Tag Archive: induction

Inducing absolute truth

Universal generalisations are certainly testable, even if not provable, in the sense that it is always possible that the experiments we perform or the observations we make should turn out to falsify them. So the substitution of testability for provability allows universal generalisations to be included in science all right. Indeed Karl Popper has built a whole philosophy of science on the principle that what distinguishes science from non-science is its ‘falsifiability’.

This weakening of the empiricist requirements on science does not really solve the problem of induction. Even if the requirement of testability succeeds in picking out what people standardly and intuitively count as proper science, it leaves us with a problem of explaining why such proper science is a good thing. We have still been given no account of why success in past tests should be a good basis for accepting generalisations which predict the future. [21]

Vague induction

It is clear that, if one uses the word “induction” widely and vaguely enough, any tentative acceptance of the result of any investigation can be called “induction”. In that sense, but (I must emphasize) in no other, Professor Putnam is quite right to detect an “inductivist quaver” in one of the passages he quotes (section 3). But in general he has not read, or if read not understood, what I have written … . [994]

Infinite learning

Thus every statement (or ‘basic statement’) remains essentially conjectural; but it is a conjecture which can be easily tested. These tests, in their turn, involve new conjectural and testable statements, and so on, ad infinitum; and should we try to establish anything with our tests, we should be involved in an infinite regress. But as I explained in my Logic of Scientific Discovery (especially section 29), we do not establish anything by this procedure: we do not wish to ‘justify’ the ‘acceptance’ of anything, we only test our theories critically, in order to see whether or not we can bring a case against them. [521]

Severely risky

A serious empirical test always consists in the attempt to find a refutation, a counterexample. In the search for a counterexample, we have to use our background knowledge; for we always try to refute first the most risky predictions, the ‘most unlikely … consequences’ (as Peirce already saw); which means that we always look in the most probable kinds of places for the most probable kinds of counterexamples—most probable in the sense that we should expect to find them in the light of our background knowledge. Now if a theory stands up to many such tests, then, owing to the incorporation of the results of our tests into our background knowledge, there may be, after a time, no places left where (in the light of our new background knowledge) counter examples can with a high probability be expected to occur. But this means that the degree of severity of our test declines. This is also the reason why an often repeated test will no longer be considered as significant or as severe: there is something like a law of diminishing returns from repeated tests (as opposed to tests which, in the light of our background knowledge, are of a new kind, and which therefore may still be felt to be significant). These are facts which are inherent in the knowledge-situation; and they have often been described—especially by John Maynard Keynes and by Ernest Nagel—as difficult to explain by an inductivist theory of science. But for us it is all very easy. And we can even explain, by a similar analysis of the knowledge-situation, why the empirical character of a very successful theory always grows stale, after a time. We may then feel (as Poincaré did with respect to Newton’s theory) that the theory is nothing but a set of implicit definitions or conventions—until we progress again and, by refuting it, incidentally re-establish its lost empirical character. (De mortuis nil nisi bene: once a theory is refuted, its empirical character is secure and shines without blemish.) [325-6]

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]

Older posts «