4. The modern world-view The Renaissance 1 The Reformation 6 The Scientific Revolution 16 Copernicus 16 The religious reaction 18 Kepler 19 Galileo 21 Forging

Newtonian Cosmology (Newton, 1642-1727)

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Newtonian Cosmology (Newton, 1642-1727)
Kepler’s (1571-1630) mathematical theory and Galileo’s (1564-1642) observational support insured the success of the heliocentric theory and yet the theory still lacked a coherent cosmology within which it could be fitted. That the earth and other planets moved about the sun in elliptical orbits was clear but how did the planets including the earth move at all?
If the earth moved (displacing Aristotelian physics) then why did objects on the earth fall to the earth?
If the stars are so numerous and so distant then just how large is the universe?
What is the structure of the universe, and what is its center, if any?
What happened to the long recognized division between celestial and terrestrial if the earth was merely another planet and other planets had earth-like qualities?
Where was God in this cosmos?
Until these questions could be answered we had a new heliocentric theory but not yet a new cosmology.
Both Kepler and Galileo demonstrated that the universe was mathematically ordered and that scientific progress was achieved by comparing mathematical hypotheses with empirical observations. Copernicus (1473-1543) had made the fertile suggestion of a new cosmology by making the earth a planet in order to explain the sun’s apparent motion and so implied that the distinction between earth and heaven was not absolute. Kepler went further and suggested terrestrial forces could be applied to celestial bodies.
Ptolemaic and Copernican circular orbits were deemed to be “natural” (by their elemental nature the aesthetic spheres moved in perfect circles, just as heavy elements (water/earth) moved downward and light elements (fire/air) moved up. Kepler’s ellipses were not circular however nor were they constant; the planets changed speed and direction at each pint in their orbits. Elliptical motion in the new heliocentric universe required a new explanation beyond that of natural motion.
Kepler suggested as an alternative the concept of a constantly imposed force. Influenced as always by the neo-Platonic exaltation of the sun, he believed that the sun was an active force that was the source of movement in the universe. He therefore proposed an anima motrix, a moving force akin to astrological influences which emanated from the sun, less so when distant. But Kepler still had to explain why the orbits curved in ellipses. Having absorbed William Gilbert’s recent work on magnetism with the thesis that the earth is a giant magnet, Kepler extended his principle to all celestial bodies and hypothesized that the sun’s anima motrix combined with its own magnetism and that of the planets created the elliptical orbits. Kepler thereby made the first proposal that the planets in their orbits were moved by mechanical forces rather than by the automatic geometrical motion of the Aristotelian-Ptolemaic spheres. Despite its rather primitive form, Kepler’s concept of the solar system as a self-governing machine based on notions of terrestrial dynamics correctly anticipated the emerging cosmology.
In the meantime Galileo had pursued this mechanical-mathematical mode of analysis on the terrestrial plane with systematic rigor and extraordinary success. Like his fellow renaissance scientists Kepler and Copernicus, Galileo had imbibed from the neo-Platonic humanist the belief that the physical world could be understood geometrically and arithmetically. With Pythagorean fervor he declared the Book of Nature is written in mathematical characters. But with his more down to earth sensibility, Galileo developed mathematics as a less mystical key to the heavens than as a straightforward tool for understanding the matter of motion and for the defeat of his Aristotelian opponents. Although Kepler’s understanding of celestial motion was more advanced than Galileo’s (who like Copernicus still believed in self-sustaining circular motion), it was Galileo’s insight into the terrestrial dynamics that, when applied to the heavens, would begin to solve the physical problems created by Copernicus’ revolution.
Aristotle’s physics based on perceptible qualities and verbal logic still ruled contemporary scientific thinking and dominated the universities. But Galileo’s preferred model was Archimedes the mathematical physicist (whose writings were recently rediscovered by humanists) rather than Aristotle the descriptive biologist. To combat the Aristotelians, Galileo developed a new procedure for analyzing phenomena and a new basis for testing theories. He argued that to make accurate judgments concerning nature, scientists should consider only precisely measurable objective qualities (size, shape, number, weight, and motion – primary qualities) and therefore ignore perceptible qualities (color, sound, taste, touch, smell – secondary qualities). Only by exclusively quantitative analysis could science attain certain knowledge of the world. In addition, while Aristotle’s empiricism had been predominantly descriptive, and by later Aristotelians the verbal-logical approach, Galileo established the quantitative experiment as the final test of hypotheses. Finally, to further penetrate nature’s mathematical regularities and therefore is true character, Galileo employed, developed, or invented a host of instruments: lens, telescope, microscope, geometric compass, magnet, and air thermometer, hydrostatic balance (i.e., technology and science go hand in hand). The use of these instruments (technology) gave empiricism an entirely new dimension that undercut both the theories and the practices of Aristotelian academics. Galileo replaced interminable deductive justification of the Aristotelian organismic universe with an impersonal mathematical mechanical universe.
Employing new categories and new methodology, Galileo set out to demolish the spurious dogma of academic physics.
Aristotle had believed that the heavier body would fall at a faster rate than a lighter one, because of its elemental propensity to seek the center of the earth as it natural position (the heavier the body the greater its propensity). Through repeated application of mathematical analysis to physical experiments, Galileo refuted this tenet and formulated the law of uniform accelerated motion in falling bodies (motion independent of the composition of the body). Building on the impetus theory of Aristotle’s Scholastic critics Buridan and Oresme, Galileo analyzed projectile motion and developed the crucial idea of inertia. Contrary to Aristotle who held that bodies sought their natural place and that nothing continued to move otherwise without a constantly applied external push, Galileo held that just as a body at rest would remain so unless pushed, so too a moving body would remain in constant motion unless stopped or deflected. Force was required to explain only change in motion, not constant motion. In this way Galileo met one of Aristotle’s chief physical arguments against planetary earth – that objects on a moving earth would be forcibly knocked about and that a projectile thrown directly upward fro a moving earth would necessarily land some distance away from its point of departure. Since neither of these phenomena was observed, Aristotle concluded that the earth must be stationary. But through the concept of inertia, Galileo demonstrated that a moving earth would automatically endow all its objects and projectiles with the earth’s own motion, and therefore the collective inertial motion would be imperceptible to anyone on earth.
In the course of his life work, Galileo had effectively supported the Copernican theory, initiated the full mathematization of nature, grasped the idea of force as a mechanical agent, laid the foundations of modern mechanics and experimental physics, and developed the working principles of modern scientific method (i.e., the “new science”).
But the question of how to explain physically the celestial movements, including the motion of the earth itself, still remained unresolved. Because Galileo missed the significance of Kepler’s planetary laws, he continued to hold the traditional view of celestial motion as circular orbits, only now centered about the sun. His concept of inertia – which he understood as applicable on the earth only to motion on horizontal surfaces (where gravity was not a factor) and which was therefore circular motion around the earth’s surface – was applied to the heavens accordingly:
The planets continued to move in their orbits about the sun because their natural inertia tendency was circular.
However, Galileo’s circular inertia could not explain Kepler’s ellipses. It was also all the more implausible if the earth, which as the unique center of the universe in Aristotle’s cosmology had defined the surrounding space and given an absolute motive and reference point for circling spheres, was now understood to be a planet. The Copernican universe had created and was still plagued by a fundamental enigma.
But at this point another influx of Greek philosophers was brought to bear: the atomism of Leucippus and Democritus, which would both point to a solution to the problem of celestial motion and help shape the future course of Western scientific thought. The philosophy of atomism as passed on Democritus’ successors Epicurus and Lucretius had resurfaced during the Renaissance humanist recovery of ancient literature, in particular the manuscript of Lucretius’ poem De Rerum Natura (On the nature of things) outlining the Epicurean system. Originally developed as an attempt to meet the logical objections against the change and motion leveled by Parmenides, Greek atomism had posited a universe of invisible small indivisible particles moving freely in an infinite neutral void, and creating by their collisions all other phenomena. In this void there was no absolute up and down or universal center, every position in the void being neutral and equal to every other. Since the entire universe was composed of the same material particles on the same principles, the earth itself was merely an aggregate of particles and was neither at rest nor at the center of the universe. There was therefore no celestial-terrestrial distinction, and since both the size of the void and the number of particles were infinite, the universe was potentially populated by many moving earths and suns, each created by the atoms’ random movements.
The evolving Copernican universe obviously resembled in many ways this ancient Greek conception. Making the earth a planet had gotten rid of the Aristotelian idea of an absolute (non-neutral) space centered on a stationary earth. A planetary earth also required a much larger universe to satisfy the absence of observable stellar parallax. With the earth no longer the center of the universe, the universe did not have to be finite (obvious a universal center requires a finite universe since infinite space can have no center). The outermost sphere of stars was now unnecessary as an explanation for the movement of the heavens, and so the stars could be dispersed infinitely, as the neo-Platonists had suggested. Galileo’s telescopic discoveries had revealed a multitude of new starts at apparently great distances which further undermined the celestial-terrestrial dichotomy. The implications of the Copernican universe, a non-unique moving earth; a neutral, center-less, multi-populated, and perhaps infinite space, and the elimination of the celestial-terrestrial distinction, all coincided with an atomistic cosmos. With the Aristotelian cosmos collapsing and no other to replace it, the atomists’ universe represented an already well-developed and uniquely appropriate framework within which the new Copernican system could be placed. The esoteric philosopher-scientist Giordano Bruno (1548-1600) was the first to perceive the congruence between the two systems. Through his work, the neo-Platonic mage of an infinite universe enunciated by Nicholas of Cusa (Cardinal theologian- mathematician b. in Germany, 1401-1464 who postulated a moving earth prior to Copernicus) was reinforced by the atomistic conception to create an immensely expanded Copernican cosmos.
Atomism also provided other contributions to the developing cosmology. Not only was the structure of the atomistic cosmos congruent with the Copernican theory, but the atomistic conception of matter was also entirely appropriate to the new natural science. Democritus’ atoms were characterized exclusively in quantitative (primary qualities) terms (not by perceptible qualities). All apparently qualitative changes in phenomena were created by differing quantities of atoms combined in different arrangements, and hence the atomistic cosmos was in principle open to mathematical analysis. The material atoms possessed neither purpose nor intelligence, but moved sole according to mechanical principles. Thus, the cosmological and physical structures of ancient atomism invited very modern analysis – mechanistic and mathematical – already chosen and rapidly being developed in the 17th c. Atomism influenced Galileo (1564-1642) in his approach to nature as matter in motion, was admired by Francis Bacon (1561-1626) and employed by Thomas Hobbes (1588-1679) in his mechanical materialism, and was popularized in scientific circles by Pierre Gassendi (1592-1655). It was Rene Descartes (1596-1650), of course, who undertook the task of systematically adapting atomism to provide a physical explanation for the Copernican universe.
The basic principles of ancient atomism offered many parallels to Descartes’ image of nature as an intricate impersonal machine strictly ordered by mathematical laws. Descartes assumed that the world was composed of an infinite set of particles (“corpuscles”) which mechanically collided and aggregated. As a Christian however Descartes did not assume that these particles moved at random but obeyed certain laws imposed by a providential God at the time of creation. Descartes challenge was to discover those laws and his first step was to ask how a single particle would freely move in an infinite universe possessing neither absolute direction nor Aristotelian tendencies to motion. By employing the Scholastics’ impetus theory in the new context of an atomistic space, he concluded that a particle at rest would remain so unless pushed otherwise, and a particle in motion would remain so in motion in a straight line unless its speed was deflected. Thus, Descartes (1596-1650) articulated the first formal principle of inertia (including the critical element of inertial linearity), in contrast to Galileo (1564-1642) more rudimentary and empirical conceived earth-oriented inertia with its implication of circularity. Descartes also reasoned that since all motion in the corpuscular universe must be in principle mechanistic, any deviation from these inertial tendencies must occur as a result of corpuscular collisions. He then set out to establish the principles governing the collisions by way of intuitive deduction.
With its freely moving particles in infinite neutral space, atomism had suggested new way of looking at motion. Descartes notion of corpuscular collision allowed his successors to develop further Galileo’s insight into the nature of force and momentum. But of immediate significance for Copernican theory, Descartes applied his theory of inertia and corpuscular collision to the problem of planetary motion, and thereby began to clear away the last residue of Aristotelian physics from the heavens. For the automatic circular motions of the celestial bodies still espoused by Copernicus and Galileo were not possible in an atomistic universe in which particles only move in a straight line or remain at rest. By applying his inertial and corpuscular theories to the heavens, Descartes isolated the crucial missing factor in the explanation of planetary motion.
Unless there was some kind of inhibiting force, the inertial motion of the planets, including the earth, would necessarily tend to propel them in a tangential straight line away from the curving orbit of the sun. Since, however, their orbits were maintained in continuous closed curves without such centrifugal breaks, it was evident that some factor was forcing the planets toward the sun, or as Descartes formulated it, something was continually forcing the planets to “fall” toward the sun. To discover what force caused this “fall” was the fundamental dilemma facing the new cosmology. The fact that the planets moved at all was now explained by inertia. But the form that motion took (ellipses) still required explanation.
Many of Descartes intuitive deduced hypotheses concerning his corpuscular universe (laws of collision such as vortices of moving particles which were to push the planets into orbits) were rejected by his successors. But his basic conception of the physical universe as an atomistic system ruled by a few mechanical laws became the guiding model for 17th c scientists grappling with the Copernican innovation. Because the riddle of planetary motion still remained an outstanding problem for post-Copernican science in its efforts to establish a self-consistent cosmology, Descartes; isolation of the “fall” factor was indispensable. With Descartes’ concept of inertia applied to Kepler’s ellipses, and with the general principle of mechanistic explanation implicit in both their rudimentary theories of planetary motion (Kepler’s anima motrix and magnetism and Descartes’ corpuscular vortices), the problem had gained a definition which subsequent scientists (such as Borreli, Hooke, and Huygens) could fruitfully work. Galileo’s terrestrial dynamics had further defined the problem by contravening Aristotelian physics, and by giving precise mathematical measurement to heavy bodies falling to earth. Thus, two fundamental questions remained:
1. Given inertia, why did the earth and other planets continually fall towards the sun?
2. Given the non-central earth, why did terrestrial objects fall to the earth at all?
The possibility that both these questions had the same answer had been growing in the work of Kepler, Galileo, and Descartes. The notion of an attractive force acting between material bodies had also been developing. Among the Greeks, Empedocles had posited such a force; among the Scholastics, Oresme had suggested that if Aristotle were mistaken about the earth’s unique central position, an alternative explanation of bodies falling to the earth could be that matter naturally attracted matter. Both Copernicus and Kepler had invoked such a possibility in defending their moving earth. By the late 17th c Robert Hooke had clearly glimpsed the synthesis, namely that a single attractive force governed both planetary motions and falling bodies. He also mechanically demonstrated this idea with a pendulum swing in an elongated circular path, its linear motion being continuously deflected by a central attraction. Such a demonstration illustrated the relevance of terrestrial mechanics for the explanation of celestial phenomena. Hooke’s pendulum signaled the extent to which the scientific imagination had radically transformed the heavens from being a transcendent realm with its own special laws to being in principle no different from the mundane realm of the earth.
It fell to Isaac Newton (1642-1727), born the year of Galileo’s death, to complete the Copernican revolution by quantitatively establishing “gravity” as a universal force – one that could cause bodies to fall to earth and closed the orbits of the planets around the sun. Newton thereby synthesized Descartes mechanistic philosophy, Kepler’s laws of planetary motion, and Galileo’s laws of terrestrial motion in one comprehensive theory. In an unprecedented series of mathematical discoveries and intuitions, Newton established that to maintain their stable orbits at the relevant speeds and distances specified in Kepler’s third law, the planets must be pulled towards the sun with an attractive force that decreased inversely as the square of the distance from the sun, and that bodies falling towards the earth (including not only the stone but also the moon) conformed to the same law. Newton derived mathematically from this inverse law both the elliptical shapes of the planetary orbits and their speed variation (equal areas equal times) as defined by Kepler’s first and second laws. Thus all the major cosmological problems confronting the Copernicans were solved – what moved the planets, how they remained in orbit, why heavy bodies fall to the earth, the basic structure of the universe, the celestial-terrestrial dichotomy. The Copernican hypothesis provoked a comprehensive and entire new cosmology.
With a combination of empirical and deductive rigor, Newton formulated a very few overarching laws that appeared to govern the entire cosmos. Through his three laws of motion (inertia, force, and equal reaction) and the theory of universal gravitation, he established the physical basis of Kepler’s laws, and was able to derive the movements of the tides, the precession of equinoxes, the orbits of comets, the trajectory of motion of cannonballs – indeed, all the known phenomena and terrestrial and celestial mechanics were no unified under one set of laws. Every particle in the universe attracted every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distances between them. Newton discovered the grand design of the universe: a perfectly ordered machine, governed by mathematical laws, and comprehensible by science – a vision fulfilled.
Notably, Newton’s concept of gravity as a force acting at a distance – a concept he got from his studies of the sympathies and antipathies of Hermetic philosophy and alchemy – was insufficiently mechanical not only to continental philosophers but also to Newton himself. The trouble was that his mathematical derivations were just too compelling. Through the concept of a quantitatively defined attractive force, he had integrated two major themes of 17th c science: mechanistic philosophy and the Pythagorean tradition. It was not long before his method and conclusion were recognized as paradigmatic of science. In 1686-87, the Royal Society of London published Newton’s Principia Mathematica Philosophiae Naturalis, and in the following decades the triumph of the modern mind over the medieval mind was evident in Voltaire’s claim that Newton was the greatest man who ever lived.
The Newtonian-Cartesian cosmology was now established as the basis for a new worldview (the “new science” was also the beginning of “modernity”). By the beginning of the 18th c, every educated person in Europe knew that God created the universe as a complex mechanical system composed of basic material particles moving in an infinite neutral space according to a few principles (inertia and gravity that could be mathematically analyzed, In this universe the earth moved about the sun which was itself a star among many others. A single set of laws governed both the celestial and terrestrial realms which were therefore no longer distinct. It also seemed plausible that after God created this mechanical universe he withdrew himself from nature and allowed it to function in accord with its immutable laws. God thereby became the divine architect, the master mathematician, and clock maker, and the universe became an utterly impersonal phenomenon. Human beings’ roles were, now that they had discovered the order of this universe, to use that knowledge to empower and benefit humankind – the notion of infinite progress - and hence one could scarcely doubt that human beings man were the jewel of creation. The scientific revolution and the birth of the modern era were now complete.

The philosophical revolution
Philosophy during this entire period was closely tied to the scientific revolution which it accompanied and stimulated and for which it provided a foundation even as it was critically molded by the scientific evolution. In fact, philosophy acquired an entirely new identity a structure as it entered the third great period of its Western history.
(1) During it first classical/ancient period, philosophy while influenced by religion and science was relatively autonomous as the definer and judge of the literate culture’s worldview.
(2) During the medieval period the Christian religion assumed preeminent status and philosophy took the subordinate role of attempting to reconcile faith and reason.
(3) With the modern era, philosophy began to establish itself as an independent force in the intellectual life of the culture. Philosophy began it re-alliance from religion to science.

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