Tag: theory

Science: a growing system of problems

It seems to me that most philosophers of science use the term ‘accepted’ or ‘acceptable’ as a substitute for ‘believed in’ or ‘worthy of being believed in’. There may be a lot of theories in science that are true and therefore worthy of being be­lieved in. But according to my view of the matter, this worthiness is no concern of science. For science does not attempt positively to justify or to establish this worthiness. On the contrary, it is mainly concerned with criticizing it. It regards, or should regard, the overthrow of even its most admirable and beautiful theories as a triumph, an advance. For we cannot overthrow a good theory without learning an immense amount from it and from its failure. As always, we learn from our mistakes.

The overthrow of a theory always creates new problems. But even if a new theory is not yet overthrown, it will, as we have seen from the example of Bohr’s theory, create new problems. And the quality, the fertility, and the depth of the new problems which a theory creates are the best measures of its intrinsic scientific interest.

To sum up, the question of the acceptance of theories should, I propose, be demoted to the status of a minor problem. For science may be regarded as a growing system of problems, rather than as a system of beliefs. And for a system of problems, the tentative acceptance of a theory or a conjecture means hardly more than that it is considered worthy of further criticism. [103]

Understanding a theory’s underlying problems

Or take as an example Bohr’s theory (1913) of the hydrogen atom. This theory was describing a model, and was there­fore intuitive and visualizable. Yet it was also very perplexing. Not because of any intuitive difficulty, but because it assumed, contrary to Maxwell’s and Lorentz’s theory and to well-known experimental effects, that a periodically moving electron, a moving electric charge, need not always create a disturbance of the eletromagnetic field, and so need not always send out electromagnetic waves. This difficulty is a logical one – a clash with other theories. And no one can be said to understand Bohr’s theory who does not understand this difficulty and the reasons why Bohr boldly accepted it, thus departing in a revolutionary way from earlier and well-established theories.

But the only way to understand Bohr’s reasons is to understand his problem – the problem of combining Rutherford’s atom model with a theory of emission and absorption of light, and thus with Einstein’s photon theory, and with the dis­creteness of atomic spectra. The understanding of Bohr’s theory does not lie in visualizing it intuitively but in gaining familiarity with the problems it tries to solve, and in the appreciation of both the explanatory power of the solution and the fact, that the new difficulty that it creates constitutes an entirely new problem of great fertility.

The question whether or not a theory or a conjecture is more or less satisfactory or, if you like prima facie acceptable as a solution of the problem which it sets out to solve is largely a question of purely deductive logic. It is a matter of getting acquainted with the logical conclusions which may be drawn from the theory, and of judging whether or not these con­clusions (a) yield the desired solution and (b) yield undesirable by-products – for example some insoluble paradox, some absurdity. [102]

Letting our theories die in our stead

As opposed to this, traditional epistemology is interested in the second world [World 2]: in knowledge as a certain kind of belief—justifiable belief, such as belief based upon perception. As a consequence, this kind of belief philosophy cannot explain (and dos not even try to explain) the decisive phenomenon that scientists criticize their theories and so kill them. Scientists try to eliminate their false theories, they try to let them die in their stead. The believer—whether animal or man—perishes with his false beliefs. [122]

Science is a way of thinking

Science is a way of thinking much more than it is a body of knowledge. Its goal is to find out how the world works, to seek what regularities there may be, to penetrate the connections of things—from subnuclear particles, which may be the constituents of all matter, to living organisms, the human social community, and thence to the cosmos as a whole. Our intuition is by no means an infallible guide. Our perceptions may be distorted by training and prejudice or merely because of the limitations of our sense organs, which, of course, perceive directly but a small fraction of the phenomena of the world. Even so straightforward a question as whether in the absence of friction a pound of lead falls faster than a gram of fluff was answered incorrectly by Aristotle and almost everyone else before the time of Galileo. Science is based on experiment, on a willingness to challenge old dogma, on an openness to see the universe as it really is. Accordingly, science sometimes requires courage—at the very least the courage to question the conventional wisdom.

Beyond this the main trick of science is to really think of something: the shape of clouds and their occasional sharp bottom edges at the same altitude everywhere in the sky; the formation of the dewdrop on a leaf; the origin of a name or a word—Shakespeare, say, or “philanthropic”; the reason for human social customs—the incest taboo, for example; how it is that a lens in sunlight can make paper burn; how a “walking stick” got to look so much like a twig; why the Moon seems to follow us as we walk; what prevents us from digging a hole down to the center of the Earth; what the definition is of “down” on a spherical Earth; how it is possible for the body to convert yesterday’s lunch into today’s muscle and sinew; or how far is up—does the universe go on forever, or if it does not, is there any meaning to the question of what lies on the other side? Some of these questions are pretty easy. Others, especially the last, are mys­teries to which no one even today knows the answer. They are natural questions to ask. Every culture has posed such questions in one way or another. Almost always the proposed answers are in the nature of “Just So Stories,” attempted explanations divorced from experiment, or even from careful comparative observations.

But the scientific cast of mind examines the world critically as if many alternative worlds might exist, as if other things might be here which are not. Then we are forced to ask why what we see is present and not something else. Why are the Sun and the Moon and the planets spheres? Why not pyramids, or cubes, or dodecahedra? Why not irregular, jumbly shapes? Why so symmetrical worlds? If you spend any time spinning hypotheses, checking to see whether they make sense, whether they conform to what else we know, thinking of tests you can pose to substantiate or deflate your hypotheses, you will find yourself doing science. And as you come to practice this habit of thought more and more you will get better and better at it. To penetrate into the heart of the thing—even a little thing, a blade of grass, as Walt Whitman said—is to experience a kind of exhilaration that, it may be, only human beings of all the beings on this planet can feel. We are an intelligent species and the use of our intelligence quite properly gives us pleasure. In this respect the brain is like a muscle. When we think well, we feel good. Understanding is a kind of ecstasy. [15]

Facts do not a science make

Even a science is not merely a ‘body of facts’. It is, at the very least, a collection, and as such it is dependent upon the collector’s interests, upon a point of view. In science, this point of view is usually determined by a scientific theory; that is to say, we select from the infinite variety of facts, and from the infinite variety of aspects of facts, those facts and those aspects which are interesting because they are connected with some more or less preconceived scientific theory. [ch. 25, 535-6]

On auxiliary hypotheses

As regards auxiliary hypotheses we propose to lay down the rule that only those are acceptable whose introduction does not diminish the degree of falsifiability or testability of the system in question, but, on the contrary, increases it. … If the degree of falsifiability is increased, then introducing the hypothesis has actually strengthened the theory: the system now rules out more than it did previously: it prohibits more. We can also put it like this. The introduction of an auxiliary hypothesis should always be regarded as an attempt to construct a new system; and this new system should then always be judged on the issue of whether it would, if adopted, constitute a real advance in our knowledge of the world. An example of an auxiliary hypothesis which is eminently acceptable in this sense is Pauli’s exclusion principle. An example of an unsatisfactory auxiliary hypothesis would be the contraction hypothesis of Fitzgerald and Lorentz which had no falsifiable consequences but merely served to restore the agreement between theory and experiment … . [62]

The logic of scientific methodology

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, 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—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 [the] theory withstands detailed and severe tests and is not superseded by another theory 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’. [9-10]

The thousand-fold experience of induction

I found that those of my friends who were admirers of Marx, Freud, and Adler, were impressed by a number of points common to these theories, and especially by their apparent explanatory power. These theories appeared to be able to explain practically everything that happened within the fields to which they referred. The study of any of them seemed to have the effect of an intellectual conversion or revelation, opening your eyes to a new truth hidden from those not yet initiated. Once your eyes were thus opened you saw confirming instances everywhere: the world was full of verifi­cations of the theory. Whatever happened always confirmed it. Thus its truth appeared manifest; and unbelievers were clearly people who did not want to see the manifest truth; who refuse to see it, either because it was against their class interest, or because of their repressions which were still ‘un-analyzed’ and crying out for treatment.

The most characteristic element in this situation seemed to me the incessant stream of confirmations, of observations which ‘verified’ the theories in question; and this point was constantly emphasize by their adherents. A Marxist could not open a newspaper without finding on every page confirming evidence for his interpretation of history; not only in the news, but also in its presentation—which revealed the class bias of the paper—and especially of course what the paper did not say. The Freudian analysts emphasized that their theories were constantly verified by their ‘clinical observa­tions’. As for Adler, I was much impressed by a personal experience. Once, in 1919, I reported to him a case which to me did not seem particularly Adlerian, but which he found no difficulty in analyzing in terms of his theory of inferiority feelings, although he had not even seen the child. Slightly shocked, I asked him how he could be so sure. ‘Because of my thousandfold experience’, he replied; whereupon I could not help saying: ‘And with this new case, I suppose, your experience has become thousand-and-one-fold.’ [45-6]

Rational policy-making

How can we formulate policies for the unknown? If we cannot derive them from our best existing knowledge, or from dogmatic rules of thumb like blind optimism or pessimism, where can we derive them from? Like scientific theories, policies cannot be derived from anything. They are conjectures. And we should choose between them not on the basis of their origin, but according to how good they are as explanations: how hard to vary. …

The question ‘How can we hope to detect and eliminate error?’ is echoed by Feynman’s remark that ‘science is what we have learned about how to keep from fooling ourselves’. And the answer is basically the same for human decision-­making as it is for science: it requires a tradition of criticism, in which good explanations are sought – for example, explanations of what has gone wrong, what would be better, what effect various policies have had in the past and would have in the future.

But what use are explanations if they cannot make predictions and so cannot be tested through experience, as they can be in science? This is really the question: how is progress possible in philosophy? As I discussed in Chapter 5, it is obtained by seeking good explanations. The misconception that evidence can play no legitimate role in philosophy is a relic of empiricism. Objective progress is indeed possible in politics just as it is in morality generally and in science. [208-9]

Rejecting unscientific theories out of hand

We do not test every testable theory, but only the few that we find are good explanations. Science would be impossible if it were not for the fact that the overwhelming majority of false theories can be rejected out of hand without any experi­ment, simply for being bad explanations. [25]