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PREFACE TO THE FIRST ENGLISH EDITION, 1959 In my old preface of 1934 I tried to explain—too briefly, I am afraid— my attitude towards the then prevailing situation in philosophy, and especially towards linguistic philosophy and the school of language analysts of those days. In this new preface I intend to explain my attitude towards the present situation, and towards the two main schools of language analysts of today. Now as then, language analysts are important to me; not only as opponents, but also as allies, in so far as they seem to be almost the only philosophers left who keep alive some of the traditions of rational philosophy. 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. All science is cosmology, I believe, and for me the interest of philosophy, no less than of science, lies solely in the contributions which it has made to it. For me, at any rate, both philosophy and science would lose all their attraction if they were to give up that pursuit. Admittedly, understand- ing the functions of our language is an important part of it; but explaining away our problems as merely linguistic ‘puzzles’ is not.preface, 1959 xix Language analysts regard themselves as practitioners of a method peculiar to philosophy. I think they are wrong, for I believe in the following thesis. Philosophers are as free as others to use any method in searching for truth. There is no method peculiar to philosophy. A second thesis which I should like to propound here is this. The central problem of epistemology has always been and still is the problem of the growth of knowledge. And the growth of knowledge can be studied best by studying the growth of scientific knowledge. I do not think that the study of the growth of knowledge can be replaced by the study of linguistic usages, or of language systems. And yet, I am quite ready to admit that there is a method which might be described as ‘the one method of philosophy’. But it is not characteristic of philosophy alone; it is, rather, the one method of all rational discussion, and therefore of the natural sciences as well as of phil- osophy. The method I have in mind is that of stating one’s problem clearly and of examining its various proposed solutions critically. I have italicized the words ‘rational discussion’ and ‘critically’ in order to stress that I equate the rational attitude and the critical attitude. The point is that, whenever we propose a solution to a problem, we ought to try as hard as we can to overthrow our solution, rather than defend it. Few of us, unfortunately, practise this precept; but other people, fortunately, will supply the criticism for us if we fail to supply it ourselves. Yet criticism will be fruitful only if we state our problem as clearly as we can and put our solution in a sufficiently definite form—a form in which it can be critically discussed. I do not deny that something which may be called ‘logical analysis’ can play a role in this process of clarifying and scrutinizing our prob- lems and our proposed solutions; and I do not assert that the methods of ‘logical analysis’ or ‘language analysis’ are necessarily useless. My thesis is, rather, that these methods are far from being the only ones which a philosopher can use with advantage, and that they are in no way characteristic of philosophy. They are no more characteristic of philosophy than of any other scientific or rational inquiry. It may perhaps be asked what other ‘methods’ a philosopher might use. My answer is that though there are any number of differentxx preface, 1959 ‘methods’, 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. Among the many methods which he may use—always depending, of course, on the problem in hand—one method seems to me worth mentioning. It is 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 it is part of the general method of rational discus- sion. 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 philo- sophizing 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. There are several interesting historical reasons for the widespread belief that what is called ‘linguistic analysis’ is the true method of philosophy. One such reason is the correct belief that logical paradoxes, like that of the liar (‘I am now lying’) or those found by Russell, Richard, and others, need the method of linguistic analysis for their solution, with its famous distinction between meaningful (or ‘well-formed’) and meaningless linguistic expressions. This correct belief is then com- bined with the mistaken belief that the traditional problems of philosophy arise from the attempt to solve philosophical paradoxes whose structure is analogous to that of logical paradoxes, so that the distinc- tion between meaningful and meaningless talk must be of central im- portance for philosophy also. That this belief is mistaken can be shown very easily. It can be shown, in fact, by logical analysis. For this reveals that a certain characteristic kind of reflexivity or self-reference which is present in all logical paradoxes is absent from all the so-called philosophical paradoxes—even from Kant’s antinomies.xxii preface, 1959 perception or knowledge or belief by the analysis of the phrases ‘I see’ or ‘I perceive’, or ‘I know’, ‘I believe’, ‘I hold that it is probable’; or perhaps by that of the word ‘perhaps’. Now to those who favour this approach to the theory of knowledge I should reply as follows. Although I agree that scientific knowledge is merely a development of ordinary knowledge or common-sense know- ledge, I contend that the most important and most exciting problems of epistemology must remain completely invisible to those who con- fine themselves to analysing ordinary or common-sense knowledge or its formulation in ordinary language. I wish to refer here only to one example of the kind of problem I have in mind: the problem of the growth of our knowledge. A little reflection will show that most problems connected with the growth of our knowledge must necessarily transcend any study which is confined to common-sense knowledge as opposed to scientific knowledge. For the most important way in which common-sense knowledge grows is, precisely, by turning into scientific knowledge. Moreover, it seems clear that the growth of scientific knowledge is the most important and interesting case of the growth of knowledge. It should be remembered, in this context, that almost all the prob- lems of traditional epistemology are connected with the problem of the growth of knowledge. I am inclined to say even more: 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. (The only possible exception to this rule among the great philosophers I can think of is Berkeley.) Most of the philosophers who believe that the characteristic method of philosophy is the analysis of ordinary language seem to have lost this admirable optimism which once inspired the rationalist trad- ition. Their attitude, it seems, has become one of resignation, if not despair. They not only leave the advancement of knowledge to the scientists: they even define philosophy in such a way that it becomes, by definition, incapable of making any contribution to our knowledge of the world. The self-mutilation which this so surprisingly persuasive definition requires does not appeal to me. There is no such thing as anpreface, 1959 xxi The main reason for exalting the method of linguistic analysis, how- ever, seems to have been the following. It was felt that the so-called ‘new way of ideas’ of Locke, Berkeley, and Hume, that is to say the psycho- logical or rather pseudo-psychological method of analysing our ideas and their origin in our senses, should be replaced by a more ‘objective’ and a less genetic method. It was felt that we should analyse words and their meanings or usages rather than ‘ideas’ or ‘conceptions’ or ‘notions’; that we should analyse propositions or statements or sen- tences rather than ‘thoughts’ or ‘beliefs’ or ‘judgments’. I readily admit that this replacement of Locke’s ‘new way of ideas’ by a ‘new way of words’ was an advance, and one that was urgently needed. It is understandable that those who once saw in the ‘new way of ideas’ the one true method of philosophy may thus have turned to the belief that the ‘new way of words’ is the one true method of philo- sophy. From this challenging belief I strongly dissent. But I will make only two critical comments on it. First, the ‘new way of ideas’ should never have been taken for the main method of philosophy, let alone for its one true method. Even Locke introduced it merely as a method of dealing with certain preliminaries (preliminaries for a science of ethics); and it was used by both Berkeley and Hume chiefly as a weapon for harrying their opponents. Their own interpretation of the world—the world of things and of men—which they were anxious to impart to us was never based upon this method. Berkeley did not base his religious views on it, nor Hume his political theories (though he based his determinism on it). But my gravest objection to the belief that either the ‘new way of ideas’ or the ‘new way of words’ is the main method of epistemology—or perhaps even of philosophy—is this. The problem of epistemology may be approached from two sides: (1) as the problem of ordinary or common-sense knowledge, or (2) as the problem of scientific knowledge. Those philosophers who favour the first approach think, rightly, that scientific knowledge can only be an exten- sion of common-sense knowledge, and they also think, wrongly, that common-sense knowledge is the easier of the two to analyse. In this way these philosophers come to replace the ‘new way of ideas’ by an analysis of ordinary language—the language in which common-sense knowledge is formulated. They replace the analysis of vision orpreface, 1959 xxiii essence of philosophy, to be distilled and condensed into a definition. A definition of the word ‘philosophy’ can only have the character of a convention, of an agreement; and I, at any rate, see no merit in the arbitrary proposal to define the word ‘philosophy’ in a way that may well prevent a student of philosophy from trying to contribute, qua philosopher, to the advancement of our knowledge of the world. Also, 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 contribu- tion 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. Such are, in brief, my reasons for believing that even within the province of epistemology, the first approach mentioned above—that is to say, the analysis of knowledge by way of an analysis of ordinary language—is too narrow, and that it is bound to miss the most interesting problems. Yet I am far from agreeing with all those philosophers who favour that other approach to epistemology—the approach by way of an analysis of scientific knowledge. In order to explain more easily where I disagree and where I agree, I am going to sub-divide the philosophers who adopt this second approach into two groups—the goats and the sheep, as it were. The first group consists of those whose aim is to study ‘the language of science’, and whose chosen philosophical method is the construc- tion of artificial model languages; that is to say, the construction of what they believe to be models of ‘the language of science’. The second group does not confine itself to the study of the language of science, or any other language, and it has no such chosen philo- sophical method. Its members philosophize in many different ways, because they have many different problems which they want to solve; and any method is welcome to them if they think that it may help themxxiv preface, 1959 to see their problems more clearly, or to hit upon a solution, however tentative. I turn first to those whose chosen method is the construction of artificial models of the language of science. Historically, they too take their departure from the ‘new way of ideas’. They too replace the (pseudo-) psychological method of the old ‘new way’ by linguistic analysis. But perhaps owing to the spiritual consolations offered by the hope for knowledge that is ‘exact’ or ‘precise’ or ‘formalized’, the chosen object of their linguistic analysis is ‘the language of science’ rather than ordinary language. Yet unfortunately there seems to be no such thing as ‘the language of science’. It therefore becomes necessary for them to construct one. However, the construction of a full-scale working model of a language of science—one in which we could operate a real science such as physics—turns out a little difficult in practice; and for this reason we find them engaged in the construction of intricate working models in miniature—of vast systems of minute gadgets. In my opinion, this group of philosophers gets the worst of both worlds. By their method of constructing miniature model languages they miss the most exciting problems of the theory of knowledge— those connected with its advancement. For the intricacy of the outfit bears no relation to its effectiveness, and practically no scientific theory of any interest can be expressed in these vast systems of minutiae. These model languages have no bearing on either science or common sense. Indeed, the models of ‘the language of science’ which these philo- sophers construct have nothing to do with the language of modern science. This may be seen from the following remarks which apply to the three most widely known model languages. (They are referred to in notes 13 and 15 to appendix vii, and in note 2 to section 38.) The first of these model languages lacks even the means of expressing iden- tity. As a consequence, it cannot express an equation: it does not con- tain even the most primitive arithmetic. The second model language works only as long as we do not add to it the means of proving the usual theorems of arithmetic—for example, Euclid’s theorem that there is no greatest prime number, or even the principle that every number has a successor. In the third model language—the mostpreface, 1959 xxv elaborate and famous of all—mathematics can again not be formulated; and, what is still more interesting, there are no measurable properties expressible in it. For these reasons, and for many others, the three model languages are too poor to be of use to any science. They are also, of course, essentially poorer than ordinary languages, including even the most primitive ones. The limitations mentioned were imposed upon the model languages simply because otherwise the solutions offered by the authors to their problems would not have worked. This fact can be easily proved, and it has been partly proved by the authors themselves. Nevertheless, they all seem to claim two things: (a) that their methods are, in some sense or other, capable of solving problems of the theory of scientific know- ledge, or in other words, that they are applicable to science (while in fact they are applicable with any precision only to discourse of an extremely primitive kind), and (b) that their methods are ‘exact’ or ‘precise’. Clearly these two claims cannot both be upheld. Thus the method of constructing artificial model languages is incap- able of tackling the problems of the growth of our knowledge; and it is even less able to do so than the method of analysing ordinary lan- guages, simply because these model languages are poorer than ordin- ary languages. It is a result of their poverty that they yield only the most crude and the most misleading model of the growth of knowledge— the model of an accumulating heap of observation statements. I now turn to the last group of epistemologists—those who do not pledge themselves in advance to any philosophical method, and who make use, in epistemology, of the analysis of scientific problems, theor- ies, and procedures, and, most important, of scientific discussions. This group can claim, among its ancestors, almost all the great philosophers of the West. (It can claim even the ancestry of Berkeley despite the fact that he was, in an important sense, an enemy of the very idea of rational scientific knowledge, and that he feared its advance.) Its most important representatives during the last two hundred years were Kant, Whewell, Mill, Peirce, Duhem, Poincaré, Meyerson, Russell, and—at least in some of his phases—Whitehead. Most of those who belong to this group would agree that scientific knowledge is the result of the growth of common-sense knowledge. But all of them discovered that scientific knowledge can be more easily studied than common-sensexxvi preface, 1959 knowledge. For it is common-sense knowledge writ large, as it were. Its very problems are enlargements of the problems of common-sense know- ledge. For example, it replaces the Humean problem of ‘reasonable belief’ by the problem of the reasons for accepting or rejecting scien- tific theories. And since we possess many detailed reports of the discus- sions pertaining to the problem whether a theory such as Newton’s or Maxwell’s or Einstein’s should be accepted or rejected, we may look at these discussions as if through a microscope that allows us to study in detail, and objectively, some of the more important problems of ‘reasonable belief’. This approach to the problems of epistemology gets rid (as do the other two mentioned) of the pseudo-psychological or ‘subjective’ method of the new way of ideas (a method still used by Kant). It suggests that we analyse scientific discussions, and also scientific prob- lem situations. And so it can help us to understand the history of scientific thought. I have tried to show that the most important of the traditional prob- lems of epistemology—those connected with the growth of knowledge— transcend the two standard methods of linguistic analysis and require the analysis of scientific knowledge. But the last thing I wish to do, however, is to advocate another dogma. Even the analysis of science— the ‘philosophy of science’—is threatening to become a fashion, a specialism. yet philosophers should not be specialists. For myself, 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.preface, 1959 xxvii ACKNOWLEDGMENTS, 1960 and 1968 I wish to thank Mr. David G. Nicholls for communicating to me the admirable passage, now printed on page xvii, which he discovered among the Acton Manuscripts in the Library of Cambridge University (Add. MSS 5011:266). The reprint of the book gives me the welcome opportunity to quote this passage. Summer 1959 In this second English edition four short Addenda have been added to the appendices. Minor mistakes have been corrected, and I have made a few linguistic improvements. Misprints have been corrected that were brought to my notice by Imre Lakatos, David Miller, and Alan Musgrave. They also suggested many new entries in the Index of Subjects. I am very grateful to them. My greatest debt is to Paul Bernays who, shortly after this book had appeared in English, checked through my axiomatization of the prob- ability calculus, especially the new appendix v. I value his approval more highly than I can express in words. It does not, of course, absolve me from bearing the sole responsibility for any mistake I may have made. November 1967 K. R. P.Part I Introduction to the Logic of Science1 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 sys- tems 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. 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 singular4 the logic of science 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 mat- ter 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 the validity or the truth of universal statements which are based on experience, such as the hypotheses and 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 itsa survey of some fundamental problems 5 theories from the fanciful and arbitrary creations of the poet’s 1 mind.’ 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 deductive 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 2 principle in everyday life either’. 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 prin- 1 ciple of induction should have been clear from the work of Hume; 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 1 H. Reichenbach, Erkenntnis 1, 1930, p. 186 (cf. also pp. 64 f.). Cf. the penultimate paragraph of Russell’s chapter xii, on Hume, in his History of Western Philosophy, 1946, p. 699. 2 Reichenbach ibid., p. 67. 1 The decisive passages from Hume are quoted in appendix vii, text to footnotes 4, 5, and 6; see also note 2 to section 81, below.6 the logic of science principle of induction (which he formulated as the ‘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 here sketched are insurmountable. So also, I fear, are those inherent in the doctrine, so widely current today, that inductive inference, although not ‘strictly valid’, can attain some degree of ‘reliability’ or of ‘probability’. According to this doctrine, inductive inferences are ‘probable infer- 3 ences’. ‘We have described’, says Reichenbach, ‘the principle of induc- tion as the means whereby science decides upon truth. To be more exact, we should say that it serves to decide upon probability. For it is not given to science to reach either truth or falsity . . . but scientific statements can only attain continuous degrees of probability whose 4 unattainable upper and lower limits are truth and falsity’. At this stage I can disregard the fact that the believers in inductive logic entertain an idea of probability that I shall later reject as highly unsuitable for their own purposes (see section 80, below). I can do so because the difficulties mentioned are not even touched by an appeal to probability. For if a certain degree of probability is to be assigned to statements based on inductive inference, then this will have to be justi- fied by invoking a new principle of induction, appropriately modified. And this new principle in its turn will have to be justified, and so on. Nothing is gained, moreover, if the principle of induction, in its turn, is taken not as ‘true’ but only as ‘probable’. In short, like every other form of inductive logic, the logic of probable inference, or ‘probability logic’, leads either to an infinite regress, or to the doctrine of 2 apriorism. The theory to be developed in the following pages stands directly opposed to all attempts to operate with the ideas of inductive logic. It 3 Cf. J. M. Keynes, A Treatise on Probability, 1921; O. Külpe, Vorlesungen über Logic (ed. by Selz, 1923); Reichenbach (who uses the term ‘probability implications’), Axiomatik der Wahrscheinlichkeitsrechnung, Mathem. Zeitschr. 34, 1932; and elsewhere. 4 Reichenbach, Erkenntnis 1, 1930, p. 186. 2 See also chapter 10, below, especially note 2 to section 81, and chapter ii of the Postscript for a fuller statement of this criticism.a survey of some fundamental problems 7 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 ‘deductiv- 5 ism’, in contrast to ‘inductivism’ ) I must first make clear the distinc- tion 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 psycho- logical 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 5 Liebig (in Induktion und Deduktion, 1865) was probably the first to reject the inductive method from the standpoint of natural science; his attack is directed against Bacon. Duhem (in La théorie physique, son objet et sa structure, 1906; English translation by P. P. Wiener: The Aim and Structure of Physical Theory, Princeton, 1954) holds pronounced deductivist views. (But there are also inductivist views to be found in Duhem’s book, for example in the third chapter, Part One, where we are told that only experiment, induction, and generalization have produced Descartes’s law of refraction; cf. the English translation, p. 34.) So does V. Kraft, Die Grundformen der Wissenschaftlichen Methoden, 1925; see also Carnap, Erkenntnis 2, 1932, p. 440.8 the logic of science us. Someone must have formulated it, and submitted it to logical examination. Accordingly I shall distinguish sharply between the process of con- ceiving a new idea, and the methods and results of examining it logic- ally. 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 sys- tematic 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 critically 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 cre- ative 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