§ 1. The Double Movement of Reflection
The characteristic outcome of thinking we saw to be the organization of facts and conditions which, just as they stand, are isolated5, fragmentary, and discrepant6, the organization being effected through the introduction of connecting links, or middle terms. The facts as they stand are the data, the raw material of reflection; their lack of coherence7 perplexes and stimulates8 to reflection. There follows the suggestion of some meaning which, if it can be substantiated9, will give a whole in which various fragmentary and seemingly incompatible10 data find their proper place. The meaning suggested supplies a mental platform, an intellectual point of view, from which to note and define the data more carefully, to seek for additional observations, and to institute, experimentally, changed conditions.
Inductive and deductive
There is thus a double movement in all reflection: a movement from the given partial and confused data to a suggested comprehensive (or inclusive) entire situation; and back from this suggested whole—which as suggested is a meaning, an idea—to the particular facts, so as to connect these with one another and with additional facts to which the suggestion has directed attention. Roughly speaking, the first of these movements[Pg 80] is inductive; the second deductive. A complete act of thought involves both—it involves, that is, a fruitful interaction of observed (or recollected) particular considerations and of inclusive and far-reaching (general) meanings.
This double movement to and from a meaning may occur, however, in a casual, uncritical way, or in a cautious and regulated manner. To think means, in any case, to bridge a gap in experience, to bind12 together facts or deeds otherwise isolated. But we may make only a hurried jump from one consideration to another, allowing our aversion to mental disquietude to override13 the gaps; or, we may insist upon noting the road traveled in making connections. We may, in short, accept readily any suggestion that seems plausible14; or we may hunt out additional factors, new difficulties, to see whether the suggested conclusion really ends the matter. The latter method involves definite formulation of the connecting links; the statement of a principle, or, in logical phrase, the use of a universal. If we thus formulate16 the whole situation, the original data are transformed into premises17 of reasoning; the final belief is a logical or rational conclusion, not a mere18 de facto termination.
Continuity of relationship the mark of the latter
The importance of connections binding19 isolated items into a coherent single whole is embodied20 in all the phrases that denote the relation of premises and conclusions to each other. (1) The premises are called grounds, foundations, bases, and are said to underlie21, uphold, support the conclusion. (2) We "descend22" from the premises to the conclusion, and "ascend23" or "mount" in the opposite direction—as a river may be continuously traced from source to sea or vice24 versa. So the conclusion springs, flows, or is drawn25 from its premises.[Pg 81] (3) The conclusion—as the word itself implies—closes, shuts in, locks up together the various factors stated in the premises. We say that the premises "contain" the conclusion, and that the conclusion "contains" the premises, thereby26 marking our sense of the inclusive and comprehensive unity27 in which the elements of reasoning are bound tightly together.[15] Systematic inference, in short, means the recognition of definite relations of interdependence between considerations previously28 unorganized and disconnected, this recognition being brought about by the discovery and insertion of new facts and properties.
Scientific induction and deduction
This more systematic thinking is, however, like the cruder forms in its double movement, the movement toward the suggestion or hypothesis and the movement back to facts. The difference is in the greater conscious care with which each phase of the process is performed. The conditions under which suggestions are allowed to spring up and develop are regulated. Hasty acceptance of any idea that is plausible, that seems to solve the difficulty, is changed into a conditional29 acceptance pending30 further inquiry31. The idea is accepted as a working hypothesis, as something to guide investigation32 and bring to light new facts, not as a final conclusion. When pains are taken to make each aspect of the movement as accurate as possible, the movement toward building up the idea is known as inductive discovery (induction, for short); the movement toward developing, applying, and testing, as deductive proof (deduction, for short).
Particular and universal
While induction moves from fragmentary details (or[Pg 82] particulars) to a connected view of a situation (universal), deduction begins with the latter and works back again to particulars, connecting them and binding them together. The inductive movement is toward discovery of a binding principle; the deductive toward its testing—confirming, refuting, modifying it on the basis of its capacity to interpret isolated details into a unified33 experience. So far as we conduct each of these processes in the light of the other, we get valid34 discovery or verified critical thinking.
Illustration from everyday experience
A commonplace illustration may enforce the points of this formula. A man who has left his rooms in order finds them upon his return in a state of confusion, articles being scattered35 at random36. Automatically, the notion comes to his mind that burglary would account for the disorder37. He has not seen the burglars; their presence is not a fact of observation, but is a thought, an idea. Moreover, the man has no special burglars in mind; it is the relation, the meaning of burglary—something general—that comes to mind. The state of his room is perceived and is particular, definite,—exactly as it is; burglars are inferred, and have a general status. The state of the room is a fact, certain and speaking for itself; the presence of burglars is a possible meaning which may explain the facts.
of induction,
So far there is an inductive tendency, suggested by particular and present facts. In the same inductive way, it occurs to him that his children are mischievous38, and that they may have thrown the things about. This rival hypothesis (or conditional principle of explanation) prevents him from dogmatically accepting the first suggestion. Judgment39 is held in suspense40 and a positive conclusion postponed41.[Pg 83]
of deduction
Then deductive movement begins. Further observations, recollections, reasonings are conducted on the basis of a development of the ideas suggested: if burglars were responsible, such and such things would have happened; articles of value would be missing. Here the man is going from a general principle or relation to special features that accompany it, to particulars,—not back, however, merely to the original particulars (which would be fruitless or take him in a circle), but to new details, the actual discovery or nondiscovery of which will test the principle. The man turns to a box of valuables; some things are gone; some, however, are still there. Perhaps he has himself removed the missing articles, but has forgotten it. His experiment is not a decisive test. He thinks of the silver in the sideboard—the children would not have taken that nor would he absent-mindedly have changed its place. He looks; all the solid ware42 is gone. The conception of burglars is confirmed; examination of windows and doors shows that they have been tampered43 with. Belief culminates44; the original isolated facts have been woven into a coherent fabric45. The idea first suggested (inductively) has been employed to reason out hypothetically certain additional particulars not yet experienced, that ought to be there, if the suggestion is correct. Then new acts of observation have shown that the particulars theoretically called for are present, and by this process the hypothesis is strengthened, corroborated46. This moving back and forth between the observed facts and the conditional idea is kept up till a coherent experience of an object is substituted for the experience of conflicting details—or else the whole matter is given up as a bad job.
Science is the same operations carefully performed
Sciences exemplify similar attitudes and operations,[Pg 84] but with a higher degree of elaboration of the instruments of caution, exactness and thoroughness. This greater elaboration brings about specialization, an accurate marking off of various types of problems from one another, and a corresponding segregation47 and classification of the materials of experience associated with each type of problem. We shall devote the remainder of this chapter to a consideration of the devices by which the discovery, the development, and the testing of meanings are scientifically carried on.
§ 2. Guidance of the Inductive Movement
Guidance is indirect
Control of the formation of suggestion is necessarily indirect, not direct; imperfect, not perfect. Just because all discovery, all apprehension48 involving thought of the new, goes from the known, the present, to the unknown and absent, no rules can be stated that will guarantee correct inference. Just what is suggested to a person in a given situation depends upon his native constitution (his originality49, his genius), temperament50, the prevalent direction of his interests, his early environment, the general tenor51 of his past experiences, his special training, the things that have recently occupied him continuously or vividly52, and so on; to some extent even upon an accidental conjunction of present circumstances. These matters, so far as they lie in the past or in external conditions, clearly escape regulation. A suggestion simply does or does not occur; this or that suggestion just happens, occurs, springs up. If, however, prior experience and training have developed an attitude of patience in a condition of doubt, a capacity for suspended judgment, and a liking53 for inquiry, indirect control of the course of suggestions is possible.[Pg 85] The individual may return upon, revise, restate, enlarge, and analyze54 the facts out of which suggestion springs. Inductive methods, in the technical sense, all have to do with regulating the conditions under which observation, memory, and the acceptance of the testimony55 of others (the operations supplying the raw data) proceed.
Method of indirect regulation
Given the facts A B C D on one side and certain individual habits on the other, suggestion occurs automatically. But if the facts A B C D are carefully looked into and thereby resolved into the facts A′ B′′ R S, a suggestion will automatically present itself different from that called up by the facts in their first form. To inventory56 the facts, to describe exactly and minutely their respective traits, to magnify artificially those that are obscure and feeble, to reduce artificially those that are so conspicuous57 and glaring as to be distracting,—these are ways of modifying the facts that exercise suggestive force, and thereby indirectly58 guiding the formation of suggested inferences.
Consider, for example, how a physician makes his diagnosis—his inductive interpretation60. If he is scientifically trained, he suspends—postpones—reaching a conclusion in order that he may not be led by superficial occurrences into a snap judgment. Certain conspicuous phenomena61 may forcibly suggest typhoid, but he avoids a conclusion, or even any strong preference for this or that conclusion until he has greatly (i) enlarged the scope of his data, and (ii) rendered them more minute. He not only questions the patient as to his feelings and as to his acts prior to the disease, but by various manipulations with his hands (and with instruments made for the purpose) brings to light a large number of facts of which the patient is quite unaware62. The state of tem[Pg 86]perature, respiration63, and heart-action is accurately64 noted65, and their fluctuations66 from time to time are exactly recorded. Until this examination has worked out toward a wider collection and in toward a minuter scrutiny67 of details, inference is deferred68.
Summary: definition of scientific induction
Scientific induction means, in short, all the processes by which the observing and amassing69 of data are regulated with a view to facilitating the formation of explanatory conceptions and theories. These devices are all directed toward selecting the precise facts to which weight and significance shall attach in forming suggestions or ideas. Specifically, this selective determination involves devices of (1) elimination70 by analysis of what is likely to be misleading and irrelevant71, (2) emphasis of the important by collection and comparison of cases, (3) deliberate construction of data by experimental variation.
Elimination of irrelevant meanings
(1) It is a common saying that one must learn to discriminate72 between observed facts and judgments73 based upon them. Taken literally74, such advice cannot be carried out; in every observed thing there is—if the thing have any meaning at all—some consolidation75 of meaning with what is sensibly and physically76 present, such that, if this were entirely77 excluded, what is left would have no sense. A says: "I saw my brother." The term brother, however, involves a relation that cannot be sensibly or physically observed; it is inferential in status. If A contents himself with saying, "I saw a man," the factor of classification, of intellectual reference, is less complex, but still exists. If, as a last resort, A were to say, "Anyway, I saw a colored object," some relationship, though more rudimentary and undefined, still subsists78. Theoretically, it is possible that no[Pg 87] object was there, only an unusual mode of nerve stimulation79. None the less, the advice to discriminate what is observed from what is inferred is sound practical advice. Its working import is that one should eliminate or exclude those inferences as to which experience has shown that there is greatest liability to error. This, of course, is a relative matter. Under ordinary circumstances no reasonable doubt would attach to the observation, "I see my brother"; it would be pedantic80 and silly to resolve this recognition back into a more elementary form. Under other circumstances it might be a perfectly81 genuine question as to whether A saw even a colored thing, or whether the color was due to a stimulation of the sensory82 optical apparatus83 (like "seeing stars" upon a blow) or to a disordered circulation. In general, the scientific man is one who knows that he is likely to be hurried to a conclusion, and that part of this precipitancy is due to certain habits which tend to make him "read" certain meanings into the situation that confronts him, so that he must be on the lookout84 against errors arising from his interests, habits, and current preconceptions.
The technique of conclusion
The technique of scientific inquiry thus consists in various processes that tend to exclude over-hasty "reading in" of meanings; devices that aim to give a purely85 "objective" unbiased rendering86 of the data to be interpreted. Flushed cheeks usually mean heightened temperature; paleness means lowered temperature. The clinical thermometer records automatically the actual temperature and hence checks up the habitual87 associations that might lead to error in a given case. All the instrumentalities of observation—the various -meters and -graphs and -scopes—fill a part[Pg 88] of their scientific r?le in helping88 to eliminate meanings supplied because of habit, prejudice, the strong momentary89 preoccupation of excitement and anticipation90, and by the vogue91 of existing theories. Photographs, phonographs, kymographs, actinographs, seismographs, plethysmographs, and the like, moreover, give records that are permanent, so that they can be employed by different persons, and by the same person in different states of mind, i.e. under the influence of varying expectations and dominant92 beliefs. Thus purely personal prepossessions (due to habit, to desire, to after-effects of recent experience) may be largely eliminated. In ordinary language, the facts are objectively, rather than subjectively93, determined94. In this way tendencies to premature95 interpretation are held in check.
Collection of instances
(2) Another important method of control consists in the multiplication96 of cases or instances. If I doubt whether a certain handful gives a fair sample, or representative, for purposes of judging value, of a whole carload of grain, I take a number of handfuls from various parts of the car and compare them. If they agree in quality, well and good; if they disagree, we try to get enough samples so that when they are thoroughly97 mixed the result will be a fair basis for an evaluation98. This illustration represents roughly the value of that aspect of scientific control in induction which insists upon multiplying observations instead of basing the conclusion upon one or a few cases.
This method not the whole of induction
So prominent, indeed, is this aspect 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[Pg 89] 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 wary99 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.
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 dictate101 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 like[Pg 90]ness 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 germination102 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 loam103, 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 generalization104, 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.[Pg 91]
§ 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 experimentation105 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 subtlety106 and minuteness (or the violence), and (c) the rigid107 fixity of facts as we ordinarily experience them. The following quotations109 from Jevons's Elementary Lessons in Logic15 bring out all these points:
(i) "We might have to wait years or centuries to meet[Pg 92] 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 quotation108 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 Aurora110 Borealis, or in a piece of rubbed amber111. 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 magnetism112 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 fixed113 and uniform way.
(iii) "Thus carbonic acid is only met in the form of a gas, proceeding114 from the combustion115 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[Pg 93] like manner been liquefied or solidified116, 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 sufficiently117 varied118. 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 investigators119 have developed in various subjects for analyzing120 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 dealing121 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 applied122 deductively to the examination or construction of particular cases as they come up. If the physician does not know the general laws of the physiology123 of the human body, he has little way of telling what is either peculiarly significant or peculiarly[Pg 94] exceptional in any particular case that he is called upon to treat. If he knows the laws of circulation, digestion124, 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 deviations125 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 apprehended126 is likely to suggest its own solution,—while a vague and miscellaneous perception of the problem leads to groping and fumbling127. Deductive systems are necessary in order to put the question in a fruitful form.
"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 inchoate128 and incomplete. Deduction is their elaboration into fullness and completeness of meaning (see p. 76). The phenomena which the physician isolates129 from the total mass 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 deliberately130 to see whether[Pg 95] 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 haphazard131.
Such reasoning implies systematized knowledge,
These considerations indicate the method by which the deductive movement is guided. Deduction requires a system of allied132 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 substitutions, 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.
or definition and classification
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 substitutions of equivalents are possible, and reasoning can trace out, without having recourse to specific observations, very remote consequences of any suggested principle. Definition, general formul?, and classification are the devices by which the fixation and elaboration of a meaning into its detailed133 ramifications134 are carried on. They are not ends in themselves—as they are frequently regarded even in elementary education—but instrumentalities for facilitating[Pg 96] the development of a conception into the form where its applicability to given facts may best be tested.[17]
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 justified135 in accepting the deduction as giving a valid conclusion. Thinking, in short, must end as well as begin in the domain136 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
Educational counterparts of false logical theoriesIsolation of "facts"
Some of the points of the foregoing logical analysis may be clinched139 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 gleaned140 by observation and memory, or accepted on hearsay141 and authority). Induction is treated as beginning and ending with the amassing 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[Pg 97] 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 retailed142 and detailed, without reference to a more general character which they stand for and mean. Or, in the laboratory, the student becomes engrossed143 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 consecutive144 relationships, and only when relationships are held in view does learning become more than a miscellaneous scrap-bag.
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 amplification145 of the idea occurs, it is[Pg 98] quite likely carried through by the teacher, who thereby assumes 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, assuming 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 stimulated146 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 isolation137 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.
Isolation of deduction by commencing with it
(iii) Beginning with definitions, rules, general principles, classifications, 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[Pg 99] 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 tirade147 against all definition, all systematization, all use of general principles, instead of confining himself to pointing out their futility148 and their deadness when not properly motivated by familiarity with concrete experiences.
Isolation of deduction from direction of new observations
(iv) The isolation of deduction is seen, at the other end, wherever there is failure to clinch138 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 assimilating 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 manifestation149 from the cases used in reaching the generalization. Too often the text-book or teacher is contented150 with a series of somewhat perfunctory examples and illustrations, and the student is not forced to carry the principle that he has formulated151 over into further cases of his own experience. In so far, the principle is inert152 and dead.
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 experi[Pg 100]mental method in some form is used. Some recognition of this principle is evinced in higher institutions of learning, colleges and high schools. But in elementary education, it is still assumed, 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 passively observed but not manipulated do not furnish the provision required.
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systematic
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| adj.有系统的，有计划的，有方法的 | |
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induction
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| n.感应，感应现象 | |
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deduction
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| n.减除，扣除，减除额；推论，推理，演绎 | |
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forth
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isolated
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discrepant
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| 差异的 | |
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coherence
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| n.紧凑；连贯；一致性 | |
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stimulates
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| v.刺激( stimulate的第三人称单数 )；激励；使兴奋；起兴奋作用，起刺激作用，起促进作用 | |
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substantiated
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| v.用事实支持（某主张、说法等），证明，证实( substantiate的过去式和过去分词 ) | |
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10
incompatible
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| adj.不相容的，不协调的，不相配的 | |
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11
versus
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| prep.以…为对手，对；与…相比之下 | |
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12
bind
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| vt.捆，包扎；装订；约束；使凝固；vi.变硬 | |
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override
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| vt.不顾，不理睬，否决；压倒，优先于 | |
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plausible
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| adj.似真实的，似乎有理的，似乎可信的 | |
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15
logic
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| n.逻辑(学)；逻辑性 | |
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16
formulate
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| v.用公式表示；规划；设计；系统地阐述 | |
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premises
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| n.建筑物，房屋 | |
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18
mere
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| adj.纯粹的；仅仅，只不过 | |
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19
binding
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| 有约束力的，有效的，应遵守的 | |
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20
embodied
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| v.表现( embody的过去式和过去分词 )；象征；包括；包含 | |
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21
underlie
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| v.位于...之下，成为...的基础 | |
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22
descend
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| vt./vi.传下来，下来，下降 | |
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23
ascend
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| vi.渐渐上升，升高；vt.攀登，登上 | |
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24
vice
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| n.坏事；恶习；[pl.]台钳，老虎钳；adj.副的 | |
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25
drawn
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| v.拖，拉，拔出；adj.憔悴的，紧张的 | |
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26
thereby
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| adv.因此，从而 | |
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27
unity
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| n.团结，联合，统一；和睦，协调 | |
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28
previously
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| adv.以前，先前（地） | |
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29
conditional
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| adj.条件的，带有条件的 | |
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30
pending
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| prep.直到，等待…期间；adj.待定的；迫近的 | |
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31
inquiry
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| n.打听，询问，调查，查问 | |
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32
investigation
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| n.调查，调查研究 | |
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33
unified
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| (unify 的过去式和过去分词)； 统一的； 统一标准的； 一元化的 | |
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34
valid
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| adj.有确实根据的；有效的；正当的，合法的 | |
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35
scattered
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| adj.分散的，稀疏的；散步的；疏疏落落的 | |
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random
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| adj.随机的；任意的；n.偶然的(或随便的)行动 | |
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37
disorder
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| n.紊乱，混乱；骚动，骚乱；疾病，失调 | |
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38
mischievous
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| adj.调皮的，恶作剧的，有害的，伤人的 | |
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39
judgment
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| n.审判；判断力，识别力，看法，意见 | |
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40
suspense
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| n.（对可能发生的事）紧张感，担心，挂虑 | |
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41
postponed
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| vt.& vi.延期，缓办，（使）延迟vt.把…放在次要地位；[语]把…放在后面（或句尾）vi.（疟疾等）延缓发作（或复发） | |
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42
ware
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| n.(常用复数)商品，货物 | |
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43
tampered
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| v.窜改( tamper的过去式 )；篡改；（用不正当手段）影响；瞎摆弄 | |
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44
culminates
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| v.达到极点( culminate的第三人称单数 ) | |
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45
fabric
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| n.织物，织品，布；构造，结构，组织 | |
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46
corroborated
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| v.证实，支持（某种说法、信仰、理论等）( corroborate的过去式 ) | |
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47
segregation
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| n.隔离，种族隔离 | |
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48
apprehension
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| n.理解，领悟；逮捕，拘捕；忧虑 | |
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49
originality
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| n.创造力，独创性；新颖 | |
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50
temperament
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| n.气质，性格，性情 | |
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51
tenor
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| n.男高音（歌手），次中音（乐器），要旨，大意 | |
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52
vividly
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| adv.清楚地，鲜明地，生动地 | |
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53
liking
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| n.爱好；嗜好；喜欢 | |
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54
analyze
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| vt.分析，解析 (=analyse) | |
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55
testimony
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| n.证词；见证，证明 | |
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56
inventory
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| n.详细目录，存货清单 | |
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57
conspicuous
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| adj.明眼的，惹人注目的；炫耀的，摆阔气的 | |
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58
indirectly
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| adv.间接地，不直接了当地 | |
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59
diagnosis
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| n.诊断，诊断结果，调查分析，判断 | |
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60
interpretation
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| n.解释，说明，描述；艺术处理 | |
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61
phenomena
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| n.现象 | |
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62
unaware
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| a.不知道的，未意识到的 | |
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63
respiration
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| n.呼吸作用；一次呼吸；植物光合作用 | |
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64
accurately
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| adv.准确地，精确地 | |
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65
noted
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| adj.著名的，知名的 | |
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66
fluctuations
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| 波动，涨落，起伏( fluctuation的名词复数 ) | |
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67
scrutiny
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| n.详细检查，仔细观察 | |
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68
deferred
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|
| adj.延期的，缓召的v.拖延，延缓，推迟( defer的过去式和过去分词 )；服从某人的意愿，遵从 | |
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69
amassing
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| v.积累，积聚( amass的现在分词 ) | |
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70
elimination
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| n.排除，消除，消灭 | |
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71
irrelevant
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| adj.不恰当的，无关系的，不相干的 | |
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72
discriminate
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| v.区别，辨别，区分；有区别地对待 | |
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73
judgments
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| 判断( judgment的名词复数 )； 鉴定； 评价； 审判 | |
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74
literally
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| adv.照字面意义，逐字地；确实 | |
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75
consolidation
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| n.合并,巩固 | |
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76
physically
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| adj.物质上，体格上，身体上，按自然规律 | |
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77
entirely
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| ad.全部地，完整地；完全地，彻底地 | |
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78
subsists
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| v.（靠很少的钱或食物）维持生活，生存下去( subsist的第三人称单数 ) | |
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79
stimulation
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| n.刺激，激励，鼓舞 | |
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80
pedantic
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| adj.卖弄学问的；迂腐的 | |
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81
perfectly
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| adv.完美地，无可非议地，彻底地 | |
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82
sensory
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| adj.知觉的，感觉的，知觉器官的 | |
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83
apparatus
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| n.装置，器械；器具，设备 | |
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84
lookout
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| n.注意，前途，瞭望台 | |
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85
purely
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| adv.纯粹地，完全地 | |
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86
rendering
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| n.表现，描写 | |
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87
habitual
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| adj.习惯性的；通常的，惯常的 | |
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88
helping
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| n.食物的一份&adj.帮助人的，辅助的 | |
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89
momentary
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| adj.片刻的，瞬息的；短暂的 | |
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90
anticipation
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| n.预期，预料，期望 | |
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91
Vogue
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| n.时髦，时尚；adj.流行的 | |
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92
dominant
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|
| adj.支配的，统治的；占优势的；显性的；n.主因，要素，主要的人(或物)；显性基因 | |
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93
subjectively
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| 主观地； 臆 | |
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94
determined
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| adj.坚定的；有决心的 | |
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95
premature
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| adj.比预期时间早的；不成熟的，仓促的 | |
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96
multiplication
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| n.增加，增多，倍增；增殖，繁殖；乘法 | |
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97
thoroughly
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| adv.完全地，彻底地，十足地 | |
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98
evaluation
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| n.估价，评价；赋值 | |
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99
wary
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| adj.谨慎的，机警的，小心的 | |
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100
likeness
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| n.相像，相似（之处） | |
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101
dictate
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| v.口授；(使)听写；指令，指示，命令 | |
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102
germination
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| n.萌芽，发生；萌发；生芽；催芽 | |
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103
loam
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| n.沃土 | |
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104
generalization
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| n.普遍性，一般性，概括 | |
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105
experimentation
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| n.实验，试验，实验法 | |
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106
subtlety
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| n.微妙，敏锐，精巧；微妙之处，细微的区别 | |
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107
rigid
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| adj.严格的，死板的；刚硬的，僵硬的 | |
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108
quotation
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| n.引文，引语，语录；报价，牌价，行情 | |
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109
quotations
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| n.引用( quotation的名词复数 )；[商业]行情（报告）；（货物或股票的）市价；时价 | |
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110
aurora
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| n.极光 | |
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111
amber
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| n.琥珀；琥珀色；adj.琥珀制的 | |
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112
magnetism
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| n.磁性，吸引力，磁学 | |
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113
fixed
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| adj.固定的，不变的，准备好的；(计算机)固定的 | |
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114
proceeding
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| n.行动，进行，(pl.)会议录，学报 | |
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115
combustion
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| n.燃烧；氧化；骚动 | |
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116
solidified
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| （使）成为固体，（使）变硬，（使）变得坚固( solidify的过去式和过去分词 )； 使团结一致； 充实，巩固； 具体化 | |
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117
sufficiently
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| adv.足够地，充分地 | |
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118
varied
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| adj.多样的，多变化的 | |
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119
investigators
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| n.调查者，审查者( investigator的名词复数 ) | |
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120
analyzing
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| v.分析；分析( analyze的现在分词 )；分解；解释；对…进行心理分析n.分析 | |
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121
dealing
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| n.经商方法，待人态度 | |
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122
applied
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| adj.应用的；v.应用，适用 | |
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123
physiology
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| n.生理学，生理机能 | |
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124
digestion
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| n.消化，吸收 | |
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125
deviations
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| 背离，偏离( deviation的名词复数 )； 离经叛道的行为 | |
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126
apprehended
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| 逮捕，拘押( apprehend的过去式和过去分词 )； 理解 | |
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127
fumbling
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| n. 摸索,漏接 v. 摸索,摸弄,笨拙的处理 | |
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128
inchoate
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| adj.才开始的，初期的 | |
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129
isolates
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| v.使隔离( isolate的第三人称单数 )；将…剔出（以便看清和单独处理）；使（某物质、细胞等）分离；使离析 | |
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130
deliberately
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| adv.审慎地；蓄意地；故意地 | |
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131
haphazard
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| adj.无计划的，随意的，杂乱无章的 | |
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132
allied
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| adj.协约国的；同盟国的 | |
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133
detailed
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| adj.详细的，详尽的，极注意细节的，完全的 | |
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134
ramifications
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| n.结果，后果( ramification的名词复数 ) | |
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135
justified
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| a.正当的，有理的 | |
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136
domain
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| n.(活动等)领域，范围；领地，势力范围 | |
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137
isolation
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| n.隔离，孤立，分解，分离 | |
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138
clinch
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| v.敲弯，钉牢；确定；扭住对方 [参]clench | |
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139
clinched
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| v.（尤指两人）互相紧紧抱[扭]住( clinch的过去式和过去分词 )；解决（争端、交易），达成（协议） | |
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140
gleaned
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| v.一点点地收集（资料、事实）( glean的过去式和过去分词 )；（收割后）拾穗 | |
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141
hearsay
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| n.谣传，风闻 | |
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142
retailed
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| vt.零售（retail的过去式与过去分词形式） | |
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143
engrossed
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| adj.全神贯注的 | |
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144
consecutive
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| adj.连续的，联贯的，始终一贯的 | |
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145
amplification
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| n.扩大，发挥 | |
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146
stimulated
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| a.刺激的 | |
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147
tirade
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| n.冗长的攻击性演说 | |
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148
futility
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| n.无用 | |
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149
manifestation
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| n.表现形式；表明；现象 | |
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150
contented
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| adj.满意的，安心的，知足的 | |
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151
formulated
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| v.构想出( formulate的过去式和过去分词 )；规划；确切地阐述；用公式表示 | |
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152
inert
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| adj.无活动能力的，惰性的；迟钝的 | |
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