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From the Closed World to the Infinite Universe, by Alexander Koyré, [1957], at

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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

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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

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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

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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

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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

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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.

Next: XII. Conclusion: The Divine Artifex and the Dieu Fainéant