The Critical Rationalist Vol. 01 No. 03 ISSN: 1393-3809 30-Dec-1996
References
Part I
(34) I am almost certain that no readers of this article will accept this. How can anyone presume to know more about physics than Einstein? But remember that I am not competing with Einstein in questions of physics, or mathematics, but in questions of methodology, and thanks to Karl Popper methodology has made wonderful progress since Einstein's time. You may have noticed that, so far, I did not use one single mathematical formula in this text[16], and yet I have questioned all the premises from which Einstein started. And I am not only relying on my own arguments, but on those supplied by Karl Popper, most of all on his methodological nominalism[17]. So I may be wrong, but then, I think, Karl Popper would also have been wrong. At any rate--since it is impossible to reach a final result on this in one single article--I challenge every reader of this article to disprove my arguments in writing. As a practising lawyer I know only too well that oral discussion always has an element of chance in it, and that is why I am longing to be able to publish my views--I have a lot more to say--and get a public discussion, if only the physicists would let me. But this is a "Popperian Journal" and I have been speaking on physics already too long. Let me therefore return to the theory of scientific knowledge.
(35) I consider it as definitely established that Einstein's theory of relativity and Popper's theory of scientific knowledge are incompatible. Einstein's theory of "curved space" is non-empirical, and the empirical parts of his theory concerning time and gravitation have been empirically refuted. If I am right, then physical science now has the task of re-interpreting a tremendous number of experiments, and of finding new solutions for several important problems, most of all the problem of gravitation which has never been solved. The theory of the "Big Bang" and the theory of the "Black Holes" will both break down, and we may find that we know even less about our universe than we thought we did. What physics desperately needs, and apparently totally lacks at the moment, is a critical discussion of the premises on which the various theories rely which are at present happily co-existing despite all their contradictions. And to permit this discussion it seems that physics will first have to open its mind (and its institutions) to the possibility of error, and, instead of getting lost in mathematical formulae, find the courage to put forward new and daring ideas. And for the pupils and admirers of Karl Popper there remains the question why he himself did not see these implications--if they are as I see them.
(36) The answer, I believe, has been given by Lessing: "Not all are free who mock at their own fetters." I think Karl Popper was so impressed by Einstein's boldly stating the exact conditions under which his theory would break down, and by the contrast in which this stood to the dogmatism of psychoanalysis, and so overwhelmed by the outcome of Eddington's experiment, that he never extended his own criticism to Einstein himself. He was a boy of thirteen when Einstein published the general theory of relativity, and barely seventeen years old when he heard Einstein's lecture in Vienna just after Eddington's first experiment. At that time he had not yet developed the criterion of falsifiability as a demarcation between science and metaphysics, but Eddington's experiment gave the impulse from which it was eventually to emerge. It would have been almost superhuman for Popper to apply his criticism to the very theory which had inspired his own discovery. In later years he was critical of the theory of relativity in the sense that he did not consider it as the final truth, as was Einstein himself, who spent the last thirty years of his life in search of a better theory, and once wrote that:
... the most beautiful lot of a scientific theory is if it shows the way to a more comprehensive theory in which it continues to live as a borderline case.
(37) But I think Popper simply never felt the necessity to call the theory of relativity itself into question. He said that it took him years to discover the bearing which his demarcation criterion of falsifiability had on the problem of induction. In the case of the theory of relativity, I think, he continued to live with an inconsistency without being aware of it.
(38) But Einstein, I believe, was less of a critical rationalist than Popper thought. He did say:
Insofar as the expressions of mathematics refer to reality they are not certain, and insofar as they are certain they do not refer to reality.
So he held the instrument of criticism in his hands. But the superstition in which he had been brought up had not lost its power over him. The most important "confirmations" of his theory were, in fact, observations already known before, or at least expected at, the time he wrote. The redshift of light from distant galaxies, the deflection of light in the gravitational field, and the perihelion-rotation of the course of Mercury, were all known, or at least surmised, before 1914, as can easily be seen from the fact that Einstein himself discussed them in his early papers (Einstein 1916, Einstein 1915). They were the facts from which he started, and to which he adapted his theory by logical or mathematical inference. I am almost sure that if he had been asked he would have said that he was working by induction because he said so almost explicitly[18]. The power of his theory lay in the fact that it was the first to offer one solution for a whole set of different problems hitherto unconnected. But Einstein did not know what we have since learned from Karl Popper, that falsifiability of a theory is no vice, but a virtue. So even after he had published the general theory of relativity he kept adapting it to whatever new observations came his way, including Hubble's discovery (Einstein 1990, pp. 116ff.). Thus he could never be refuted because he would always change his theory. For a pupil of Karl Popper, Einstein's early publications on the theory of relativity are indeed quite astonishing to read because he was permanently mending his theory in view of criticism and new discoveries. But he never stooped to discussing the compatibility of his premises with Hubble's new observations. And the very fact that, in the above quotation, he spoke of the "expressions of mathematics" with respect to reality shows that he did not distinguish between mathematics and physics as sharply as Bertrand Russell, Alfred Tarski and Karl Popper have since taught us to do. Today we know, in Russell's famous words, that:
... pure mathematics is the subject matter in which we do not know what we are talking about, or whether what we are saying is true.
(39) But we should not forget that it was a difficult process to reach this point of knowledge, and that some of the most eminent scientists were involved in reaching it. Even today, and in spite of their teaching, the view is widely spread that the rules of logic, and the calculi of arithmetic, are "laws of thought". So we should learn to be still more critical of our own views and theories because even the best knowledge we have, or believe to have, will not automatically put right all those mistakes on which it has a bearing. Our brain may be superior to any computer because it can create new and revolutionary ideas. But it is also inferior to any computer because it may overlook inconsistencies which no computer would tolerate. If men like Einstein and Popper can fail then anyone can fail. That is why we should extend our criticism to everyone, to Einstein, and even to Popper, and most of all to ourselves. And the best service we can do to the memory of Karl Popper, as I understood his intentions, is by keeping in mind his words that:
... there are experts, but no authorities,
not even Einstein or Popper. Let us begin a new period of enlightenment by daring to use our own intelligence: Sapere aude! (in this context I should probably be saying "Sapere audiemus", but I am quoting Kant). Let us use logic and mathematics where they can be helpful, but let us also beware of being carried away by their beauty. We must keep criticizing the premises of our theories, and for this we need logic and mathematics. But beyond that we should leave them to the computers wherever possible, and use our wonderfully creative human intelligence for developing new and daring ideas--and take the risk of being wrong!
References
Part I
The Critical Rationalist Vol. 01 No. 03 ISSN: 1393-3809 30-Dec-1996
Copyright © 1996 All Rights Reserved.
TCR Issue Timestamp: Mon Dec 30 17:41:04 GMT 1996