Tag Archive: induction

What argument can do

No argument can force us to accept the truth of any belief. But a valid deductive argument can force us to choose be­tween the truth of its conclusion on the one hand and the falsity of its premises on the other. [10]

The lapse from enlightenment to positivism

Our prognosis regarding the associated lapse from enlightenment into positivism, into the myth of that which is the case, and finally of the identity of intelligence and hostility to mind, has been overwhelmingly confirmed. Our concept of history does not believe itself elevated above history, but it does not merely chase after information in the positivist manner. [xii]

Decisions cannot be derived from facts

It is important for the understanding of this attitude to realize that these decisions can never be derived from facts (or from statements of facts), although they pertain to facts. The decision, for instance, to oppose slavery does not depend upon the fact that all men are born free and equal, and that no man is born in chains. For even if all were born free, some men might perhaps try to put others in chains, and they may even believe that they ought to put them in chains. And conversely, even if men were born in chains, many of us might demand the removal of these chains. Or to put this matter more precisely, if we consider a fact as alterable—such as the fact that many people are suffering from dis­eases—then we can always adopt a number of different attitudes towards this fact: more especially, we can decide to make an attempt to alter it; or we can decide to resist any such attempt; or we can decide not to take action at all.

All moral decisions pertain in this way to some fact or other, especially to some fact of social life, and all (alterable) facts of social life can give rise to many different decisions. Which shows that the decisions can never be derivable from these facts, or from a description of these facts. [ch. 5, 67]

Fisher on Bayesianism

[A]dvocates of inverse probability seem forced to regard mathematical probability, not as an objective quantity mea­sured by observable frequencies, but as measuring merely psychological tendencies, theorems respecting which are useless for scientific purposes. [6-7]

Weak statistical tests

The distinction between the strong and the weak use of significance tests is logical or epistemological; it is not a statistical issue. The weak use of significance tests asks merely whether the observations are attributable to “chance” (i.e., no relation exists) when a weak theory can only predict some sort of relation, but not what or how much. The strong use of significance tests asks whether observations differ significantly from the numerical values that a strong theory predicts, and it leads to the fourth figure of the syllogism—p ⊃ q, ~q , infer ~p—which is formally valid, the logician’s modus tollens (“destroying mode”). Psychologists should work hard to formulate theories that, even if somewhat weak, permit derivation of numerical point values or narrow ranges, yielding the possibility of modus tollens refutations. [422]

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]

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