Tag: science

Scientific methodology (German edition)

3. Die deduktive Überprüfung der Theorien. Die Methode der kritischen Nachprüfung, der Auslese der Theorien, ist nach unserer Auffassung immer die folgende: Aus der vorläufig unbegründeten Antizipation, dem Einfall, der Hypothese, dem theoretischen System, werden auf logisch-deduktivem Weg Folgerungen abgeleitet; diese werden untereinander und mit anderen Sätzen verglichen, indem man feststellt, welche logischen Beziehungen (z. B. Äquivalenz, Ableitbarkeit, Vereinbarkeit, Widerspruch) zwischen ihnen bestehen.

Dabei lassen sich insbesondere vier Richtungen unterscheiden, nach denen die Prüfung durchgeführt wird: der logische Vergleich der Folgerungen untereinander, durch den das System auf seine innere Widerspruchslosigkeit hin zu unter­suchen ist; eine Untersuchung der logischen Form der Theorie mit dem Ziel, festzustellen, ob es den Charakter einer empirisch-wissenschaftlichen Theorie hat, also z. B. nicht tautologisch ist; der Vergleich mit anderen Theorien, um unter anderem festzustellen, ob die zu prüfende Theorie, falls sie sich in den verschiedenen Prüfungen bewähren sollte, als wissenschaftlicher Fortschritt zu bewerten wäre; schließlich die Prüfung durch „empirische Anwendung“ der abgeleiteten Folgerungen.

Diese letzte Prüfung soll feststellen, ob sich das Neue, das die Theorie behauptet, auch praktisch bewährt, etwa in wis­senschaftlichen Experimenten oder in der technisch-praktischen Anwendung. Auch hier ist das Prüfungsverfahren ein deduktives: Aus dem System werden (unter Verwendung bereits anerkannter Sätze) empirisch moglichst leicht nach­prüf­bare bzw. anwendbare singuläre Folgerungen („Prognosen“) deduziert und aus diesen insbesondere jene ausgewählt, die aus bekannten Systemen nicht ableitbar sind, bzw. mit ihnen in Widerspruch stehen. Über diese – und andere – Folgerungen wird nun im Zusammenhang mit der praktischen Anwendung, den Experimenten usw. entschieden. Fällt die Entscheidung positiv aus, werden die singulären Folgerungen anerkannt, verifiziert, so hat das System die Prüfung vorläufig bestanden; wir haben keinen Anlaß, es zu verwerfen. Fällt eine Entscheidung negativ aus, werden Folgerungen falsifiziert, so trifft ihre Falsifikation auch das System, aus dem sie deduziert wurden.

Die positive Entscheidung kann das System immer nur vorläufig stützen; es kann durch spätere negative Entscheidungen immer wieder umgestoßen werden. Solang ein System eingehenden und strengen deduktiven Nachprüfungen standhält und durch die fortschreitende Entwicklung der Wissenschaft nicht überholt wird, sagen wir, daß es sich bewährt.

Induktionslogische Elemente treten in dem hier skizzierten Verfahren nicht auf; niemals schließen wir von der Geltung der singulären Satze auf die der Theorien. Auch durch ihre verifizierten Folgerungen können Theorien niemals als „wahr“ oder auch nur als „wahrscheinlich“ erwiesen werden.

The problem of the growth of knowledge

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.

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 philosophy. The method I have in mind is that of stating one’s problem clearly and of examining its various proposed solutions critically. [Preface, 1959]

The problem of the growth of knowledge (2)

Thus I see the problem of knowledge in a different way from that of my predecessors. Security and justification of claims to knowledge are not my problem. Instead, my problem is the growth of knowledge: in which sense can we speak of the growth or the progress of knowledge, and how can we achieve it? [37]

Open to suspicion

In preparing this table [a variation of Elderton’s Table of Goodness of Fit] we have borne in mind that in practice we do not want to know the exact value of P for any observed χ², but, in the first place, whether or not the observed value is open to suspicion. If P is between ·1 and ·9 there is certainly no reason to suspect the hypothesis tested. If it is below ·02 it is strongly indicated that the hypothesis fails to account for the whole of the facts. We shall not often be astray if we draw a conventional line at ·05, and consider that higher values of χ² indicate a real discrepancy. [80, 11th ed.]

In preparing this table [a variation of Elderton’s Table of Goodness of Fit] we have borne in mind that in practice we do not want to know the exact value of P for any observed χ², but, in the first place, whether or not the observed value is open to suspicion. If P is between ·1 and ·9 there is certainly no reason to suspect the hypothesis tested. If it is below ·02 it is strongly indicated that the hypothesis fails to account for the whole of the facts. Belief in the hypothesis as an accurate representation of the population sampled is confronted by the logical disjuction: Either the hypothesis is untrue, or the value χ² has attained by chance an exceptionally high value. The actual value of P obtainable from the table by interpolation indicates the strength of the evidence against the hypothesis. A value of χ² exceeding the 5 per cent. point is seldom to be disregarded. [80, 14th ed.]

Fisher’s severe tests

In choosing the grounds upon which a general hypothesis should be rejected, the exprimenter will rightly consider all points on which, in the light of current knowledge, the hypothesis may be imperfectly accurate, and will select tests, so far as possible, sensitive to these possible faults, rather than to others. [47]

The misuse of significance tests

The examples elaborated in the foregoing sections of numerical discrepancies arising from tbe rigid formulation of a rule, which at first acquaintance it seemed natural to apply to all tests of significance, constitute only one aspect of the deep-seated difference in point of view which arises when Tests of Significance are reinterpreted on the analogy of Acceptance Decisions. It is indeed not only numerically erroneous conclusions, serious as these are, that are to be feared from an uncritical acceptance of this analogy.

An important difference is that Decisions are final, while the state of opinion derived from a test of significance is provisional, and capable, not only of confirmation, but of revision. An acceptance procedure is devised for a whole class of cases. No particular thought is given to each case as it arises, nor is the tester’s capacity for learning exercised. A test of significance on the other hand is intended to aid the process of learning by observational experience.[100]

Unnatural science

If a broad line of demarcation is drawn between the natural sciences and what can only be described as the unnatural sciences, it will at once be recognized as a distinguishing mark of the latter that their practitioners try most painstakingly to imitate what they believe—quite wrongly, alas for them—to be the distinctive manners and observances of the natural sciences. Among these are:

(a) the belief that measurement and numeration are intrinsically praiseworthy activities (the worship, indeed, of what Ernst Gombrich calls idola quantitatis);

(b) the whole discredited farrago of inductivism—especially the belief that facts are prior to ideas and that a sufficiently voluminous compilation of facts can be processed by a calculus of discovery in such a way as to yield general prin­ciples and natural-seeming laws;

(c) another distinguishing mark of unnatural scientists is their faith in the efficacy of statistical formulas, particularly when processed by a computer—the use of which is in itself interpreted as a mark of scientific manhood. There is no need to cause offense by specifying the unnatural sciences, for their practitioners will recognize themselves easily: the shoe belongs where it fits. [167]

Scientific politics

According to this piecemeal view, there is no clearly marked division between the pre-scientific and the scientific ex­perimental approaches, even though the more and more conscious application of scientific, that is to say, of critical methods, is of great importance. Both approaches may be described, fundamentally, as utilizing the method of trial and error. We try; that is, we do not merely register an observation, but make active attempts to solve some more or less practical and definite problems. And we make progress if, and only if, we are prepared to learn from our mistakes: to recognize our errors and to utilize them critically instead of persevering in them dogmatically. Though this analysis may sound trivial, it describes, I believe, the method of all empirical sciences. This method assumes a more and more scien­tific character the more freely and consciously we are prepared to risk a trial, and the more critically we watch for the mistakes we always make. …

For the piecemeal technologist or engineer these views mean that, if he wishes to introduce scientific methods into the study of society and into politics, what is needed most is the adoption of a critical attitude, and the realization that not only trial but also error is necessary. And he must learn not only to expect mistakes, but consciously to search for them. We all have an unscientific weakness for being always in the right, and this weakness seems to be particularly common among professional and amateur politicians. But the only way to apply something like scientific method in politics is to proceed on the assumption that there can be no political move which has no drawbacks, no undesirable consequen­ces. To look out for these mistakes, to find them, to bring them into the open, to analyse them, and to learn from them, this is what a scientific politician as well as a political scientist must do. Scientific method in politics means that the great art of convincing ourselves that we have not made any mistakes, of ignoring them, of hiding them, and of blaming others for them, is replaced by the greater art of accepting the responsibility for them, of trying to learn from them, and of applying this knowledge so that we may avoid them in future. [80-1]

Criticism as respect

The Open Society – and by this I mean both the society and the book – is opposed not just to this or that authority, and not just to Plato, Hegel, and Marx. It is opposed to the very idea that there can be anything like cognitive authorities whom we can rely upon or the truth.

So if we are going to understand open society as scientific or rational society, then we must also understand science and rationality in Popper’s terms. We must think of science not as an institutionalized hierarchy of experts, but as a never-ending process of problem-solving in which we propose tentative solutions to our problems and then try to elim­inate the errors in our proposals. We must think of rationality not in terms of justification, but in terms of criticism. And we must think of criticism not as an offense, or as a show of contempt or disdain, but as one of the greatest signs of respetct that one mind can show to another. [47]

On piecemeal reform vs revolution

And it is a fact that my social theory (which favours gradual and piecemeal reform, reform controlled by a critical com­parison between expected and achieved results) contrasts with my theory of method, which happens to be a theory of scientific and intellectual revolutions. [68]