of inductive method that it is frequently treated as the whole of induction. It is supposed that all inductive inference is based upon collecting and comparing a number of like cases. But in fact such comparison and collection is a secondary development within the process of securing a correct conclusion in some single case. 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 more probably correct. In like fashion, the reasoning that led up to the burglary idea in the instance already cited (p. 83) was inductive, though there was but one single case examined. The particulars upon which the general meaning (or relation) of burglary was grounded were simply the sum total of the unlike items and qualities that made up the one case examined. Had this case presented very great obscurities and difficulties, recourse might then have been had to examination of a number of similar cases. But this comparison would not make inductive a process which was not previously of that character; it would only render induction more wary and adequate. The object of bringing into consideration a multitude of cases is to facilitate the selection of the evidential or significant features upon which to base inference in some single case.
Contrast as important as likeness
Accordingly, points of unlikeness are as important as points of likeness among the cases examined. Comparison, without contrast, does not amount to anything logically. In the degree in which other cases observed or remembered merely duplicate the case in question, we are no better off for purposes of inference than if we had permitted our single original fact to dictate a conclusion. 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.16 If we are endeavoring to get a child to regulate his conclusions about the germination of a seed by taking into account a number of instances, very little is gained if the conditions in all these instances closely approximate one another. But if one seed is placed in pure sand, another in loam, and another on blotting-paper, and if in each case there are two conditions, one with and another without moisture, the unlike factors tend to throw into relief the factors that are significant (or "essential") for reaching a conclusion. Unless, in short, the observer takes care to have the differences in the observed cases as extreme as conditions allow, and unless he notes unlikenesses as carefully as likenesses, he has no way of determining the evidential force of the data that confront him.
Importance of exceptions and contrary cases
Another way of bringing out this importance of unlikeness is the emphasis put by the scientist upon negative cases—upon instances which it would seem ought to fall into line but which as matter of fact do not. Anomalies, exceptions, things which agree in most respects but disagree in some crucial point, are so important that many of the devices of scientific technique are designed purely to detect, record, and impress upon memory contrasting cases. Darwin remarked that so easy is it to pass over cases that oppose a favorite generalization, that he had made it a habit not merely to hunt for contrary instances, but also to write down any exception he noted or thought of—as otherwise it was almost sure to be forgotten.
§ 3. Experimental Variation of Conditions
Experiment the typical method of introducing contrast factors
We have already trenched upon this factor of inductive method, the one that is the most important of all wherever it is feasible. Theoretically, one sample case of the right kind will be as good a basis for an inference as a thousand cases; but cases of the "right kind" rarely turn up spontaneously. We have to search for them, and we may have to make them. If we take cases just as we find them—whether one case or many cases—they contain much that is irrelevant to the problem in hand, while much that is relevant is obscure, hidden. The object of experimentation is the construction, by regular steps taken on the basis of a plan thought out in advance, of a typical, crucial case, a case formed with express reference to throwing light on the difficulty in question. All inductive methods rest (as already stated, p. 85) upon regulation of the conditions of observation and memory; experiment is simply the most adequate regulation possible of these conditions. We try to make the observation such that every factor entering into it, together with the mode and the amount of its operation, may be open to recognition. Such making of observations constitutes experiment.
Three advantages of experiment
Such observations have many and obvious advantages over observations—no matter how extensive—with respect to which we simply wait for an event to happen or an object to present itself. Experiment overcomes the defects due to (a) the rarity, (b) the subtlety and minuteness (or the violence), and (c) the rigid fixity of facts as we ordinarily experience them. The following quotations from Jevons's Elementary Lessons in Logic bring out all these points:
(i) "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 most 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."
This quotation refers to the infrequency or rarity of certain facts of nature, even very important ones. The passage then goes on to speak of the minuteness of many phenomena which makes them escape ordinary experience:
(ii) "Electricity doubtless operates in every particle of matter, perhaps at every moment of time; and even the ancients could not but notice its action in the loadstone, in lightning, in the Aurora Borealis, or in a piece of rubbed amber. But in lightning electricity was too intense and dangerous; in the other cases it was too feeble to be properly understood. The science of electricity and magnetism could only advance by getting regular supplies of electricity from the common electric machine or the galvanic battery and by making powerful electromagnets. Most, if not all, the effects which electricity produces must go on in nature, but altogether too obscurely for observation."
Jevons then deals with the fact that, under ordinary conditions of experience, phenomena which can be understood only by seeing them under varying conditions are presented in a fixed and uniform way.
(iii) "Thus carbonic acid is only met in the form of a gas, proceeding from the combustion of carbon; but when exposed to extreme pressure and cold, it is condensed into a liquid, and may even be converted into a snowlike solid substance. Many other gases have in like manner been liquefied or solidified, and there is reason to believe that every substance is capable of taking all three forms of solid, liquid, and gas, if only the conditions of temperature and pressure can be sufficiently varied. Mere observation of nature would have led us, on the contrary, to suppose that nearly all substances were fixed in one condition only, and could not be converted from solid into liquid and from liquid into gas."
Many volumes would be required to describe in detail all the methods that investigators have developed in various subjects for analyzing and restating the facts of ordinary experience so that we may escape from capricious and routine suggestions, and may get the facts in such a form and in such a light (or context) that exact and far-reaching explanations may be suggested in place of vague and limited ones. But these various devices of inductive inquiry all have one goal in view: the indirect regulation of the function of suggestion, or formation of ideas; and, in the main, they will be found to reduce to some combination of the three types of selecting and arranging subject-matter just described.
§ 4. Guidance of the Deductive Movement
Value of deduction for guiding induction
Before dealing directly with this topic, we must note that systematic regulation of induction depends
