Part 35 (1/2)
In the words of Poincare:
The most interesting facts are those which may serve many times; these are the facts which have a chance of coming up again. We have been so fortunate as to have been born in a world where there are such. Suppose that instead of sixty chemical elements there were sixty milliards of them, that they were not some common, the others rare, but that they were equally distributed. Then, every time we picked up a new pebble there would be great probability of its being formed of some unknown substance; all that we knew of other pebbles would be worthless for it; before each new object we should be as the new-born babe; like it we could only obey our caprices or our needs. Biologists would be just as much at a loss if there were only individuals and no species, and if heredity did not make sons like their fathers.[1]
[Footnote 1: Poincare: _Foundations of Science_, p. 363.]
The aim of cla.s.sification in science is grouping in such a way as to make manifest at once similarities in the behavior of objects. That characteristic is selected as a basis of cla.s.sification with which is correlated the greatest number of other characteristics belonging to the facts in question. It would be possible to cla.s.sify all living things according to color, but such a cla.s.sification would be dest.i.tute of scientific value.
Biology offers some interesting examples of how an illuminating cla.s.sification may be made on the basis of a single characteristic.
It has been found, for example, that the differences or resemblances of animals are correlated with corresponding differences or resemblances in their teeth. In general, the function of cla.s.sification may be summarized in Huxley's definition as modified by Jevons:
By the cla.s.sification of any series of objects is meant the actual or ideal arrangement together of those things which are like and the separation of those things which are unlike, the purpose of the arrangement being, primarily, to disclose the correlations or laws of union of properties and circ.u.mstances, and, secondarily, to facilitate the operations of the mind in clearly conceiving and retaining in memory the characters of the object in question.
It should be noted that the object of cla.s.sification is not simply to indicate similarities but to indicate distinctions or differences. In scientific inquiry, differences are as crucial in the forming of generalizations as similarities. It is only possible to cla.s.sify a given fact under a scientific generalization when the given fact is set off from other facts, when it is seen to be the result of certain special conditions.
If a man infers from a single sample of grain as to the grade of wheat of the car as a whole, it is induction, and under certain circ.u.mstances, a _sound_ induction; other cases are resorted to simply for the sake of rendering that induction more guarded and correct. In the case of the various samples of grain, it is the fact that the samples are unlike, at least in the part of the carload from which they are taken, that is important. Were it not for this unlikeness, their likeness in quality would be of no avail in a.s.sisting inference.[1]
[Footnote 1: Dewey: _How We Think_, pp. 89-90.]
EXPERIMENTAL VARIATION OF CONDITIONS. In forming our generalizations from the observation of situations as they occur in Nature, we are at a disadvantage. If we observe cases just as we find them, there is much present that is irrelevant to our problem; much that is of genuine importance in its solution is hidden or obscure. In experimental investigation we are, in the words of Sir John Herschel, ”active observers”; we deliberately invent crucial or test cases. That is, we deliberately arrange conditions so that every factor is definitely known and recognized. We then introduce into this set of completely known conditions one change, one new circ.u.mstance, and observe its effect. In Mill's phrase, we ”take a phenomenon home with us,” and watch its behavior. Mill states clearly the outstanding advantage of experimentation over observation:
When we can produce a phenomenon artificially, we can take it, as it were, home with us, and observe it in the midst of circ.u.mstances with which in all other respects we are accurately acquainted. If we desire to know what are the effects of the cause _A_, and are able to produce _A_ by means at our disposal, we can generally determine at our own discretion ... the whole of the circ.u.mstances which shall be present along with it; and thus, knowing exactly the simultaneous state of everything else which is within the reach of _A's_ influence, we have only to observe what alteration is made in that state by the presence of _A_.
For example, by the electric machine we can produce, in the midst of known circ.u.mstances, the phenomena which Nature exhibits on a grander scale in the form of lightning and thunder. Now let any one consider what amount of knowledge of the effects and laws of electric agency mankind could have obtained from the mere observation of thunderstorms, and compare it with that which they have gained, and may expect to gain, from electrical and galvanic experiments....
When we have succeeded in isolating the phenomenon which is the subject of inquiry, by placing it among known circ.u.mstances, we may produce further variations of circ.u.mstances to any extent, and of such kinds as we think best calculated to bring the laws of the phenomenon into a clear light. By introducing one well-defined circ.u.mstance after another into the experiment, we obtain a.s.surance of the manner in which the phenomenon behaves under an indefinite variety of possible circ.u.mstances. Thus, chemists, after having obtained some newly discovered substance in a pure state, ... introduce various other substances, one by one, to ascertain whether it will combine with them, or decompose them, and with what result; and also apply heat or electricity or pressure, to discover what will happen to the substance under each of these circ.u.mstances.[1]
[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 reexamination 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 reexamined 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 QUANt.i.tATIVE 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 repet.i.tion with a view to their exact determination, quant.i.ties 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 quant.i.ties, have been immeasurably more certain and secure than such sciences as psychology and sociology, where the measurement of exact quant.i.ties is more difficult and rare. Jevons writes in his _Principles of Science_:
As physical science advances, it becomes more and more accurately quant.i.tative. 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]