The LOGIC OF SCIENTIFIC DISCOVERY (1959)
"REPLIES TO My CRITICS" (1974)
THE POVERTY OF HISTORICISM (1957)
AMERICAN UNIVERSITY OF BEIRUT
The Logic of Scientific Discovery
(First published in German in 1934, English translation 1959)
from Chapter I, 'A Survey of Some Fundamental Problems',
introduction and sections 1,2, 3,4 and 6.
A SCIENTIST, whether theorist or experimenter, puts forward statements, and tests them step by step. In the field of the empirical sciences, more particularly, he constructs hypotheses, or systems of theories, and tests them against experience by observation and experiment.
I suggest that it is the task of the logic of scientific discovery, or the logic of knowledge, to give a logical analysis of this procedure; that is, to analyze the method of the empirical sciences.
But what are these 'methods of the empirical sciences'? And what do we call 'empirical science'?
1. The Problem of Induction.
According to a widely accepted view - to be opposed in this book - the empirical sciences can be characterized by the fact that they use 'inductive methods', as they are called. According to this view, the logic of scientific discovery would be identical with inductive logic, i.e. with the logical analysis of these inductive methods.
It is usual to call an inference 'inductive' if it passes from singular statements (sometimes also called 'particular' statements), such as accounts of the results of observations or experiments, to universal statements, such as hypotheses or theories.
Now it is far from obvious, from a logical point of view, that we are justified in inferring universal statements from singular ones, no matter how numerous; for any conclusion drawn in this way may always turn out to be false: no matter how many instances of white swans we may have observed, this does not justify the conclusion that all swans are white.
The question whether inductive inferences are justified, or under what conditions, is known as the problem of induction.
The problem of induction may also be formulated as the question of how to establish the truth of universal statements which are based on experience, such as the hypotheses arid theoretical systems of the empirical sciences. For many people believe that the truth of these universal statements is 'known by experience'; yet it is clear that an account of an experience - of an observation or the result of an experiment - can in the first place be only a singular statement and not a universal one. Accordingly, people who say of a universal statement that we know its truth from experience usually mean that the truth of this universal statement can somehow be reduced to the truth of singular ones, and that these singular ones are known by experience to be true; which amounts to saying that the universal statement is based on inductive inference. Thus to ask whether there are natural laws known to be true appears to be only another way of asking whether inductive inferences are logically justified.
Yet if we want to find a way of justifying inductive inferences, we must first of all try to establish a principle of induction. A principle of induction would be a statement with the help of which we could put inductive inferences into a logically acceptable form. In the eyes of the upholders of inductive logic, a principle of induction is of supreme importance for scientific method: "... this principle", says Reichenbach, "determines the truth of scientific theories. To eliminate it from science would mean nothing less than to deprive science of the power to decide the truth or falsity of its theories. Without it, clearly, science would no longer have the right to distinguish its theories from the fanciful and arbitrary creations of the poet's mind." 1
Now this principle of induction cannot be a purely logical truth like a tautology or an analytic statement. Indeed, if there were such a thing as a purely logical principle of induction, there would be no problem of induction; for in this case, all inductive inferences would have to be regarded as purely logical or tautological transformations, just like inferences in inductive logic. Thus the principle of induction must be a synthetic statement; that is, a statement whose negation is not self-contradictory but logically possible. So the question arises why such a principle should be accepted at all, and how we can justify its acceptance on rational grounds.
Some who believe in inductive logic are anxious to point out, with Reichenbach, that "the principle of induction is unreservedly accepted by the whole of science and that no man can seriously doubt this principle in everyday life either.'2 Yet even supposing this were the case - for after all, 'the whole of science' might err - I should still contend that a principle of induction is superfluous, and that it must lead to logical inconsistencies.
That inconsistencies may easily arise in connection with the principle of induction should have been clear from the work of Burne; also, that they can be avoided, if at all, only with difficulty. For the principle of induction must be a universal statement in its turn. Thus if we try to regard its truth as known from experience, then the very same problems which occasioned its introduction will arise all over again. To justify it, we should have to employ inductive inferences; and to justify these we should have to assume an inductive principle of a higher order; and so on. Thus the attempt to base the principle of induction on experience breaks down, since it must lead to an infinite regress.
Kant tried to force his way out of this difficulty by taking the principle of induction (whicq he formulated as the 'principle of universal causation') to be 'a priori valid'. But I do not think that his ing_nious attempt to provide an a priori justification for synthetic statements was successful.
My own view is that the various difficulties of inductive logic here sketched are insurmountable. (...)
THE THEORY to be developed in the following pages stands directly opposed to all attempts to operate with the ideas of inductive logic. It might be described as the theory of the deductive method of testing, or as the view that a hypothesis can only be empirically tested - and only after it has been advanced.
Before I can elaborate this view (which might be called 'deductivism', in contrast to 'inductivism') I must first make clear the distinction between the psychology of
knowledge which deals with empirical facts, and the logic of knowledge which is concerned only with logical relations. For the belief in inductive logic is largely due to a confusion of psychological problems with epistemological ones. It may be worth noticing, by the way, that this confusion spells trouble not only for the logic of knowledge but for its psychology as well.
2. Elimination of Psychologism.
I said above that the work of the scientist consists in putting forward and testing theories.
The initial stage, the act of conceiving or inventing a theory, seems to me neither to call for logical analysis nor to be susceptible of it. The question how it happens that a new idea occurs to a man - whether it is a musical theme, a dramatic conflict, or a scientific theory - may be of great interest to empirical psychology; but it is irrelevant to the logical analysis of scientific knowledge. This latter is concerned not with questions of fact (Kant's quid facti?), but only with questions of justification or validity (Kant's quid juris?). Its questions are of the following kind. Can a statement be justified? And if so, how? Is it testable? Is it logically dependent on certain other statements? Or does it perhaps contradict them? In order that a statement may be logically examined in this way, it must already have been presented to us. Someone must have formulated it, and submitted it to logical examination.
Accordingly I shall distinguish sharply between the process of conceiving a new idea, and the methods and results of examining it logically. As to the task of the logic of knowledge - in contradistinction to the psychology of knowledge - I shall proceed on the assumption that it consists solely in investigating the methods employed in those systematic tests to which every new idea must be subjected if it is to be seriously entertained.
Some might object that it would be more to the purpose to regard it as the business of epistemology to produce what has been called a 'rational reconstruction' of the steps that have led the scientist to a discovery - to the finding of some new truth. But the question is: what, precisely, do we want to reconstruct? If it is the processes involved in the stimulation and release of an inspiration which are to be reconstructed, then I should refuse to take it as the task of the logic of knowledge. Such processes are the concern of empirical psychology but hardly of logic. It is another matter if we want to reconstruct rationally the subsequent tests whereby the inspiration may be discovered to be a discovery, or become known to be knowledge. In so far as the scientist critical
judges, alters, or rejects his own inspiration we may, if we like, regard the methodological analysis undertaken here as a kind of 'rational reconstruction' of the corresponding thought-processes. But this reconstruction would not describe these processes as they actually happen: it can give only a logical skeleton of the procedure of testing. Still, this is perhaps all that is meant by those who speak of a 'rational reconstruction' of the ways in which we gain knowledge.
It so happens that my arguments in this book are quite independent of this problem. However, my view of the matter, for what it is worth, is that there is no such thing as a logical method of having new ideas, or a logical reconstruction of this process. My view may be expressed by saying that every discovery contains 'an irrational element', or 'a creative intuition', in Bergson's sense. In a similar way Einstein speaks of
"... the search for those highly universal... laws from which a picture of the world can be obtained by pure deduction. There is no logical path", he says, "leading to these... laws. They can only be reached by intuition, based upon something like an intellectual love ('Einfuhlung') of the objects of experience."3
3. Deductive Testing of Theories.
According to the view that will be put forward here, the method of critically testing theories, and selecting them according to the results of tests, always proceeds on the following lines. From a new idea, put up tentatively, and not yet justified in any way- an anticipation, a hypothesis, a theoretical system, or what you will - conclusions are drawn by means of logical deduction. These conclusions are then compared with one another and with other relevant statements, so as to find what logical relations (such as equivalence, derivability, compatibility, or incompatibility) exist between them.
We may if we like distinguish four different lines along which the testing of a theory could be carried out. First there is the logical comparison of the conclusions among themselves, by which the internal consistency of the system is tested. Secondly, there is the investigation of the logical form of the theory, with the object of determining whether it has the character of an empirical or scientific theory, or whether it is, for example, tautological. Thirdly, there is the comparison with other theories, chiefly with the aim of determining whether the theory would constitute a scientific advance should it survive our various tests. And finally, there is the testing of the theory by way of empirical applications of the conclusions which can be derived from it.
The purpose of this last kind of test is to find out how far the new consequences of the theory - whatever may be new in what it asserts - stand up to the demands of practice, whether raised by purely scientific experiments, or by practical technological applications. Here too the procedure of testing turns out to be deductive. With the help of other statements, previously accepted, certain singular statements - which we may call 'predictions' - are deduced from the theory; especially predictions that are easily testable or applicable. From among these statements, those are selected which are not derivable
from the current theory, and more especially those which the current theory contradicts. Next we seek a decision as regards these '(and other) derived statements by comparing them with the results of practical applications and experiments. If this decision is positive, that is, if the singular conclusions turn out to be acceptable, or verified, then the theory has, for the time being, passed its test: we have found no reason to discard it. But if the decision is negative, or in other words, if the conclusions have been falsified, then their falsification also falsifies the theory from which they were logically deduced.
It should be noticed that a positive decision can only temporarily support the theory, for subsequent negative decisions may always overthrow it. So long as a theory withstands detailed and severe tests and is not superseded by another in the course of scientific progress, we may say that it has 'proved its mettle' or that it is 'corroborated' [by past experience].
Nothing resembling inductive logic appears in the procedure here outlined. I never assume that we can argue from the truth of singular statements to the truth of theories. I never assume that by force of 'verified' conclusions, theories can be established as 'true', or even as merely 'probable'.
4. The Problem of Demarcation.
Of the many objections which are likely to be raised against the view here advanced, the most serious is perhaps the following. In rejecting the method of induction, it may be said, I deprive empirical science of what appears to be its most important characteristic; and this means that I remove the barriers which separate science from metaphysical speculation. My reply to this objection is that my main reason for rejecting inductive logic is precisely that it does not provide a suitable distinguishing mark of the empirical, non-metaphysical character of a theoretical system; or in other words, that it does not provide a suitable 'criterion of demarcation '.
The problem of finding a criterion which would enable us to distinguish between the empirical sciences on the one hand, and mathematics and logic as well as 'metaphysical' systems on the other, I call the problem of demarcation.
6. Falsifiability as a Criterion of Demarcation.
Now in my view there is no such thing as induction. Thus inference to theories, from singular statements which are 'verified by experience' (whatever that may mean), is logically inadmissible. Theories are, therefore, never empirically verifiable. If we wish to avoid the positivist's mistake of eliminating, by our criterion of demarcation, the theoretical systems of natural science, then we must choose a criterion which allows us to admit to the domain of empirical science even statements which cannot be verified.
But I shall certainly admit a system as empirical or scientific only if it is capable of being tested by experience. These considerations suggest that not the verifiability but the falsifiability of a system is to be taken as a criterion of demarcation. In other words: I shall not require of a scientific system that it shall be capable of being singled out, once and for all, in a positive sense; but I shall require that its logical form shall be such that it can be singled out, by means of empirical tests, in a negative sense: it must be possible for an empirical scientific system to be refuted by experience.
(Thus the statement, 'It will rain or not rain here tomorrow' will not be regarded as empirical, simply because it cannot be refuted; whereas the statement, 'It will rain here tomorrow' will be regarded as empirical.)
(...) My proposal is based upon an asymmetry between verifiability and falsifiability; an asymmetry which results from the logical form of universal statements. For these are never derivable from singular statements, but can be contradicted by singular statements. Consequently it is possible by means of purely deductive inferences (with the help of the modus tollens of c1assicallogic) to argue from the truth of singular statements to the falsity of universal statements. Such an argument to the falsity of universal statements is the only strictly deductive kind of inference that proceeds, as it were, in the 'inductive direction'; that is, from singular to universal statements.
"Replies to my Critics"
(Part Three, 'The Philosopher Replies', of The Philosophy of Karl Popper,
ed. by P.A. Schilpp, 1974, Vol. 2, pp. 961-1197)
from Chapter 2, 'The Problem of Demarcation', sections 5-8.
5. The Centre of the dispute: The Problem of Demarcation.
I now turn to my problem of demarcation, and to explaining how this problem is related to the problems of empirical content and of testability.
The great scientists, such as Galileo, Kepler, Newton, Einstein, and Bohr (to confine myself, to a few of the dead) represent to me a simple but impressive idea of science. Obviously, no such list, however much extended, would define scientist or science in extenso. But it suggests for me an oversimplification, one from which we can, I think, learn a lot. It is the working of great scientists which I have in my mind as my paradigm for science. Not that I lack respect for the lesser ones; there are hundreds of great men and great scientists who come into the almost heroic category.
But with all respect for the lesser scientists, I wish to convey here a heroic and romantic idea of science and its workers: men who humb1y devoted themselves to the
search for truth, to the growth of our knowledge; men whose life consisted in an adventure of bold ideas. I am prepared to consider with them many of their less brilliant helpers who were equally devoted to the search for truth - for great truth. But I do not count among them those for whom science is no more than a profession, a technique: those who are not deeply moved by great problems and by the oversimplifications of bold solutions.
It is science in this heroic sense that I wish to study. As a side result I find that we can throw a lot of light even on the more modest workers in applied science.
This, then, for me is science. I do not try to define it, for very good reasons. I only wish to draw a simple picture of the kind of men I have in mind, and of their activities. And the picture will be an oversimplification: these are men of bold ideas, but highly critical of their own ideas; they try to find whether their ideas are right by trying first to find whether they are not perhaps wrong. They work with bold conjectures and severe attempts at refuting their own conjectures.
My criterion of demarcation between science and non science is a simple logical analysis of this picture. How good or bad it is will be shown by its fertility.
BOLD IDEAS are new, daring, hypotheses or conjectures. And severe attempts at refutations are severe critical discussions and severe empirical tests.
When is a conjecture daring and when is it not daring, in the sense here proposed?
Answer: it is daring if and only if it takes a great risk of being false - if matters could be otherwise, and seem at the time to be otherwise.
Let us consider a simple example. Copernicus's or Aristarchus's conjecture that the sun rather than the earth rests at the centre of the universe was an incredibly daring one. It was, incidentally, false; nobody accepts today the conjecture that the sun is (in the sense of Aristarchus and Copernicus) at rest in the centre of the universe. But this does not affect the boldness of the conjecture, nor its fertility. And one of its main consequences - that the earth does not rest at the centre of the universe but that it has (at least) a daily and an annual motion - is still fully accepted, in spite of some misunderstandings of relativity.
But it is not the present acceptance of the theory which I wish to discuss, but its boldness. It was bold because it clashed with all then accepted views, and with the prima facie evidence of the senses. It was bold because it postulated a hitherto unknown hidden reality behind the appearances.
It was not bold in another very important sense: neither Aristarchus nor Copernicus suggested a feasible crucial experiment. In fact, they did not suggest that anything was, wrong with the traditional appearances: they let the accepted appearances severely alone; they only reinterpreted them. They were not anxious to stick out their necks by predicting new observable appearances.
To the degree that this is so, Aristarchus's and Copernicus's theories may be described in my terminology as unscientific or metaphysical. To the degree that Copernicus did make a number of minor predictions, his theory is, in my terminology,
scientific. But even as a metaphysical theory it was far from meaningless; and in proposing a new bold view of the universe it made a tremendous contribution to the advent of the new science.
Kepler went much further. He too had a bold metaphysical view, partly based upon the Copernican theory, of the reality of the world. But his view led him to many new detailed predictions of the appearances. At first these predictions did not tally with the observations. He tried to reinterpret the observations in the light of his theories; but his addiction to the search for truth was even greater than his enthusiasm for the metaphysical harmony of the world. Thus he felt forced to give up a number of his favoured theories, one by one, and to replace them by others which fitted the facts. It was a great and a heartrending struggle. The final outcome, his famous and immensely important three laws, he did not really like - except the third. But they stood up to his severest tests - they agreed with the detailed appearances, the observations which he had inherited from Tycho.
Kepler's laws are excellent approximations to what we think today are the true movements of the planets of our solar system. They are even excellent approximations to the movements of the distant binary star systems which have since been discovered. Yet they are merely approximations to what seems to be the truth; they are not true.
They have been tested in the light of new theories - of Newton's theory and of Einstein's - which predicted small deviations from Kepler's laws. (According to Newton, Kepler's laws are correct only for two-body systems.) Thus the crucial experiments went against Kepler, very slightly, but sufficiently clearly.
Of these three theories - Kepler's, Newton's, and Einstein's - the latest and still the most successful is Einstein's; and it was this theory which led me into the philosophy of science. What impressed me so greatly about Einstein's theory of gravitation were the following points.
(1) It was a very bold theory. It greatly deviated in its fundamental outlook from Newton's theory which at that time was utterly successfu1.4
(2) From the point of view of Einstein's theory, Newton's theory was an excellent approximation, though false Gust as from the point of view of Newton's theory, Kepler's and Galileo's theories were excellent approximations, though false). Thus it is not its truth which decides the scientific character of a theory.