[Footnote 1: Poincaré: Foundations of Science, p. 363.]
The aim of classification 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 classification with which is correlated the greatest number of other characteristics belonging to the facts in question. It would be possible to classify all living things according to color, but such a classification would be destitute of scientific value. Biology offers some interesting examples of how an illuminating classification 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 classification may be summarized in Huxley's definition as modified by Jevons:
By the classification 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 circumstances, 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 classification 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 classify 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 circumstances, 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 assisting 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 circumstance, 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 circumstances 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 circumstances 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 circumstances, 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 circumstances, we may produce further variations of circumstances 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 circumstance after another into the experiment, we obtain assurance of the manner in which the phenomenon behaves under an indefinite variety of possible circumstances. 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 circumstances.[1]