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

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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.

Next: IX. God and the World: Space, Matter, Ether and Spirit