# Popular Science Monthly/Volume 78/February 1911/The Disciplinary Value of Geography I

Next in series
Layout 4
THE
POPULAR SCIENCE
MONTHLY
FEBRUARY, 1911
* THE DISCIPLINARY VALUE OF GEOGRAPHY
By Professor W. M. DAVIS
HARVARD UNIVERSITY
Part I. The Science of Geographical Investigation
Educational Values.—Any study that is worthy of a place in a university must have a value of its own, must stand in a serviceable relation to other subjects, and must offer a serious mental discipline for those who follow it. The modern treatment of geography by explanatory instead of by empirical methods, and in view of an evolutionary instead of a teleological philosophy, satisfies all these requirements. That geography has a value of its own is sufficiently indicated by the abundance of useful and interesting material that an otherwise well-prepared student may acquire from it, and from no other source. That it stands in a serviceable relation to other subjects is proved by the fundamental position that it occupies with respect to biology and history, as well as to commerce and diplomacy. That it provides a serious mental discipline will, it is hoped, be apparent to any one who cares to read the following pages. A discussion of the science of geographical investigation, here presented with particular respect to the study of land forms, but equally applicable to other divisions of the subject, will show that geography, like various other sciences, gives abundant exercise to various mental faculties, such as observation, invention, deduction, comparison and judgment; while a consideration of the art of geographical presentation will show that geography, like other sciences, encourages the development of various styles of composition, such as narrative, inductive, analytical, systematic and regional, each of which is particularly well adapted to the exposition of certain geographical problems.
The Student and the World.—It has been well remarked by an experienced university professor, that an advanced student would profit ​greatly if he guarded himself against a too great absorption and isolation in his investigation of a limited field of study, by giving conscious attention to the presentation of his results in the best possible form for their full appreciation by so many of the rest of the world as may be interested in them; for he would be thereby placed in a more sympathetic relation with at least some of the rest of humanity, from whom he might otherwise remain too long estranged. Success in this effort is greatly promoted if the student recognizes the essential differences between investigation, which tends to isolate him from the world, and presentation, which ought to bring him into relation with it. The chief of these differences may be here pointed out, with particular relation to geographical problems.
Investigation.—During the progress of an investigation the student is properly enough alone with his subject for a large part of his time, whether he is in the field, the laboratory or the library. This is quite as it should be, for if during this period his attention is much distracted by outside matters, he can not develop a single-minded concentration of his best efforts on his work; he can not form that close intimacy with his problem which comes from uninterrupted association with it. Several weeks or months may be devoted to reaching his conclusions, and during this period the student may rightly enough find himself increasingly absorbed in his work and correspondingly withdrawn from outside relations; but he must remember that isolation does not involve secrecy. The pleasure of progress and discovery is increased by sharing it with appropriate companions. If some ideas are thus planted in better soil than that from which they sprang, let the larger growth that they reach there cause rejoicing, not envy; for as Gilbert has so well said in an admirable essay on "Scientific Method": "It is only the man of small caliber who has no ideas to spare, and secretiveness in matters of science is ordinarily a confession of weakness."
In the course of progress, facts and theories are come upon in an irregular and unforeseen order; only towards the close of his work is the student in a position to reconsider everything that he has learned and to give it all a well-ordered arrangement. During his advance he must ever be alert in discovering new facts, open-minded towards new ideas, critical of every statement, jealously watchful of his mental independence, judicial in reaching conclusions: but in all these activities, his work should be carried on for the most part alone, for only when isolated is he sufficiently thrown on his own resources; and only when thus depending on himself can he learn whether he is really able to carry on an independent investigation. His opinions may ​frequently change as his collection of facts and his invention of explanations advance; new facts and new ideas may frequently call for the revision of earlier facts and ideas, and for the change of first-formed opinions; all such revision and change are best accomplished when the student is alone with his problem. At the end of his study, the net results gained may appear to be of small volume, in view of the time and labor spent in reaching them; but if they include a matured and well-balanced judgment on the problem under discussion, as well as an intimate acquaintance with its sources of material, a comprehensive knowledge of its historical development, and a close familiarity with all the factors involved in its investigation, the time and labor will have been well expended.
Presentation.—Occasion then arises for the oral or printed presentation of the results of all this independent work, in form for their best understanding by others. The student must then emerge from his isolation, in which the world may have seemed to him to be occupied chiefly by his problem and himself; he must recognize that the real world is crowded with other problems and other workers, among which he and his interests may be rudely jostled in course of finding the place that they deserve. He must now awake to a realization of his surroundings, and consider particularly what sort of presentation will place his results most effectively and favorably before the public. He no longer has to consider the nature of his own work; that he has done sufficiently already. He has now to consider the nature of other persons whose interests are more or less akin to his own, in order to discover how he can best bring his work before them. When his presentation has been made, he will learn that those of his hearers or readers who meet him with unselfish sympathy and just appreciation become his most helpful and encouraging friends; and he ought at the same time to learn what his own bearing should be when it is his turn to listen to reports by his colleagues on their work. We will here examine briefly the requirements of an oral presentation, postponing the discussion of a printed report to a later page.
When a student rises to make an oral report in the presence of his teachers and his comrades, he is no longer an investigator alone with his problem; he takes his place as a speaker, between his problem and his hearers. There may be cases in which his personal experience deserves narration; but in scientific communications, personal items should, as a general rule, be relegated to the background; the speaker had best try to obliterate personal matters, which always give a more or less subjective flavor to a report, and strive to make himself simply the conduit through which the essence of his subject, in the most objective form, shall flow to the minds of his hearers. He has no longer abundant time, but is limited to half an hour, or an hour at the most; at ​the end of which time his audience ought to have acquired the gist of what has taken him weeks or months to learn. Evidently then the speaker must present only a selection of his best facts, theories and conclusions, in the most carefully planned order. He must say nothing at all about much of the material that he has gathered; he must touch very lightly and briefly on various subordinate items, and he must bring forward only those statements for fuller presentation which bear most significantly on his problem, and which can as far as possible be easily understood and remembered by his hearers. For this purpose he must, of course, before he begins to speak, know what grade of audience he is to address: for however useful the exercise of merely addressing an audience may be to an inexperienced speaker, whether what he says is understood or not, he must remember that an audience which has listened for half an hour or more and learned little, has wasted its time. A courteous consideration of those present, as well as a selfish regard for the opinion they will form of him and his work, should lead the speaker to make every effort to repay them for their time and attention, by making his presentation as intelligible and interesting as possible. He must therefore strive to produce a clear and definite understanding of his results in the mind of each hearer, in such form that a good share of them can be carried away and remembered. Hence it is not only on the ground of a generous consideration for the feelings of his audience, but, as above said, also from a selfish interest in his own progress, that he ought now to strive to make himself clearly intelligible. If he does not do this, he will be like an unsociable goldwasher, who, with patient endurance, has worked over a great volume of gravel for the sake of finding a few grains of gold, and who then, instead of having the gold refined and coined in form for current circulation among his fellows, keeps it in the comparatively useless form in which he found it; and at the same time complains that the value of his patient work is not recognized.
In view of all this it is manifestly desirable that a student should give due attention to the presentation of his results, as well as to the methods of investigation by which the results were gained. He will be aided in both these worthy efforts if he recognizes clearly the striking differences between the two processes, and then gives to each process the attention necessary to its best development. An analysis of the method of investigation, as applied to the study of land forms, here follows. A fuller statement regarding presentation will be given in a second article.
Analysis of Investigation.—As long as geography was concerned only with the observation and record of visible facts, its methods were relatively simple. They included, as far as land forms are concerned, the determination of latitude and longitude, the measurement of ​directions, distances and altitudes, and the preparation of maps of appropriate scales, along with an empirical description of the facts observed. For those geographers, however, who, in these modern days, enter whole-souled into the explanatory method of describing land forms, there is needed, in addition to all the earlier requirements—for every modern geographer ought to be well exercised in the preparation of empirical descriptions, as well as in the arts of surveying and cartography—a careful and conscious training in theoretical investigation; because every explanatory description, in so far as it introduces the supposed facts of the past as the best means of describing the visible facts of the present, goes beyond observation and employs theories; and theories can be successfully established only by the critical use of scientific methods of investigation.
The different mental processes involved in an investigation of the kind with which we are here concerned may be arranged as follows: observation and record of accessible facts; induction of generalizations; search for fuller explanation; invention of hypotheses or supposed mental counterparts of invisible facts; deduction of consequences from each of the invented hypotheses; confrontation of the consequences with appropriate facts; preliminary judgment; revision and improvement of each process; final judgment of the degree of correctness of various invented hypotheses.
Observation and Record of Accessible Facts.—The first step in a problem is the acquisition of a certain number of facts. This may involve original observation, as in the outdoor exploration of a geographical field, or it may be based on second-hand observation, as in the study of some other observer's records in books and maps. In either case, the investigator must be alert to avoid deception by mistaken appearances and by misleading subjective sensations; at the same time the mind must be kept sensitive to every real impression, to which it must respond in the most docile manner, submissively recognizing the facts as they stand, not constraining them in the least one way or the other. The investigator must be untiringly active in traversing his outdoor field, and omnivorous in devouring all pertinent material in the library. Indeed during the process of acquisition, outdoors and indoors, the investigator's mind must be like a fresh and sensitive photographic plate, on which no previous impressions blur the new ones that are made on it.
The facts mentally acquired must in some way, graphic or verbal, be recorded; and at the outset the records should be made in colorless empirical form, as free as possible from theoretical prepossessions. It will be chiefly in proportion to the larger or smaller measure of previously acquired experience that the observer will, at this early stage of his study, employ roundabout phrases or technical terms in recording ​the facts that he comes upon. If he says: "That is a promontory," this simple empirical statement implies that he sees a certain configuration of land and water, and recognizes that it possesses the essential features of a typical configuration already known from previous experience, for which the empirical term, promontory, has been adopted by general consent. But if he says: "That is a delta," the statement involves some measure of theory. It implies, as before, that he sees a certain number of features in the land form before him, and that he recognizes their correspondence with the essential features of the concept or type, for which the name, delta, has been agreed upon; but inasmuch as a delta is the product of a certain process acting under certain conditions through some unobservable period of past time, the observer has here made a leap into theory, although he may be hardly aware of it. As soon as such a leap is recognized, the visible features of the land form before the observer should be reexamined and stated for the time being in purely empirical terms; that is, in terms based on what is immediately seen, instead of in part on what is inferred. All this calls for fair-minded deliberation, the development of which demands time and training. If this cautious procedure seems slow and cumbersome, it should be practised with respect to various explanatory terms now commonly in use, such as delta, dune, volcano, moraine and so on, until it can be performed with ease and speed. During the progress of such training, a few examples of this elementary kind of analysis should be written out in extenso in the investigator's note book. The number of pages of careful records may at this time serve as a better measure of progress made by a young geographer than the number of miles traversed over hill and valley.
Induction of Generalizations.—When new facts are encountered they are, as has just been shown, more or less consciously compared, in the way of likeness or contrast, with acquisitions of previous experience. As progress is made, groups of similar facts are formed, the several members of a group being alike in respect to certain features that are therefore taken to be essential. An active-minded student quickly generalizes the repeated features by which all the observed members of a group are characterized; thus he conceives an idealized type; and at the same time relegates individual features to a lower rank. As new facts fall into groups already formed and give further warrant for the provisional generalizations previously made, a careful phrasing or formulation of the generalized features should be attempted, with some mention of the way in which individual examples depart from the idealized type. Thus an advancing investigation passes from the recognition of separate facts to the induction of generalized ideas. Certain classes of facts are so fully accessible to observation that the generalizations induced from accumulating records suffice to provide a reasonable ​understanding or explanation of the phenomena concerned; for example, the work of the wind in sweeping sand across a desert and whirling dust high into the air may be seen in operation; or the behavior of rivers in draining their basins and in transporting land waste may be closely studied by direct observation: hence wind action and river action may in these respects come to be understood by induction alone. But the larger action of these agents, as in the erosion of elaborate valley systems by rivers, and in the sculpture of peculiar desert forms by the winds, demand much unseen work in long past time; and even if induction on a widely extended basis could ultimately bring forth the full explanation of such problems, the mind is too impatient to wait for so long postponed a result, and seeks other means of reaching the same end.
Search for Theoretical Explanation.—One sometimes meets inductive investigators who say that they believe it best not to enter upon the speculative aspects of their work, even in complicated problems, until all the facts have been gathered; but such caution is unwise, even if it be mentally possible in one who is capable of conducting an original investigation. An unintelligent person may indeed see various outdoor facts, and continue to observe, collect and record them, and yet never ask himself or anyone else about their cause; but such a person is not mentally fitted to undertake the investigation of new problems, such as are here considered. On the other hand, when an earnest investigator comes upon facts of a complicated nature, he can not help wondering how they came to be what they are; he is not satisfied with the slow progress of induction toward their explanation; he inevitably feels some curiosity as to their invisible origin, that is, as to so much of their history as has already passed; he is discontent to remain ignorant; his mind is alert to find hidden meanings, just as his eyes are watchful to see visible features. He wishes to know about past facts which, in their time, were as veritable as are the facts of to-day, and which taken with to-day's facts assume that reasonable relation which we call explanation. This is precisely as it should be. If by good fortune the student's wonder and curiosity are so much aroused by what he sees, that they excite the invention of a possible explanation for his novel facts, the part of wisdom is surely not to turn his mind away from this invention, which may prove to be an extremely useful one, but merely to refuse immediate belief in it, before its value has been tested. The danger here lies not in the wish for explanation, nor in any ingenious invention of an explanation, but in the acceptance of such an invention as if it were the final truth. That is truly a serious error; an error that is not to be guarded against by stifling the inventive faculty, but, as will be shown below, by arousing the critical faculties to a rigorous examination of any suggestions that the inventive faculty may bring forth.
​Invention of Hypotheses.—The search for explanation of observed facts may be made in some cases by the memory, which may recall an explanation previously learned. In physics and chemistry, the search for explanation is largely aided by experiment; but in the study of land forms experiment serves chiefly to illustrate explanations already reached, rather than to lead to new ones. We are here chiefly concerned with the kind of search which calls the investigator's own faculty of invention into play—the kind of search which tries to make a new combination of some pertinent facts or principles of previous acquisition with some of the facts of new observation, in the hope of thereby bringing about a clear understanding of all the facts under discussion.
The faculty of invention is peculiar in working to a large extent subconsciously. Facts to be explained can be intentionally observed; previously gained knowledge may for the most part be consciously reviewed; but the desired explanatory combination of old knowledge and new facts may not be immediately found while the conscious search for it is going on. Invention is, however, much favored by active observation, and spurred on by an eager spirit of inquiry; it is greatly aided by mental ingenuity, but it is seldom immediately accomplished by conscious intention. However, the faculty of invention can be cultivated if many facts, old and new, are frequently brought to conscious attention, and the wish for explanation and the search for it are often renewed. Then the subconscious mind will continue the search, and after an interval, during which the matter has been apparently out of mind, an explanation may most unexpectedly awaken attention by springing into consciousness.
The sudden birth of an apparently successful explanation is truly a most delightful experience; indeed so delightful and encouraging that many an investigator has mistaken it for the climax or crown of his work, and accepted it as the whole truth without further question. But, as has already been pointed out, the too-ready acceptance of an untested invention, as if it were true, is dangerous. The investigator must recognize that it is no great recommendation of an invention, that it explains the partial group of facts that it was made to explain. Of course it must do that; it would deserve no consideration at all if it did not. But in order to deserve acceptance as the true counterpart of past facts, it must do much more. It must explain various facts that it was not made to explain; facts that it did not expect to explain; facts that were not thought of, or were not even known at the time of invention, as will appear more fully below.
The investigator of course hopes that his invention, based on some of the observed facts, will prove to be the true counterpart of some past facts, or of some invisible principle or process, by means of which ​he shall gain a full explanation of all the observed facts; that is, an understanding of the manner in which they have been produced. While the invented counterpart remains of uncertain value, because untested, it is often called an hypothesis; and its uncertainty may be further indicated by calling it a provisional, or a working hypothesis. If later on, it survives all the tests that can be applied to it, it is then usually called a theory; or in order to emphasize its proved value, an established theory. But it is never, so far as the unseen facts of the past are concerned, anything more than the mental counterpart of those facts. Indeed, inasmuch as an hypothesis, when first invented, is usually based on only a few of the observed facts, it will then be only the counterpart of a few of the facts of the past, or of some general principle that suggests the genetic relation of partial groups of facts, past and present. Much more than the mere invention of such an hypothesis must be done before a complete explanation of all the facts is reached; and it is through the additional work, by which supplementary facts and fancies are correlated, that an invented hypothesis ia tested.
As soon as the tentative nature of an hypothesis is understood and its possible failure is recognized, the investigator should realize that he must not stop inventing when his first hypothesis is brought forth; he must urge his subconscious mind to continue bringing forth inventions as actively and ingeniously as possible. He must thus equip himself with several rival working hypotheses, to each of which he must give warm welcome and impartial friendship, but to none of which must he offer special protection or advocacy. The defence for a hypothesis is provided chiefly from new details that are added to it after its invention, or by new facts which are brought to light by its aid. If no defense of this kind is found, the hypothesis must be regarded as only a tentative speculation.
Deduction of the Consequences of an Hypothesis.—Before any decision as to the truth of a hypothesis is attempted, the question must be asked: What consequences must it have in addition to those facts which it was made to explain? An altogether new faculty is now called into play, the faculty of deduction, by which the consequences of a hypothesis are logically worked out. Here again experimentation is extremely useful in physics and chemistry, and it is coming to be more useful than it has been in biology and geology; but in the study of land forms experiment is at present rather imitative than demonstrative, and it will not be further considered here. What we have to examine now is a logical faculty that can be more consciously used than invention, but one which, unlike observation, can be carried ​on in the dark with the eyes shut. During the exercise of this faculty the investigator must in the most critical manner and with the aid of all necessary pertinent knowledge, think out or deduce everything that would happen, if an invented hypothesis were really true; and this he must do for each hypothesis in turn. The consequences appropriate to each hypothesis must be kept in groups by themselves; and these groups of hypothetical consequences must be carefully distinguished from the facts of observation.
In a geographical problem, the investigator must mentally search out, in view of each hypothesis that he has invented, the whole sequence of changes that would take place, the whole sequence of land forms that would be developed, if the class of forms with which he is dealing were followed all through its history, past, present and future. No invention should be hastily discarded, because it appears at first sight to be improbable; for such appearance may be more determined by the scientific fashion of the time, or by the mental habit of the investigator, than by anything inherent in the invention itself. Particular attention should be given to the deduction of unlike consequences of rival hypotheses; for, as will soon appear, it is particularly by means of these instantiæ crucis that successful and unsuccessful hypotheses are discriminated. Those who find deduction irksome should be advised to practise it until it becomes easy and agreeable; just as careless observers should be urged to continue observation until they can perform this fundamental process with accuracy and enjoyment. In no case should an investigator, particularly an unpractised investigator, put his trust in that rapid mental process called intuition, and hope by its uncertain aid to leap from invention to conviction. Let intuition be welcomed, just as invention is; but after it has leaped to its goal, its half-conscious path should be carefully retraced and the safety of its leap tested.
Confrontation of Consequences with Facts.—We now reach a stage in which the faculty of impartial comparison is brought into play. Facts have been gathered abundantly by the active observer, who is still at work gathering yet more of them; hypotheses have been brought forward in good number by the ingenious inventor, who is, however, still at work in the hope to find new ones; the consequences of each hypothesis have been carefully worked out, group by group, by the patient and logical deducer, who stands ready to elaborate the consequences of new hypotheses as soon as they are found; and the consequences are now to be confronted, group after group, with the facts by the impartial comparer, in order to see how close an agreement they reach. This is as if the observer should marshal his battallion of facts in good order on one side of a parade ground, and the deducer should lead forth the battalions of consequences one after another and halt them opposite the marshalled facts, so that the comparer could to best ​advantage inspect the opposed arrays, with the intention of seeing how closely any battalion of consequences matches the battalion of facts. In making this inspection, the comparer must evidently give particular attention to the facts from which an invention did not spring; and look closely to see how successfully they are matched by the consequences of the invention. There must be no pressure to force an agreement where none exists; no constraining of the facts or torturing of the consequences to make them look like each other; but simply a fair-minded comparison, followed by a clear unbiased report as to where agreement and disagreement occur.
Preliminary Judgment.—If two rival hypotheses have yielded only identical consequences, all of which agree nicely with the corresponding facts, no decision in favor of either hypothesis can be made, and judgment must be suspended. The comparer must then ask the deducer if he can not find unlike consequences of the rival hypotheses; and if such are found close attention must be given to the degree of success with which they match the corresponding facts. Evidently, then, some consequences have a greater value than others in discriminating among rival hypotheses. If the consequences which are peculiar to one hypothesis match the appropriate facts, while the contrasted consequences of other hypotheses fail to do so, then a higher value may be given to this one of the several rival hypotheses, although before it had no greater value than its now defeated competitors.
Revision.—It will often happen, when confrontation is made and an encouraging amount of agreement is found between the consequences of a certain hypothesis and the corresponding facts of observation, that the agreement is nevertheless in some respects imperfect. It may be that, for some of the facts, no corresponding consequences have been deduced; or that, for certain deduced consequences, there are no corresponding facts. Then the investigator must revise his work. He must return to the stage of deduction, and look closely to see if those consequences which are only partly successful in meeting the facts, were rightly deduced; he must inquire if the absence of a certain consequence, with which some well ascertained fact ought to be matched, is perhaps due to oversight in his deduction. He must examine with particular care all the principles, introduced by memory from previous acquisition, to see if they are safely established and correctly applied; he must be especially careful not to overlook any tacit postulate, which, without being consciously recognized as such, has nevertheless been taken for granted without sufficient proof, and used as an essential basis for some of his deductions. He must go still farther back and modify his inventions in one way or another, in the hope that, after such modification, some one of them may lead to new consequences that will better than before fit the previously unmatched facts: hence it is ​important to regard each invented hypothesis as an elastic conception, whose form may be changed as necessity demands. The investigator must even return to his field of observation and reexamine the facts, particularly such as do not match with the well defined consequences of a partly successful hypothesis; and he must search his field with the sharpest scrutiny to see if any facts, previously unnoticed, really do occur in the manner indicated by unmatched consequences. In every way, the utmost care must be taken not to allow oneself to be satisfied with imperfect or incomplete agreements.
If these various recommendations are carefully carried out, the danger, often feared, that an investigator may, Procrustes-like, force the facts to fit the needs of a favorite hypothesis, is practically ruled out; for if the investigator has several unlike hypotheses in mind, and has deduced several unlike series of consequences from them, it will evidently be impossible for him to force his facts to agree with all of them, however much the facts may be trimmed or stretched.
Irregular Order of Procedure.—In practise the several processes that have been necessarily considered in systematic succession, are carried on in a much more irregular fashion. It has already been pointed out that invention may advisedly go hand in hand with observation. It is evident that, after a hypothesis has been invented, any time spared from observation may be devoted to deduction; and it often happens that the consequences of the hypothesis may grow to a greater number than that of the classes of observed facts then accumulated. Confrontation and comparison may be made repeatedly as observation advances, and revision is always in order the moment there seems to be occasion for it. The active-minded investigator, thus continually reviewing the different aspects of his problem, may gradually come to feel that one hypothesis, modified as far as needs be from its original form, appears to deserve greater acceptance than any of its rivals; then arises the great question: Is this hypothesis really true? Is it surely a correct counterpart of the invisible facts of the past? Clearly it is essential that an investigator, on reaching this stage in his work, should fully understand the nature of scientific proof.
Final Judgment.—It is at this advanced stage of an investigation that the exercise of a sound judgment is needed, in order to estimate the measure of confidence that may be given to an apparently successful hypothesis. The most important point to emphasize now is that, in such problems as we are here dealing with, the only available method of testing the truth of any hypothesis is to measure the agreement of its deduced consequences with the appropriate facts of observation. In this respect scientific proof is altogether unlike geometrical proof, in which the correctness of a theorem is never tested by its agreement with observable facts, but only by the continuity with which successively ​deduced steps lead forward from the postulated premises to the announced end. Geometry therefore corresponds—so far as a correspondence can be traced between a mathematical and an observational science—chiefly to that part of geological or geographical investigation which is concerned with invention and deduction; for these processes, like the similar processes in geometry, can be performed by mental reflection in the dark, and have no close dependence on observation.
In observational sciences it is necessary to examine critically the different degrees of agreement that may exist between the deduced consequences of an hypothesis and the facts gathered by observation, in order to pass a safe judgment on the value of the hypothesis from which the consequences were deduced. This return to the facts is one of the most important as well as one of the most characteristic elements of scientific work.
If observation has discovered but few classes of simple facts, and if invention has brought forth only one hypothesis, which leads only to a few simple consequences, the value of the hypothesis must remain in doubt, even if its consequences agree rather closely with the facts; because agreement in such a case may be a matter of chance. Here no decided opinion as to the value of the hypothesis should be expressed; judgment must be suspended, and the mind held open for further light, either from observation, invention or deduction. Again, if, as above pointed out, the groups of consequences deduced from two or more rival hypotheses are about equally successful in matching the facts, no judgment must be pronounced in favor of either, however strong the investigator's desire to reach a conclusion may be. But if the peculiar and numerous consequences of a certain hypothesis agree to a remarkable extent with the highly specialized groups of abundant and varied facts, such an hypothesis is strongly commended thereby, for the possibility of accidental agreement is greatly diminished as the facts and consequences to be matched become more complicated, and as the number of agreements increases. Furthermore, if the facts, as at first collected, seem of arbitrary occurrence and unrelated distribution, and yet are afterwards found, by the suggestive aid of an hypothesis and its deduced consequences, really to possess a previously unsuspected order and many previously unseen relationships, the hypothesis which leads to this larger and clearer view is thereby greatly recommended; for it is highly commendable to a theory, if it leads to the discovery of reasonable system where confusion seemed to prevail.
But we must go further; for it often happens that, after an hypothesis has been invented, and after its consequences have been successfully confronted with the previously observed facts, new classes of facts may be discovered for which deduction had provided no appropriate ​consequences. If an impartial revision of deduction then leads to the detection of new consequences which agree with the new facts, such added agreement greatly increases the probability of correctness adjudged on the previous agreement. More significant still is it, when certain peculiar or complicated consequences are deduced, for which no corresponding facts had been previously discovered, and when a return to the field of observation discovers facts of the peculiar character and in the significant situation assigned to them by deduction. This gives wonderful strength to the hypothesis from which consequences so prophetic can be derived: indeed, evidence of this is usually regarded as convincing, for the possibility of such a degree of accordance of consequence and fact being the work of chance is practically ruled out. Finally, if in the course of years, many investigators find many complicated facts in many parts of the world, all of which are successfully matched by the elaborate consequences of an hypothesis that was invented long before observation was so widely extended, the probability of correctness rises to so high an order that the truth of the hypothesis may be accepted, and it may be promoted to the rank of an established theory. The unseen facts that such a theory reveals are commonly accepted as of an equal degree of verity with the facts of direct observation.
The will or the wish of the sane investigator has no power to withhold belief, when this stage of theorizing is reached. And yet it can not be too carefully borne in mind that even if all the above requirements are satisfied, the most that can be said for the established theory is that its probability of correctness is so high that its chance of error may be disregarded. The fair-minded Playfair phrased this aspect of our problem admirably a hundred years ago in the case of river valleys:
Every river appears to consist of a main trunk, fed from a variety of branches, each running in a valley proportioned to its size, and all of them together forming a system of vallies, communicating with one another, and having such a nice adjustment of their declivities, that none of them join the principal valley either on too high or too low a level; a circumstance which would be infinitely improbable if each of these vallies were not the work of the stream that flows in it.
It is particularly in this matter of the increasing probability of correctness that the nature of geological or geographical proof is so unlike that of geometrical proof. There is never any talk of increasing the probable correctness of a geometrical theorem, when several different demonstrations are given for it. Each demonstration is absolutely correct alone, as far as anything can be absolute in the limited experience of our finite minds. But in our subject, it is always appropriate ​to speak of the increasing probability of correctness of a conclusion, even though general acceptance was given to it before.
It is, furthermore, important to recognize that a fundamental but unprovable postulate underlies all this discussion; namely, that the present order of nature is persistent; that is, that time is continuous, and that physical forces have always conformed to the laws which now prevail. For however ingenious or amusing may be the speculations of the metaphysician as to another order of things—for example, as to a past condition of existence in which gravitation worked irregularly and variably, or as to a period of time when energy was created and matter was destroyed in haphazard order, or when time itself began or stopped—the scientist is not concerned with them, because they utterly transcend experience. All his discussions and conclusions as to the events of past time and the origin of the present features of the earth are of no avail, if his essential postulate of the persistence of the present order of nature is erroneous; but the frank recognition of this fundamental principle need disturb no earnest observer of the face of nature. Whatever doubts regarding the conclusions of science may be expressed by the ingenious metaphysician, with his fancied possibilities as to such inconceivable conditions a§ the beginning of time or the creation of matter; and whatever dissatisfaction may be expressed, regarding conclusions that are based merely on an unproved postulate and measured only in terms of high probability, by the absolutist who wishes to reach unconditional demonstration in all things, the scientist need not be disconcerted. He must still base all his work on the long accumulated and carefully tested results of thoughtful experience, for his work can have no other base; and he must accept as satisfying, even if not as absolutely certain in the absolutist sense, those high degrees of probability that are attained by well established theories, for there is no other satisfaction he can reach.
* ↑ G. K. Gilbert, "The Inculcation of Scientific Method by Example," Amer. Journ. Sci., XXXI., 1886, 284-299.
* ↑ T. C. Chamberlin, "The Method of Multiple Working Hypotheses," Journ. Geol., v., 1897, 837-848.
* ↑ J. Playfair, "Illustrations of the Huttonian Theory of the Earth," Edinburgh, 1802, 102.
* ↑ "Bearing of Physiography on Uniformitarianism," Bull. Geol. Soc. Amer., VII., 1896, 8-11.