SOURCE: "Isaac Newton (1642-1727)," in Newton and the Culture of Newtonianism, Humanities Press, 1995, pp. 3-31.

Newton's Youth

Isaac Newton was born on Christmas Day 1642, the premature, posthumous, and only child of an illiterate yeoman farmer of Lincolnshire in England. Not really expected at first to live—he was later to remark that at his birth he was so small that he might have been put into a quart mug—he survived war, revolution, plague, and the seventeenth-century pharmacopoeia to the age of 84, to be buried in Westminster Abbey (the traditional place of interment for the queens and kings of England), idolized by many of his countrymen and admired by much of the Western world.

His genius appeared more mechanical than intellectual at first: as a boy he constructed water clocks, windmills, kites, and sundials and cleverly used the force of the wind to enable himself to outjump the other boys. But, nurtured by neighboring village schools and the King's School at Grantham, his intellectual prowess and his enormous powers of concentration slowly became apparent. Recalled from school by his mother to learn the art of farming, he spent his time under the hedges with his books and his calculations, to the utter neglect of the life of his ancestors. Eventually a maternal uncle, a Cambridge man himself, intervened to have him returned to the school at Grantham to be prepared for Cambridge University, and Isaac went up to that venerable seat of learning in 1661, entering Trinity College. He was aged 18, a little older than most entering students and probably less well prepared than many, but evidently with all his faculties ready to flower. [9; 13; 17; 66; 101]

Early University Studies

Since the great period of the translation of Greek and Arabic scientific literature into Latin in the eleventh, twelfth, and thirteenth centuries, core curricula in the universities of western Europe had been based on the work of Aristotle (384-322 B.c.). And even though one may see in retrospect that a number of challenges to it had developed both within and without the university world in the sixteenth and seventeenth centuries, when Newton entered Cambridge in 1661 the core curriculum was still based on the Latin or Greek texts of Aristotle and on medieval and Renaissance commentators on and expositors of Aristotelian doctrines. For about two years the young Newton applied himself to learning Aristotelian logic, ethics, rhetoric, metaphysics, and natural philosophy. [55; 98:23-44]

In natural philosophy, that would have meant that he learned that the cosmos (the entire created world) was organized around the earth at the center and was made up of nesting spheres. The first set of spheres comprised the four Aristotelian elements: earth at the center, then the spheres of water, air, and fire, filling all the volume up to the sphere of the Moon; there were no empty spaces in the Aristotelian cosmos.

The sphere of the moon was a great dividing line, with change limited to the world below the moon where motions of various sorts brought about changes of several kinds. Aristotle designated four types of change: (1) generation/corruption, as in the birth and death of a living creature; (2) qualitative, like changes in such qualities as heat, cold, dryness, and wetness; (3) quantitative, as in the enlargement of something that has the ability to expand (Aristotle's example would perhaps have been inflating a sheep's bladder; a more modern example might be blowing up a balloon); (4) change of place or "local motion"—from which our word locomotion is derived—as a car traveling down a highway, or in Aristotle's case more likely a man walking from his home to Aristotle's school in the center of Athens.

Above the sphere of the moon, on the other hand, were the eternal and changeless spheres of the other planets, those that (including the moon) comprised the anciently known planets for which the days of the week are named: Moon, Venus, Sun, Mars, Jupiter, and Saturn. Finally, at the edge of the closed system was the sphere of the "fixed stars" that appeared not to change at all in relation to each other, only to whirl around the earth once every 24 hours. The planets (the word means "wanderers") do appear to move in relation to each other, as well as in relation to the earth and to the fixed background of stars. But the only motion allowed to those celestial objects was a circular one, a movement always returning to its beginning point and hence eternal. No real change occurred on the moon or above, and, again, there were no empty spaces; the heavens were perhaps filled with an invisible celestial "quintessence" or fifth element, or perhaps the planets and stars were embedded in crystalline (invisible) spheres that fitted neatly together. Aristotle, like many other Greek thinkers, seems to have thought of the cosmos as all fitted together like a living creature, an organism, that was alive in its own self and that human beings could understand by rational and logical thought processes. [45; 55]

Nevertheless, even though Aristotle was still being taught in the universities, western Europe was by the seventeenth century saturated with machines and labor-saving devices that went far beyond the purview of Aristotelian patterns of thought: mechanical clocks that utilized the force of gravity; windmills and water mills that similarly exploited the motive forces of wind and water. The early mechanical genius of Newton's childhood constructions shows him aligned in significant ways with the mechanistic aspects of Western culture, so it comes as no surprise to find him adopting the new mechanical natural philosophies of the seventeenth century about halfway through his undergraduate career.

Mechanism and Other Influences on Newton

The appearance of mechanistic philosophies of nature in the seventeenth century was a broad-based phenomenon but one that was in sharp contrast to Aristotelianism, for the mechanical philosophies held that nature acts like a machine rather than like a living organism. No doubt encouraged by the prevalence of mechanical devices developed in Christian Europe, mechanical philosophies also had ancient roots in the works of Lucretius, a Roman poet of the first century B.c., and in the work of Epicurus, a Hellenistic Greek philosopher of the fourth and third centuries B.c. Revived by humanistic scholarship, interest in these ancient systems of thought, antithetical as they were to Aristotelian doctrines as well as Christian ones, had spread across national boundaries from Italy to northern Europe to England.

In general, the seventeenth-century philosophies that were at least partially based on ancient mechanism argued for the existence of very small—indeed imperceptible—particles that were all made of the same sort of matter and had only mathematical properties such as extension, size, shape, and perhaps weight. The particles could combine with each other to form larger material masses, or they could dissociate from each other and be re-formed in other ways. Such corporeal associations and dissociations accounted for much change in the natural world; the analogy frequently invoked was that of the alphabet: the letters can be associated in various ways to form words, and the words in turn dissociated to yield the basic letters that can then be re-formed into different words. But if the imperceptible particles of matter were thought to be like letters of the alphabet, similar to the movable type used in contemporary printing presses, the world as a whole was thought to be organized like an intricate machine designed and ordered by the Creator God of Judeo-Christian tradition. Just as human artisans designed and ordered the intricate mechanical clocks, printing presses, and wind and water mills that were common in western Europe, so the Deity had created a world-machine and set it in motion in ways that human beings could learn to understand. [19; 45]

Of the many varieties of mechanical philosophy available in the 1660s, those of the French philosophers René Descartes (1596-1650) and Pierre Gassendi (1592-1655) were important to Newton, as were those of the English philosophers Walter Charleton (1619-1707), Robert Boyle (1627-91), Thomas Hobbes (1588-1679), Kenelm Digby (1603-65), and Henry More (1614-87). Descartes had created the first total world system since that of Aristotle: his system was a plenum (completely full of matter) like that of Aristotle, but indefinite in extent rather than limited and bounded by the sphere of the fixed stars as Aristotle's had been. The matter in Descartes's system could be ground down into ever finer pieces. Gassendi, on the other hand, paid more attention to the ancient version of Epicurus, and so argued that the particles of matter were really atoms and therefore "uncuttable," which is what the Greek word atomos means. Uncuttable atoms moving in void (empty) space made Gassendi's system quite different from that of Descartes, and Gassendi's work was made widely known in England by an English version of it published by Charleton. Boyle had studied both Descartes's and Gassendi's systems but, declining to choose between them, utilized elements from each. Hobbes's version was much too materialistic in the eyes of most English natural philosophers, because Hobbes did not make sufficient room in his system for spirit, soul, and the Deity, and Henry More thought there were similar materialistic tendencies even in Descartes's version. Digby, who was not a very systematic thinker, was much influenced by Descartes but kept. so many elements of Aristotelian thought also that his version of the mechanical philosophy was marked by severe inconsistencies. Although there indeed were many problems with these various mechanical philosophies, problems both scientific and theological, they were the cutting edge of natural philosophical thought in the seventeenth century, and after Newton absorbed their basic principles he seldom utilized Aristotelian doctrines again, though he was later to supplement mechanistic thought with other ancient systems in good humanistic fashion. [14; 17; 18; 27; 45; 47; 50; 51; 62; 79; 80; 81; 101; 104]

Newton's later fame could hardly have been predicted during his student years, but he was soon to tackle—and solve—many of the physical and mathematical questions that engaged his contemporaries. In January 1665 he took his Bachelor of Arts degree, but in the summer of 1665 he was forced to retire to his home at Woolsthorpe because the university was closed from an outbreak of bubonic plague (endemic in Europe since the first great pandemic in 1348-49 known as the Black Death). The university remained closed most of the time until the spring of 1667, and Newton's enforced sojourn at Woolsthorpe has come to be known as his annus mirabilis, the marvelous year in which he invented his "fluxions" (the calculus), discovered white light to be compounded of all the distinctly colored rays of the spectrum, and found a mathematical law of gravity, at least in alternative form. [9; 40; 73; 101; 104]

The gradual development and unfolding to the world throughout subsequent years of the productions of that brief period were to establish his reputation upon the granite foundation it still enjoys. We will return to a consideration of each of these major achievements, which are still recognized and admired by the modern world, but we must also give due consideration to the fact that physical and mathematical problems were not the issues of greatest concern to most people in the seventeenth century, nor were they the issues of greatest concern to Newton himself. He lavished much more of his time on alchemy, church history, theology, prophecy, ancient philosophy, and "the chronology of ancient kingdoms."

Newton was born into the crucible of civil war in England, and the religious and political struggles of the period were to affect him deeply. The Reformation of the sixteenth century had shattered Christendom irrevocably, and, as religious sects had proliferated, especially in northern Europe, the intensity of political issues had grown as well, for church and state had formerly been perceived as a unity, like the two sides of a single coin. With such an understanding of the relationship of religious belief and political power, the notion of religious toleration was at first virtually inconceivable: divisions in creed and dogma were thus fought out on physical as well as intellectual battlefields. The full force of the tumult that had already torn Continental Europe for over a century arrived in England just at the time of Newton's birth. So even though Newton's long life carried him well into the eighteenth century and he came to be perceived as one of the principal founders of eighteenth-century Enlightenment thought, his own concerns remained centered to a great extent on the political and religious problems of the mid-seventeenth century, and he himself desired above all else to restore religion to the pristine purity, power, and centrality it had once enjoyed in human life. [6; 9; 18; 45; 50; 65; 66; 67; 99; 101]

In looking backward to the pure original religion he supposed humanity to have known and practiced at the beginninig of time, Newton reflected the reverence for antiquity that had been the hallmark of Renaissance humanism. In many ways, indeed, Newton's intellectual development is best understood as a product of the late Renaissance, a time when the revival of antiquity had conditionied the thinkers of western Europe to look backward for Truth. The Renaissance humanists of the fourteenth century had rediscovered the glories of Roman poetry and prose, while in the fifteenth century a newly restored proficiency in the Greek language had revealed the awesome philosophical power and beauty of the works of Plato (427'?-347 B.c.) and the Neoplatonists, as well as the mysterious doctrines of the Hemietic Corpus. Henres Trismegistus (his surname meant "Thrice Greatest"), the supposed author of the Henretic Corpus, was not a real person, although the thinkers of the Renaissance believed him to be not only real but also very ancient, perhaps even more ancient than Moses (who had composed several of the first books of the Judeo-Christian Bible). His supposed antiquity gave Hermes great authority in the eyes of Renaissance scholars, and Henretic doctrines supported all sorts of magical, astrological, and alchemical enterprises in the sixteenth and seventeenth centuries. [18; 21; 52; 58; 69; 94; 99]

Humanist scholars revived innumerable other treatises from antiquity as well: treatises on medicine, mathematics, natural philosophy, astronomy, magic, alchemy, astrology, and cosmology, including the works of Lucretius and Epicurus mentioned above. Such materials were previously unknown in western Europe or known before only through inadequate translations. What an intellectual ferment they created! And as the new printing presses of western Europe spread the new editions of ancient works, and as the Renaissance spread north from its original Italian base, materials from Jewish, Egyptian, and Christian antiquity were added to the heady mixture, where they contributed to Reformation scholarship, to an interest in the Hebrew language and the cabala, and to early attempts to decipher Egyptian hieroglyphics. [5; 6; 21; 65; 69; 99]

Newton's Way of Thinking and Working

Thanks to this great revival of ancient thought, to humanist scholarship, to the quarrels of the Reformation, and to new developments in medicine, science, mathematics, and natural philosophy prior to or contemporary with his most intense period of study, Newton clearly had access to an unusually large number of systems of thought. Each system had its own set of guiding assumptions, so in that particular historical milieu some comparative judgment between and among competing systems was perhaps inevitable. One could hardly accept them all as equally valid. But such judgments were difficult to make without a culturally conditioned consensus on standards of evaluation. By the mid-seventeenth century the old verities in both religion and natural philosophy had been subverted but no new ones agreed upon.

A standard of evaluation was precisely what was lacking, a situation that led many people to adopt a skeptical attitude and to doubt that any true knowledge about the world or God could ever be attained. The formalized skepticism of Pyrrhonism had been revived along with other aspects of antiquity, but one may trace an increase in a less formal but rather generalized skepticism at least from the beginning of the sixteenth century, as competing systems laid claim to Truth and denied the claims of their rivals. As a consequence, western Europe underwent something of an intellectual crisis in the sixteenth and seventeenth centuries. What, indeed, was it possible for one to know without lingering and bewildering doubts? Among so many competing systems, how was one to achieve certainty? Could the human being attain Truth? [18; 69; 83; 84; 99]

Newton was not a skeptic. On the contrary, he seems to have adopted a contemporary response to questions of valid knowledge called the doctrine of "the unity of Truth," a position that was in face one answer to the problem of skepticism. Not only did Newton respect the idea that Truth was accessible to the human mind, but also he was very much inclined to accord to several systems of thought the right to claim access to some aspect of the Truth. For those who adopted this point of view, the many different systems they encountered tended to appear complementary rather than competitive. The assumption they made was that Truth did indeed exist somewhere beyond the apparently conflicting representations of it currently available. True knowledge was unitary, and its unity was guaranteed by the unity of the Deity, He being the source of all Truth. As a practical matter, those who followed this doctrine of the unity of Truth became quite eclectic, which is to say that each thinker selected parts of different systems and welded them into a new synthetic whole that seemed to him (or her) to be closer to Truth. That was certainly Newton's method, and in the course of his long life he marshaled the evidence from every source of knowledge available to him: mathematics, experiment, observation, reason, the divine revelations in biblical texts, historical records, mythology, contemporary scientific texts, the tattered remnants of ancient philosophical wisdom, and the literature and practice of alchemy. [18; 84; 85]

One must realize, however, that in making selections from the various sources of knowledge available to him Newton utilized a sophisticated balancing procedure that enabled him to make critical judgments about the relative validity of each. Perhaps the most important element in Newton's contribution to scientific method as it developed in subsequent centuries was the element of balance, for no single approach to knowledge ever proved to be effective in settling the knowledge crisis of the Renaissance and early modern periods. Human senses are subject to error; so is human reason. So is the interpretation of revelation; so is the mathematico-deductive scientific method put forward by Descartes earlier in the century. Since every single approach to knowledge was subject to error, a more certain knowledge was to be obtained by utilizing each approach to correct the other: the senses to be rectified by reason, reason to be rectified by revelation, and so forth. [18]

The self-correcting character of Newton's procedure constitutes the superiority of Newton's method over that of earlier natural philosophers, for others had certainly used the separate elements of inductive reasoning, deductive reasoning, mathematics, experiment, and observation before him, and often in some combination. But Newton's method was not limited to the balancing of those approaches to knowledge that still constitute the elements of modern scientific methodology, nor has one any reason to assume that he would deliberately have limited himself to those familiar approaches even if he had been prescient enough to realize that those were all the future would consider important. Newton's goal was much broader than the goal of modern science. Modern science focuses on a knowledge of nature and only on that. In contrast, Newton's goal was a Truth that encompassed natural principles but also divine ones as well. He had a deep religious concern to establish the relationship between God and His creation (nature), and so he constantly searched for the boundaries between God and nature where divine and natural principles met and fused. As a result, Newton's balancing procedure included also the knowledge he had garnered from theology, revelation, alchemy, history, and the wise ancients. [18]

Blinded by the brilliance of the laws of motion, the laws of optics, the calculus, the concept of universal gravitation, the rigorous experimentation, and the methodological success, subsequent generations have seldom wondered whether the discovery of the laws of nature was all Newton had in mind. Scholars have often missed the religious foundation of his quest and taken the stunningly successful by-products for his primary goal. But Newton wished to look through nature to see God, and it was not false modesty when in old age he said he had been only like a boy at the seashore picking up now and again a smoother pebble or a prettier shell than usual while the great ocean of Truth lay all undiscovered before him. [18]

Eighteenth-, nineteenth-, and early twentieth-century views of Newton were developed almost entirely on the basis of his principal published works: Philosophiae naturalis principia mathematica (1687, 1713, 1726); Opticks: or, a Treatise of the Reflexions, Refractions, Inflexions and Colours of Light. Also Two Treatises of the speciesand Magnitude of curvilinear Figures (1704, 1706, 1721, and the posthumous edition of 1730); Arithmetica universalis (1707); De analysi and Methodus differentialis (1711). The Newtonian worldview, developed almost wholly on the basis of his successes in mathematics and physical science, so subtly and deeply colored the outlook of succeeding generations that the fuller seventeenth-century context in which Newton's thought had developed was lost to view. Thus it became a curious anomaly—and one to be explained away—that Newton's studies in astronomy, optics, and mathematics only occupied a small portion of his time. In fact most of his great powers were poured out quite otherwise.

The fact might never have been recognized, however, except for the survival of great quantities of manuscripts in Newton's hand. When Newton died in 1727 without leaving a will, his possessions passed to his niece, Catherine Barton Conduitt, and afterward to her descendants. The papers were examined with a view to possible publication later in 1727, and a few were published shortly afterward, but many of them were marked "not fit to be printed," and almost all of them were put back in their boxes. In the nineteenth century the family offered them to Cambridge University. The university appointed a group of men, mostly eminent scientists of the period, to examine the papers, and they selected for retention those focused on mathematics and physical science. These now comprise the Portsmouth Collection, University Library, Cambridge. The rest were returned to the family as being of no interest to the university and so remained largely unknown until they were sold at auction in 1936. The auction scattered them all over the world; although a number of them are still in the hands of private collectors, most of them are now held by research libraries and so are available for study. It is from detailed studies of these manuscripts of Newton's that our new and historically more accurate portrait of him has emerged. [7; 8; 11; 18; 23; 40; 61; 63; 65; 66; 67; 73; 76; 78; 87; 91; 98; 100; 101; 102; 103; 104]

Once one grasps the immensity of Newton's goal, many otherwise inexplicable aspects of his career fall into place. Now it is no longer necessary to explain away his fierce interest in alchemy or his dogged attempts at the correct interpretation of biblical prophecies, as many earlier biographers and scientists tried to do. If Newton's purpose was to construct a unified system of God and nature, as indeed it was, then it becomes possible to see all of his various fields of study as potential contributors to his overarching goal. It also becomes possible from this point of view to recognize that Newton's belief in the unity of Truth contributed greatly to his remarkable scientific creativity. For in the course of his long search for Truth he constructed many different partial systems and changed from one to another in ways that have often appeared erratic and inconsistent to later scholars. One may now see, however, that the pattern of change resulted from his slow fusion and selective disentanglement of essentially antithetical systems: Neoplatonism, mechanical philosophy, Stoicism; chemistry, alchemy, atomism; biblical, patristic, and pagan religions. It was precisely where his many different lines of investigation met, where he tried to synthesize their discrepancies into a more fundamental unity, when he attempted to fit partial Truth to partial Truth, that he achieved his greatest insights.

Newton's Early Mechanism: Cohesion and Gravity

With this broad view of Newton's work in hand, one may now begin to explore the intricate and marvelous development of the views that ultimately brought him so much acclaim.

Sometime during his student years Newton began to study the mechanical philosophers, as noted above, and he became a "corpuscularian." In the seventeenth century the term "corpuscularian" referred to anyone who believed that matter was comprised of small material particles or "corpuscles," whether the particles were understood to be infinitely divisible or whether there was supposed to be a limit to divisibility as in atomism, atom simply meaning "uncuttable," as we saw above. Newton chose elements of matter theory from Descartes, Gassendi (via Charleton), Boyle, Hobbes, Digby, and More and left a record of his thoughts in his student notebook. He seems to have acceptable the notion that matter had least parts or atoms that were not further divisible. [18; 62]

At first Newton, like other mechanical philosophers of his time, placed considerable faith in the existence of an all-pervasive material medium that served as an agent of change in the natural world. By postulating a subtle aether, a medium imperceptible to the senses but capable of transmitting effects by pressure and impact, mechanical philosophers had devised a convention that rid natural philosophy of incomprehensible occult influences acting at a distance (e.g., magnetic attraction and lunar effects). For Newton just such a mechanical aether, pervading and filling the whole world, became an unquestioned assumption. By it he explained gravity and, to a certain extent, the cohesion of particles of matter. But because of the general passivity of matter in the mechanical philosophy, certain problems arose for many contemporary philosophers regarding cohesion and life, and eventually, for Newton, regarding gravity also. [18; 62]

The question of cohesion—that is, the problem of what makes the tiny corpuscles stick together—had always plagued theories of discrete particles, atomism having been criticized even in antiquity on this point. The cohesion of living forms seems intuitively to be qualitatively different from anything that the random, mechanical motion of small particles of matter might produce. Nor does atomism explain even mechanical cohesion in nonliving materials very well (such as, for example, the regular patterns in crystals of salts or gemstones), for any explanation of such regularity seems to require unverifiable hypotheses about the geometric configurations of the atoms or else speculation about their quiescence (or rest) under certain circumstances. [18; 51; 62; 105]

In the various forms in which corpuscularianism was revived in the seventeenth century, the problems remained and variants of ancient answers were redeployed. Descartes, for example, held that an external pressure from surrounding subtle matter (the aether) just balanced the internal pressure of the coarser particles that constituted the cohesive body. Thus no special explanation for cohesion was required, he claimed: the parts cohered simply because they were at rest close to each other in an equilibrated system. Gassendi's atoms, on the other hand, stuck together through the interlacing of antlers or hooks and claws, much as the atoms of Lucretius had before them, in what one might call a sort of primitive Velcro system. Charleton found not only hooks and claws but also the pressure of neighboring atoms and the absence of disturbing atoms necessary to account for cohesion. Francis Bacon (1561-1626) introduced certain spirits or "pneumaticals" into his speculations. In a system reminiscent of the Stoics, who were ancient critics of atomism, Bacon concluded that gross matter must be associated with active, shaping, material spirits, the spirits being responsible for the forms and qualities of tangible bodies, producing organized shapes and effecting digestion, assimilation, and so forth. For Newton during his student years, with his mechanical aether ready at hand as an explanatory device, a pressure mechanism seemed sufficient to explain cohesion. He did not think that the simple resting (quiescence) of the particles close to each other could account for cohesion, but he did think that the "crowding" or pressure of the aethereal matter that filled all space might account for it. He noted the occasional geometric approach of Descartes but did not himself develop it. Newton was later to offer a radically different explanation of cohesion, one based on alchemical and Stoic considerations, but not while he was still an undergraduate. [18; 62; 68]

At first, in the 1660s, Newton considered gravity to be a mechanical mode of action. What is gravity, and what causes it? Modern science has still not found all the answers to these fundamental questions, but we know from common everyday experience that something makes bodies like ripe apples fall to the ground when they are detached from their trees, and that something will surely make us do likewise if we lean too far out an open window. Newton began to ponder the problem of gravity about 1664, and his first mechanical theory was derivative and nonmathematical, influenced by the theories of Descartes, Digby, and Boyle. Though the precise form was Newton's own, his theory was a restatement of impact physics, a conventional, orthodox (at that time) variety of mechanical philosophy: in short, an aether theory of gravitation. Bodies descend to earth, he said, through the impulsion of fine material particles; it is a mechanical stream of aethereal matter causing gravity, just as a flowing stream of water will carry wood chips downstream. [18; 62]

No hint exists in Newton's earliest statement of what gravity is later to become for him: an active principle (not mechanical) directly or indirectly dependent upon the activity of the Deity, the Creator God Who had made the world-machine and Who kept it in motion. Newton seems never to have focused solely on the material part of the natural world, as modern scientists usually do, but he always remained conscious of the presence of the Deity. Even in his undergraduate student notebook there is a recognition of God's omnipresence, the literally "being present everywhere" of the Deity that is later to subsume universal gravity in Newton's system of the world. When bodies are in motion in a world full of the aether, Newton said in this early notebook, some of the matter has to be crowded out of the way, so the motion meets with resistance. But in a vacuum that would not be the case. Even though God is present in the vacuum, God is a spirit and penetrates all matter, Newton added. God's presence causes no resistance, however, just as if nothing were in the way. Newton was to repeat much later his conviction that God is present where there is no body, as well as present where body is also present. There, as in the student notebook, God penetrates all matter. But whereas later the omnipresence of God and His ability to penetrate matter have the utmost significance with respect to gravity, that was not the case in the student notebook, where gravity was caused by the mechanical motion of small particles of matter to which God's presence simply constituted no obstacle. [18; 41; 62]

Newton's Early Mathematics: The Binomial
Theorem and the "Fluxions"

At about the same time, in 1664, Newton began seriously to study mathematics. His preuniversity training had probably been limited to the basic rules of arithmetic, an elementary knowledge of weights and measure, and simple accounting techniques. Then he bought a book at a fair; he later called it a book on astrology, but it might equally well have been a book on astronomy, for the two terms were often used interchangeably in the seventeenth century. He could not understand it, however, not then being acquainted with trigonometry, so he bought a book on trigonometry only to discover that he was deficient in the background to that topic, never having studied the great fundamental work on plane geometry from antiquity, the Elements of Euclid. So he began to read Euclid. At first he found the propositions so easy to understand that he wondered why anyone would bother to write demonstrations of them, but he soon found propositions that were not intuitively obvious to him and then studied them with greater care. [104]

Once he had come to appreciate the logical power of Euclid's demonstrations, Newton turned to more modern mathematicians, reading the Clavis mathematicae of William Oughtred (1575-1660) and the Geometry of Descartes, both of which at first gave him some difficulty. By degrees he mastered them and soon moved on to the mathematical miscellanies of Franz van Schooten (1615-60) and the Arithmetica infinitorum of John Wallis (1616-1703). A few additional works apparently completed Newton's self-directed apprenticeship, and he began to discover and formulate new theorems of his own. [2; 3; 20; 73; 101; 103; 104]

The first of these of lasting significance was his discovery of the general binomial expansion in the winter of 1664-65, inspired by his reading of Wallis's work. A binomial is a mathematical expression with two terms in it, such as an x and a y. If the terms are added together, or if one is subtracted from the other, as in the expressions "x + y" or "x-y," the expression with the two terms in it is called a binomial. Suppose, then, that one wishes to multiply the term "x + y" by itself (or square it). The procedure may be expressed in mathematical notation as (x + y)2, where the 2 is known as the power or exponent to which the binomial is to be raised. The exponent might be 2 or any higher positive number (integer). If the designated multiplication is actually carried out, one obtains an expansion of the binomial, which in this case would be x² + 2xy + y², where the coefficients of the three terms are 1, 2, 1. Mathematicians prior to Newton's time had discovered rules for finding the coefficients for other positive powers to which the binomial could be raised, and such general rules were of great value in obtaining binomial expansions, for they made it unnecessary actually to carry out the lengthy process of multiplication. But whereas binomial coefficients for such positive integral powers had been known for some time, Newton's method was much more general, for it allowed the use of negative or fractional exponents also. [2; 20; 73; 104]

When the exponent is neither a positive integer nor zero, some binomial expansions constitute series with infinitely many terms. Newton was able to demonstrate that when such binomial expansions form infinite series the results do not just yield approximations (as mathematicians had previously supposed) but are subject to general definite laws, just as the algebra of finite quantities is. Infinite series expansions soon came to play a central role in his development of the calculus. [20; 73; 104]

His work on the fluxional calculus began in the autumn of 1664, and by the spring of 1665 Newton had resolved his several approaches into a general procedure for differentiation. Inspired in this case by Descartes's Geometry, in which algebra and geometry were combined to yield analytic geometry, Newton had focused on problems of finding tangents to curves, as well as normals and the radius of curvature at a general point. Newton regarded the curve as the locus of a moving point in a suitable coordinate system, the point itself being the intersection of two moving lines, one vertical and the other horizontal. The vertical and horizontal components changed with the "flux" or flow of time, and the "fluxions" of the variables were their derivatives with respect to time, indefinitely small and ultimately vanishing increments of the variables. By October of 1666 Newton had also mastered a general method for the reverse procedure, integration, to compute the area under the curve. Although various limited procedures for finding areas and tangents had been in use by the early seventeenth century, Newton's methods yielded general and systematic techniques and demonstrated the inverse relation between area problems and tangent problems. For a young man not yet 24, and apparently completely self-taught in this area, that was quite a dramatic achievement, and he himself said much later that he was then in the prime of his life for invention. But of course there was more to come. [20; 33; 73; 103; 104]

As Newton sat in the garden at Woolsthorpe one day during his annus mirabilis, some apples fell to the ground close to him. The event prompted him to consider the power of gravity that had brought the apples down and to speculate that the power of gravity might extend as high as the moon and help keep the moon in its orbit around the earth. The story of the apples is so well known now that in a recent set of British postage stamps commemorating the life and work of Isaac Newton one stamp had no design on it but an apple, the symbol of Newton's solution to the problem of gravity. [21; 100]

But the exact significance of the episode in Newton's developing thought on the subject of gravity has been less well understood. For a long time it was supposed that his creative genius allowed Newton at that time to formulate the law of universal gravity, so there was much scholarly speculation regarding the 20-year "delay" before he published his new discovery. Now the predominant interpretation of the episode of the falling apples is quite different: at most Newton then worked through an inconclusive comparison of the fall of an apple with the fall of the moon that yielded an approximation of the so-called inverse-square relationship, that is, the mathematical law that indicates that the power of gravity diminishes as the square of the distance between two gravitating bodies increases. It was only much later that the full generality and universality of the law emerged, for it required from Newton some major conceptual revisions. [12; 18; 40; 71; 73; 77; 78; 102]

In 1666, when the apples fell and he was prompted to consider also the fall of the moon, Newton had accepted the doctrine of a mechanical aether as the cause of gravity, as noted above. In particular, he had accepted Descartes's version of the aether, a version in which the aether swirled around the earth in a vortex pattern, a sort of imperceptible whirlpool that carried the moon in its orbit around the earth and accounted for the fall of objects like apples to the surface of the earth. Other planets had their own vortices also in Descartes's system, and around the sun there was supposed to be a giant whirlpool that carried the planets, including earth, around the sun in their regular cycles. Newton held to that general belief until about 1684. Indeed, in 1666 the manuscript evidence shows him thinking only about gravity with respect to the earth and the earth-moon system; he apparently did not generalize the system even to include the sun and other planets until 1675. So it seems that in 1666 his concept of gravity was far from the universal one that appeared in the Principia in 1687. [12; 18]

Acting against the downward pressure of the gravitational aether in Newton's early mechanics was the opposing endeavor to recede from the center, a centrifugal (center-fleeing) force. The term "centrifugal" was coined by Christiaan Huygens (1629-95), a Dutch natural philosopher and mathematician who was also a follower of Descartes. The centrifugal force accounted for the tendency of objects in circular motion to fly away from the center of motion, as in the case of a stone whirled at the end of a sling. Treated by physicists now as an illusory force, in the 1660s, 1670s, and early 1680s Newton accepted it as a real force that balanced and was balanced by the pressure of the vortex, the balance of the two forces being what kept the moon in its orbit. The same sort of analysis of forces appeared also in his early work on terrestrial mechanics during this period. But in the 1680s, when writing the Principia, Newton recognized the illusory nature of the centrifugal force and of the aethereal vortex as well. At that time he changed his analytic framework to two other opposing forces: inertia (the tendency of a body to continue in straight-line motion or at rest unless a force is applied to it) and a centripetal (center-seeking) force, a term he coined himself and one that reflects his new understanding of the center-seeking force as the mirror image of Huygens's center-fleeing force. We will return later to the insights of the 1680s that allowed Newton to revise his understanding of celestial mechanics, to generalize and universalize the force of gravity, and to construct a system of the world that would last virtually unchallenged for three centuries. [12; 18; 40; 71; 73; 77; 78; 102]

Newton's Early Optics. Particles and Prisms

Still in a white heat of creativity, what he later called his prime time of invention, Newton also began about 1666 to revise and reform contemporary views on the nature of light and color. Descartes had argued that the light from the sun that we see is simply a pressure in the aether. On the analogy of a blind person's walking stick, the pressure on the end of which is transmitted instantaneously to the hand, the sun's light sets up a chain of pressure from sun to eye that one then experiences as the sensation of light. That theory really would not do at all, Newton observed, because if light is just pressure on the eyeball, then one should be able to see perfectly well at night by running forward, since the forward motion of the runner would generate pressure of air and aether against the eye. [62]

Newton opted for a particulate definition of light, that is, the emission by the sun and other luminous bodies of extrafine corpuscles that we experience as light. Newton's theory of particulate emission implies that the transmission of light is not instantaneous but, on the contrary, must have a definite velocity. Early measurements of the speed of light later in the seventeenth century seemed to justify Newton's views, and light was then treated as particulate until the early nineteenth century. At that time a wave theory of light came to dominate scientific thought on the subject. Newton had recognized certain wavelike phenomena associated with light but had supposed them to be explained by motions in the all-pervading aether as the light corpuscles passed through it; he had denied that light itself might be a wave. It did not appear to him to spread out into the shadow of obstacles it passed (as water waves, for example, will do). More precise measurements in the nineteenth century having demonstrated conclusively that light does have the wave properties Newton had denied, his theory was thoroughly rejected for about a century—one of the very few cases of a total rejection of Newton's theories by later scientists. But modern quantum theory has at least partially reinstated Newton's views in the twentieth century, for it is now recognized that light does sometimes appear as quanta (tiny particulate packets of energy) while under other circumstances its continuous wave properties predominate. [75; 101]

As for colors, Newton tackled that issue with prisms. Robert Hooke (1635-1702) had published his Micrographia in 1665, a book rightly famous for its wonderful illustrations of observations made with the then new microscope. Hooke was an English natural philosopher, sometime employed as an experimental operator by Robert Boyle and later Curator of Experiments for the Royal Society of London for Improving of Natural Knowledge. In his book Micrographia Hooke argued for a theory of colors as oblique and confused pulses of light. The color blue was for Hooke such a pulse in which the weakest part comes first with the strongest following; the color red had its parts in reverse order. In general, according to Hooke, the colors formed a scale of strength between lightness and darkness, with red closest to pure white light and blue the last step before darkness. Newton attacked Hooke's theory at the root by analyzing white light into the spectrum of colors with the prism and showing how the different colors were refracted at different angles thereby. Refraction is the change of direction of a ray (of light, in this case) when it passes from one medium into another, from air into and out of the glass prism in Newton's experiment.

If the ray of white light passes into the glass at an oblique angle, it is split into all the colors of the rainbow, because each color acts as an independent ray and has its own precise and specific angle of changed direction. An oblong rainbow of separate colors thus becomes visible as the rays leave the prism. The colored rays kept their unique angles of refraction when passed through a second prism, Newton demonstrated, and they also could be recombined to constitute white light. So, Newton argued, the colored rays are the fundamental individuals, and white light is a confused mixture of them. With respect to the colors of bodies, he continued, it is clear that most of the colored rays are absorbed by the body while one is reflected back to our eyes, such as green, for example, in the case of most living plants. [75; 101]

Utilizing both experimental and mathematical analyses, Newton developed his insights into light and color over several years. When he was appointed to the Lucasian Chair of Mathematics at Cambridge in 1669 he gave his first set of lectures on his optical discoveries. He sent papers on optics to the Royal Society in the 1670s also, but the strong opposition his papers encountered from Hooke and others discouraged him from further publication to such an extent that he never published the full text of Opticks until 1704, by which time Hooke had died and so could no longer attack Newton's views. The laws of optics reported there were, however, virtually all established while Newton was less than 30 years of age. [71; 75; 101]

But light had significance for Newton that went far beyond the laws of optics, for in both Christian and Neoplatonic traditions light carried with it the aura of divinity. Light was God's first created creature in the Genesis account of creation, and it was both symbol and agent of divinity in Neoplatonism. The metaphysics of light had a long and distinguished career in Christian Europe; as Newton was soon to discover, it was also closely associated with divine creativity in the literature of alchemy. [15; 18; 42; 56; 63]

Newton's Early Alchemy: Life, Cohesion, and
Divine Guidance

Newton turned to a study of alchemy about 1668. It is possible that he had already learned some of the rudiments of chemistry before he entered Cambridge, when he lodged with a local apothecary (or druggist) in Grantham while attending the King's School there. But Newton certainly made himself the master of contemporary chemistry shortly after his return to Cambridge after the plague years, in 1667 or 1668, the date of the chemical dictionary he compiled then. Newton's turn to alchemy, however, was altogether a different enterprise from learning basic chemistry. [17]

Even though in the seventeenth century there was some overlap between chemistry and alchemy, and of course both fields shared some mutual interest in the manipulation and transformation of the different forms of matter by chemical techniques, chemistry and alchemy had quite distinct goals. Alchemy never was, and never was intended to be, solely a study of matter for its own sake. Nor was it, strictly speaking, a branch of natural philosophy, for there was a spiritual dimension to alchemy—a search for spiritual perfection for the alchemist himself or herself, or a search for an agent of perfection (the "philosopher's stone") that could transform base metals into silver or gold or perhaps could even redeem the world. It was in fact the spiritual dimension to alchemy that led Newton to study it, but his goal was not exactly one of the traditional ones. He perceived alchemy as an arena in which natural and divine principles met and fused, and he understood that through alchemy it might be possible for him to correct the theological and scientific problems of the seventeenth-century mechanical philosophies. [15; 16; 17; 18; 58]

Since sometime earlier in the 1660s Newton had been troubled by a theological problem, and he hoped alchemy could provide a solution. He was, as were his older contemporaries Isaac Barrow (1630-77), Henry More, and Ralph Cudworth (1617-88), alarmed at the atheistic potentialities of the revived corpuscularianism of their century, particularly of Cartesianism (the mechanical philosophy of Descartes). Although the ancient atomists had not really been atheists in any precise modern sense, they had frequently been so labeled because their atoms in random mechanical motion received no guidance from the gods. Descartes, Gassendi, and Charleton had been at pains to allay the fear that the revived corpuscular philosophy would carry the stigma of atheism adhering to ancient atomism. They had solved the problem, they thought, by having God endow the particles of matter with motion at the moment of creation. All that resulted then was due not to random corpuscular action but to the initial intention of the Deity. [6; 17; 18; 30; 79; 80; 81]

Later writers, going further, had carefully instated a Christian Providence among the atoms (where the ancients, of course, had never had it). Only Providence could account for the obviously designed concatenations (or organization) of the particles, and so, via Christianity, a fundamental Stoic critique of the ancient atomists actually came to be incorporated into seventeenth-century atomism. This development was all to the good in the eyes of most Christian philosophers: atomism now supported religion, because without the providential action of God the atoms could never have assumed the lovely forms of plants and animals so perfectly fitted to their habitats. This was called "the argument from design" for the existence of a Deity: the presence of design (planned organization) in the natural world implied the existence of a Designer, a Deity Who had done the planning and organizing of the so obviously designed creatures in the natural world. The "argument from design" had quite ancient roots and had been present in Christianity from a very early period, but it assumed unparalleled importance in the seventeenth century. For if the new heliocentric astronomy, having moved the earth out of its central location in the cosmos, raised doubts about the focus of Providence upon such an obscure minor planet as earth now seemed, the new atomism seemed to relieve such doubts and reassure human beings that indeed divine Providence still cared for the world. [18; 57; 64; 96; 97]

The difficulty came when one began to wonder how Providence operated in the law-bound universe that was emerging from the new science, and that difficulty was especially severe in the Cartesian system, where only matter and motion were acceptable explanations. Even though Descartes had argued that God constantly and actively supported the universe with His will, it seemed to Henry More and others that Descartes's Deity was in danger of becoming a sort of absentee landlord, a Deity Who had set matter in motion in the beginning but Who then had no way of exercising His providential care. [18]

Newton faced this theological difficulty squarely and directly. The mechanical action of matter in motion was not enough. Granted that such mechanical action existed among the particles and could account for large classes of phenomena, yet it could not account for all. It could not account for the processes of life, where cohesive and guiding principles were clearly operative. It could not account even for the manifold riches of the phenomenal world. All forms of matter, never mind how various they appeared, could be reduced back to a common primordial matter according to the mechanical philosophers, but how had they been produced in the first place'? From the particles of a universal matter with only primary mathematical properties, there seemed no sufficient reason for the forms and qualities of the phenomenal world to emerge at all. But emerge they did, and in such incredible and well-crafted plenitude that causal explanations based on mechanical interactions seemed totally insufficient. As Newton was finally to say in the General Scholium to the Principia, mechanical action (what he called "blind metaphysical necessity") could not produce variety because it is always and everywhere the same. Variety requires some further cause, a divine agent, and that is what he began to search for in his alchemical studies. [18; 30; 77]

In addition to learning contemporary chemistry and beginning his study of alchemy when he returned to Cambridge, Newton proceeded to Master of Arts and was elected a Fellow of Trinity College, a position that assured him an income and position in academic life—assured, that is, if he complied with the Fellowship regulation that he become an ordained Anglican priest within the next seven years. As we shall see, the prospect of ordination in the Church of England eventually became a source of deep anxiety to him.

Newton also polished some of his mathematical work from the Woolsthorpe period and showed portions of it to Isaac Barrow, who was then Lucasian Professor of Mathematics at Cambridge; he immediately put Newton's work into circulation (in manuscript form) among interested English mathematicians. The mathematical professorship had recently been created and endowed by Henry Lucas, and Barrow was its first incumbent. But Barrow soon resigned to return to his preferred life of theological study and preaching, and Newton was elected to replace him in 1669. His age was not yet quite 27 years. Already he could add the luster of his new optics and his new calculus to the Chair; in 1687 he would also add the Principia.

But the truth of the matter was that, for all the honor the Lucasian Professorship brought to Newton and for all the honor he brought to it, he had already immersed himself in the study of alchemy, and that was to be his most consuming passion for many years. Probably he had begun to read alchemical literature in 1668; in 1669 he purchased chemicals, chemical glassware, materials for furnaces, and the six massive folio volumes of Theatrum chemicumn, a compilation of alchemical treatises. He established a laboratory of his own at Trinity College, and the records of his subsequent laboratory experimentation still exist in manuscript. Each brief, and often cryptic, laboratory report hides behind itself untold hours with hand-built furnaces of brick, with crucibles, with mortar and pestle, with the apparatus of distillation, and with charcoal fires; experimental sequences sometimes ran for weeks, months, or even years. He combed the literature of alchemy also, compiling voluminous notes and even transcribing entire treatises in his own hand. Eventually he drafted treatises of his own, filled with references to the older literature. The manuscript legacy of his scholarly endeavor is very large and represents a huge commitment of his time, but to it one must add the record of that extensive experimentation, a record that involves an amount of time impossible to estimate but surely equally huge. He seems to have continued his serious work on alchemy from about 1668 until 1696, when he left Cambridge for London and the Royal Mint, and even after 1696 he continued to study alchemical texts and to rework his own alchemical papers. [17; 18]

The focus of Newton's work in alchemy was already apparent in one of his very earliest independent alchemical papers; easily distinguishable from his reading notes and transcriptions, it is a short paper of alchemical propositions, in which he argued for the existence of a vital agent diffused through all things. This paper was probably written in 1669 (though Newton left it undated, as he did most of his papers), and it represents one of his earliest attempts to order the chaotic alchemical literature he was encounterinig.

The vital agent Newton described in that paper was universal in its operations. It had a general method of operating in all things but accommodated itself to the particular nature of particular subjects, and it assumed the particular form of each subject so as to be indistinguishable from the subject. In this manuscript Newton called the vital agent "the mercurial spirit": later he was to call it a "fermental virtue" or the "vegetable spirit" and eventually, in the Opticks, the "force of fermentation." It was responsible for organizing particles of matter into all the various forms of the phenomenal world; it was also responsible for disorganizing them, for reducing organized forms back to the primordial particles. It was the natural agent God used to organize matter and put His will into effect in the natural world. [18]

Alchemy and the mechanical philosophies of the seventeenth century seem to have shared the doctrine of the unity of matter, the idea that ultimately all forms of matter were capable of being reduced back to a primordial condition in which all matter was alike and without form. In the philosophy of Aristotle, upon which much alchemical thouglht was predicated, such formless material would have been called "prime matter" and would not have been treated as particulate, as it was in the mechanical philosophies. Nevertheless, the notion that the material substances of ordinary, everyday experience could all be reduced to something more primal, something without the ordinary properties of color, taste, odor, texture, and so forth, was not foreign to either sort of matter theory. So there was nothing antimechanistic about the idea Newton expressed in his alchemical propositions paper: that something might act upon a substance to break down the formed aggregate and reduce it to a chaotic condition in which it had no ordinary properties.

On the other hand, it seems impossible to find a mechanistic counterpart to the agent itself, for it was indeed profoundly antimechanistic. It did not act by pressure or impact, as mechanistic particles did, but instead acted in a way that suggested design and willed or planned activity, for example, in the beautifully regular patterns that form in mineral crystallization, or in the changes that occur in fermentation as grape juice is transfomed into wine, or in the marvelous transmutation of an acorn into an oak or an egg into a chick. There was no distinction made in seventeenth-century alchemical thought between what we would call the chemical and the biological realms. [15; 18]

Newton had become preoccupied with a process of disorganization and reorganization by which developed species of matter might be radically reduced, revivified, and led to generate new forms. The alchemiical agent was able to cause death and putrefaction, returning matter to an unformed condition; but it was equally able to infuse the unformed matter with new life and to lead it to new forms of organization. For as he himself said later, all matter duly formed is attended by signs of life. The implication of that statement of Newton's is, of course, that matter In a formed condition is quite different from the passive ultimate particles of unformed matter. Formed matter has somehow acquired the quality of being alive, a quality conveyed to it by the active, vital alchemical agent that acts In the formation of everything. [18; 30]

From what sources has Newton derived his ideas on the universal vital agent that he is here busily attaching to seventeenth-century mechanism'? Quite possibly only from alchemy at this early stage in his development, though his vitalistic ideas were soon reinforced by other sources, especially the Stoic philosophers. [18]

Vitalism seems to belong to the very origins of alchemy. In the early Christian centuries, when alchemical ideas were taking shape, metals had not been well characterized as distinct species. They were sometimes thought to have variable properties, like modern alloys. More frequently, they were thought to be like a mix of dough, in which the introduction of a leaven might produce desired changes by a process of fermentation, or even similar to a material matrix of unformed matter, in which the injection of an active male sperm or seed might lead to a process of generation. By analogy, alchemists referred to this critical phase of the alchemical process as fermentation or generation, and the search for the vital metallic ferment or seed became a fundamental part of their quest. Similar ideas occur in Aristotle and were commonplace in Newton's time.

Inspired by his interest in a vital agent, Newton had begun to grope his way toward mending the deficiencies of ancient atomism and contemporary corpuscularianism. He had concerned himself with life and cohesion. He now sought the source of all the apparently spontaneous processes of fermentation, putrefaction, generation, and vegetation—that is, everything associated with normal life and growth, such as digestion and assimilation, vegetation being originally from the Latin vegetare, "to animate, enliven." These processes produced the endless variety of living forms and could not be relegated to the mechanical actions of gross corpuscles, a point he emphasized in the 1670s and to which we will return later. Mechanical action could never account for the process of assimilation, in which foodstuffs were turned into the bodies of animals, vegetables, and minerals. Nor could it account for the sheer variety of forms in this world, all of which had somehow sprung from the common matter. [18]

Newton's Discovery of Stoic Philosophy and His
Later Alchemy

The most comprehensive answer to such problems of life and cohesion in antiquity had been given by the Stoics. The Stoics postulated a continuous material medium, the tension and activity of which molded the cosmos into a living whole and the various parts of the cosmic animal into coherent bodies as well. Compounded of air and a creative fire, this medium was the Stoic pneuma (a Greek work meaning "breath" or "an airy matter") and was related to the concept of the "breath of life" that escapes from a living body at the time of death and allows the formerly coherent body in which it had resided to disintegrate into its disparate parts. Although always material, the pneuma becomes finer and more active as one ascends the scale of being, and the (more corporeal) air decreases as the (less corporeal) fire increases. The Stoic Deity, literally omnipresent in the universe, is the hottest, most tense and creative form of the cosmic pneuma or aether, pure fire or nearly so. The cosmos permeated and shaped by the pneuma is not only living, it is rational and orderly and under the benevolent, providential care of the Deity. Though the Stoics were determinists, their Deity was immanent and active in the cosmos, and one of their most telling arguments against the atomists was that the order, beauty, symmetry, and purpose to be seen in the world could never have come from random, mechanical action. Only a providential God could produce and maintain such lovely, meaningful forms, and this "argument from design" for the existence of a Deity was later adopted by Christian thinkers, as we saw above. The universe, as a living body, was born when the creative fire generated the four elements of earth, water, air, and fire; it lived out its life span, permeated by vital heat and breath, cycling back to final conflagration in the divine active principle, and always regenerated itself in a perpetual circle of life and death. [17; 32; 46; 54; 86; 88; 94; 96]

The original writings of the Stoics were mostly lost, but not before ideas of pneuma and spiritus (a Latin word with a similar meaning) came to pervade medical doctrine, alchemical theory, and indeed the general culture with form-giving spirits, souls, and vital principles, for Stoicism was one of the dominant philosophies of late antiquity. Spiritualized forms of the pneuma entered early Christian theology in discussions of the immanence and transcendence of God and of the Holy Ghost, just as the Stoic arguments that order and beauty demonstrate the existence of God and of Providence entered Christianity as the argument from design for the existence of a Deity. The creative emanations of Stoic fire melded with the creative emanations of light in Neoplatonism. In addition to this broad spectrum of at least vaguely Stoic ideas, excellent, though not always sympathetic, summaries of philosophical Stoicism were available in many of the learned authors of late antiquity: Cicero, Seneca, Plutarch, Diogenes Laertius, Sextus Empiricus, and others. By the seventeenth century ideas compatible with Stoicism were very widely diffused, and latter-day Stoics, Pythagoreans, Platonists, medical men, chemists, alchemists, and even the followers of Aristotle vied with each other in celebrating the occult (hidden, secret) virtues of a cosmic aether that was the vehicle of a pure, hidden, creative fire.

Nonetheless, such a vital aether or pneuma was to be found in its most developed form in philosophical Stoicism. It is probable, as Newton's concern for the processes of life and cohesion grew apace in the early 1670s, that he amplified his mechanical philosophy further by a close reading of the available literature on the Stoics. Virtually all of the scanty fragments of ancient Stoicism known today had already been recovered by western Europe during the Renaissance, and Newton had most of them. Newton could surely have reconstructed for himself a reasonably sophisticated and comprehensive knowledge of Stoic thought from books in his own library. [18; 34]

Such reading would have affected Newton's alchemy only in reinforcing certain critical ideas, for most of his early alchemical sources were distinctly Neoplatonic in tone, and in them the universal spirit or soul of the world already permeated the cosmos with its fermental virtue. But Stoic ideas would have affected his views on the mechanical aether of his student years. It seems one may conclude that if Newton had not read the Stoics, then he must independently have reached answers similar to theirs when confronted with similar problems, for by about 1672 the original mechanical aether of his student notebook had assumed a strongly Stoic cast.

Newton described his new vitalistic aether in an alchemical treatise of about 1672, "Of Natures obvious laws & processes in vegetation." There he described the earth as a great animal or vegetable that inhales an aethereal breath for its vital processes and exhales again with a grosser breath. He called the aethereal breath a subtle spirit, nature's universal agent, her secret fire, and the material soul of all matter. The similarity between this particular Newtonian aether and the Stoic pneuma is unmistakable: they are both material, and both somehow inspire the forms of bodies and give to bodies the continuity and coherence of form that is associated with life. Furthermore, Newton was quite explicit in this treatise that the processes of life, what he called vegetation, were similar in all three kingdoms of nature: the animal, the vegetable, and the mineral. In this treatise Newton made a sharp distinction between mechanism and the life processes of vegetation: "Nature's actions are either vegetable or purely mechanical," he said. As purely mechanical he listed two items of special interest, gravity (to which we will return later) and what he called vulgar or common chemistry. [15; 18:30]

In common chemistry, of course, nature (or the chemist) may effect many changes in textures, and so forth, but, Newton argued, that sort of change occurs just by rearranging the corpuscles. On the other hand, vegetative or growth processes require some further cause, and the difference between the two sorts of chemistry (mechanical and vegetable) is "vast and fundamental." [18:30] Vegetable chemistry in the mineral kingdom is what we usually call alchemy, for the alchemists believed that metals grow in the earth just as plants grow on the surface of the earth. Newton was convinced that metals were the only part of the mineral kingdom that vegetate, other mineral substances being formed mechanically. Vegetation in metals, of which the alchemists wrote, was thus the simplest case for study, the vegetation of the animals and vegetables in the other kingdoms of nature being obviously more complex. So in the vegetation of metals (alchemy) lay the most accessible key to the problem of nonmechanical action, the kind of divinely guided activity in nature that Newton thought was necessary to correct the overly mechanized system of Descartes. [15; 18]

Newton's distinction between mechanical and vegetable chemistry thus emerges as crucial to his solution of the theological problem posed by his Cartesian inheritance. Mechanical chemistry may be accounted for simply by the mechanical coalitions and separations of the particles and requires no further explanation. But for all that great class of beings that nature produces by vegetation, we must have recourse to some further cause. Ultimately the cause is God, and within the realm of vegetable chemistry one may find an area of continuing divine guidance of the world and of matter, an area of providential care. It is God's will that directs the motion of the particles of matter and guides them into their designed arrangements. The vital Stoic and alchemical agent, the subtle spirit of life, the secret fire in the earth's aethereal breath is thus simply the natural agent God uses in directing the motion of the passive particles of matter.

One may now see that Newton was concerned from the first in his alchemical work to find evidence for the existence of a vegetative principle operating in the natural world, a principle that he understood to be the secret, universal, animating spirit of which the alchemists spoke. His early conviction was amplified by Stoic doctrines on the breath of life, the Stoic pneuma or spiritus or vital aether. He later came to see analogies between the vegetable principle and light, drawing on the Christian and Neoplatonic metaphysics of light, and he also came to see analogies between the alchemical process and the work of the Deity at the time of the creation of the world, when matter was first guided into organized forms. But above all Newton thought, and continued to think for the rest of his life, that by the use of this active vegetative principle God constantly molded the universe to His providential design, producing all manner of generations, resurrections, fermentations, and vegetation.

In short, the action of the secret animating spirit of alchemy kept the universe from being the sort of closed mechanical system for which Descartes had argued. Left to run by itself without provision for divine providential care, the Cartesian universe threatened traditional Christian values. Newton thought that belief in the Cartesian mechanical system, where matter filled all space and there was little or no room for spirit, and where no divine guidance seemed to be required on a daily basis, could lead to a materialist philosophy, to deism, or even to atheism. [18; 50; 62]

A materialist would emphasize matter to the exclusion of spirit; a deist might still believe that a Deity created the world and set it in motion but then left it to run by itself; an atheist would deny the existence of the Deity completely. Newton had a horror of all those philosophico-religious positions and was determined to do everything he could to counteract them. He thought that an irrefutable scientific demonstration of divine providential guidance of the small particles of matter would provide the needed evidence for the existence and activity of the Deity and would restore to humanity the true religion that had been lost. Given the importance of what he hoped to gain from his alchemical studies, it is easy enough to understand why he experimented and studied in that field with such persistence, year after year after year.

None of Newton's convictions in this area of his work ever suffered substantial change, and though later he revised his terms "vegetable" and "mechanical" to the terminology of "active" and "passive" (terms he had learned from Stoic philosophy), the new terminology served exactly the same metaphysical purpose as the old. The foundational thinking about "active" (divine) and "passive" (material) principles that Newton first developed in his alchemical work later supported his basic patterns of thought in both the Principia and the Opticks, but let us next see how his other religious studies developed. [18]

Newton's Work in Other Religious Subjects

We have just seen that Newton's work in alchemy had a religious motivation, for he was convinced that a demonstration of divine activity in the guidance of the passive particles of matter was possible through alchemy. Other areas of his interests were even more directly and obviously focused on religion, but the ultimate goal of one of them at least was virtually identical to his goal in studying alchemy. That was the correct interpretation of biblical prophecy and its correlation with the recorded events of history, for such a correlation would also demonstrate divine activity in the world. Newton began work on the prophecies in the 1670s if not earlier, and he is thought to have still been working on his last version of their interpretation the night before he died in 1727. [18; 24; 1011

As alchemy was the story of God's ongoing activity in the world of matter for Newton, so history was the story of God's ongoing activity in the moral world, and as such it was a key for the interpretation of prophecy. Prophecy in the Bible was divinely inspired, and Newton spent untold hours on the writings of Daniel and the Apocalypse of St. John. But human beings could fully understand prophecy only after it had been fulfilled, for it was written in "mystical" language that was not readily accessible. In any event, Newton argued, a person was not to presume to interpret it with an eye for concrete prediction of the future. Only after the prophesied events had occurred could one see that they had been the fulfillment of prophecy. Then God's action in the world was demonstrated. [18; 24; 67; 71; 74; 76; 101]

The folly of Interpreters has been, to foretel times and things by this Prophecy [John's], as if God had designed to make them prophets. By this rashness they have not only exposed themselves, but brought the Prophecy also into contempt. The design of God was much otherwise. He gave this and the Prophecies of the Old Testament, not to gratify men's curiosities by enabling them to foreknow things, but that after they were fulfilled they might be interpreted by the event, and his own Providence, not the Interpreters, be then manifested thereby to the world. For the event of things predicted many ages before, will then be a convincing argument that the world is governed by providence. [74:251]

Newton's methodology in prophetic interpretation was undoubtedly influenced by the methods of others, particularly of recent Protestant interpreters including Joseph Mede (1586-1638) and Henry More, both of Cambridge University. Yet there was in addition something peculiarly Newtonian about it. In Newton's mind history seemed to bear a direct correspondence with experimental or even mathematical demonstration. Just as an experiment might enable the investigator to decide between alternative theories of natural pheniomena, so historical facts might enable the interpreter to choose between possible interpretations of prophecy. For Newton only the firm correspondence of fact with correctly interpreted prophecy provided an adequate demonstration of God's providential action. What had been adumbrated or prophesied by divine agency in the prophecy had then been fulfilled by divine agency. What God had said He would do, He had done. That, and only that, provided for Newton a "convincinig argument" for God's providential governance of the moral world. When actual historical developments exactly matched predicted ones in "the event of thinigs predicted many ages before," one hears an echo of that Universally satisfying geometrical conclusion, (qutod erat demonstrandum: QED. [74:251-52] That was exactly what Newton wanted to demonstrate with his prophetic and historical studies—God's providential action in the moral world—just as he desired by his alchemical studies to demonstrate God's providential action in the natural world. [18; 24; 74; 99]

Probably Newton labored over prophetical interpretations for fifty years, if not more, but in another part of his religious work he labored intensively for only a few years. After that relatively brief time, he was convinced that the entire Christian tradition since the fourth century had been in error and that he, Newton, had come closer to the Truth of primitive Christianity. Afterwards he adhered to his new convictions in spite of the problems they caused him in his own society. The issue was a doctrinal or theological one having to do with the nature of the Deity. Orthodox Christian doctrine in the seventeenth century was trinitarian; that is to say, the accepted belief was that God was "Three-in-One" or "One-in-Three," one God in Three Persons (God the Father, God the Son, and God the Holy Ghost) all coequal and coeternal and ultimately One. Newton disagreed. [22; 23; 76; 101]

The problem arose initially because Newton's Fellowship at his Cambridge college required that he accept ordination as a member of the clergy of the Church of England after seven years, or else resign his Fellowship, as we saw above. During the years preceding that deadline, Newton understandably immersed himself in theological studies, and in so doing read exhaustively in the patristic literature, that is, the treatises written by the fathers of the church in the early centuries of Christianity. Among those documents he found traces of the views of Arius, a theologian of the third and fourth centuries, and of the debates on the nature of Christ (God the Son) that culminated in the decision of a church council, the Council of Nicaea in 325, that Christ, God's Son, was of the same substance as God the Father and was "begotten, not made, being of one substance with the Father," in the words of the Nicaean Creed issued by the council. Arius, who lost the argument, had believed that the Son was created, not begotten, and was not of the same substance as the Father. Newton decided, on the basis of the documents in the case, that Arius was right and that all of Christendom had been in error since 325. In the eyes of his contemporaries, however, had they but known of Newton's decision for Arius, Newton would have been the heretic and in mortal danger of losing not only his college Fellowship but also his Lucasian Chair of Mathematics. [28; 82; 101]

The viewpoint of Arius that Newton accepted was not trinitarian and thus was not orthodox, for in Arian theology the Son was created by the Supreme Deity and so was not coeternal with the Almighty God. Newton did think for a while that he would lose his Fellowship, but he cautiously let it be known that he preferred not to be ordained even while maintaining a discreet silence on the reason for that preference. The outcome was favorable for Newton: a permanent dispensation from the Fellowship requirement for ordination was obtained from the crown for the Lucasian Professor. Thus Newton was saved: he neither had to perjure himself by claiming to believe the trinitarian doctrine that he no longer believed, nor did he lose his university and college positions. [101]

Newton was so discreet about the whole matter that hardly anyone knew until the twentieth century that Newton had become an Arian in the early 1670s. Religious heterodoxy is not always a burning issue in the modern world, but getting at the Truth was a burning issue for Newton, and he was clearly prepared to relinquish his academic honors for the sake of his convictions. He remained a convinced Arian to the end of his days, and late in life he formulated an Arian creed that he presumably hoped would replace the Nicaean Creed for all believers. His Arian theology had an interesting impact on his natural philosophy also, for, as we have seen, Newton believed that Truth from any area of his studies should coalesce with Truth from any other area. We will return to a discussion of Arianism in connection with Newton's changing ideas on the cause of gravity, and in Part II we will see that a number of Newton's followers also became Arians in theology. [18; 22]

Newton's Mechanistic Theories of Gravity

As we have seen, when Newton first learned about the new mechanical philosophies of nature in his undergraduate years, he adopted a mechanistic explanation of gravity, relying on a shower of imperceptible aethereal particles that pressed bodies down toward earth. In his student notebook he even sketched two bits of machinery that might be built to take advantage of the shower of fine particles to produce perpetual motion, one machine constructed like a water wheel, the other with vanes somewhat like those of a windmill. Each was designed to operate from the impacts of the mechanical stream of aethereal matter causing gravity. [62]

A similar but more developed mechanistic explanation of gravity appeared a few years later in another of Newton's private papers, the alchemical treatise "Of Natures obvious laws & processes in vegetation," probably written about 1672. That may seem a very odd place for Newton to offer a speculative scenario about gravity, but that treatise is one of the prime exemplars of a small group of papers in which Newton was trying to fit partial Truth to partial Truth from some of his different lines of investigation. So although the mechanical aether for gravity and the vitalistic aether that carried the secret vivifying fire of the alchemists had originated in quite different studies in his early work, in this alchemical treatise Newton had combined them. The complex aether Newton then described followed a great circulatory path, not unlike that of the Cartesian vortices. It swept down to earth, making bodies heavy, but its finer and more active parts also provided the vivifying alchemical spirit. When it reached the earth, it continued into the earth's interior where it helped to generate air. The air in turn ascended from the interior to constitute the atmosphere, vapors, clouds, and so forth, until it reached the aethereal regions above. There the air pressed on the aether, forcing it to descend again toward the earth. [15; 18]

In 1675 Newton sent a paper to the Royal Society in London that contained a very similar system, but one in which the gravitational and vegetative functions of the aether were even more thoroughly combined. The movement up of air and the movement down of aether continued, with the air being "attenuated into its first principle" of aether when it reached the great aethereal spaces above. "For nature is a perpetuall circulatory worker …, Some things to ascend & make the upper terrestrial juices, Rivers and the Atmosphere; & by consequence others to descend for a Requittal to the former." [18:103; 71]

But in the 1675 paper there is one striking difference, and that is that the whole speculative system has moved toward universality. Appearing almost as an afterthought at the end of his description of the earthbound circulatory pattern, the operations of the gravitational-vegetative aether expanded to include the solar system. [18; 71]

And as the Earth, so perhaps may the Sun imbibe this Spirit copiously to conserve his Shineing, & keep the Planets from recedeing further from him. And they that will, may also suppose, that this Spirit affords or carrys with it thither the solary fewell [fuel] & materiall Principle of Light; And that the vast aethereall Spaces between us, & the stars are for a sufficient repository for this food of the Sunn & Planets. [71]

Newton's speculative aethereal system was enormously expanded in its scale of application when he thus extended it to the sun and other planets, but in no way did that expansion affect the mode of operation of the system, for both gravitational and vegetative functions were still attributed to the "Spirit." The "Spirit" had the stated gravitational function of keeping the planets in their orbits: the sun imbibed the "Spirit" to "keep the Planets from recedeing further from him." The vegetative function of the "Spirit," on the other hand, is readily apparent in other phrases: this spirit provided "food" and "fewell." It furthermore carried with it the "materiall Principle of Light," a sharp and unmistakable echo of Newton's identification of the vegetable spirit with "the body of light" in an earlier alchemical paper. [15; 18:104]

This combination of functions, both gravitational and vegetative, in Newton's speculative aethers was not to last, however. By 1679, in a letter to Robert Boyle, Newton had completely separated them and had formulated two new mechanistic scenarios to explain gravity. The new systems did not rely on a stream of aethereal particles as the old ones had done. Instead of a stream of particles flowing like a stream of water, Newton used in 1679 a nonmoving aether that was more dense in some places than in others. In both systems described to Boyle, however, gravity was again fully mechanized and detached from the vital alchemical agent.

Newton told Boyle that one of the gravitational conjectures in his letter came into his mind only as he was writing the letter, and, though we will meet a variant of that particular aethereal system again, it did not have a very long life in its original form. For a few months later, toward the end of 1679, Robert Hooke's challenges to Newton regarding the motion of bodies set Newton on a course of development that changed forever the conditions for aethereal speculation. [18; 71]

The correspondence with Hooke provided the stimulus for Newton's first solution to the problem of celestial dynamics in the terms later to appear in the Principia. As we have seen, Newton's earlier analysis of celestial motion had been cast in terms of a center-fleeing (centrifugal) force counterbalanced by the pressure of the aethereal vortex that carried the moon around the earth or the planets around the sun. In 1679 Hooke argued for a different way of approaching the problem: an attractive force toward the center of the orbit (what Newton later called the centripetal or center-seeking force), counterbalanced by the tendency of the planet or moon to move away from its orbit in a tangent (a straight line only touching the orbit in one place), due to its inertia. Having been very busy with his alchemical and theological studies during the 1670s, Newton had barely considered celestial dynamics quantitatively and had done no original work in that area since the 1660s. Hooke diverted him from his other studies and irritated him by correcting some errors Newton had made and by what Newton called Hooke's "dogmaticalnes," so Newton was "inclined" to try Hooke's mode of analysis using the centripetal force and inertia and then found the theorem by which he "afterward examined ye Ellipsis." It is possible that Newton made his trial of the new method late in 1679 or early in 1680, but even if so he once more quickly put his calculations aside for other studies, primarily alchemical and theological ones. [18:119; 71; 101]

Newton's conceptualization of gravity remained unsettled for several years following his interchange with Hooke. In an exchange of letters with Thomas Burnet (1635-1715) late in 1680 and early in the following year, Newton suggested a mechanism of vortical pressure for gravity, discussed the centrifugal force of the planets (a component of his pre-Hookian dynamical analysis), and mentioned "gravitation towards a center" without offering any mechanism for it. When conferring with John Flamsteed (1646-1719), Astronomer-Royal of England, about the comet of 1680, Newton mentioned the "attraction of ye earth by its gravity" but also mentioned the "motion of a Vortex." He was willing to "allow an attractive power" in the sun "whereby the Planets are kept in their courses about him from going away in tangent lines," which seems to presuppose Hooke's analysis, but, in refuting Flamsteed's notion that such an attraction might be magnetic, Newton utilized both the idea of the sun's vortex and the concept of the centrifugal force. About 1682 he referred to the material fluid of the heavens that gyrates around the center of the cosmic system according to the course of the planets. Not until 1684 do Newton's papers reflect the clarity of thought on dynamical principles that enabled him to launch the writing of the Principia, and only in the course of writing that work did Newton confront the problems that inhered in all his various early aethereal gravitational systems. [18:126; 71; 101; 102] …

Bibliography

Excellent reference works for students of intellectual history and the history of science are the multivolume sets The Dictionary of the History of Ideas and The Dictionary of Scientific Biography. Both will provide not only information but also additional bibliography to guide further research. For Newton himself The Newton Handbook by Derek Gjertsen (item [26] below) is perhaps the best starting place. All of the works listed below will also guide the student toward additional sources for research.

[1] H. G. Alexander, ed. The Leibniz-Clarke Correspondence, Together with Extracts from Newton's "Principia" and "Opticks." Introduction and notes by H. G. Alexander. Philosophical Classics, general ed., Peter G. Lucas. Manchester: Manchester University Press, 1956.

[2] Carl B. Boyer. A History of Mathematics. New York, London, and Sydney: John Wiley and Sons, 1968.

[3] Carl B. Boyer. The History of the Calculus and Its Conceptual Development (The Concepts of the Calculus). Foreword by Richard Courant. 1949; rpt. New York: Dover, 1959.

[4] Edwin Arthur Burtt. The Metaphysical Foundations of Modern Science. 2d rev. ed. Rpt. Garden City, NY: Doubleday, 1954.

[5] Max Caspar. Kepler. Trans. and ed. C. Doris Hellman. London: Abelard-Schuman, 1959.

[6] Ernst Cassirer. The Platonic Renaissance in England. Trans. James P. Pettegrove. Austin: University of Texas Press, 1953.

[7] Catalogue of the Newton Papers Sold by Order of the Viscount Lymington to Whom They Have Descended from Catherine Conduitt, Viscountess Lymington, Great-Niece of Sir Isaac Newton. London: Sotheby, 1936.

[8] A Catalogue of the Portsmouth Collection of Books and Papers written by or belonging to Sir Isaac Newton, the scientific portion of which has been presented by the Earl of Portsmouth to the University of Cambridge. Drawn up by the Syndicate appointed the 6th November, 1872. Cambridge: Cambridge University Press, 1888.

[9] Gale E. Christianson. In the Presence of the Creator: Isaac Newton and His Times. New York: Free Press; London: Collier Macmillan, 1984.

[10] I. Bernard. Cohen. The Birth of a New Physics. Rev. and updated. New York and London: Norton, 1985.

[11] I. Bernard Cohen. Introduction to Newton's "Principia." Cambridge: Harvard University Press; Cambridge: Cambridge University Press, 1971.

[12] I. Bernard Cohen. The Newtonian Revolution: With Illustrations of the Transformation of Scientific Ideas. Cambridge and New York: Cambridge University Press, 1980.

[13] John Conduitt. "Memoirs of Sir Isaac Newton, sent by Mr. Conduitt to Monsieur Fontenelle, in 1727." In Edmund Turnor, Collections for the History of the Town and Soke of Grantham. Containing Authentic Memoirs of Sir Isaac Newton, Now First Published From the Original MSS. in the Possession of the Earl of Portsmouth. London: Printed for William Miller, Albemarle-Street, by W. Bulmer and Co., Cleveland-Row, St. James's, 1806.

[14] René Descartes. Oeuvres de Descartes publiées par Charles Adam et Paul Tannery. 11 vols. Paris: Librairie Philosophique J. Vrin, 1964-74.

[15] B. J. T. Dobbs. Alchemical Death and Resurrection: The Significance of Alchemy in the Age of Newton. A lecture sponsored by the Smithsonian Institution Libraries in conjunction with the Washington Collegium for the Humanities Lecture Series: Death and the Afterlife in Art and Literature. Presented at the Smithsonian Institution, February 16, 1988. Washington, DC: Smithsonian Institution Libraries, 1990.

[16] B. J. T. Dobbs. "From the Secrecy of Alchemy to the Openness of Chemistry." In Tore Frängsmyr, ed., Solomon's House Revisited: The Organization and Institutionalization of Science. Nobel Symposium 75. Canton, MA.: Science History Publications, 1990.

[17] B. J. T. Dobbs. The Foundations of Newton's Alchemy, or "The Hunting of the Greene Lyon." Cambridge and New York: Cambridge University Press, 1975.

[18] B. J. T. Dobbs. The Janus Faces of Genius: The Role of Alchemy in Newton's Thought. Cambridge and New York: Cambridge University Press, 1991.

[19] Samuel Y. Edgerton, Jr. The Heritage of Giotto's Geometry: Art and Science on the Eve of the Scientific Revolution. Ithaca and London: Cornell University Press, 1991.

[20] C. H. Edwards, Jr. The Historical Development of the Calculus. New York, Heidelberg, and Berlin: Springer-Verlag, 1979.

[21] John Fauvel, Raymond Flood, Michael Shortland, and Robin Wilson, eds. Let Newton Be! Oxford: Oxford University Press, 1988.

[22] James E. Force. William Whiston: Honest Newtonian. Cambridge and New York: Cambridge University Press, 1985.

[23] James E. Force and Richard H. Popkin. Essays on the Context, Nature, and Influence of Isaac Newton's Theology. International Archives of the History of Ideas, no. 129. Dordrecht: Kluwer Academic Publishers, 1990.

[24] LeRoy Edwin Froom. The Prophetic Faith of Our Fathers: The Historical Development of Prophetic Interpretation. 4 vols. Washington, DC: Review and Herald, 1946-54.

[25] Sara Schechner Genuth. "Comets, Teleology, and the Relationship of Chemistry to Cosmology in Newton's Thought." Annali dell' Instituto e Museo di Storia della Scienza di Firenze 10 (1985): 31-65.

[26] Derek Gjertsen. The Newton Handbook. London and New York: Routledge and Kegan Paul, 1986.

[27] Edward Grant. Much Ado about Nothing: Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution. Cambridge and New York: Cambridge University Press, 1981.

[28] Robert C. Gregg and Dennis E. Groh. Early Arianism: A View of Salvation. Philadelphia: Fortress Press, 1981.

[29] Henry Guerlac. Essays and Papers in the History of Modern Science. Baltimore: Johns Hopkins University Press, 1977.

[30] Henry Guerlac. "Theological Voluntarism and Biological Analogies in Newton's Physical Thought." Journal of the History of Ideas 44 (1983): 219-29.

[31] Henry Guerlac and M. C. Jacob. "Bentley, Newton, and Providence (The Boyle Lectures Once More)." Journal of the History of Ideas 30 (1969): 307-18.

[32] David E. Hahm. The Origins of Stoic Cosmology. Columbus: Ohio State University Press, 1977.

[33] A. Rupert Hall. Philosophers at War: The Quarrel between Newton and Leibniz. Cambridge and London: Cambridge University Press, 1980.

[34] John Harrison. The Library of Isaac Newton. Cambridge and London: Cambridge University Press, 1978.

[35] Joan L. Hawes. "Newton and the 'Electrical Attraction Unexcited.'" Annals of Science 24 (1968): 121-30.

[36] Joan L. Hawes. "Newton's Revival of the Aether Hypothesis and the Explanation of Gravitational Attraction." Notes and Records of the Royal Society of London 23 (1968): 200-212.

[37] Joan L. Hawes. "Newton's Two Electricities." Annals of Science 27 (1971): 95-103. [38] J. L. Heilbron. Electricity in the Seventeenth and Eighteenth Centuries: A Study of Early Modern Physics. Berkeley and Los Angeles: University of California Press, 1979.

[39] J. L. Heilbron. Physics at the Royal Society during Newton's Presidency. Los Angeles: William Andrews Clark Memorial Library, UCLA, 1983.

[40] John Herivel. The Background to Newton's "Principia ": A Study of Newton's Dynamical Researches in the Years 1664-84. Oxford: Clarendon Press, 1965.

[41] W. G. Hiscock, ed. David Gregory, Isaac Newton, and Their Circle: Extracts from David Gregory's Memoranda, 1677-1708. Oxford: Printed for the Editor, 1937.

[42] The Holy Bible containing the Old and New Testaments. Authorized King James Version. Oxford: Oxford University Press, n.d.

[43] R. W. Home. "Force, Electricity, and the Powers of Living Matter in Newton's Mature Philosophy of Nature." In Margaret J. Osler and Paul Lawrence Farber, eds., Religion, Science, and Worldview: Essays in Honor of Richard S. Westfall. Cambridge and New York: Cambridge University Press, 1985.

[44] R. W. Home. "Newton on Electricity and the Aether." In Zev Bechler, ed., Contemporary Newtonian Research. Studies in the History of Modern Science, no. 9. Dordrecht: D. Reidel, 1982.

[45] Reijer Hooykaas. Religion and the Rise of Modern Science. Edinburgh: Scottish Academic Press, 1973.

[46] H. A. K. Hunt. A Physical Interpretation of the Universe: The Doctrines of Zeno the Stoic. Melbourne: Melbourne University Press, 1976.

[47] Keith Hutchinson. "Supernaturalism and the Mechanical Philosophy." History of Science 21 (1983): 297-333.

[48] Margaret C. Jacob. "Newton and the French Prophets: New Evidence." History of Science 16 (1978): 134-42.

[49] Margaret C. Jacob. The Newtonians and the English Revolution, 1689-1720. 1976; rpt. New York: Gordon and Breach, 1991.

[50] Margaret C. Jacob. The Cultural Meaning of the Scientific Revolution. 1988; new ed. New York: Oxford University Press, 1995.

[51] Robert Hugh Kargon. Atomism in England from Hariot to Newton. Oxford: Clarendon Press, 1966.

[52] Alexandre Koyré. From the Closed World to the Infinite Universe. 1957; rpt. New York: Harper and Brothers, 1958.

[53] Alexandre Koyr6. Newtonian Studies. Cambridge: Harvard University Press, 1965.

[54] David Charles Kubrin. "Newton and the Cyclical Cosmos: Providence and the Mechanical Philosophy." Journal of the History of Ideas 28 (1967): 325-46.

[55] David C. Lindberg. The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious, and Institutionial Context, 600 B.c. to A.D. 1450. Chicago and London: University of Chicago Press, 1992.

[56] David C. Lindberg. "The Genesis of Kepler's Theory of Light: Light Metaphysics from Plotinusto Kepler." Osiris, 2d ser. 2 (1986): 5-42.

[57] David C. Lindberg and Ronald L. Numbers, eds. God and Nature.: Historical Essays on the Encounter between Christianity and Science. Berkeley and Los Angeles: University of California Press, 1986.

[58] Jack Lindsay. The Origins of Alchemy in Graeco-Roman Egypt. New York: Barnes and Noble, 1970.

[59] A. A. Long. Hellenistic Philosophy.: Stoics, Epicureans, Sceptics. London: Duckworth, 1974.

[60] J. E. McGuire and P. M. Heimann. "The Rejection of Newton's Concept of Matter in the Eighteenth Century." In Ernan McMullin, ed., The Concept of Matter in Modern Philosophy. Notre Dame and London: University of Notre Dame Press, 1978.

[61] J. E. McGuire and P. M. Rattansi. "Newton and the 'Pipes of Pan.'" Notes and Records of the Royal Society of London 21 (1966): 108-43.

[62] J. E. McGuire and Martin Tammy. Certain Philosophical Questions.: Newton's Trinity Notebook. Cambridge and London: Cambridge: University Press, 1983.

[63] Ernan McMullin. Newton on Matter and Activity. Notre Dame: University of Notre Dame Press, 1978.

[64] Elizabeth Mackenzie. "The Growth of Plants: A Seventeenth-Century Metaphor." In English Renaissance Studies Presented to Dame Helen Gardner in Honour of Her Seventieth Birthday. Oxford: Clarendon Press, 1980.

[65] Frank E. Manuel. Isaac Newtoni, Historian. Cambridge: Belknap Press of Harvard University Press, 1963.

[66] Frank E. Manuel. A Portrait of Isaac Newton. Cambridge: Belknap Press of Harvard University Press, 1968.

[67] Frank E. Manuel. The Religion of Isaac Newton.: The Freniantle Lectures 1973. Oxford: Clarendon Press, 1974.

[68] E. C. Millington. "Theories of Cohesion in the Seventeenth Century." Annals of Science 5 (1941-47): 253-69.

[69] Charles G. Nauert, Jr. Agrippa and the Crisis of Renaissance Thought. Illinois Studies in the Social Sciences, no. 55. Urbana: University of Illinois Press, 1965.

[70] Isaac Newton. The Chronology of Anicient Kingdoms Amended. To which is Prefixd, A Short Chronicle from the First Memory of Things in Europe to the Conquest of Persia by Alexander the Great. London: Printed for J. Tonson in the Strand, and J. Osborn and T. Longman in Paternoster Row, 1728.

[71] Isaac Newton. The Correspondenc of Isaac Newton. Ed. H. W. Turnbull, J. P. Scott, A. R. Hall, and Laura Tilling. 7 vols. Cambridge: Published for the Royal Society at the University Press, 1959-77.

[72] Isaac Newton. Manuscripts and Papers Collected and Published on Microfilm by Chawyck-Healey. Ed. Peter Jones. Cambridge: Chadwyck-Healey, 1991.

[73] Isaac Newton. The Mathematical Papers of Isaac Newtoni. Ed. Derek T. Whiteside with the assistance in publication of M. A. Hoskin. 8 vols. Cambridge: Cambridge University Press, 1967-80.

[74] Isaac Newton. Observations upon the Prophecies of Daniel, and the Apocalypse of St. Johni. In Two Parts. London: Printed by J. Darby and T. Browne in Bartholomew-Close. And sold by J. Roberts in Warwick-lane, J. Tonson in the Strand, W. Innys and R. Manby at the West End of St. Paul's Church-Yard, J. Osborn and T. Longman in Pater-Noster-Row, J. Noon near Mercers Chapel in Cheapside, T. Hatchett at the Royal Exchange, S. Harding in St. Martin's lane, J. Stagg in Westminster-Hall, J. Parker in Pall-mall, and J. Brindley in New Bond-street, 1733.

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[78] Isaac Newton. Unpublished Scientific Papers of Isaac Newton: A Selection from the Portsmouth Collection in the University Library, Cambridge. Chosen, edited, and translated by A. Rupert Hall and Marie Boas Hall. Cambridge: Cambridge University Press, 1962.

[79] Margaret J. Osler. "Descartes and Charleton on Nature and God." Journal of the History of Ideas 40 (1979): 445-56.

[80] Margaret J. Osler. "Eternal Truths and the Laws of Nature: The Theological Foundations of Descartes' Philosophy of Nature." Journal of the History of Ideas 46 (1985): 349-62.

[81] Margaret J. Osler. "Providence and Divine Will in Gassendi's Views on Scientific Knowledge." Journal of the History of Ideas 44 (1983): 549-60.

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[83] Richard H. Popkin. The History of Scepticism from Erasmus to Spinoza. Berkeley and Los Angeles: University of California Press, 1979.

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[85] Arthur Quinn. The Confidence of British Philosophers: An Essay in Historical Narrative. Studies in the History of Christian Thought, vol. 17. Ed. Heiko A. Oberman, in cooperation with Henry Chadwick, Edward A. Dowey, Jaroslav Pelikan, and E. David Willis. Leiden: E. J. Brill, 1977.

[86] John Rist, ed. The Stoics. Berkeley and Los Angeles: University of California Press, 1978.

[87] Danton B. Sailor. "Newton's Debt to Cudworth." Journal of the History of Ideas 49 (1988): 511-18.

[88] Samuel Sambursky. Physics of the Stoics. 1959; rpt. London: Hutchinson, 1971.

[89] Samuel Sandmel. Philo of Alexandria: An Introduction. New York: Oxford University Press, 1979.

[90] Jason Lewis Saunders. Justus Lipsius: The Philosophy of Renaissance Stoicism. New York: Liberal Arts Press, 1955.

[91] Simon Schaffer. "Newton's Comets and the Transformation of Astrology." In Patrick Curry, ed., Astrology, Science and Society. Historical Essays. Woodbridge, Suffolk: Boydell Press, 1987.

[92] P. B. Scheuer and G. Debrock, eds. Newton's Scientific and Philosophical Legacy. International Archives of the History of Ideas, no. 123. Dordrecht: Kluwer Academic Publishers, 1988.

[93] Hillel Schwartz. The French Prophets: The History of a Millenarian Group in Eighteenth-Century England. Berkeley and Los Angeles: University of California Press, 1980.

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