly put strict mathematical necessity in it. Hence mathematical knowledge is not merely true but is substantially sacred even more than the Holy Bible. While there are plenty of interpretations of the Bible, the mathematical truths are unique and should be relentlessly kept out of discussions.

At the sake of mathematization, Galileo had radically transformed the subtle methodology of natural science: he had relentlessly elevated mathematization, as well as (real and thought) experimenting up to the highest ranks of leading scientific methods [43]. Eventually, it made it possible for the Florentine to contrive the paramount ‘principle of inertia’ and even to come close to the second law of Newton’s dynamics [44].

Yet the very opportunity of implementation of mathematical methods in natural science turned out to be grounded on the wayward procedure of idealization. Correspondingly, the modern exact science commenced with taking all natural phenomena as more or less adequate approximations of some Platonic ‘ideal essences’. The latter lack, contra Aristotle, profound existence within the natural phenomena but exist alongside them as the ‘certain limits of infinitely small sensory becoming’; hence they can be freely contrived by the ingenious human mind. And they are the stiff relations between the ideal ‘quasi-essences’ that are depicted by the exact Laws of Nature. At the same time, the relations between real objects (e.g. rods and clocks / tables and chairs) are exhibited merely by the approximations to the strict laws. Just as Galileo had succinctly put it, ‘the search for essences, in my judgment, is a vain and hopeless kind of pursuit”.

Consimilar platonic (and neo-platonic) motives that found their distinctive expression in the alluring tenet of ‘delightful accordance between the [base] Cosmos and the Holy Trinity’ induced Kepler to the strenuous search for the stout mathematical laws stiffly governing the planet motions. Properly educated in strict Lutheran faith, Kepler had passionately devoted himself to delve into the sacred ‘Book of Nature’.

“We astronomers are priests of the highest God concerning the book of Nature” [45]. But the innovative views of Kepler and Copernicus differed significantly. In Copernicus’s plain theory, the planetary motions were impeccably circular; they demanded no causes and took part due to the inertia of the bodies. Hence the Sun was not the actual center of force. Only Kepler’s distinctive reflections on the true source of planetary motion revealed the leading role of the Sun and buttressed him in describing the subtle mechanics of planetary motion.

On the firm and stout grounds of Trinitarian thoroughgoing doctrine, Kepler decidedly took the Sun as the geometric and dynamical center of the cosmos. The coequality of Father, Son, and Spirit implied the continuity of the Center, Periphery, and space of the Cosmos. Herewith the Sun epitomized God the Father, the Stars respectively referred to God the Son, while the wonted planets humbly incarnated the Holy Ghost. Furthermore, Kepler plied to discover an immaculate universal law that would meticulously picture the motion of both the Earth and the planets. His relentless quest was invigorated by the alluring analogy between the base Cosmos and the Holy Trinity.

Whereupon Kepler took the second drastic step towards the deep interpenetration of mathematical astronomy and qualitative physics and elicited the laws roughly breaking the Aristotelian stiff principle of uniform rotation of divine bodies. His three laws were famously the first scientific laws taking mathematical form. The Skies relentlessly commenced ruining the qualitative physics of Aristotle. Fruitful reconciliation of the divine and sublunary realms masterly moved Aristotelian physics aside [46].

Incidentally, the epistemological essence of the Copernican-Galilean scientific revolution (unification of the celestial and terrestrial physics) found its startling expression in the title of Kepler’s masterpiece: ‘Astronomia Nova seu Physica Coelestis’ (The New Astronomy of Physics of the Heavens).

Kepler was not alone in rejecting Aristotle’s natural philosophy from the vantage standpoint of Christian theology. In 1644 Rene Descartes had published ‘Principia Philosophiae’ where he proposed a theory of motion directly grounded on heliocentric model. However, while Copernicus and Galileo were unable to properly explain the physical processes that resulted in the motion of planets around the Sun, Descartes had successfully hit the target relying on the arguments on ‘God’s immutability’. In his thoughtful doctrine, motion occurred thanks to divine intervention [47]. Thereafter, conservation of motion existed thanks to immutability of God’s creation; the immutability of God surely abhors vacuum. Any disturbance causes vortexes to appear, which is the ultimate reason why the Sun and the planets exist, and why the planets obediently rotate around the Sun. Eventually, Descartes’ masterpiece epitomized the final elimination of the Aristotelean stale system. According to modern historians, it was Cartesianism which turned the queer heliocentric surmise into a dominant paradigm [9].

Sir Isaac Newton’s main purpose was to elicit the stout laws that firmly dictate the motion of both terrestrial and divine bodies. He had pioneered in demonstrating, - thanks to powerful heuristic of Copernicus and Galileo, - that it was the same force that attracted all the bodies to the Earth that compelled the Moon to obediently orbit the Earth.

Sir Isaac masterly amended the ‘hard core’ of the Copernican celebrated program by efficaciously unifying and generalizing the partial theoretical schemes of Copernicus, Kepler, Hook, Descartes , and Galileo and coming up to the whimsical conjunction of three laws of dynamics with the mysterious gravitation law.

Eventually, in the powerful science of modernity Aristotelian qualitative ‘essences’ had been ingeniously replaced with immaculate mathematical abstract objects. This is especially clear in Newton’s “Principia.

“Since the ancients (as we are told by Pappus) made great account of the Science of Mechanics in the investigation of natural things; and the moderns, laying aside substantial forms and occult qualities, have endeavoured to subject the phenomena of nature to the laws of mathematics; I have in this treatise cultivated Mathematics, so far as it regards Philosophy” (p.1) [48].

In Newton’s resolute methodology the relentless dictum ‘to subject the phenomena of nature to the laws of mathematics’ constitutes the most robust one. A man of science should while sedulously examining the intricate phenomena of nature, force his sense data in such a dry and suitable for experimental purposes way as to proffer them for immaculate analytical treatment. Exactly in this way the basic mathematical abstract objects of classical mechanics, beginning with a material point, were gradually contrived [49, 50, 51, 52, 53].

It is a pleasure to thank Professor Michal Kokowski for critical comments and valuable advice.