Tag Archive: Einstein

Destroying authoritarianism in science

For there never was a more successful theory, or a better tested theory, than Newton’s theory of gravity. It succeeded in explaining both terrestrial and celestial mechanics. It was most severely tested in both fields for centuries. The great physicist and mathematician Henri Poincaré believed not only that it was true – this of course was everybodys belief – but that it was true by definition, and that it would therefore remain the invariable basis of physics to the end of man’s search for truth. And Poincaré believed this in spite of the fact that he actually anticipated – or that he came very close to anticipating – Einstein’s special theory of relativity. I mention this in order to illustrate the tremendous authority of Newton’s theory down to the very last.

Now the question whether or not Einstein’s theory of gravity is an improvement upon Newton’s, as most physicists think it is, may be left open. But the mere fact that there was now an alternative theory which explained everything that Newton could explain and, in addition, many more things, and which passed at least one of the crucial tests that Newton’s theory seemed to fail, destroyed the unique place held by Newton’s theory in its field. Newton’s theory was thus reduced to the status of an excellent and successful conjecture, a hypothesis competing with others, and one whose acceptability was an open question. Einstein’s theory thus destroyed the authority of Newton’s, and with it some­thing of even greater importance – authoritarianism in science. [91]

The question of the authoritative sources of knowledge

Yet the traditional question of the authoritative sources of knowledge is repeated even today — and very often by posi­tivists, and by other philosophers who believe themselves to be in revolt against authority.

The proper answer to my question ‘How can we hope to detect and eliminate error?’ is, I believe, ‘By criticizing the theories or guesses of others and — if we can train ourselves to do so — by criticizing our own theories or guesses.’ (The latter point is highly desirable, but not indispensable; for if we fail to criticize our own theories, there may be others to do it for us.) This answer sums up a position which I propose to call ‘critical rationalism’. It is a view, an attitude, and a tradition, which we owe to the Greeks. It is very different from the ‘rationalism’ or ‘intellectualism’ of Descartes and his school, and very different even from the epistemology of Kant. Yet in the field of ethics, of moral knowledge, it was approached by Kant with his principle of autonomy. This principle expresses his realization that we must not accept the command of an authority, however exalted, as the basis of ethics. For whenever we are faced with a command by an authority, it is for us to judge, critically, whether it is moral or immoral to obey. The authority may have power to enforce its commands, and we may be powerless to resist. But if we have the physical power of choice, then the ultimate respon­sibility remains with us. It is our own critical decision whether to obey a command; whether to submit to an authority.

Kant boldly carried this idea into the field of religion: ‘…in whatever way’, he writes, ‘the Deity should be made known to you, and even … if He should reveal Himself to you: it is you … who must judge whether you are permitted to believe in Him, and to worship Him.’

In view of this bold statement, it seems strange that Kant did not adopt the same attitude — that of critical examination, of the critical search for error — in the field of science. I feel certain that it was only his acceptance of the authority of Newton’s cosmology — a result of its almost unbelievable success in passing the most severe tests — which prevented Kant from doing so. If this interpretation of Kant is correct, then the critical rationalism (and also the critical empiricism) which I advocate merely puts the finishing touch to Kant’s own critical philosophy. And this was made possible by Einstein, who taught us that Newton’s theory may well be mistaken in spite of its overwhelming success.

So my answer to the questions ‘How do you know? What is the source or the basis of your assertion? What obser­vations have led you to it?’ would be: ‘I do not know: my assertion was merely a guess. Never mind the source, or the sources, from which it may spring — there are many possible sources, and I may not be aware of half of them; and origins or pedigrees have in any case little bearing upon truth. But if you are interested in the problem which I tried to solve by my tentative assertion, you may help me by criticizing it as severely as you can; and if you can design some experimental test which you think might refute my assertion, I shall gladly, and to the best of my powers, help you to refute it.’ [34-5]

Science: Conjectures and Refutations

Now the impressive thing about this case [Eddington’s expedition] is the risk involved in a prediction of this kind. If observation shows that the predicted effect is definitely absent, then the theory is simply refuted. The theory is incom­patible with certain possible results of observation — in fact with results which everybody before Einstein would have expected. This is quite different from the situation I have previously described, when it turned out that the theories in question were compatible with the most divergent human behavior, so that it was practically impossible to describe any human behavior that might not be claimed to be a verification of these theories.

These considerations led me in the winter of 1919-20 to conclusions which I may now reformulate as follows.

(1) It is easy to obtain confirmations, or verifications, for nearly every theory — if we look for confirmations.

(2) Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in question, we should have expected an event which was incompatible with the theory — an event which would have refuted the theory.

(3) Every ‘good’ scientific theory is a prohibition: it forbids certain things to happen. The more a theory forbids, the better it is.

(4) A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice.

(5) Every genuine test of a theory is an attempt to falsify it, or to refute it. Testability is falsifiability; but there are de­grees of testability: some theories are more testable, more exposed to refutation, than others; they take, as it were, greater risks.

(6) Confirming evidence should not count except when it is the result of a genuine test of the theory; and this means that it can be presented as a serious but unsuccessful attempt to falsify the theory. (I now speak in such cases of ‘corroborating evidence’.)

(7) Some genuinely testable theories, when found to be false, are still upheld by their admirers—for example by in­troducing ad hoc some auxiliary assumption, or by reinterpreting the theory ad hoc in such a way that it escapes refutation. Such a procedure is always possible, but it rescues the theory from refutation only at the price of destroying, or at least lowering, its scientific status. (I later described such a rescuing operation as a ‘conventionalist twist’ or a ‘conventionalist stratagem’.)

One can sum up all this by saying that the criterion of the scientific status of a theory is its falsifiability, or refutability, or testability. [47-8]

No, not even maths is certain

Thanks to Gödel, we know that there will never be a fixed method of determining whether a mathematical proposition is true, any more than there is a fixed way of determining whether a scientific theory is true. Nor will there ever be a fixed way of generating new mathematical knowledge. Therefore progress in mathematics will always depend on the exer­cise of creativity. It will always be possible, and necessary, for mathematicians to invent new types of proof. They will validate them by new arguments and by new modes of explanation depending on their ever improving understanding of the abstract entities involved. Gödel’s own theorems were a case in point: to prove them, he had to invent a new method of proof. I said the method was based on the ‘diagonal argument’, but Gödel extended that argument in a new way. Nothing had ever been proved in this way before; no rules of inference laid down by someone who had never seen Gödel’s method could possibly have been prescient enough to designate it as valid. Yet it is self-evidently valid. Where did this self-evidentness come from? It came from Gödel’s understanding of the nature of proof. Gödel’s proofs are as compelling as any in mathematics, but only if one first understands the explanation that accompanies them.

So explanation does, after all, play the same paramount role in pure mathematics as it does in science. Explaining and understanding the world – the physical world and the world of mathematical abstractions – is in both cases the object of the exercise. Proof and observation are merely means by which we check our explanations. [235-6]

Gould on fact and theory

Well, evolution is a theory. It is also a fact. And facts and theories are different things, not rungs in a hierarchy of in­creasing certainty. Facts are the world’s data. Theories are structures of ideas that explain and interpret facts. Facts do not go away when scientists debate rival theories to explain them. Einstein’s theory of gravitation replaced Newton’s, but apples did not suspend themselves in mid-air, pending the outcome. And humans evolved from apelike ancestors whether they did so by Darwin’s proposed mechanism or by some other, yet to be discovered.

Moreover, “fact” does not mean “absolute certainty.” The final proofs of logic and mathematics flow deductively from stated premises and achieve certainty only because they are not about the empirical world. Evolutionists make no claim for perpetual truth, though creationists often do (and then attack us for a style of argument that they themselves favor). In science, “fact” can only mean “confirmed to such a degree that it would be perverse to withhold provisional assent.” I suppose that apples might start to rise tomorrow, but the possibility does not merit equal time in physics classrooms. [254-5]