The Logic of Scientific Discovery
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"Science may be described as the art of systematic oversimplification"
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Popper was born in 1902 in Vienna to a prosperous Jewish family who had converted to Lutheran Christianity. He took a doctorate in at the Faculty of Philosophy in his home city, and, in 1934, while working as a schoolteacher, wrote this, his first book - Logik der Forschung (The Logic of Scientific Discovery). In it he criticises the customary ways of determining scientific truth; psychologism, naturalism, inductionism, and riles against both the logical positivism of the likes of AJ Ayer and the linguistic "philosophy" of Wittgenstein. Instead he puts forward his theory of falsifiability as the criterion which should demark true science from non-science. Roughly, that we should only be willing to accept as scientifically 'true' that which we know how to prove false.
In 1937, with the threat of Nazism, Popper left Austria for New Zealand to teach philosophy at Canterbury University College. It was there that he wrote his influential social work The Open Society and its Enemies. In 1946, he moved to England to become reader in logic and scientific method at London.
This is a very short abridgement of just the first part of Popper's book, reducing the original 100,000 or-so words to about 4000. The second part provides a more detailed explanation and justification of the themes outlined in the first. The original book is in copyright and I am grateful to the Karl Popper Library at Klagenfurt University, Austria for permission to use it here.
Have a look at competing theories of truth from the same period by AJ Ayer and Ludwig Wittgenstein.
See what other Squashed Books there are on Science and Truth
Read the Squashed version of Euclid's Elements to see where this sort of stuff started.
Have a poke round the internet for Larry Laudan’s "The Demise of the Demarcation Problem", with its suggeston that even flat-earthers can claim to be scientific by Popper's rules.
For a quick run-down on Popper's other great book 'The Open Society and its Enemies', we rather like this little graphic from http://pictoline.com/
Sir Karl Popper
Squashed version edited by Glyn Hughes © 2011
PREFACE TO THE FIRST EDITION, 1934
I assert that whenever a dispute has raged for any length of time, especially in philosophy, there was, at the bottom of it, never a problem about mere words, but always a genuine problem about things. I. Kant (1786)
A scientist engaged in a piece of research, say in physics, can attack his problem straight away, for a structure of scientific doctrines is already in existence, and with it, a generally accepted problem-situation. The philosopher finds himself in a different position. He does not face an organized structure, but rather something resembling a heap of ruins (though perhaps with treasure buried underneath). Nevertheless there are still some who do believe that philosophy can pose genuine problems about things, and who therefore still hope to get these problems discussed, and to have done with those depressing monologues which now pass for philosophical discussions. And if by chance they find themselves unable to accept any of the existing creeds, all they can do is to begin afresh from the beginning.
Vienna, Autumn 1934.
PREFACE TO THE FIRST ENGLISH EDITION, 1959
The linguistic philosophers and the school of language analysts believe that there are no genuine philosophical problems, or that the problems of philosophy, if any, are problems of linguistic usage, or of the meaning of words. I, however, believe that there is at least one philosophical problem in which all thinking men are interested. It is the problem of cosmology: the problem of understanding the world - including ourselves, and our knowledge, as part of the world. Admittedly, understanding the functions of our language is an important part of it; but explaining away our problems as merely linguistic ‘puzzles’ is not.
Philosophers are as free as others to use any method in searching for truth. There is no method peculiar to philosophy. And yet there is a method which might be described as ‘the one method of philosophy’. It is the one method of all rational discussion, and therefore of the natural sciences as well as of philosophy. The method is that of stating one’s problem clearly and of examining its various proposed solutions critically.
I do not deny that something called ‘logical analysis’ can play a role in this process, but these methods are far from being the only ones which a philosopher can use with advantage. There are other ‘methods’ a philosopher might use, but I am really not interested in enumerating them. I do not care what methods a philosopher (or anybody else) may use so long as he has an interesting problem, and so long as he is sincerely trying to solve it.
But one method seems to me worth mentioning, a variant of the (at present unfashionable) historical method. It consists, simply, in trying to find out what other people have thought and said about the problem in hand: why they had to face it: how they formulated it: how they tried to solve it. This seems to me important because, if we ignore what other people are thinking, or have thought in the past, then rational discussion must come to an end, though each of us may go on happily talking to himself.
Some philosophers have made a virtue of talking to themselves; perhaps because they felt that there was nobody else worth talking to. I fear that the practice of philosophizing on this somewhat exalted plane may be a symptom of the decline of rational discussion. No doubt God talks mainly to Himself because He has no one worth talking to. But a philosopher should know that he is no more godlike than any other man.
From Plato to Descartes, Leibniz, Kant, Duhem and Poincaré; and from Bacon, Hobbes, and Locke, to Hume, Mill, and Russell, the theory of knowledge was inspired by the hope that it would enable us not only to know more about knowledge, but also to contribute to the advance of knowledge - of scientific knowledge, that is.
It seems to me paradoxical that philosophers who take pride in specializing in the study of ordinary language nevertheless believe that they know enough about cosmology to be sure that it is in essence so different from philosophy that philosophy cannot make any contribution to it. And indeed they are mistaken. For it is a fact that purely metaphysical ideas - and therefore philosophical ideas - have been of the greatest importance for cosmology. From Thales to Einstein, from ancient atomism to Descartes’s speculation about matter, from the speculations of Gilbert and Newton and Leibniz and Boscovic about forces to those of Faraday and Einstein about fields of forces, metaphysical ideas have shown the way.
Philosophers should not be specialists. I am interested in science and in philosophy only because I want to learn something about the riddle of the world in which we live, and the riddle of man’s knowledge of that world. And I believe that only a revival of interest in these riddles can save the sciences and philosophy from narrow specialization and from an obscurantist faith in the expert’s special skill, and in his personal knowledge and authority; a faith that so well fits our ‘post-rationalist’ and ‘post-critical’ age, proudly dedicated to the destruction of the tradition of rational philosophy, and of rational thought itself.
Penn, Buckinghamshire, Spring 1958.
1: A SURVEY OF SOME FUNDAMENTAL PROBLEMS
A scientist, whether theorist or experimenter, puts forward statements, or systems of 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 analyse 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.
It is usual to call an inference ‘inductive’ if it passes from singular statements (sometimes 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. In the eyes of the upholders of inductive logic, a principle of induction is of supreme importance for scientific method. Without it, science would no longer have the right to distinguish its theories from the fanciful and arbitrary creations of the poet’s mind.
Now this principle of induction cannot be a purely logical truth like a tautology or an analytic statement. The principle of induction must be a synthetic statement; that is, a statement whose negation is not self-contradictory but logically possible. But to justify it, we should have to employ inductive inferences; and so on, leading to an infinite regress.
Kant tried to force his way out of this difficulty by taking the principle of induction (‘principle of universal causation’) to be ‘a priori valid’. But I do not think that his ingenious attempt to provide an a priori justification for synthetic statements was successful.
My own view is that the various difficulties of inductive logic 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’) 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.
2 ELIMINATION OF PSYCHOLOGISM
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. My view is that there is no such thing as a logical method of having new ideas, that every discovery contains ‘an irrational element’, or ‘a creative intuition’, in Bergson’s sense. Einstein speaks of the “search for those highly universal laws ... [which] can only be reached by intuition, based upon something like an intellectual love (‘Einfühlung’) of the objects of experience.”
3 DEDUCTIVE TESTING OF THEORIES
According to the view to be put forward here, the method of critically testing theories 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, compatiblity, 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 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.
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’.
In this book I intend to give a more detailed analysis of the methods of deductive testing.
4 THE PROBLEM OF DEMARCATION
My main reason for rejecting inductive logic is 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’.
Finding an acceptable criterion of demarcation must be a crucial task for any epistemology which does not accept inductive logic.
My criterion of demarcation will have to be regarded as a proposal for an agreement or convention. As to the suitability of such a convention opinions may differ; and a reasonable discussion of these questions is only possible between parties having some purpose in common. The choice of that purpose must, of course, be ultimately a matter of decision, going beyond rational argument. Thus I freely admit that in arriving at my proposals I have been guided, in the last analysis, by value judgements and predilections.
I have accused the positivists of trying to kill metaphysics by calling it names, but I do not even go so far as to assert that metaphysics has no value for empirical science. For it cannot be denied that along with metaphysical ideas which have obstructed the advance of science there have been others - such as speculative atomism - which have aided it. And, from the psychological angle, I am inclined to think that scientific discovery is impossible without faith in ideas which are of a purely speculative kind, and sometimes even quite hazy; a faith which is completely unwarranted from the point of view of science, and which, to that extent, is ‘metaphysical’.
Yet having issued all these warnings, I still take it to be the first task of the logic of knowledge to put forward a concept of empirical science, in order to make linguistic usage, now somewhat uncertain, as definite as possible, and in order to draw a clear line of demarcation between science and metaphysical ideas - even though these ideas may have furthered the advance of science throughout its history.
5 EXPERIENCE AS A METHOD
The task of formulating an acceptable definition of the idea of an ‘empirical science’ is not without its difficulties. This situation is sometimes described by saying that there is a great number - presumably an infinite number - of ‘logically possible worlds’. Yet the system called ‘empirical science’ is intended to represent only one world: the ‘real world’ or the ‘world of our experience’.
In order to make this idea a little more precise, we may distinguish three requirements which our empirical theoretical system will have to satisfy.
First, it must be synthetic, so that it may represent a non-contradictory, a possible world.
Secondly, it must satisfy the criterion of demarcation, ie. it must not be metaphysical, but must represent a world of possible experience.
Thirdly, it must be a system distinguished in some way from other such systems as the one which represents our world of experience.
6 FALSIFIABILITY AS A CRITERION OF DEMARCATION
The criterion of demarcation inherent in inductive logic - that is, the positivistic dogma of meaning - is equivalent to the requirement that all the statements of empirical science (or all ‘meaningful’ statements) must be capable of being finally decided, with respect to their truth and falsity; that they must be ‘conclusively decidable’.
Now in my view there is no such thing as induction. Theories are, therefore, never empirically verifiable.
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.
Various objections might be raised: it may well seem somewhat wrong-headed to suggest that science, which is supposed to give us positive information, should be characterized as satisfying a negative requirement such as refutability. Again, objections can be raised against falsifiability similar to those which I myself raised against verifiability. Thirdly, it might be said that it is impossible that any theoretical system should ever be conclusively falsified.
The root of this problem is the apparent contradiction between what may be called ‘the fundamental thesis of empiricism’ - the thesis that experience alone can decide upon the truth or falsity of scientific statements - and Hume’s realization of the inadmissibility of inductive arguments.
This contradiction arises only if it is assumed that all empirical scientific statements must be ‘conclusively decidable’, ie. that their verification and their falsification must both in principle be possible. If we renounce this requirement and admit as empirical also statements which are decidable in one sense only - unilaterally decidable and falsifiable - and which may be tested by systematic attempts to falsify them, the contradiction disappears: the method of falsification presupposes no inductive inference, but only the tautological transformations of deductive logic whose validity is not in dispute.
7 THE PROBLEM OF THE ‘EMPIRICAL BASIS'
If falsifiability is to be at all applicable as a criterion of demarcation, then we must clearly separate the psychological from the logical and methodological aspects of the problem. We must distinguish between our subjective experiences or our feelings of conviction and, on the other hand, the objective logical relations subsisting among the various systems of scientific statements, and within each of them.
8 SCIENTIFIC OBJECTIVITY AND SUBJECTIVE CONVICTION
The words ‘objective’ and ‘subjective’ are philosophical terms heavily burdened with a heritage of contradictory usages. My use of the terms is not unlike Kant’s. He uses the word ‘objective’ to indicate that scientific knowledge should be justifiable, independently of anybody’s whim: a justification is ‘objective’ if in principle it can be tested and understood by anybody.
The word ‘subjective’ is applied by Kant to our feelings of conviction (of varying degrees). To examine how these come about is the business of psychology. They may arise, for example, ‘in accordance with the laws of association’.
Only when certain events recur in accordance with rules or regularities, as is the case with repeatable experiments, can our observations be tested - in principle - by anyone. But every experimental physicist knows those surprising and inexplicable apparent ‘effects’ which in his laboratory can perhaps even be reproduced for some time, but which finally disappear without trace. No serious physicist would offer for publication, as a scientific discovery, any such ‘occult effect’, one for whose reproduction he could give no instructions.
I may be utterly convinced of the truth of a statement; certain of the evidence of my perceptions; overwhelmed by the intensity of my experience: every doubt may seem to me absurd. But can any statement be justified by the fact that K.R.P. is utterly convinced of its truth? The answer is, ‘No’.
A feeling of conviction cannot appear within the field of objective science, except in the form of a psychological hypothesis which, of course, calls for inter-subjective testing. But from the epistemological point of view, it is quite irrelevant.
Whatever may be our eventual answer to the question of the empirical basis, one thing must be clear: if we adhere to our demand that scientific statements must be objective, then those statements which belong to the empirical basis of science must also be objective, ie. inter-subjectively testable. Yet if the basic statements in their turn are to be inter-subjectively testable, there can be no ultimate statements in science. We arrive at the following view. Systems of theories are tested by deducing from them statements of a lesser level of universality. These statements in their turn, since they are to be inter-subjectively testable, must be testable in like manner - and so ad infinitum. It might be thought that this view leads to an infinite regress, and that it is therefore untenable. However, this is not so.
I do not demand that every scientific statement must have in fact been tested before it is accepted. I only demand that every such statement must be capable of being tested; or in other words, I refuse to accept the view that there are statements in science which we have, resignedly, to accept as true merely because it does not seem possible, for logical reasons, to test them.
In accordance with my proposal made above, epistemology, or the logic of scientific discovery, should be identified with the theory of scientific method. The decision here proposed for laying down suitable rules for what I call the ‘empirical method’ is closely connected with my criterion of demarcation: I propose to adopt such rules as will ensure the testability of scientific statements; which is to say, their falsifiability.
9 WHY METHODOLOGICAL DECISIONS ARE INDISPENSABLE
What are rules of scientific method, and why do we need them? Can there be a theory of such rules, a methodology? I admit that there is a need for a purely logical analysis of theories, but this kind of analysis does not elucidate those aspects of the empirical sciences which I, for one, so highly prize.
A system such as classical mechanics may be ‘scientific’ to any degree you like; but those who uphold it dogmatically are adopting the very reverse of that critical attitude which in my view is the proper one for the scientist. In point of fact, no conclusive disproof of a theory can ever be produced; for it is always possible to say that the experimental results are not reliable, or that the discrepancies exist. If you insist on strict proof (or disproof) in the empirical sciences, you will never benefit from experience, and never learn from it how wrong you are.
If therefore we characterize empirical science merely by the formal or logical structure of its statements, we shall not be able to exclude from it that prevalent form of metaphysics which results from elevating an obsolete scientific theory into an incontrovertible truth.
Thus I shall try to establish the rules, or norms, by which the scientist is guided when he is engaged in research or in discovery, in the sense here understood.
10 THE NATURALISTIC APPROACH TO THE THEORY OF METHOD
The positivist wishes to see in alleged philosophical problems mere ‘pseudo-problems’ or ‘puzzles’. For nothing is easier than to unmask a problem as ‘meaningless’ or ‘pseudo’. All you have to do is to fix upon a conveniently narrow meaning for ‘meaning’, and you will soon be bound to say of any inconvenient question that you are unable to detect any meaning in it. The dogma of meaning, once enthroned, is elevated forever above the battle, it can no longer be attacked. It has become (in Wittgenstein’s own words) ‘unassailable and definitive’.
The view according to which methodology is an empirical science in its turn - a study of the actual behaviour of scientists, or of the actual procedure of ‘science’ - may be described as ‘naturalistic’. Thus I reject the naturalistic view. It is uncritical. Its upholders fail to notice that whenever they believe themselves to have discovered a fact, they have only proposed a convention, and the convention is liable to turn into a dogma.
11 METHODOLOGICAL RULES AS CONVENTIONS
Methodological rules are here regarded as conventions. They might be described as the rules of the game of empirical science, for instance;
(1) The game of science is, in principle, without end. He who decides one day that scientific statements do not call for any further test, that they can be regarded as finally verified, retires from the game.
(2) Once a hypothesis has been proposed and tested, and has proved its mettle, it may not be allowed to drop out without ‘good reason’. A ‘good reason’ may be, for instance: replacement of the hypothesis by another which is better testable; or the falsification of one of the consequences of the hypothesis.
These two examples show what methodological rules look like. Clearly they are very different from the rules usually called ‘logical’. Although logic may perhaps set up criteria for deciding whether a statement is testable, it certainly is not concerned with the question whether anyone exerts himself to test it.
In establishing these rules we may proceed systematically. First a supreme rule is laid down which serves as a kind of norm for deciding upon the remaining rules, and which is thus a rule of a higher type. It is the rule which says that the other rules of scientific procedure must be designed in such a way that they do not protect any statement in science against falsification.
Methodological rules are thus closely connected both with other methodological rules and with our criterion of demarcation. But the connection is not a strictly deductive or logical one. It might indeed be said that the majority of the problems of theoretical philosophy, and the most interesting ones, can be re-interpreted in this way as problems of method.
END OF PART I
Sir Karl Popper
Popper died in England, his ashes were buried alongside his wife in Vienna
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