From the Closed World to the Infinite Universe, by Alexander Koyré, , at sacred-texts.com
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 is and crosses all the ts.
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
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
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
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.
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
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
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
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.
[paragraph continues] motion indeed implies divisibility.
[paragraph continues] which; vice versa, implies, immediately and by necessity, its absolute immovability.
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
But let us not think that space is a kind of immaterial stuffRaphson, obviously, wants to oppose space to More's spirit:13
It is clear thus that14
7. Space is immutable.
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
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
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
[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
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
perfections in the First Cause, and, in relation to it, they are both equally imperfect.20
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
Thus, even if it were infinitely extendedwhich it is notmatter 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 asparadoxicallyto 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
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 determinableby usdimensions. Quite the contrary: in infinite space there is room enough for a practically indeterminate and indefinitely large world. Thus he tells us that if24
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,
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,
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 whichthough their nature is hidden from usis 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