It would be tedious to give illustrations; they abound everywhere. However, we may quote a few paragraphs of Einstein’s from his paper, “Cosmological Considerations on the General Theory of Relativity.” We shall see that he hesitated a long time between a number of alternatives before even considering the finite universe. We read:
“In the present paragraph I shall conduct the reader over the road that I have myself travelled, rather a rough and winding road, because otherwise I cannot hope he will take much interest in the result at the end of the journey. At this stage, with the kind assistance of the mathematician J. Grommer, I investigated centrally symmetrical gravitational fields, degenerating at infinity in the way mentioned. But here it proved that for the system of the fixed stars no boundary conditions of the kind can come into question at all, as was also rightly emphasised by the astronomer de Sitter recently.... At any rate, our calculations have convinced me that such conditions of degeneration for the
’s in spatial infinity may not be postulated.
“After the failure of this attempt, two possibilities next present themselves.[144] ... From what has been said it will be seen that I have not succeeded in formulating boundary conditions for spatial infinity. Nevertheless, there is still a possible way out, without resigning as suggested under (b). For if it were possible to regard the universe as a continuum which is finite (closed) with respect to its spatial dimensions, we should have no need at all for any such boundary conditions.”
And it is the same in every other case. A number of attempts are made to co-ordinate the facts, and the simplest solution is the one which is accepted by the scientific world, until such time as some newly discovered experimental result conflicts with it.
Of course, all these statements would suffer from an incurable vagueness, were any argument to develop as to what constitutes simplicity. But whatever the reason may be, we find that the agreement among scientists is striking in this respect. There have never been two highly developed theories co-ordinating the same number of facts, in which by common consent one was not recognised as vastly simpler than the other; just as a mathematical expression containing one term is simpler than one containing two.
A case in point would be afforded by a comparison of Einstein’s and Newton’s co-ordination of gravitation and mechanics. If we are concerned solely with the facts of planetary motion and mechanics known to Newton, then Newton’s laws of mechanics and his law of gravitation are by far the simpler. But if we supplement the facts known to him with those more recently discovered, Einstein’s synthesis has the advantage, for Newton’s co-ordination would necessitate a number of additional hypotheses ad hoc. In the same way, so far as our everyday experience is concerned, a non-rotating earth is the simpler solution, whereas, when the planetary motions are taken into consideration, the reverse holds true. It may happen, of course, that the simpler synthesis will conflict with certain philosophical prejudices, but objections of this sort will always give way eventually before the higher criterion of simplicity. Indeed, we know that men finally accepted Galileo’s stand.
If, then, we may assume that the criterion of simplicity presents no further difficulty, the problem reduces to determining whether or not the theoretical physicist introduces presuppositions and assumptions uncritically. We are here concerned solely with the physicist and theoretical physicist, not with the pure mathematician, whose procedure is entirely different. In order to clear up these points, we shall give a rapid survey of some of the basic presuppositions that are common to physicists. Although we fear that it will be impossible to avoid a certain amount of repetition, yet the importance of the subject is such that a mere matter of elegance of presentation will have to be sacrificed.
The purpose of science is, as we have said, to co-ordinate facts and to obtain thereby a common knowledge which will hold for all men. But our co-ordinations, deductions and inductions must be conducted according to rigid rules which all men will recognise. In the absence of such common rules, two men starting from the same premises would arrive at different conclusions; as a result, a common knowledge, and therefore a science, would be impossible. We shall assume that the rules of logical reasoning will serve our purpose in this respect.