[Footnote 1: Mill: Logic (London, 1872), vol. I, pp. 441-42.]
Through experiment, we are thus enabled to observe the relation of specific elements in a situation. We are, furthermore, enabled to observe phenomena which are so rare in occurrence that it is impossible to form generalizations from them or improbable that we should even notice them: "We might have to wait years or centuries to meet accidentally with facts which we can readily produce at any moment in a laboratory; and it is probable that many of the chemical substances now known, and many excessively useful products, would never have been discovered at all, by waiting till Nature presented them spontaneously to our observation." And phenomena, such as that of electricity, which can only be understood when the conditions of their occurrence are varied, are presented to us in Nature most frequently in a fixed and invariable form.
Generalizations, their elaboration and testing. So far we have been concerned with the steps in the control of suggestion, the reëxamination of the facts so that significant suggestions may be derived, and the elimination of the significant from the insignificant in the elements of the situation as it first confronts us. In logically elaborating a suggestion, as we have already seen, we trace out the bearings of a given situation. We expand it; we see what it implies, what it means. Thus, if we came, for example, to a meeting that had been scheduled, and found no one present, we might have several solutions arise in our minds. The meeting, we might suppose, had been transferred to another room. If that were the case, there would probably be some notice posted. In all cases of deductive elaboration, we go through what might be called the If-Then process. If such-and-such is the case, then such-and-such will follow. We can then verify our suggested solution to a problem, by going back to the facts, to see whether they correspond with the implications of our suggestion. We may, to take another example, think that a man who enters our office is an insurance agent, or a book solicitor who had said he would call upon us at a definite date. If such is the case, he will say such-and-such things. If he does say them, then our suggestion is seen to be correct. The advantages of developing a suggestion include the fact that some link in the logical chain may bear a more obvious relation to our problem than did the undeveloped suggestion itself.
The systematic sciences consist of such sets of principles so related that any single term implies certain others, which imply certain others and so on ad infinitum.
After the facts have been elaborated, the generalization, however plausible it may seem, must be subjected to experimental corroboration. That is, if a suggestion is found through local elaboration to mean A, B, C, then the situation must be reëxamined to see if the facts to be found tally with the facts deduced. In the case cited, the suggestion that the man who entered the room was the insurance agent we expected would be verified if he immediately broached the subject and the fact, say, of a previous conversation. In the case of disease, if the illness is typhoid, we shall find certain specific conditions in the patient. If these are found, the suggestion of typhoid is verified.
The reliability of generalizations made by this scientific procedure varies according to several factors. It varies, in the first place, according to the correspondence of the predictions made on the basis of the generalization, with subsequent events. The reason we say the law of gravitation holds true is because in every instance where observations or experiments have been made, the results have tallied precisely with expectations based upon the generalization. We can, to a certain extent, determine the reliability of a generalization before comparing our predictions with subsequent events. If a generalization made contradicts laws that have been established in so many instances that they are practically beyond peradventure, it is suspect. A law, for example, that should be an exception to the laws of motion or gravitation, is a priori dubious.
If an induction conflicts with stronger inductions, or with conclusions capable of being correctly deduced from them, then, unless on reconsideration it should appear that some of the stronger inductions have been expressed with greater universality than their evidence warrants, the weaker one must give way. The opinion so long prevalent that a comet, or any other unusual appearance in the heavenly regions, was the precursor of calamities to mankind, or to those at least who witnessed it; the belief in the veracity of the oracles of Delphi or Dodona; the reliance on astrology, or on the weather prophecies in almanacs, were doubtless inductions supposed to be grounded on experience.... What has really put an end to these insufficient inductions is their inconsistency with the stronger inductions subsequently obtained by scientific inquiry, respecting the causes on which terrestrial events really depend.[1]
[Footnote 1: Mill: Logic (London, 1872), vol. I, pp. 370-71.]
The quantitative basis of scientific procedure. Science is science, some scientists insist, in so far as it is mathematical. That is, in the precise determination of facts, and in their repetition with a view to their exact determination, quantities must be known. The sciences have developed in exactness, in so far as they have succeeded in expressing their formulations in numerical terms. The physical sciences, such as physics and chemistry, which have been able to frame their generalizations from precise quantities, have been immeasurably more certain and secure than such sciences as psychology and sociology, where the measurement of exact quantities is more difficult and rare. Jevons writes in his Principles of Science:
As physical science advances, it becomes more and more accurately quantitative. Questions of simple logical fact resolve themselves after a while into questions of degree, time, distance, or weight. Forces hardly suspected to exist by one generation are clearly recognized by the next, and precisely measured by the third generation.[1]