Einstein

by Philipp Frank

  Criticism of nineteenth-century physics in this direction was carried on chiefly by the French mathematician Henri Poincaré. His writings on the logical character of the general laws of nature probably exerted more influence on mathematicians and physicists toward the end of the nineteenth century than any other similar writings. He paved the way for a new, logically satisfying conception of nature, and his ideas also played an outstanding part in the reception and discussion of Einstein’s theories.

  Poincaré’s view is often described as “conventionalism.” According to him, the general propositions of science, such as the theorem about the sum of the angles of a triangle, the law of inertia in mechanics, the law of conservation of energy, and so on, are not statements about reality, but arbitrary stipulations about how words, such as “straight lines,” “force,” “energy,” are to be employed in the propositions of geometry, mechanics, and physics. Consequently one can never say whether one of those propositions is true or false; they are free creations of the human mind and one can only question whether these stipulations or conventions have been expedient or not.

  This conception may be elucidated by means of two examples. Let us first consider the geometrical theorem referred to above: namely, that the sum of the angles of a triangle is equal to two right angles. According to nineteenth-century tradition this is an unshakable proposition, which is a product of human reasoning and at the same time a statement concerning what is actually observed in nature. On the one hand, we can derive this proposition from the axioms of geometry, which are “directly evident to the mind”; on the other hand, by measuring the angle of an actual material triangle, we can corroborate this relationship. Poincaré, however, says: if an actual triangle is formed from, say, three iron rods, and the measurement shows that the sum of the angles is not exactly equal to two right angles, one of two different conclusions can be drawn: either that the geometrical theorem is not valid, or that the rods forming the triangle are not straight lines. We have the two alternatives, and we can never decide by experiments the validity of geometrical theorems. Consequently we can say that the propositions of geometry are arbitrary stipulations or definitions and not statements about empirical facts. They establish under what circumstances we wish to call a rod a “straight line.” Thus geometrical theorems are not statements about the nature of space, as it is often expressed, but rather definitions of such words as “straight lines.”

  According to Poincaré, the laws of mechanics are of somewhat similar character to the propositions of geometry. Let us, therefore, consider the law of inertia as the second example. The possibility of verification of the law rests on our ability to determine whether or not a body moves with uniform velocity in a straight line. As long as we cannot do this, the law of inertia can only be characterized in some such statement as this: “When a body moves without being influenced by forces, we call this state a uniform motion along a straight line.” It is simply a definition of the expression “uniform motion in a straight line,” or, according to our discussions in sections 3 and 4, a definition of the term “inertial system.”

  Thus the general principles, such as the theorem about the sum of the angles of a triangle or the law of inertia, do not describe observable phenomena, but are rather definitions of expressions such as “straight line” or “uniform motion along a straight line.” One has to add definitions by which one recognizes whether a given rod is straight or the motion of a ball is uniform and along a straight line and which have been named “operational definitions” by P. W. Bridgman. These, together with the physical laws (e.g., the law of inertia), constitute a a system of propositions that can be verified by experience.

  One of the chief consequences of this conception is that it makes no sense in science to inquire into the philosophical significance or the “nature” of such physical expressions as “force,” “matter,” “electric charge,” “duration of time,” etc. The use of such concepts is always justified if statements permitting experimental verification can be derived from the propositions in which these expressions occur. Apart from this they have no meaning. Because Newtonian mechanics was able to describe very complex phenomena such as the motion of the planets in simple statements with the aid of the words “force” and “mass,” these terms have scientific meaning. There is no need to puzzle one’s brain over whether “force” can be explained from a “mechanistic” standpoint or “matter” from an “organismic” one. “Force” and “matter” are constructions of the human mind.

  10. Positivistic and Pragmatic Movements

  The idea of Mach that the general laws of science are simple summaries of experimental facts, and the idea of Poincaré that they are free creations of the human mind, appear to be diametrically opposed to each other; but when we consider the intellectual currents of the last quarter of the nineteenth century, we can see that they were only two wings of the same intellectual movement, generally known as the positivistic movement. It was directed chiefly against the metaphysical foundations of science. The proponents of this view asserted that the validity of the general principles of science cannot be proved by showing that they are in agreement with some eternal philosophical truths, and they set out to investigate how the validity can be judged within science itself. They found that two criteria are possible, an empirical and a logical. In the former the observable facts that follow from the general principles must have experimental confirmation, and in the latter the principles and operational definitions must form a practical and consistent system. The emphasis put on the empirical or the logical criterion determined one’s position in one or the other wing of the movement. Mach was on the extreme empirical wing, while Poincaré was on the extreme logical side. There was therefore no conflict between them; it was only that two different aspects of the same scientific method were being emphasized.

  The positivistic movement exerted a great influence in central and western Europe during the last quarter of the nineteenth century. The central European positivism, chiefly centered in the Austrian Ernst Mach, was to be found in the universities of Vienna and Prague. It had but little influence and few followers in the universities of the German Reich. At this time Germany was completely under the influence of various versions of Kantian philosophy, whose status was almost that of a state religion. Since German was also the chief language of science in Austria, Central European positivism developed largely as the critic and rival of Kantian philosophy. For this reason it was more militant than French positivism, led by Poincaré.

  About this time there appeared independently in the United States a movement that is related to European positivism in its chief line of thought. In 1878 C. S. Peirce published an essay on the logical character of scientific statements. Like Mach and Poincaré, he pointed out that the meaning of general statements cannot be derived from agreement with still more general metaphysical truths, but must be drawn from the observed facts that follow from them. In contrast to the European positivists, however, Peirce emphasized particularly the role of propositions as the basis for our actions. He therefore called his doctrine “pragmatism.” “The essence of a belief,” he said, “is the establishment of a habit, and different beliefs are distinguished by different modes of action to which they give rise.” Like Mach, Peirce also warned against the trivial metaphysics that we have imbibed with our education since childhood. He said: “The truth is that common sense or thought as it first emerges above the level of the narrowly practical is deeply imbued with that bad logical quality to which the epithet metaphysical is commonly applied.” He also emphasized that words such as “force” are only expedients for the representation of facts and that every question as to their “actual nature” is superfluous and useless. In the same article he said:

  “Whether we ought to say that a force is an acceleration or that it causes an acceleration is a mere question of propriety of language which has no more to do with the real meaning than the difference between the French idiom ‘il fait froid’ a
nd the English equivalent ‘it is cold.’ ”

  An approach very similar to that of Mach was manifested by John Dewey in his first scientific article: “The Metaphysical Assumptions of Materialism,” published in 1882. Dismissing the opinion that the reduction of all phenomena to the motions of material bodies is an explanation of nature, he said:

  “First, it assumes the possibility of ontological knowledge, by which we mean knowledge of being or substance apart from a mere succession of phenomena.… Secondly, it assumes the reality of causal nexus and the possibility of real causation. In declaring that matter causes mind it declares that the relation is one of dependency and not one of succession.”

  The struggle against materialism here is not carried on in the service of an idealistic philosophy, as with the average professors of philosophy in European and American universities, but entirely along the lines of central European positivism, which opposed mechanistic physics on the ground that it is not a sufficiently broad basis of science.

  American pragmatism since then has developed into a powerful movement, finding its most characteristic expression in John Dewey and William James. It has devoted itself more to the problems of human life than to the logic of the physical sciences, in contrast to the development of positivism in Europe. Considered from the purely logical point of view, however, the basic tendency was the same on both sides of the Atlantic. The medieval idea of a philosophical explanation in contrast to a practical representation of facts vital to life lost prestige to an ever increasing degree. From a logical basis of science, metaphysics developed into a means of satisfying emotional needs.

  11. Science at the End of the Nineteenth Century

  During the golden age of mechanistic physics it was generally felt that outside of its application lay the realm of the unknowable and the unintelligible, since “to understand” meant “to represent by analogy to a mechanism.” In 1872 the German scientist Du Bois-Reymond, in his famous lecture on “Die Grenzen des Naturerkennens (The Limits of Our Knowledge of Nature)” took as his point of departure the assertion, then regarded as self-evident, that “understanding” means “reduction to the laws of Newtonian mechanics.” He indicated two important problems of science that can certainly not be reduced to mechanics. These are, first, the problem of what “actually occurs in space where a force is acting” and, secondly, how it happens that “matter in the human brain can think and feel.” Since the answers to these questions can obviously not be obtained within the framework of mechanistic physics, he concluded that there are “insoluble problems” that are inaccessible to human knowledge. To these questions we should say “ignorabimus” (“we shall never know”) instead of “ignoramus” (“we do not know”). This word “ignorabimus” became the slogan of an entire period, the slogan of defeatism in science, which delighted all anti-scientific tendencies of the period. Toward the end of the nineteenth century more and more facts became known in physics and biology that could not be explained or controlled by means of the laws of mechanics, with the result that the catchword “ignorabimus” was soon converted into the even more exciting slogan, “the bankruptcy of science.”

  This feeling of the failure of rational scientific thought was intensified by various social developments. Science — that is, science guided by the spirit of mechanistic physics — had led men during the eighteenth and nineteenth centuries to believe in the possibility of continual progress. If men only acted according to the teachings of science instead of irrational superstitions, mankind would be freed from all need. The political expression of this faith was liberalism. Toward the end of the nineteenth century, however, it became ever clearer that the attempts based on science and the faith in progress had not succeeded in abolishing the economic misery of the great mass of the population, or in eliminating the psychological suffering of individual human beings. A feeling of despair developed which expressed the conviction that scientific theory and practice were a disappointment. Alongside liberalism, new political currents developed that had their own conceptions of science, conceptions differing from the mechanistic view. One tendency propagated a return to the organismic science of the Middle Ages, and from it developed the authoritarian socialism that became the germ-cell of later fascism in all its varieties. Another movement, represented by Karl Marx, wanted to transform “mechanistic” materialism into “dialetical” materialism, and from it developed the communism of the twentieth century.

  It was impossible to deny that science was still the basis of technological progress, but it was believed that it could be disparaged by speaking of it as the church did about the Copernican system of the world: that mechanistic natural science provided only a useful guide for action, and no true knowledge of nature. Around 1900 Abel Rey, a French philosopher and historian of science, gave a very acute and trenchant description of the dangers for general intellectual life entailed by such an attitude of despair. He said:

  “If these sciences which have had an essentially emancipating effect in history go down in a crisis which leaves them only with the significance of technically useful information but robs them of every value in connection with the cognition of nature, this must bring about a complete revolution. The emancipation of the mind as we owe it to physics is a most fatally erroneous idea. One must introduce another way, and give credit to subjective intuition, to a mystical sense of reality.”

  There have been two ways out of this crisis of science which had developed in consequence of the breakdown of mechanistic physics. In his book The Idealistic Reaction against Science, Aliotta, an Italian, described the situation in the following very striking manner:

  “Could thought rest easy in this complacent agnosticism? There were two ways of escaping this intolerable situation: either to turn to the other function of the mind (besides intellect) or to eliminate the problem altogether by proving that it is due to a faulty perspective and false conception of science. Both ways have been tried. On the one hand, by a return to the moralism of Fichte and the æstheticism of the romanticists, into which the rebellious genius of Nietzsche has breathed new life, the will as the creative source of all values and of unfettered æsthetic intuition is exalted above intelligence. On the other hand, the bases of the mechanical conception and its chief instruments — geometrical intuition and mathematical calculation — are subjected to a searching examination. This analysis, to which men of science themselves were impelled by the discovery of the new principle of energy and by metageometrical concepts, resulted in stress being laid upon the active work of the mind in the construction of scientific laws and theories.”

  The second alternative mentioned here was the view taken by the advocates of positivism and pragmatism. Their way out of the “bankruptcy of science” was to proclaim that mechanistic science had formulated the problem in a manner that necessarily led into a cul-de-sac; it had not correctly defined the goal of science. The unattainable something, for which the despairing solution of “ignorabimus” was proposed, had been recognized as a phantom, a chimera that has nothing to do with science. Through an analysis of the really successful methods of science, men such as Mach and Poincaré in Europe, and Peirce and Dewey in America, have shown that it is of no significance whatsoever whether observations are presented in terms of a certain preferred analogy. All that matters is that the statements of science are useful; the specific language and the equation by which they are formulated do not matter. Thus with the goal of science defined in the positivistic and pragmatic sense, it becomes evident that the end of the nineteenth century does not represent a crisis, but rather one phase of the gradual progress of science toward its goal, which is the creation of an instrument for predicting and controlling the phenomena.

  In a certain sense this positivistic-pragmatic movement, so characteristic of the turn of the century, belonged to the group of movements that were directed against the overestimation of the role of the intellect. Professor Ralph Barton Perry very correctly said:

  “Much the mo
st sophisticated form of anti-intellectualism and at the same time the form most characteristic of our age is that form which has now come very generally to be called ‘instrumentalism’ and which is represented at present by the school of James and Dewey in America.… According to this view the intellect instead of being an oracle is a practical instrument to be judged by the success with which it does work.”

  Nevertheless, the new movement, no matter whether it was called pragmatism, positivism, or instrumentalism, could be characterized as anti-intellectual only in so far as it warned against occupying the intellect with meaningless problems. The adherents said that the intellect is unable to discover the metaphysical reality behind phenomena. But this is not a diminution of its role, since to speak of such a metaphysical reality does not make sense for science. It is sterile and leads only to confusion. The creation of an “instrument,” which is now what is meant by “science,” can be accomplished only by means of the intellect, even though we cannot produce a blueprint for discovering general principles. The discovery of laws such as the energy principle or the law of inertia is the work of a genius, like the composition of a symphony. But when the general law has been enunciated, it is then the function of the methodically proceeding intellect to make its meaning clear to all. Only the intellect can test the principle and pronounce judgment on its truth — that is, whether it is of value in realizing the aims of science.

  So ends the nineteenth century. Its faith in the ability of science to reveal the ultimate reality behind phenomena was shaken; but in its place appeared the sober consolation of positivism that science had become more flexible and girded for new tasks of a boldness never dreamed of. During the twilight period characterized by a devaluation of the intellect and an increased regard for action, there appeared, like a silver glow on the horizon, the hope that a more acute logical analysis would give an entirely new form of science based on a methodically operating intellect. The twentieth century ushered in this dawn.