Tag: logic

Evading falsification

A third objection may seem more serious. It might be said that even if the asymmetry is admitted, it is still impossible, for various reasons, that any theoretical system should ever be conclusively falsified. For it is always possible to find some way of evading falsification, for example by introducing ad hoc an auxiliary hypothesis, or by changing ad hoc a defini­tion. It is even possible without logical inconsistency to adopt the position of simply refusing to acknowledge any falsi­fying experience whatsoever. Admittedly, scientists do not usually proceed in this way, but logically such procedure is possible; and this fact, it might be claimed, makes the logical value of my proposed criterion of demarcation dubious, to say the least.

I must admit the justice of this criticism; but I need not therefore withdraw my proposal to adopt falsifiability as a criterion of demarcation. For I am going to propose that the empirical method shall be characterized as a method that excludes precisely those ways of evading falsification which, as my imaginary critic rightly insists, are logically possible. Accord­ing to my proposal, what characterizes the empirical method is its manner of exposing to falsification, in every conceiv­able way, the system to be tested. Its aim is not to save the lives of untenable systems but, on the contrary, to select the one which is by comparison the fittest, by exposing them all to the fiercest struggle for survival. [19-20]

Singled out by experience

Now in my view there is no such thing as induction. Thus inference to theories, from singular statements which are ‘veri­fied by experience’ (whatever that may mean), is logically inadmissible. Theories are, therefore, never empirically veri­fiable. If we wish to avoid the positivist’s mistake of eliminating, by our criterion of demarcation, the theoretical systems of natural science, then we must choose a criterion which allows us to admit to the domain of empirical science even statements which cannot be verified.

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. [18]

Experience as a method

[W]e 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, i.e. 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.

But how is the system that represents our world of experience to be distinguished? The answer is: by the fact that it has been submitted to tests, and has stood up to tests. This means that it is to be distinguished by applying to it that deduc­tive method which it is my aim to analyse, and to describe.

‘Experience’, on this view, appears as a distinctive method whereby one theoretical system may be distinguished from others; so that empirical science seems to be characterized not only by its logical form but, in addition, by its distinctive method. [16-7]

The pivotal importance of a common purpose

My criterion of demarcation will accordingly have to be regarded as a proposal for an agreement or convention. As to the suitability of any such 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 anyone who envisages a system of absolutely certain, irrevocably true statements as the end and purpose of science will certainly reject the proposals I shall make here. And so will those who see ‘the essence of science … in its dignity’, which they think resides in its ‘wholeness’ and its ‘real truth and essentiality’. They will hardly be ready to grant this dignity to modern theoretical physics in which I and others see the most complete realization to date of what I call ‘empirical science’.

The aims of science which I have in mind are different. I do not try to justify them, however, by representing them as the true or the essential aims of science. This would only distort the issue, and it would mean a relapse into positivist dog­matism. There is only one way, as far as I can see, of arguing rationally in support of my proposals. This is to analyse their logical consequences: to point out their fertility—their power to elucidate the problems of the theory of knowledge.

Thus I freely admit that in arriving at my proposals I have been guided, in the last analysis, by value judgments and pre­dilections. But I hope that my proposals may be acceptable to those who value not only logical rigour but also freedom from dogmatism; who seek practical applicability, but are even more attracted by the adventure of science, and by discoveries which again and again confront us with new and unexpected questions, challenging us to try out new and hitherto undreamed-of answers. [15]

Vorläufer des Falsifikationsprinzips

Das Falsifikationsprinzip wurde erstmals von Karl Popper ausgesprochen. Erstmals? Alle philosophischen Ideen ha­ben Vorläufer. In unserem Falle ist der Oxforder Gelehrte Robert Grosseteste (etwa 1168-1253) ein besonders interes­santes Beispiel. Nach Losee war er der erste mittelalterliche Denker, der die logischen und methodologischen Pro­bleme von Induktion, Verifikation und Falsifikation systematisch untersuchte. (Bei Popper wird er, soweit ich sehe, nir­gends erwähnt. Aber Kopernikus erwähnt seinen wichtigsten Vorgänger, Aristarch, ja auch nicht.) Grosseteste benutzte und empfahl die Methode der Falsifikation, um mit Hilfe des modus tollens von einer Gruppe konkurrierender Hypo­thesen alle bis auf eine zu eliminieren. Die wesentliche Asymmetrie zwischen Verifizierbarkeit und Falsifizierbarkeit scheint er jedoch nicht er­kannt zu haben. [117]

How to get acquainted with a problem

We start, I say, with a problem – a difficulty. It is perhaps a practical problem, or a theoretical problem. Whatever it may be, when we first encounter the problem we cannot, obviously, know much about it. At best, we have only a vague idea what our problem really consists of. How, then, can we produce an adequate solution? Obviously, we cannot. We must first get better acquainted with the problem. But how?

My answer is very simple: by producing a very inadequate solution, and by criticizing this inadequate solution. Only in this way can we come to understand the problem. For to understand a problem means to understand why it is not easily soluble – why the more obvious solutions do not work. We must therefore produce these obvious solutions and try to find out why they will not do. In this way, we become acquainted with the problem. And in this way we may proceed from bad solutions to slightly better ones – provided always that we have the ability to guess again. [97-8]

The childish induction

In establishing axioms, another form of induction must be devised than has hitherto been employed, and it must be used for proving and discovering not first principles (as they are called) only, but also the lesser axioms, and the middle, and indeed all. For the induction which proceeds by simple enumeration is childish; its conclusions are precarious and exposed to peril from a contradictory instance; and it generally decides on too small a number of facts, and on those only which are at hand. But the induction which is to be available for the discovery and demonstration of sciences and arts, must analyze nature by proper rejections and exclusions; and then, after a sufficient number of negatives, come to a conclusion on the affirmative instances […]. [I/105]

Two concepts of induction

In the past, the term ‘induction’ has been used mainly in two senses. The first is repetitive induction (or induction by enumeration). This consists of often repeated observations and experiments, which are supposed to serve as premises in an argument establishing some generalization or theory. The invalidity of this kind of argument is obvious: no amount of observation of white swans establishes that all swans are white (or that the probability of finding a non-white swan is small). In the same way, no amount of observed spectra of hydrogen atoms on earth establishes that all hydrogen atoms emit spectra of the same kind. Theoretical considerations, however, may suggest the latter generalization, and further theoretical considerations may suggest that we should modify it by introducing Doppler shifts and Einsteinian gravitational redshifts.

Thus repetitive induction is out: it cannot establish anything.

The second main sense in which the term ‘induction’ has been used in the past is eliminative induction – induction by the method of eliminating or refuting false theories. This may look at first sight very much like the method of critical dis­cussion that I am advocating. But in fact it is very different. For Bacon and Mill and other exponents of this method of eliminative induction believed that by eliminating all false theories we can finally establish the true theory. In other words, they were unaware of the fact that the number of competing theories is always infinite – even though there are as a rule at any particular moment only a finite number of theories before us for consideration. [104-5]

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 mental process of critical rationalism

It is the fashion of the present time to disparage negative logic—that which points out weaknesses in theory or errors in practice, without establishing positive truths. Such negative criticism would indeed be poor enough as an ultimate re­sult; but as a means to attaining any positive knowledge or conviction worthy the name, it cannot be valued too highly; and until people are again systematically trained to it, there will be few great thinkers, and a low general average of intellect, in any but the mathematical and physical departments of speculation. On any other subject no one’s opinions deserve the name of knowledge, except so far as he has either had forced upon him by others, or gone through of him­self, the same mental process which would have been required of him in carrying on an active controversy with oppo­nents. That, therefore, which when absent, it is so indispensable, but so difficult, to create, how worse than absurd is it to forego, when spontaneously offering itself! If there are any persons who contest a received opinion, or who will do so if law or opinion will let them, let us thank them for it, open our minds to listen to them, and rejoice that there is some one to do for us what we otherwise ought, if we have any regard for either the certainty or the vitality of our convictions, to do with much greater labour for ourselves. [ch. II, 57-8]