From the Closed World to the Infinite Universe (07-09)

01.08.2015 09:16

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

Malebranche, Newton & Bentley

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

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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


. . . eternal, immense, necessary. It is the immensity of the Divine Being, as infinitely participable by the corporeal creature, as representative of an immense matter; it is, in a word, the intelligible idea of possible worlds. It is what your mind contemplates when you think about the infinite. It is by means of this intelligible extension that you know the visible world.


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


But you have to distinguish two kinds of extension, the one intelligible, and the other material.


The intelligible extension is "eternal, necessary, infinite," whereas the3


. . . other kind of extension is that which is created; it is


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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


I beg you, had I not some reason to believe that extension is eternal? Must one not judge things according to one's ideas, and is it even possible to judge otherwise? And,


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as I cannot prevent myself from regarding intelligible extension as immense, eternal, necessary, had I not grounds for thinking that material extension has the same attributes?


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.

Antoine Arnauld considered the Malebranchian distinction

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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,

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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

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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


Absolute, true and mathematical time, of itself and from its own nature, flows equably without regard to anything external,


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

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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.

But, of course,13


. . . relative, apparent and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time: such as an hour, a day, a month, a year.


It is just the same concerning space:14


Absolute space, in its own nature, without regard to anything external, remains always similar and immovable,


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


For if the earth, for instance, moves, a space of our air, which relatively and in respect of the earth always remains


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the same, will at one time be one part of the absolute space into which the air passes; and another time will be another part of the same and so, absolutely understood, it will be perpetually mutable.


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

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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

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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


. . . all motions, from places in motion, are no other than parts of entire and absolute motions; and every entire motion is composed of the motion of the body out of its first place and the motion of this place out of its place; and so on, until we come to some immovable place, as in the before-mentioned example of the sailor. Wherefore entire and absolute motions cannot be otherwise determined than


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by immovable places; and for that reason I did before refer those absolute motions to immovable places, but relative ones to movable places. Now no other places are immovable but those that, from infinity to infinity, do all retain the same given position one to another, and upon this account must ever remain unmoved and do thereby constitute immovable space.


"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


The causes by which true and relative motions are distinguished, one from the other, are the forces impressed upon bodies to generate motion. True motion is neither generated nor altered but by some force impressed upon the body moved, but relative motion may be generated or altered without any force impressed upon the body. For it


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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


The effects which distinguish absolute from relative motion are the forces of receding from the axis of circular motion. For there are no such forces in a circular motion purely relative, but in a true and absolute circular motion they are greater or less, according to the quantity of the motion.


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

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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.

The Newtonian interpretation of circular motion as

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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,

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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


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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


. . . for though they are carried in oblique paths and sometimes contrary to the course of the planets, yet they move every way with the greatest freedom, and preserve their motion for an exceeding long time, even when contrary


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to the course of the planets. Hence also it is evident that the celestial spaces are void of resistance,


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


if all the solid particles of all bodies are of the same density and cannot be rarefied without pores, then a void space, or vacuum, must be granted.


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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


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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


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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


. . . it is reasonable to suppose that forces which are directed to bodies should depend upon the nature and quantity of those bodies, as we see they do in magnetical experiments. And when such cases occur, we are to compute the attractions of the bodies by assigning to each of their particles its proper force, and then finding the sum of them all.


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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

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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


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enter upon physics, we compare these proportions with the phenomena of Nature, that we may know what conditions of these forces answer to the several kinds of attractive bodies. And this preparation being made, we argue more safely concerning the physical species, causes, and proportion of the forces.


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


You sometimes speak of gravity as essential and inherent to matter. Pray do not ascribe that notion to me, for the cause of gravity is what I do not pretend to know and therefore would take more time to consider of it.


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


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from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws, but whether this agent be material or immaterial I have left to the consideration of my readers.


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.

The atheists Mr. Bentley deals with are essentially the

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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,

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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


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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.


It is clear that with this immense void at their disposal:37


. . . every single particle would have a sphere of void space around it 8,575 hundred thousand million million times bigger than the dimension of that particle.


[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.

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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


that such a mutual gravitation or spontaneous attraction can neither be inherent and essential to matter, nor ever supervene to it, unless impressed and infused into it by a divine power,


just because action at a distance39


. . . 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.


Now, if we admit, as we must do, that this mutual

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


. . . would be a new and invincible argument for the being of God, being a direct and positive proof that an immaterial living mind doth inform and actuate the dead matter and support the frame of the world.


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

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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,


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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.


Having learnt his lesson, Bentley writes therefore:42


. . . 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


p. 187


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,

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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


For matter hath no life nor perception, is not conscious of its own existence, not capable of happiness, nor gives the


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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



VIII. The Divinization of Space

Joseph Raphson

Newton, as far as I know, never quoted More; nor did he make an explicit reference to his teachings. Yet the relations between the theories of the two Cambridge men could not, of course, escape their contemporaries. It is therefore not surprising that, fifteen years after the publication of the Mathematical Principles of Natural Philosophy, their connection was openly proclaimed by Joseph Raphson, a promising young mathematician, Master of Arts and Fellow of the Royal Society,1 in an extremely interesting and valuable Appendix which he added, in 1702, to the second edition of his Universal Analysis of Equations.2

In this Appendix, which bears the title On the real space or the Infinite Being, Joseph Raphson, who obviously has neither Newton's subjective inclination for reticence and secrecy, nor his objective reasons for prudence, dots all the i’s and crosses all the t’s.

Starting with a historical account of the development of the conception of space which begins with Lucretius and culminates in Henry More's criticism of the Cartesian

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identification of extension with matter, his characterization of matter by impenetrability, and his demonstration of the existence of an immovable and immaterial extension, Raphson states his conclusion:3


Thus from every motion (extended and corporeal), even from the [only] possible ones follows necessarily [the existence of] an immovable and incorporeal extended [entity], because everything which moves in the extension must necessarily move through extension. The extension of the real motion demonstrates the real existence of this immovable extended [entity], because otherwise it [the motion] can be neither expressed nor conceived, and because that which we cannot but conceive is necessarily true. It could be argued in the same manner concerning the supposed motion of figures in geometry. The possibility of these motions demonstrates the hypothetical necessity of this immovable extended [entity], and the reality of the physical motions, the absolute.


There is an unmistakable Spinozistic flavor in Raphson's terminology and manner of speaking. Yet, though deeply influenced by Spinoza,4 Raphson is by no means Spinozist. On the contrary, More's distinction between the infinite, immovable, immaterial extension and the material, mobile and therefore finite one is, according to him, the sole and only means of avoiding the Spinozistic identification of God with the world. But let us proceed with Raphson's presentation of Henry More's theories.

The existence of motion implies, indeed, not only the distinction between the immovable, immaterial extension and the material one, and thus the rejection of the Cartesian identification; it implies also the rejection of the Cartesian negation of vacuum: in a world completely and

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continuously filled with matter rectilinear motion would be utterly impossible, and even circular motion would be extremely difficult to achieve.5 The real existence of really void spaces can thus be considered as fully demonstrated. Wherefrom we can draw the following corollaries:6


1. The universal mass of movable [bodies] (or of the world) must necessarily be finite, because, on account of the vacuum and the mobility, each and every system of it may be compressed into a smaller place; the finitude of the ensemble of these systems, that is, of the world, follows herefrom necessarily, though the human mind will never be able to arrive at its limit.


2. All the finite [beings] existing separately can be comprehended by a number. It is possible that no created mind is able to comprehend it. Nevertheless, to their numerating Author, they will be in a finite number: this can also be shown as follows: let, for example, (a) be the minimum of what can exist, then (a) infinitely multiplied will turn out to be infinite; indeed, if it gave a finite sum


the true minimum (or atom) would not be (a) but another infinitely smaller, or infinitely small, body. This, however, as Raphson states, is "against the hypothesis." Of course we are not studying here the composition of space: we are dealing with impenetrable extended beings, that is, with bodies.


3. Herefrom can be argued the falsity of the teaching of Spinoza, who, misusing his 6th definition, makes it so wide as to force matter, insofar as it expresses essence, to express the essence of the Infinite Being, and to be one of its attributes. I recognize, however, and I can demonstrate, that everything of which the essence implies an absolute


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infinity pertains necessarily to the absolutely Infinite Being; it is in this way that I derive my idea of the absolutely Infinite Being, which involves the supreme and absolute necessity.


The error of Spinoza is thus at once elucidated and corrected. Raphson obviously thinks that Spinoza was perfectly right in following the (Cartesian) principle of attributing to God all that is essentially infinite; right also in rejecting the Cartesian distinction between the infinite and the indefinite and in claiming for His extension actual and not only potential infinity. But he is wrong in accepting the Cartesian identification of extension and matter. Owing to Henry More's criticism of Descartes, Raphson believes he is able to escape the Spinozistic conclusion by attributing the infinite, immaterial extension to God, and reducing matter to the status of creature.

Matter, as we know, is characterized by Raphson by its mobility (which implies finitude) and impenetrability. As for the immaterial extension, or more simply, space, its properties, nature and existence are derived by him more geometrico "from the necessary and natural concatenation of simple ideas."7

Space is defined as8 "the innermost extended [entity] (whatever it be) which is the first by nature and the very last to be obtained by continuous division and separation"; Raphson informs us that it is an imperfect definition or description of the defined object; it does not tell us anything about its essence, but, on the other hand, it has the advantage of being immediately acceptable as designating something the existence of which is perfectly evident and indubitable. Moreover, the analysis of the

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ideas used in this definition will lead us towards important consequences, namely towards the affirmation of the existence of a real space really distinct from matter.

The investigation starts with a postulate, according to which a "given idea" always enables us to derive from it the properties of the object, even making abstraction of its existence. Three corollaries are added, and these tell us that:9


All finite extended can be divided (if only by the mind) or, what is the same, be conceived as divided.


And it is (even if only for the concept) movable and possesses an actual figure.

And [its] parts can be separated or removed from each other (if only by the mind), or be conceived as being removed.


An axiom then asserts that:10


Between things separated or removed from each other there is always a distance (be it great or small), that is something extended.


A series of propositions now follows in quick succession:11


1. Space (or the innermost extended) is by its nature, and absolutely, indivisible, nor can it be conceived as divided


[paragraph continues] —which, if division means separation and mutual removal of parts, that is, divisibility means discerpibility, is, of course, a cogent consequence of the above-quoted corollaries.


2. Space is absolutely, and by its nature, immovable


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[paragraph continues] —motion indeed implies divisibility.


3. Space is actually infinite


[paragraph continues] —which; vice versa, implies, immediately and by necessity, its absolute immovability.


4. Space is pure act.


5. Space is all-containing and all-penetrating.


To pave the way to further development, that is, to the identification of space with an attribute of God, Raphson adds that12


. . . doubtlessly this is the reason why for the Hebrews the name of this Infinite was Makom; as it is that of St Paul's 'it is nearer to us than we are to ourselves.' It is to this Infinite that assuredly must be referred a great number of passages of the Holy Scripture as well as the hidden wisdom of the old Hebrews about the highest and incomprehensible amplitude of the Ensoph; as well as the teaching of the Gentiles about the all permeant, the all-embracing etc.


But let us not think that space is a kind of immaterial stuff—Raphson, obviously, wants to oppose space to More's spirit:13


It is patent that space is not penetrated by anything: being infinite and undivided it penetrates everything by its innermost essence, and therefore cannot itself be penetrated by anything, nor even can it be conceived as penetrated.


It is clear thus that14


6. Space is incorporeal.


7. Space is immutable.


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8. Space is one in itself, [and therefore] . . . it is the most simple entity, not composed of any things and not divisible into any things.


9. Space is eternal [because] the actually infinite cannot not be . . . in other words, that it cannot not be is essential to the actually infinite. It was therefore always.


[paragraph continues] This means that it is, or has, a necessary being, that the eternity of the infinite is the same thing as its existence, and that both imply the same necessity15


10. Space is incomprehensible to us, [just because it is infinite].


11. Space is most perfect in its kind [genus].

12. Extended things can neither be nor be conceived without it. And therefore

13. Space is an attribute (namely the immensity) of the First Cause.


This last proposition, according to Raphson, can also be demonstrated in a much easier and more direct way: as, indeed, the First Cause16


. . . can neither give anything that it does not possess, nor be the cause of any perfection that it does not contain (in a certain manner) in the same degree if not in a greater one; and as there can be nothing in rerum natura except extended and unextended [things]; and as we have demonstrated that extension is perfection, existing everywhere, and is even infinite, necessary, eternal, etc., it follows necessarily that it must be found in the First Cause of the extended [things] without which the extended [things] cannot exist. Which it was proper to demonstrate. For the true and reciprocal reason of the omniform, true and actual infinity is found to consist in the most absolute unity, just as,


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vice versa, the highest reason of the unity culminates in and is absorbed by the infinity. For whatever expresses the actual, and in its kind most absolute, infinity, necessarily expresses the essence of the First Cause, the Author of everything that is.


It is rather curious to see Raphson use the Cartesian and even Spinozistic logic and patterns of reasoning to promote Henry More's metaphysical doctrine. Yet it cannot be denied that by these means Raphson succeeded in giving it a much higher degree of consistency than it had from its author. Henry More, indeed, could only present us with a list of "titles" applicable both to space and to God. Raphson shows their inner connection; moreover, by identifying infinity, on the one hand, with highest perfection, and, on the other hand, by transforming extension itself into perfection, he makes the attribution of extension to God logically as well as metaphysically unavoidable.

Having established the attribution to the First Cause of infinite space (which taken abstractly is the object of geometry, and taken as reality is the very immensity of God), Raphson now goes on to a more careful consideration of their connection:17


That its [the First Cause's] true and essential presence is a necessary prerequisite as well of the essential being as of the real existence of all things is recognized by a number of contemporaries. But, how this essential and intimate presence can be explained in the hypothesis of the nonextension [of the First Cause] without a manifest contradiction has not yet been made clear; and it will never be possible to make it clear. Indeed, to be present by essence in places diverse and distant from each other, for instance


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in the globe of the Moon and in that of the earth, and also in the intermediate space, what else is it but, precisely, to extend oneself? Now, we have demonstrated that this extension is truly real, indivisible, immaterial (or, if you wish, spiritual). What else is there to be desired in order to infer its perfection, supreme and infinite of its kind (insofar as it is an inadequate concept of the Infinite Being)?


[paragraph continues] I do not see, concludes Raphson, by what other name than extension or space this essential omnipresence of the First Cause could be expressed.

The philosophers were right, of course, in removing from the First Cause the imperfect, divisible, material extension. Yet, by the rejection from it of all kinds of extension, they opened up the way towards atheism, or rather hylotheism, to a great many people, namely, to those who did not want to be hemmed in by ingenuous circuits of ambiguous circumlocutions and embarrassed by obscure and unintelligible notions and terms. Such are Hobbes and some others: because they did not find anywhere in the world this infinite and eternal, unextended Supreme Being, they thought that it did not exist at all, and boldly proposed their opinions to the world. So too had some of the ancients, who insisted upon the incomprehensibility of the Supreme Being. The explanation of all these aberrations is to be sought, according to Raphson, in the misunderstanding of the very essence of extension that has been falsely held to be necessarily something imperfect and lacking all unity and reality. In truth, however, extension, as such, is something positive and denotes a very real perfection. Accordingly, as generally18

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. . . everything positive and substantial that is found in the essence of things as their primary and constitutive attribute, such as extension in matter, etc., must necessarily be really and truly present in the First Cause, and be in it in a degree of infinite excellence in the manner most perfect of its kind,


the infinite extension must be truly and really, and not only metaphorically, attributed to the First Cause.

The First Cause appears thus as the twofold source, or cause, of the perfections of the created things that it contains, as the Schoolmen say, in an eminent and transcendent manner.19


For (as they say) it gives nothing that it does not have (in a more perfect manner) in itself.


[paragraph continues] Consequently they assert that God is a thinking Being: how could, indeed, a thinking being (like ourselves) proceed from a non-thinking one? But we can reverse the question and, with exactly the same right, ask: how can an extended being come forth from an unextended one? The Schoolmen, of course, want both perfections to be contained in the First Cause in the transcendent manner. As for extension, such as it is in matter, they justly argue that it is imperfect. We, however, and we can quote good authorities in favor of this opinion, for instance, Father Malebranche, regard cogitation, or thought (such as it is in human minds, or in the created spirits), to be just as imperfect in comparison to that of the Absolutely Infinite Being. And though, perhaps, cogitation in finite thinking beings is much more perfect than extension, as it is in matter, it is doubtless removed by the same interval, that is, by an infinite one, from the source of these

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perfections in the First Cause, and, in relation to it, they are both equally imperfect.20


The infinite amplitude of extension expresses the immense diffusion of being in the First Cause, or its infinite and truly interminate essence. This [amplitude] is that originary extensive perfection, which we have found, so imperfectly counterfeited, in matter.


The infinite (whatever it be) and most perfect energy, everywhere indivisibly the same, which produces and perpetually conserves everything (and which this never-sufficiently-to-be-admired series of Divine Ratiocination, that is, the whole fabric of nature, more than sufficiently demonstrates to us a posteriori), is this intensive perfection, which though [distant from it] by an infinite interval in kind as well as in degree, we, miserable examples of the infinite Archetype, flatter ourselves to imitate.


Raphson's assertions are to be taken verbatim: extension as such is a perfection, even gross, material extension. The modus of its realization in bodies is, to be sure, extremely defective, precisely as our discoursive thought is an extremely defective modus of cogitation; but, just as in spite of its discoursiveness our thought is an imitation of, and a participation in, God's cogitativeness, so in spite of its divisibility and mobility our bodily extension is an imitation of, and a participation in, God's own and perfect extensiveness.

As for the latter, we have already proved that:21


[paragraph continues] . . . this internal or truly innermost locus penetrates everything by its essence and, undivided, is most intimately present in everything; that it cannot be, or even be thought of, as penetrated by any thing, and that it is infinite, most


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perfect, one and indivisible. Hence it clearly appears by what infinite interval are distant from it all other things that have only an evanescent being and, to use the elegant expression of the Prophet (Isaiah, 40), are as nothing to this Infinite and Eternal and, so to speak, essential (οὐσιότατον) Being. They are, as it were, light shadows of the true Reality and even if they were everywhere, they would by no means express even in the lowest degree that Infinity which we understand to be supremely positive and supremely real in the First Cause.


Thus, even if it were infinitely extended—which it is not—matter would never be identical with the divine extension and would never be able to become an attribute of God. Joseph Raphson is to such a degree elated and ravished by the contemplation of the idea of infinity that we could apply to him (though modifying it somewhat) the expression used by Moses Mendelssohn for Spinoza: he is drunk with infinity. He goes so far as—paradoxically—to reject Henry More's reassertion of the fundamental and primary validity of the category or question: "where?" In infinity it has no meaning. The infinite is not something, a sphere, of which the center is everywhere and the limits nowhere; it is something of which the center is nowhere also, something that has neither limits nor center, something in respect to which the question "where?" cannot be asked, as in respect to it everywhere is nowhere, nullibi.22


In respect to this immense locus a system of finite bodies, be it ever so large, is truly said to be nowhere. It is indeed utterly immeasurable; here, there, in the middle, etc. vanish in it completely.


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Raphson is obviously right. In the infinite homogeneous space all "places" are perfectly equivalent and cannot be distinguished from each other: they all have the same "position" in respect to the whole.23


The illustrious Guericke has very well written about it in his Magdeburgian Experiments, p. 65: If in this immensity (which has no beginning, nor end, nor middle) somebody marched for an infinitely long [time], and traversed innumerable thousands of miles, he would, in relation to this immensity, be in the same place; and if he repeated his action and arrived ten infinities farther, he would nevertheless be in this immensity in the same way and in the same place and would not be a single step nearer to the end, or the fulfillment of his intention, because in the Immeasurable (Immensum) there is no relation. All relations in it are conceived in reference to ourselves or to some other created thing. Indeed this immense locus is truly everywhere; and everything that has its finite where? (as they are wont to speak about spirits) has it as a relation to some other finite [thing]; but in relation to the Immensity it is truly nowhere.


Yet, if Raphson insists so strongly upon the infinity of uncreated space in contradistinction to the finitude of the created world, it is by no means his intention to assign to this latter determinate, or even determinable—by us—dimensions. Quite the contrary: in infinite space there is room enough for a practically indeterminate and indefinitely large world. Thus he tells us that if24


[paragraph continues] . . . there can be absolutely no reason why [the world] should extend itself to the infinity of its immense locus, as it does not possess an absolute plenitude and is composed of movable parts . . . whereas the absolutely Infinite


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is utterly immovable and absolutely one or full of itself . . . [nevertheless] . . . how great the universe is or how far it extends, is completely hidden to us.


Raphson himself would25


[paragraph continues] . . . easily believe that it can be immeasurable in respect to our capacity of understanding, and that we shall never be able to comprehend it. Indeed, it does not follow that we can comprehend by our cogitation all magnitude that is not infinite, or that we should ever be able to depict it in our mind as so large that the universe could not, in truth, be even larger. We can, for instance, conceive a series of numbers, disposed in a straight line, to extend from this our earth to the Dog-Star, or to any one in the Milky Way or to whatever visible limit, the unity of these [numbers] expressing the distance between the earth and that limit; we can also conceive this number to be squared, raised to the third, fourth, and so on, power, until the index of this power becomes equal to the first number, or to its first root; we can finally consider this power as a root of others, progressing in the same manner. And yet it is, perhaps, as nothing compared to the magnitude of the universe which can, and possibly does, surpass the capacity of any finite numbering [mind], not only ours, and cannot be comprehended by any other than its immense Author. Yet it is certain that it cannot be infinite in that absolute manner in which the First Cause is, insofar as it is considered as the immense locus of things.


We see it thus quite clearly: the difference between the infinite and the finite is not a difference between "more" and "less"; it is not a quantitative, but a qualitative one, and, though studied by mathematicians, it is fundamentally a metaphysical difference. It is this difference which,

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fully understood, enables us not to lapse into the error of a pantheistic confusion of the Creator God with the created world, and it is this selfsame difference which provides us with a firm ground for the study of the nearly infinite variety of created things. Indeed, those26


who will [study] this part of the universe, visible to us, not only in books, but who will diligently read and carefully contemplate [the book of Nature], using his own observations and the [analysis] of the constitution of the skies, will hardly fail to recognize not only that there can be a plurality of worlds, but that, in truth, there are a nearly infinite number of systems, various laws of motion, exhibiting various (nearly innumerable) phenomena and creatures.


[paragraph continues] Why, even on this earth there are so many and such varied creatures, endowed with so many different faculties, possibly even with some that are completely unknown to us. How many more could there be elsewhere that can be called into being by the infinite combinative art of the Infinite Architect.

As for us, the only doors open to the true cogitation of the universe are observation and experience. By the first we arrive at the system of visible motions of the world; by the second we discover the forces, the (sensible) qualities and mutual relations of bodies. Mathematics (mathematical physics) and chemistry are the sciences that arise on these empirical foundations. As for the "hypotheses" that go beyond these empirical data, they may be plausible, and even, sometimes, useful for the investigation of truth; yet they breed prejudices and therefore cause more harm than good. Hypothesomania,

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the invention of new hypotheses, belongs to poetical and fictitious philosophy, not to the pursuit of knowledge. For the latter, according to Raphson, the method established by the supreme philosopher, Newton, in his Principia, consisting in the study of the phenomena of nature by means of experiments and rational mechanics, reducing them to forces the action of which—though their nature is hidden from us—is obvious and patent in the world.

As we see, empiricism and metaphysics, and even a very definite kind of metaphysics, the creationist, are closely linked together. What other means, indeed, but observation and experience can we possibly use for the study of a world freely created by an Infinite God? Raphson concludes therefore:27


Neither can Human Philosophy theoretically compose the smallest mouse or the simplest plant, nor can human praxis build them, much less the whole universe. These are problems worthy of the Primordial Wisdom and Power which produces these things. As for us, they offer us only a progress in aeternum of our knowledge both of the things themselves and of the perpetually geometrizing God.

IX. God and the World:


Isaac Newton

It is difficult to tell what the reasons were that determined Newton to enlarge, in the Latin edition (translation) of his Opticks, the number of Queries appended by him to the third book of his work, and to include among the additional ones two rather long and extremely important and interesting papers which, in contradistinction to the purely technical Queries of the first English edition, deal, not with optical, but with methodological, epistemological and metaphysical problems.1

The publication of Raphson's book could not have been the motive: the De spatio reali was published in 1702, the Latin translation of the Opticks in 1706; but the English edition appeared in 1704 and if Newton wanted to make his position clear in relation to Raphson's, he could, and should have done it in 1704. It is possible, in my opinion—though it is only a conjecture—that it was the publication of Dr. George Cheyne's Philosophical

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[paragraph continues] Principles of Natural Religion that gave Newton the incentive, usually lacking, to come into the open.2

Now, be this as it may, it is these Queries (which, curiously enough, seem to have been ignored by Berkeley) which build the subject of the famous polemics between Leibniz and Clarke. It is, indeed, in these Queries (21 and 22) that, in a much more precise and clear manner than anywhere else—the General Scholium of the second edition of the Principia not excluded—Newton states his conceptions about the purpose and aim of philosophy and develops, at the same time, his general world-view: an extremely interesting and fairly consistent system of "corpuscular philosophy"—already sketched in his letters to Bentley—asserting the fundamental unity of matter and light, and presenting the material components of the universe, that is, hard, indivisible particles, as constantly acted upon by quite a system of various non-material attractive and repulsive forces. Thus Query 20 (28 in the second edition) explains at length the physical (astronomical) inadmissibility of the plenum (a completely full space would oppose such a strong resistance to motion that it would be practically impossible and would have ceased long ago), as well as the physical (astronomical) admissibility of the celestial spaces’ being filled with an extremely thin, rare and tenuous ether, of which the density can be made as small as we wish (is not our air "at the height of 70, 140, 210 miles 100,000, 100,000,000,000 or 100,000,000,000,000 times rarer, and so on" than on the earth?), which implies the granular structure of this ether, the existence of a vacuum and the rejection of a continuous medium, and concludes:3

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And for rejecting such a Medium, we have the Authority of those oldest and most celebrated Philosophers of Greece and Phoenicia, who made a Vacuum, and Atoms, and the Gravity of Atoms, the first Principles of their Philosophy; tacitly attributing Gravity to some other Cause than dense Matter. Later Philosophers banish the Consideration of such a Cause out of natural Philosophy, feigning Hypotheses for explaining all things mechanically, and referring other Causes to Metaphysicks: Whereas the main Business of natural Philosophy is to argue from Phaenomena without feigning Hypotheses, and to deduce Causes from Effects, till we come to the very first Cause, which certainly is not mechanical; and not only to unfold the Mechanism of the World, but chiefly to resolve these and such like Questions. What is there in places almost empty of Matter, and whence is it that the Sun and Planets gravitate towards one another, without dense Matter between them? Whence is it that Nature doth nothing in vain; and whence arises all that Order and Beauty which we see in the World? To what end are Comets, and whence is it that Planets move all one and the same way in Orbs concentrick, while Comets move all manner of ways in Orbs very excentrick; and what hinders the fix’d Stars from falling upon one another? How came the Bodies of Animals to be contrived with so much Art, and for what ends were their several Parts? Was the Eye contrived without Skill in Opticks, and the Ear without Knowledge of Sounds? How do the Motions of the Body follow from the Will, and whence is the instinct in Animals? Is not the Sensory of Animals that place to which the sensitive Substance is present, and into which the sensible Species of Things are carried through the Nerves and Brain, that there they may be perceived by their immediate presence to that Substance? And these things being rightly dispatch’d, does it not appear from Phaenomena that there


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is a Being incorporeal, living, intelligent, omnipresent, who in infinite Space, as it were in his Sensory, sees the things themselves intimately, and thoroughly perceives them, and comprehends them wholly by their immediate presence to himself: Of which things the Images only carried through the Organs of Sense into our little Sensoriums, are there seen and beheld by that which in us perceives and thinks. And though every true Step made in this Philosophy brings us not immediately to the Knowledge of the first Cause, yet it brings us nearer to it, and on that account is to be highly valued.


As for Query 23 (31), it starts with the question:


Have not the small Particles of Bodies certain Powers, Virtues, or Forces, by which they act at a distance, not only upon the Rays of Light for reflecting, refracting, and inflecting them, but also upon one another for producing a great Part of the Phaenomena of Nature? For it's well known, that Bodies act one upon another by the Attractions of Gravity, Magnetism, and Electricity; and these Instances shew the Tenor and the Course of Nature, and make it not improbable but that there may be more attractive Powers than these. For Nature is very consonant and conformable to her self.


Newton does not tell us outright—any more than he does in the Principia—what these various "Powers" are. Just as in the Principia, he leaves that question open, though, as we know, he holds them to be non-mechanical, immaterial and even "spiritual" energy extraneous to matter.'


How these Attractions may be perform’d, I do not here consider. What I call attraction may be perform’d by impulse, or by some other means unknown to me. I use


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that Word here to signify only in general any Force by which Bodies tend towards one another, whatsoever be the Cause. For we must learn from the Phaenomena of Nature what Bodies attract one another, and what are the Laws and Properties of the Attraction, before we enquire the Cause by which the Attraction is perform’d. The Attractions of Gravity, Magnetism, and Electricity, reach to very sensible distances, and so have been observed by vulgar Eyes, and there may be others which reach to so small distances as hitherto escape Observation; and perhaps electrical Attraction may reach to such small distances, even without being excited by Friction.


Whatever these "Powers" may be, they are, in any case, real forces and perfectly indispensable for the explanation—even a hypothetical one—of the existence of bodies, that is, of the sticking together of the material particles that compose them; a purely materialistic pattern of nature is utterly impossible (and a purely materialistic or mechanistic physics, such as that of Lucretius or of Descartes, is impossible, too):6


The Parts of all homogeneal hard Bodies which fully touch one another, stick together very strongly. And for explaining how this may be, some have invented hooked Atoms, which is begging the Question; and others tell us that Bodies are glued together by rest, that is, by an occult Quality, or rather by nothing; and others, that they stick together by conspiring Motions, that is, by relative rest amongst themselves. I had rather infer from their Cohesion, that their Particles attract one another by some Force, which in immediate Contact is exceeding strong, at small distances performs the chymical Operations above-mention’d, and reaches not far from the Particles with any sensible Effect.


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It could be argued, of course (and was to be argued by Leibniz) that Newton is wrong to stick to the classical atomic conception of hard, impenetrable, indivisible last components of matter, a conception which implies great difficulties for dynamics. It is indeed, impossible to say what would happen if two absolutely hard bodies should collide. Let us take, for instance, two perfectly similar and perfectly hard, that is, absolutely unyielding and indeformable, bodies, and let them approach each other—the classical case of dynamics—with the same speed. What will they do after the impact? Rebound, as elastic bodies would do? Or stop each other as would be the case with inelastic ones? As a matter of fact, they should not do either—yet, tertium non datur. As we know, Descartes, in order to preserve the principle of conservation of energy, asserted the rebounding. But he was obviously wrong. If we admit, however, that they would stop each other, that is, that motion is lost in every impact, would not the world-machine run down very quickly and very quickly come to a stop? Should we not, in order to avoid these difficulties, discard completely the atomic conception and admit, for instance, that matter is infinitely divisible or that its "last" components are not hard atoms but soft, or elastic, particles, or even "physical monads"? Newton, therefore, continues7


All bodies seem to be composed of hard Particles: for otherwise Fluids would not congeal; as Water, Oils, Vinegar, and Spirit or Oil of Vitriol do by freezing; Mercury by fumes of Lead; Spirit of Nitre and Mercury, by dissolving the Mercury and evaporating the Flegm; Spirit of Wine and Spirit of Urine, by deflegming and mixing them; and Spirit of Urine and Spirit of Salt, by subliming them


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together to make Sal-amoniac. Even the Rays of Light seem to be hard Bodies; for otherwise they would not retain different Properties in their different Sides. And therefore Hardness may be reckon’d the Property of all uncompounded Matter. At least, this seems to be as evident as the universal Impenetrability of Matter. For all Bodies, so far as Experience reaches, are either hard, or may be harden’d; and we have no other Evidence of universal Impenetrability, besides a large Experience without an experimental Exception. Now if compound Bodies are so very hard as we find some of them to be, and yet are very porous, and consist of Parts which are only laid together; the simple Particles which are void of Pores, and were never yet divided, must be much harder. For such hard Particles being heaped together, can scarce touch one another in more than a few Points, and therefore must be separable by much less Force than is requisite to break a solid Particle, whose Parts touch in all the Space between them, without any Pores or Interstices to weaken their Cohesion. And how such very hard Particles which are only laid together, hold and that so firmly as they do, without the assistance of something which causes them to be attracted or press’d towards one another, is very difficult to conceive.


This "something," as we know, and as it is clear from the very texts I am quoting, cannot be other, smaller, "ethereal" particles, at least not in the last analysis, because the same question, that is, the question about their interaction, can obviously be raised concerning the "ethereal" particles themselves, and cannot be answered by postulating an ultra-ether, which moreover, would imply the existence of an ultra-ultra-ether, and so on.

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[paragraph continues] Forces of attraction, and also of repulsion are therefore fundamental, though non-material, elements of nature:8


There are therefore Agents in Nature able to make the Particles of Bodies stick together by very strong Attractions. And it is the Business of experimental Philosophy to find them out.


Thus we see it once more: good, empirical and experimental natural philosophy does not exclude from the fabric of the world and the furniture of heaven immaterial or transmaterial forces. It only renounces the discussion of their nature, and, dealing with them simply as causes of the observable effects, treats them—being a mathematical natural philosophy—as mathematical causes or forces, that is, as mathematical concepts or relations. It is, on the contrary, the a priori philosophy of the classical Greek atomists, who at least recognized the existence of void space and probably even the non-mechanical character of gravity, and of course that of Descartes, that is guilty of this exclusion and of the impossible attempts to explain everything by matter and motion. As for Newton himself, he is so deeply convinced of the reality of these immaterial, and, in this sense, transphysical forces, that this conviction enables him to devise a most extraordinary and truly prophetic picture of the general structure of material beings:9


Now the smallest Particles of Matter may cohere by the strongest Attractions, and compose bigger Particles of weaker Virtue; and many of these may cohere and compose bigger Particles whose Virtue is still weaker, and so on for divers Successions, until the Progression end in the biggest Particles on which the Operations in Chymistry,


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and the Colours of natural Bodies depend, and which by cohering compose Bodies of a sensible Magnitude. If the Body is compact, and bends or yields inward to Pression without any sliding of its Parts, it is hard and elastick, returning to its Figure with a Force rising from the mutual Attraction of its Parts. If the Parts slide upon one another, the Body is malleable or soft. If they slip easily, and are of a fit Size to be agitated by Heat, and the Heat is big enough to keep them in Agitation, the Body is fluid; and if it be apt to stick to things, it is humid; and the Drops of every fluid affect a round Figure by the mutual Attraction of their Parts, as the Globe of the Earth and Sea affects a round Figure by the mutual Attraction of its Parts by Gravity.


Moreover, as I have already hinted before, the admission of various immaterial forces acting upon or distributed around the bodies or particles according to strict mathematical laws—or to express it in a more modern way: the admission of the existence of different fields of forces connected with bodies and particles—enables us, and that is an invaluable advantage, to superimpose them one upon the other, and even to transform them into their contraries. Indeed,10


Since Metals dissolved in Acids attract but a small quantity of the Acid, their attractive Force can reach but to a small distance from them. And as in Algebra, where affirmative Quantities vanish and cease, there negative ones begin; so in Mechanicks, where Attraction ceases, there a repulsive Virtue ought to succeed. And that there is such a Virtue, seems to follow from the Reflexions and Inflexions of the Rays of Light. For the Rays are repelled by Bodies in both these Cases, without the immediate Contact of the


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reflecting or inflecting Body. It seems also to follow from the Emission of Light; the Ray so soon as it is shaken off from a shining Body by the vibrating Motion of the Parts of the Body, and gets beyond the reach of Attraction, being driven away with exceeding great Velocity. For that Force which is sufficient to turn it back in Reflexion, may be sufficient to emit it. It seems also to follow from the Production of Air and Vapour. The Particles when they are shaken off from Bodies by Heat or Fermentation, so soon as they are beyond the reach of the Attraction of the Body, receding from it, and also from one another with great Strength, and keeping at a distance, so as sometimes to take up above a Million of Times more space than they did before in the form of a dense Body. Which vast Contraction and Expansion seems unintelligible, by feigning the Particles of Air to be springy and ramous, or rolled up like Hoops, or by any other means than a repulsive Power.


Thus, the admission of immaterial "virtues" offers us an immediate and elegant solution of the most important and crucial problem of elasticity, or "springiness" of bodies; and vice versa, this very solution demonstrates the impossibility of explaining this property of bodies by purely mechanical means (as Descartes and Boyle tried to do) and therefore confirms the insufficiency of pure materialism not only for philosophy in general, but also for natural philosophy. As a matter of fact, without the immaterial Powers and Virtues, there would not be any Nature to philosophize about, because there would be no cohesion, no unity and no motion; or if there were, at the beginning, it would have ceased long ago. On the contrary, if we admit the double, material as well as immaterial, structure of Nature,11

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[paragraph continues] . . . Nature will be very conformable to her self and very simple, performing all the great Motions of the heavenly Bodies by the Attraction of Gravity which intercedes those Bodies, and almost all the small ones of their Particles by some other attractive and repelling Powers which intercede the Particles. The vis inertiae is a passive Principle by which Bodies persist in their Motion or Rest, receive Motion in proportion to the Force impressing it, and resist as much as they are resisted. By this Principle alone there never could have been any Motion in the World. Some other Principle was necessary for putting Bodies into Motion; and now they are in Motion, some other Principle is necessary for conserving the Motion. For from the various Composition of two Motions, ’tis very certain that there is not always the same quantity of Motion in the World. For if two Globes joined by a slender Rod, revolve about their common Center of Gravity with an uniform Motion, while that Center moves on uniformly in a right Line drawn in the Plane of their circular Motion; the Sum of the Motions of the two Globes, as often as the Globes are in the right Line described by their common Center of Gravity, will be bigger than the Sum of their Motions, when they are in a Line perpendicular to that right Line. By this Instance it appears that Motion may be got or lost.11a But by reason of the Tenacity of Fluids, and Attrition of their Parts, and the Weakness of Elasticity in Solids, Motion is much more apt to be lost than got, and is always upon the Decay. For Bodies which are either absolutely hard, or so soft as to be void of Elasticity, will not rebound from one another. Impenetrability makes them only stop. If two equal Bodies meet directly in vacuo, they will by the Laws of Motion stop where they meet, and lose all their Motion, and remain in rest, unless they be elastick, and receive new Motion from their Spring.


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Yet, even if they be elastic, they cannot be absolutely elastic, and thus, by each and every impact, some motion (that is, momentum) will be lost. And if the world were full, as the Cartesians want it to be, then the "vortical" motion assumed by Descartes would cease very quickly, because12


[paragraph continues] . . . unless the Matter were void of all Tenacity and Attrition of Parts, and Communication of Motion (which is not to be supposed,) the Motion would constantly decay. Seeing therefore the variety of Motion that we find in the World is always decreasing, there is a necessity of conserving it and recruiting it by active Principles,


that is, in the last analysis by the constant action in the world of the Omnipresent and All-powerful God. Newton therefore continues:13


All these things being consider’d, it seems probable to me, that God in the Beginning form’d Matter in solid, massy, hard, impenetrable, moveable Particles, of such Sizes and Figures, and with such other Properties, and in such Proportion to Space, as most conducted to the End for which he form’d them; and that these primitive Particles being Solids, are incomparably harder than any porous Bodies compounded of them; even so very hard, as never to wear or break in pieces; no ordinary Power being able to divide what God himself made one in the first Creation. While the Particles continue entire, they may compose Bodies of one and the same Nature and Texture in all Ages: But should they wear away, or break in pieces, the Nature of Things depending on them, would be changed. Water and Earth, composed of old worn Particles and Fragments of Particles, would not be of the same Nature and Texture now, with Water and Earth composed of entire


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[paragraph continues] Particles in the Beginning. And therefore, that Nature may be lasting, the Changes of corporeal Things are to be placed only in the various Separations and new Associations and Motions of these permanent Particles; compound Bodies being apt to break, not in the midst of solid Particles, but where those Particles are laid together, and only touch in a few Points.


It seems to me farther, that these Particles have not only a Vis inertiae, accompanied with such passive Laws of Motion as naturally result from that Force, but also that they are moved by certain active Principles. . . .


and it is the action of these principles, or, more exactly, the action of God by means of these principles that gives to the world its structure and order, and it is this structure and order that enables us to recognize that the world is an effect of choice, and not chance or necessity. Natural philosophy—at least the good one, that is, the Newtonian and not the Cartesian—thus transcends itself and leads us to God:14


. . . by the help of these Principles, all material Things seem to have been composed of the hard and solid Particles above-mention’d, variously associated in the first Creation by the Counsel of an intelligent Agent. For it became him who created them to set them in order. And if he did so, it's unphilosophical to seek for any other Origin of the World, or to pretend that it might arise out of Chaos by the mere Laws of Nature; though being once form’d, it may continue by those Laws for many Ages. For while Comets move in very excentrick Orbs in all manner of Positions, blind Fate could never make all the Planets move one and the same way in Orbs concentrick, some inconsiderable Irregularities excepted, which may have risen


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from the mutual Actions of Comets and Planets upon one another, and which will be apt to increase, till this System wants a Reformation. Such a wonderful Uniformity in the Planetary System must be allowed the Effect of Choice. And so must the Uniformity in the Bodies of Animals. . . .


All that, and much more besides,15


[paragraph continues] . . . can be the effect of nothing else than the Wisdom and Skill of a powerful ever-living Agent, who being in all Places, is more able by his Will to move the Bodies within his boundless uniform Sensorium, and thereby to form and reform the Parts of the Universe, than we are by our Will to move the parts of our own Bodies. And yet we are not to consider the World as the Body of God, or the several Parts thereof, as the Parts of God. He is an uniform Being, void of Organs, Members or Parts, and they are his Creatures subordinate to him, and subservient to his Will; and he is no more the Soul of them, than the Soul of Man is the Soul of the Species of Things carried through the Organs of Sense into the place of its Sensation, where it perceives them by means of its immediate Presence, without the Intervention of any third thing. The Organs of Sense are not for enabling the Soul to perceive the Species of Things in its Sensorium, but only for conveying them thither; and God has no need of such Organs, he being everywhere present in the Things themselves. And since Space is divisible in infinitum, and Matter is not necessarily in all places, it may be also allow’d that God is able to create Particles of Matter of several Sizes and Figures, and in several Proportions to Space, and perhaps of different Densities and Forces, and thereby to vary the Laws of Nature, and make Worlds of several sorts in several Parts of the Universe. At least, I see nothing of Contradiction in all this,


p. 220

concludes Newton, who could have added that in the Principia he had already shown—without insisting upon it—that the inverse square law of attraction, the actual law of this world, was by no means the only possible—although the most convenient one—and that God, had He wanted to, could have adopted another. As he could have quoted his friend Robert Boyle who believed that God had actually tried out, in different worlds, different laws of motion; or Joseph Raphson who had just expressed the same opinion. Yet he did not. As he did not quote Henry More when he made infinite space the sensorium of the nevertheless transcendent God.