From the Closed World to the Infinite Universe: V. Indefinite Extension or Infinite Space

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

V. Indefinite Extension or Infinite Space

Henry More was one of the first partisans of Descartes in England even though, as a matter of fact, he never was a Cartesian and later in life turned against Descartes and even accused the Cartesians of being promoters of atheism.1 More exchanged with the French philosopher a series of extremely interesting letters which throws a vivid light on the respective positions of the two thinkers.2

More starts, naturally, by expressing his admiration for the great man who has done so much to establish truth and dissipate error, continues by complaining about the difficulty he has in understanding some of his teachings, and ends by presenting some doubts, and even some objections.

Thus, it seems to him difficult to understand or to admit the radical opposition established by Descartes between body and soul. How indeed can a purely spiritual soul, that is, something which, according to Descartes, has no extension whatever, be joined to a purely material

body, that is, to something which is only and solely extension? Is it not better to assume that the soul, though immaterial, is also extended; that everything, even God, is extended? How could He otherwise be present in the world?

First, you establish a definition of matter, or of body, which is much too wide. It seems, indeed, that God is an extended thing (res), as well as the Angel; and in general everything that subsists by itself, so that it appears that extension is enclosed by the same limits as the absolute essence of things, which however can vary according to the variety of these very essences. As for myself, I believe it to be clear that God is extended in His manner just because He is omnipresent and occupies intimately the whole machine of the world as well as its singular particles. How indeed could He communicate motion to matter, which He did once, and which, according to you, He does even now, if He did not touch the matter of the universe in practically the closest manner, or at least had not touched it at a certain time? Which certainly He would never be able to do if He were not present everywhere and did not occupy all the spaces. God, therefore, extends and expands in this manner; and is, therefore, an extended thing (res).

Having thus established that the concept of extension cannot be used for the definition of matter since it is too wide and embraces both body and spirit which both are extended, though in a different manner (the Cartesian demonstration of the contrary appears to More to be not only false but even pure sophistry), More suggests secondly that matter, being necessarily sensible, should be defined only by its relation to sense, that is, by tangibility.

[paragraph continues] But if Descartes insists on avoiding all reference to sense-perception, then matter should be defined by the ability of bodies to be in mutual contact, and by the impenetrability which matter possesses in contradistinction to spirit. The latter, though extended, is freely penetrable and cannot be touched. Thus spirit and body can co-exist in the same place, and, of course, two—or any number of—spirits can have the same identical location and "penetrate" each other, whereas for bodies this is impossible.

The rejection of the Cartesian identification of extension and matter leads naturally to the rejection by Henry More of Descartes’ denial of the possibility of vacuum. Why should not God be able to destroy all matter contained in a certain vessel without—as Descartes asserts—its walls being obliged to come together? Descartes, indeed, explains that to be separated by "nothing" is contradictory and that to attribute dimensions to "void" space is exactly the same as to attribute properties to nothing; yet More is not convinced, all the more so as "learned Antiquity"—that is Democritus, Epicurus, Lucretius—was of quite a different opinion. It is possible, of course, that the walls of the vessel will be brought together by the pressure of matter outside them. But if that happens, it will be because of a natural necessity and not because of a logical one. Moreover, this void space will not be absolutely void, for it will continue to be filled with God's extension. It will only be void of matter, or body, properly speaking.

In the third place Henry More does not understand the "singular subtlety" of Descartes’ negation of the existence of atoms, of his assertion of the indefinite divisibility

of matter, combined with the use of corpuscular conceptions in his own physics. To say that the admission of atoms is limiting God's omnipotence, and that we cannot deny that God could, if He wanted to, divide the atoms into parts, is of no avail: the indivisibility of atoms means their indivisibility by any created power, and that is something that is perfectly compatible with God's own power to divide them, if He wanted to do so. There are a great many things that He could have done, but did not, or even those that He can do but does not. Indeed, if God wanted to preserve his omnipotence in its absolute, status, He would never create matter at all: for, as matter is always divisible into parts that are themselves divisible, it is clear that God will never be able to bring this division to its end and that there will always be something which evades His omnipotence.

Henry More is obviously right and Descartes himself, though insisting on God's omnipotence and refusing to have it limited and bounded even by the rules of logic and mathematics, cannot avoid declaring that there are a great many things that God cannot do, either because to do them would be, or imply, an imperfection (thus, for instance, God cannot lie and deceive), or because it would make no sense. It is just because of that, Descartes asserts, that even God cannot make a void, or an atom. True, according to Descartes, God could have created quite a different world and could have made twice two equal to five, and not to four. On the other hand, it is equally true that He did not do it and that in this world even God cannot make twice two equal to anything but four.

From the general trend of his objections it is clear that the Platonist, or rather Neoplatonist, More was deeply

influenced by the tradition of Greek atomism, which is not surprising in view of the fact that one of his earliest works bears the revealing title, Democritus Platonissans. . .4

What he wants is just to avoid the Cartesian geometrization of being, and to maintain the old distinction between space and the things that are in space; that are moving in space and not only relatively to each other; that occupy space in virtue of a special and proper quality or force—impenetrability—by which they resist each other and exclude each other from their "places."

Grosso modo, these are Democritian conceptions and that explains the far-reaching similarity of Henry More's objections to Descartes to those of Gassendi, the chief representative of atomism in the XVIIth century.5 Yet Henry More is by no means a pure Democritian. He does not reduce being to matter. And his space is not the infinite void of Lucretius: it is full, and not full of "ether" like the infinite space of Bruno. It is full of God, and in a certain sense it is God Himself as we shall see more clearly hereafter.

Fourth, I do not understand your indefinite extension of the world. Indeed this indefinite extension is either simpliciter infinite, or only in respect to us. If you understand extension to be infinite simpliciter, why do you obscure your thought by too low and too modest words? If it is infinite only in respect to us, extension, in reality, will be finite; for our mind is the measure neither of the things nor of truth. And therefore, as there is another simpliciter infinite expansion, that of the divine essence, the matter of your

[paragraph continues] Having thus impaled Descartes on the horns of the dilemma, More continues:8

To the perplexity and objections of his English admirer and critic Descartes replies10—and his answer is surprisingly mild and courteous—that it is an error to define matter by its relation to senses, because by doing so we are in danger of missing its true essence, which does not depend on the existence of men and which would be the same if there were no men in the world; that, moreover, if divided into sufficiently small parts, all matter becomes utterly insensible; that his proof of the identity of extension and matter is by no means a sophism but is as clear and demonstrative as it could be; and that it is perfectly unnecessary to postulate a special property of impenetrability in order to define matter because it is a mere consequence of its extension.

Turning then to More's concept of immaterial or spiritual extension, Descartes writes:11

object. But I deny that there is in God, in an Angel, in our soul, and in any substance that is not a body, a true extension, such as is usually conceived by everybody. For by an extended thing everybody understands something [which is] imaginable (be it an ens rations or a real thing), and in which, by imagination, can be distinguished different parts of a determined magnitude and figure, of which the one is in no way the other; so that it is possible, by imagination, to transfer any one of them to the place of another, but not to imagine two of them in the same place.

Nothing of that kind applies to God, or to our souls, which are not objects of imagination, but of pure understanding, and have no separable parts, especially no parts of determinate size and figure. Lack of extension is precisely the reason why God, the human soul, and any number of angels can be all together in the same place. As for atoms and void, it is certain that, our intelligence being finite and God's power infinite, it is not proper for us to impose limits upon it. Thus we must boldly assert "that God can do all that we conceive to be possible, but not that He cannot do what is repugnant to our concept." Nevertheless, we can judge only according to our concepts, and, as it is repugnant to our manner of thinking to conceive that, if all matter were removed from a vessel, extension, distance, etc., would still remain, or that parts of matter be indivisible, we say simply that all that implies contradiction.

Descartes’ attempt to save God's omnipotence and, nevertheless, to deny the possibility of void space as incompatible with our manner of thinking, is, to say the truth, by no means convincing. The Cartesian God is a Deus verax and He guarantees the truth of our clear and

distinct ideas. Thus it is not only repugnant to our thought, but impossible that something of which we clearly see that it implies contradiction be real. There are no contradictory objects in this world, though there could have been in another.

Coming now to More's criticism of his distinction between " infinite " and " indefinite," Descartes assures him that it is not because of12

. . . an affectation of modesty, but as a precaution, and, in my opinion a necessary one, that I call certain things indefinite rather than infinite. For it is God alone whom I understand positively to be infinite; as for the others, such as the extension of the world, the number of parts into which matter is divisible, and so on, whether they are simpliciter infinite or not, I confess not to know. I only know that I do not discern in them any end, and therefore, in respect to me, I say they are indefinite. And though our mind is not the measure of things or of truth, it must, assuredly, be the measure of things that we affirm or deny. What indeed is more absurd or more inconsiderate than to wish to make a judgment about things which we confess to be unable to perceive with our mind?

Thus I am surprised that you not only seem to want to do so, as when you say that if extension is infinite only in respect to us then extension in truth will be finite, etc., but that you imagine beyond this one a certain divine extension, which would stretch farther than the extension of bodies, and thus suppose that God has partes extra partes, and that He is divisible, and, in short, attribute to Him all the essence of a corporeal being.

Descartes, indeed, is perfectly justified in pointing out that More has somewhat misunderstood him: a space

beyond the world of extension has never been admitted by him as possible or imaginable, and even if the world had these limits which we are unable to find, there certainly would be nothing beyond them, or, better to say, there would be no beyond. Thus, in order to dispel completely More's doubts, he declares:13

When I say that the extension of matter is indefinite, I believe it to be sufficient to prevent any one imagining a place outside it, into which the small particles of my vortices could escape; because wherever this place be conceived, it would already, in my opinion, contain some matter; for, when I say that it is indefinitely extended, I am saying that it extends farther than all that can be conceived by man.

But I think, nevertheless, that there is a very great difference between the amplitude of this corporeal extension and the amplitude of the divine, I shall not say, extension, because properly speaking there is none, but substance or essence; and therefore I call this one simpliciter infinite, and the other, indefinite.

Descartes is certainly right in wanting to maintain the distinction between the "intensive" infinity of God, which not only excludes all limit, but also precludes all multiplicity, division and number, from the mere endlessness, indefiniteness, of space, or of the series of numbers, which necessarily include and presuppose them. This distinction, moreover, is quite traditional, and we have seen it asserted not only by Nicholas of Cusa, but even by Bruno.

Henry More does not deny this distinction; at least not completely. In his own conception it expresses itself in the opposition between the material and the divine extension. Yet, as he states it in his second letter to

[paragraph continues] Descartes,14 it has nothing to do with Descartes’ assertion that there may be limits to space and with his attempt to build a concept intermediate between the finite and the infinite; the world is finite or infinite, tertium non dater. And if we admit, as we must, that God is infinite and everywhere present, this "everywhere" can only mean infinite space. In this case, pursues More, re-editing an argument already used by Bruno, there must also be matter everywhere, that is, the world must be infinite.15

You can hardly ignore that it is either simpliciter infinite or, in point of fact, finite, though you cannot as easily decide whether it is the one or the other. That, however, your vortices are not disrupted and do not come apart seems to be a rather clear sign that the world is really infinite. For my part, I confess freely that though I can boldly give my approval to this axiom: The world is finite, or not finite, or, what is here the same thing, infinite, I cannot, nevertheless, fully understand the infinity of any thing whatsoever. But here there comes to my imagination what Julius Scaliger wrote somewhere about the contraction and the dilatation of the Angels: namely, that they cannot extend themselves in infinitum, or contract themselves to an imperceptible (οὐδενότητα) point. Yet if one recognizes God to be positively infinite (that is, existing everywhere), as you yourself rightly do, I do not see whether it is permitted to the unbiassed reason to hesitate to admit forthwith also that He is nowhere idle, and that with the same right, and with the same facility with which [He created] this matter in which we live, or that to which our eyes and our mind can reach, He produced matter everywhere.

[paragraph continues] Nor is it absurd or inconsiderate to say that, if the extension is infinite only quoad nos, it will, in truth and in reality, be finite:16

I will add that this consequence is perfectly manifest, because the particle "only" (tantum) clearly excludes all real infinity of the thing which is said to be infinite only in respect to us, and therefore in reality the extension will be finite; moreover my mind does perceive these things of which I judge, as it is perfectly clear to me that the world is either finite or infinite, as I have just mentioned.

As for Descartes’ contention that the impossibility of the void already results from the fact that "nothing" can have no properties or dimensions and therefore cannot be measured, More replies by denying this very premise:17

. . . for, if God annihilated this universe and then, after a certain time, created from nothing another one, this intermundium or this absence of the world would have its duration which would be measured by a certain number of days, years or centuries. There is thus a duration of something that does not exist, which duration is a kind of extension. Consequently, the amplitude of nothing, that is of void, can be measured by ells or leagues, just as the duration of what does not exist can be measured in its inexistence by hours, days and months.

We have seen Henry More defend, against Descartes, the infinity of the world, and even tell the latter that his own physics necessarily implies this infinity. Yet it seems that, at times, he feels himself assailed by doubt. He is perfectly sure that space, that is, God's extension, is infinite. On the other hand, the material world may, perhaps, be finite. After all, nearly everybody believes it; spatial infinity and temporal eternity are strictly parallel, and so both seem to be absurd. Moreover Cartesian cosmology can be put in agreement with a finite world. Could

[paragraph continues] Descartes not tell what would happen, in this case, if somebody sitting at the extremity of the world pushed his sword through the limiting wall? On the one hand, indeed, this seems easy, as there would be nothing to resist it; on the other, impossible, as there would be no place where it could be pushed.18

Descartes’ answer to this second letter of More19 is much shorter, terser, less cordial than to the first one. One feels that Descartes is a bit disappointed in his correspondent who obviously does not understand his, Descartes’, great discovery, that of the essential opposition between mind and extension, and who persists in attributing extension to souls, angels, and even to God. He restates20

. . . that he does not conceive any extension of substance in God, in the angels, or in our mind, but only an extension of power, so that an angel can proportionate this power to a greater or smaller part of corporeal substance; for if there were no body at all, this power of God or of an angel would not correspond to any extension whatever. To attribute to substance what pertains only to power is an effect of the same prejudice which makes us suppose all substance, even that of God, to be something that can be imagined.

If there were no world, there would be no time either. To More's contention that the intermundium would last a certain time, Descartes replies:21

I believe that it implies a contradiction to conceive a duration between the destruction of the first world and the creation of the second one; for, if we refer this duration or something similar to the succession of God's ideas, this will be an error of our intellect and not a true perception of something.

Indeed, it would mean introducing time into God, and thus making God a temporal, changing being. It would mean denying His eternity, replacing it by mere sempiternity—an error no less grave than the error of making Him an extended thing. For in both cases God is menaced with losing His transcendence, with becoming immanent to the world.

Now Descartes’ God is perhaps not the Christian God, but a philosophical one.22 He is, nevertheless, God, not the soul of the world that penetrates, vivifies and moves it. Therefore he maintains, in accordance with mediaeval tradition, that, in spite of the fact that in God power and essence are one—an identity pointed out by More in favour of God's actual extension—God has nothing in common with the material world. He is a pure mind, an infinite mind, whose very infinity is of a unique and incomparable non-quantitative and non-dimensional kind, of which spatial extension is neither an image nor even a symbol. The world therefore, must not be called infinite; though of course we must not enclose it in limits:23

It is repugnant to my concept to attribute any limit to the world, and I have no other measure than my perception for what I have to assert or to deny. I say, therefore, that the world is indeterminate or indefinite, because I do not recognize in it any limits. But I dare not call it infinite as I perceive that God is greater than the world, not in respect to His extension, because, as I have already said, I do not acknowledge in God any proper [extension], but in respect to His perfection.

Once more Descartes asserts that God's presence in the world does not imply His extension. As for the world

itself which More wants to be either simpliciter finite, or simpliciter infinite, Descartes still refuses to call it infinite. And yet, either because he is somewhat angry with More, or because he is in a hurry and therefore less careful, he practically abandons his former assertion about the possibility of the world's having limits (though we cannot find them) and treats this conception in the same manner in which he treated that of the void, that is, as nonsensical and even contradictory; thus, rejecting as meaningless the question about the possibility of pushing a sword through the boundary of the world, he says:24

It is repugnant to my mind, or what amounts to the same thing, it implies a contradiction, that the world be finite or limited, because I cannot but conceive a space outside the boundaries of the world wherever I presuppose them. But, for me, this space is a true body. I do not care if it is called by others imaginary, and that therefore the world is believed to be finite; indeed, I know from what prejudices this error takes its origin.

Henry More, needless to say, was not convinced—one philosopher seldom convinces another. He persisted, therefore, in believing "with all the ancient Platonists" that all substance, souls, angels and God are extended, and that the world, in the most literal sense of this word, is in God just as God is in the world. More accordingly sent Descartes a third letter,25 which he answered,26 and a fourth,27 which he did not.28 I shall not attempt to examine them here as they bear chiefly on questions which, though interesting in themselves—for example, the discussion about motion and rest—are outside our subject.

Summing up, we can say that we have seen Descartes, under More's pressure, move somewhat from the position he had taken at first: to assert the indefiniteness of the world, or of space, does not mean, negatively, that perhaps it has limits that we are unable to ascertain; it means, quite positively, that it has none because it would be contradictory to posit them. But he cannot go farther. He has to maintain his distinction, as he has to maintain the identification of extension and matter, if he is to maintain his contention that the physical world is an object of pure intellection and, at the same time, of imagination—the precondition of Cartesian science—and that the world, in spite of its lack of limits, refers us to God as its creator and cause.

Infinity, indeed, has always been the essential character, or attribute, of God; especially since Duns Scotus, who could accept the famous Anselmian a priori proof of the existence of God (a proof revived by Descartes) only after he had "colored" it by substituting the concept of the infinite being (ens infinitum) for the Anselmian concept of a being than which we cannot think of a greater (ens quo maius cogitari nequit). Infinity thus—and it is particularly true of Descartes whose God exists in virtue of the infinite "superabundance of His essence" which enables Him to be His own cause (causa sui) and to give Himself His own existence29—means or implies being, even necessary being. Therefore it cannot be attributed to creature. The distinction, or opposition, between God and creature is parallel and exactly equivalent to that of infinite and of finite being.