Modern Science and Its Philosophy

Philipp Frank

CHAPTER 13

the philosophic meaning of the Copernican revolution

In 1543, four hundred years ago, Copernicus died. This year was in a certain sense also the year of the birth of the Copernican system. His great book, "The Revolutions of the Celestial Bodies," [1] was published in the same year. When this book was published, nearly fifty years had passed since Columbus discovered America. This event was one of Copernicus' starting points. He refers in one of the first pages of his book to this discovery as the final proof of the spherical shape of the earth. (Incidentally, he does not mention Columbus and says, as a matter of course, that "America is named after her discoverer.") The earth was now definitely a globe, and, to speak in terms of today, "global thinking" could begin.

To understand a phenomenon means to interpret our present experience as the repetition of a similar phenomenon of the past. This is true in science, but it is true as well in history. Today, we understand the French Revolution better than our parents did because we are contemporaries of the Russian revolution, and we understand the Copernican revolution better than nineteenth‑century scientists did because we are contemporaries of the Einsteinian revolution.

Let us formulate the central problem of all philosophy of science in the simplest possible terms. We have to face two worlds: on one hand, that of our sense observations, such as, in astronomy, the observed [216/217] positions of the stars in the sky; on the other hand, that of the general principles of science, such as the law of gravitation and the principle of relativity. To what extent are these general principles justified by those sense observations?

This sounds simple enough, but to appreciate the immense gap between these two worlds means to start grasping the central problem of all philosophy of science. Unfortunately, the pedagogic effort of science teachers has been often directed towards camouflaging this gap. If, however, the very goal of science teaching is to help the students in the understanding of nature, the actual depth and width of that gap must be emphasized over and over again. The state of mind acquired by the average student of science as the result of inadequate training has been largely responsible for the failure to appreciate exactly the philosophic meaning of the Copernican revolution.

Only recently, under the violent impact of twentieth‑century physics, particularly the theory of relativity, have the eyes of science students been opened and has the meaning of the Copernican revolution become clear.

If we look into a typical textbook or listen to an average teacher, we learn that before Copernicus, men believed in the testimony of their senses, which told them that our earth is at rest, that the planet Jupiter traverses in twelve years a closed orbit on the celestial sphere and that this curve contains twelve loops. Finally, Copernicus recognized the fallacy of this testimony and proved that "in reality" our earth is in motion and that the planet Jupiter traverses "in reality" a smooth circle around the sun as center. Copernicus exposed the illusions of our senses. Human reason thus scored a clear victory in its struggle against naive sense experience.

This description of Copernicus' achievement seems to me, conservatively speaking, inadequate. The loops traced by the planets are by no means a sort of optical illusion and neither is the immobility of the earth. As a matter of fact, the planet Jupiter actually traverses every year a loop with respect to a system of reference that participates in the annual revolution of the earth. But the same Jupiter traverses just as truly every twelve years a smooth circle with respect to the system of [217/218] fixed stars. Neither the loops nor the smooth circle are results of our naive sense experience. They are two different diagrams representing one and the same set of sense observations. Therefore, the interpretation of Copernicus' achievement as a victory of abstract reason over naive sense experience is hardly justifiable.

However, we meet occasionally a second interpretation which says almost the opposite of the first one. The hard facts of our sense experience became more and more incompatible with medieval philosophy, which had its roots in speculative reasoning rather than in sense observation. Copernicus finally decided to overthrow the obsolete doctrines of Aristotle and Ptolemy and scored a victory for experience in its struggle against pure speculation. As a matter of fact, Copernicus was not particularly "tough minded," if we may use the famous phrase of William James to describe the empirical scientist as distinct from the "tender‑minded" believer in pure reasoning. No new facts had been discovered by Copernicus, which had forced him to abandon the geocentric doctrine. The astronomical tables calculated from the Copernican system were in no better agreement with the observed positions of the stars than the previous tables.

Therefore we have to start from the fact that the Copernican revolution meant neither a victory of reason over the illusion of our senses nor a victory of hard facts over pure speculation. To be sure, Copernicus invented a new pattern of description for our observations. His genius manifests itself in the beautiful simplicity of this pattern: he replaced loops by concentric circles.

Copernicus died in 1543. The Roman Holy Office did not utter an official judgment on the Copernican system until 1616, seventy‑three years after Copernicus' death. This Roman verdict will give us the best hint about the philosophic meaning of the Copernican revolution. For the verdict considered specifically the philosophic merit of the new system. The Copernican theory was called "philosophically foolish and absurd."

But not even Copernicus' greatest opponents ever doubted that his system meant a great advance in astronomy. The general opinion in these quarters was that the heliocentric system is "astronomically true," [218/219] or as it was sometimes phrased, "mathematically true,” but in any case “philosophically false" or even "absurd."

We have to do here with a conflict between two conceptions of truth. This conflict has existed through the ages and has created quite often a great confusion of mind. This double meaning of truth has never been dramatized so clearly as by the Copernican revolution and its repercussions. To understand and to evaluate this conflict is the great lesson we can learn from the history of the Copernican ideas.

The medieval philosopher St. Thomas Aquinas described very distinctly two different criteria of truth:

There are two ways to prove the truth of an assertion. The first way consists in proving the truth of a principle from which this assertion follows logically. In this way, one proves in physics the uniformity of the motion of the celestial spheres. The second way consists not in proving a principle from which our assertion can be derived but in assuming our assertion tentatively and in deriving results from it which can be compared with our observations. In this way one derives, in astrology, the consequences of the hypothesis of eccentrics or epicycles concerning the motion of celestial bodies. However, we cannot conclude in this way that the same assumptions cannot be derived, perhaps, from a different hypothesis also. [2]

If a statement of astronomy met only the second criterion, the agreement with observed facts, it was termed "mathematically true." Only if it met also the first criterion, that is, if it could be derived from an evident principle, was it recognized to be "philosophically true." Since Aristotle's physics was supposed to be derived from evident principles, to be philosophically true meant practically to be in agreement with Aristotelian physics.

As Copernicus had been anxious lest his system might not be philosophically true in this sense, he feared some hostility on the part of theologians who were strict believers in Aristotelian philosophy. He looked for advice on how to behave in this situation, and strange as it may seem to us, the Catholic churchman Copernicus asked a Lutheran theologian from Nuremberg how to avoid trouble. The Nuremberg scholar, Osiander, answered him in a letter of 1541: [219/220]

As for my part, I have always felt about hypotheses that they are not articles of faith but bases of calculation. Even if they are false, it does not matter much provided that they describe the observed phenomena correctly . . . It would, therefore, be an excellent thing for you to play up a little this point in your preface. For you would appease in this way Aristotelians and theologians, the opposition of whom you fear.

This advice meant precisely that Copernicus should not claim "philosophic truth" for his system but should be satisfied with a claim for "mathematical truth."

But Copernicus did not like this compromise. He claimed his system to be at least as philosophically true as the Ptolemaic system, and perhaps even more so. In this way a conflict flared up, the issue of which was a very subtle distinction. Was the Copernican doctrine a true description of the universe or was it merely an hypothesis which served for calculating the positions of the stars? And how did Copernicus himself look upon this question? Most of the scientists of today are accustomed to regard every theory as a working hypothesis only, and would hardly be prepared to give serious thought to that subtle distinction which is rather an issue of the philosophy of science. But if we go a little deeper into the logical structure of science, we have to recognize that, as a matter of fact, every scientific theory, of whatever period, had to meet the two requirements of a "true theory" which were already familiar to Thomas Aquinas. In reality, no theory was accepted merely because it was a good working hypothesis. In every period of the history of science a theory had to be in agreement with the general principles of physics. The physicists of the nineteenth century would hardly have admitted a theory that was in disagreement with the principle of conservation of energy.

For that reason, practically every theory has been a compromise between these two requirements. This is particularly true of the Ptolemaic system. We read and hear frequently that the Ptolemaic system was in agreement with the Aristotelian philosophy and physics. But Copernicus, we are told, disturbed this harmony and advanced a theory that would contradict explicitly the laws of medieval physics. This was certainly not the opinion of the medieval philosophers them [220/221] selves. One of the basic principles of medieval physics was the law that terrestrial bodies move in rectilinear paths toward or away from the earth while celestial bodies move in circular orbits with the earth as center, but the Ptolemaic system assumes that sun and planets traverse eccentric circles or epicycles the center of which is not the earth. Therefore, the Ptolemaic system could not be regarded as philosophically true, but at most as a hypothesis that might serve as a basis of calculation.

Thomas Aquinas judged the Ptolemaic system as follows:

The assumptions made by the astronomers are not necessarily true. Although these hypotheses seem to be in agreement with the observed phenomena we must not claim that they are true. Perhaps one could explain the observed motion of the celestial bodies in a different way which has not been discovered up to this time.

The twelfth‑century Arabian philosopher Averroes and his school emphasized very strictly the philosophical criterion of truth and declined to ascribe any truth value to the Ptolemaic system. Says Averroes:

The astronomers start from the assumption that these [eccentric or epicyclic] orbits exist. From this assumption they derive results that are in agreement with our sense observations. But they have not proved by any means that the presuppositions from which they started are, in turn, necessary causes of these observations. In this case, only the observed results are known but the principles themselves are unknown, for the principles cannot be logically derived from the results. Therefore new research work is necessary in order to find the "true" astronomy, which can be derived from the true principles of physics. As a matter of fact, today there is no astronomy at all, and what we call astronomy is in agreement with our computations but not with the physical reality.

The common opinion among philosophers was rather that the true picture of the universe cannot be discovered by the astronomer, who is restricted to finding out what hypotheses are in agreement with observed facts. If different hypotheses meet this requirement, science cannot decide which is true and, as the Jewish medieval philosopher Moses Maimonides puts it: [221/222]

Man knows only these poor mathematical theories about the heavens, and only God knows the real motions of the heavens and their causes.

It is certain, therefore, that before the Copernican revolution no theory of the motions of the celestial bodies existed that would meet both criteria of truth. There was in every theory a discrepancy between mathematical and philosophic truth. Against this background we have to interpret the famous dedication letter which Copernicus published as a preface to his great book and in which he recommended his work to the good will of Pope Paul III.

Copernicus affirms that he did not advance his new theory of the motions of the heavens in a spirit of opposition against the established doctrine. His only motive was his conviction that there was no established doctrine. The hypothesis of a circular motion of planets around the earth as center did not account for the observed facts, and the hypotheses of eccentrics or epicycles were not in agreement with the general principles of physics which required uniform circular motions around the earth as center. Since no doctrine existed which could be regarded as "true" from the philosophic as well as from the mathematical angle, Copernicus felt free to suggest a new hypothesis assuming the mobility of the earth.

This hypothesis accounted for the observed motions nearly as well as the Ptolemaic theory of epicycles, but removed some of the epicycles. The motions of the planets became now circular orbits around the sun as center, except for the epicycles which were necessary to account for the inequalities in the motion of planets. In any case there were fewer epicycles and more homocentric orbits in the Copernican, than in the Ptolemaic, system. Therefore Copernicus claimed that his theory was in some sense nearer to the requirements of Aristotelian physics than was the geocentric system. The Ptolemaic system was a compromise between the two criteria of truth. Copernicus claimed that his system was in the same sense a compromise and, as he believed, a better one.

In any case, Copernicus claimed to give in his theory a true picture of the universe, true in every sense of the word. By a strange coincidence. Copernicus' book was edited by the same Osiander of Nuremberg whose advice Copernicus did not like to follow. We understand [222/223] now the famous words of the editor's preface, which had been originally ascribed to the author himself but which reflect only the editor's opinion:

The hypotheses of this book are not necessarily true or even probable. Only one thing matters. They must lead by computation to results that are in agreement with the observed phenomena.

While Copernicus tried to achieve the compromise by arguing that his theory is to a large extent in agreement with the principles of Aristotelian physics, Galileo Galilei, in his famous Dialogue on the Copernican and Ptolemaic Systems of the World, went a good deal further in the overthrow of medieval science. He no longer attempted to reach the compromise by adjusting his working hypotheses to the requirements of the established principles of physics. On the contrary, he ventured to adjust the principles of physics to the best suitable working hypotheses. This meant dropping the bulk of Aristotelian physics and starting a movement in science that led in time to the philosophy of science which we would call today positivism or pragmatism. The two criteria of truth which were for medieval thinkers like St. Thomas Aquinas two distinct requirements, have fused more and more into one single requirement: to derive the best description of the observed phenomena from the simplest possible principles, while these principles are justified solely by the fact that they permit this derivation.

Galileo's ideas were not brought into a coherent system of propositions until Isaac Newton advanced his celebrated laws of motion in his Mathematical Principles of Natural Philosophy. This book appeared in 1687, approximately 150 years after the Copernican revolution. From the Newtonian principles the Copernican doctrines could be logically derived. Therefore, to the believer in these principles, the Copernican system was now true in the full sense of the word, philosophically and mathematically true.

Let us now ask, What did the Copernican hypothesis look like when it was derived from the Newtonian principles? It said that the earth is rotating with respect to absolute space and that the planet Jupiter traverses smooth circular orbits with respect to absolute space. But [223/224] Newton himself was very well aware that "motion relative to absolute space" has, to use P. W. Bridgman's term, no operational meaning, that is, that by no physical experiment can the speed of a body in rectilinear motion with respect to absolute space be measured.

Therefore, the Newtonian system of principles is not a logically coherent system within the domain of physics. Newton himself restored logical coherence by enlarging his system of physical statements by the addition of some theologic propositions. As we read in Burtt's book on the Metaphysical Foundations of Modern Physical Science:

Certainly, at least God must know whether any given motion is absolute or relative. The divine consciousness furnishes the ultimate center of reference for absolute motion. Moreover the animism in Newton's conception of force plays a part in the premises of the position. God is the ultimate originator of motion. Thus real or absolute motion in the last analysis is the expenditure of divine energy. Whenever the divine intelligence is cognizant of such an expenditure the motion so added to the system of the world must be absolute.

Under the influence of the spirit of the eighteenth century the mixing of theology into science began to be regarded as illegitimate. Strange as it may seem, by the abandonment of theologic argument the Newtonian physics lost logical coherence. Burtt says very correctly:

When in the twentieth century Newton's conception of the world was gradually shorn of its religious relations, the ultimate justification for absolute space and time as he had portrayed them disappeared and the entities were left empty.

Therefore the new principles of physics from which the Copernican theory could be derived were far from being satisfactory. The "philosophic truth" of the Copernican system was still a doubtful thing.

Toward the end of the nineteenth century, Ernst Mach exposed very specifically the logical incoherency of the Newtonian mechanics as a purely physical system. He claimed on good grounds that the principles from which the Copernican system was derived are essentially theologic or metaphysical principles. Mach claimed in the nineteenth century, as Averroes had done in the period of the Ptolemean [224/225] system, that we have no true astronomy, if "true" means "derived from a coherent system of principles of physics."

Mach asked for the removal of the concept of absolute space from physics and for a new physics which contains only terms which have within physics, to speak again with Bridgman, operational meaning.

This program, however, was not carried out until Einstein created his general theory of relativity and gravitation between 1911 and 1915. This theory, as a matter of fact, was the first system of purely physical principles from which the Copernican system of planetary motions could be derived. But the description of these motions looked now very different from the way it had looked as derived from Newton's principles. The concept of absolute space was no longer present. Therefore the statement of the rotation of the earth and of the smooth circular orbits of the planets had now to be formulated quite differently.

From Einstein's principles one could derive the description of the motions of celestial bodies relative to any system of reference. One could demonstrate that the description of the motion of planets becomes particularly simple if one uses the system of fixed stars as a system of reference, but there was still no objection to using the earth as system of reference. In this case, one obtains a description in which the earth is at rest and the fixed stars are in a rotational motion. What appears to be in the Copernican heliocentric system the centrifugal force of the rotating earth becomes in the geocentric system a gravitational effect of the rotating fixed stars upon the earth.

The Copernican system became for the first time in its history not only mathematically but also philosophically true. But at the same moment the geocentric system became philosophically true, also. The system of reference had lost all philosophic meaning. For each astronomical problem, one had to pick the system of reference that rendered the simplest description of the motions of the celestial bodies involved.

The reception of the Einsteinian revolution by the scientists of the twentieth century reminds us in many respects of the reception of the Copernican revolution by the scientists of the sixteenth century. This comparison might help us to understand the philosophical meaning of both. [225/226]

We may take as an example the way in which Einstein deals with the contraction of moving bodies in the direction of their motion. The verdict of quite a few twentieth‑century physicists was: the theory of relativity permits us to derive the observed phenomena from hypothetical principles but it does not give a physical explanation of the contraction. This was an exact repetition of the Roman verdict against the Copernican system. For the meaning was: the theory of relativity may be "mathematically true" but it is certainly "philosophically false." Now "philosophically false" meant not to be in agreement with Newton's principles of physics, while in the sixteenth century the same expression meant not to be in agreement with Aristotle's physics and Scholastic philosophy.

But what are the facts affirmed by the Copernican doctrine which are still accepted today as true? Copernicus enthusiastically proclaimed the sun as the center of the universe and said:

In the center of the Universe the sun has its residence. Who could locate this lamp in this beautiful temple in a different or better place than in the center wherefrom it can illuminate the whole of it simultaneously?

Even if we restrict the meaning of the word "universe" to our galactic system, the Milky Way, this universe is not spherical and the sun is not located in the center. It has been known for a long time that our galactic system has the shape of a lens. Before the distance of very remote stars could be estimated, it was plausible to believe that our sun, with our earth as attendant, is located in the center of this lens. However, in the twentieth century new methods were developed for estimating the great distances of remote stars, in large part by Harlow Shapley and his collaborators of the Harvard Observatory. In particular, Shapley found that our sun is not located near the center of that lens, but approximately 30,000 light years away from it. This means that the sun with our planetary system is near the edge of the lens. According to Copernicus, we inhabitants of the earth have no longer the great satisfaction of being the center of the universe, but we have at least the small satisfaction of being the attendant of a master who has his residence at this center. But according to Shapley, man [226/227] has lost all reasons for complacency. He is not even the attendant of a master who occupies the central stage of the universe.

Copernicus probably believed that the orbits of celestial bodies can be described in the best and simplest way by taking the sun as a body of reference. In our twentieth century, we know that this cannot be true universally. According to Einstein's theory of gravitation, there is no "all‑purpose system of reference." Copernicus' suggestion of using the sun is practical only if we restrict ourselves to the motions in our planetary system. For every particular purpose a particular system may be the most suitable.

Copernicus did not discover any new fact that could be regarded as established for all eternity. But he denied to the earth its former role as the only legitimate body of reference, be demonstrated that the sun is the most suitable system for a particular purpose, and he cleared the way for the great new truth that we have complete freedom in our choice of a system of reference.

The Copernican revolution did not end by replacing the earth as master of the Universe by the sun or by absolute space, but it was only the first step in a series of revolutions that culminated, so far as we know today, in depicting a democratic order of the universe in which all celestial bodies play an equal part.

Notes

1  De Revolutionibus Orbium Celestium. [—> main text]

2  Summa Theologiae. [—> main text]

SOURCE: Frank, Philipp. Modern Science and Its Philosophy. Cambridge, MA: Harvard University Press, 1949. Reprint: New York: George Braziller, 1955. Chapter 13, The Philosophic Meaning of the Copernican Revolution, pp. 216-227.

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