From the Closed World to the Infinite Universe, by Alexander Koyré, , at sacred-texts.com
THE DISCOVERY OF NEW STARS IN THE WORLD SPACE AND THE MATERIALIZATION OF SPACE
Galileo & Descartes
I have already mentioned the Sidereus Nuncius1 of Galileo Galilei, a work of which the influenceand the importancecannot be overestimated, a work which announced a series of discoveries more strange and more significant than any that had ever been made before. Reading it today we can no longer, of course, experience the impact of the unheard-of message; yet we can still feel the excitement and pride glowing beneath the cool and sober wording of Galileo's report:2
It is assuredly important to add to the great number of fixed stars that up to now men have been able to see by their natural sight, and to set before the eyes innumerable others which have never been seen before and which surpass the old and previously known [stars] in number more than ten times.
It is most beautiful and most pleasant to the sight to see the body of the moon, distant from us by nearly sixty semidiameters of the earth, as near as if it were at a distance of only two and a half of these measures.
[paragraph continues] So that
Then to have settled disputes about the Galaxy or Milky Way and to have made its essence manifest to the senses, and even more to the intellect, seems by no means a matter to be considered of small importance; in addition to this, to demonstrate directly the substance of those stars which all astronomers up to this time have called nebulous, and to demonstrate that it is very different from what has hitherto been believed, will be very pleasant and very beautiful.
But what by far surpasses all admiration, and what in the first place moved me to present it to the attention of astronomers and philosophers, is this: namely, that we have discovered four planets, neither known nor observed by any one before us, which have their periods around a certain big star of the number of the previously known ones, like Venus and Mercury around the sun, which sometimes precede
To sum up: mountains on the moon, new "planets" in the sky, new fixed stars in tremendous numbers, things that no human eye had ever seen, and no human mind conceived before. And not only this: besides these new, amazing and wholly unexpected and unforeseen facts, there was also the description of an astonishing invention, that of an instrumentthe first scientific instrumentthe perspicillum, which made all these discoveries possible and enabled Galileo to transcend the limitation imposed by natureor by Godon human senses and human knowledge.3
No wonder that the Message of the Stars was, at first, received with misgivings and incredulity, and that it played a decisive part in the whole subsequent development of astronomical science, which from now on became so closely linked together with that of its instruments that every progress of the one implied and involved a progress of the other. One could even say that not only astronomy, but science as such, began, with Galileo's invention, a new phase of its development, the phase that we might call the instrumental one.
The perspicilli not only increased the number of the fixed, and errant, stars: they changed their aspect. I have already dealt with this effect of the use of the telescope. Yet it is worth while quoting Galileo himself on this subject:
According to Galileo, this "adventitious" and "accidental" character of the halo surrounding the stars is clearly demonstrated by the fact that, when they are seen at dawn, stars, even of the first magnitude, appear quite small; and even Venus, if seen by daylight, is hardly larger than a star of the last magnitude. Daylight, so to say, cuts off their luminous fringes; and not only light, but diaphanous clouds or black veils and colored glass have the same effect.5
This, indeed, is extremely important as it destroys the basis of Tycho Brahe's most impressivefor his contemporariesobjection to heliocentric astronomy, according to which the fixed starsif the Copernican world-system were trueshould be as big, nay much bigger, than the whole orbis magnus of the annual circuit of the earth. The perspicillum reduces their visible diameter from 2 minutes to 5 seconds and thus disposes of the necessity to increase the size of the fixed stars beyond that of the sun. Yet the decrease in size is more than compensated by an increase in number:6
Click to enlarge
Galileo's star-picture of the shield and sword of Orion
(from the Sidereus Nuncius, 1610)
As a second example we have depicted the six stars of Taurus, called the Pleiades (we say six, because the seventh is scarcely ever visible), which are enclosed in the sky within very narrow boundaries, and near which are adjacent more than forty other visible ones, none of which is more than half a degree distant from the aforesaid six.
We have already seen that the invisibility for the human eye of the fixed stars discovered by Galileo, and, accordingly, the role of his perspicillum in revealing them, could be interpreted in two different ways: it could be explained by their being (a) too small to be seen, (b) too far away. The perspicillum would act in the first case as a kind of celestial microscope, in enlarging, so to say, the stars to perceivable dimensions; in the second it would be a " telescope " and, so to say, bring the stars nearer to us, to a distance at which they become visible. The second interpretation, that which makes visibility a function of the distance, appears to us now to be the only one possible. Yet this was not the case in the seventeenth century. As a matter of fact both interpretations fit the optical data equally well and a man of that period had no scientific, but only philosophical, reasons for choosing between them. And it was for philosophical reasons that the prevailing trend of seventeenth century thinking rejected the first interpretation and adopted the second.
There is no doubt whatever that Galileo adopted it too, though he very seldom asserts it. As a matter of fact he does it only once, in a curious passage of his Letter to Ingoli where he tells the latter that:7
[paragraph continues] Indeed, in the debate about the finiteness or the infinity of the universe, the great Florentine, to whom modern science owes perhaps more than to any other man, takes no part. He never tells us whether he believes the one or the other. He seems not to have made up his mind, or even, though inclining towards infinity, to consider the question as being insoluble. He does not hide, of course, that in contradistinction to Ptolemy, Copernicus and Kepler, he does not admit the limitation of the world or its enclosure by a real sphere of fixed stars. Thus in the letter to Ingoli already quoted he tells him:9
[paragraph continues] And, what is more, not only is it not proved that they are arranged in a sphere but neither Ingoli himself,10
Consequently, once more in opposition to Ptolemy, Copernicus and Kepler, and in accordance with Nicholas of Cusa and Giordano Bruno, Galileo rejects the conception of a center of the universe where the earth, or the sun, should be placed, "the center of the universe which we do not know where to find or whether it exists at all." He even tells us that "the fixed stars are so many suns." Yet, in the selfsame Dialogue on the Two Greatest World-Systems from which the last two quotations are taken, discussing ex professo the distribution of the fixed stars in the universe, he does not assert that the stars are scattered in space without end:11
Simp.I would rather take a middle way and would assign them a circle described about a determinate center and comprised within two spherical surfaces, to wit, one very high and concave, the other lower and convex betwixt which I would constitute the innumerable multitude of stars, but yet at diverse altitudes, and this might be called
Salv.But now we have all this while, Simplicius, disposed the mundane bodies exactly according to the order of Copernicus. . . .
We can assuredly explain the moderation of Salviati, who does not criticize the conception presented by Simpliciothough he does not share itand who accepts it, for the purpose of the discussion, as agreeing perfectly with Copernican astronomy, by the very nature of the Dialogue: a book intended for the "general reader," a book which aims at the destruction of the Aristotelian world-view in favor of that of Copernicus, a book which pretends, moreover, not to do it, and where, therefore, subjects both difficult and dangerous are obviously to be avoided.
We could even go as far as to discard the outright negation of the infinity of space in the Dialoguewhich had to pass the censorship of the Churchand to oppose to it the passage of the letter to Ingoli where its possibility is just as strongly asserted. In the Dialogue, indeed, Galileo tells us, just as Kepler does, that it is:12
Whereas in the Letter to Ingoli he writes:13
[paragraph continues] We must not forget, however, that in the selfsame Dialogue where he so energetically denied the infinity of space, he makes Salviati tell Simpliciojust as he himself had told Ingolithat:14
[paragraph continues] Moreover, we cannot reject the testimony of Galileo's Letter to Liceti, where, coming back to the problem of the finiteness and the infinity of the world, he writes:15
It is possible, of course, that all the pronouncements of Galileo have to be taken cum grano salis, and that the fate of Bruno, the condemnation of Copernicus in 1616,
his own condemnation in 1633 incited him to practise the virtue of prudence: he never mentions Bruno, either in his writings or in his letters; yet it is also possibleit is even quite probablethat this problem, like, generally speaking, the problems of cosmology or even of celestial mechanics, did not interest him very much. Indeed he concentrates on the question: a quo moventur projecta? but never asks: a quo moventur planetae? It may be, therefore, that, like Copernicus himself, he never took up the question, and thus never made the decisionthough it is implied in the geometrization of space of which he was one of the foremost promotersto make his world infinite. Some features of his dynamics, the fact that he never could completely free himself from the obsession of circularityhis planets move circularly around the sun without developing any centrifugal force in their motionseem to suggest that his world was not infinite. If it was not finite it was probably, like the world of Nicholas of Cusa, indeterminate; and it is, perhaps, more than a pure contingent coincidence that in his letter to Liceti he uses the expression also employed by Cusa: interminate.
Be this as it may, it is not Galileo, in any case, nor Bruno, but Descartes who clearly and distinctly formulated principles of the new science, its dream de reductione scientiae ad mathematicam, and of the new, mathematical, cosmology. Though, as we shall see, he overshot the mark and by his premature identification of matter and space deprived himself of the means of giving a correct solution to the problems that seventeenth century science had placed before him.
The God of a philosopher and his world are correlated. Now Descartes God, in contradistinction to most previous Gods, is not symbolized by the things He created; He does not express Himself in them. There is no analogy between God and the world; no imagines and vestigia Dei in mundo; the only exception is our soul, that is, a pure mind, a being, a substance of which all essence consists in thought, a mind endowed with an intelligence able to grasp the idea of God, that is, of the infinite (which is even innate to it), and with will, that is, with infinite freedom. The Cartesian God gives us some clear and distinct ideas that enable us to find out the truth, provided we stick to them and take care not to fall into error. The Cartesian God is a truthful God; thus the knowledge about the world created by Him that our clear and distinct ideas enable us to reach is a true and authentic knowledge. As for this world, He created it by pure will, and even if He had some reasons for doing it, these reasons are only known to Himself; we have not, and cannot have, the slightest idea of them. It is therefore not only hopeless, but even preposterous to try to find out His aims. Teleological conceptions and explanations have no place and no value in physical science, just as they have no place and no meaning in mathematics, all the more so as the world created by the Cartesian God, that is, the world of Descartes, is by no means the colorful, multiform and qualitatively determined world of the Aristotelian, the world of our daily life and experiencethat world is only a subjective world of unstable and inconsistent opinion based upon the untruthful testimony of confused and erroneous sense-perceptionbut a strictly uniform mathematical world, a world of geometry made
real about which our clear and distinct ideas give us a certain and evident knowledge. There is nothing else in this world but matter and motion; or, matter being identical with space or extension, there is nothing else but extension and motion.
The famous Cartesian identification of extension and matter (that is, the assertion that "it is not heaviness, or hardness, or color which constitutes the nature of body but only extension,"16 in other words, that "nature of body, taken generally, does not consist in the fact that it is a hard, or a heavy, or a colored thing, or a thing that touches our senses in any other manner, but only in that it is a substance extended in length, breadth and depth," and that conversely, extension in length, breadth and depth can only be conceivedand therefore can only existas belonging to a material substance) implies very far-reaching consequences, the first being the negation of the void, which is rejected by Descartes in a manner even more radical than by Aristotle himself.
Indeed, the void, according to Descartes, is not only physically impossible, it is essentially impossible. Void spaceif there were anything of that kindwould be a contradictio in adjecto, an existing nothing. Those who assert its existence, Democritus, Lucretius and their followers, are victims of false imagination and confused thinking. They do not realize that nothing can have no properties and therefore no dimensions. To speak of ten feet of void space separating two bodies is meaningless; if there were a void, there would be no separation, and bodies separated by nothing would be in contact. And if there is separation and distance, this distance is not a length, breadth or depth of nothing but of something, that is, of
substance or matter, a "subtle" matter, a matter that we do not sensethat is precisely why people who are accustomed to imagining instead of thinking speak of void spacebut nevertheless a matter just as real and as "material" (there are no degrees in materiality) as the "gross" matter of which trees and stones are made.
Thus Descartes does not content himself with stating, as did Giordano Bruno and Kepler, that there is no really void space in the world and that the world-space is everywhere filled with "ether." He goes much farther and denies that there is such a thing at all as "space," an entity distinct from "matter" that "fills" it. Matter and space are identical and can be distinguished only by abstraction. Bodies are not in space, but only among other bodies; the space that they "occupy" is not anything different from themselves:17
[paragraph continues] But that, of course, is an error. And,18
[paragraph continues] We can, indeed, divest and deprive any given body of all its sensible qualities and19
[paragraph continues] Thus,20
The second important consequence of the identification of extension and matter consists in the rejection not only of the finiteness and limitation of space, but also that of the real material world. To assign boundaries to it becomes not only false, or even absurd, but contradictory. We cannot posit a limit without transcending it in this very act. We have to acknowledge therefore that the real world is infinite, or ratherDescartes, indeed, refuses to use this term in connection with the worldindefinite.
It is clear, of course, that we cannot limit Euclidean space. Thus Descartes is perfectly right in pursuing:22
There is no longer any need to discuss the question whether fixed stars are big or small, far or near; more exactly this problem becomes a factual one, a problem of astronomy and observational technics and calculation. The question no longer has metaphysical meaning since it is perfectly certain that, be the stars far or near, they are, like ourselves and our sun, in the midst of other stars without end.
It is exactly the same concerning the problem of the constitution of the stars. This, too, becomes a purely scientific, factual question. The old opposition of the earthly world of change and decay to the changeless world of the skies which, as we have seen, was not abolished by the Copernican revolution, but persisted as the opposition of the moving world of the sun and the planets to the motionless, fixed stars, disappears without trace. The unification and the uniformization of the universe in its contents and laws becomes a self-evident fact23"The matter of the sky and of the earth is one and the same; and there cannot be a plurality of worlds"at least if we take the term "world" in its full sense, in which it was used by Greek and mediaeval tradition, as meaning a complete and self-centered whole. The world is not an unconnected multiplicity of such wholes utterly separated from each other: it is a unity in whichjust as in the universe of Giordano Bruno (it is a pity that Descartes does not use Bruno's terminology)there are an infinite number of subordinate and interconnected systems, such as our system with its sun and planets, immense vortices of matter everywhere identical joining and limiting each other in boundless space.24
The infinity of the world seems thus to be established beyond doubt and beyond dispute. Yet, as a matter of fact, Descartes never asserts it. Like Nicholas of Cusa two centuries before him, he applies the term "infinite" to God alone. God is infinite. The world is only indefinite.
The idea of the infinite plays an important part in the philosophy of Descartes, so important that Cartesian-ism may be considered as being wholly based upon that idea. Indeed, it is only as an absolutely infinite being that God can be conceived; it is only as such that He can be proved to exist; it is only by the possession of this idea that man's very naturethat of a finite being endowed with the idea of Godcan be defined.
Moreover, it is a very peculiar, and even unique, idea: it is certainly a clear and positive onewe do not reach infinity by negating finitude; on the contrary, it is by negating the infinite that we conceive finiteness, and yet it is not distinct. It so far surpasses the level of our finite understanding that we can neither comprehend nor even analyse it completely. Descartes thus rejects as perfectly worthless all the discussions about the infinite, especially those de compositione continui, so popular in the late Middle Ages, and also in the xviith century. He tells us that:25
In this way we shall avoid the Keplerian objections based upon the absurdity of an actually infinite distance between ourselves and a given star, and also the theological objections against the possibility of an actually infinite creature. We shall restrict ourselves to the assertion that, just as in the series of numbers, so in world-extension we can always go on without ever coming to an end:28
The Cartesian distinction between the infinite and the indefinite thus seems to correspond to the traditional one between actual and potential infinity, and Descartes world, therefore, seems to be only potentially infinite. And yet . . . what is the exact meaning of the assertion that the limits of the world cannot be found by us? Why can they not? Is it not, in spite of the fact that we do not understand it in a positive way, simply because there are none? Descartes, it is true, tells us that God alone is clearly understood by us to be infinite and infinitely, that is absolutely, perfect. As for other things:27
But it is hard to admit that the impossibility of conceiving a limit to space must be explained as a result of a defect of our understanding, and not as that of an insight into the nature of the extended substance itself. It is even harder to believe that Descartes himself could seriously espouse this opinion, that is, that he could really think that his inability to conceive, or even imagine, a finite world could be explained in this way. This is all the more so as somewhat farther on, in the beginning of the third part of the Principia Philosophiae, from which
the passages we have quoted are taken, we find Descartes telling us that in order to avoid error,28
The second of these necessary precautions is that,29
which seems to teach us that the limitations of our reason manifest themselves in assigning limits to the world, and not in denying outright their existence. Thus, in spite of the fact that Descartes, as we shall see in a moment, had really very good reasons for opposing the "infinity" of God to the "indefiniteness" of the world, the common opinion of his time held that it was a pseudo-distinction, made for the purpose of placating the theologians.
That is, more or less, what Henry More, the famous Cambridge Platonist and friend of Newton, was to tell him.