From the Closed World to the Infinite Universe: VII. Absolute Space, Absolute Time and Their Relations to God

From the Closed World to the Infinite Universe, by Alexander Koyré, [1957], at sacred-texts.com

VII. Absolute Space, Absolute Time and Their Relations to God

Henry More's conception of space, which makes it an attribute of God, is by no means—I have said it already, but I should like to insist upon it—an aberrant, odd and curious invention, a "fancy," of a Neoplatonic mystic lost in the world of the new science. Quite the contrary. It is, in its fundamental features, shared by a number of the great thinkers of his time, precisely those who identified themselves with the new scientific world-view.

I need not insist on Spinoza who, though he denied the existence of void space and maintained the Cartesian identification of extension and matter, carefully distinguishes between extension, as given to the senses and represented by the imagination, and extension as perceived by the understanding—the former, being divisible and movable (and corresponding to the Cartesian indefinitely extended world), constituting the sempiternal many-fold of ever-changing and finite modi, the latter, truly and fully infinite and therefore indivisible, constituting

the eternal and essential attribute of the a se and per se existing Being, that is, of God.

Infinity belongs unavoidably to God, not only to the very dubious God of Spinoza, but also to the God of the Christian religion. Thus, not only Spinoza, the by no means pious Dutch philosopher, but also the very pious Father Malebranche, having grasped the essential infinity of geometrical space, is obliged to connect it with God. The space of geometers or, as Malebranche calls it, the "intelligible extension," is, according to Christ Himself, who appears as one of the interlocutors of the Christian Meditations of Malebranche,1

Malebranche, of course, does not want to put matter into God and to spatialize God in the manner in which Henry More or Spinoza did it. He distinguishes therefore the idea of space, or "intelligible extension," which he places in God, from the gross material extension of the world created by God.2

the matter out of which the world is built. . . . This world began and can cease to be. It has certain limits that it cannot lack. . . . Intelligible extension appears to you eternal, necessary, infinite; believe what you see; but do not believe that the world is eternal, or that the matter that composes it is immense, necessary, eternal. Do not attribute to the creature what pertains only to the Creator, and do not confuse My [Christ's] substance which God engenders by the necessity of His Being with My work which I produce with the Father and the Holy Spirit by an entirely free operation.

It is just the confusion between the intelligible extension and the created one that induces some people to assert the eternity of the world and to deny its creation by God. For,4

there is another reason which leads men to believe that matter is untreated; indeed, when they think about extension they cannot prevent themselves from regarding it as a necessary being. For they conceive that the world has been created in immense spaces, that these spaces never had a beginning, and that God Himself cannot destroy them. Thus, confusing matter with these spaces, as matter effectively is nothing else but space or extension, they regard matter as an Eternal being.

This is, as a matter of fact, a rather natural error as Malebranche himself does not fail to point out to his Divine Master; he recognizes, of course, that his doubts are removed, and that he now sees the distinction that formerly escaped him. Still5

By no means. In spite of the Cartesian axiom hinted at by Malebranche (in the role of the discipulus of the dialogue), according to which we are entitled to assert of the thing what we clearly perceive to belong to its idea, the reasoning attributing infinity and eternity to material extension was illegitimate; thus the Divine Master replies:6

We must, my dear Disciple, judge things according to their ideas; it is only thus that we have to judge them. But that concerns their essential attributes, and not the circumstances of their existence. The idea you have of extension represents it to you as divisible, mobile, impenetrable: judge without fear that it has essentially these properties. But do not judge that it is immense, or that it is eternal. It may not exist at all, or possess very narrow limits. [The contemplation of the idea of extension] gives you no reason to believe that there is [in existence] even one foot of material extension, though you have present in your mind an infinite immensity of intelligible extension; and much less are you entitled to judge that the world is infinite as some philosophers assert. Do not judge either that the world is eternal because you regard intelligible extension as a necessary being of which the duration has no beginning and cannot have an end. For, though you must judge the essence of things according to the ideas which represent them, you must never judge by them of their existence.

The Disciple of Malebranche's dialogue is fully convinced—who, indeed, would not be by such a Master? Nobody else, alas, shared his conviction.

between "intelligible" and "created" extension as perfectly spurious and corresponding only and solely to the Cartesian distinction between (real) extension given to the senses and the same real extension as object of pure understanding. According to him Malebranche's "intelligible extension" was simply the infinite extension of the material universe. Thirty years later, Dortous de Mairan made fundamentally the same reproach, though he formulated it in a somewhat different and much nastier manner: according to him Malebranche's "intelligible extension" was indistinguishable from that of Spinoza. . . .7

But not only philosophers shared, more or less, Henry More's conception of space: it was shared by Newton, and this, because of the unrivaled influence of Newton on the whole subsequent development, is, indeed, of overwhelming importance.

It may seem strange, at first glance, to link together Henry More and Isaac Newton. . . . And yet, this link is perfectly established.8 Moreover, as we shall see, More's explicit teaching will throw some light on the implicit premises of Newtonian thinking, a light all the more necessary as Isaac Newton, in contradistinction not only to Henry More but also to René Descartes, is neither a professional metaphysician like the former, nor, like the latter, at once a great philosopher and a great scientist: he is a professional scientist, and though science, at that time, had not yet accomplished its disastrous divorce from philosophy, and though physics was still not only designated, but also thought of, as "natural philosophy," it is nevertheless true that his primary interests are in the field of "science," and not of "philosophy." He deals,

therefore, with metaphysics not ex professo, but only insofar as he needs it to establish the foundations of his intentionally empirical and allegedly positivistic mathematical investigation of nature. Thus the metaphysical pronouncements of Newton are not very numerous and, Newton being a very cautious and secretive person as well as a very careful writer, they are rather reticent and reserved. And yet they are sufficiently clear so as not to be misunderstood by his contemporaries.

Newton's physics, or, it would be better to say, Newton's natural philosophy, stands or falls with the concepts of absolute time and absolute space, the selfsame concepts for which Henry More fought his long-drawn-out and relentless battle against Descartes. Curiously enough, the Cartesian conception of the only relative, or relational, character of these and connected notions is branded by Newton as being "vulgar" and as based upon "prejudices."

Thus in the famous scholium which follows the Definitions that are placed at the very beginning of the Principia, Newton writes:9

Hitherto I have laid down the definitions of such words as are less known, and explain the sense in which I would have them to be understood in the following discourse. I do not define time, space, place, and motion as being well known to all. Only I must observe that the vulgar conceive those quantities under no other notions but from the relations they bear to sensible objects. And thence arise certain prejudices, for the removing of which, it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.

Absolute, true and mathematical time and space—for Newton these qualifications are equivalent and determine

the nature both of the concepts in question and of the entities corresponding to them—are thus, in a manner of which we have already seen some examples, opposed to the merely common-sense time and space. As a matter of fact, they could just as well be called "intelligible" time and space in contradistinction to "sensible." Indeed, according to the "empiricist" Newton,10 "in philosophical disquisitions we ought to abstract from our senses and consider things themselves, distinct from what are only sensible measures of them." Thus:11

It may be that there is no such thing as an equable motion whereby time may be accurately measured. All motion may be accelerated and retarded, but the flowing of absolute time is liable to no change. The duration or perseverance of the existence of things remains the same; whether the motions are swift or slow, or none at all: and therefore it ought to be distinguished from what are only sensible measures thereof.

Time is not only not linked with motion—like Henry More before him, Newton takes up against Aristotle the Neoplatonic position—it is a reality in its own right:12

that is, it is not, as Descartes wants us to believe, something which pertains only to the external, material world and which would not exist if there were no such world, but something which has its own nature (a rather equivocal and dangerous assertion which Newton later had to correct by relating time, as well as space, to God), "and by another name is called duration"; that is, once more, time is not, as Descartes wants us to believe, something

subjective and distinct from the duration which he, Descartes, identifies with the amount of reality of the created being. Time and duration are only two names for the same objective and absolute entity.

that is, space is not Cartesian extension which moves around, and which by Descartes is identified with, bodies. This is, at most, relative space, which is mistaken for the absolute space that subtends it by both Cartesians and Aristotelians.15

Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies, and which is vulgarly taken for immovable space; such is the dimension of a subterraneous, an aereal, or celestial space, determined by its position in respect of the earth. Absolute and relative space are the same in figure and magnitude; but they do not remain always numerically the same,

because relative space, which is, so to speak, attached to the body, moves with that body through absolute space16

Just as we have distinguished absolute, immovable space from the relative spaces that are and move in it, so we have to make a distinction between absolute and relative places which bodies occupy in space. Thus, elaborating More's analysis of this concept and his criticism of the traditional as well as the Cartesian conceptions, Newton states:17

Place is a part of space which a body takes up and is, according to the space, either absolute or relative. I say, a part of space; not the situation nor the external surface of the body. For the places of equal solids are always equal; but their surfaces, by reason of their dissimilar figures, are often unequal. Positions properly have no quantity; nor are they so much the places themselves as the properties of places. The motion of the whole is the same with the sum of the motions of the parts; that is, the translation of the whole, out of its place, is the same thing with the sum of the translations of the parts out of their places; and therefore the place of the whole is the same as the sum of the places of the parts, and for that reason it is internal and in the whole body.

Place—locus—is thus something which is in the bodies, and in which bodies are in their turn. And as motion is a process in which bodies change their places, not taking them along with them but relinquishing them for others, the distinction between absolute and relative spaces implies necessarily that of absolute and relative motion, and vice versa, is implied by it:18

Absolute motion is the translation of a body from one absolute place into another, and relative motion the translation from one relative place into another. Thus in a ship under sail the relative place of a body is that part of the ship which the body possesses, or that part of the cavity which the body fills and which therefore moves together with the ship, and relative rest is the continuance of the body in the same part of the ship or of its cavity. But real, absolute rest is the continuance of the body in the same part of that immovable space in which the ship itself, its cavity, and all that it contains is moved. Wherefore, if the ship is really at rest, the body, which relatively rests in the ship, will really and absolutely move with the same velocity which the ship has on the earth. But if the earth also moves, the true and absolute motion of the body will arise, partly from the true motion of the earth in immovable space, partly from the relative motion of the ship on the earth; and if the body moves also relatively in the ship, its true motion will arise, partly from the true motion of the earth in immovable space and partly from the relative motions as well of the ship on the earth as of the body in the ship; and from these relative motions will arise the relative motion of the body on the earth. As if that part of the earth where the ship is was truly moved toward the east with a velocity of 10,000 parts, while the ship itself, with a fresh gale and full sails, is carried toward the west with a velocity expressed by 10 of those parts, but a sailor walks in the ship toward the east with 1 part of the said velocity; then the sailor will be moved truly in immovable space toward the east, with a velocity of 10,001 parts, and relatively on the earth toward the west, with a velocity of 9 of those parts.

As for the inner structure of space, it is characterized by Newton in terms that strongly remind us of the analysis made by Henry More:19

As the order of the parts of time is immutable, so also is the order of the parts of space. Suppose those parts to be moved out of their places, and they will be moved (if the expression may be allowed) out of themselves. For times and spaces are, as it were, the places as well of themselves as of all other things. All things are placed in time as to order of succession and in space as to order of situation. It is from their essence or nature that they are places, and that the primary places of things should be movable is absurd. These are therefore the absolute places, and translations out of those places are the only absolute motions.

Newton, it is true, does not tell us that space is "indivisible" or "indiscerpible";20 yet it is obvious that to "divide" Newton's space, that is, actually and really to separate its "parts," is just as impossible as it is impossible to do so with More's, an impossibility that does not preclude the making of "abstract" or "logical" distinctions and divisions, or prevent us from distinguishing inseparable "parts" in absolute space and from asserting its indefinite, or even infinite "divisibility." Indeed, for Henry More, as well as for Newton, the infinity and the continuity of absolute space imply the one as well as the other.

Absolute motion is motion in respect to absolute space, and all relative motions imply absolute ones:21

"From infinity to infinity retain the same position. . . ." What does infinity mean in this place? Obviously not only the spatial, but also the temporal: absolute places retain from eternity to eternity their positions in the absolute, that is, infinite and eternal space, and it is in respect to this space that the motion of a body is defined as being absolute.

Alas, absolute motion is very difficult, or even impossible, to determine. We do not perceive space—it is, as we know, inaccessible to our senses. We perceive things in space, their motions in respect to other things, that is, their relative motions, not their absolute motions in respect to space itself. Moreover, motion itself, or in itself, the status of motion, though utterly opposed to the status of rest, is nevertheless (as we see it clearly in the fundamental case of uniform, rectilinear, inertial motion) absolutely indistinguishable from the latter.

It is only by their causes and effects that absolute and relative motions can be distinguished and determined:22

is sufficient only to impress some force on other bodies with which the former is compared that, by their giving way, that relation may be changed in which the relative rest or motion of this other body did consist. Again, true motion suffers always some change from any force impressed upon the moving body, but relative motion does not necessarily undergo any change by such forces. For if the same forces are likewise impressed on those other bodies with which the comparison is made, that the relative position may be preserved, then that condition will be preserved in which the relative motion consists. And therefore any relative motion may be changed when the true motion remains unaltered, and the relative may be preserved when the true suffers some change. Thus, true motion by no means consists in such relations.

Thus it is only in the cases where our determination of the forces acting upon the bodies is not based upon the perception of the change of the mutual relations of the bodies in question that we are actually able to distinguish absolute motions from relative ones, or even from rest. Rectilinear motion, as we know, does not offer us this possibility. But circular or rotational motion does.23

Rotational or circular motion, everywhere on the earth as in the skies, gives birth to centrifugal forces, the determination of which enables us to recognize its existence in a given body, and even to measure its speed, without taking into account the positions or behavior of any

other body outside the gyrating one. The purely relative conception finds its limit—and its refutation—in the case of circular motion and, at the same time, the Cartesian endeavor to extend this conception to celestial motions appears as it really is: a clumsy attempt to disregard the facts, a gross misinterpretation or misrepresentation of the structure of the universe.24

[paragraph continues] There is only one real circular motion of any one revolving body, corresponding to only one power of endeavoring to recede from its axis of motion, as its proper and adequate effect; but relative motions, in one and the same body, are innumerable, according to the various relations it bears to external bodies, and, like other relations, are altogether destitute of any real effect, any otherwise than they may perhaps partake of that one only true motion. And therefore in their system who suppose that our heavens, revolving below the sphere of the fixed stars, carry the planets along with them, the several parts of those heavens and the planets, which are indeed relatively at rest in their heavens, do yet really move. For they change their position one to another (which never happens to bodies truly at rest) and, being carried together with their heavens, partake of their motions and, as parts of revolving wholes, endeavour to recede from the axis of their motions.

The Newtonian discovery of the absolute character of rotation—in contradistinction to rectilinear translation—constitutes a decisive confirmation of his conception of space; it makes it accessible to our empirical knowledge and, without depriving it of its metaphysical function and status, it ensures its role and its place as a fundamental concept of science.

motion "relative" to absolute space, and, of course, the very idea of absolute space with its physico-metaphysical implications, met, as we know, with rather strong opposition. For two hundred years, from the times of Huygens and Leibniz to those of Mach and Duhem, it was subjected to searching and vigorous criticism.24a It has, in my opinion, withstood victoriously all the assaults, which is, by the way, not so very surprising: it is indeed the necessary and inevitable consequence of the "bursting of the sphere," the "breaking of the circle," the geometrization of space, of the discovery or assertion of the law of inertia as the first and foremost law or axiom of motion. Indeed, if it is the inertial, that is, the rectilinear uniform motion that becomes—just like rest—the "natural" status of a body, then the circular one, which at any point of its trajectory changes its direction though maintaining constant its angular velocity, appears, from the point of view of the law of inertia, not as a uniform, but as a constantly accelerated motion. But acceleration, in contradistinction to mere translation, has always been something absolute, and it remained so until 1915, when, for the first time in the history of physics, the general relativity theory of Einstein deprived it of its absoluteness. Yet as, in so doing, it reclosed the universe and denied the Euclidean structure of space, it has, by this very fact, confirmed the correctness of the Newtonian conception.

Newton thus was perfectly right in stating that we are able to determine the absolute rotational or circular motion of bodies without needing, for that purpose, a term of reference represented by a body at absolute rest; though he was wrong, of course, in his pious hope of being able,

finally, to achieve the determination of all "true" motions. The difficulties that stood in his path were not merely—as he believed them to be—very great. They were insurmountable.25

It is indeed a matter of great difficulty to discover and effectively to distinguish the true motions of particular bodies from the apparent, because the parts of that immovable space in which those motions are performed do by no means come under the observation of our senses. Yet the thing is not altogether desperate; for we have some arguments to guide us, partly from the apparent motions, which are the differences of the true motions; partly from the forces, which are the causes and effects of the true motions. For instance, if two globes, kept at a given distance one from the other by means of a cord that connects them, were revolved about their common center of gravity, we might, from the tension of the cord, discover the endeavor of the globes to recede from the axis of their motion, and from thence we might compute the quantity of their circular motions. And then if any equal forces should be impressed at once on the alternate faces of the globe to augment or diminish their circular motions, from the increase or decrease of the tension of the cord we might infer the increment or decrement of their motions, and thence would be found on what faces those forces ought to be impressed that the motions of the globes might be most augmented; that is, we might discover their hindmost faces, or those which, in the circular motion, do follow. But the faces which follow being known, and consequently the opposite ones that precede, we should likewise know the determination of their motions. And thus we might find the quantity and the determination of this circular motion, even in an immense vacuum, where there was nothing external or

sensible with which the globes could be compared. But now, if in that space some remote bodies were placed that kept always a given position one to another, as the fixed stars do in our regions, we could not indeed determine from the relative translation of the globes among those bodies whether the motion did belong to the globes or to the bodies. But if we observed the cord and found that its tension was that very tension which the motion of the globes required, we might conclude the motion to be in the globes and the bodies to be at rest; and then, lastly, from the translation of the globes among the bodies, we should find the determination of their motions. But how we are to obtain the true motions from their causes, effects, and apparent differences, and the converse, shall be explained at large in the following treatise. For to this end it was that I composed it.

The real distinction between space and matter, though it involves the rejection of the Cartesian identification of the essence of matter with extension, does not, as we know, necessarily imply the acceptance of the existence of an actual vacuum: we have seen Bruno, and Kepler too, assert that space is everywhere full of "ether." As for Newton, though he, too, believes in an ether that fills at least the space of our "world" (solar system), his ether is only a very thin and very elastic substance, a kind of exceedingly rare gas, and it does not completely fill the world space. It does not extend itself to infinity as is sufficiently clear from the motion of comets:26

and as unresisting matter, that is, matter deprived of the vis inertiae, is unthinkable, it is obvious that the celestial spaces are void also of matter. Moreover, even where it is present, Newtonian ether does not possess a continuous structure. It is composed of exceedingly small particles between which, of course, there is vacuum. Elasticity, indeed, implies vacuum. In a Cartesian world, that is, in a world constituted by a continuously-spread uniform matter, elasticity would be impossible. Nay, if all spaces were equally full (as they must be according to Descartes) even motion would not be possible.27

All spaces are not equally full; for if all spaces were equally full, then the specific gravity of the fluid which fills the region of the air, on account of the extreme density of the matter, would fall nothing short of the specific gravity of quicksilver, or gold, or any other the most dense body; and, therefore, neither gold nor any other body could descend in air; for bodies do not descend in fluids, unless they are specifically heavier than the fluids. And if the quantity of matter in a given space can, by any rarefaction, be diminished, what should hinder a diminution to infinity?

Matter, according to Newton, who shares the atomic conceptions of his contemporaries (and even improves upon them in a very interesting manner), has an essentially granular structure. It is composed of small, solid, particles and therefore28

As for matter itself, the essential properties that Newton ascribes to it are nearly the same as those that have been listed by Henry More,28 by the old atomists and the modern partisans of corpuscular philosophy: extension, hardness, impenetrability, mobility, to which is added—a most important addition—inertia, in the precise, new meaning of this word. In a curious combination of anti-Cartesian empiricism and ontological rationalism, Newton wants to admit as essential properties of matter only those that are (a) empirically given to us, and (b) can be neither increased nor diminished. Thus he writes in the third of his Rules of Reasoning in Philosophy, by which he replaced the third fundamental Hypothesis of the first edition of the Principia:30

The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.

For since the qualities of bodies are only known to us by experiments, we are to hold for universal all such as universally agree with experiments, and such as are not liable to diminution can never be quite taken away. We are certainly not to relinquish the evidence of experiments for the sake of dreams and vain fictions of our own devising; nor are we to recede from the analogy of Nature, which is wont to be simple and always consonant to itself. We in no other way know the extension of bodies than by our senses, nor do these reach it in all bodies; but because we perceive extension in all that are sensible, therefore we ascribe it universally to all others also. That abundance of bodies are hard we learn by experience; and because the hardness of the whole arises from the hardness of the parts, we therefore justly infer the hardness of the undivided

particles, not only of the bodies we feel, but of all others. That all bodies are impenetrable, we gather not from reason, but from sensation. The bodies which we handle we find impenetrable, and -hence conclude impenetrability to be a universal property of all bodies whatsoever. That all bodies are movable and endowed with certain powers (which we call the inertia) of persevering in their motion, or in their rest, we only infer from the like properties observed in the bodies which we have seen. The extension, hardness, impenetrability, mobility, and inertia of the whole result from the extension, hardness, impenetrability, mobility, and inertia of the parts and hence we conclude the least particles of all bodies to be also all extended, and hard and impenetrable, and movable, and endowed with their proper inertia. And this is the foundation of all philosophy. Moreover, that the divided but contiguous particles of bodies may be separated from one another is a matter of observation; and, in the particles that remain undivided, our minds are able to distinguish yet lesser parts, as is mathematically demonstrated. But whether the parts so distinguished and not yet divided may, by the powers of Nature, be actually divided and separated from one another we cannot certainly determine. Yet had we the proof of but one experiment that any undivided particle, in breaking a hard and solid body, suffered a division, we might by virtue of this rule conclude that the undivided as well as the divided particles may be divided and actually separated to infinity.

Lastly, if it universally appears, by experiments and astronomical observations, that all bodies about the earth gravitate toward the earth, and that in proportion to the quantity of matter which they severally contain; that the moon likewise, according to the quantity of its matter, gravitates toward the earth; that, on the other hand, our sea gravitates toward the moon; and all the planets one

toward another; and the comets in like manner toward the sun: we must, in consequence of this rule, universally allow that all bodies whatsoever are endowed with a principle of mutual gravitation. For the argument from the appearances concludes with more force for the universal gravitation of all bodies than for their impenetrability, of which, among those in the celestial regions, we have no experiments nor any manner of observation. Not that I affirm gravity to be essential to bodies; by their vis insita I mean nothing but their inertia. This is immutable. Their gravity is diminished as they recede from the earth.

We see, therefore, that Newton, no more than Galileo or even Descartes, includes gravity, or mutual attraction, in the essential properties of bodies in spite of the fact that its empirical foundations are much stronger than those of such a fundamental property as impenetrability. Newton seems to suggest that the reason for this exclusion consists in the variability of gravitation as opposed to the immutability of the inertia. But this is by no means the case. The weight of a body "gravitating" toward the earth is indeed diminished as it recedes from it: but the attractive force of the earth—or any other body—is constant, and, just as in the case of inertia, proportional to its mass, and it is as such that it appears in the famous inverse square formula of universal gravitation. This is so because31

Thus the attraction of a body is a function, or sum, of the attractions of its (atomic) particles, just as its mass is the sum of the masses of the selfsame particles. And yet it is not an "essential property" of the body, or of its particles. As a matter of fact it is not even an adventitious property of them; it is in no sense their property. It is an effect of some extraneous force acting upon them according to a fixed rule.

It is—or should be—a well-known fact that Newton did not believe in attraction as a real, physical force. No more than Descartes, Huygens or Henry More could he admit that matter is able to act at a distance, or be animated by a spontaneous tendency. The empirical corroboration of the fact could not prevail against the rational impossibility of the process. Thus, just like Descartes or Huygens, he tried at first to explain attraction—or to explain it away—by reducing it to some kind of effect of purely mechanical occurrences and forces. But in contradistinction to the former, who believed that they were able to devise a mechanical theory of gravity, Newton seems to have become convinced of the utter futility of such an attempt. He discovered, for example, that he could indeed explain attraction, but that in order to do so he had to postulate repulsion, which, perhaps, was somewhat better, but not very much so.

Fortunately, as Newton knew full well, we need not have a clear conception of the way in which certain effects are produced in order to be able to study the phenomena and to treat them mathematically. Galileo was not obliged to develop a theory of gravity—he even claimed his right to ignore completely its nature—in order to establish a mathematical dynamics and to determine the laws of fall.32

Thus nothing prevented Newton from studying the laws of "attraction" or "gravitation" without being obliged to give an account of the real forces that produced the centripetal motion of the bodies. It was perfectly sufficient to assume only that these forces—whether physical or metaphysical—were acting according to strict mathematical laws (an assumption fully confirmed by the observation of astronomical phenomena and also by well-interpreted experiments) and to treat these "forces" as mathematical forces, and not as real ones. Although only part of the task, it is a very necessary part; only when this preliminary stage is accomplished can we proceed to the investigation of the real causes of the phenomena.

This is precisely what Newton does in the book so significantly called not Principia Philosophiae, that is, Principles of Philosophy (like Descartes’), but Philosophiae naturalis principia mathematica, that is, Mathematical Principles of Natural Philosophy. He warns us that:33

I here use the word "attraction" in general for any endeavor whatever made by bodies to approach each other, whether that endeavor arise from the action of the bodies themselves, as tending to each other or agitating each other by spirits emitted; or whether it arises from the action of the ether or of the air, or of any medium whatever, whether corporeal or incorporeal, in any manner impelling bodies placed therein toward each other. In the same general sense I use the word impulse, not defining in this treatise the species or physical qualities of forces, but investigating the quantities and mathematical proportions of them, as I observed before in the definitions. In mathematics we are to investigate the quantities of forces with their proportions consequent upon any conditions supposed; then, when we

In his Letters (written five years after the publication of the Principia) to Richard Bentley who, like nearly everybody else, missed the warning just quoted and interpreted Newton in the way that became common in the eighteenth century, namely as asserting the physical reality of attraction and of attractive force as inherent to matter, Newton is somewhat less reserved. He first tells Bentley (in his second letter):34

In the third one, he practically comes into the open. Though he does not tell Bentley what he, Newton, believes the force of attraction to be in rerum, he tells him that:35

It is inconceivable that inanimate brute matter should, without mediation of something else which is not material, operate upon and affect other matter without mutual contact, as it must be if gravitation, in the sense of Epicurus, be essential and inherent in it. And this is one reason why I desired you would not ascribe innate gravity to me. That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed

As we see, Newton does not pretend any longer not to know the cause of gravity; he only informs us that he left this question unanswered, leaving it to his readers to find out themselves the solution, namely that the "agent" which "causes" gravity cannot be material, but must be a spirit, that is, either the spirit of nature of his colleague Henry More, or, more simply, God—a solution that, rightly or wrongly, Newton was too cautious to announce himself. But that Dr. Bentley could not—and did not—fail to understand.

As for Dr. Bentley (or more exactly Mr. Richard Bentley, M. A.—he became DD. in 1696), who did not know much physics—he was by training a classicist—and obviously did not grasp the ultimate implications of Newton's natural philosophy, he espouses it wholeheartedly, as far, at least, as he understands it, and turns it into a weapon for the Confutation of Atheism in the Boyle Lectures which he gave in 1692.

Richard Bentley follows so closely, and even so servilely, Newton's teaching, or lessons—he copied nearly verbatim the letters he received from him, adding, of course, some references to the Scriptures and a good deal of rhetoric—that the views he expresses can be considered as representing, in a large measure, those of Newton himself.

materialists, more precisely those of the Epicurean brand, and it is rather amusing to see that Bentley accepts the fundamentals of their conception, that is, the corpuscular theory of matter, the reduction of material being to atoms and void, not only without the apparent hesitations and cautious reserve of Newton, but even as something that goes without saying and without discussion. He only objects, as it has always been done, that it is not enough, and that they cannot explain the orderly structure of our universe without superadding to matter and motion some purposeful action of a non-material cause: the fortuitous and disorderly motion of atoms cannot transform chaos into a cosmos.

Yet, if the pattern of his reasoning is quite traditional—but we must not blame Mr. Bentley for that: it is also the Newtonian pattern and, moreover, did not Kant himself tell us a century later that the physico-teleological proof of the existence of God is the only one that has any value?—the contents of the demonstration are adapted to the present-day (Bentley's present day) level of scientific philosophy.

Thus, for instance, he accepts without the slightest criticism the contemporary version of Giordano Bruno's conception of the universe: an infinite space with an immense number of star-suns. Bentley maintains, of course, that the stars are finite in number—he thinks he can prove it—and would even like them to be arranged in space so as to build a "firmament." But if this cannot be done, he will accept their dispersion in the boundless void. Bentley, indeed, insists upon the void. He needs it, of course, as we shall see in a moment, in order to be able to demonstrate the existence and the action, in the world,

of non-material, non-mechanical forces—first and foremost of the Newtonian universal attraction—but he is also somehow elated and ravished by the idea that this our world is chiefly composed of void spaces, and he indulges in calculations that show that the amount of matter in the universe is so small as practically not to be worth speaking of:36

Let us allow, then, that all the matter of the system of our sun may be 50,000 times as much as the whole mass of the earth; and we appeal to astronomy, if we are not liberal enough and even prodigal in this concession. And let us suppose further, that the whole globe of the earth is entirely solid and compact, without any void interstices; notwithstanding what hath been shewed before, as to the texture of gold itself. Now, though we have made such ample allowances, we shall find, notwithstanding, that the void space of our system is immensely bigger than all its corporeal mass. For, to proceed upon supposition, that all the matter within the firmament is 50,000 times bigger than the solid globe of the earth; if we assume the diameter of the orbis magnus (wherein the earth moves about the sun) to be only 7,000 times as big as the diameter of the earth, (though the latest and most accurate observations make it thrice 7,000), and the diameter of the firmament to be only 100,000 times as long as the diameter of the orbis magnus (though it cannot possibly be less than that, but may be vastly and unspeakably bigger), we must pronounce, after such large concessions on that side, and such great abatements on ours, that the sum of empty spaces within the concave of the firmament is 6,860 million million million times bigger than all the matter contained in it.

. . . . . . . . . . .

And first, because every fixed star is supposed by astronomers

to be of the same nature with our sun, and each may very possibly have planets about them, though, by reason of their vast distance, they may be invisible to us; we will assume this reasonable supposition, that the same proportion of void space to matter, which is found in our sun's region within the sphere of the fixed stars, may competently well hold in the whole mundane space. I am aware that in this computation we must not assign the whole capacity of that sphere for the region of our sun, but allow half of its diameter for the radii of the several regions of the next fixed stars; so that, diminishing our former number, as this last consideration requires, we may safely affirm, from certain and demonstrated principles, that the empty space of our solar region (comprehending half of the diameter of the firmament) is 8,575 hundred thousand million million times more ample than all the corporeal substance in it. And we may fairly suppose, that the same proportion may hold through the whole extent of the universe.

[paragraph continues] Accordingly, Democritian atoms, whatever their initial disposition in space, would pretty soon be completely dispersed and would be unable to form even the most simple bodies, and much less, of course, such an artful and well-ordered system as, for instance, our solar world. Fortunately for its—and for our—existence, atoms are not free and independent of each other but are bound together by mutual gravitation.

Now this is already a refutation of atheism—Bentley, as we have seen, has learnt from Newton that gravitation cannot be attributed to matter—as it is clear38

. . . is repugnant to common sense and reason. ’Tis utterly inconceivable, that inanimate brute matter, without the mediation of some immaterial being, should operate upon and affect other matter without mutual contact; that distant bodies should act upon each other through a vacuum, without the intervention of something else, by and through which the action may be conveyed from one to the other. We will not obscure and perplex with multitude of words what is so clear and evident by its own light, and must needs be allowed by all that have competent use of thinking, and are initiated into, I do not say the mysteries, but the plainest principles of philosophy. Now, mutual gravitation or attraction, in our present acceptation of the words, is the same thing with this, ’tis an operation, or virtue, or influence of distant bodies upon each other through an empty interval, without any effluvia, or exhalations, or other corporeal medium to convey and transmit it. This power, therefore, cannot be innate and essential to matter: and if it be not essential, it is consequently most manifest, since it doth not depend upon motion or rest, or figure or position of parts, which are all the ways that matter can diversify itself, that it could never supervene to it, unless impressed and infused into it by an immaterial and divine power.

attraction cannot be explained by any "material and mechanical agent," the indubitable reality of this power of mutual gravitation.40

Moreover, even if reciprocal attraction were essential to matter, or if it were simply a blind law of action of some immaterial agent, it would not suffice to explain the actual fabric of our world, or even the existence of any world whatever. Indeed, under the unhampered influence of mutual gravitation, would not all matter convene together into the middle of the world?

Bentley seems to have been rather proud of having found that God not only pulled or pushed bodies towards each other, but also counteracted His action—or, more simply, suspended it—in the case of the fixed stars, at least of the outermost ones, which He prevented in this manner from leaving their places and maintained at rest.

Alas, Newton explained to him that his reasoning implied a finite world and that there was no reason to deny its possible infinity, that the difficulties Bentley found in the concept of an infinite sum or series were not contradictions, and that his refutation of the infinity (or eternity) of the world was a paralogism. Newton confirmed, however, that even in the case of an infinite world the mere and pure action of gravity could not explain its structure, and that choice and purpose were clearly apparent in the actual distribution of the heavenly bodies in space, as well as in the mutual adjustment of their masses, velocities and so on:41

As to your first query, it seems to me that if the matter of our sun and planets, and all the matter of the universe, were evenly scattered throughout all the heavens, and every particle had an innate gravity towards all the rest, and the whole space throughout which this matter was scattered was but finite; the matter on the outside of this space would, by its gravity, tend towards all the matter on the inside, and, by consequence, fall down into the middle of the whole space, and there compose one great spherical mass. But if the matter was evenly disposed throughout an infinite space, it could never convene into one mass; but some of it would convene into one mass, and some into another, so as to make an infinite number of great masses, scattered at great distances from one to another throughout all that infinite space. And thus might the sun and fixed stars be formed, supposing the matter were of a lucid nature. But how the matter should divide itself into two sorts, and that part of it which is fit to compose a shining body should fall down into one mass and make a sun, and the rest which is fit to compose an opaque body should coalesce, not into one great body, like the shining matter, but into many little ones; or if the sun at first were an opaque body like the planets, or the planets lucid bodies like the sun, how he alone should be changed into a shining body, whilst all they continue opaque, or all they be changed into opaque ones, whilst he remains unchanged; I do not think explicable by mere natural causes, but am forced to ascribe it to the counsel and contrivance of a voluntary Agent.

. . . . . . . . . . .

To your second query, I answer, that the motions which the planets now have could not spring from any natural cause alone, but were impressed by an intelligent Agent. For since comets descend into the region of our planets,

and here move all manner of ways, going sometimes the same way with the planets, sometimes the contrary way, and sometimes in cross ways, in planes inclined to the plane of the ecliptic, and at all kinds of angles, ’tis plain that there is no natural cause which could determine all the planets, both primary and secondary, to move the same way and in the same plane, without any considerable variation: this must have been the effect of counsel. Nor is there any natural cause which could give the planets those just degrees of velocity, in proportion to their distances from the sun and other central bodies, which were requisite to make them move in such concentric orbs about those bodies.

. . . . . . . . . . .

To make this system, therefore, with all its motions, required a cause which understood and compared together the quantities of matter in the several bodies of the sun and planets, and the gravitating powers resulting from thence; the several distances of the primary planets from the sun, and of the secondary ones from Saturn, Jupiter, and the earth; and the velocities with which these planets could revolve about those quantities of matter in the central bodies; and to compare and adjust all these things together, in so great a variety of bodies, argues that cause to be, not blind and fortuitous, but very well skilled in mechanics and geometry.

. . . we affirm, that though we should allow that reciprocal attraction is essential to matter, yet the atoms of a chaos could never so convene by it as to form the present system; or, if they could form it, yet it could neither acquire these revolutions, nor subsist in the present condition, without the conservation and providence of a divine Being.

I. For, first, if the matter of the universe, and consequently the space through which it's diffused, be supposed

to be finite, (and I think it might be demonstrated to be so, but that we have already exceeded the just measures of a sermon,) then, since every single particle hath an innate gravitation toward all others, proportioned by matter and distance; it evidently appears, that the outward atoms of the chaos would necessarily tend inwards, and descend from all quarters toward the middle of the whole space. For, in respect to every atom, there would lie through the middle the greatest quantity of matter and the most vigorous attraction; and those atoms would there form and constitute one huge spherical mass, which would be the only body in the universe. It is plain, therefore, that upon this supposition the matter of the chaos could never compose such divided and different masses as the stars and planets of the present world.

Furthermore, even if the matter of the chaos could build the separate bodies of the planets, they "could not possibly acquire such revolutions in circular orbs, or in ellipses very little eccentric," as they actually perform, by the mere action of the forces of inertia and gravity, and finally, "if we should grant . . . that these circular revolutions could be naturally attained," it still requires a divine power and providence to preserve them, and, generally speaking, to preserve the fabric of the world. For, even if we admitted that the combination of inertia and gravity would suffice for the maintaining of the orbital motion of the planets, what about the fixed stars? What prevents them from coming together? "If the fixed stars . . . are supposed to have no power of gravitation, ’tis plain proof of divine Being" as it shows the non-natural character of gravitation. "And ’tis as plain a proof of a divine Being if they have the power of gravitation." For,

in that case, only a divine power can compel them to remain in their assigned places. But what if the world were not finite, but infinite? According to Bentley it does not make a very great difference:43

. . . in the supposition of an infinite chaos, ’tis hard indeed to determine what would follow in this imaginary case from an innate principle of gravity. But, to hasten to a conclusion, we will grant for the present, that the diffused matter might convene into an infinite number of great masses, at great distances from one another, like the stars and planets of this visible part of the world. But then it is impossible that the planets should naturally attain these circular revolutions, either by principle of gravitation, or by impulse of ambient bodies. It is plain there is no difference as to this, whether the world be infinite or finite; so that the same arguments that we have used before may be equally urged in this supposition.

In spite of these clear proofs of God's purposeful action in the world, there are, as we know, people who refuse to be convinced by them and who argue that an infinite world can have no purpose. What indeed can be the usefulness of these innumerable stars that are not even seen by us, either by the unassisted eye or through the strongest telescope? But, replies Bentley, embracing the pattern of reasoning based on the principle of plenitude, "We must not confine and determine the purposes in creating all mundane bodies merely to human ends and uses." For, though, as it is evident, they are not created for our sakes, they are certainly not made for their own:44

sacrifice of praise and worship to the Author of its being. It remains, therefore, that all bodies were formed for the sake of intelligent minds: and as the earth was principally designed for the being and service and contemplation of men, why may not all other planets be created for the like uses, each for their own inhabitants which have life and understanding? If any man will indulge himself in this speculation, he need not quarrel with revealed religion upon such account. The holy Scriptures do not forbid him to suppose as great a multitude of systems, and as much inhabited as he pleases. . . . God Almighty, by the inexhausted fecundity of his creative power, may have made innumerable orders and classes of rational minds; some in their natural perfections higher than human souls, others inferior.

An indefinitely extended and populated world, immersed in an infinite space, a world governed by the wisdom and moved by the power of an Almighty and Omnipresent God, such is, finally, the universe of the very orthodox Richard Bentley, future Bishop of Worcester and Master of Trinity College. Such is, doubtlessly too, the universe of the very heretical Lucasian Professor of Mathematics, Isaac Newton, Fellow of the Royal Society and of the same Trinity College41