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7. Descartes, Newton, Leibniz, Kant

These lectures have something like a circular structure. The general question about scientism led us to the question of the origin of scientism in history. For this narrower question I used Bentley’s sermons and Kant’s theory as a starting point. This brought me to the question of the relationship between myth and science, a question that induced me to take my starting point in history in the very early times of genuine myths. Having trodden the path of historical development we are to reach Bentley and Kant again in this lecture. Thus a first, greater circle will be closed today. But I shall pass by the meeting point, adding another smaller circle on the scientific cosmogony of our own time. It will lead us back to today’s scientism, thereby transforming the travelled path into the shape of the figure 8.

To make a scientific cosmogony possible, heaven and earth had to be brought together under a common natural law. This was Newton’s achievement. But as often happens, the question was first brought to the full consciousness of the république des savants by a premature answer. We must glance at this answer, which is the system of René Descartes.

Descartes offered an explanation of the planetary motions by his famous theory of the vortices. The planets are floating in an enormous eddy of very thin matter that moves around the sun. They are carried by it like pieces of cork in water.

This theory has the great advantage of answering precisely those questions about the celestial system which are not answered by Kepler’s laws. According to Kepler’s first law the planets move in ellipses, the sun occupying one focus of the ellipse. This leaves open two questions:

  1. An ellipse can be nearly circular or very long-stretched or anything between these extremes. The orbits of the planets are not exact circles but very nearly so; their eccentricities are very small. Is there any reason for that?
  2. Since the ellipse is a plane curve, the orbit of each planet defines a plane going through the sun. Kepler’s law would not exclude these planes all stretching in different directions. Actually they are nearly identical. All planets move nearly in the same plane, and they all move in the same direction; they have the same axis and sense of revolution. The intersection of this common plane and the imaginary sphere of the sky is the great circle called the zodiac. Why do the planets follow this well-ordered pattern of motion?

In Descartes’ view the explanation is obvious. The great eddy going around the sun has a unique axis of its rotation. The common plane of the planetary motions is the plane perpendicular to it and going through the sun. In this plane all the planets are carried in the same direction in the circular orbits prescribed by the eddying thin fluid in which they swim. Again, since these fluid motions are never quite precise, the slight deviations from the common plane and from the circular shape are not surprising.

This picture is not too different from the picture drawn by the Greek atomists 2000 years before Descartes. Their solid spherical sky, the “skin” as they called it, is now replaced by the fluid extending through space, in order to account for the known differences of distance of the planets from the earth; some assumption of this sort would have been necessary even to reconcile the view of the atomists with the Ptolemaic astronomy. Besides, the sun now takes the central position instead of the earth; Descartes is a Copernican, even if he uses diplomatically guarded language on this as on other dangerous points. But the eddy is there, the infinity of space is assumed again, and the fixed stars are understood to be suns similar to our own, surrounded by their own eddies, thus repeating the atomists’ view that there is an infinite number of systems, or worlds, as they call them. Then, the atomistic cosmogony can easily be resumed. Eddies can slow down, new eddies can originate, as we see it in every flowing stream. Thus our system has arisen once out of a newly-formed eddy, and Descartes tries to describe this process in details that no longer interest us. That these processes can go on for ever is assured by a law of nature stated explicitly by Descartes: the quantity of motion in the universe is a constant. This law ought to be considered as an attempt to formulate a principle corresponding to what we call the conservation of energy; although Descartes, not yet possessing the correct laws of mechanics which were discovered by Huygens and Newton, after his time, formulated his principle in an untenable way.

Thus all the ingredients are ready for a world infinite in time in which cosmogony just means the origin of an ordered partial world like ours. The Christian concept of creation seems unnecessary if we do not want to say that God, being beyond time, created infinite time with the world. But Descartes tells us that the world has been made by God in time, and that God then gave it just that quantity of motion which is still present in it. He even says that he willingly submits to the teaching of the Church that God made heaven and earth and all the kinds of plants and animals individually within six days, and that his description of a different cosmogony only tends to show how God might have made the world in a different way, had he not chosen to do it as the Bible tells us. Here we easily recognize the diplomacy of a man who was resolved not to suffer Galileo’s fate. The only difficulty is to know the boundary between his sincere views and his diplomacy. I think that he believed sincerely in God since he needed the philosophical concept of God, and that he considered the Church to be a necessary and useful institution, and that for these reasons he wanted not to attack but to convince the Church; but that he was not in any serious way concerned about Christ and about faith, hope, and charity, being a Stoic rather than a Christian. Whether or not he believed in an infinite duration of the universe, I am unable to say.

He was certainly sincere in another aspect of his system, and this aspect is modern in a strange manner. He thought he had done better than all his predecessors by having erected a strictly consistent system of thought of an intuitive clearness corresponding to that of mathematics. I can only indicate the structure of this system in a few sentences, using his cosmology as a starting point for an analysis that works backwards from the achieved system to its basic ideas.

Although his cosmology follows the atomistic pattern he denies the existence both of atoms and of empty space. Matter to him is continuous. Hence he claims to deduce the existence of the eddies; if continuous matter, which is described by him in terms that would correspond to the more recent concept of an incompressible fluid, is to move at all, the only motions which will not stretch into infinity recur in closed curves: they are eddies. That matter must be continuous follows from his denial of any distinction between matter and space; in his view matter and space are identical. This again follows from his view that nature can be described completely in terms of mathematics. The only discipline of pure mathematics that can be applied to extended things is geometry. Hence matter can have no properties besides the geometrical ones; matter is extension and nothing else. That nature should be described by mathematics again follows from the idea that all true knowledge must be clear and distinct, which is the case with mathematics but not with sense-perception. Only clear and distinct knowledge, in fact, is guaranteed to be true by the reliability of the all-wise and all-bountiful God who created us; assent to apparent knowledge that is not clear and distinct is a misuse of our free will. The existence of the all-perfect God can be proved strictly out of the existence of the idea of an all-perfect being which is present in my own mind, and this proof is necessary to overcome the doubt to which every belief can be subjected with the exception of my own existence, which is proved by my very doubting.

I shall not insist on the flaws in this deduction that have become more and more evident by the criticism of three subsequent centuries. Descartes’ system will always remain important as the symbolic expression of modern man who is certain of nothing but of his ability to say “I” in a meaningful way, and who wants to assert his autonomy with respect to all existing things. He still needs the omnipotent God for his proof that science is trustworthy; but he no longer needs God within science. Nature is satisfactorily described by geometry.

But if we go on to the details that interest us here, the failure of this titanic attempt to do all the work of modern science in one man’s life stands out in a pathetic manner. Descartes wanted to prove the truth of his system with mathematical rigour, and he was not even able to explain the one mathematical fact known about the planets in his time: Kepler’s laws. The eddy explains why the planetary orbits are nearly circular, but it does not explain why they are precisely elliptical. Newton was able to explain precisely that, and hence he completely rejected Descartes’ eddies.

I shall not repeat here the details of Newton’s explanation of the planetary motions. In general terms they are well-known and in mathematical rigour they are not easy even for a physics undergraduate of our days. But I want to point out the conceptual structure of Newton’s physics. If we want to explain any motion of bodies, like that of the planets, three things, according to Newton, must be known:

  1. The general laws of motion.
  2. A special law of force.
  3. The particular initial conditions.

The general laws of motion have been given by Newton in the beginning of the Principia. The first law is the law of inertia, stating that a body which is not under the influence of a force will stay in its state of rest or of uniform rectilinear motion. The second law is Newton’s most important own addition: the change of motion is proportional to the force. This law is not too easily interpreted, but I shall leave its inherent problems aside. In modern mathematical language it states that the force produces an acceleration proportional to it, the acceleration being defined as the second derivative of position with respect to time. Since the law of inertia has shown that no force is needed for a change of position, it is most natural to assume that the force causes the change of velocity, or, as Newton says, of the quantity of motion.

Evidently this general law will be of practical use only if we know the force acting on a given body. Here is Newton’s second great contribution: the law of gravity. Gravitation is not the only force of nature, but according to Newton it is acting between any pair of bodies in the universe. From the law of gravitation, and using the general laws of motion, Newton was able to deduce Kepler’s laws. The essence of his explanation can be expressed in popular terms by saying: If the inertia alone were acting (i.e. if there were no gravity) the planet would move on uniformly in a straight line, and thus would leave the neighbourhood of the sun. If gravity alone were acting (i.e. if the planet had no initial motion of its own) the planet would fall into the sun. The actual orbit is a compromise of the two effects of inertia and gravity; gravity binding the planet to the sun, inertia keeping it from falling into the sun. In addition to explaining Kepler’s laws Newton was able to improve on them. Kepler’s laws follow strictly if there is just the sun and one planet. But the gravitational influence of the other planets disturbs the orbit of a planet, and these disturbances Newton was able to predict according to the observations with every desired degree of precision.

It is completely justifiable that Newton’s system, once it had come to be understood, impressed the public opinion of the coming centuries as the greatest work of natural science. Now for the first time natural science had achieved what was done in Greek mathematics: it had deduced statements which proved true in every detail, from a few clear and simple axioms. It is not surprising that an explanation of nature was considered for two centuries to be a reduction of observed phenomena to the principles discovered by Newton.

But, strictly speaking, Newton had not even achieved a complete reduction of the observed planetary motions to his own principles, and he knew it very well. Newton was on the line of Kepler. He was able to explain and to improve on Kepler’s laws, a thing Descartes had been unable to do. But Newton, on the other hand, could offer no explanation of those facts that were explained satisfactorily by Descartes’ eddy: the nearly circular shape of the orbits and their common orientation in space. As I said before, three things must be known to explain a particular motion, the third being the particular initial conditions. Mathematically this is due to the fact that Newton’s laws imply differential equations with respect to time. The force only determines the change of the motion. Hence the motion in a later moment of time will depend on the motion in an earlier moment as well as on the force. A planetary orbit is fixed only when the position and velocity of the planet at some particular time is given.

Thus particular initial values and directions of the velocities of the individual planets had to be assumed in order to explain the high regularity of the system which had seemed so natural to Descartes. If, say, the original motion of one planet had been perpendicular to the plane in which the other planets move, it would have gone on moving in a plane perpendicular to the plane of the other planets. Similarly, had its initial velocity been too great, too small, or not directed in the tangent of a circle around the sun, the planet would have moved in a more or less eccentric ellipse or perhaps even in a parabola or a hyperbola. Newton could point to examples for these other cases: the comets are moving through the same space as the planets but all with odd eccentric elliptical and hyperbolical orbits oriented in all directions. This was even his most cogent argument against Descartes: how could there be such different motions of celestial bodies through the same space if the motion in this space was governed by one huge vortex of continuous matter? We can be certain that there is no continuous medium in the solar system that would exert any appreciable influence on the motions of planets and comets.

But then the regularity of the system remains unexplained. We can just say: God has been pleased to arrange the initial motions of the planets in such a way that they would follow these highly regular circular co-planar orbits. That is what Newton actually said. And Bentley in his sermons transformed this thought into a proof of the existence of God, the proof from the gaps of science. Science explains Kepler’s laws, but it does not explain the initial conditions. But the initial conditions show a high regularity. Hence recourse must be had to the idea of an intelligent maker of the universe, of the demiourgos. It is true that Newton and Bentley considered the laws of nature to be ordained by God as well as the initial conditions. But the laws did not convince the sceptics of their divine origin; nature may just have laws of her own, depending on a God that made them. But where no laws of nature explain the order of nature, God must become manifest in his works even to the sceptic.

I said in the first lecture that in accepting this turn of the argument religion has already lost her case. I then pointed to the historical fact that the gaps of science are to be closed at some later date. We are to follow this development more closely. But now I should like to make use of the language I introduced in the lecture on Christianity. The concept of a nature obeying her own laws independent of the existence of God, seems to express precisely that post-Christian, secularized reality which I introduced there as a third element after nature and Christianity. Here equivocations must be avoided. The word nature then meant human nature as interpreted by Christianity, it meant the world of natural drives, of traditional institutions, of self-interpretation by myth. As I tried to point out when speaking of Galileo, the concept of exact mathematical laws of nature which was only dimly present in Greek thought gained far greater convincing power by means of the Christian concept of creation. Thus I think it is a gift of Christianity to the modern mind. Now we see how this inherited gift is used against the religion whence it came. And this killing of one’s own parent by the weapon inherited from him becomes more and more naive. Kepler was a sincere Christian who adored God in the mathematical order of the world. Galileo, and even more Newton, being a more religious man, were sincere Christians who were interested in God’s work. But while Galileo had still to defend his right to read God’s greatness in the book of nature, Newton had to defend his idea of nature as a book written by God. Modern scientists in general find it very difficult to think of a religious interpretation of natural law as anything but an additional tenet, probably mythical and certainly not logically connected with the concept of laws of nature. No good will and no religious fervour can reverse this development. Modern secularized reality can in fact be interpreted in terms that take no account of religion at all. Science does not prove the existence of God. This should never be forgotten by those who want to understand the modern world in religious terms. On the other hand it will be good to see that the tree on which this now floating seed of modern science has grown was Christianity; that it was a sort of Christian radicalism which transformed nature from the house of gods into the realm of law.

I shall go ahead to Kant’s cosmogony only by an intermediate step. The greatest contemporary and, in a sense, adversary of Newton was Leibniz; and in his philosophical outlook, the young Kant of the cosmogony follows the lines of Leibniz. The difference between Newton and Leibniz is probably most clearly seen in the letters exchanged between Leibniz and Samuel Clarke (who is there just Newton’s spokesman) during the last years of Leibniz’s life.

Leibniz there attacks Newton’s concept of absolute space. This concept has a long pre-history of its own. As I said in the fourth lecture, Greek philosophy and mathematics had no concept of an independent entity like Newton’s space. Plato’s chora is more like a matter than like space, the atomists’ kenon is somehow the non-existent, and Aristotle defines the topos, the place of a body, relative to the surrounding bodies, thus consciously avoiding the puzzling problem of a non-corporeal space. In a finite world every motion can be referred to the frame of the world itself. The idea of an infinite world made the question urgent: are position and motion only relative concepts, describing relations between bodies, or is there such a thing as absolute position and absolute motion? If this question is not answered, the law of inertia is meaningless, for how are we to know what we mean by uniform motion in a straight line if we do not know what is the frame of reference? Newton answered the question by his idea that there is an absolute space and an absolute time, which define absolute motion and hence the meaning of inertial motion. Under the aspects of physics I shall return to this idea and its criticism as given by Mach and Einstein, in the second series of lectures.

Leibniz opposed absolute space for philosophical reasons. What is the difference (thus we may briefly express his argument) between our actual world and a world that would result from it by transplanting everything ten miles without changing any relative positions; or between this world and a world which God would have created an hour earlier without changing any temporal relations? The two worlds cannot be distinguished. Hence, Leibniz says with an argument that might appeal to modern positivists, the two worlds are the same world. This means that absolute space and absolute time are nonsense. Now Leibniz’ principle of the identity of indiscernibles does not apply to cases where we are just unable to distinguish two things practically. He only says that things are identical which have exactly identical attributes. This, he maintains, however, is just the case of the two worlds. Clarke replies that since Sir Isaac Newton has proved the existence of absolute space the two worlds do have different attributes: their different positions in absolute space, and their different initial moments in absolute time. Leibniz retorts that God would not have had a sufficient reason to create the world rather here than there, and rather now than then, and that hence the principle of sufficient reason would have been violated in the creation if Newton were right. Clarke says that there is a sufficient reason for God’s having created the world here rather than there: God’s will. Leibniz thinks that Clarke has too low a notion of God, thinking that God, like man, can act wilfully; God’s will is always guided by God’s reason. Clarke on his side thinks that Leibniz has too low a notion of God, thinking that his own human reason can fathom the depth of God’s reasons for his decisions. Leibniz died before his final reply.

Leibniz here argues along the lines of his theodicy. God had the choice between an infinite number of possible worlds. He created this world because it was the best of all possible worlds. This was the sufficient reason for his choice. It is the best world because of its order, and in principle everything in it must be understandable out of its optimality. Mathematical laws express this order on a certain level of universality; the structure of the planetary system expresses it in a great particular example, but the same considerations must be able, in principle, to explain both. This is the philosophical background to the earlier years of Kant.

What Kant tried in his cosmogonical theory was in fact to unite the virtues of Descartes’ cosmology with those of the science founded by Newton. Newton had proved that there was no vortex of continuous matter in the planetary system as we see it. Descartes, however, demonstrated that the motions of the planets show a regularity which might be explained by assuming such a vortex. Newton was unable to explain this regularity and said that God made the system like that long ago. This is not to be denied, but perhaps we can find out how God then made the system. Perhaps he made use of the Cartesian eddy? Kant does not expose his problem exactly in these words, but I think this is what he really achieves. In the beginning of the solar system there was, according to Kant, a large rotating nebula. Gravity made its main bulk condense in the centre, giving rise to the sun, and made parts of it condense in the outer regions, where they became the planets with their satellites. As to the origin of the first cloud Kant had ideas similar to those of the atomists and of Descartes, only he now applied Newton’s laws consistently. He understood correctly that the galaxy was a large disk, a system of stars to which the sun belongs, and he explained its development by applying the same argument on a higher level. He rightly interpreted some elliptical nebulae—we know today that most of them have a spiral structure—as being similar systems outside our own galaxy. He ended by speculations on evolution passing in infinite time through infinite spaces, and on possible inhabitants of other planets and their moral values, thereby charmingly fitting in with the 18th century frame of mind.

Mathematically Kant’s work is not more elaborate than that of Descartes. Forty years later Laplace proposed a similar theory in a simple and concise form, but still without attempting calculations about it which would, indeed, have been very difficult. Only then was Kant’s theory brought out of oblivion, and through the 19th century the theory of Kant and Laplace was considered to be the mechanical explanation of the origin of the world. Then for the first time the methods of science had advanced so far that a quantitative treatment of the problem could be tried. I shall say a few words in the ninth lecture about the varying views on the theory to which these calculations led. I may say now that astrophysicists of our days have come to think that Kant was right in principle.

Kant’s theology, as expressed in the preface of his book, is still more or less Leibnizian. Of course, in contrast to Leibniz, he now accepts Newton’s mechanics without any qualifications. But he thinks that God made the world by using his own laws of nature. The view that “blind necessity” can have produced the order we see in the system is repugnant to him. Theologically he can argue that the necessity of a law installed by God is not blind; the material agent may not know where it is led by necessity, but God knew where it would be led. Historically it may be added that the concept of blind necessity has its origin in a non-mathematical theory of nature, or, in Plato, is opposed to mathematics, while the natural laws of science are just mathematical laws, corresponding to reason. I think he is right in thinking that he argues according to the Christian idea of creation.

Yet in Kant’s own life this was not to be the final standpoint. In his later philosophy the mathematical structure which we find in science is no longer ascribed to God’s creation but to the a priori forms of intuition and categories of the perceiving and knowing mind. Reason itself prescribes the laws to nature. We no longer understand the order of God’s work because we are made in his image, but we understand the order of the phenomena because the phenomena of our experience have only become possible by the structure of the mind which experiences them. There is no longer a theoretical proof for the existence of God, neither in metaphysics, and neither by the gaps nor by the successes of sciences; the gaps are to be closed, and to explain the successes is the task of the Critique of Pure Reason. In this sense secularization has now reached the light of reason itself. Kant did not therefore cease to ask for God; on the contrary, this question can be understood to have been the impelling force behind all of his philosophy. Yet the weight of the question is transferred to the field of morality. In theoretical metaphysics the idea of God is now of regulative use only, and as such it influences science no longer in physics, but still in biology. According to the Critique of Judgment we can never hope to explain by physics the wonderful aspects of purpose in living organisms, and hence we must treat them, methodically, as though they were works of a purposeful divine reason. Thus Kant takes up the theme to which I shall devote the following lecture.

However, Kant was concerned till the end of his life with the explanation of the special laws of nature such as those which he used when in his youth he explained the origin of the planets. I think, it cannot be said that he solved this problem. I shall revert to Kant’s theory of experience in the second lecture-series. Here I had to mention it in order to show that the youthful Kant’s vindication of the Christian concept of creation against the inverted Platonism in Bentley’s argument was in itself ambiguous. In fact, Kant’s theory is a further step of secularization, whatever its author wanted it to be.

From the book: