How We Think Part 8

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 a.s.sisting 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.

[16] In terms of the phrases used in logical treatises, the so-called "methods of agreement" (comparison) and "difference"

(contrast) must accompany each other or const.i.tute a "joint method"

in order to be of logical use.

[Sidenote: 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 pa.s.s 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_

[Sidenote: 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 const.i.tutes experiment.

[Sidenote: 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 pa.s.sage 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 a.n.a.lyzing 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_

[Sidenote: Value of deduction for guiding induction]

Before dealing directly with this topic, we must note that systematic regulation of induction depends upon the possession of a body of general principles that may be applied deductively to the examination or construction of particular cases as they come up. If the physician does not know the general laws of the physiology of the human body, he has little way of telling what is either peculiarly significant or peculiarly exceptional in any particular case that he is called upon to treat. If he knows the laws of circulation, digestion, and respiration, he can deduce the conditions that should normally be found in a given case. These considerations give a base line from which the deviations and abnormalities of a particular case may be measured. In this way, _the nature of the problem at hand is located and defined_. Attention is not wasted upon features which though conspicuous have nothing to do with the case; it is concentrated upon just those traits which are out of the way and hence require explanation. A question well put is half answered; _i.e._ a difficulty clearly apprehended is likely to suggest its own solution,--while a vague and miscellaneous perception of the problem leads to groping and fumbling. Deductive systems are necessary in order to put the question in a fruitful form.

[Sidenote: "Reasoning a thing out"]

The control of the origin and development of hypotheses by deduction does not cease, however, with locating the problem. Ideas as they first present themselves are inchoate and incomplete. _Deduction is their elaboration into fullness and completeness of meaning_ (see p. 76). The phenomena which the physician isolates from the total ma.s.s of facts that exist in front of him suggest, we will say, typhoid fever. Now this conception of typhoid fever is one that is capable of development. _If_ there is typhoid, _wherever_ there is typhoid, there are certain results, certain characteristic symptoms. By going over mentally the full bearing of the concept of typhoid, the scientist is instructed as to further phenomena to be found. Its development gives him an instrument of inquiry, of observation and experimentation. He can go to work deliberately to see whether the case presents those features that it should have if the supposition is valid. The deduced results form a basis for comparison with observed results. Except where there is a system of principles capable of being elaborated by theoretical reasoning, the process of testing (or proof) of a hypothesis is incomplete and haphazard.

[Sidenote: Such reasoning implies systematized knowledge,]

These considerations indicate the method by which the deductive movement is guided. Deduction requires a system of allied ideas which may be translated into one another by regular or graded steps. The question is whether the facts that confront us can be identified as typhoid fever.

To all appearances, there is a great gap between them and typhoid. But if we can, by some method of subst.i.tutions, go through a series of intermediary terms (see p. 72), the gap may, after all, be easily bridged. Typhoid may mean _p_ which in turn means _o_, which means _n_ which means _m_, which is very similar to the data selected as the key to the problem.

[Sidenote: or definition and cla.s.sification]

One of the chief objects of science is to provide for every typical branch of subject-matter a set of meanings and principles so closely interknit that any one implies some other according to definite conditions, which under certain other conditions implies another, and so on. In this way, various subst.i.tutions of equivalents are possible, and reasoning can trace out, without having recourse to specific observations, very remote consequences of any suggested principle.

Definition, general formulae, and cla.s.sification are the devices by which the fixation and elaboration of a meaning into its detailed ramifications are carried on. They are not ends in themselves--as they are frequently regarded even in elementary education--but instrumentalities for facilitating the development of a conception into the form where its applicability to given facts may best be tested.[17]

[17] These processes are further discussed in Chapter IX.

[Sidenote: The final control of deduction]

The final test of deduction lies in experimental observation.

Elaboration by reasoning may make a suggested idea very rich and very plausible, but it will not settle the validity of that idea. Only if facts can be observed (by methods either of collection or of experimentation), that agree in detail and without exception with the deduced results, are we justified in accepting the deduction as giving a valid conclusion. Thinking, in short, must end as well as begin in the domain of concrete observations, if it is to be complete thinking. And the ultimate educative value of all deductive processes is measured by the degree to which they become working tools in the creation and development of new experiences.

-- 5. _Some Educational Bearings of the Discussion_

[Sidenote: Educational counterparts of false logical theories]

[Sidenote: Isolation of "facts"]

Some of the points of the foregoing logical a.n.a.lysis may be clinched by a consideration of their educational implications, especially with reference to certain practices that grow out of a false separation by which each is thought to be independent of the other and complete in itself. (_i_) In some school subjects, or at all events in some topics or in some lessons, the pupils are immersed in details; their minds are loaded with disconnected items (whether gleaned by observation and memory, or accepted on hearsay and authority). Induction is treated as beginning and ending with the ama.s.sing of facts, of particular isolated pieces of information. That these items are educative only as suggesting a view of some larger situation in which the particulars are included and thereby accounted for, is ignored. In object lessons in elementary education and in laboratory instruction in higher education, the subject is often so treated that the student fails to "see the forest on account of the trees." Things and their qualities are retailed and detailed, without reference to a more general character which they stand for and mean. Or, in the laboratory, the student becomes engrossed in the processes of manipulation,--irrespective of the reason for their performance, without recognizing a typical problem for the solution of which they afford the appropriate method. Only deduction brings out and emphasizes consecutive relations.h.i.+ps, and only when _relations.h.i.+ps_ are held in view does learning become more than a miscellaneous sc.r.a.p-bag.

[Sidenote: Failure to follow up by reasoning]

(_ii_) Again, the mind is allowed to hurry on to a vague notion of the whole of which the fragmentary facts are portions, without any attempt to become conscious of _how_ they are bound together as parts of this whole. The student feels that "in a general way," as we say, the facts of the history or geography lesson are related thus and so; but "in a general way" here stands only for "in a vague way," somehow or other, with no clear recognition of just how.

The pupil is encouraged to form, on the basis of the particular facts, a general notion, a conception of how they stand related; but no pains are taken to make the student follow up the notion, to elaborate it and see just what its bearings are upon the case in hand and upon similar cases.

The inductive inference, the guess, is formed by the student; if it happens to be correct, it is at once accepted by the teacher; or if it is false, it is rejected. If any amplification of the idea occurs, it is quite likely carried through by the teacher, who thereby a.s.sumes the responsibility for its intellectual development. But a complete, an integral, act of thought requires that the person making the suggestion (the guess) be responsible also for reasoning out its bearings upon the problem in hand; that he develop the suggestion at least enough to indicate the ways in which it applies to and accounts for the specific data of the case. Too often when a recitation does not consist in simply testing the ability of the student to display some form of technical skill, or to repeat facts and principles accepted on the authority of text-book or lecturer, the teacher goes to the opposite extreme; and after calling out the spontaneous reflections of the pupils, their guesses or ideas about the matter, merely accepts or rejects them, a.s.suming himself the responsibility for their elaboration. In this way, the function of suggestion and of interpretation is excited, but it is not directed and trained. Induction is stimulated but is not carried over into the _reasoning_ phase necessary to complete it.

In other subjects and topics, the deductive phase is isolated, and is treated as if it were complete in itself. This false isolation may show itself in either (and both) of two points; namely, at the beginning or at the end of the resort to general intellectual procedure.

[Sidenote: Isolation of deduction by commencing with it]

(_iii_) Beginning with definitions, rules, general principles, cla.s.sifications, and the like, is a common form of the first error. This method has been such a uniform object of attack on the part of all educational reformers that it is not necessary to dwell upon it further than to note that the mistake is, logically, due to the attempt to introduce deductive considerations without first making acquaintance with the particular facts that create a need for the generalizing rational devices. Unfortunately, the reformer sometimes carries his objection too far, or rather locates it in the wrong place. He is led into a tirade against _all_ definition, all systematization, all use of general principles, instead of confining himself to pointing out their futility and their deadness when not properly motivated by familiarity with concrete experiences.

[Sidenote: Isolation of deduction from direction of new observations]

(_iv_) The isolation of deduction is seen, at the other end, wherever there is failure to clinch and test the results of the general reasoning processes by application to new concrete cases. The final point of the deductive devices lies in their use in a.s.similating and comprehending individual cases. No one understands a general principle fully--no matter how adequately he can demonstrate it, to say nothing of repeating it--till he can employ it in the mastery of new situations, which, if they _are_ new, differ in manifestation from the cases used in reaching the generalization. Too often the text-book or teacher is contented with a series of somewhat perfunctory examples and ill.u.s.trations, and the student is not forced to carry the principle that he has formulated over into further cases of his own experience. In so far, the principle is inert and dead.

[Sidenote: Lack of provision for experimentation]

(_v_) It is only a variation upon this same theme to say that every complete act of reflective inquiry makes provision for experimentation--for testing suggested and accepted principles by employing them for the active construction of new cases, in which new qualities emerge. Only slowly do our schools accommodate themselves to the general advance of scientific method. From the scientific side, it is demonstrated that effective and integral thinking is possible only where the experimental method in some form is used. Some recognition of this principle is evinced in higher inst.i.tutions of learning, colleges and high schools. But in elementary education, it is still a.s.sumed, for the most part, that the pupil's natural range of observations, supplemented by what he accepts on hearsay, is adequate for intellectual growth. Of course it is not necessary that laboratories shall be introduced under that name, much less that elaborate apparatus be secured; but the entire scientific history of humanity demonstrates that the conditions for complete mental activity will not be obtained till adequate provision is made for the carrying on of activities that actually modify physical conditions, and that books, pictures, and even objects that are pa.s.sively observed but not manipulated do not furnish the provision required.

CHAPTER EIGHT

JUDGMENT: THE INTERPRETATION OF FACTS