Tag Archive: problems

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]


The belief that science proceeds from observation to theory is still so widely and so firmly held that my denial of it is often met with incredulity. I have even been suspected of being insincere – of denying what nobody in his senses can doubt.

But in fact the belief that we can start with pure observations alone, without anything in the nature of a theory, is absurd; as may be illustrated by the story of the man who dedicated his life to natural science, wrote down everything he could observe, and bequeathed his priceless collection of observations to the Royal Society to be used as inductive evi­dence. This story should show us that though beetles may profitably be collected, observations may not.

Twenty-five years ago I tried to bring home the same point to a group of physics students in Vienna by beginning a lec­ture with the following instructions: ‘Take pencil and paper; carefully observe, and write down what you have observed!’ They asked, of course, what I wanted them to observe. Clearly the instruction, ‘Observe!’ is absurd. (It is not even idio­matic, unless the object of the transitive verb can be taken as understood.) Observation is always selective. It needs a chosen object, a definite task, an interest, a point of view, a problem. And its description presupposes a descriptive lan­guage, with property words; it presupposes similarity and classification, which in its turn presupposes interests, points of view, and problems. [61]

Science: answers to our problems

Thus we accept the idea that the task of science is the search for truth, that is, for true theories (even though as Xeno­phanes pointed out we may never get them, or know them as true if we get them). Yet we also stress that truth is not the only aim of science. We want more than mere truth: what we look for is interesting truth – truth which is hard to come by. And in the natural sciences (as distinct from mathematics) what we look for is truth which has a high degree of explana­tory power, which implies that it is logically improbable.

For it is clear, first of all, that we do not merely want truth – we want more truth, and new truth. We are not content with ‘twice two equals four’, even though it is true: we do not resort to reciting the multiplication table if we are faced with a difficult problem in topology or in physics. Mere truth is not enough; what we look for are answers to our problems.

Only if it is an answer to a problem – a difficult, a fertile problem, a problem of some depth – does a truth, or a conjecture about the truth, become relevant to science. This is so in pure mathematics, and it is so in the natural sciences. And in the latter, we have something like a logical measure of the depth or significance of the problem in the increase of logical improbability or explanatory power of the proposed new answer, as compared with the best theory or conjecture pre­viously proposed in the field. [311-2]

The question of the authoritative sources of knowledge

Yet the traditional question of the authoritative sources of knowledge is repeated even today — and very often by posi­tivists, and by other philosophers who believe themselves to be in revolt against authority.

The proper answer to my question ‘How can we hope to detect and eliminate error?’ is, I believe, ‘By criticizing the theories or guesses of others and — if we can train ourselves to do so — by criticizing our own theories or guesses.’ (The latter point is highly desirable, but not indispensable; for if we fail to criticize our own theories, there may be others to do it for us.) This answer sums up a position which I propose to call ‘critical rationalism’. It is a view, an attitude, and a tradition, which we owe to the Greeks. It is very different from the ‘rationalism’ or ‘intellectualism’ of Descartes and his school, and very different even from the epistemology of Kant. Yet in the field of ethics, of moral knowledge, it was approached by Kant with his principle of autonomy. This principle expresses his realization that we must not accept the command of an authority, however exalted, as the basis of ethics. For whenever we are faced with a command by an authority, it is for us to judge, critically, whether it is moral or immoral to obey. The authority may have power to enforce its commands, and we may be powerless to resist. But if we have the physical power of choice, then the ultimate respon­sibility remains with us. It is our own critical decision whether to obey a command; whether to submit to an authority.

Kant boldly carried this idea into the field of religion: ‘…in whatever way’, he writes, ‘the Deity should be made known to you, and even … if He should reveal Himself to you: it is you … who must judge whether you are permitted to believe in Him, and to worship Him.’

In view of this bold statement, it seems strange that Kant did not adopt the same attitude — that of critical examination, of the critical search for error — in the field of science. I feel certain that it was only his acceptance of the authority of Newton’s cosmology — a result of its almost unbelievable success in passing the most severe tests — which prevented Kant from doing so. If this interpretation of Kant is correct, then the critical rationalism (and also the critical empiricism) which I advocate merely puts the finishing touch to Kant’s own critical philosophy. And this was made possible by Einstein, who taught us that Newton’s theory may well be mistaken in spite of its overwhelming success.

So my answer to the questions ‘How do you know? What is the source or the basis of your assertion? What obser­vations have led you to it?’ would be: ‘I do not know: my assertion was merely a guess. Never mind the source, or the sources, from which it may spring — there are many possible sources, and I may not be aware of half of them; and origins or pedigrees have in any case little bearing upon truth. But if you are interested in the problem which I tried to solve by my tentative assertion, you may help me by criticizing it as severely as you can; and if you can design some experimental test which you think might refute my assertion, I shall gladly, and to the best of my powers, help you to refute it.’ [34-5]

Knowledge is born out of problems

Vierte These: Soweit man überhaupt davon sprechen kann, daß die Wissenschaft oder die Erkenntnis irgendwo be­ginnt, so gilt folgendes: Die Erkenntnis beginnt nicht mit Wahrnehmungen oder Beobachtungen oder der Sammlung von Daten oder von Tatsachen, sondern sie beginnt mit Problemen. Kein Wissen ohne Probleme – aber auch kein Problem ohne Wissen. Das heißt, daß sie mit der Spannung zwischen Wissen und Nichtwissen beginnt: Kein Problem ohne Wissen – kein Problem ohne Nichtwissen. Denn jedes Problem entsteht durch die Entdeckung, daß etwas in unserem vermeintlichen Wissen nicht in Ordnung ist; oder logisch betrachtet, in der Entdeckung eines inneren Wider­spruches in unserem vermeintlichen Wissen, oder eines Widerspruches zwischen unserem vermeintlichen Wissen und den Tatsachen; oder vielleicht noch etwas richtiger ausgedrückt, in der Entdeckung eines anscheinenden Wider­spruches zwischen unserem vermeintlichen Wissen und den vermeintlichen Tatsachen. [80-1]

The evolution of problems

This consideration of the fact that theories or expectations are built into our very sense organs shows that the episte­mology of induction breaks down even before taking its first step. It cannot start from sense data or perceptions and build our theories upon them, since there are no such things a sense data or perceptions which are not built upon theories (or expectations—that is, the biological predecessors of linguistically formulated theories). Thus the ‘data’ are no basis of, no guarantee for, the theories. They are not more secure than any of our theories or ‘prejudices’ but, if anything, less so (assuming for argument’s sake that sense data exist and are not philosophers’ inventions). Sense organs incorporate the equivalent of primitive and uncritically accepted theories, which are less widely tested than scientific theories. …

Thus life proceeds, like scientific discovery, from old problems to the discovery of new and undreamt-of problems. And this process—that of invention and selection—contains in itself a rational theory of emergence. The steps of emergence which lead to a new level are in the first instance the new problems (P2) which are created by the error-elimination (EE) of a tentative theoretical solution (TT) of an old problem (P1). [146]

Not subjects but problems

Disciplines are distinguished partly for historical reasons and reasons of administrative convenience (such as the orga­nisation of teaching and appointments), and partly because the theories which we construct to solve our problems have a tendency to grow into unified systems. But all this classification and distinction is a comparatively unimportant and superficial affair. We are not students of some subject matter but students of problems. And problems may cut right across the borders of any subject matter or discipline. [88]

Truth relative to our problems

When the judge tells a witness that he should speak ‘The truth, the whole truth, and nothing but the truth’, then what he looks for is as much of the relevant truth as the witness may be able to offer. A witness who likes to wander off into irrelevancies is unsatisfactory as a witness, even though these irrelevancies may be truisms, and thus part of ‘the whole truth’. It is quite obvious that what the judge — or anybody else — wants when he asks for ‘the whole truth’ is as much interesting and relevant true information as can be got; and many perfectly candid witnesses have failed to disclose some important information simply because they were unaware of its relevance to the case.

Thus when we stress, with Busch, that we are not interested in mere truth but in interesting and relevant truth, then, I contend, we only emphasize a point which everybody accepts. And if we are interested in bold conjectures,even if these should soon turn out to be false, then this interest is due to our methodological conviction that only with the help of such bold conjectures can we hope to discover interesting and relevant truth.

There is a point here which, I suggest, it is the particular task of the logician to analyse. ‘Interest’, or ‘relevance’, in the sense here intended, can be objectively analysed; it is relative to our problems; and it depends on the explanatory power, and thus on the content or improbability, of the information. The measures alluded to earlier […] are precisely such measures as take account of some relative content of the information — its content relative to a hypothesis or to a problem. [312-3]

Science starts from problems

As to the starting point of science, I do not say that science starts from intuitions but that it starts from problems; that we arrive at a new theory, in the main, by trying to solve problems; that these problems arise in our attempts to understand the world as we know it […]. [209]

Piecemeal engineering in economics

This book is an invitation to think again, again: to turn away from the feeling that the fight against poverty is too over­whelming, and to start to think of the challenge as a set of concrete problems that, once properly identified and under­stood, can be solved one at a time. [2-3]

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