From the Closed World to the Infinite Universe (10-12)

01.08.2015 09:17

X. Absolute Space and Absolute Time:


Berkeley & Newton

It is certainly Raphson's interpretation, or, it would be better to say, Raphson's disclosure of the metaphysical background of Newtonianism, that Bishop Berkeley had in mind, when, in 1710, in his Principles of Human Knowledge, he not only made a vigorous attack upon its fundamental concepts, absolute space and absolute time, but also pointed out the great danger that they implied from the theological point of view. One of the chief advantages of the radical immaterialistic and sensualistic empiricism advocated by Berkeley is, according to him, the possibility it gives us of getting rid of these entities, asserted in1


[paragraph continues] . . . a certain celebrated treatise of mechanics: in the entrance of which justly admired treatise, time, space and motion, are distinguished into absolute and relative, true and apparent, mathematical and vulgar; which distinction, as it is at large explained by the author, doth suppose those quantities to have an existence without the mind; and


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that they are ordinarily conceived with relation to sensible things, to which nevertheless, in their own nature, they bear no relation at all.


"This celebrated author," continues Berkeley, who offers us a very precise account (largely in Newton's words) of the theory he is about to criticize, holds that


[paragraph continues] . . . there is an absolute space, which being unperceivable to sense, remains in itself similar and immovable, and relative space to be the measure thereof, which being movable, and defined by its situation in respect of sensible bodies, is vulgarly taken for immovable space.


Berkeley, of course, does not accept this theory; an unperceivable reality is unthinkable and "philosophic considerations of motion doth not imply the being of absolute space distinct from what is perceived by sense and related to bodies," Newton's assertions to the contrary notwithstanding. Moreover, and though last, not least,3


What is here laid down seems to put an end to all those disputes and difficulties which have sprung up amongst the learned concerning the nature of pure space. But the chief advantage arising from it is, that we are freed from that dangerous dilemma, to which several who have employed their thoughts on this subject imagine themselves reduced, to wit, of thinking either that real space is God, or else that there is something beside God which is eternal, un-created, infinite, indivisible, immutable. Both of which may justly be thought pernicious and absurd notions. It is certain that not a few divines, as well as philosophers of great note, have, from the difficulty they found in conceiving either limit or annihilation of space, concluded it must be


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divine. And some of late have set themselves particularly to show, that the incommunicable attributes of God agree to it. Which doctrines, how unworthy soever it may seem of the divine nature, yet I do not see how we can get clear of it, so long as we adhere to the received opinions.


Berkeley's attack, though it certainly did not affect Newton as strongly as was thought by some of his historians, seems nevertheless to have been the reason, or at least one of the reasons—the second being Leibniz's accusation of introducing, by his theory of universal gravitation, the use of a senseless occult quality into natural philosophy4—that induced Newton to add to the second edition of his Principia the famous General Scholium which expresses so forcefully the religious conceptions that crown and support its empirico-mathematical construction and thus reveal the real meaning of his "philosophical" method. It seems to me rather probable that he wanted to dissociate himself from the somewhat compromising allies hinted at by Berkeley4a and, by exposing his views in his own manner, to demonstrate—as Bentley had already attempted to do—that natural philosophy, that is, his natural philosophy, leads necessarily not to the denial but to the affirmation of God's existence and of his action in the world. At the same time he obviously does not want to disavow or reject them, and in spite of Berkeley's warning, he asserts not only the existence of absolute time and space but also their necessary connection with God.

Compared to the statements made by Newton in his letters to Bentley—and much more so if compared to Bentley's elaboration of these statements and Newton's own developments in the Queries of the Opticks—Newton's

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pronouncements in the General Scholium, at least those concerning God's action in the world, are not very explicit. Thus, Newton does not tell us anything about the necessity of God's continuous concourse for the preservation of its structure; he seems even to admit that, once started, the motion of the heavenly bodies could continue forever; it is only at their beginning that God's direct intervention appears indispensable. On the other hand, the actual structure of the world (that is, of the solar system) is, of course, asserted to be the result of a conscious and intelligent choice:5


. . . in the celestial spaces where there is no air to resist their motions, all bodies will move with the greatest freedom; and the planets and comets will constantly pursue their revolutions in orbits given in kind and position, according to the laws above explained; but though these bodies may, indeed, continue in their orbits by the mere laws of gravity, yet they could by no means have at first derived the regular position of the orbits themselves from those laws.


The six primary planets are revolved about the sun in circles concentric with the sun, and with motions directed towards the same parts, and almost in the same plane. Ten moons are revolved about the earth, Jupiter, and Saturn, in circles concentric with them, with the same direction of motion, and nearly in the planes of the orbits of those planets; but it is not to be conceived that mere mechanical causes could give birth to so many regular motions, since the comets range over all parts of the heavens in very eccentric orbits; for by that kind of motion they pass easily through the orbs of the planets, and with great rapidity; and in their aphelions, where they move the slowest, and are detained the longest, they recede to the greatest


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distances from each other, and hence suffer the least disturbance from their mutual attractions. This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being. And if the fixed stars are the centres of other like systems, these, being formed by the like wise counsel, must be all subject to the dominion of One; especially since the light of the fixed stars is of the same nature with the light of the sun, and from every system light passes into all the other systems; and lest the systems of the fixed stars should, by their gravity, fall on each other, he hath placed those systems at immense distances from one another.


Newton's God is not merely a "philosophical" God, the impersonal and uninterested First Cause of the Aristotelians, or the—for Newton—utterly indifferent and world-absent God of Descartes. He is—or, in any case, Newton wants him to be—the Biblical God, the effective Master and Ruler of the world created by him:6


This Being governs all things, not as the soul of the world, but as Lord over all; and on account of his dominion he is wont to be called Lord God παντοκράτωρ or Universal Ruler; for God is a relative word, and has a respect to servants; and Deity is the dominion of God not over his own body, as those imagine who fancy God to be the soul of the world, but over servants. The Supreme God is a Being eternal, infinite, absolutely perfect; but a being, however perfect, without dominion, cannot be said to be Lord God; for we say, my God, your God, the God of Israel, the God of Gods, the Lord of Lords; but we do not say, my Eternal, your Eternal, the Eternal of Israel, the Eternal of Gods; we do not say, my Infinite, or my Perfect: these arc titles which have no respect to servants. The word God usually signifies Lord; but every Lord is not a God. It is


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the dominion of a spiritual being which constitutes a God: a true, supreme, or imaginary God. And from this true dominion it follows that the true God is a living, intelligent, and powerful Being; and from his other perfections, that he is supreme, or most perfect. He is eternal and infinite, omnipotent and omniscient; that is, his duration reaches from eternity to eternity; his presence from infinity to infinity; he governs all things, and knows all things that are or can be done.


His duration reaches from eternity to eternity; his presence from infinity to infinity . . . the Newtonian God is, patently, not above time and space: His eternity is sempiternal duration, His omnipresence is infinite extension. This being so, it is clear why Newton insists:7


He is not eternity and infinity, but eternal and infinite; he is not duration or space, but he endures and is present.


[paragraph continues] And yet, like the God of Henry More and of Joseph Raphson, he not only "endures forever and is everywhere present"; but it is "by existing always and everywhere" that "he constitutes duration and space." It is not surprising therefore that8


since every particle of space is always, and every indivisible moment of duration is everywhere, certainly the Maker and Lord of all things cannot be never and nowhere. Every soul that has perception is, though in different times and in different organs of sense and motion, still the same indivisible person. There are given successive parts in duration, coexistent parts in space, but neither the one nor the other in the person of a man, or his thinking principle; and much less can they be found in the thinking substance of God. Every man, so far as he is a thing that has perception, is


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one and the same man during his whole life, in all and each of his organs of sense.


And that,9


He is omnipresent not virtually only, but also substantially; for virtue cannot subsist without substance. In him are all things contained and moved; yet neither affects the other: God suffers nothing from the motion of bodies; bodies find no resistance from the omnipresence of God. It is allowed by all that the Supreme God exists necessarily; and by the same necessity he exists always and everywhere.


Thus "in Him we live, we move and we are," not metaphorically or metaphysically as St. Paul meant it, but in the most proper and literal meaning of these words.

We—that is, the world—are in God; in God's space, and in God's time. And it is because of this ubiquitous and sempiternal co-presence with things that God is able to exercise His dominion upon them; and it is this dominion or, more exactly, the effect of this dominion that reveals to us His otherwise unknowable and incomprehensible essence:10


We know him only by his most wise and excellent contrivances of things, and final causes; we admire him for his perfections; but we reverence and adore him on account of his dominion: for we adore him as his servants; and a god without dominion, providence, and final causes, is nothing else but Fate and Nature. Blind metaphysical necessity, which is certainly the same always and everywhere, could produce no variety of things. All that diversity of natural things which we find suited to different times and places could arise from nothing but the ideas and will of a Being necessarily existing. But, by way of allegory, God is said


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to see, to speak, to laugh, to love, to hate, to desire, to give, to receive, to rejoice, to be angry, to fight, to frame, to work, to build; for all our notions of God are taken from the ways of mankind by a certain similitude, which, though not perfect, has some likeness, however. And thus much concerning God; to discourse of whom from the appearances of things, does certainly belong to Natural Philosophy.


Thus much for God; or for Berkeley. As for gravity, or for Leibniz, Newton explains that he does not introduce into philosophy " occult qualities " and magical causes, but, on the contrary, restricts his investigation to the study and analysis of observable, patent phenomena, renouncing, at least for the time being, the causal explanation of the experientially and experimentally established laws:11


Hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power. This is certain, that it must proceed from a cause that penetrates to the very centres of the sun and planets, without suffering the least diminution of its force; that operates not according to the quantity of the surfaces of the particles upon which it acts (as mechanical causes used to do), but according to the quantity of the solid matter which they contain, and propagates its virtue on all sides to immense distances, decreasing always as the inverse square of the distances. . . . But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I feign no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the


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phenomena, and afterwards rendered general by induction. Thus it was that the impenetrability, the mobility, and the impulsive force of bodies, and the laws of motion and of gravitation, were discovered. And to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.


"I feign no hypotheses . . . "12 Hypotheses non fingo . . . a phrase that became extremely famous and also like all, or nearly all, celebrated utterances torn out of their context, completely perverted in its meaning. "I feign no hypotheses." Of course not; why should Newton "feign hypotheses," that is, fictitious and fanciful conceptions not deduced from phenomena and having therefore no basis in reality? Hypotheses, "whether of occult qualities or mechanical have no place in experimental philosophy"—of course not, as this kind of hypothesis is, by definition, either false or at least unable to conduce to experiments and be checked and confirmed (or disproved) by them. Gravity is not a hypothesis, or an "occult" quality. The existence of gravity, insofar as it is a statement about the behaviour of bodies, or about the existence of centripetal forces in consequence of which bodies, instead of moving in straight lines (as they should, according to the principle or law of inertia), are deflected and move in curves, is a patent fact; the identification of the cosmical "force" which determines the motion of planets with that in consequence to which bodies fall, that is, move towards the center of the earth, is certainly an important discovery. But the assumption of the existence in bodies of a certain force which enables them to act upon other bodies and to attract them is not a

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hypothesis either. Not even one that makes use of occult qualities. It is mere and pure nonsense.

As for "mechanical" hypotheses, that is, those of Descartes, Huygens and Leibniz, they have no place in experimental philosophy simply because they attempt to do something that cannot be done, as Newton hints rather broadly, indeed at the very beginning of the General Scholium where he shows that "the hypothesis of vortices is pressed with many difficulties." Mechanical—feigned—hypotheses, as his pupil and editor Roger Cotes explains in his famous preface to the second edition of the Principia, are the special and favorite dish of the Cartesians, who, moreover, are conduced by them into the assumptions of truly and really "occult" properties and realities. Thus having explained the sterility of Aristotelian and scholastic philosophy of nature, Cotes continues:13


Others have endeavored to apply their labors to greater advantage by rejecting that useless medley of words [of the scholastic natural philosophy]. They assume that all matter is homogeneous, and that the variety of forms which is seen in bodies arises from some very plain and simple relations of the component particles. And by going from simple things to those which are more compounded they certainly proceed right, if they attribute to those primary relations no other relations than those which Nature has given. But when they take a liberty of imagining at pleasure unknown figures and magnitudes, and uncertain situations and motions of the parts, and moreover of supposing occult fluids, freely pervading the pores of bodies, endued with an all-performing subtility, and agitated with occult motions, they run out into dreams and chimeras, and neglect the true constitution of things, which certainly is not to be


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derived from fallacious conjectures, when we can scarce reach it by the most certain observations. Those who assume hypotheses as first principles of their speculations, although they afterwards proceed with the greatest accuracy from those principles, may indeed form an ingenious romance, but a romance it will still be.


As for Leibniz, whom Cotes does not mention by name, yet clearly, though somewhat parodistically, hints at, he is no better than the Cartesians; or perhaps even worse, as he assumes the existence around "the comets and planets . . . of atmospheres . . . which by their own nature move around the sun and describe conic sections" (an unmistakable allusion to the "harmonic circulation" of the great German mathematician and arch-foe of Newton), a theory which Cotes declares to be a "fable" as fantastic as that of the Cartesian vortices, and of which he presents a rather witty and biting parody:14


Galileo has shown that when a stone projected moves in a parabola, its deflection into that curve from its rectilinear path is occasioned by the gravity of the stone towards the earth, that is, by an occult quality. But now somebody, more cunning than he, may come to explain the cause after this manner. He will suppose a certain subtile matter, not discernible by our sight, our touch, or any other of our senses, which fills the spaces which are near and contiguous to the surface of the earth, and that this matter is carried with different directions, and various, and often contrary, motions, describing parabolic curves. Then see how easily he may account for the deflection of the stone above spoken of. The stone, says he, floats in this subtile fluid, and following its motion, can't choose but describe the same figure. But the fluid moves in parabolic curves, and therefore the


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stone must move in a parabola, of course. Would not the acuteness of this philosopher be thought very extraordinary, who could deduce the appearances of Nature from mechanical causes, matter and motion, so clearly that the meanest man may understand it? Or indeed should not we smile to see this new Galileo taking so much mathematical pains to introduce occult qualities into philosophy, from whence they have been so happily excluded? But I am ashamed to dwell so long upon trifles.


Trifles? As a matter of fact, we are not dealing with trifles. The use of "hypotheses" constitutes, indeed, a deep and dangerous perversion of the very meaning and aim of natural philosophy:15


[paragraph continues] The business of true philosophy is to derive the natures of things from causes truly existent, and to inquire after those laws on which the Great Creator actually chose to found this most beautiful Frame of the World, not those by which he might have done the same, had he so pleased.


Yet the partisans of mechanical hypotheses, that is, once more, the Cartesians—and Leibniz—not only forget this fundamental rule, they go much farther and, by the denial of void space as impossible, they impose upon God a certain determinate manner of action, restrict his power and freedom, and subject him, thus, to necessity; finally, they deny altogether that the world was freely created by God. A teaching not only infamous, but also false (as Newton has shown):16


Therefore they will at last sink into the mire of that infamous herd who dream that all things are governed by fate and not by providence, and that matter exists by the necessity of its nature always and everywhere, being infinite


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and eternal. But supposing these things, it must be also everywhere uniform; for variety of forms is entirely inconsistent with necessity. It must be also unmoved; for if it be necessarily moved in any determinate direction, with any determinate velocity, it will by a like necessity be moved in a different direction with a different velocity; but it can never move in different directions with different velocities; therefore it must be unmoved. Without all doubt this world, so diversified with that variety of forms and motions we find in it, could arise from nothing but the perfectly free will of God directing and presiding over all.


From this fountain it is that those laws, which we call the laws of Nature, have flowed, in which there appear many traces indeed of the most wise contrivance, but not the least shadow of necessity. These therefore we must not seek from uncertain conjectures, but learn them from observations and experiments. He who is presumptuous enough to think that he can find the true principles of physics and the laws of natural things by the force alone of his own mind, and the internal light of his reason, must either suppose that the world exists by necessity, and by the same necessity follows the laws proposed; or if the order of Nature was established by the will of God, that himself, a miserable reptile, can tell what was fittest to be done. All sound and true philosophy is founded on the appearance of things; and if these phenomena inevitably draw us, against our wills, to such principles as most clearly manifest to us the most excellent counsel and supreme dominion of the All-wise and Almighty Being, they are not therefore to be laid aside because some men may perhaps dislike them. These men may call them miracles or occult qualities, but names maliciously given ought not to be a disadvantage to the things themselves, unless these men will say at last that all philosophy ought to be founded in atheism. Philosophy


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must not be corrupted in compliance with these men, for the order of things will not be changed.


We see now clearly why we must not feign hypotheses. Hypotheses, especially mechanical ones, implying the rejection of void space and the assertion of infinity and therefore of the necessity of matter, are not only false; they lead straight away towards atheism.

Mechanical hypotheses concerning gravity, as a matter of fact, deny God's action in the world and push him out of it. It is indeed, practically certain—and this knowledge makes the "feigning of hypotheses" completely nonsensical—that the true and ultimate cause of gravity is the action of the "spirit" of God. Newton therefore concludes his General Scholium:11


And now we might add something concerning a certain most subtle spirit which pervades and lies hid in all gross bodies; by the force and action of which spirit the particles of bodies attract one another at near distances, and cohere, if contiguous; and electric bodies operate to greater distances, as well repelling as attracting the neighbouring corpuscles; and light is emitted, reflected, refracted, inflected, and heats bodies; and all sensation is excited, and the members of animal bodies move at the command of the will, namely, by the vibrations of this spirit, mutually propagated along the solid filaments of the nerves, from the outward organs of sense to the brain, and from the brain into the muscles. But these are things that cannot be explained in few words, nor are we furnished with that sufficiency of experiments which is required to an accurate determination and demonstration of the laws by which this electric and elastic spirit operates.

XI. The Work-Day God and the God of the Sabbath

Newton & Leibniz

Newton's veiled and Roger Cotes’ open counterattack upon the "plenists" did not remain unanswered. If the Cartesians, properly speaking, did not react, Leibniz, in a letter to the Princess of Wales,1 written in November 1715, replied to the accusations formulated by Cotes by expressing to his august correspondent his misgivings concerning the weakening of religion and the spread of materialism and godless philosophies in England, where some people attributed materiality not only to souls but even to God, where Mr. Locke doubted the immateriality and the immortality of the soul, and where Sir Isaac Newton and his followers professed rather low and unworthy ideas about the power and wisdom of God. Leibniz wrote:2


Sir Isaac Newton says, that Space is an Organ, which God makes use of to perceive Things by. But if God stands in need of any Organ to perceive Things by, it will follow, that they do not depend altogether upon him, nor were produced by him.


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Sir Isaac Newton, and his Followers, have also a very odd Opinion concerning the Work of God. According to their Doctrine, God Almighty wants to wind up his Watch from Time to Time: Otherwise it would cease to move. He had not, it seems, sufficient Foresight to make it a perpetual Motion. Nay, the Machine of God's making, is so imperfect, according to these Gentlemen, that he is obliged to clean it now and then by an extraordinary Concourse, and even to mend it, as a Clockmaker mends his Work; who must consequently be so much the more unskilful a Workman, as he is often obliged to mend his Work and to set it Right. According to My Opinion, the same Force and Vigour remains always in the World, and only passes from one part of Matter to another, agreeably to the Laws of Nature, and the beautiful pre-established Order.


An accusation of the kind formulated by Leibniz could not, of course, be left without refutation. Yet, as it was obviously below the dignity and standing of Sir Isaac—who, moreover, hated all polemics and public discussions—to do it himself, the task fell upon the shoulders of Dr. Samuel Clarke, the faithful pupil and friend of Newton, who translated his Opticks into Latin,3 and, as far back as 1697, stuffed with Newtonian footnotes his translation of Rohault's Cartesian Physics. A long-drawn-out and extremely interesting correspondence resulted, which ended only with the death of Leibniz, and which throws a vivid light upon the conflicting positions of the two philosophers (Leibniz and Newton) as well as upon the fundamental issues that were in question.

Thus, Dr. Clarke, though recognizing the deplorable fact that there were, in England as elsewhere, persons who denied even natural religion or corrupted it entirely,

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explained that it was due to the spread of false materialistic philosophies (which were also responsible for the materialization of the soul and even God, mentioned by Leibniz); pointed out that these people were most effectively combatted by the mathematical philosophy, the only philosophy which proves that matter is the smallest and the least important part of the universe.4 As for Sir Isaac Newton, he does not say that space is an organ which God uses in order to perceive things, nor that God needs any means for perceiving them. Quite the contrary, he says that God, being everywhere, perceives them by his immediate presence in the very space where they are. And it is just in order to explain the immediacy of this perception that Sir Isaac Newton—comparing God's perception of things with the mind's perception of ideas—said that infinite space is, so to speak, as the sensorium of the Omnipresent God."

From the point of view of the Newtonian, Leibniz's reproach of belittling God's power and wisdom by obliging Him to repair and to wind up the world clock is both unfair and unjustified; on the contrary, it is just by His constant and vigilant action, by conferring on the world new energy that prevents its decay into chaotic disorder and immobility, that God manifests His presence in the world and the blessing of His providence. A Cartesian, or a Leibnizian God, interested only in conserving in its being a mechanical clockwork set once and forever, and endowed, once and forever with a constant amount of energy, would be nothing better than an absent God. Clarke therefore states rather wickedly that the assimilation of the world to a perfect mechanism moving without God's intervention,5

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. . . is the Notion of Materialism and Fate, and tends (under pretence of making God a Supra-Mundane Intelligence) to exclude Providence and God's Government in reality out of the World. And by the same Reason that a Philosopher can represent all Things going on from the beginning of the Creation, without any Government or Interposition of Providence, a Sceptick will easily Argue still farther Backwards, and suppose that Things have from Eternity gone on (as they now do) without any true Creation or Original Author at all, but only what such Arguers call All-Wise and Eternal Nature. If a King had a Kingdom wherein all Things would continually go on without his Government or Interposition, or without his Attending to and Ordering what is done therein; It would be to him, merely a Nominal Kingdom; nor would he in reality deserve at all the Title of King or Governor. And as those Men, who pretend that in an Earthly Government Things may go on perfectly well without the King himself ordering or disposing of any Thing, may reasonably be suspected that they would like very well to set the King aside: so whosoever contends, that the Course of the World can go on without the Continual direction of God, the Supreme Governor; his Doctrine does in Effect tend to exclude God out of the World.


Confronted with Dr. Clarke's reply that rather unexpectedly placed him under the obligation to defend himself against Clarke's sly insinuations, Leibniz struck back by pointing out that "mathematical" principles are not opposed to, but identical with, those of materialism and have been claimed by Democritus and Epicurus as well as by Hobbes; that the problem dealt with is not a mathematical but a metaphysical one, and that metaphysics, in contradistinction to mere mathematics, has to be based

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on the principle of sufficient reason; that this principle, applied to God, necessarily implies the consideration of God's wisdom in planning and creating the universe, and that, vice versa, the neglect of this principle (Leibniz does not say so outright, yet he suggests that such is the case of the Newtonians) leads directly to the world-view of Spinoza, or, on the other hand, to a conception of God closely resembling that of the Socinians,5a whose God is so utterly lacking in foresight that He has "to live from day to day." The Newtonians point out that, according to them, and in contradistinction to the materialists, matter is the least important part of the universe, which is chiefly constituted by void space. But after all, Democritus and Epicurus admitted void space just as Newton does, and if they differed from him in believing that there was much more matter in the world than there is according to Newton, they were in this respect preferable to the latter; indeed, more matter means more opportunities for God to exercise His wisdom and power, and that is a reason, or at least one of the reasons, why, in truth, there is no void space at all in the universe, and that space is everywhere full of matter.

But to come back to Newton. In spite of all the explanations of his friends,6


I find [writes Leibniz] in express Words, in the Appendix to Sir Isaac Newton's Opticks, that Space is the Sensorium of God. But the Word Sensorium hath always signified the Organ of Sensation. He, and his Friends, may now, if they think fit, explain themselves quite otherwise: I shall not be against it.


And as for the accusation of making the world a self-sufficing

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mechanism and reducing God to the status of an intelligentia supra-mundana, Leibniz replies that he never did so, that is, that he never denied that the created world needed God's continuous concourse, but only asserted that the world is a clock that does not need mending, since, before creating it, God saw, or foresaw, everything; and that he never excluded God from the world, though he did not, as his adversaries seem to do, transform Him into the soul of the world. Indeed, if God has, from time to time, to correct the natural development of the world, he can do it either by supernatural means, that is, by a miracle (but to explain natural things and processes by miracles is absurd); or He can do it in a natural way: in this case God is included in nature and becomes anima mundi. Finally,7


The comparison of a King, under whose Reign every thing should go on without his Interposition, is by no means to the present Purpose; since God preserves every thing continually, and nothing can subsist without him. His Kingdom therefore is not a Nominal one.


[paragraph continues] Otherwise we should have to say that a Prince who has so well educated his subjects that they never infringe his laws is a Prince only in name.

Leibniz does not express, as yet, his ultimate objections to Newton; the fundamental opposition appears nevertheless pretty clearly: the God of Leibniz is not the Newtonian Overlord who makes the world as he wants it and continues to act upon it as the Biblical God did in the first six days of Creation. He is, if I may continue the simile, the Biblical God on the Sabbath Day, the God who has finished his work and who finds it good,

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nay, the very best of all possible worlds, and who, therefore, has no more to act upon it, or in it, but only to conserve it and to preserve it in being. This God is, at the same time—once more in contradistinction to the Newtonian one—the supremely rational Being, the principle of sufficient reason personified, and for this very reason, He can act only according to this principle, that is, only in order to produce the greatest perfection and plenitude. He cannot therefore—any more than the God of Giordano Bruno with whom (in spite of His being a mathematician and a scientist) He has a great deal in common—either make a finite universe, or suffer void space either inside or outside the world.


It is hardly surprising that, having read Leibniz's answer to his criticism, Dr. Clarke felt himself compelled to reply: Leibniz's hints were too damaging,8 his tone too superior, and, moreover, his insistence on the implications of the term "sensorium," somewhat hastily and perhaps unhappily used by Newton, far too menacing to allow Clarke to leave Leibniz in the position of having had the last word.

Starting thus from the beginning, Clarke explains9 that the "principles of mathematical philosophy" are by no means identical with, but radically opposed to, those of materialism, precisely in that they deny the possibility of a purely naturalistic explanation of the world and postulate—or demonstrate—its production by the purposeful action of a free and intelligent Being. And as for Leibniz's appeal to the principle of sufficient reason, it is true that nothing exists without sufficient reason: where there is no cause, there is also no effect; yet the said

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sufficient reason can be simply the will of God. Thus, for instance, if one considers why a system, or a certain piece, of matter is created in one place, and another one in another, and not vice versa, there can be no other reason for that than the pure will of God. If it were not so—that is, if the principle of sufficient reason were taken absolutely, as Leibniz does—and if this will could never act unless predetermined by some cause, as a balance cannot move unless some weight make it turn, God would have no liberty of choice, which would be replaced by necessity.

As a matter of fact, Dr. Clarke subtly suggests that Leibniz, indeed, deprives his God of all liberty. Thus he forbids him to create a limited quantity of matter . . . yet by the same argument one could prove that the number of men or of any kind of creatures whatsoever should be infinite (which, of course, would imply the eternity and necessity of the world).

As for the (Newtonian) God, he is neither an intelligentia mundana, nor an intelligentia supra-mundana; nor is he an anima mundi, but an intelligence which is everywhere, in the world and outside it, in everything, and above everything. And he has no organs as Leibniz persists in insisting.10


The Word Sensory does not properly signify the Organ, but the Place of Sensation. The Eye, the Ear, &c. are Organs, but not Sensoria.


[paragraph continues] Moreover, Newton does not say that place is a sensorium, but calls it thus only by way of comparison, in order to indicate that God really and effectively perceives things in themselves, where they are, being present to them,

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and not purely transcendent—present, acting, forming and reforming (which last term, just as the term "correcting," must be understood in respect to us, or to God's works, not indeed as implying change in God's designs): thus if11


the present Frame of the Solar System (for instance) according to the present Laws of Motion, will in time fall into Confusion; and perhaps, after That, will be amended or put into a new Form


it will be new in respect to us, or to itself, not new in respect to God whose eternal plan implied just such an intervention in the normal course of events. To forbid God to do that, or to declare all God's action in the world to be miraculous or supernatural, means excluding God from the government of the world. It may be, concedes Clarke, that in this case He would still remain its Creator; He would certainly no longer be its governor.


The second paper of Dr. Clarke made Leibniz angry. Why, he complains, did they grant me this important principle that nothing happens without a sufficient reason why it should be so rather than otherwise, but they grant it only in words, not in fact. Moreover, they use against me one of my own demonstrations against real absolute space, that idol (in the sense of Bacon) of some modern Englishmen. Leibniz is right, of course: to say, as Clarke does, that God's will is, as such, a sufficient reason for anything, is to reject the principle, and to reject also the thorough-going rationalism which supports it. And to use the conception of homogeneous, infinite, real space as a basis for the demonstration that God's free (that is,

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unmotivated, irrational) will can, and must, be considered as a "sufficient reason" for something, is to insult the intelligence; and to force Leibniz to discuss the problem of space (something he did not very much want to do):12


These Gentlemen maintain therefore, that Space is a real absolute Being. But this involves them in great difficulties; for such a Being must needs be Eternal and Infinite. Hence Some have believed it to be God himself, or, one of his Attributes, his Immensity. But since Space consists of Parts, it is not a thing which can belong to God.


All that, as we know, is perfectly true. Nevertheless Leibniz's criticism of the Newtonian or, more generally, the absolutist conception of space, forgets that those who hold it deny that space consists of parts—partes extra partes—and assert, on the contrary, that it is indivisible. Leibniz is perfectly right, too, in asserting that13


[paragraph continues] Space is Something absolutely Uniform; and, without the Things placed in it, One Point of Space does not absolutely differ in any respect whatsoever from Another Point of Space. Now from hence it follows, (supposing Space to be Something in it self, besides the Order of Bodies among themselves,) that it is impossible there should be a Reason, why God, preserving the same Situations of Bodies among themselves, should have placed them in Space after one certain particular manner, and not otherwise; why every thing was not placed the quite contrary way, for instance, by changing East into West.


Yet the conclusions drawn by Leibniz and by Clarke from the same, hypothetically admitted facts are diametrically opposed. Leibniz believes that in this case, that is, in the absence of reasons for choice, God would

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not be able to act; and vice versa, from the fact of the choice and of acting, he deduces the rejection of the fundamental hypothesis, that is, the existence of an absolute space, and proclaims that space, like motion, is purely relative, or even more, is nothing else but the order of coexistence of bodies and would not exist if there were none, just as time is nothing else but the order of succession of things and events, and would not exist if there were no things or events to be ordered.

The Newtonian, on the other hand, concludes the freedom of God, that is, the non-necessity of a determining reason or motive for God's choice and action. For Leibniz, of course, this unmotivated choice is vague indifference, which is the contrary of true freedom; but for the Newtonian, it is the absolutely motivated action of the Leibnizian God which is synonymous with necessity.

The Newtonians assert that, left to itself, the motive force of the universe would decrease and finally disappear. But, objects Leibniz,14


if active Force should diminish in the Universe, by the Natural Laws which God has established; so that there should be need for him to give a new Impression in order to restore that Force, like an Artist, Mending the Imperfections of his Machine; the Disorder would not only be with respect to Us, but also with respect to God himself. He might have prevented it and taken better Measures to avoid such an Inconvenience: And therefore, indeed, he has actually done it.


The Newtonians protest against Leibniz's assertion that they make nature a perpetual miracle. And yet, if God wanted to make a free body revolve around a fixed center, though not acted upon by any other creature, He would

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not be able to achieve it without a miracle since such a motion cannot be explained by the nature of bodies. For a free body naturally moves away from a curved line along its tangent. Thus mutual attraction of bodies is something miraculous as it cannot be explained by their nature.


From now on the discussion broadens and deepens. The "papers" become longer and longer. The skirmish develops into a pitched battle. Leibniz and Clarke go at each other hammer and tongs. It is true that, to a large extent, they simply repeat, or elaborate, the same arguments—philosophers, I have already said it, seldom, if ever, convince each other, and a discussion between two philosophers resembles as often as not a "dialogue de sourds"—and yet they come more and more into the open, and the fundamental issues come more and more to the foreground.

Thus, for instance, in his third paper, Dr. Clarke re-objects to Leibniz that it is preposterous to subject God to the law of strict motivation and to deprive Him of the faculty of making a choice between two identical cases. Indeed, when God creates a particle of matter in one place rather than in another, or when He places three identical particles in a certain order rather than in another, He cannot have any reason for doing so except His pure will. The perfect equivalence of the cases, a consequence of the identity of material particles and of the isomorphism of space, is no more a reason for denying God's freedom of choice than it is an objection to the existence of an absolute, real and infinite space. And as

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for its relation to God, misrepresented by Leibniz, Clarke states the correct, Newtonian, that is, More's, doctrine:15


Space is not a Being, an eternal and infinite Being, but a Property [attribute], or a consequence of the Existence of a Being infinite and eternal. Infinite Space, is Immensity. But Immensity is not God: And therefore Infinite Space, is not God. Nor is there any Difficulty in what is here alleged about Space having Parts. For Infinite Space is One, absolutely and essentially indivisible: And to suppose it parted, is a contradiction in Terms; because there must be Space in the Partition it self; which is to suppose it parted, and yet not parted at the same time. The Immensity or Omnipresence of God, is no more a dividing of his Substance into Parts; than his Duration, or continuance of existing is a dividing of his existence into Parts. There is no difficulty here, but what arises from the figurative Abuse of the Word, Parts.


It is not Newton's admission, it is Leibniz's denial, of absolute space that leads to difficulties and absurdities. Indeed, if space were only relative, and nothing but the order and arrangement of things, then a mere displacement of a system of bodies from one place to another (for instance, of our world to the region of the farthest fixed stars) would be no change at all, and it would follow therefrom that the two places would be the same place. . . .16 It would follow also that, if God should move the whole world in a straight line, then, whatever the speed of this motion, the world would remain in the same place, and that nothing would happen if that motion were suddenly stopped.17

And if time were only an order of succession, then it would follow that, if God had created the world some

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millions of years earlier, it would, nevertheless, have been created at the same time.

We shall see in a moment what Leibniz has to object to in Dr. Clarke's reasonings (he will find them meaningless); as for us, we have to admit that they are by no means as absurd as may seem at first glance; they only represent, or imply, a formal breach (already accomplished by Henry More) with the main philosophico-theological tradition to which Leibniz remains fundamentally faithful: the Newtonians, as we know, do not attach time and space to creation but to God, and do not oppose God's eternity and immensity to sempiternity and spatial infinity, but, on the contrary, identify them. Clarke thus explains:18


God, being Omnipresent, is really present to everything, Essentially and Substantially. His Presence manifests it self indeed by its Operation, but it could not operate if it was not There.


[paragraph continues] Nothing, indeed, can act without being there; not even God: there is no action at a distance; not even for God. Yet as God is everywhere "there," He can, and does, act everywhere, and therefore, Leibniz's assertion to the contrary notwithstanding, He can achieve without miracle, but by His own—or some creature's—action that a body be deflected from the tangent and can even make a body turn around a fixed center instead of running away along the tangent; whether God in order to produce this effect acts Himself, or through a creature, is of no avail: in neither case would it be a miracle as Leibniz pretends.

It is clear that, for Clarke, Leibniz's assertion—as well as his rejection as " imperfection " of the diminution of

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the moving power in the world—is based on the assumption of the necessary self-sufficiency of nature; a conception, as we know, utterly unacceptable for the Newtonians who see in it a means of excluding God from the world.

But let us come back to Clarke's objection to Leibniz's conception of space. The first argument of Samuel Clarke is not very good, as the displacement imagined by him would be not only absolute but also relative to the aggregate of the fixed stars. But the second one is perfectly valid: in the infinite universe of Newtonian physics any, and every, body can be considered as possessing—or not possessing—a uniform, rectilinear motion in a certain direction, and though the two cases would be perfectly indistinguishable one from another, the passage from the one to the other would be accompanied by very determined effects. And if the motion were not uniform but accelerated, we should even be able to perceive it (something that would not happen if motion and space were only relative): all that is an inevitable consequence of the Newtonian principle of inertia.

Clarke, of course, does not stop here. For him—as for Bentley or Raphson—the radical distinction of matter and space implies the belief in the possible and perhaps even real finitude of the universe. Why, indeed, should matter, which occupies so small a part of space, be infinite? Why should we not admit, on the contrary, that God has created a determined amount of it, just as much as was needed for this very world, that is, for the realization of the aims that God had in creating it?


The fourth paper of Leibniz leads us directly to the deepest metaphysical problems. Leibniz starts by asserting

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with the utmost energy the absolute panarchy of the principle of sufficient reason: no action without choice, no choice without determining motive, no motive without a difference between the conflicting possibilities; and therefore—an affirmation of overwhelming importance—no two identical objects or equivalent situations are real, or even possible, in the world.19

As for space, Leibniz reasserts just as vigorously that space is a function of bodies and that, where there are no bodies, there is also no space20


The same reason, which shows that extra-mundane Space is imaginary, proves that All empty Space is an imaginary thing; for they differ only as greater and less.


[paragraph continues] This does not mean, of course, that, according to Leibniz, the world and space are both limited in extension, as was thought by the mediaeval philosophers who spoke about the "imaginary" space "outside" of the world; but, on the contrary, that void space, be it outside or inside the world, is pure fiction. Space, everywhere, is full; indeed,21


There is no possible Reason, that can limit the quantity of Matter; and therefore such limitation can have no place.


Now, let us fancy a Space wholly empty, God could have placed some Matter in it, without derogating in any respect from all other things; Therefore he hath actually placed some Matter in That Space: Therefore, there is no Space wholly Empty: Therefore All is full.22 The same Argument proves that there is no Corpuscle, but what is Subdivided.23


Moreover, the idea of void space is a metaphysically impossible idea, against which Leibniz erects objections

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analogous to, and probably derived from, those that Descartes opposed to Henry More:24


If Space is a property or Attribute, it must be the Property of some Substance. But what Substance will that Bounded empty Space be an Affection or Property of, which the Persons I am arguing with, suppose to be between Two Bodies?


[paragraph continues] This is a reasonable question, but a question to which Henry More had already given an answer, which Leibniz however chooses to disregard; he continues therefore:25


If Infinite Space is Immensity, finite Space will be the Opposite to Immensity, that is, ’twill be Mensurability, or limited Extension. Now Extension must be the Affection of some thing extended. But if That Space be empty, it will be an Attribute without a Subject, an Extension without any thing extended. Wherefore by making Space a Property, the Author falls in with My Opinion, which makes it an Order of things, and not any thing absolute.


By no means; of course there is no attribute without substance; but as we know, for the "Author" that substance is God. Leibniz does not admit it, and develops the awkward consequences of the absolutist conception:26


If Space is an absolute reality; far from being a Property or an Accident opposed to Substance, it will have a greater reality than Substances themselves. God cannot destroy it, nor even change it in any respect. It will be not only immense in the whole, but also Immutable and Eternal in every part. There will be an infinite number of Eternal things besides God.


As we know, it is just what the Newtonians, or the Henry

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[paragraph continues] More-ists assert, denying, of course, that space is something "besides" God. But their teaching, according to Leibniz, implies contradictions:27


To say that Infinite Space has no Parts, is to say that it does not consist of finite Spaces; and that Infinite Space might subsist, though all finite Spaces should be reduced to nothing. It would be as if one should say, in the Cartesian Supposition of a material extended unlimited World that such a World might subsist, though all the Bodies of which it consists, should be reduced to nothing.


By no means; Leibniz does not understand the difference between his own conception of space—a lattice of quantitative relations—and that of Newton, for whom space is a unity which precedes and makes possible all relations that can be discovered in it. Or, more probably, since it is rather difficult to believe that there was something that Leibniz did not understand, he does understand, but does not admit the conception of Newton. Thus he writes:28


If Space and Time were anything absolute, that is, if they were any thing else, besides certain Orders of Things; then indeed my assertion would be a Contradiction. But since it is not so, the Hypothesis [that Space and Time are any thing absolute] is contradictory, that is ’tis an impossible Fiction.


As for the examples and counter-objection of Dr. Clarke, Leibniz deals with them in a rather off-hand manner. Thus he reasserts that those who fancy that the active powers decrease by themselves in the world do not know the principal laws of nature; that to imagine God moving the world in a straight line is to compel him to do something

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wholly meaningless, an action without rime or reason, that is, an action that it is impossible to attribute to God. Finally, concerning attraction, which Clarke endeavors to present as something natural, Leibniz repeats:29


’Tis also a supernatural thing, that Bodies should attract one another at a distance, without any intermediate Means; and that a Body should move round, without receding in the Tangent, though nothing hinders it from so receding. For these Effects cannot be explained by the Nature of things.


Leibniz's repeated appeal to the principle of sufficient reason did not, needless to say, convince or even appease Clarke. Quite the contrary: it seemed to him to confirm his worst apprehensions. In the fourth reply he writes:30


This Notion leads to universal Necessity and Fate, by supposing that Motives have the same relation to the Will of an Intelligent Agent, as Weights have to a Balance; so that of two things absolutely indifferent, an Intelligent Agent can no more choose Either, than a Balance can move it self when the Weights on both sides are Equal. But the Difference lies here


in the distinction, disregarded by Leibniz, between a free and intelligent being, who is a self-determining agent, and a mere mechanism, which, in the last analysis, is always passive. If Leibniz were right about the impossibility of a plurality of identical objects, no creation would ever have been possible; matter, indeed, has one identical nature, and we can always suppose that its parts have the same dimension and figure.31 In other terms: the

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atomic theory is utterly incompatible with Leibniz's conception; which is, of course, perfectly true. For Leibniz there cannot be in the world two identical objects; moreover Leibniz, like Descartes, denies the existence of last, indivisible, hard particles of matter, without which Newtonian physics is inconceivable.

Leibniz's linking space (and time) with the world, and his assertion of the fictitious (imaginary) character of void space and "void" time seem to Clarke utterly unreasonable; and also full of danger. It is perfectly clear that32


Extra-mundane Space, (if the material would be Finite in its Dimensions,) is not imaginary, but Real. Nor are void Spaces in the World, merely imaginary.


It is the same in respect to time:33


Had God created the World but This Moment, it would not have been created at the Time it was created.


The denial of the possibility for God to give motion to the world is no more convincing:34


And if God has made (or can make) Matter Finite in Dimensions, the material Universe must consequently be in its Nature Moveable; For nothing that is finite, is immoveable.


Leibniz's criticism of the concept of void space is, for Clarke, based on a complete misunderstanding of its nature and on misuse of metaphysical concepts:35


Space void of Body, is the Property [attribute] of an incorporeal Substance. Space is not Bounded by Bodies, but exists equally within and without Bodies. Space is not


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inclosed between Bodies; but Bodies, existing in unbounded Space, are, themselves only, terminated by their own Dimensions.


Void Space, is not an Attribute without a Subject, because, by void Space, we never mean Space void of every thing, but void of Body only. In All void Space, God is certainly present, and possibly many other Substances which are not Matter; being neither Tangible, nor Objects of any of Our Senses.

Space is not a Substance, but a Property [attribute]; And if it be a Property [attribute] of That which is necessary, it will consequently (as all other Properties [attributes] of That which is necessary must do), exist more necessarily, though it be not itself a Substance, than those Substances Themselves which are not necessary. Space is immense, and immutable, and eternal; and so also is Duration. Yet it does not at all from hence follow, that any thing is eternal hors de Dieu. For Space and Duration are not hors de Dieu, but are caused by, and are immediate and necessary Consequences of His Existence. And without them, his Eternity and Ubiquity (or Omnipresence) would be taken away.


Having thus established the ontological status of space as an attribute of God, Clarke proceeds to the demonstration that its attribution to God does not constitute a slur on His perfection: thus it does not make God divisible. Bodies are divisible, that is, can be broken up into parts,36


but infinite Space, though it may by Us be partially apprehended, that is, may in our Imagination be conceived as composed of Parts; yet Those Parts (improperly so called) being essentially indiscerpible37 and immoveable from each other, and not partable without an express Contradiction


p. 256


in Terms, Space consequently is in itself essentially One, and absolutely indivisible.


[paragraph continues] It is this space which is a precondition of motion; and motion in the true and full sense of the word, is absolute motion, that is, motion in respect to this space, in which places, though perfectly similar, are nevertheless different. The reality of this motion proves, at the same time, the reality of absolute space:38


It is largely insisted on by Sir Isaac Newton in his Mathematical Principles (Definit. 8) where, from the Consideration of the Properties, Causes and Effects of Motion, he shows the difference between real Motion, or a Bodie's being carried from one part of Space to another; and relative Motion, which is merely a change of the Order or Situation of Bodies with respect to each other.


The problem of time is exactly parallel to that of space:39


It was no impossibility for God to make the World sooner or later than he did: Nor is it at all impossible for him to destroy it sooner or later than it shall actually be destroyed. As to the Notion of the World's Eternity; They who suppose Matter and Space to be the same, must indeed suppose the World to be not only Infinite and Eternal, but necessarily so; even as necessarily as Space and Duration, which depend not only on the Will, but on the Existence of God. But they who believe that God created Matter in what Quantity, and at what particular Time, and in what particular Spaces he pleased, are here under no difficulty. For the Wisdom of God may have very good reasons for creating This World, at That Particular Time he did.


Clarke's reasoning follows the well-trodden path: infinity implies necessity, and therefore:40

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That God Cannot limit the Quantity of Matter, is an Assertion of too great consequence, to be admitted without Proof. If he cannot limit the Duration of it neither, then the material World is both infinite and eternal necessarily and independently upon God.


Thus we see it once more: the acceptance of absolute space as an attribute of God and as the universal container or receptacle of everything is the means—the only one—to avoid infinity, that is, self-sufficiency of matter, and to save the concept of creation:41


Space is the Place of All Things, and of All Ideas: Just as Duration is the Duration of All Things, and of All Ideas. . . . This has no Tendency to make God the Soul of the World.


[paragraph continues] Far from making God immersed in the world and thus, as Leibniz insinuates, dependent upon the world, the Newtonian conception is, according to Clarke, the only one that makes Him fully and truly independent of it; fully and truly free:42


There is no Union between God and the World. The Mind of Man might with greater propriety be stiled The Soul of the Images of things which he perceives, than God can be stiled the Soul of the World, to which he is present throughout, and acts upon it as he pleases, without being acted upon by it.


[paragraph continues] And it is just because of this independence of God from the world that43


[paragraph continues] . . . If no Creatures existed, yet the Ubiquity of God, and Continuance of his Existence, would make Space and Duration to be exactly the same as they are Now.


Finally, coming back to Leibniz's persistence in misunderstanding

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[paragraph continues] Newton's theory of attraction and in wanting to make it a miracle, Clarke (who pointed out that Leibniz's own theory of the "pre-established harmony" between the non-communicating and non-acting-upon-each-other mind and body has much more right to imply a perpetual miracle) explains,44


That One Body should attract another without any intermediate Means, is indeed not a Miracle, but a Contradiction: For ’tis supposing something to act where it is not. But the Means by which Two Bodies attract each other, may be invisible and intangible, and of a different nature from mechanism; and yet, acting regularly and constantly, may well be called natural; being much less wonderful than Animal-motion, which yet is never called a Miracle.


Indeed, it is only from the point of view of the Cartesio-Leibnizian rigid dualism of mind and body, with its negation of all intermediate entities and consequent reduction of material nature to a pure, self-sustaining and self-perpetuating mechanism, that the intervention in nature of non-mechanical and therefore non-material agencies becomes a miracle. For Clarke, as for Henry More before him, this dualism is, of course, unacceptable. Matter does not constitute the whole of nature, but is only a part of it. Nature, therefore, includes both mechanical (stricto sensu) and non-mechanical forces and agencies, just as "natural" as the purely mechanical ones, material as well as immaterial entities which "fill" and pervade space and without which there would be no unity or structure in the world, or better to say, there would not be a world.

The world, of course, is not an organism, like the animal,

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and possesses no "soul." Yet it can no more be reduced to pure mechanism than the animal, in spite of Descartes.


The vigorous (or, from Leibniz's point of view, obstinate) defense by Dr. Clarke of his (untenable) position; the assurance with which he not only accepted the (absurd and damaging) consequences deduced by Leibniz from his premises—the eternity of space—but even went beyond them by openly proclaiming that space (and time) were necessary and untreated attributes of God; the lack of insight (or perfidy) with which he persisted in misinterpreting and misrepresenting Leibniz's principle of sufficient reason by identifying the supreme freedom of his supremely perfect God, unable to act except according to His supreme wisdom (that is, for the realization of the absolutely best universe unerringly recognized by Him among the infinite number of possible ones), with the fatality, necessity and passivity of a perfect mechanism, convinced Leibniz that he had to devote even more space and effort to the refutation of his adversary; and to the correction of the image that the latter presented of Leibniz's own views.

Thus the fifth (and last) paper addressed by Leibniz to the Princess of Wales became a lengthy treatise, the full analysis of which would lead us too far from our topic. It is, for us, sufficient to state that it starts with an admirable explanation of the difference between a motive, which inclines without compelling and thus preserves the spontaneity and the freedom of the subject, and a real cause, which necessarily produces its effect, and of the infinite distance that separates the moral—that is, free

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[paragraph continues] —necessity of a fully motivated action from the unfree and passive necessity of a mechanism.

Freedom, indeed, for Leibniz, as for most philosophers, means doing what is good, or best, or what one ought to do, not simply doing what one wants to.45 The laymen, alas—and Newton is no better than they—cannot make that distinction; they do not recognize freedom in the absolute determination of God's action. The laymen, and the theologians, therefore, accuse the philosophers of rejecting freedom in favor of necessity, and attribute to God actions utterly unworthy of Him. It is, however, evident that it is unreasonable to ask God to act in a purposeless irrational manner even if, strictly speaking, He is able—being all-powerful—to perform such an action. Thus, for instance:46


Absolutely speaking, it appears that God can make the material Universe finite in Extension; but the contrary appears more agreeable to his Wisdom.


And it is, of course, even less "agreeable to his Wisdom" to move the world in a straight line—why, indeed, should God do such a meaningless thing?47


And therefore the Fiction of a material finite Universe, moving forward in an infinite empty Space cannot be admitted. It is altogether unreasonable and impracticable. For, besides that there is no real Space out of the material Universe, such an Action would be without any Design in it: It would be working without doing any thing, agendo nihil agere. There would happen no Change, which could be observed by Any Person whatsoever. These are Imaginations of Philosophers who have incomplete notions, who make Space an absolute Reality.


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Leibniz had already said it in his preceding paper, and even in stronger terms. Yet, in that paper he did not tell us all his reasons for rejecting this kind of motion. He did not mention precisely the most important one, namely that such a motion would be unobservable. It is perfectly clear that, if we accept the principle of observability, absolute motion, or at least absolute uniform motion in a straight line, which everybody agrees to be unobservable, will be ruled out as meaningless, and only relative motion will be acceptable. Yet in that case, the Newtonian formulation of the principle of inertia, stating that a body remains in its status of rest or uniform motion irrespective of what happens to others, and would remain in its status of motion or rest even if no other body existed, or if all of them were destroyed by God, will have to be rejected as meaningless and therefore impossible. But as it is only in such a case that the principle of inertia is fully valid, it is not only Newton's formulation of it, but the principle itself that becomes meaningless. These are rather far-reaching consequences of an innocent-looking principle, fully confirmed by the recent discussions about relativity, that are, as a matter of fact, an aftermath of the largely forgotten discussions of the XVIIth century.

Leibniz, of course, does not require that any and every motion be actually observed; yet, according to him, it must be possible to do so, and that for a rather surprising reason, a reason that shows us the depth of Leibniz's opposition to Newton, and the fidelity of Leibniz to old Aristotelian conceptions which modern science has been at such pains to reject and to reform: for Leibniz, indeed, motion is still conceived as a change, and not as a status:48

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[paragraph continues] . . . Motion does not indeed depend upon being Observed; but it does depend upon being possible to be Observed. There is no Motion, when there is no Change that can be Observed. And when there is no Change that can be Observed, there is no Change at all. The contrary Opinion is grounded upon the Supposition of a real absolute Space, which I have demonstratively confuted by the Principle of the want of a sufficient Reason of things.


The principle of observability confirms the relative character of motion and space. But relations—another far-reaching statement—have no "real", but only an "ideal", existence. Therefore,49


since Space in it self is an Ideal thing, like Time; Space out of the World must needs be imaginary, as the Schoolmen themselves have acknowledged. The case is the Same with empty Space within the World; which I take also to be imaginary, for the reason before alleged.


The Schoolmen, to tell the truth, meant something quite different, and Leibniz knows it better than anyone: they conceived the world as finite and wanted to deny the existence of real space (and time) outside the world—Leibniz, on the contrary, denies the limitation of the universe. But in a sense he is right to appeal to them: for both time and space are intramundane and have no existence outside—or independently from—the created world. How, indeed, could time be something in itself, something real or even eternal?50


It cannot be said, that Duration is Eternal; but that Things, which continue always, are Eternal. Whatever exists of Time and Duration, perishes continually: And how can a thing exist Eternally, which, (to speak exactly),


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does never exist at all? For, how can a thing exist, whereof no Part does ever exist? Nothing of Time does ever exist, but Instants; and an Instant is not even it self a part of Time. Whoever considers These Observations, will easily apprehend that Time can only be an Ideal thing. And the Analogy between Time and Space, will easily make it appear that the one is as merely Ideal as the other.


Yet we must not unduly stress the parallelism between space and time in order not to be conduced to admit either the infinity of time, that is, the eternity of the world, or the possibility of a finite universe:51


[paragraph continues] . . . the World's having a Beginning, does not derogate from the Infinity of its Duration a parte post; but Bounds of the Universe would derogate from the Infinity of its Extension. And therefore it is more reasonable to admit a Beginning of the World, than to admit any Bounds of it; that the Character of its infinite Author, may be in Both Respects preserved.


However, those who have admitted the Eternity of the World, or, at least, (as some famous Divines have done) the possibility of its Eternity, did not, for all that, deny its dependence upon God; as the Author here lays to their Charge, without any Ground.


The Newtonians, of course, do not accept these Leibnizian "axioms" (and we have just seen that they have very good reasons for not doing so, as they overthrow the .very foundations of their physics), and try to save absolute space by relating it to God. Leibniz, therefore, reminds us of his already formulated objections, which he repeats in the pious hope that, finally, he will succeed in convincing his opponent (or, at least, the Princess of

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[paragraph continues] Wales) how utterly impossible it is to confer an absolute existence on void space.52


I objected, that Space, taken for something real and absolute without Bodies, would be a thing eternal, impassible, and independent upon God. The Author endeavours to elude this Difficulty, by saying that Space is a property [attribute] of God.


I objected further, that if Space be a property [attribute], and infinite Space be the Immensity of God; finite Space will be the Extension or Mensurability of something finite. And therefore the Space taken up by a Body, will be the Extension of that Body. Which is an absurdity; since a Body can change Space, but cannot leave its Extension.


[paragraph continues] Rather amusing to see Leibniz use against Clarke the same arguments that Henry More used against Descartes. But let us continue:53


If infinite Space is God's Immensity, infinite Time will be God's Eternity; and therefore we must say, that what is in Space, is in God's Immensity, and consequently in his Essence; and that what is in Time, is also in the Essence of God. Strange Expressions; which plainly show, that the Author makes a wrong use of Terms.


Assuredly, at least if we follow the traditional scholastic conceptions. But the Newtonians, as we know, reinterpret these terms and expressly identify God's immensity with infinite extension and God's eternity with infinite duration. They will therefore acknowledge that everything is in God, without being obliged to put everything in his essence. But Leibniz insists:54


I shall give another Instance of This. God's Immensity makes him actually present in all Spaces. But now if God


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is in Space, how can it be said that Space is in God, or that it is a Property [attribute] of God? We have often heard, that a Property [attribute] is in its Subject; but we never heard, that a Subject is in its Property [attribute]. In Like manner, God exists in all Time. How then can Time be in God; and how can it be a Property [attribute] of God? These are perpetual Alloglossies.


Once more, the Newtonians would object that the preposition in is obviously taken in two different meanings, and that nobody has ever interpreted the attribute being in the substance as a spatial relation; that, moreover, they only draw a correct conclusion from God's omnipresence, which everybody admits, and God's simplicity, which everybody admits also, by refusing to recognize, in God, a separation between His substance and His power and asserting therefore His substantial presence everywhere. They would deny Leibniz's contention that55


It appears that the Author confounds Immensity or the Extension of Things, with the Space according to which that Extension is taken. Infinite Space, is not the Immensity of God; Finite Space, is not the Extension of Bodies: As Time is not their Duration. Things keep their Extension; but they do not always keep their Space. Every Thing has its own Extension, its own Duration; but it has not its own Time, and does not keep its own Space.


Of course not. But for the Newtonians, it means precisely that time and space do not belong to things, nor are relations based upon the existence of things, but belong to God as a framework in which things and events have and take place. Leibniz knows it, of course, but he cannot admit this conception:56

p. 266


Space is not the Place of all Things; for it is not the Place of God. Otherwise there would be a thing co-eternal with God, and independent upon him; nay, he himself would depend upon it, if he has need of Place.


If the reality of Space and Time, is necessary to the Immensity and Eternity of God, if God must be in Space; if being in Space is a Property [attribute] of God; he will, in some measure, depend upon Time and Space, and stand in need of them. For I have already prevented That Subterfuge, that Space and Time are Properties [attributes] of God.


Still, Leibniz knows that his own position implies difficulties (they are not proper to it, but are those of the whole scholastic tradition): if space and time are only innerworldly entities, and did not exist before Creation, must we not assume that the creation of the world brought about change in God; and that, before it, He was neither immense nor omnipresent? is not, therefore, God, in his own conception, dependent upon creatures? Leibniz writes then:57


’Tis true, the Immensity and Eternity of God would subsist, though there were no Creatures; but those Attributes would have no dependence either on Times or Places. If there were no Creatures, there would be neither Time nor Place, and consequently no actual Space. The Immensity of God is independent upon Space, as Eternity is independent upon Time. These attributes signify only, that God would be present and co-existent with all the Things that should exist.


A perfect answer. . . . Alas, the Newtonian will not accept it, and will persist in his affirmation that though, of course, God cannot be co-present with things that do

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not exist, their existence or non-existence does not make him more, or less, present in those places where these things, once created, will co-exist with him.


Having dealt with the general problem of space and time, Leibniz passes to the re-examination of the particular problem of attraction. Dr. Clarke's explanation did not satisfy him; quite the contrary. A miracle is not defined by its being an exceptional and rare happening: a miracle is defined by the very nature of the event. Something that cannot be explained naturally, that is, something that cannot result from the interplay of natural forces, that is, forces derived from the nature of things, is and remains a miracle. Now the nature of things does not admit action at a distance. Attraction therefore would be a miracle, though a perpetual one. Moreover, according to Leibniz, the suggestion made by Dr. Clarke to explain it by the action of non-mechanical, "spiritual " forces, is even worse; this, indeed, would mean going back behind Descartes, renouncing science for magic. Once more we see expressed in this debate the radical opposition of two conflicting views of nature, and of science: Leibniz can accept neither the Newtonian conception of the insufficiency of the material nature nor the provisional positivism of his conception of "mathematical philosophy":58


I objected, that an Attraction, properly so called, or in the Scholastic Sense, would be an Operation at a Distance, without any Means intervening. The Author answers here, that an attraction without any means intervening would be indeed a Contradiction. Very well! But then what does he mean, when he will have the Sun to attract the Globe of


p. 268


the Earth through an empty Space? It is God himself that performs it? But this would be a Miracle, if ever there was any. This would surely exceed the Powers of Creatures.


Or, are perhaps some immaterial Substances, or some spiritual Rays, or some Accident without a Substance, or some Kind of Species Intentionalis, or some other I know not what, the Means by which this is pretended to be performed? Of which sort of things, the Author seems to have still a good stock in his Head, without explaining himself sufficiently?

That Means of communication (says he) is invisible, intangible, not Mechanical. He might as well have added, inexplicable, unintelligible, precarious, groundless, and unexampled.

If the Means, which causes an Attraction properly so called, be constant, and at the same time inexplicable by the Powers of Creatures, and yet be true; it must be a perpetual Miracle: And if it is not miraculous, it is false. ’Tis a Chimerical Thing, a Scholastic occult quality.

The Case would be the same, as in a Body going round without receding in the Tangent, though nothing that can be explained, hindered it from receding. Which is an Instance I have already alleged; and the Author has not thought fit to answer it, because it shows too clearly the difference between what is truely Natural on the one side, and a chimerical occult Quality of the Schools on the other.


Once more Dr. Clarke replied. He was, needless to say, not convinced. Leibniz's subtle distinctions did not succeed in hiding the brute fact that his God was subjected to a strict and unescapable determinism. He lacked not only the true freedom that belongs to a spiritual being but even the spontaneity (Leibniz, moreover, seemed to Clarke to confound the two) belonging to an animal

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one: He was no more than a pure mechanism enchained by an absolute necessity. If Dr. Clarke had the gift of foreseeing things, he would say: a mere calculating machine!

Leibniz's renewed attack on Newton's conceptions of time, space and motion is not more successful.59


It is affirmed, that Motion necessarily implies a Relative Change of Situation in one Body, with regard to other Bodies; And yet no way is shown to avoid this absurd Consequence, that then the Mobility of one Body depends on the Existence of other Bodies; and that any single Body existing Alone, would be incapable of Motion; or that the Parts of a circulating Body (suppose the Sun) would lose the vis centrifuga arising from their circular Motion, if all the extrinsick Matter around them were annihilated, ’tis affirmed that the Infinity of Matter is an Effect of the Will of God.


[paragraph continues] And yet, if it were true that—as taught by Descartes—a finite universe is contradictory, is it not clear that, in this case, God neither is, nor was, able to limit the quantity of matter and therefore did not create, and can not destroy it? Indeed,60


if the Material Universe can possibly, by the Will of God, be finite and Moveable: (which this learned Author here finds himself necessitated to grant, though he perpetually treats it as an impossible supposition;) then Space (in which That Motion is performed) is manifestly independent upon Matter. But if, on the contrary, the material Universe Cannot be finite and moveable and Space cannot be independent upon Matter; then (I say) it follows evidently, that God neither Can nor ever Could set Bounds to Matter; and consequently the material Universe must be not only


p. 270


boundless, but eternal also, both a parte ante and a parte post necessarily and independent of the Will of God.


As for the relation between space, body and God, Clarke restates his position with perfect clarity:61


The space occupied by a body is not the extension of that body; but the extended body exists in this space.


There is no bounded space; but our imagination considers in the space, which has no limits and cannot have any, such a part, or such a quantity that it judges convenient to consider.

Space is not the affection of one or several bodies, nor that of any bounded thing, and it does not pass from one subject to another, but it is always, and without variation, the immensity of an immense being, which never ceases to be the same.

Bounded spaces are not properties of bounded substances; they are only parts of the infinite space in which the bounded substances exist.

If matter were infinite, infinite space would no more be a property of this infinite body than finite spaces are properties of finite bodies. But, in this case, infinite matter would be in infinite space as finite bodies are in it now.

Immensity, as well as Eternity, is essential to God. The Parts of Immensity, (being totally of a different Kind from corporeal, partable, separable, divisible, moveable Parts, which are the ground of Corruptibility), do no more hinder Immensity from being essentially One, than the Parts of Duration hinder Eternity from being essentially One.

God himself is not subjected to any change by the diversity and the change of things that are in him, and which in him have life, motion and being.

This strange Doctrine is the express Assertion of St. Paul, as well as the plain Voice of Nature and Reason.


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God is not in space or in time; but his existence is the cause of space and time. And when we say, in conformity with the language of the vulgar, that God exists in all the spaces and in all the times,


These Words mean only that he is Omnipresent and Eternal, that is, that Boundless Space and Time are necessary Consequences of his Existence; and not, that Space and Time are Beings distinct from him, and in which he exists.




to say that Immensity does not signify Boundless Space, and that Eternity does not signify Duration or Time without Beginning and End, is (I think) affirming that Words have no meaning.


As for the criticism of attraction, Clarke, of course, maintains his point of view: miracles are rare and meaningful events produced by God for definite reasons; a perpetual miracle is a contradiction in terms; and if not, then the pre-established Harmony of Leibniz is a much greater one. Moreover—Clarke is rather astonished that Leibniz does not understand this—in Newtonian science or mathematical philosophy, attraction (whatever be its ultimate physical or metaphysical explanation) appears only as a phenomenon, as a general fact and as a mathematical expression. Therefore,63


it is very unreasonable to call Attraction a Miracle and an unphilosophical Term; after it has been so often distinctly declared, that by That Term we do not mean to express the Cause of Bodies tending towards each other, but barely the Effect, or the Phaenomenon it self, and the Laws or Proportions of that Tendency, discovered by Experience


p. 272

which clearly shows


that the Sun attracts the Earth, through the intermediate void Space; that is that the Earth and Sun gravitate towards each other, or tend (whatever be the Cause of that Tendency) towards each other, with a Force, which is in a direct proportion of their Masses, or Magnitudes and Densities together, and in an inverse duplicate proportion of their Distances.


But, of course, there is much more behind this Leibnizian opposition to attraction than a mere unwillingness to adopt the point of view of "mathematical" philosophy with its admission into the body of science of incomprehensible and inexplicable "facts" imposed upon us by empiricism: what Leibniz really aims at is the self-sufficiency of the world-mechanism, and there is very little doubt that the law of conservation of the vis viva achieves it in a still better way than the Cartesian law of conservation of motion.

The Newtonian world—a clock running down—requires a constant renewal by God of its energetic endowment; the Leibnizian one, by its very perfection, rules out any intervention of God into its perpetual motion. Thus it is not surprising that for Dr. Clarke the fight for void space, hard atoms and absolute motion becomes a fight for God's Lordship and presence, and that he asks Leibniz why64


. . . so great Concern should be shown, to exclude God's actual Government of the World, and to allow his Providence to act no further than barely in concurring (as the Phrase is) to let all Things do only what they would do of themselves of mere Mechanism.

XII. Conclusion:


Why, indeed? Leibniz, who was much more interested in morals than in physics and in man than in the cosmos, could have answered that it was the only means to avoid making God responsible for the actual management, or mismanagement, of this our world. God just did not do what He wanted, or would like to do. There were laws, and rules, that He could neither change nor tamper with. Things had natures that He could not modify. He had made a perfect mechanism in the working of which He could not interfere. Could not and should not, as this world was the best of all the possible worlds that He could create. God, therefore, was blameless for the evils that He could not prevent or amend. After all, this world was only the best possible world, not a perfectly good one; that was not possible.

Leibniz might have said this in reply to Clarke. But he did not read Clarke's fifth reply. He died before he received it. Thus their fight, a fight in which both sides fought pro majore Dei gloria, ended as abruptly as it started. The outcome of the Homeric struggle was not conclusive; neither side, as we have seen, budged an inch. Yet, in the decades that followed, Newtonian science and

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[paragraph continues] Newtonian philosophy gained more and more ground, gradually overcoming the resistance of the Cartesians and the Leibnizians who, though opposing each other on many points, made a common front against the common foe.

At the end of the century Newton's victory was complete. The Newtonian God reigned supreme in the infinite void of absolute space in which the force of universal attraction linked together the atomically structured bodies of the immense universe and made them move around in accordance with strict mathematical laws.

Yet it can be argued that this victory was a Pyrrhic one, and that the price paid for it was disastrously high. Thus, for instance, the force of attraction which, for Newton, was a proof of the insufficiency of pure mechanism, a demonstration of the existence of higher, non-mechanical powers, the manifestation of God's presence and action in the world, ceased to play this role, and became a purely natural force, a property of matter, that enriched mechanism instead of supplanting it. As Dr. Cheyne explained quite reasonably, attraction was assuredly not an essential property of body, but why should not God have endowed matter with unessential properties? Or, as Henry More and Roger Cotes—and later, Voltaire—pointed out, since we possess no knowledge of the substances of things, and know nothing about the link that connects property with substance, even in the cases of hardness or impenetrability, we cannot deny that attraction belongs to matter just because we do not understand how it works.

As for the dimensions of the material universe which Newtonians at first had opposed to the actual infinity of absolute space, the relentless pressure of the principles

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of plenitude and sufficient reason, by which Leibniz managed to infect his successful rivals, made it co-extensive with space itself. God, even the Newtonian one, could obviously not limit His creative action and treat a certain part of infinite homogeneous space—though able to distinguish it from the rest—in a way so utterly different from the others. Thus the material universe, in spite of filling only an exceedingly small part of the infinite void, became just as infinite as this. The same reasoning which prevented God from limiting His creative action in respect to space could, just as well, be applied to time. An infinite, immutable and sempiternal God could not be conceived as behaving in a different manner at different times, and as limiting His creative action to a small stretch of it. Moreover, an infinite universe existing only for a limited duration seems illogical. Thus the created world became infinite both in Space and in Time. But an infinite and eternal world, as Clarke had so strongly objected to Leibniz, can hardly admit creation. It does not need it; it exists by virtue of this very infinity.

Furthermore, the gradual dissolution of traditional ontology under the impact of the new philosophy undermined the validity of the inference from the attribute to its supporting substance. Space, consequently, lost progressively its attributive or substantial character; from the ultimate stuff which the world was made of (the substantial space of Descartes) or the attribute of God, the frame of his presence and action (the space of Newton), it became more and more the void of the atomists, neither substance nor accident, the infinite, uncreated nothingness, the frame of the absence of all being; consequently also of God's.

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Last but not least, the world-clock made by the Divine Artifex was much better than Newton had thought it to be. Every progress of Newtonian science brought new proofs for Leibniz's contention: the moving force of the universe, its vis viva, did not decrease; the world-clock needed neither rewinding, nor mending.

The Divine Artifex had therefore less and less to do in the world. He did not even need to conserve it, as the world, more and more, became able to dispense with this service.

Thus the mighty, energetic God of Newton who actually "ran" the universe according to His free will and decision, became, in quick succession, a conservative power, an intelligentia supra-mundana, a "Dieu fainéant."

Laplace who, a hundred years after Newton, brought the New Cosmology to its final perfection, told Napoleon, who asked him about the role of God in his System of the World: "Sire, je n’ai pas eu besoin de cette hypothèse." (I did not need this hypothesis) But it was not Laplace's System, it was the world described in it that no longer needed the hypothesis God.

The infinite Universe of the New Cosmology, infinite in Duration as well as in Extension, in which eternal matter in accordance with eternal and necessary laws moves endlessly and aimlessly in eternal space, inherited all the ontological attributes of Divinity. Yet only those—all the others the departed God took away with Him.





1. Cf. A. N. Whitehead, Science and the modern world, New York, 1925; E. A. Burtt, The metaphysical foundations of modern physical science, New York, 1926; J. H. Randall, The making of the modern mind, Boston, 1926; Arthur O. Lovejoy's classical Great chain of being, Cambridge, Mass., 1936, and my own Études Galiléennes, Paris, 1939.

2. The cosmos conception is only practically, that is, historically, linked together with the geocentric world-view. Yet it can be completely divorced from the latter as, for example, by Kepler.

3. The full story of the transformation of the space conception from the Middle Ages to modern times should include the history of the Platonic and Neoplatonic revival from the Florentine Academy to the Cambridge Platonists as well as that of the atomic conceptions of matter and the discussions about the vacuum following the experiments of Galileo, Torricelli and Pascal. But this would double the volume of this work and, besides, distract us somewhat from the very definite and precise line of development which we are following here. Moreover, for some of these problems we can refer our readers to the classical books of Kurd Lasswitz, Geschichte des Atomistik, 2 vols., Hamburg und Berlin, 1890, and Ernst Cassirer, Das Erkenntnisproblem in der Philosophie und Wissenschaft der neuen Zeit, 2 vols., Berlin, 1911, as well as to the recent works of Cornelis de Waard, L’expérience barométrique, ses antécédents et ses explications, Thouars, 1936, and Miss Marie Boas, "Establishment of the mechanical philosophy," Osiris, vol. x, 1952. See now Max Jammer, Concepts of space, Harvard Univ. Press, Cambridge, Mass., 1954, and Markus Fierz, "Ueber den Ursprung und Bedeutung von Newtons Lehre vom absoluten Raum," Gesnerus, vol. xi, fasc. 3 / 4, 1954, especially for the space conceptions of Telesio Pattrizzi and Campanella.

4. On the Greek conceptions of the universe cf. Pierre Duhem, Le système du monde, vol. i and ii, Paris, 1913, 1914; R. Mondolfo, L’infinito nel pensiero dei Greci, Firenze, 1934, and Charles Mugler, Devenir cyclique et la pluralité des mondes, Paris, 1953.

p. 278

5. The MS of De rerum natura was discovered in 1417. On its reception and influence cf. J. H. Sandys, History of classical scholarship, Cambridge, 1908, and G. Hadzitz, Lucretius and his influence, New York, 1935.

6. The first Latin translation of Diogenes Laertius’ De vita et moribus philosophorum by Ambrosius Civenius appeared in Venice in 1475 and was immediately reprinted in Nürnberg in 1476 and 1479.

7. The atomism of the ancients, at least in the aspect presented to us by Epicurus and Lucretius—it may be that it was different with Democritus, but we know very little about Democritus—was not a scientific theory, and though some of its precepts, as for instance, that which enjoins us to explain the celestial phenomena on the pattern of the terrestrial ones, seem to lead to the unification of the world achieved by modern science, it has never been able to yield a foundation for development of a physics; not even in modern times: indeed, its revival by Gassendi remained perfectly sterile. The explanation of this sterility lies, in my opinion, in the extreme sensualism of the Epicurean tradition; it is only when this sensualism was rejected by the founders of modern science and replaced by a mathematical approach to nature that atomism—in the works of Galileo, R. Boyle, Newton, etc.—became a scientifically valid conception, and Lucretius and Epicurus appeared as forerunners of modern science. It is possible, of course, and even probable, that, in linking mathematism with atomism, modern science revived the deepest intuitions and intentions of Democritus.

8. Cf. René Descartes, "Lettre à Chanut," June 6, 1647, Oeuvres, ed. Adam Tannery, vol. v, p. 50 sq., Paris, 1903.

9. Nicholas of Cusa (Nicholas Krebs or Chrypffs) was born in 1401 in Cues (or Cusa) on the Moselle. He studied law and mathematics in Padua, then theology in Cologne. As archdeacon of Liège he was a member of the Council of Basel (1437), was sent to Constantinople to bring about a union of the Eastern and Western churches, and to Germany as papal legate (1440). In 1448 he was raised by Pope Nicholas V to the cardinalate, and in 1450 he was appointed Bishop of Britten. He died August 11, 1464. On Nicholas of Cusa cf. Edmond Vansteenberghe, Le Cardinal Nicolas de Cues, Paris, 1920; Henry Bett, Nicolas of Cusa, London, 1932; Maurice de Gandillac, La philosophie de Nicolas de Cues, Paris, 1941.

10. Cf. Ernst Hoffmann, Das Universum von Nikolas von Cues, especially the Textbeilage by Raymond Klibansky, pp. 41 sq., which gives the text of Nicholas of Cusa in a critical edition as well as the bibliography of the problem. The booklet of E. Hoffmann appeared as "Cusanus

p. 279

[paragraph continues] Studien, I" in the Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Philosophisch-Historische Klasse, Jahrgang 19291930, 3. Abhandlung, Heidelberg, 1930.

11. Cf. De docta ignorantia, 1. ii, cap. ii, p. 99. I am following the text of the latest, critical, edition of the works of Nicholas of Cusa by E. Hoffmann-R. Klibansky (Opera omnia, Jussu et auctoritate Academiae litterarum Heidelbergensii ad codicum fidem edita, vol. i, Lipsiae, 1932). There is, now, an English translation of the De docta ignorantia by Fr. Germain Heron: Of learned ignorance by Nicholas Cusanus, London, 1954. I have, nevertheless, preferred to give my own translation of the texts I am quoting.

12. Ibid., p. 99 sq.

13. Ibid., p. 100.

14. Ibid., p. 100 sq. It is to be remembered, however, that the conception of the relativity of motion, at least in the sense of the necessity to relate motion to a resting reference-point (or body) is nothing new and can already be found in Aristotle; cf. P. Duhem, Le mouvement absolu et le mouvement relatif, Montlignon, 1909; the optical relativity of motion is studied at length by Witello (cf. Opticae libri decem, p. 167, Basilae, 1572) and, even more extensively, by Nicole Oresme, (cf. Le livre du ciel et de la terre, ed. by A. D. Meuret and A. J. Denomy, C. S. B., pp. 271 sq., Toronto, 1943).

15. Ibid., p. 102.

16. Ibid., p. 102 sq.

17. De docta ignorantia, l. ii, cap. 12, p. 103.

18. Cf. the famous passage of Virgil, Provehimur portu terraeque urbesque recedunt, quoted by Copernicus.

19. This famous saying which describes God as a sphaera cuius centrum ubique, circumferentia nullibi appears for the first time in this form in the pseudo-Hermetic Book of the XXIV philosophers, an anonymous compilation of the XIIth century; cf. Clemens Baemker, Das pseudohermetische Buch der XXIV Meister (Beiträge zur Geschichte der Philosophie und Theologie des Mittelalters, fasc. xxv), Münster, 1928; Dietrich Mahnke, Unendliche Sphaere und Allmittelpunct, Halle/Saale, 1937. In this Book of the XXIV philosophers, the above-mentioned formula forms the proposition ii.

20. He is, however, referred to by Giovanni Francesco Pico in his Examen doctae vanitatis gentium (Opera, t. ii, p. 773, Basileae, 1573) and Celio Calcagnini in his Quod coelum stet, terra moveatur, vel de perenni motu terrae (Opera aliquot, p. 395, Basileae, 1544); cf. R. Klibansky, op. cit., p. 41.

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21. Cf. L. A. Birkenmajer, Mikolaj Kopernik, vol. i, p. 248, Cracow, 1900. Birkenmajer denies any influence of Nicholas of Cusa on Copernicus. On the medieval "forerunners" of Copernicus cf. G. McColley, "The theory of the diurnal rotation of the earth," Isis, xxvi, 1937.

22. De docta ignorantia, ii, 12, p. 104.

23. Nicholas of Cusa's conception could be treated as an anticipation of that of Sir William Herschell; and even of more modern ones.

24. De docta ignorantia, ii, 12, p. 104.

25. Ibid., p. 105.

26. Ibid., p. 107. Once more, one could see in this conception of Nicholas of Cusa a prefiguration of the theory of the mutual attraction of the heavenly bodies.

27. Ibid., p. 107.

28. Ibid., p. 108 sq.

29. Marcellus Stellatus Palingenius, whose true name was Pier Angelo Manzoli, born at La Stellata some time between 1500 and 1503, wrote, under the title of Zodiacus vitae, a didactical poem, which was printed in Venice (probably) in 1534, rapidly became extremely popular, especially among Protestants, and was even translated into English, French and German. The English translation (Zodiake of life) by Barnaby Goodge, appeared in 1560 (the first three books), and in 1565 the entire poem was printed. It seems that Palingenius was at a certain time suspected of heresy, but it was only 15 years after his death (he died in 1543) that, in 1558, the Zodiacus vitae was put on the Index librorum prohibitorum. Under Pope Paul II his bones were disinterred and burnt; cf. F. W. Watson, The Zodiacus Vitae of Marcellus Palingenius Stellatus: An old school book, London, 1908 and F. R. Johnson, Astronomical thought in Renaissance England, pp. 145 sq., Baltimore, 1937.

30. Zodiacus vitae, l. vii, Libra, ll. 497-99; Engl. transl., p. 118; cf. A. O. Lovejoy, The great chain of being, pp. 115 sq., Cambridge, Mass., 1936; F. R. Johnson, op. cit., pp. 147 sq.

31. Zodiacus vitae, l. ix, Aquarius, ll. 601-3 (transl., p. 218).

32. Ibid., l. xi, Aquarius, ll. 612-616 (transl., p. 218).

33. A. O. Lovejoy, The great chain of being, p. 52 and passim.

34. Zodiacus vitae, l. xii, Pisces, ll. 20-35 (transl., p. 228).

35. Ibid., ll. 71-85 (transl., p. 229). The world-view of Palingenius is beautifully expressed by Edmund Spenser in his Hymn of heavenly beauty (quoted by E. M. W. Tillyard, The Elizabethan world picture, p. 45, London, 1943):


Far above these heavens which here we see, p. 281
Be others far exceeding these in light,
Not bounded, not corrupt, as these same be,
But infinite in largeness and in height,
Unmoving, incorrupt and spotless bright
That need no sun t’illuminate their spheres
But their own native light far passing theirs
And as these heavens still by degree arise
Untill they come to their first mover's bound,
That in his mighty compass doth comprise
And carry all the rest with him around;
So those likewise do by degree redound
And rise more fair till they at last arrive
To the most fair, whereto they all do strive.



1. In the technical sense of the word, Copernicus is a Ptolemean.

2. Cf. Joachim Rheticus, Narratio prima. I am quoting the excellent translation of E. Rosen in his Three Copernican treatises, p. 147, New York, 1939.

3. F. R. Johnson, Astronomical thought in Renaissance England, pp. 24549, Baltimore, 1937; cf. A. O. Lovejoy, op. cit., pp. 109 sq.

4. John Donne, Anatomy of the world, First Anniversary (1611) ed., Nonesuch Press, p. 202. The disastrous effects of the seventeenth century's spiritual revolution have recently been studied with great care and some nostalgic regret by a number of scholars; cf. inter alia, E. M. W. Tillyard, The Elizabethan world picture, London, 1943; Victor Harris, All coherence gone, Chicago, 1949; Miss Marjorie H. Nicolson, The breaking of the circle, Evanston, Ill., 1950; S. L. Bethell, The cultural revolution of the XVIIth century, London, 1951. For a non-nostalgic treatment cf. A. O. Lovejoy, The great chain of being, and Basil Willey, The seventeenth century background, Cambridge, 1934.

5. Nicolaus Copernicus, De revolutionibus orbium coelestium, l. i, cap. viii.,

6. According to the mediaeval conception the central position of the earth is the lowest possible; only Hell is "lower" than our earthly abode.

7. For the pre-modern, that is, pre-telescopic astronomy, fixed stars possess a visible and even measurable diameter. Since, on the other hand, they are rather far away from us and in the Copernican conception even exceedingly far (cf. infra, pp. 92-9), their real dimensions must be extremely large.

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8. Cf. Grant McColley, "The seventeenth century doctrine of a plurality of worlds," Annals of Science, i, 1936, and "Copernicus and the infinite universe," Popular Astronomy, xliv, 1936; cf. Francis R. Johnson, op. cit., pp. 107 sq.

9. Nicolaus Copernicus, De revolutionibus orbium coelestium, l. i, cap. i.

10. Ibid., l. i, cap. viii.

11. Ibid., l. i, cap. x.

12. A. O. Lovejoy, op. cit., pp. 99 sq.

13. Cf. Sir Walter Raleigh, The historie of the world, London, 1652, pp. 93 sq.; cf. Bethell, op. cit., pp. 46 sq.

14. Cf. infra, p. 94.

15. Giordano Bruno understands them as teaching the infinity of the universe. I have already examined the case of Nicholas of Cusa; as for Lucretius, he asserts, indeed, the infinity of space and that of the worlds, but maintains the finiteness of our visible world and the existence of a limiting heavenly sphere, outside of which, but inaccessible to our perception, there are other identical or analogous "worlds." Anachronistically we could consider his conception as prefigurating the modern conception of island-universes dispersed in an infinite space, though with a very important difference: the Lucretian worlds are closed and not connected with each other.

16. Cf. Francis R. Johnson and Sanford V. Larkey, "Thomas Digges, the Copernican system and the idea of the infinity of the universe," The Huntington Library Bulletin, n. 5 (1934), and Francis R. Johnson, op. cit., pp. 164 sq.; cf. also A. O. Lovejoy, op. cit., p. 116.

18. A Perfit Description, sigs N 3-N 4; cf. Johnson-Larkey, pp. 88 sq.; Johnson, pp. 165-167.

19. A. O. Lovejoy, op. cit., p. 116. Giordano Bruno was born in Nola (near Naples) in 1548, became a Dominican in 1566, but, ten years later in 1576, on account of some rather heretical views held by him on transubstantiation and the Immaculate Conception, had to leave both the order and Italy. In 1579 he came to Geneva (where he could not stay), then to Toulouse, and to Paris (1581) where he lectured on the logical system of Raymundus Lullus (and wrote some philosophical works, i. e. De umbris idearum and a satiric comedy, Il Candelajo); in 1583 he went to England where he lectured and published some of his best works, such as La Cana de le Ceneri, De la causa, principio et uno and De l’infinito universo e mondi. From 1585 to 1592 Bruno wandered in Europe (Paris, Marburg, Wittenberg, Prague, Helmstadt, Zürich), publishing the De immenso et innumerabilibus in 1591. Finally, in 1592 he accepted an invitation to Venice. Denounced and arrested by the

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[paragraph continues] Inquisition (in 1593), he was brought to Rome, where he remained imprisoned for seven years, until he was excommunicated and burnt at the stake on February 17, 1600. Cf. Dorothea Waley Singer Giordano Bruno, his life and thought, New York, 1950.

20. Written in 1584.

21. Cf. my Études Galiléenes, iii, p. ii sq., and "Galileo and the scientific revolution of the XVIIth century," The Philosophical Review, 1943.

22. Giordano Bruno, La Cena de le Ceneri, dial. terzo, Opere Italiane, ed. G. Gentile, vol. i, p. 73, Bari, 1907.

23. Ibid., pp. 73 sq.

24. The De l’infinito universo e mondi was written in 1584; the De immenso et innumerabilibus, or to quote the full title, De innumerabilibus, immenso et infigurabili: sive de universo et mundis libri octo, in 1591. I shall base my exposition on the De l’infinito universo e mondi and quote it in the excellent recent translation of Mrs. Dorothea Waley Singer, adjoined to her Giordano Bruno, his life and work, New York, 1950. I shall give the reference first to the edition of Gentile (Opere Italiane, vol. i); then to Mrs. Singer's translation.

25. Bruno's space is a void; but this void is nowhere really void; it is everywhere full of being. A vacuum with nothing filling it would mean a limitation of God's creative action and, moreover, a sin against the principle of sufficient reason which forbids God to treat any part of space in a manner different from any other.

26. De l’inf. univ. e mondi, p. 309 sq., transl., p. 280; cf. De immenso . . . Opera Latina, vol. i, part i, p. 259.

27. A. O. Lovejoy, op. cit., p. 119.

28. De l’inf. universo, dedic. epistle, p. 275 (transl., p. 246).

29. The famous phrase "le silence éternel de ces espaces infinis m’effraye" does not express Pascal's own feeling—as is usually assumed by Pascal's historians—but that of the atheistic "libertin."

30. De l’inf. universo, p. 274 (transl., p. 245).

31. De l’inf. universo, p. 280 (transl., p. 250); cf. De immenso, i, 4, Opera, i, i, p. 214.

32. Ibid., p. 281 (transl., p. 251).

33. This very famous argument against the finitude of the universe—or of space—is a good example of the continuity of philosophical tradition and discussion. Giordano Bruno probably borrows it from Lucretius (De rerum natura, l. i, v. 968 sq.), but it was already widely used in the discussions of the XIII-XIVth centuries about the plurality of the worlds and the possibility of the void (cf. my paper quoted in chap. in, 40) and will be used by Henry More (cf. infra, p. 139) and even by Locke

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[paragraph continues] (cf. An essay on human understanding, l. ii, §§13, 21). According to the Commentaire exégétique et critique of A. Ernout and L. Robin to their edition of the De rerun natura (p. 180 sq., Paris, 1925), the argument originates with Architas and is used by Endemios in his Physics (cf. H. Diels, Fragmente der Vorsocratiker, c. xxxv, A 24, Berlin, 1912). What is more important, it is to be found in Cicero, De natura deorum, i, 20, 54; cf. Cyril Bailey, Lucretius, De rerun natura, vol. ii, pp. 958 sq., Oxford, 1947.

34. De l’inf. universo, p. 282 (transl., p. 253).

35. Ibid., p. 283 (transl., p. 254); cf. Acrotismus Camoeracensis, Opera, i, i, pp. 133, 134, 140.

36. Cf. Acrotismus Camoeracensis, p. 175.

37. De l’inf. univ., p. 286 (transl., p. 256).

38. Ibid., p. 289 (transl., p. 259).

39. Ibid., p. 334 (transl., p. 304); cf. De immenso, Opera, i, i, p. 218.

40. Ibid., p. 335 (transl., p. 304); cf. De immenso, Opera, i; i, p. 290; i, ii, p. 66.

41. Ibid., p. 336 (transl., p. 305); cf. De immenso, i, ii, p. 121.

42. Ibid., p. 336 (transl., p. 305).

43. Ibid., p. 286 (transl., p. 257).

44. Ibid., p. 289 (transl., p. 260).

45. As a scientist he was, sometimes, far behind it.

46. Cf. F. R. Johnson, Astronomical thought in Renaissance England, p. 216.

47. G. Guillielmi Gilberti Colcestrensis, medici Londinensis, De magnete, magnetisque corporibus, et de magno magnete tellure physiologia nova, c. vi, cap. iii; pp. 215 sq., London, 1600; Gilbert's work was translated by P. Fleury Mottelay in 1892 and by Sylvanus P. Thompson in 1900. The Mottelay translation was reprinted in 1941 as one of "The Classics of the St. John's Program" under the title: William Gilbert of Colchester, physician of London, On the load stone and magnetic bodies and on the great magnet the Earth; cf. pp. 319 sq. According to J. L. E. Dreyer, A history of astronomy from Thales to Kepler, 2nd ed., New York, 1953, p. 348, Gilbert, in his posthumous work, De mundo nostro sublunari philosophia nova (Amstelodami, 1651), "appears to hesitate between the system of Tycho and Copernicus." This is not quite exact, since Gilbert, in contradistinction to Tycho Brahe, (a) asserts the rotation of the earth which Tycho Brahe rejects, and (b) denies the existence of a sphere of fixed stars, and even the finitude of the universe still taught by Brahe. Thus Gilbert tells us that though the majority of the philosophers placed the earth in the center of the world, there is no reason to do so (l. 2, cap. ii, De telluris loco, p. 115): "Telluris

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vero globum in centro universi manentem omnis fere philosophorum turba collocavit. At si motum aliquem habuerit praeter diurnam revolutionem (ut nonnulli existimant) erronem etiam illam oportet esse; sin in suo sede volveretur tantum, non in circulo, planetarum ritu moveretur. Non tamen inde, aut ullis aliunde depromptis rationibus, certo persuadetur eam in universae rerum naturae centro, aut circa centrum, permanere." He adds, indeed (ibid., p. 117), that "Non est autem quo persuaderi possit in centro universi magis terram reponi quam Lunam, quam Solem; nec ut in motivo mundo horum unum in centro sit, necesse esse," and that, moreover, the world itself has no center (p. 119).

On the other hand, though he puts the sun and not the earth in the center of the moving world (p. 120): "locus telluris non in medio quia planetae in motu circulari tellurem non observant, tanquam centrum motionum, sed Solem magis," and tells us that the sun (p. 158) "maximam vim egendi et impellendi habet, qui etiam motivi mundi centrum est," he does not tell us outright that the earth belongs to this "moving world" of the planets.

Though he quotes Copernicus and even tells us that Copernicus erred in ascribing to the earth three motions, instead of two (around its axis and around the sun), the third one, that which, according to Copernicus, turned the axis of the earth in order to keep it pointing always in the same direction being not a motion at all, but lack of it (p. 165): "Tertius motus a Copernico inductus non est motus omnino, sed telluris est directio stabilis," he does not assert the truth of the heliocentric world-view.

He tells us, indeed (l. i, cap. xx, De vacuo separato), that the Aristotelian objections against the void are worthless, that things can just as well move in the void space as remain immobile in it and that the earth can very well be a planet and turn around the sun like the others; that, nevertheless, he does not want to discuss this question (l. i, cap. xx, De vacuo separato, p. 49): "Cujus rei veritatem sic habeto. Omnia quiescunt in vacuo posita; ita quies plurimis globis mundi. At nonnulli globi et infinitis viribus et actu aliorum corporum aguntur circa quaedam corpora, ut planetae circa Solem, Luna circa Tellurem et erga Solem.

"Quod si Sol in medio quiescit ut Canis, ut Orion, ut Arcturus, turn planetae, tum etiam tellus, a Sole aguntur in orbem, consentientibus propter bonum ipsis globorum formis: si vero tellus in medio quiescat (de cujus motu annuo non est huius loci disceptare) aguntur circa ipsam cetera moventia."

It is possible, of course, that Gilbert really considered that the discussion of the annual motion of the earth was out of place in a book

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devoted to the development of a new philosophy of our sublunar world. Yet it is difficult to admit that, if he was fully convinced of the truth of the Copernican astronomy, he would so consistently avoid saying it, even when asserting its daily rotation, as, for instance in chap. VI of book II of the Philosophia nova (p. 135): "Terram circumvolvi diurno motu, verisimile videtur: an vero circulari aliquo motu annuo cietur, non hujus est loci inquirere." It seems, thus, that Gilbert was either not very much interested in the problem, or sceptical about the possibility to reach a solution and that he hesitated between an improved Copernicanism (such as Kepler's) and an improved Tycho Brah-ism (such as Longomontanus’).


1. In pointing out the analogy between Kepler's views and those of some modern scientists and philosophers of science I am not committing an anachronism: epistemology and logic are, indeed, nearly as old as science itself and empiricism or positivism are by no means new inventions.

2. The sun represents, symbolizes, and perhaps even embodies God the Father, the stellar vault, the Son, and the space in between, the Holy Ghost.

3. Cf. De stella nova in pede Serpentarii, cap. xxi, pp. 687 (Opera omnia, ed. Frisch, vol. ii, Frankofurti et Erlangae, 1859). The De stella nova was published in 1606.

4. Ibid., p. 688.

5. Ibidem.

6. Ibidem.

7. Ibidem.

8. Ibidem.

9. A perfectly reasonable assumption, and quite analogous to that of contemporary astronomy, about the distribution of galaxies.

10. De stella nova, p. 689.

11. Ibidem.

12. Ibidem.

13. The sky being "above" us, the stars are "elevated" in respect to us; thus to place them at a greater distance from us (or the centre of the world) is to give them a greater "elevation."

14. Ibid., pp. 689 sq.

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15. The absence of stellar parallaxes imposes a minimum to the distance separating us from the fixed stars.

15a. Marcus Manilius, a Stoic, who lived in the Augustan age, author of a great astrological poem, Astronomicon libri quinque, which was edited by Regiomontanus in Nürnberg in 1473.

16. Ibid., p. 690.

17. Ibidem.

18. Two minutes is the magnitude of the visible diameter of a star for the unassisted eye.

19. Ibidem.

20. Ibid., p. 691.

21. Ibidem.

22. Ibidem.

23. Ibidem.

24. J. Kepler, Dissertatio cum Nuntio Sidereo nuper ad mortales misso a Galileo Galilei, p. 490 (Opera omnia, vol. ii), Frankoforti et Erlangae, 1859. Wacherus = the Imperial Councillor Wackher von Wackenfels who was the first to inform Kepler about the discoveries of Galileo. Brutus = the Englishman Edward Bruce who was a partisan of Giordano Bruno and who, some years before (Nov. 5, 1603), sent to Kepler a letter (from Venice) in which he expressed his belief in the infinity of the world; according to Bruce fixed stars were suns surrounded by planets like our sun, and, like our sun, endowed with a rotational motion. Bruce's letter is quoted by Frisch, Opera omnia, vol. ii, p. 568, and published by Max Caspar in his edition of Kepler (Johannes Kepler, Gesammelte Werke, vol. iv, p. 450, München, 1938).

25. The fixed stars, as seen by a Galilean telescope, do not appear as light-points; they still have visible dimensions; cf. supra, p. 191.

26. Epitome astronomiae Copernicanae, liber i, pars ii, p. 136 (Opera omnia, vol. vi, Frankoforti et Erlangae, 1866).

27. Ibidem.

28. Ibidem.

29. ibid., p. 137.

30. Ibidem.

31. Ibid., p. 138.

32. Ibidem.

33. Ibidem.

34. Ibidem.

35. Ibidem.

36. Ibid., p. 139.

37. Contemporary cosmology, on the other hand, seems to have recognized

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the value of the old doubts about the possibility of an actually infinite world, and turned back to a finitist conception.

38. That is the conception ascribed by Plutarch (or Pseudo-Plutarch) to the Stoics.

39. Ibid., p. 139.

40. Cf. my paper, "Le vide et l’espace infini au XIVème siècle," Archives d’histoire doctrinale et littéraire du Moyen-Age, xvii, 1949.


1. Galileo Galilei, Sidereus nuncius . . . Venetiis, 1610; there is an English translation by E. S. Carlos, The sidereal messenger, London, 1880. Large parts of this translation are reprinted in Harlow Shapley and Helen E. Howarth, A source book in astronomy, New York, 1929. Though not using this translation I refer to it whenever possible. The expression Sidereus Nuncius was used by Galileo as meaning: the message of the stars. Yet Kepler understood it as meaning: the messenger of stars. This mistranslation became generally accepted and was corrected only in the recent edition of the Nuncius by Mrs. M. Timpanaro-Cardini, Florence, 1948.

2. Cf. Sidereus nuncius, pp. 59 sq. (Opere, Edizione Nazionale, v. iii, Firenze, 1892), Source book, p. 41.

3. On the discovery of the telescope cf. Vasco Ronchi, Galileo e il cannochiale, Udine, 1942, and Storia della luce, 2 ed., Bologna, 1952.

4. Sidereus nuncius, p. 75, Source book, p. 46.

5. Ibid., p. 76.

6. Ibid., p. 78.

7. Galileo Galilei, Letter to Ingoli, p. 526. Opere, Ed. Naz., vol. vi, Firenze, 1896.

8. It is interesting to note that the conception according to which heavenly bodies are inhabited is referred to by Galileo as "commonly held."

9. Letter to Ingoli, p. 525.

10. Ibid., p. 518.

11. Galileo Galilei, Dialogo sopra i due massimi sistemi del mondo (Opere, Ed. Naz., vol. vii), p. 44; Firenze, 1897; cf. also p. 333. The Dialogue is easily available now in the excellent modernization of the old Salusbury translation by Professor Giorgio di Santillana, Galileo Galilei, Dialogue on the great world systems, Chicago, 1953, as well as in the new translation by Stillman Drake, Galileo Galilei, Dialogue concerning the two

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chief world systems, Ptolemaic and Copernican, Berkeley and Los Angeles, 1953.

12. Dialogo, p. 306.

13. Letter to Ingoli (Opere, vol. vi), pp. 518, 529.

14. Dialogo, loc. cit.

15. Cf. Letter to Liceti, of February 10, 1640; Opere, vol. xviii, pp. 293 sq., Firenze, 1906.

16. Cf. R. Descartes, Principia philosophiae, part ii, §4, p. 42. (Oeuvres, ed. Adam Tannery, vol. viii, Paris, 1905.)

17. Principia philosophiae, pt. ii, §10, p. 45.

18. ibid., §11, p. 46.

19. Ibid., §13, p. 47.

20. Ibid., §13, p. 47.

21. Ibid., §16, p. 49.

22. Ibid., §21, p. 52.

23. Ibid., §22, p. 52.

24. Ibidem.

25. Principia philosophiae, p. i, §26, p. 54.

26. Ibid., §27, p. 55.

27. Ibidem.

28. Principia philosophiae, p. iii, §1, p. 80.

29. Ibid., §2, pp. 81 sq.


1. Cf. Miss Marjorie H. Nicolson, "The early stages of Cartesianism in England," Studies in Philology, vol. xxviii, 1929. Henry More accepted Cartesian physics, though only partially, and the Cartesian rejection of substantial forms, but he never abandoned his belief in the existence, and action, of "spiritual" agents in nature and never adopted the Cartesian strict opposition of matter—reduced to extension—to spirit, defined by self-consciousness and freedom. Henry More, accordingly, believes in animals 'having souls and in souls' having a non-material extension; cf. also Miss Nicolson's The breaking of the circle, Evanston, Ill., 1950.

2. These letters were published by Clersellier in his edition of the correspondence of Descartes (Lettres de M. Descartes où sont traittées les plus belles questions de la morale, de la physique, de la médecine et des mathématiques . . . Paris, 1657) and republished by Henry More

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himself (with a rather angry preface) in his Collection of severall philosophical writings of 1662. I am quoting them according to the text of the Adam-Tannery edition of the works of Descartes (Oeuvres, vol. v, Paris, 1903).

3. Letter to Descartes, ii-xii, 1648, pp. 238 sq.

4. In this work, written in 1646, he shows himself an enthusiastic follower of the Lucretian-Brunonian doctrine of the infinity of worlds; cf. Lovejoy, op. cit., pp. 125, 347.

5. On Gassendi see K. Lasswitz, op. cit., and R. P. Gaston Sortais, La philosophie moderne, depuis Bacon jusqu’à Leibniz, vol. ii, Paris, 1922; also Pierre Gassendi, sa vie et son oeuvre, Paris, 1955. Gassendi is not an original thinker and does not play any role in the discussion I am studying. He is a rather timorous mind and accepts, obviously for theological reasons, the finitude of the world immersed in void space; yet, by his revival of Epicurean atomism and his insistence upon the existence of the void, he undermined the very basis of the discussion, that is, the traditional ontology which still dominated the thought not only of Descartes and More but also of Newton and Leibniz.

6. Letter to Descartes, p. 242.

7. In the Cartesian world vortices which surround fixed stars limit each other and prevent each other from spreading and dissolving under the influence of centrifugal force; if they were limited in number, and therefore in extension, then, first the outermost ones and then all the others would be dispersed and dissipated.

8. Letter to Descartes, p. 242.

9. Namely, by arguments based upon the consideration of God's omnipotence.

10. Descartes to Henry More, 5, ii, 1649, pp. 267 sq.

11. Ibid., pp. 269 sq.

12. Ibid., p. 274.

13. Ibid., p. 275.

14. Second letter of H. More to Descartes, 5, iii, 49; pp. 298 sq.

15. Ibid., pp. 304 sq.

16. Ibid., p. 305.

17. Ibid., p. 302. More's argument against Descartes is a re-edition of Plotinus’ argument against Aristotle.

18. Ibid., p. 312; cf. supra.

19. Second letter of Descartes to Henry More, 15, iv, 1649; pp. 340 sq.

20. Ibid., p. 342.

21. Ibid., p. 343.

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22. Such was, in any case, the opinion of Pascal. Yet, after all, what is the God of a philosopher supposed to be if not a philosophical God?

23. Ibid., p. 344.

24. Ibid., p. 345.

25. Dated the 23rd of July, 1649 (Oeuvres, vol. v, pp. 376 sq.).

26. At least, he started writing an answer—in August 1649—though he did not send it to Henry More.

27. Dated the 21st of October, 1649, vol. v, pp. 434 sq.

28. It is possible, of course, that, as he went to Sweden on Sept. 1, 1649 and died there on Feb. 11, 1650, Descartes did not receive this last letter of Henry More.

29. Cf. my Essai sur les preuves de l’existence de Dieu chez Descartes, Paris, 1923, and "Descartes after three hundred years," The University of Buffalo Studies, vol. xix, 1951.


1. Henry More has not received the monographical treatment to which he is undoubtedly entitled. On him, and on the Cambridge Platonists in general, cf. John Tulloch, Rational theology and Christian philosophy in England in the XVIIIth century, vol. ii, Edinburgh and London, 1874; F. J. Powicke, The Cambridge Platonists, London, 1926; J. H. Muirhead, The Platonic tradition in Anglo-Saxon philosophy, London, 1931; T. Cassirer, Die Platonische Renaissance in England und die Schule von Cambridge, Leipzig, 1932; English translation: The Platonic Renaissance in England and the Cambridge School, New Haven, 1953. Selections of the philosophical writings of Henry More (namely from The antidote against atheism, The immortality of the soul, and the Enchiridium metaphysicum in translation) were published in 1925 by Miss Flora J. Mackinnon with an interesting introduction, valuable notes, and an excellent bibliography: Philosophical writings of Henry More, New York, 1925. Cf. Marjorie Nicolson, Conway letters, the correspondence of Anna, Viscountess Conway, Henry More and their friends, 1642-1684, London, 1930; Markus Fierz, "Ueber den Ursprung und Bedeutung der Lehre Newtons vom absolutem Raum," Gesnerus, vol. xi, fasc. 3 / 4, 1954; Max Jammer, Concept of space, Harvard Univ. Press, Cambridge, Mass., 1954. Both Markus Fierz and Max Jammer seem to me to exaggerate the real influence of cabalist space conceptions on Henry More (and his predecessors). In my opinion, it was a typical

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case of reprojection into the past of modern conceptions in order to back them up by sacred or venerable authorities; yet, as we know, misunderstanding and misinterpretation play an important part in the history of thought. It seems to me, moreover, that Fierz and Jammer themselves are not quite innocent of the sin of retroprojection, forgetting that space conceptions formed before the invention of geometry were not, and could not, be identical or even similar to the conceptions devised after this momentous event.

2. Henry More, An antidote against atheisme, or an appeal to the natural faculties of the minde of man, whether there be not a God, London, 1652; second ed. corrected and enlarged, London, 1655; third edition, corrected, and enlarged, "with an Appendix thereunto annexed," London, 1662. I am quoting this edition as given in Henry More's Collection of severall philosophical writings, London, 1662.

3. Henry More, The immortality of the soul, so farre forth as it is demonstrable from the knowledge of nature and the light of reason, London, 1669; second edition in the Collection of severall philosophical writings of 1662. It is this edition that I am quoting.

4. Henricus Morus, Enchiridium metaphysicum sive de rebus incorporeis succincta et luculenta dissertatio, Londini, 1671.

5. Henry More, An antidote against atheism, book i, cap. iv, §3, p. 15.

6. Henry More, The immortality of the soul, b. i, c. ii, axiom ix, p. 19.

7. Cf. R. Zimmerman, "Henry More and die vierte Dimension des Raumes," Kaiserliche Akademie der Wissenschaften, Philosophisch-historische Klasse, Sitzungsberichte, Bd. 98, pp. 403-sq., Wien, 1881.

8. Henry More, The immortality of the soul, b. i, c. ii, §11, p. 20.

9. Ibid., 6, i, c. iii, §§1 and 2, pp. 21 sq.

10. Axiom ix (b. i, c. ii, p. 19) tells us that "There are some Properties, Powers and Operations, immediately appertaining to a thing, of which no reasons can be given, nor ought to be demanded, nor the Way or Manner of the cohesion of the Attribute with the subject can by any means be fancied or imagined."

11. Cf. William Gilbert, De magnete, ch. xii, p. 308: "The magnetic force is animate, or imitates the soul; in many respects it surpasses the human soul while that is united to an organic body."

11a. Cf. also Markus Fierz, op. cit., pp. 91 sq.

12. Henry More, The immortality of the soul, b. iii, c. xii, §1, p. 193.

13. Ibid., preface, §12, p. 12.

14. An antidote against atheism, c. ii, c. ii, §1, p. 43.

15. Ibid., Appendix (of 1655), cap. vii, §1, p. 163.

16. Ibidem.

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17. Ibid., §§4, 5, 6, pp. 164 sq.

18. Enchiridium metaphysicum, part i, cap. vi, v. 42.

19. Ibidem.

20. Ibidem.

21. Ibid., cap. vi, 4, p. 44.

22. Ibid., cap. vi, 11, p. 51.

23. Ibid., cap. vii, 3, p. 53.

24. This definition is given by Descartes in the Principia philosophiae, part ii, §25.

25. Enchiridium metaphysicum, cap. vii, 7, p. 56.

26. Ibid., c. vii, 6, p. 55.

27. Ibidem.

28. Ibidem.

29. Ibidem.

30. Ibid., c. viii, 6, p. 68.

31. Ibid., c. viii, 7, p. 69.

32. Ibid., c. viii, 8, pp. 69 sq.

33. Ibid., c. viii, 9, p. 70.

34. Ibid., c. viii, 10, p. 71.

35. Ibid., c. viii, 11, p. 72.

36. Ibid., c. viii, 12, p. 72.

37. Ibidem.


1. Cf. Nicolas Malebranche, Méditations chrétiennes, méd. ix, §9, p. 172, Paris, 1926. On Malebranche cf. H. Gouhier, La philosophie de Malebranche, Paris, 1925.

2. Ibidem.

3. Ibid., §10, p. 173.

4. Ibid., §8, pp. 171 sq.

5. Ibid., §11, p. 174.

6. Ibid., §12, pp. 174 sq.

7. Cf. Malebranche, Correspondance avec J. J. Dortous de Mairan, ed. nouvelle, précédée d’une introduction par Joseph Moreau, Paris, 1947.

8. Cf., e. g., the already quoted book of E. A. Burtt, The metaphysical foundations of modern physical science, New York, 1925; second ed., London, 1932.

9. Cf. Sir Isaac Newton's mathematical principles of natural philosophy,

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translated into English by Andrew Motte in 1729, the translation revised by Florian Cajori, p. 6, Berkeley, Calif., 1946.

10. Ibid., p. 8.

11. Ibidem.

12. Ibid., p. 6.

13. Ibidem.

14. Ibidem.

15. Ibidem.

16. Ibidem.

17. Ibidem.

18. Ibid., p. 7. The example of the sailor is discussed by Descartes in the Principia philosophiae, ii, 13, 32.

19. Ibid., p. 8.

20. His pupil, Dr. Clarke, will indeed do it; cf. infra, p. 275.

21. Ibid., p. 9.

22. Ibid., p. 10.

23. Ibidem.

24. Ibid., p. 11. As against Descartes, Principia, ii, 13.

24a. Cf. Ernst Mach, The science of mechanics, Chicago, 1902, pp. 232 sq.; cf. also Max Jammer, op. cit., pp. 104 sq.; 121 sq.; 140 sq.

25. Ibid., p. 12.

26. Ibid., book iii, The system of the world, Lemma IV, cor. III, p. 497.

27. Ibid., book iii, The system of the world, prop. V, theorem VI, scholium, cor. III, p. 414.

28. Ibid., cor. IV, p. 415.

29. As a matter of fact, they have been listed also by Boyle and Gassendi who, in contradistinction to Descartes, insist on impenetrability as an irreducible property of body distinct from mere extension.

30. Ibid., rule III, pp. 398 sq. The text I am referring to appeared in the second edition of the Principia; yet, as it represents the fundamental views of Newton which inspired his whole system, I feel it necessary to quote it here. On the difference between the first and the subsequent editions of the Principia, cf. my papers "Pour une édition critique des oeuvres de Newton," Revue d’Histoire des Sciences, 1955, and "Expérience et hypothèse chez Newton," Bulletin de la Société Française de Philosophie, 1956.

31. Ibid., book I, sect. XI, prop. LXIX, schol., p. 192.

32. Cf. my Études Galiléennes. II, La loi de la chute des corps, and III, Galilée et la loi d’inertie.

33. Ibid., loc. cit.

34. Four Letters from Sir Isaac Newton to the Reverend Dr. Bentley,

p. 295

[paragraph continues] Letter II (Jan. 17, 1692-93), p. 210, London, 1756; reprinted in Opera omnia, ed. by Samuel Horsley, 5 vols., London, 1779-85 (vol. iv, pp. 429-442), and also in the Works of R. Bentley, vol. in, London, 1838. I am quoting this edition.

35. Letter III (Feb. 25, 1692-93), ibid., p. 211.

36. Eight sermons preach’d at the Honourable Robert Boyle lecture in the first year MDCXCII, By Richard Bentley, Master of Arts, London, 1693. The first sermon proves The folly of atheism and . . . Deism even with respect to the present life, the second demonstrates that matter and motion cannot think, the third, fourth and fifth present A confutation of atheism from the structure of the human body, the sixth, seventh and eighth, forming the second part of the work, A confutation of atheism from the origin and frame of the world. I am quoting the last edition (Works, v. iii) of this book that has seen nine of them in English, and one in Latin (Berolini, 1696); cf. Part II, sermon VII (preached Nov. 7th, 1692), pp. 152 sq.

37. Ibid., p. 154.

38. Ibid., p. 157.

39. Ibid., pp. 162 sq.

40. Ibid., p. 163.

41. Letters from Sir Isaac Newton to the Reverend Dr. Bentley, Letter I, pp. 203 sq.

42. A confutation of atheism from the origin and frame of the world, p. 165.

43. Ibid., p. 170.

44. Ibid., pp. 175 sq.

45. On the cosmical optimism of the XVIIIth century, cf. Lovejoy, op. cit., pp. 133 sq.; E. Cassirer, Die Philosophie der Aufklärung, Tübingen, 1932.


1. Joseph Raphson is chiefly known as the author of the violently pro-Newtonian Historia Fluxionum, sive Tractatus Originem et Progressum Peregregiae Istius Methodis Brevissimo Compendio (Et quasi synoptice) Exhibens, Londini, 1715.

2. Analysis Æquationum Universalis seu ad Aequationes Algebraicas Resolvendas Methodus Generalis et Expedita, Ex nova Infinitarum Serierum Methodo, Deducta et Demonstrata. Editio secunda cui accedit Appendix de Infinito Infinitarum Serierum progressu ad Equationum Algebraicarum Radices eliciendas. Cui etiam Annexum est De Spatio Reali seu Ente Infinito conamen Mathematico Metaphysicum, Authore

p. 296

[paragraph continues] Josepho Raphson A. M. et Reg. Soc. Socio., Londini, 1702. The first edition of J. Raphson's work, without the above-mentioned appendices, appeared in 1697.

3. De ente infinito, cap. iv, p. 67.

4. Cf. infra, pp. 193, 196.

5. De ente infinito, cap. iv, pp. 57 sq.

6. Ibid., pp. 70 sq.

7. Ibid., cap. v, p. 72.

8. Ibid., Def. I.

9. Ibid., Scholium, p. 73.

10. Ibidem.

11. Ibid., pp. 74 sq.

12. Ibid., Scholium, p. 76. On the space theories of the Cabala cf. Max Jammer, op. cit., pp. 30 sq.

13. Ibid., corollarium.

14. Ibidem.

15. Ibid., p. 78.

16. Ibid., p. 80.

17. Ibid., cap. vi, p. 82.

18. Ibid., p. 83.

19. Ibid., pp. 83 sq.

20. Ibid., p. 85.

21. Ibid., pp. 90 sq.

22. Ibid., p. 91.

23. Ibid., p. 91.

24. Ibid., pp. 91 sq.

25. Ibid., p. 94.

26. Ibid., p. 93.

27. Ibid., p. 95.


1. Strange as it may seem, the adjunction of these "queries," numbered 17 to 43, to the Latin edition of the Opticks in 1706 seems to have escaped the attention of Newton's historians who, usually, attribute these queries to the second (English) edition of 1617 of his Opticks. Thus, for instance, L. T. More, Isaak Newton, New York-London, 1934, p. 506, note: "A second edition (octavo) bears the advertisement 1717. It was published in 1718. . . . The number of new Queries added

p. 297

begins with the seventeenth." Leon Bloch's La philosophie de Newton, Paris, 1908, is an honorable exception to the afore-mentioned rule; and today, Mr. H. G. Alexander, editor of The Leibniz-Clarke correspondence, Manchester University Press, 1956.

2. Philosophical principles of natural religion by George Cheyne, M. D. and F. R. S., London, 1705. The second edition of Cheyne's book, published under the title Philosophical principles of religion, natural and revealed, London, 1615, "corrected and enlarged," contains two parts: Part I, "containing the Elements of Natural Philosophy and the Proofs of Natural Religion arising from them," and a Part II, "containing the Nature and Kinds of Infinities, the Arithmetick and Uses, and the Philosophick Principles of Reveal’d Religion, now first published." Strangely enough the common title page, as well as that of the second part, bears the date 1715, whereas that of the first part, the date 1716. As a matter of fact, or at least according to David Gregory who held this information from Newton himself, it was the publication by Dr. Cheyne of his Fluxionum methodus inversa sive quantitatum fluentium leges generales, London, 1703 (rather sharply criticized by A. De Moivre in his Animadversiones in Dr. G. Cheyne's Fluxionum methodus . . . London, 1704), which prompted Newton to publish the Two treatises on the species and magnitudes of curvilinear figures, that is, The quadrature of curves and The enumeration of the lines of the third order; (cf. David Gregory, Isaak Newton and their circle, Extracts from David Gregory's Memoranda, edited by W. G. Hiscock, pp. 22 sq., Oxford, 1937). In the selfsame Memoranda under the date of December 21, 1705, we find also the following, very interesting passage (ibid., pp. 29-30): "Sir Isaak Newton was with me and told me that he had put 7 pages of Addenda to his Book of Lights and Colours in this new latin edition of it. He has by way of quaere explained the explosion of Gun powder, all the chief Operations of Chymistry. He has shewed that Light is neither a communication of motion nor of a Pressure. He inclines to believe it to be projected minute bodys. He has explained in those Quaerys the double Refraction in Iseland Crystall. His Doubt was whether he should put the last Quaere thus. What the space that is empty of bodies is filled with. The plain truth is that he believes God to be omnipresent in the literal sense. And that as we are sensible of Objects where their images are brought within the brain, so God must be sensible of every thing being intimately present with every thing: for he supposes that as God is present in space where there is no body, he is present in space where a body is also present. But if this way of proposing this his notion be too bold, he thinks of doing it thus. What cause did the Ancients assign of

p. 298

[paragraph continues] Gravity. He believes that they reckoned God the Cause of it, nothing else, that is no body being the cause; since every body is heavy.

"Sir Isaak believes that the Rays of Light enter into the composition of most Natural Bodies that is the small particles that are projected from a lucid body in form of Rays. As plain this may be the case with most combustible, inflammable bodies." On the relations of light and matter according to Newton cf. Helène Metzger, Newton, Stahl, Boerhaave et la doctrine chimique, Paris, 1930.

3. Optice . . . l. iii, qu. 20, pp. 312 sq.; London, 1706; qu. 28 of the English edition; cf. I. Bernard Cohen's edition of the Opticks, New York, 1952, p. 369. As the English edition certainly gives the original text of Newton himself, I will quote this latter giving first the page numbers of the Latin, and then those of the afore-mentioned edition.

4. Ibid., pp. 322 sq.; pp. 375-76. The existence of various "impellent" and "repellent" forces acting between the "particles" of bodies is already asserted by Newton in the preface of the Principia.

5. Ibid., p. 376.

6. Ibid., p. 335; pp. 388 sq.

7. Ibid., p. 335 sq.; pp. 389 sq.

8. Ibid., p. 337; p. 394.

9. Ibid., pp. 337 sq.; pp. 394 sq.

10. Ibid., pp. 338 sq.; pp. 395-396.

11. Ibid., pp. 340 sq.; pp. 397 sq.

11a. The reasoning is, of course, utterly false and it is rather astonishing that Newton could have made it and that neither he himself nor his editors noticed this falsehood.

12. Ibid., p. 343; p. 399.

13. Ibid., pp. 343 sq.; p. 400.

14. Ibid., p. 345; p. 402.

15. Ibid., p. 346; p. 403.


1. George Berkeley, Principles of human knowledge, §110; p. 89 (The works of George Berkeley Bishop of Cloyne, ed. by A. A. Luce and T. E. Jessop, vol. i, Edinburgh, 1949).

2. Ibid., §111, p. 90.

3. Ibid., §117, p. 94.

4. On the 18th of February 1673. Roger Cotes wrote to Newton (cf.

p. 299

[paragraph continues] Correspondence of Sir Isaak Newton and Professor Cotes . . . ed. J. Edleston, London, 1850, pp. 153 sq.): ". . . I think it will be proper [to] add something by which your book may be cleared from some prejudices which have been industriously laid against it. As that it deserts mechanical causes, is built upon miracles and recurrs to Occult qualities. That you may not think it unnecessary to answer such Objections you may be pleased to consult a Weekly Paper called Memoires of Literature and sold by Ann Baldwin in Warwick-Lane. In the 18th Number of ye second Volume of those Papers which was published May 5th, 1712, you will find a very extraordinary letter of Mr. Leibnitz to Mr. Hartsoeker which will confirm what I have said." Indeed, in this letter, dated Hanover, February 10, 1711, Leibniz who, as a matter of fact already had attacked Newton in his Théodicée (Essai de Théodicée, Discours de la Conformité de la Foi avec la Raison, §19, Amsterdam, 1710) assimilated the Newtonian gravity to an "occult quality," so "occult" that it could never be cleared up even by God. It is well known that neither Leibniz nor Huygens had ever accepted the Newtonian conception of gravitation, or attraction. Cf. René Dugas, Histoire de la mécanique au XXVIIe siècle, Neuchatel, 1954, cap. xii, Retour au Continent, pp. 446 sq. and cap. xvi, Réaction des Newtoniens, pp. 556 sq.

4a. In the first line, Henry More and Joseph Raphson.

5. Cf. Mathematical principles of natural philosophy, translated into English by Andrew Motte in 1729. The translation revised . . . by Florian Cajori, General Scholium, pp. 543 sq., Berkeley, Cal., 1946.

6. Ibid., pp. 544 sq.

7. Ibid., p. 545.

8. Ibidem.

9. Ibidem.

10. Ibid., p. 546.

11. Ibid., pp. 546 sq.

12. Professor Cajori follows Andrew Motte in translating Newton's fingo by frame. It seems to be that the old term feign (used by Newton himself) is both more correct and more expressive.

13. Principles, preface, p. xx.

14. Ibid., p. xxix.

15. Ibid., p. xxvii.

16. Ibid., pp. xxxi sq.

17. Principles, p. 547. On the XVIIth century conception of "spirit" cf. E. A. Burtt, op. cit., and A. J. Snow, Matter and gravity in Newton's philosophy, Oxford, 1926.

p. 300


1. Wilhelmine Caroline, later Queen Caroline, was born Princess of Brandenburg-Anspach and in 1705 became the wife of George Augustus, Electoral Prince of Hanover. It was as Princess of Hanover that she became intimate with Leibniz; as Leibniz put it himself, she "inherited" him from Sophie Charlotte of Prussia.

2. Cf. "An extract of a letter written in November 1715," §§3 and 4, published in A Collection of papers, which passed between the late learned Mr. Leibnitz and Dr. Clarke. In the years 1715 and 1716 Relating to the Principles of Natural Philosophy and Religion. With an Appendix, pp. 3 and 5, London, 1717. Leibniz writes, of course, in French, and Clarke, in English. But he accompanies the publication of the originals by a translation of Leibniz's "papers" into English (probably made by himself) and of his own "replies" into French (probably made by the Abbé Conti). Moreover, he adds to the text a series of footnotes with references to relevant passages in Newton's writings. This polemic is now available in the excellent edition of G. H. Alexander, The Leibniz-Clarke correspondence, Manchester Univ. Press, 1956; cf. also René Dugas, La mécanique au XVII siècle, cap. xvi, §3, pp. 561 sq.

3. The choice of Dr. Samuel Clarke was rather obvious. Dr. Clarke, Rector of St. James’, Westminster, was not only a philosophical theologian—in 1704-5 he gave the Boyle Lectures—but also was former chaplain of Queen Anne, removed, to say the truth, from this charge for lack of orthodoxy (he was practically an Arian). However, after Queen Anne's death he became an intimate of Princess Caroline with whom, at her request, he had weekly philosophical conversations in which other gentlemen interested in discussing philosophical problems participated. Thus it was only natural that, as Des Maizeaux tells us in the preface to his own French re-edition of the Collection of papers (Recueil de diverses pièces sur la philosophie, la religion naturelle, l’histoire, les mathématiques etc., 2 vols., Amsterdam, 1720, p. II): "Madame la Princesse de Galles, accoutumée aux Recherches Philosophiques les plus abstraites et les plus sublimes fit voir cette Lettre à M. Clarke et souhaita qu’il y répondit. . . . Elle envoyait à M. Leibniz les Réponses de M. Clarke et communiquait à M. Clarke les nouvelles difficultés, ou les Instances de M. Leibniz." Indeed, Dr. Clarke as an intimate friend of Sir Isaac, and a Newtonian of long standing, could be relied upon to represent the philosophical views of his master.

p. 301

In my opinion we must go even farther: it is utterly unconceivable that Clarke should accept the role of philosophical spokesman (and defender) of Newton without being entrusted by the latter to do it, nay, without having secured the collaboration of the great man, at least in the form of approval.

I am, thus, morally certain that Clarke communicated to Newton both Leibniz's letters and his own replies to them. It is indeed unthinkable that in the midst of his bitter fight with Leibniz about the priority of the invention of the calculus, Newton who "aided" both Keill and Raphson in their attacks against Leibniz, as he "aided" Des Maiseaux some years later in the preparation of his edition of the "Collection of papers" (the second volume of his edition carries the history of the calculus controversy by publishing translations of selected pieces of the Commercium epistolicum), should remain aloof and disinterested in the face of an assault upon his religious view and an accusation, practically, of atheism, by the selfsame Leibniz. As a matter of fact, the Princess of Wales informed Leibniz (Caroline to Leibniz, Jan. 10, 1716, in O. Klopp, Die Werke von Leibniz, Hanover, 1864-84, vol. xi, p. 71, quoted in The Leibniz-Clarke correspondence, Manchester Univ. Press, 1956, p. 193) that he was right in his supposition that these letters were not written without the advice of Newton. Strange as it may seem, the importance of Clarke's papers as representing literally the metaphysical views of Newton has never been recognized, with the result that their study was completely neglected by the historians both of Newton and of Leibniz. Thus, for instance, L. T. More, op. cit., p. 649: "It seems probable that Newton was even more exasperated by Leibniz's attack on the anti-Christian influence of the Principia than by the controversy over the invention of the calculus. To justify himself he guided Des Maizeaux in preparing for publication the long debate between Leibniz and Samuel Clarke on the religious significance of the Newtonian Philosophy. For this purpose he gave to the author the documents relating to the controversy, and assisted him in preparing an historical preface which reviewed the whole affair."

4. Cf. supra, pp. 181-89.

4a. As a matter of fact (cf. supra, p. 209) Newton, at least once, identified space with God's sensorium.

5. "Dr. Clarke's first reply," A collection of papers . . ., pp. 15 sq.

5a. The Socinians did not believe in predestination, nor in the Trinity.

6. " Mr. Leibniz's second paper," ibid., p. 25.

7. Ibid., p. 33.

8. Especially his allusion to Socinianism, because, as a matter of fact both

p. 302

[paragraph continues] Sir Isaac Newton and Dr. Samuel Clarke were much nearer to Socinianism than to the teaching of the Established Church: neither of them, indeed, accepted the Trinitarian conception of God; they were both—as also John Locke—Unitarians; cf. H. McLachlan, The religious opinions of Milton, Locke and Newton, Manchester, 1941. On Newton's metaphysical and religious views, cf. Helène Metzger, Attraction universelle et religion naturelle, Paris, 1938, and E. W. Strong, "Newton and God," Journal of the History of Ideas, vol. xiii, 1952.

9. Or, at least, proclaims.

10. " Dr. Clarke's second reply," ibid., p. 41. Intelligentia supramundana, or more exactly, extra mundana, is an expression of Leibniz; cf. Théodicée, §217.

11. Ibid., p. 45.

12. "Mr. Leibniz's third paper," ibid., p. 57.

13. Ibid., p. 59.

14. Ibid., p. 69.

15. "Dr. Clarke's third reply," ibid., p. 77. Dr. Clarke uses the term "property" in his own "replies" as well as in the translation of Leibniz's "papers"—and one understands full well why he does not use the more correct one, "attribute": just because Leibniz has mentioned Spinoza. But Leibniz himself uses the term "attribute"; moreover the French translation of Clarke's "replies," reviewed and acknowledged by Clarke himself, uses "attribute" for "property."

16. Dr. Clarke's example is rather bad as, in this case, there would be a relative displacement of "our world" in respect to the fixed stars.

17. The use of the principle of inertia in the discussion of the old problem whether God can move the world in a straight line (cf. my paper quoted supra, cap. iii, n. 43) is rather ingenious.

18. "Dr. Clarke's third reply," ibid., p. 85.

19. For Leibniz reality and individuality are inseparable.

20. " Mr. Leibniz's fourth paper," ibid., p. 97.

21. Ibid., p. 103.

22. Thus, practically, Leibniz and Descartes are in full agreement.

23. "Mr. Leibniz's fourth paper," ibid., pp. 115 sq.

24. Ibidem.

25. Ibidem. Leibniz will mention Henry More in his fifth paper, n. 48: "To conclude. If the space (which the author fancies) void of bodies is not altogether empty: what is it then full of? Is it full of extended spirits perhaps, or immaterial substances, capable of extending and contracting of themselves; which move therein and penetrate each other without any inconveniency, as the shadows of two bodies penetrate one

p. 303

another upon the surface of a wall? Methinks I see the revival of the odd imaginations of Dr. Henry More (otherwise a learned and well meaning man) and of some others who fancied that those spirits can make themselves impenetrable whenever they please."

26. Ibidem.

27. Ibidem.

28. Ibid., p. 101.

29. Ibidem.

30. "Dr. Clarke's fourth reply," ibid., p. 121.

31. We even have to suppose it if we want to link atomism with mathematical philosophy.

32. Ibid., p. 125.

33. Ibidem.

34. Ibidem.

35. Ibid., p. 127.

36. Ibid., p. 131.

37. It is rather interesting to see Dr. Clarke use Henry More's famous concept and term.

38. Ibid., p. 127.

39. Ibid., p. 135.

40. Ibid., p. 139.

41. Ibid., p. 139.

42. Ibid., p. 141.

43. Ibid., p. 149.

44. Ibid., p. 151.

45. This latter behaviour is, more often than not, branded as "arbitrariness."

46. "Mr. Leibniz's fifth paper," ibid., p. 181.

47. Ibidem.

48. Ibid., p. 211.

49. Ibid., p. 183.

50. Ibid., p. 207.

51. Ibid., p. 231.

52. Ibid., p. 189.

53. Ibid.; p. 193.

54. Ibid., p. 195.

55. Ibidem.

56. Ibid., p. 235.

57. Ibid., p. 259.

58. Ibid., pp. 269 sq.

59. "Dr. Clarke's fifth reply," ibid., p. 295.

p. 304

60. Ibid., p. 313.

61. Ibid., pp. 301 sq.

62. Ibid., p. 349.

63. Ibid., p. 367.

64. Ibid., p. 335.





Acceleration: 169

Ancients: concept of universe, 5, 14, 16, 17, 24, 60, 112; explanation of gravity, 208, 297-98; theory of incomprehensibility of God, 198. See also Atomism

Anselmian concept: 124

Aristarchus of Samos: 28

Aristotle: 28, 30, 35, 56, 59, 100, 101, 126, 149, 261, 290; concept of God as First Cause, 225; concept of universe, 11, 34, 60, 72, 86-87, 97, 139, 140; doctrines questioned, 24, 26, 31-32, 46-47, 55, 139, 161, 230, 285; theory of relativity of motion, 56, 279

Arnauld, Antoine: attitude toward Malebranche, 158-59

Atheism: causes, 138, 198, 234; refuted by Bentley, 179-80, 182-84, 186-89

Atomic structure of universe: 113, 115, 182, 211, 254, 274, 277. See also Hardness

Atomism: 5, 141, 145, 154, 172, 173, 208, 213, 278, 303

Attraction, theory of Newton: 181, 207, 220, 234, 298; discussed, 174-79, 183-89, 209-16; inverse square law, 220, 228, 272; miraculous qualities imputed to, by Leibniz, and defense by Newton and Clarke, 223, 228, 229, 233, 234, 245-46, 248, 253, 258, 267-68, 271-72; ultimate modification of, 274, See also Gravity

Attributes: substances implied by, 145-47

Attributes of God: 124, 148-53, 155-56, 197


Bacon, Francis: 1, 3, 243

Bentley, Richard: 207, 223, 249, 295; accepts Bruno's concept of universe, 180; follows Newton's teachings, 179; misinterprets Newton's theory of gravity, 178-79; theory of influence of God in universe, 182-89

Berkeley, George, Bishop of Cloyne: 207; attack on Newton's philosophy and response by Newton, 221-28

Bodies, attraction of. See Attraction

Bodies, qualities of: discussed by Newton, 173-75

Body: definition by More, 128-130

Boyle, Robert: 3, 215, 220, 278, 294

Boyle Lectures: delivered by Bentley, 179; by Clarke, 300

Brahe, Tycho: 3, 56, 92, 284, 286

Bruce, Edward: 73, 287

Bruno, Giordano: 58, 73, 75, 78, 96, 99, 102, 105, 114, 118, 119, 171, 241, 290; argument for change from sensual to intellectual perception, 44-46; assertion of infinite space, 46-49, 52, 53; attitude toward creative power of God, 42, 48-49, 52, 53; attitude toward Lucretian cosmology, 6;

p. 306

attitude toward motion in universe, 39-40, 41, 44, 49-51; attitude toward Nicholas of Cusa, 6, 14, 18; biographical sketch, 28283; burned at stake, 98, 283; concept of infinity of universe, 35, 39-54, 60-61, 180, 282; influence on contemporaries doubted, 54-55; principle of plenitude, 42, 44, 52; principle of sufficient reason, 44, 46, 52, 283

Brutus. See Bruce, Edward


Cabala: 126

Cabalists: 148

Cartesian philosophy. See Descartes Center of universe: concept of Nicholas of Cusa, 11-21 passim; earth removed from, 3, 29-30, 32-33, 43; existence disputed, 40, 41-42, 63, 64, 65, 67, 69, 96

Centrifugal force: relation to circular motion, 167-71

Centripetal force. See Attraction Chanut: 6

Cheyne, Dr. George: 206, 274, 297

Circumference of universe: concept of, 11, 12, 17, 18

Clarke, Dr. Samuel: 207, 301; biographical sketch, 300; chosen by Newton to act as spokesman, 301; defense of Newton against attacks by Leibniz, 236-72, 273

Copernicus, Nicholas: 3, 15, 56, 59, 61, 92, 95, 96, 97, 99, 105, 281, 284, 285, 286; concept of universe, 2934, 36; condemnation of, 98; diagram of world replaced, 36-38; not influenced by Nicholas of Cusa, 8, 18, 280; sources of inspiration, 28

Cosmos: destruction of conception of, 2, 24, 29, 43, 61

Cotes, Roger: 230-32, 235-36, 274, 298-99

Creation of universe by God: concept of Leibniz, 266, 269; concept of Newton and Clarke, 256-57, 269; not necessary to infinite universe, 275

Cusa, Nicholas of. See Nicholas of Cusa


Demetrius: 140

Democritus: 3, 44, 73, 101, 112, 114, 126, 140, 141, 182, 238, 239, 278

Descartes, René: 1, 52, 139-77 passim, 190-91, 197, 210-18 passim, 225, 231, 237, 252, 254, 264, 267, 272, 290, 294; concept of matter and space as identical, 99, 101-4; concept of universe as indefinite and God as infinite, 100, 104-9, 124, 153-54; denial of void space, 136, 141-43, 145, 232; exchange of letters with More, 110-24; explanation of gravity, 133; formulated principles of mathematical cosmology, 99; influence on philosophical development of More, 125, 289; interpretation of thought of Nicholas of Cusa, 6, 19; theory of extension, 101-4, 138, 126-27, 132, 145-47, 152, 162; use of hypotheses, 230; views of, disputed by More. See More, Henry, disputes views of Descartes

Des Maiseaux: 301

d’Etaples, Lefèvre: 18

"Dieu fainéant": 276

Digges, Leonard: 35

Digges, Thomas: contribution to concept

p. 307

of infinity of universe, 35-39; diagram of infinite universe, 36-38; influence on Gilbert, 55

Diogenes Laertius: 5, 6

Donne, John: quoted, 29

Dortous de Mairan, J. J.: 159

Duhem, Pierre: 169

Duns Scotus, John: 124

Duration. See Time


Earth: comparison with rest of universe, 25, 38, 105; displacement from center of universe, 3, 29-30, 32-33, 43; low position assigned by traditional cosmology, denial of, 19-23; motion of, 40, 41, 55-56

Ecphantus: 28

Einstein, Albert: 169

Elasticity of bodies: theory of Newton, 215, 216-17

Electricity. See Attraction

Epicurus: 44, 112, 140, 178, 180, 238, 239, 278

Ether, properties of: 132, 171-72, 207-8

Experimentation. See Newton, Sir Isaac

Extension. See Space

Extension, spiritual: denial by Descartes, 138; distinction from space, 132; identification with God, 191-201; penetrates and is impenetrable, 195, 200; theories of 17th century, 130-31; theory of More, 111, 112, 116-23 passim, 126-27, 132, 138


Ficino, Marsilio: 125

Finite world. See Universe

First Cause. See God

Fixed stars: 12-13, 19; comparison with rest of universe, 21-22; conception of Copernicus, 30-33; discoveries of Galileo through telescope, 72-76, 89-95; existence of sphere denied, 35, 56-57, 95-96; infinite extent of, 36-39, 40, 41, 48, 49, 51, 53; infinity denied, 60-87; position and dimensions, 30, 32, 62-85 passim, 104, 281; world in relation to, diagram of Kepler, 79. See also Universe

Freedom of choice. See God


Galileo Galilei: 40, 54, 55, 83, 84, 175, 176, 231, 277, 278; attitude toward gravity, 133; diagram of stars in Orion, 93; invention of telescope, influence of, 72-76, 81, 84, 88-95; lack of decision on infinity of universe, 95-99

Gassendi, Pierre: 3, 114, 146, 278, 290, 294

General Scholium: published by Newton, setting forth religious conceptions. 223-30, 234

Gilbert, William: 73, 284-85; contribution to concept of infinity of universe, 55-57, 60-61; denial of existence of sphere of fixed stars, 56-57; discussion of earth's rotation, 55-56; influenced by Digges, 55; theory of magnetic forces, 131

Glanvill, Joseph: 126

God: absence from space, 275; attributes of, 124, 148-53, 155-56, 197; conception of Descartes criticized by More, 111-24, 138, 147; conception of Newton attacked by Leibniz and defended by Clarke, 235-72; considered only infinite being, 52, 100, 106, 107, 108, 109, 192-93; creator of universe, 42, 48-49,

p. 308

52, 53, 78, 100, 113, 119, 120, 121, 124, 157, 208-9, 217-20, 239-41, 256-57, 266, 269, 273, 275; decrease in position in universe, 276; freedom of choice, concept of Newton, 239-46, 250, 253, 257, 259, 260, 268-70, 272, 273; idea of, relation to idea of space, 135-36, 137-39; identification with immaterial extension, 155-56, 191-201; identification with space, 137, 147, 155, 222-23, 226; infinite extension of, distinguished from material extension, 156-58, 159; infinity of, 52, 100, 106, 107, 108, 109, 113, 11624 passim, 140, 153-54, 192-93, 297; intervention needed to move universe, 183-89, 216, 224-25, 236-40 passim, 245, 248-49, 252, 254, 272, 276; participation in gravity, 134, 179, 207-20, 234, 298; power restricted by denial of void, 138, 232; relation of time and space to, by Newton, 161; religious conception of Newton, 223-28, 232-34; works of, discussed, 208-9; world an ordered expression of, 58, 286

Gravity: 131, 133-34. See also Attraction, theory of Newton

Gravity, specific: 172

Greece. See Ancients; Atomism

Gregory, David: 297-98

Guericke, Otto von: 3


Hardness: a property of all matter, theory of Newton, 207, 210-12, 217-18, 254, 272, 274. See also Atomic structure of universe; Atomism

Heavens. See Fixed stars; Universe

Hebrews: concept of infinite, 195

Hell: position of, 281

Heraclides: 28

Hermes: 126

Herschell, Sir William: 280

Hiketas: 28

Hobbes, Thomas: 3, 133, 145, 198, 238

Huygens, Christian: 3, 31, 169, 176, 230, 299

Hypotheses: danger to experimental philosophy, 204-5, 208, 228-34


Indefinite universe. See Universe

Inertia: principle of Newton, 169, 173, 174, 175, 216, 218, 261, 302

Infinite: definition of term, 72, 201

Infinity. See God; Universe

Isaiah: 201


Johnson, Francis R.: 35


Kant, Immanuel: 150, 180

Keill, John: 301

Kepler, Johannes: 55, 95, 96, 97, 102, 107, 171; diagram "M" of, 79; effect of telescopic discoveries on, 72-76; influenced by Nicholas of Cusa, 6, 19; supporter of Aristotle, 60, 72, 86-87; theories of, 58-87, 277


Laplace, Marquis Pierre Simon de: 276

Larkey, Sanford V.: 35

"Learned ignorance": doctrine of Nicholas of Cusa, 6, 8, 9, 10, 17

Leibniz, Gottfried Wilhelm von: 169, 207, 211, 290; concept of universe, 262-63, 266, 269, 273; death of, 273; distinction between motive and cause, 259; principle of observability of space, 261-62; principle

p. 309

of sufficient reason, 44, 46, 52, 61-62, 78, 239-42, 243-45, 246, 250, 253, 259, 262, 275, 283; theory of relativity of space, motion, and time, 245, 247-48, 249, 250-52, 254, 256, 262-63

—, attack on theories of Newton, and defense by Clarke: 300-1; atomic structure of universe, 207, 210-12, 254, 272, 274; concept of God, 232-72; concept of God's freedom of choice, 239-46, 250, 253, 257, 259, 260, 268-70, 272, 273; concept of motion, 245, 269, 272; concept of space, 235, 237, 239, 243-45, 247, 248, 251-52, 254-57, 259, 260, 263-67; concept of time, 256-57, 259, 263, 264-66, 269; contrast between materialism and mathematical philosophy, 208, 238, 241, 267, 271, 272; existence of void, 239, 241, 250-51, 254-55, 260, 264, 272; importance of matter in universe, 237, 239, 250; motion of universe, God's intervention required, 236, 237-38, 239-40, 245, 248-49, 252, 254, 272, 276; " sensorium " of God, 237. 239, 241, 242. See also Attraction

Leucippus: 73, 140

Light: and matter, 132, 207, 212, 297-98; behavior of, 131, 207, 212, 215; conception of Copernicus. 30, 33; conception of Palingenius, 2627

Locke, John: 235

Locus. See Place

Lovejoy, A. O.: 25, 34, 39, 42, 44, 52

Lucretius: 46, 54, 101, 112, 114, 190, 210, 278, 290; assertion of infinity of space, 35, 282; De rerum natura, 5, 6, 283; influence on cosmological thinking, 6


Mach, Ernst: 169

Magnetism. See Attraction

Malebranche, Father Nicolas: 149, 156-58, 159, 199

Manilius, Marcus: 66, 287

Manzoli, Pier Angelo. See Palingenius

Mathematical philosophy: 19, 99, 205, 208, 215, 228-34, 238, 241, 267, 271, 272, 278

Matter: atomic composition of, theory of Newton, 207, 209-13, 217-19, 254, 272, 274; conception of Descartes, 111-19 passim, 124; importance in universe, 237, 239; nature of, 101-2. 130, 172-75, 193, 194; not attribute of God, 193, 201; question of compressibility, 128; question of density, 207-8; relation to light, 132, 207, 212, 297-98. See also Attraction; Gravity; Space

McColley, Grant: 31

Mediaeval concept of space: 277

Mediaeval concept of universe: 5, 6, 16, 24, 34, 281

Melissos: 73

Mendelsohn, Moses: 201

Metrodorus: 140

Milky Way: 69-70, 83, 89

Montaigne, Michel de: 1

More, Henry: 109, 156, 161, 163, 164, 165, 173, 176, 190, 195, 197, 201, 220, 248, 251, 252, 264, 274, 290, 291, 302-3; concept of space, 12627, 132, 137-40, 145-47, 152. 155, 159, 160; concept of spirit and matter, 125, 127-32; concept of spiritual extension, 111, 112, 11723 passim, 132, 138, 191-92; exchange

p. 310

of letters with Descartes, 110-24; philosophy of, 125-26, 289; theories related to Newton's, 190

—, disputes views of Descartes: conception of God, 111-24; denial of existence of atoms, 112-13; denial of void, 112, 116, 120, 138, 139-40, 145, 191-92; identification of matter, extension, and space, 110-12, 115, 117-18, 124, 126-27, 132; indefinite extension of universe, 114-15, 11722, 124, 152-54; opposition of spirit and matter, 110-12, 121, 125; relativity of motion, 142-45

Motion: absolute, 163-71, 256, 272; circular, 18, 167-71; indistinguishable from rest, 166; of earth, 15, 20, 39-40, 55-56; of universe, 15, 19, 30-33, 41, 44, 49-51, 56-57, 183-89, 216, 224-25, 236-40 passim, 245, 248-49, 252, 254, 269, 272, 276; planetary, allied with force by which bodies fall, 229; principle of observability, 261-62; proof of existence of God, 191-95, 202-3, 216-17, 218; rectilinear, 166, 16769; relative, 10-17 passim, 142-45, 161-71, 256, 261, 262, 269, 279; use in measuring time, 161-62


Napoleon Bonaparte: 276

Neoplatonic revival: 24, 113, 161, 277. See also Plato

Newton, Sir Isaac: 3, 109, 180, 189, 278., 290, 294, 298; correspondence with Bentley re gravity and planetary motion, 178-89, 223; publication of General Scholium, setting forth religious conceptions, 223-30, 234; publication of "queries" re metaphysical problems, 206-7, 296; success of philosophy of, 274; support of phenomena against hypotheses, 205, 208, 228-34; theories related to those of More, 159, 160, 190; theory of finitude of universe, overcome, 274-75; world-view of, 207. See also Attraction; Inertia; Leibniz, attack on theories of Newton; Mathematical philosophy

—, concepts: God, 207-20, 223-28, 232-72, 274-76; light, 207, 212, 29798; matter, 172-75, 207-8, 209-13, 217-19, 250, 254, 272, 274, 297-98; motion, 160-71, 213, 215-18, 221, 224, 236-40 passim, 245, 248-49, 252, 254, 256, 269, 272, 276; rare ether, 171-72, 207; space, 160-66, 168, 169, 171-72, 207, 221-28, 23571 passim; time, 221-28, 256-57, 259, 263, 264-66, 269; void, 239, 241, 250-51, 254-55, 260, 264, 272

Nicholas of Cusa, Cardinal: 6-24 passim, 29, 35, 42, 43, 44, 47, 52, 54, 96, 99, 106, 118, 282; belief in lack of precision in universe, 13, 16-18; biographical sketch, 278; comparison of inhabitants of parts of universe, 22-23; concept of motion, 15, 17, 18, 19; concept of universe, 8-24; conceptions disregarded by contemporaries, 18; denial of low position of earth, 19-23; forerunner of Copernicus and Kepler, 19, 280; influence on Palingenius, 24; " Learned ignorance," theory of, 6, 8, 9, 10, 17; rejects mediaeval concept of cosmos, 6; thought compared to that of Bruno, 41. 43

Nullibists, nickname of Cartesians, 138, 201

p. 311

Orion, constellation of: discussed by Kepler, 63-64, 65-66. 81; shield and sword, as seen through telescope, 93


Palingenius, Marcellus Stellatus: 28, 39; attitude toward Greek cosmologists, 24; biographical sketch, 280; conception of universe, 24-27; influenced by Nicholas of Cusa, 24; suspected of heresy, 280

Parallaxes: theory of, applied by Kepler, 66, 68, 287

Pascal, Blaise: 3, 43, 277, 283, 291

Pattrizzi, F.: 54

Perspicillum. See Telescope

Philolaos: 28

Phoenicia: 208

Place: absolute, distinguished from relative, 163-66; definition, 140, 163; relation to motion, 143-45. See also Space

Planets: compared with fixed stars, 92; discoveries enabled by invention of telescope, 73-76. 89-90, 92; motion of, 31, 33, 49-51, 229; situation in universe, 73. See also Universe

Plato: 3, 28, 54, 72, 123, 126, 140, 141. See also Neoplatonic revival

Plenitude, principle of: 25, 42, 44, 52, 188, 275

Plotinus: 290

Plutarch: 141

Poles of universe: 12, 14, 15, 16-17, 20; Copernicus' conception, 30; denial of existence by Bruno, 41

Pre-Copernican diagram of universe: 7

Princess of Wales: 235, 259, 263-64, 300

Ptolemy: 28, 32. 34, 56. 95, 96 Pythagoras: 28, 30, 59, 147

Raleigh, Sir Walter: 34

Raphson, Joseph: 206, 220, 221-23, 249, 295, 301; concept of infinity, 201-2; concept of space, 191-201; concept of universe, 202-4; influence of Spinoza on, 191; relations between theories of Newton and More pointed out by, 190-91

Rectilinear motion. See Motion

Relativity. See Motion; Space; Time

Repulsion: theory of Newton, 213, 214-15

Rest: status of, 164, 166

Rheticus: 28

Riccioli, Gianbattista: 31

Rotational motion. See Motion


St. Paul: 227, 270

Scaliger, Julius: 119

Scholastic tradition: 199, 230, 262, 264, 266, 267, 268

Scotus, John Duns. See Duns Scotus, John

Sense-perception: question of value in interpreting universe, 44-46, 59, 62, 85, 100, 111-12, 115, 160-62; scope increased by invention of telescope, 89

Sensorium of God: concept of Newton, 237, 239, 241, 242, 301

Sidereus Nuntius of Galileo, announcing discoveries of telescope, importance of, 88, 90

Socinianism: 239, 301-2

Solar system. See Universe

Space: absolute, 160-66, 168-69, 22128, 243-45, 247, 274; attribute of God, 149-50, 155, 193-201, 247;

p. 312

change in concept of, 275, 277; concept of More shared by Newton, 159, 160; concept of Newton attacked and defended, 235, 237, 239, 243-45, 247, 248, 251-52, 25457, 259, 260, 263-67, 269, 270-71; distinction from extension, 132, 264, 265; distinction from matter, 127, 135-41 passim, 145-47, 152, 17172, 194; existence acknowledged by ancients, 140-41; existence of, a precondition to all existence, 13738; filled with ether, theory of Newton, 171-72, 207; identified with God, 114, 148-53, 197, 244, 247, 271; identified with matter, 99, 101-6, 110-12, 117-18, 124, 126-27, 155, 156, 191-92, 256-57, 269; indefiniteness of 152; infinity of, 46-49, 52, 53, 126, 140-41, 15556, 194-202; intelligible distinguished from material, 156-58, 159; measurability of, 135-37, 139-40; nature of, 135-41, 145-54, 193-98; nonmeasurability of, 135-37; reality of, argued by More, 145-47; relative, 16, 162-63, 245, 247, 249, 250-52, 254, 262-63. See also Extension, spiritual; Void

Specific gravity: 172

Spenser, Edmund: quoted, 280-81

Spheres. See Universe

Spinoza, Benedict: 149, 159, 197, 201, 239; concept of extension, 155-56; identifies God with universe, 191, 192-93; identifies space with matter, 155, 156; influence on Raphson, 191

Spirit: concept of More, 127-34

Spissitude: theory of More, 129

Stars. See Fixed stars; Universe

Stoa: 126

Stoics: 140-41

Substances: implied by attributes, 145-47

Sufficient reason, principle of. See Leibniz

Sun. See Universe

Syncretism: tendency of More toward, 125-26


Telescope: astronomy before discovery of, 62, 64; influence on thought of Kepler, 72-76, 81; invention by Galileo, contribution of, 88-95; use of, 84

Thought, human: imperfection of, 199-200

Time: absolute, 160-62, 221, 223, 225-28; concept of Newton attacked and defended, 256-57, 259, 263, 264-66, 269; identified with duration, 161-62; relative, 160-62, 245, 247-48, 252, 254, 256, 262-63

Torricelli, Evangelista: 277

Tycho Brahe. See Brahe, Tycho


Universe: comparison of component parts, 20-23; concept of ancients, 5, 14, 16, 17, 24, 60, 112; concept of Copernicus, importance to philosophy, 29; concept of Nicholas of Cusa, 8-24; constituted from same matted throughout, 105; corruption in, 23; finitude of: 24-27, 30-34, 58-87, 140-41, 153, 157-58, 159, 192, 202-4, 249, 256-57, 260; hierarchical structure undermined, 19-23, 29; importance of matter in, 237, 239; indefinite nature of, concept of Descartes, 8, 104-9, 114-24 passim, 140; lack of precision, 13, 16-18, 19; mediaeval

p. 313

concept, 5, 6, 16, 24, 34, 281; populated throughout, 22-23, 25; pre-Copernican, diagram of, 7; relation of God to, theory of More, 11024; solar systems in, 49-51. See also Center of universe; God: creator of universe; Motion

—, infinity of: 2, 3, 5, 24, 34-35, 188, 275, 276; concepts of: Bentley, 180; Bruno, 39-54; Clarke, 256-57; Descartes, 104-9, 114-24 passim; Digges, 35-39; Galileo, 95-99; Gilbert, 55-57; Kepler, 58-87; Leibniz, 260, 262-63; More, 114-15, 118-21, 140, 153; Nicholas of Cusa, 6, 8, 19; Palingenius, 25-27


Vacuum. See Void

Void: 57, 277, 283; conception of ancients, 141; considered center of universe, 78, 81, 82, 83; immensity, 181-82; measurability, 139-40; position, 65, 69, 75; question of existence, 40-41, 46-48, 86, 87, 101-4, 112, 116, 120, 137-38, 145, 171, 180, 191-92, 207-8, 232, 239, 241, 250-51, 254-55, 260, 264, 272, 283; success of Newton's concept, 274

Voltaire, François Marie Arouet de: 274

von Leibniz. See Leibniz

Vortices: theory of Descartes, 115, 118, 119, 290


Wacherus. See Wackher von Wackenfels

Wackher von Wackenfels, Mattheus: 73, 287

Wales, Princess of: 235, 259, 263-64, 300

World. See Universe


Zodiac: 12