MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY
Since the ancients (as we are told by Pappus), made great account of the science of mechanics in the investigation of natural things; and the moderns, laying aside substantial forms and occult qualities, have endeavoured to subject the phænomena of nature to the laws of mathematics, I have in this treatise cultivated mathematics so far as it regards philosophy. The ancients considered mechanics in a twofold respect; as rational, which proceeds accurately by demonstration: and practical. To practical mechanics all the manual arts belong, from which mechanics took its name. But as artificers do not work with perfect accuracy, it comes to pass that mechanics is so distinguished from geometry, that what is perfectly accurate is called geometrical, what is less so, is called mechanical. But the errors are not in the art, but in the artificers. He that works with less accuracy is an imperfect mechanic; and if any could work with perfect accuracy, he would be the most perfect mechanic of all; for the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved. To describe right lines and circles are problems, but not geometrical problems. The solution of these problems is required from mechanics; and by geometry the use of them, when so solved, is shown; and it is the glory of geometry that from those few principles, brought from without, it is able to produce so many things.
Therefore geometry is founded in mechanical practice, and is nothing but that part of universal mechanics which accurately proposes and demonstrates the art of measuring. But since the manual arts are chiefly conversant in the moving of bodies, it comes to pass that geometry is commonly referred to their magnitudes, and mechanics to their motion. In this sense rational mechanics will be the science of motions resulting from any forces whatsoever, and of the forces required to produce any motions, accurately proposed and demonstrated. This part of mechanics was cultivated by the ancients in the five powers which relate to manual arts, who considered gravity (it not being a manual power), no otherwise than as it moved weights by those powers. Our design not respecting arts, but philosophy, and our subject not manual but natural powers, we consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore we offer this work as the mathematical principles of philosophy; for all the difficulty of philosophy seems to consist in this—from the phænomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phænomena; and to this end the general propositions in the first and second book are directed.
In the third book we give an example of this in the explication of the System of the World; for by the propositions mathematically demonstrated in the former books, we in the third derive from the celestial phenomena the forces of gravity with which bodies tend to the sun and the several planets. Then from these forces, by other propositions which are also mathematical, we deduce the motions of the planets, the comets, the moon, and the sea. I wish we could derive the rest of the phænomena of nature by the same kind of reasoning from mechanical principles; for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain; but I hope the principles here laid down will afford some light either to this or some truer method of philosophy.
In the publication of this work the most acute and universally learned Mr. Edmund Halley not only assisted me with his pains in correcting the press and taking care of the schemes, but it was to his solicitations that its becoming public is owing; for when he had obtained of me my demonstrations of the figure of the celestial orbits, he continually pressed me to communicate the same to the Royal Society, who afterwards, by their kind encouragement and entreaties, engaged me to think of publishing them. But after I had begun to consider the inequalities of the lunar motions, and had entered upon some other things relating to the laws and measures of gravity, and other forces: and the figures that would be described by bodies attracted according to given laws; and the motion of several bodies moving among themselves; the motion of bodies in resisting mediums; the forces, densities, and motions, of mediums; the orbits of the comets, and such like; deferred that publication till I had made a search into those matters, and could put forth the whole together.
What relates to the lunar motions (being imperfect), I have put all together in the corollaries of Prop. 66, to avoid being obliged to propose and distinctly demonstrate the several things there contained in a method more prolix than the subject deserved, and interrupt the series of the several propositions. Some things, found out after the rest, I chose to insert in places less suitable, rather than change the number of the propositions and the citations. I heartily beg that what I have here done may be read with candour; and that the defects in a subject so difficult be not so much reprehended as kindly supplied, and investigated by new endeavours of my readers.
Cambridge, Trinity College, May 8, 1686
The Age of Enlightenment reached its apex in 1686 when Isaac Newton penned his Principia Mathematica. The obvious and immediate effect was on science, but the waters of theology were rippled with implication. Suddenly it seemed clear that Galileo was right when he said “Mathematics is the language in which God has written the universe.” How could the hard science of physics ever be reconciled with metaphysics?
As author Malcolm Guite wrote in his book Mariner:
One aspect of the Enlightenment which had huge implications for modernism was the divorce between reason and imagination and the consequent reduction of knowledge itself to a so-called “objective” realm of quantiﬁable fact from which all value or meaning had been drained, which in turn led to a reductive, mechanistic, and purely material account of the cosmos.
John Mark Reynolds said this in his book The Great Books Reader:
Science, especially physics, made slow progress up to Newton, but he seemed to equal all of those centuries of gains by himself. For some time, there appeared little left to do scientifically but examine the implications of his ideas and work out the details. Newton confirmed that we live in a cosmos, an ordered structure. If anything, the structure seemed too airtight for free will or chance.
Poets like William Blake feared Newton had discovered a clockwork universe with no place for God or romance, though Newton himself remained a theist. Reformed Christians in particular had viewed science and the Scientific Revolution as an ally, but beginning with Newtonian physics the doubts began to grow.
Is science the enemy of theology?
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In the beginning was the Word, and the Word was with God, and the Word was God.
John Mark Reynolds is the president of The Saint Constantine School, a school that aspires to preschool through college education. He is also a philosopher, administrator, and joyous curmudgeon. Reynolds was the founder and first director of the Torrey Honors Institute at Biola University. He was provost at Houston Baptist University where he was instrumental in starting the graduate Apologetics program and a cinema and new media arts major. John Mark blogs at Eidos on the Patheos Evangelical platform and has written for First Things and the Washington Post. He is an owner of the Green Bay Packers.
D I G D E E P E R
Isaac Newton’s Mathematical Principles of Natural Philosophy
William A. Dembski
Isaac Newton is widely regarded as the greatest scientist of all time. His claim to fame rests chiefly on this work. In it—or, the Principia Mathematica, as it is also called—Newton invents the infinitesimal calculus and with it delineates the fundamental laws governing the structure and dynamics of physical reality. From the motion of billiard balls to the motion of planets and everything in between, Newton’s Principia was thought to give the final word.
Sometimes genius is underappreciated during the life of the genius. Not so with Newton. His genius was evident and reverenced from the start. Isaac Barrow, Newton’s predecessor in the prestigious Lucasian Chair of Mathematics at Cambridge, was so impressed with Newton that he resigned and had Newton assume the chair (a professorship subsequently held by such luminaries as Charles Babbage, Paul Dirac, and, presently, Stephen Hawking).
Newton’s contemporary Edmund Halley, the famed astronomer remembered for the comet named for him, even wrote an ode to Newton. It closes with the effusive praise,
Come celebrate with me in song the name
Of Newton, to the Muses dear; for he
Unlocked the hidden treasuries of Truth:
So richly through his mind had Phoebus cast
The radiance of his own divinity.
Nearer the gods no mortal may approach.
In the same spirit, Alexander Pope, a younger contemporary, wrote this epitaph:
Nature and Nature’s laws lay hid in night:
God said, “Let Newton be!” and all was light.
Even the twentieth-century economist John Maynard Keynes recognized how profoundly Newton’s genius had impacted seventeenth-century intellectual life, referring to him as “the last wonder-child to whom the Magi could do sincere and appropriate homage.”
Although Principia Mathematica is highly technical, it contains several extended passages of interest to the general reader. Thus, for instance, we find bold statements about God’s role as a designing intelligence behind the world. Contemporary scientists who feel passionately about the religious significance of their scientific work may still offer up such statements, but usually they will keep them off to one side. Newton, by contrast, saw no contradiction in doing his best science and then immediately, in the same written work, giving it a theological interpretation.
Although we think of Newton as the preeminent scientist of his (and, indeed, any) age, it is remarkable that science was only one of the many professional hats he wore. His higher passion seems to have been theology, and he spent much time studying and writing about the Bible.
He was also an avid alchemist. Moreover, in the 1690s, he abruptly left his ivory-tower professorship at Cambridge to assume duties heading the government mint in London. (Imagine string-theorist Ed Witten leaving Princeton’s Institute for Advanced Study to move to D.C. and head the U.S. Treasury.)
Yet for all the other hats Newton wore, he accomplished nothing like the distinction he achieved in science. There he was a soaring figure. In theology, by contrast, he was a well-read but self-schooled amateur. Also, his theological views were heterodox: Though accepting the Bible as largely factual (including the miracles ascribed to Jesus), Newton sided with Arius against Athanasius, rejecting the divinity of Christ.
In ancient Athens, Socrates would go about asking recognized experts in a given area broader philosophical questions: What is justice? What is truth? (etc.) He found that expertise in one area tends not to transfer to others, especially when these require wisdom. Newton seems to fit this mold. In the science of physics, he was preeminent. And yet when he delved into other areas, he was undistinguished and, at times, even a duffer.
What is Newton’s legacy? He properly belongs to science, where he still ranks in the number one spot, though he has some close seconds and thirds (such as Albert Einstein and James Clerk Maxwell). In Newton’s day, it was thought that he had once and for all nailed down the deep structure of the physical universe. With the revolutions in electromagnetism, general relativity, and quantum mechanics in the nineteenth and twentieth centuries, however, it’s now obvious his physics was only part of the picture.
Newtonian physics captures the motion of medium-sized objects at medium speeds. That’s why it’s still the first thing beginning physics students learn. But it’s clear that the scope of Newton’s physics is strictly limited. The odes by Halley and Pope celebrating him and his achievements could no longer be written with a straight face.
In his day, he was, as John Locke said, “the incomparable Mr. Newton.” Nowadays, he is a primus inter pares: He remains the greatest of scientists, but one who rubs shoulders with other great scientists and not as one who towers above the rest.
William Dembski, PhD, is a professor of Philosophy and the director of the Center for Cultural Engagement at Southwestern Baptist Theological Seminary. He is an advocate for Intelligent Design and the author of numerous books on the topic including Intelligent Design Uncensored and The Design of Life: Discovering Signs of Intelligence in Biological Systems.
John Mark Reynolds, The Great Books Reader: Excerpts and Essays on the Most Influential Books in Western Civilization (Grand Rapids, MI: Bethany House, 2011).