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. 
Tag Archive: induction
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]
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.
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-