With the discoveries of modern science, still other difficulties bar the route to success. It would now seem that as we wended our way into the microscopic, exact laws might vanish. If this be the case, the microscopic structures must ever elude us. Yet, even if we waive these latter difficulties, it is apparent that the scientific method can yield no knowledge of substance; the structure of reality is all we can approach.
But this reality, once again, is nothing but the expression of the simplest co-ordination of scientific facts; no genuine metaphysical reality is implied. If we discard the criterion of simplicity, we may conceive of our world in as many different ways as we please. Consider, for example, Einstein’s theory. One of the principal discoveries of the theory has been to disclose unsuspected relationships between space and time, leading to the four-dimensional space-time structure of the universe. And yet, if we wished, we might account for all of Einstein’s previsions while retaining our traditional belief in a three-dimensional structure of space and in an unrelated time. Thus, Michelson’s experiment would be accounted for by Ritz’s or Stokes’ hypothesis; Bucherer’s experiment, by the dragging along of a certain mass of ether by the moving electron just as a ship drags along part of the water surrounding it; Fizeau’s experiment, by a modification of the ether in transparent bodies (and this was, in fact, Fresnel’s original explanation). The double bending of a ray of light, and Mercury’s motion, would be accounted for by a modification of the Newtonian law of gravitation; the Einstein shift-effect, by a modification in the intra-atomic structure of the solar atom, and so on. It is a pure waste of time to consider the various hypotheses that might be suggested, for we can invent as many different ones as we choose. Needless to say, all the simple beauty and unity of nature revealed by Einstein’s theory would be lacking; and prevision would be impossible, seeing that new postulates ad hoc would be needed at all further stages. But when all is said and done, what have simplicity, beauty, unity and prevision to do with the reality of the metaphysician?
Thus the reality of structure which the metaphysician would defend (quite aside from the reality of substance) presupposes his a priori belief in the inevitable simplicity of nature. But simplicity is, after all, but an expression of human appreciation. Furthermore, even if this view were contested, there would seem to be no reason to suppose that nature should prefer simplicity to complexity in the first place. As a matter of fact, what little we know of nature proves that the reverse is true when we cease to view phenomena in an approximate macroscopic way and adopt a more microscopic standpoint. To illustrate: There is no more simple law in physics than that of perfect gases; and yet we know that this apparent simplicity is due to our macroscopic observations and that it conceals the most bewildering chaos and uncertainty. It is the same when we consider numerous other phenomena, such as intra-atomic changes.
From this it follows that it is at least a questionable procedure to identify reality with simplicity of co-ordination. And if we discard this tentative identification, reality (even reality of structure) escapes us completely. Of course, the type of reality which we have been branding as elusive is the absolute reality, the “true being” of the metaphysician. The scientist also appeals to the word “reality,” but he employs it in a different sense. For him, reality is identified with simplicity of co-ordination, and he states his views explicitly, realising full well that a reality of this type is far from being absolute and that it is essentially pragmatic. It is for reasons such as these that the vast majority of scientists are agnostics at heart, not on account of any a priori predilection, but because a proper understanding of the limitations of scientific knowledge leaves them no other alternative, refusing as they do to accept the knowledge of the mystic or the metaphysician as of any significance whatsoever. But scientific agnosticism must not be confused with that extreme form of idealism which denies the existence of any world apart from consciousness. It merely contents itself with stating that the objective world of science (that of space, time, matter, motion, in classical science, and of space-time, intervals and tensors, in relativity) is nothing but the embodiment of the simplest co-ordination of sense impressions, for which some unknowable supra-intelligible world is assumed to be responsible.
If, therefore, our minds worked differently, there would be no reason to assert that we should form the same conception of the world. We do not know whether, in the event of a Martian stepping down on earth, his mind would form the same mental construct of the universe as ours has done. For a Martian, there might be no such things as space, time and matter. Yet he might form a conception of the universe which would be perfectly intelligible to him. Those who believe in the metaphysical reality of space and time enduring in the world of things in themselves, under the plea that we can only conceive of existence in space and in time, appear to be guilty of the same error as those who, never having heard of fishes, would assert that no such creatures could exist, since they would be unable to breathe. Anthropomorphic arguments of this sort have no place in science.
In short, it is not denied that there may exist a world of things in themselves; all that is asserted is that a world of this sort defies all description. A few quotations from the writings of the leading men of science will make this attitude clearer. Thus, in Larmor’s book, “Æther and Matter,” we find: “Laws of matter are, after all, but laws of mind.” Again, in Poincaré we read: “Are the laws of nature, when considered as existing outside of the mind that creates or observes them, intrinsically invariable? Not only is the question insoluble; it is also meaningless. What is the use of wondering whether laws can vary with time in the world of things in themselves, when in a world of that type time may have no meaning? Of this world of things in themselves we can say nothing; we cannot even think of it. All we can discuss is how it would appear to minds similar to our own.” And, again, elsewhere: “The Bergsonian world has no laws. The world that may have laws is merely the more or less deformed image that scientists have conceived of it.” There is no need to give further quotations, for with slight variations the same philosophy is expressed by all scientists.
However, it cannot be emphasised too strongly that from a practical standpoint these questions are purely of academic interest. The physicist and the mathematical physicist are compelled to operate and reason as though they believed in the real existence of a real absolute objective universe, one of space and time, according to classical science; one of space-time, according to the theory of relativity. In fact, as we have said, were it impossible to conceive of a common objective world, one existing independently of the observer who discovers it bit by bit, physical science would be impossible.
Incidentally, we may recall that such problems as the relativity or the absoluteness of space and motion have nothing in common with idealism and realism. Space may be subjective, yet absolute, or real and yet relative. It is important not to confuse the meaning of the words, “absolute,” and “relative” as used by physicists, with their meaning as understood by philosophers. Much of the difficulty that philosophers appear to have experienced in understanding the attitude of science seems to have arisen from confusions of this sort.
Now, if we revert to that rational synthesis of our sense impressions which yields us the objective world of science, there remains to discuss the methodology whereby this synthesis is achieved. In the more elementary cases, the procedure is one of commonplace, logical and inductive reasoning; but in the more advanced cases, the process is exclusively mathematical. There is a close resemblance between the procedure of development pursued by pure mathematics and that of theoretical physics. In either case the tendency has been a search for unity through progressive generalisation.
Mathematics is, of course, so vast a subject that it is impossible to expose even its characteristic aspects in a few pages; but for the purpose we have in view it will be its generalising aspect which we shall mention. Mathematics deals with generalities. It seeks to obtain general laws and general theories as opposed to particular results. For instance, the sum of the first two odd numbers is found to equal the square of 2; the sum of the first three odd numbers is found to equal the square of 3. This, however, does not tell us what the sum of the first 10,000 odd numbers would be. We might proceed to add up these numbers and discover the result; but the aim of mathematics is to obviate a laborious undertaking of this sort. It succeeds in this attempt by demonstrating the existence of a mathematical law according to which the sum of the first