It would appear to be unnecessary to stress these points further, for they must appear obvious to those who are at all familiar with the achievements of science. Certain metaphysicians, however, hold that similar reconstructions should never endanger the traditional concepts of space and time. But an attitude of this sort is equivalent to removing the study of space and time from the control of experience; for all concepts which we approach empirically are necessarily subject to change as our experimentation increases in precision. Furthermore, if we adopt this attitude, why not go the limit and assert that the discoveries of the laboratory can be figured out a priori? The entire trend of modern science is hostile to the philosophy of the a priori. Non-Euclidean geometry undermined its foundations a century ago, and to-day the physical theory of relativity has completed the work. To assert in the name of logic or of reason, as so many philosophers have done, that space and time must be separate,[141] or that space cannot manifest variations of curvature from place to place,[142] or that space-time must always be flat,[143] or that matter must be a substance which is conserved, is to impose narrow philosophical doctrines which are likely to cramp the entire synthesis, rendering a simple scheme of natural relations impossible. To quote Weyl:
“Matter was imagined to be a substance involved in every change, and it was thought that every piece of matter could be measured as a quantity, and that its characteristic expression as a ‘substance’ was the Law of Conservation of Matter which asserts that matter remains constant in amount throughout every change. This, which has hitherto represented our knowledge of space and matter, and which was in many quarters claimed by philosophers as a priori knowledge, absolutely general and necessary, stands to-day a tottering structure. First, the physicists, in the persons of Faraday and Maxwell, proposed the ‘electromagnetic field’ in contradistinction to matter, as a reality of a different category. Then, during the last century, the mathematician, following a different line of thought, secretly undermined belief in the evidence of Euclidean geometry. And now, in our time, there has been unloosed a cataclysm which has swept away space, time and matter, hitherto regarded as the firmest pillars of natural science, but only to make place for a view of things of wider scope, and entailing a deeper vision.”
Summarising, we may say that in natural science it is essential to beware of fundamental premises which are claimed to be forced upon us by the requirements of logic or of crude perception.
Yet, on the other hand, it must be admitted that when we have succeeded in constructing some lofty scientific synthesis which takes in the facts of experience, our synthesis must always be such as to permit us to account for the facts of crude observation; for these, to the same extent as the results of ultra-precise experiment, constitute facts which must be co-ordinated. A theory such as Einstein’s must not go counter to the apparent separateness of space and time when phenomena are investigated only in the usual crude way by commonplace observation. In other words, the scientific synthesis must reduce to the primitive synthesis when too great accuracy is not imposed, so that the primitive synthesis must appear in the light of a first approximation. Einstein’s theory satisfies this general condition in every respect. As we have seen, for low velocities or for crude observation the classical separateness of space and time reasserts itself; hence no conflict exists between the relativity theory and commonplace observation. Similar conclusions apply to the classical addition of velocities. This also appears to be verified to a first approximation.
Now it might be contended that since all finality seems to be denied a scientific theory, it would be better to cease theorising and content ourselves with a bare accumulation of facts. But an attitude of this sort would be untenable, for scientific theories, though necessarily inaccurate from a long-range point of view, are nevertheless inevitable if knowledge is to exist. A bare accumulation of disconnected facts would not constitute a science, precisely because, the facts being disconnected, they would afford us no means of foretelling the future sequence of events. Under the circumstances, it is better to be guided by a faulty synthesis which we can improve upon as experience demands, rather than be guided by nothing at all. Furthermore, co-ordinations and theories which have since turned out to be patently inaccurate, have yet been successful in leading to the discovery of new facts.
Thus, Newton’s law, to-day recognised as inaccurate, brought about the discovery of Neptune; it permitted astronomers to assert that it was the same comet which reappeared at definite intervals. Again, it was thanks to Newton’s law that Römer, in 1675, discovered the finite velocity of light, thereby exploding the belief that the existence of an event and our perception of it were simultaneous occurrences. All these discoveries would have been arrived at by other means at some later date; yet it must be agreed that, owing to the law of gravitation, they were considerably precipitated. Indeed, it was not until the nineteenth century that the finite velocity of light was established by direct terrestrial measurement.
In other cases, a scientific theory, whether true or false, directs physicists towards crucial experiments of which they might never have thought. Eddington’s astronomical expedition was prompted by Einstein’s discoveries; had the theory been unknown, it is probable that the bending of light, when finally observed, would have been regarded as an error of observation or as due to some casual disturbing influence. Under the circumstances it might never have become a permanent scientific fact; and it is the same with the Einstein shift-effect. Regardless, then, of whether Einstein’s theory will endure or be scrapped to-morrow, it has led at least, to the discovery of new facts.
Furthermore, we must remember that each successive theory retains certain elements of the one it has supplanted. It rises to a higher plane, but it rises from a rung that has been set in position by its predecessor. It is not in the physical hypotheses that we shall find these elements of permanence, but in the equations themselves; for it is these that constitute the relations of reality. The physical hypotheses, as originally formulated, are but convenient scaffoldings of a more or less temporary nature. This is especially noticeable in the successive theories of electricity and magnetism. From the initial theories of Coulomb and Ampère to the present ones of Larmor and Lorentz, as modified by Einstein’s discoveries, we pass through the intermediary ones of Maxwell, Helmholtz and Hertz. We may follow the equations through these transformations and see how they were supplemented by the adjunction of additional terms or by the refinement of those already present. Thus, Maxwell’s equations differ from Ampère’s by the adjunction of a new term. Lorentz accepts Maxwell’s equation of the free ether without modification; it is only when matter is present that refinements are superadded. Again, Einstein’s gravitational equations degenerate into Newton’s when the field is weak and the velocities are small.
When we realise that all these successive refinements in the theories were brought about by a desire to co-ordinate an ever-increasing number of facts, it would appear that the scientist has very little control over the course his theory will follow, since in every case it is the criterion of simplicity of co-ordination which guides him.
However, it may be of interest to examine whether, in addition to these formal considerations, there may not exist other reasons which prompt scientists towards their solutions. It might be claimed that the various thinkers start from different initial philosophical presuppositions, and that these presuppositions, rather than the number of facts co-ordinated, are responsible for the differences in the nature of the theories and conclusions. Opinions of this sort have been expressed by numerous philosophers who have devoted their attention to what they call the “metaphysics of science”; but we may hasten to say that the opinion appears to be entirely unwarranted. It is solely the criterion of simplicity of co-ordination which decides on the orientation of science. Where the personal idiosyncrasies of the thinker may come into play will be in the directing of his initial attempts of co-ordination along certain lines rather than along others; but if a simple co-ordination is found to be impossible along the lines originally chosen, other attempts in totally different directions will be undertaken in due course. The final result may issue in a co-ordination presenting a philosophical import totally different from the one preferred originally; and this change is due to the facts of the case and not to a change in the philosophic fancies. Of course, it is not easy for the layman to realise this state of affairs, for scientists do not usually write a diary, mentioning all their abandoned attempts. When a theory becomes widely discussed, it is generally presented in its final form, and the numerous hesitations and partial attempts that may have extended over a period of years are lost sight of entirely. And yet, if we revert to the original scientific papers, these hesitations and changes of attitude are apparent.