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

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

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

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

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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

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

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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

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

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

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

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

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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

It is just the same concerning space:14

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

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

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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—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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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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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

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"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

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

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

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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

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

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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

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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

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

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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

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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

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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

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

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

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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

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

[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

just because action at a distance39

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

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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Having learnt his lesson, Bentley writes therefore:42

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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 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

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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

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

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.

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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

An axiom then asserts that:10

A series of propositions now follows in quick succession:11

[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.

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[paragraph continues] —motion indeed implies divisibility.

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

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

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 clear thus that14

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[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

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

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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

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[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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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

[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

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

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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

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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

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

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Raphson himself would25

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

[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

IX. God and the World:

SPACE, MATTER, ETHER AND SPIRIT

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

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.'

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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

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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

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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

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

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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

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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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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

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

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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

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All that, and much more besides,15

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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.