Tag: induction

The naive “anthropologist from Mars”

Zehnte These: Der Sieg der Anthropologie ist der Sieg einer angeblich beobachtenden, angeblich beschreibenden und angeblich induktiv-generalisierenden Methodologie, und vor allem anderen einer angeblich objektiveren und daher dem Anschein nach naturwissenschaftlichen Methode. Es ist ein Pyrrhussieg; noch ein solcher Sieg, und wir sind verloren – das heißt nämlich die Anthropologie und die Soziologie.

Meine zehnte These ist, wie ich gerne zugebe, ein wenig zu scharf gefasst. Vor allem muß ich zugeben, daß viel Interessantes und Wichtiges von der sozialen Anthropologie entdeckt wurde und daß sie eine der erfolgreichsten Sozialwissenschaften ist. Und ich will auch gerne zugeben, daß es für uns Europäer von großem Reiz und von großem Interesse sein kann, uns einmal selbst durch die Brille des sozialen Anthropologen zu betrachten. Aber obwohl diese Brille vielleicht farbiger ist als andere Brillen, so ist sie eben deshalb wohl kaum objektiver. Der Anthropologe ist nicht der Beobachter vom Mars, der er oft zu sein glaubt, und dessen soziale Rolle er nicht selten und nicht ungern zu spielen versucht; und es gibt auch keinen Grund, anzunehmen, daß ein Bewohner vom Mars uns „objektiver“ sehen würde, als wir uns zum Beispiel selbst sehen. [85]

Misguided “scientism”

Um den Gehalt dieser meiner Hauptthese und ihre Bedeutung für die Soziologie ein wenig anzudeuten, wird es zweck­mäßig sein, ihr gewisse andere Thesen einer weit verbreiteten und oft ganz unbewußt absorbierten Methodologie gegenüberzustellen.

Da ist zum Beispiel der verfehlte und mißverständliche methodologische Naturalismus oder Szientismus, der verlangt, daß die Sozialwissenschaften endlich von den Naturwissenschaften lernen, was wissenschaftliche Methode ist. Dieser verfehlte Naturalismus stellt Forderungen auf wie: Beginne mit Beobachtungen und Messungen; das heißt zum Bei­spiel, mit statistischen Erhebungen; schreite dann induktiv zu Verallgemeinerungen vor und zur Theorienbildung. Auf diese Weise wirst Du dem Ideal der wissenschaftlichen Objektivität näher kommen, soweit das in den Sozialwissen­schaften überhaupt möglich, ist. Dabei mußt Du Dir darüber klar sein, daß in den Sozialwissenschaften die Objektivität weit schwieriger zu erreichen ist (falls sie überhaupt zu erreichen ist) als in den Naturwissenschaften; denn Objektivität bedeutet Wertfreiheit, und der Sozialwissenschaftler kann sich nur in den seltensten Fällen von den Wertungen seiner eigenen Gesellschaftsschicht soweit emanzipieren, um auch nur einigermaßen zur Wertfreiheit und Objektivität vor­zudringen.

Meiner Meinung nach ist jeder der Sätze, die ich hier diesem verfehlten Naturalismus zugeschrieben habe, grund­falsch und auf ein Mißverständnis der naturwissenschaftlichen Methode begründet, ja geradezu auf einen Mythus – einen leider allzu weit verbreiteten und einflußreichen Mythus vom induktiven Charakter der naturwissenschaftlichen Methode und vom Charakter der naturwissenschaftlichen Objektivität. [83]

Induction, philosophy’s toughest zombie

Science is an exercise in inductive reasoning: we are making observations and trying to infer general rules from them. Induction can never be certain. In contrast, deductive reasoning is easier: you deduce what you would expect to ob­serve if some general rule were true and then compare it with what you actually see. The problem is that, for a scientist, deductive arguments don’t directly answer the question that you want to ask.

The problem is epistemology, not statistics

Significance tests have a role to play in social science research but their current widespread use in appraising theories is often harmful. The reason for this lies not in the mathematics but in social scientists’ poor understanding of the logical relation between theory and fact, that is, a methodological or epistemological unclarity. Theories entail observations, not conversely. Although a theory’s success in deriving a fact tends to corroborate it, this corroboration is weak unless the fact has a very low prior probability and there are few possible alternative theories. The fact of a nonzero difference or correlation, such as we infer by refuting the null hypothesis, does not have such a low probability because in social science everything correlates with almost everything else, theory aside. In the “strong” use of significance tests, the theory predicts a numerical point value, or narrow range, so the hypothesis test subjects the theory to a grave risk of being falsified if it is objectively incorrect. In general, setting up a confidence interval is preferable, being more informa­tive and entailing null hypothesis refutation if a difference falls outside the interval. Significance tests are usually more defensible in technological contexts (e.g., evaluating an intervention) than for theory appraisal. [393]

Inductive psychology vs deductive physics

Contrast this bizarre state of affairs with the state of affairs in physics. While there are of course a few exceptions, the usual situation in the experimental testing of a physical theory at least involves the prediction of a form of function (with parameters to be fitted); or, more commonly, the prediction of a quantitative magnitude (point-value). Improvements in the accuracy of determining this experimental function-form or point-value, whether by better instrumentation for control and making observations, or by the gathering of a larger number of measurements, has the effect of narrowing the band of tolerance about the theoretically predicted value. What does this mean in terms of the significance-testing model? It means: In physics, that which corresponds, in the logical structure of statistical inference, to the old-fashioned point-null hypothesis H0 is the value which flows as a consequence of the substantive theory T; so that an increase in what the statistician would call “power” or “precision” has the methodological effect of stiffening the experimental test, of setting up a more difficult observational hurdle for the theory T to surmount. Hence, in physics the effect of improving precision or power is that of decreasing the prior probability of a successful experimental outcome if the theory lacks verisimil­itude, that is, precisely the reverse of the situation obtaining in the social sciences.

As techniques of control and measurement improve or the number of observations increases, the methodological effect in physics is that a successful passing of the hurdle will mean a greater increment in corroboration of the substantive theory; whereas in psychology, comparable improvements at the experimental level result in an empirical test which can provide only a progressively weaker corroboration of the substantive theory.

In physics, the substantive theory predicts a point-value, and when physicists employ “significance tests,” their mode of employment is to compare the theoretically predicted value x0 with the observed mean x0, asking whether they differ (in either direction!) by more than the “probable error” of determination of the latter. Hence H : H0 = μx functions as a point-null hypothesis, and the prior (logical, antecedent) probability of its being correct in the absence of theory approximates zero. As the experimental error associated with our determination of x0 shrinks, values of x0 consistent with x0 (and hence, compatible with its implicans T) must lie within a narrow range. In the limit (zero probable error, corresponding to “perfect power” in the significant test) any non-zero difference (x0 – x0) provides a modus tollens refutation of T. If the theory has negligible verisimilitude, the logical probability of its surviving such a test is negligible. Whereas in psychol­ogy, the result of perfect power (i.e., certain detection of any non-zero difference in the predicted direction) is to yield a prior probability p = ½ of getting experimental results compatible with T, because perfect power would mean guaranteed detection of whatever difference exists; and a difference [quasi] always exists, being in the “theoretically expected direc­tion” half the time if our substantive theories were all of negligible verisimilitude (two-urn model). [112-3]

Methodological confirmation bias

Inadequate appreciation of the extreme weakness of the test to which a substantive theory T is subjected by merely pre­dicting a directional statistical difference d > 0 is then compounded by a truly remarkable failure to recognize the logical asymmetry between, on the one hand, (formally invalid) “confirmation” of a theory via affirming the consequent in an argument of form: [T ⊃ H1, H1, infer T], and on the other hand the deductively tight refutation of the theory modus tollens by a falsified prediction, the logical form being: [T ⊃ H1, ~H1, infer ~T].

While my own philosophical predilections are somewhat Popperian, I daresay any reader will agree that no full-fledged Popperian philosophy of science is presupposed in what I have just said. The destruction of a theory modus tollens is, after all, a matter of deductive logic; whereas that the “confirmation” of a theory by its making successful predictions involves a much weaker kind of inference. This much would be conceded by even the most anti-Popperian “inductivist.” The writing of behavior scientists often reads as though they assumed—what it is hard to believe anyone would ex­plicitly assert if challenged—that successful and unsuccessful predictions are practically on all fours in arguing for and against a substantive theory. [112]

The soft corroboration of psychology

Isn’t the social scientist’s use of the null hypothesis simply the application of Popperian (or Bayesian) thinking in con­texts in which probability plays such a big role? No, it is not. One reason it is not is that the usual use of null hypothesis testing in soft psychology as a means of “corroborating” substantive theories does not subject the theory to grave risk of refutation modus tollens, but only to a rather feeble danger. The kinds of theories and the kinds of theoretical risks to which we put them in soft psychology when we use significance testing as our method are not like testing Meehl’s theory of weather by seeing how well it forecasts the number of inches it will rain on certain days. Instead, they are depressingly close to testing the theory by seeing whether it rains in April at all, or rains several days in April, or rains in April more than in May. [821-2]

A travesty of the nature of scientific thought

The scientific paper in its orthodox form does embody a totally mistaken conception, even a travesty, of the nature of scientific thought. [42]

The scientific paper is a fraud in the sense that it does give a totally misleading narrative of the processes of thought that go into the making of scientific discoveries. The inductive format of the scientific paper should be discarded. The discussion which in the traditional scientific paper goes last should surely come at the beginning. The scientific facts and scientific acts should follow the discussion, and scientists should not be ashamed to admit, as many of them apparently are ashamed to admit, that hypotheses appear in their minds along uncharted by-ways of thought; that they are imaginative and inspirational in character; that they are indeed adventures of the mind. [43]

The mistaken theory of objectivity

No doubt the idea which inspires the inductive style—the idea of adhering strictly to the observed facts and of excluding bias and prejudice—is laudable. And no doubt those trained to write in this way are unaware that this laudable and apparently safe idea is itself the mistaken result of a prejudice—worse still, of a philosophical prejudice—and of a mistaken theory of objectivity. (Objectivity is not the result of disinterested and unprejudiced observation. Objectivity, and also unbiased observation, are the result of criticism, including the criticism of observational reports. For we cannot avoid or suppress our theories, or prevent them from influencing our observations; yet we can try to recognize them as hypotheses and to formulate them explicitly, so that they may be criticized.) [48]

The logic of discovering our errors

If the purpose of an argument is to prove its conclusion, then it is difficult to see the point of falsifiability. For deductive arguments cannot prove their conclusions any more than inductive ones can.

But if the purpose of the argument is to force us to choose, then the point of falsifiability becomes clear.

Deductive arguments force us to question, and to reexamine, and, ultimately, to deny their premises if we want to deny their conclusions. Inductive arguments simply do not.

This the real meaning of Popper’s Logic of Scientific Discovery—and it is the reason, perhaps, why so many readers have misunderstood its title and its intent. The logic of discovery is not the logic of discovering theories, and it is not the logic of discovering that they are true.

Neither deduction nor induction can serve as a logic for that.

The logic of discovery is the logic of discovering our errors. We simply cannot deny the conclusion of a deductive argu­ment without discovering that we were in error about its premises. Modus tollens can help us to do this if we use it to set problems for our theories. But while inductive arguments may persuade or induce us to believe things, they cannot help us discover that we are in error about their premises. [113-4]