BOOKS
On Scientific Method
By A. J. AYER NE of the merits of logical positivism was that kJ it aimed at annulling the divorce of philo- sophy from science. No one went so far as to revive the pretension of philosophy to be the queen of the sciences; but it was thought that she might at least find virtuous employment as their governess : a progressive governess, not one who presumed to impose tasks upon her pupils, but one who studied their characters, called their attention to their failings and helped them to develop their natural bents. The duty of philoso- phers was to purge science of metaphysics, to exhibit the logical relationships of scientific con- cepts and the logical structure of scientific systems, among other ways by constructing model lan- guages in which these relations would be clearly brought to light, to evaluate the status of scientific propositions and the nature of the support which they drew from their evidence, to determine what the strength and character of this evidence can be. There were some who thought that philosophy was also required to justify science by solving the notorious problem of induction : they did not suppose that certainty was attainable in science, but they hoped that by developing'the theory of Probability they would at least be able to show that some scientific hypotheses were very highly probable.
This is an attractive programme; the role which it assigns to philosophy is very far from trivial : the trouble with it is that it has proved un- expectedly difficult to fulfil. The method of eliminating metaphysics was to allow no state- ments to have factual meaning unless they were empirically confirmable. This method was power- ful, but the problem which it raised of formulat- ing an adequate theory of confirmation has not been satisfactorily met. Some model languages have been constructed, but it has not been shown that they suffice for the expression of any substan- tial part of current scientific theory. A great deal of valuable work has been done on the subject of Probability, particularly in the way of developing the frequency theory, but it has not yielded any answer to the problem of induction. Hume's argu- ment that the assumption of the uniformity of nature can neither be demonstrated nor even shown to be probable still stands in possession of the field.
Sometimes when a set of problems resists solu- tion, the explanation is that the problems have been wrongly formulated. That this is so in the Present case is the view taken by Karl Popper, who maintained from the start that the whole positivist Programme was misconceived. In a work of great originality and power, called Logik der Forn•huctg, Which was first published in Vienna in 1934, he argued that the positivists principle of verifiability should be replaced by a principle of falsifiability, and this should be regarded not as a criterion of meaning but as a rule of demarcation. Statements which were neither analytic nor falsifiable were not asserted to be meaningless; but they were to
be excluded from the domain of empirical science. The method of science, as Popper saw it, was to put up hypotheses and test them by trying to falsify them. So long as they survived these tests, the hypotheses were retained as part of accepted scientific theory: when they failed they were dis- carded and other hypotheses adopted in their place. The empirical content of a hypothesis depended on its degree of falsifiability; the larger the range of events with which the hypothesis was incompatible, the more empirical content it had. It was wrong, therefore, to suppose that scientists aim at putting forward probable hypotheses: the best hypotheses are those with the greatest empiri- cal content; but these, since they run the greatest risk of falsification, arc in themselves the least probable.
This squares with Popper's view that a hypo- thesis does not become more probable by being confirmed or, as he now prefers to say, corrobor- ated. The degree to which a hypothesis is cor- roborated depends upon the number and variety of the attempts to falsify it which it has success- fully resisted. But the fact that a hypothesis has survived such tests gives us no reason to suppose that it will continue to be successful in the future. It just is our habit to go on trusting hypotheses until they fail us. This practice has served us well in the past, but again this gives us no reason to suppose that its usefulness will continue. Thus Popper has not answered Hume; i do not think that he would claim to have. He would presum- ably argue that the kind of justification for scienti- fic method which is sought by those who do try to answer Hume was logically unobtainable, and therefore that the attempt should not be made.
The reason why Popper insists that empirical statements must be falsifiable, rather than veri- fiable, is that there is a logical asymmetry between verification and falsification. No finite number of positive instances will conclusively verify a uni- versal statement of unrestricted generality. From the fact that all observed As have been B it does not follow that all A's are B. On the other hand, a single negative instance will conclusively refute it. If even one A is found not to be B, the generalisa- tion is falsified. Of course, if we are determined to stick to a hypothesis, we can usually find means of protecting it from refutation by explaining away the observations which appear to contradict it. but Popper lays it down as a methodological rule that we are not to do this. Formally, the falsifiability of a hypothesis consists in its being incompatible with what Popper calls a basic statement. This is a statement to the effect that at a particular place and time there exists an object of such and such a sort : it is understood that the object and the properties which are ascribed to it are publicly observable. Statements of this kind are basic in the sense that it is by reference to their
* TIC LOGIC or• SCIEN1111C 1311WOVERY. By Karl R. Popper. (Hutchinson. 50s.)
truth or falsehood that the truth of other empirical statements is tested. But how are the basic state- ments themselves established? According to Pop- per, we just decide to accept them. Of course, these decisions are not meant to be arbitrary: they are motivated by our experience : but Popper does not explore the question in what sense, if any, they can be justified. He is rather severe on those who seek a more primitive basis in statements which describe the content of one's private experiences : but at least they are concerned with a genuine problem.
One difficulty which Popper's theory has to meet is that statements of probability, which figure so largely in science. are not faisifiable. The fact that a coin comes up tails a thousand, or a million, or a billion times in succession does not refute the statement that there is an equal probability of its coming up heads or tails: for however long the run of tails may be there is always the possibility that it will be counterbalanced at some later stage by an equal preponderance of heads. Popper is aware of this difficulty and meets it by laying down another methodological rule. When the dis- crepancy between the observed and the predicted frequency reaches a certain point the probability statement is to be treated as though it had been falsified. Popper has a good deal to say, on the sub- ject of probability and also on the subject of the quantum theory, where he boldly criticises both Heisenberg's and Bohr's interpretation of the principle of indeterminacy; though these sections are interesting in themselves, the plunge into tech- nical detail makes rather too abrupt a change in the general tempo of the book.
In the years that have passed since the first publication of Logik der Forschung, Professor Popper's ideas on the philosophy of science have become well known, but it was to be regretted that no systematic account of them was available in English. This deficiency has now been made good with the appearance of an English translation of this book, under the title of The Logic of Scienti- fic Discover %. .* The 'translation, which has been made by the author with the help of Dr. and Mrs. Freed is adequate, if a little fusty. The original text has not been modified, but Professor Popper has added a short new preface, a few explanatory notes, more modest in compass than in style, and some hundred and fifty pages of appendices. These appendices, which include an interesting letter from Einstein about the quantum theory, are mainly concerned with technical questions in the theory of probability : they contain, among other things, an ingenious proof that corroborating a hypothesis is not to be identified with making it more probable.
In these notes and appendices frequent reference is made to a forthcoming book, called Postscript: After Twenty Years, in which' Professor Popper sets out his present views on the topics covered by The Logic of Scientific Discovery. It is to be hoped that its appearance will not be long delayed. What- ever criticisms may be made of it, it is sure to deal with important problems, and to handle them ingeniously, boldly and with technical efficiency.
Previous page
