Citation: Myron Lucius Ashley. "The Nature of Hypothesis". Chapter 7 in Studies in Logical Theory edited by John Dewey. Chicago: University of Chicago (1903): 143-183.
IN the various discussions of the hypothesis which have appeared in works on inductive logic and in writings on scientific method, its structure and function have received considerable attention, while its origin has been comparatively neglected. The hypothesis has generally been treated as that part of scientific procedure which marks the stage where a definite plan or method is proposed for dealing with new or unexplained facts. It is regarded as an invention for the purpose of explaining the given, as a definite conjecture which is to be tested by an appeal to experience to see whether deductions made in accordance with it will be found true in fact. The function of the hypothesis is to unify, to furnish a method of dealing with things, and its structure must be suitable to this end. It must be so formed that it will be likely to prove valid, and writers have formulated various rules to be followed in the formation of hypotheses. These rules state the main requirements of a good hypothesis, and are intended to aid in a general way by pointing out certain limits within which it must fall.
In respect to the origin of the hypothesis, writers have usually contented themselves with pointing out the kind of situations in which hypotheses are likely to appear. But after this has been done, after favorable external conditions have been given, the rest must be left to "genius," for hypotheses arise as "happy guesses," for which no rule or law can be given. In fact, the genius differs from the ordinary plodding mortal in just this ability to form fruitful
Whether or not it can be shown that Zerah Colburn's ultimate explanation is needed in logic as little as Laplace asserted a similar one to ha required in his celestial me-
The hypothesis as predicate.—It is generally admitted that the function of the hypothesis is to provide a way of dealing with the data or subject-matter which we need to organize. In this use of the hypothesis it appears in the rôle of predicate in a judgment of which the data, or facts, to be construed constitute the subject.
In his attempts to reduce the movements of the planets about the sun to some general formula, Kepler finally hit upon the law since known as Kepler's law, viz., that the squares of the periodic times of the several planets are proportional to the cubes of their mean distances from the sun. This law was first tentatively advanced as a hypothesis. Kepler was not certain of its truth till it had proved its claim to acceptance. Neither did Newton have at first any great degree of assurance in regard to his law of gravitation, and was ready to give it up when he failed in his first attempt to test it by observation of the moon. And the same thing may be said about the caution of Darwin and other investigators in regard to accepting hypotheses. The only reason for their extreme care in not accepting at once their tentative formulations or suggestions was the fear that some other explanation might be the correct one. This rejection of other possibilities is the negative side of the matter. We become confident that our hypothesis is the right one as we lose confidence in other possible explanations; and it might be, added, without falling into a circle, that we lose confidence in the other possibilities as we become more convinced of our hypothesis.
It appears that such may be the relation of the positive and negative sides in case of such elaborate hypotheses as those of Kepler and Newton; but is it true where our hypotheses are more simple? It is not easy to understand why the fact that the hypothesis is more simple, and the time required for its formulation and test a good deal shorter, should materially change the state of affairs. The question remains: Why, if there is no opposition, should there be any uncertainty ? In all instances, then, the hypothesis appears as one among other possible predicates which may be applied to our data taken as subject-matter of a judgment.
While it will not be necessary to. give a very complete account of the various definitions of the judgment that might be adduced, still the mention of a few of the more prominent ones may serve to indicate that something further is needed. In definitions of the judgment sometimes the subjective side is emphasized, sometimes the objective side, and in other instances there are attempts to combine the two. For instance, Lotze regards the judgment as the idea of a unity or relation between two concepts, with the further implication that this connection holds true of the object referred to. J. S. Mill says that every proposition either arms or denies existence, coexistence, sequence, causation, or resemblance. Trendelenburg regards the judgment as a form of thought which corresponds to [lie real connection of things, while Ueberweg states the case a little differently, and says that the essence of judgment consists in recognizing the
Many of our judgments prove false. Not only do we err
In the views of the judgment so far brought out, reality, with which it is generally admitted that the judgment attempts to deal in some way, appears to lie outside the act of judging. Now, everyone would say that we make some advance in judging, and that we have a better grasp of things after than before. But how is this possible if reality lies without or beyond our act of judging? Is the reality we now have the same that we had to begin with? If so, then we have made no advance as far as the real itself is concerned. If merely our conception of it has changed, then it is not clear why we may not be even worse off than before. If reality does lie beyond our judgment, then how, in the nature of the case, can we ever know whether we have approached it or have gone still farther away? To make any claim of approximation implies that we do reach reality in some measure, at least, and, if so, it is difficult to understand how it lies beyond, and is independent of, the act of judging.
In this investigation of Darwin's the conflicting explanations of sinking stones appear within the main question of the formation of vegetable mold by earthworms. The facts that disagreed with the old theory about sinking stones were approached through this new one. But the theories had something in common, viz., the disappearance of the stones or other objects: they differed in their further determination of this disappearance. In this case it may seem as if the facts which ware opposed to the current theory of sinking stones were seen to be discrepant only after the earthworm hypothesis had been advanced; the conflict between the new facts
As a more simple illustration, we may cite the common experience of a person who is uncertain concerning the identity of an approaching object, say, another person. At first he may not be sure it is a person at all. He then sees that it is someone, and as the person approaches he is inclined to believe him to be an acquaintance. As the supposed acquaintance continues to approach, the observer may distinguish certain features that cause him to doubt, and then relinquish his supposition that it is an acquaintance. Or, he may conclude at once that the approaching person is another individual he knows, and the transition may be so readily made from one to the other that it would be difficult to determine whether the discordant fo are discordant before the new supposition arises, or whether they are not recognized as conflicting till this second person is in mind.
Now, marked lines of likeness appear between this relatively simple judgment and the far more involved ones of scientific research. In the more extended scientific process we find data contradicting an old theory and a new hypothesis arising to account for them. The hypothesis is tested, and along with its verification we have the rejection, or rather the modification, of the old theory. Similarly, in case of the approaching stranger all these features are present, though in less pronounced degree. In scientific investigation there is an interval of testing by means of more careful consideration of the data and even actual experimentation. Before an explanation is accepted subject to test, a number of others may have been suggested and rejected. They may not have received even explicit recognition. In case of the identification of the stranger this feature is also present. Between two fairly definite attempts to identify the mind does not remain a mere blank or stationary, but other possible identifications may be suggested which do not have sufficient plausibility to command serious attention; they are only comparatively brief suggestions or tendencies.
It is to be noted that in all these instances the first supposition was not entirely abandoned, but was modified and more exactly determined. (Why it could not be wholly false and the new one wholly new, will be considered later in connection with discussion of the persistence and reformation of habit. There was such a modification of the old theory as would meet the requirements of the new data, find the new explanations thus contained both old and new features.
In psychological terms, we may say, in explanation of the judging process, that some stimulus to action has failed to function properly as a stimulus, and that the activity
It appears, then, that the purpose of the judgment is to obtain an adequate stimulus in that, when stimulus and response are adjusted to each other, activity will be resumed. But if this reconstruction and response were to follow at once, would there be any clearly defined act of judging at all? In such a case there would be no judgment, properly speaking, and no occasion for it. There would be simply a ready transition from one line of activity to another; we should have changed our method of reaction easily and readily to meet the new requirements. On the one hand, our subject-matter would not have become a clearly recognized datum with which we must deal; on the other hand, there would be no ideal method of construing it. Activity
In order that judgment may take, place there must be interruption and suspense. Under what conditions, then, is this suspense and uncertainty possible? Our reply must be that we hesitate because of more or less sharply defined alternatives; we are not sure which predicate, which method of reaction, is the right one. The clearness with which these alternatives come to mind depends upon the degree of explicitness of the judgment, or, more exactly, the explicitness of the judgment depends upon the sharpness of these alternatives. Alternatives may be carefully weighed one against the other, as in deliberative judgments; or they may be scarcely recognized as alternatives, as in the case in the greater portion of our more simple judgments of daily conduct.
The predicate is essentially hypothetical.—If we review in a brief résumé the types of judgment we have considered, we find in the explicit scientific judgment a fairly well-defined subject-matter which we seek further to determine. Different suggestions present themselves with varying degrees of plausibility. Some are passed by as soon as they arise. Others gain a temporary recognition. Some are explicitly tested with resulting acceptance or rejection. The acceptance of any one explanation involves the rejection of some other explanation. During the process of verification or test the newly advanced supposition is recognized to be more or less doubtful. Besides the hypothesis which is tentatively applied there is recognized the possibility of others. In the disjunctive judgment these possible reactions are thought to be limited to certain clearly defined alternatives, while in the less explicit judgments they are not so clearly brought out. Throughout the various forms of judgment, from the most complex and deliberate down to
Criticism of certain views concerning the hypothesis. — The explanation we have given of the hypothesis will enable us to criticise the treatment it has received from the empirical and the rationalistic schools. We shall endeavor to point out that these schools have, in spite of their opposed views, an assumption in common—something given in a fixed, or non-instrumental way; and that consequently the hypothesis is either impossible or else futile.
Bacon is commonly recognized as a leader in the reactionary inductive movement, which arose with the decline of scholasticism, and will serve as a good example of the extreme empirical position. In place of authority and the deductive method, Bacon advocated a return to nature and induction from data given through observation. The new method which he advanced has both a positive and a
It is evident that Bacon left very little room for hypotheses, and this is in keeping with his aversion to anticipation of nature by means of "phantoms" of any sort; he even said explicitly that " our method of discovery in science is of such a nature that there is not much left to acuteness and strength of genius, but all degrees of genius and intellect are brought nearly to the same level." Bacon gave no explanation of the function of the hypothesis; in his opinion it had no lawful place in scientific procedure and must be banished as a disturbing element. Instead of the reciprocal relation between hypothesis and data, in which hypothesis is not only tested in experience, but at the same time controls in a measure the very experience which tests it, Bacon would have a gradual extraction of general laws from nature through direct observation. He is so afraid of the distorting influence of conception that he will have nothing to do with conception upon any terms. So fearful is he of the influence of pre-judgment, of prejudice, that lie will have
Less technically the failure of Bacon's denial of the worth of hypothesis—which is in such exact accord with empiricism in logic—shows itself in his attitude toward experimentation and toward observation. Bacon's neglect of experimentation is not an accidental oversight, but is bound up with his view regarding the worthlessness of conception or anticipation. To experiment means to set out from an idea as well as from facts, and to try to construe, or even to discover, facts in accordance with the idea. Experimentation not only anticipates, but strives to make good an anticipation. Of course, this struggle is checked at every point by success or failure, and thus the hypothesis is continuously undergoing in varying ratios both confirmation and transformation. But this is not to make the hypothesis secondary to the fact. It is simply to remain true to the proposition that the distinction anti the relationship of the two is n thoroughly contemporaneous one. But it is impossible to draw any fixed line between experimentation and scientific observa-
It was not long until the development of natural science compelled a better understanding of its actual procedure than Bacon possessed. Empiricism changed to experimentalism. With experimentalism inevitably came the recognition of hypotheses in observing, collecting, and comparing facts. It is clear, for instance, that Newton's fruitful investigations are not conducted in accordance with the Baconian notion. It is quite clear that his celebrated four rules for pbilosophizing are in truth statements of certain principles which are to be observed in forming hypotheses. They imply that scientific technique had advanced to a point
The subsequent history of logical theory in England is conditioned upon its attempt to combine into one system the theories of empiristic logic with recognition of the procedure of experimental science. This attempt finds its culmination in the logic of John Stuart Mill. Of his interest in and fidelity to the actual procedure of experimental science, as he saw it, there can be no doubt. Of his good faith in concluding his Introduction with the words following there can be no doubt: "I can conscientiously affirm that no one proposition laid down in this work has been adopted for the sake of establishing, or with any reference for its fitness in being employed in establishing, preconceived opinions in any department of knowledge or of inquiry on which the speculative world is still undecided." Yet Mill was equally attached to the belief that ultimate reality, as it is for the human mind, is given in sensations, independent of ideas; and that all valid ideas are combinations and convenient ways of using such given material. Mill's very sincerity made it impossible that this belief should not determine, at every point, his treatment of the thinking process and of its various instrumentalities.
In Book III, chap. 14, Mill discusses the logic of explanation, and in discussing this topic naturally finds it necessary to consider the matter of the proper use of scientific hypotheses. This is conducted from the standpoint of their use as that is reflected in the technique of scientific discovery. In Book IV, chap. 2, ho discusses "Abstraction or the Formation of Conceptions" — a topic which obviously involves the forming of hypotheses. In this chapter, his con-
The contradiction between the statements in the two chapters will serve to bring out the two points already made, viz., the correspondent character of datum and hypothesis, and the origin of the latter in a problematic situation and its consequent use as an instrument of unification and solution. Mill first points out that hypotheses are invented to enable the deductive method to be applied earlier to phenomena; that it does this by suppressing the first of the three steps, induction, ratiocination, and verification. He states that:
If in addition we recognize that, according to Mill, our direct experience of nature always presents us with a complicated and confused set of appearances, we shall be in no doubt as to the importance of ideas as anticipations of a possible experience not yet had. Thus he says:
The order of nature, as perceived at a first glance, presents at every instant a chaos followed by another chaos. We must decompose each chaos into single facts. We must learn to see in the chaotic antecedent a multitude of distinct antecedents, in the chaotic consequent a multitude of distinct consequents.
We have only to take these statements in their logical connection with each other (and this connection runs through the entire treatment by Mill of scientific inquiry), to recognize the absolute necessity of hypothesis to undertaking any directed inquiry or scientific operation. Consequently we are not surprised at finding him saying that " the function of hypotheses is one which must be reckoned absolutely indispensable in science;" and again that " the hypothesis by suggesting observations and experiments puts us on the road to independent evidence."
Since Mill's virtual retraction, from the theoretical point of view, of what is here said from the standpoint of scientific procedure, regarding the necessity of ideas is an accompaniment of his criticism of Whewll, it will put the discussion in better perspective if we turn first to Whewell's views.
The conclusion is that the distinction is a historic one, depending upon the state of knowledge at the time, and upon the attitude of the individual. What is theory for one epoch, or for one inquirer in a given epoch, is fact for some other epoch, or even for some other more advanced inquirer in the same epoch. It is theory when the element of inference involved in judging any fact is consciously brought out; it is fact when the conditions are such that we have never been led to question the inference involved, or else, having questioned it, have so thoroughly examined into the inferential process that there is no need of holding it further before the mind, and it relapses into unconsciousness again. " If this greater or less consciousness of our own internal act be all that distinguishes fact from theory, we must allow that the distinction is still untenable " (untenable, that is to say, as a fixed separation). Again, " fact and theory have no essential difference except in the degree of their certainty and familiarity. Theory, when it becomes firmly established and steadily lodged in the mind becomes fact." (P. 45; italics mine.) And, of course, it is equally true that as fast as facts are suspected or doubted, certain aspects of them
I say this conception might have been developed in a way entirely congruous with the position of this chapter. This would have happened if the final distinction between fact and idea had been formulated upon the basis simply of the points, 1° relative certainty and familiarity." From this point of view the distinction between fact and idea is one purely relative to the doubt-inquiry function. It has to do with the evolution of an experience as regards its conscious surety. It has its origin in problematic situations. Whatever appears to us as a problem appears as contrasted with a possible solution. Whatever objects of thought refer particularly to the problematic side are theories, ideas, hypotheses; whatever relates to the solution side is surety, unquestioned familiarity, fact. This point of view makes the distinctions entirely relative to the exigencies of the process of reflective transformation of experience.
Whewell, however, had no sooner started in this train of thought than he turns his back upon it. In chap. 3 he transforms what he had proclaimed to be a relative, historic, and working distinction into a fixed and absolute one. He distinguishes between sensations and ideas, not upon a genetic basis with reference to establishing the conditions of further operation; but with reference to a fundamentally fixed line of demarkation between what is passively given to the mind and the activity put forth by the mind. Thus he reinstates in its most generalized and fixed, and therefore most vicious, form the separation which he has just rejected. Sensations are a brute unchangeable element of fact which exists and persists independent of ideas; an idea is a mode of mental operation which occurs and recurs in an independent individuality of its own. If he had carried out the line of thought with which he began, sensation as fact
But since Whewell did not follow out his own line of thought, choosing rather to fall back on the Kantian antithesis of sense and thought, he had no sooner separated his fact and idea, his given datum and his mental relation, than he is compelled to get them together again. The idea becomes "a general relation which is imposed upon perception by an act of the mind, and which is different from anything which our senses directly offer to us" (p. 26). Such conceptions are necessary to connect the facts which we learn from our senses into truths. " The ideal conception which the mind itself supplies is superinduced upon the facts as they are originally presented to observation. Before the inductive truth is detected, the facts are there, but they are many and unconnected. The conception which the discoverer applies to them gives them connection and unity." (P. 42.) All induction, according to Whewell, thus depends upon superinduction -imposition upon sensory data of certain ideas or general relations existing independently in the mind.
We do not need to present again the objections already offered to this view: the impossibility of any orderly stimulation of ideas by facts, and the impossibility of any check in the imposition of idea upon fact. "Facts" and conception are so thoroughly separate and independent that any sensory datum is indifferently and equally related to any conceivable idea. There is no basis for " superinducing"
In the chapter already referred to upon abstraction, or the formation of conceptions, Mill seizes upon this difficulty. Yet he and Whewell have one point in common: they both agree in the existence of a certain subject-matter which is given for logical purposes quite outside of the logical process itself. Mill agrees with Whewell in postulating a raw material of pure sensational data. In criticising Whewell's theory of superinduction of idea upon fact, he is therefore led to the opposite assertion of the complete dependence of ideas as such upon the given facts as such—in other words, he is led to a reiteration of the fundamental Baconian empiricism; and thus to a virtual retraction of what he had asserted regarding the necessity of ideas to fruitful scientific inquiry, whether in the way of observation or experimentation. The following quotation gives a fair notion of the extent of Mill's retraction:
The conceptions then which we employ for the colligation and methodization of facts, do not develop themselves from within, but are impressed upon the mind from without; they are never obtained otherwise than by way of comparison and abstraction, and, in the most important and most numerous cases, are evolved by abstraction from the very phenomena which it is their office to colligate.
Of course, there is a sense in which Mill's view is very much nearer the truth than is Whewell's. Mill at least sees that "idea " must be relevant to the facts or data which it is to arrange, which are to have "light and order" introduced into them by means of the idea. He sees clearly enough that this is impossible save as the idea develops within the same experience in which the "dark and confused" facts are presented. He goes on to show correctly enough how conflicting data lead the mind to a "confused feeling of an analogy " between the data of the confused experience and of some other experience which is orderly (or already colligated and methodized) ; and how this vague feeling, through processes of further exploration and comparison of experiences, gets a clearer and more adequate form until we finally accept it. He shows how in this process we continually judge of the worth of the idea which is in process of formation, by reference to its appropriateness to our purpose. He goes so far as to say: "The question of appropriateness is relative to the particular object we haze in view." He sums up his discussion by stating: "We cannot frame good general conceptions beforehand. That the conception we have obtained is the one we want can only be known when we have done the work for the sake of which we wanted it." 
This all describes the actual state of the case, but it is consistent only with a logical theory which makes the distinction between fact and hypothesis instrumental in the transformation of experience from a confused into an organized form; not with Mill's notion that sensations are somehow finally and completely given as ultimate facts, and
It would be interesting to follow the history of discussion of the hypothesis since the time of Whewell and of Mill, particularly in the writings of Jevons, Venn, and Bosanquet. This history would refine the terms of our discussion by introducing more complex distinctions and relations. But it would be found, I think, only to refine, not to introduce any fundamentally new principles. In each case, we find the writer struggling with the necessity of distinguishing between fact and idea; of giving the fact a certain primacy with respect to testing of idea and of giving the idea a primacy with respect to the significance and orderliness of the fact; and of holding throughout to a relationship of idea with
But we can only note one or two points. Jevons's "infinite ballot-box" of nature which is absolutely neutral as to any particular conception or idea, and which accordingly requires as its correlate the formation of every possible hypothesis (all standing in themselves upon the same level of probability) is an interesting example of the logical consequences of feeling the need of both fact and hypothesis for scientific procedure and yet .regarding them as somehow arising independently of each other. It is an attempt to combine extreme empiricism and extreme rationalism. The process of forming hypotheses and of deducing their rational consequences goes on at random, because the disconnectedness of facts as given is so ultimate that the facts suggest one hypothesis no more readily than another. Mathematics, in its two forms of measurements as applied to the facts, and of calculation as applied in deduction, furnishes Jevons the bridge by which he finally covers the gulf which he has first himself created. Venn's theory requires little or no restatement to bring it into line with the position taken in the text. He holds to the origin of hypothesis in the original practical needs of mankind, and to its gradual development into present scientific form. He states expressly:
The distinction between what is known and what is not known is essemtial to Logic, and peculiarly characteristic of it in a degree not to be found in any other science. Inference is the
Origin of the hypothesis.— In our analysis of the process of judgment, we attempted to show that the predicate arises in case of failure of some line of activity going on in terms of an established habit. When the old habit is checked through failure to deal with new conditions (i. e., when the situation is such as to stimulate two habits with distinct aims the problem is to find a new method of response—that is, to co-ordinate the conflicting tendencies by building up a single aim—which will function the existing situation. As we saw that, in case of judgment, habit when checked became ideal, an idea, so the new habit is first formalized as an ideal type of reaction and is the hypothesis by which we attempt to construe new data. In our inquiry as to how this formulation is effected, i. e., how the hypothesis is developed, it will be convenient to take some of the currently accepted statements as to their origin, and show how these statements stand in reference to the analysis proposed.
Enumerative induction and allied processes.—It is pointed out by Welton that the various ways in which hypotheses are suggested may be reduced to three classes, viz., enumerative induction, conversion of propositions, and analogy. Under the head of "enumeration" he reminds us that "every observed regularity of connection between phenomena suggests a question as to whether it is universal." There are numerous instances of this in mathematics. For example, it is noticed that 1+3 = 22, 1+3+5 = 32, 1+3+5+7=42, etc.; and one is led to ask whether there is any general principle involved, so that the sum of the first n odd numbers will be n2, where n is any number, however great. In this early form of inductive inference there are two divergent tendencies. One is the tendency to complete enumeration. This tendency is clearly ideal—it transcends the facts as given. To look for all the eases is thus itself an experimental inquiry, based upon a hypothesis which it endeavors to test. But in most cases enumeration can be only incomplete, and we are able to reach nothing better than probability. Hence the other tendency in the direction of an analysis of content in search for a principle of connection in the elements in any one case. For if a characteristic belonging to a number of individuals suggests a class where it belongs to all individuals, it must be that it is found in every individual as such. The hypothesis of complete class involves a hypothesis as to the character of each individual in the class. Thus a hypothesis as to extension transforms itself into one as to intension.
But it is analogy which Welton considers "the chief source from which new hypotheses are drawn." In the second tendency mentioned under enumerative induction, that is, the tendency to analysis of content or intension, we are naturally led to analogy, for in our search for the char-
In addition to enumerative induction, which Welton has mentioned, it is to be noted that there are a number of other processes which are very similar to it in that a number of particulars appear to furnish a basis for a general principle or method. Such instances are common in induction, in instruction, and in methods of proof.
If one is to be instructed in some new kind of labor, he is supposed to acquire a grasp of the method after having been shown in a few instances how this particular work is to be done; and, if he performs the manipulations himself, so much the better. It is not asked why the experience of a few cases should be of any assistance, for it seems self-evident that an experienced man, a man who has acquired the skill, or knack, of doing things, should deal better with all other cases of similar nature.
There is something very similar in inductive proofs, as they are called. The inductive proof is common in algebra. Suppose we are concerned in proving the law of expansion of the binomial theorem. We show by actual calculation that, if the law holds good for the nth power. it is true for the n +first power. That is, if it holds for any power, it holds for the next also. But we can easily show that it does
In geometry we find a class of proofs in which the successive steps seem to have great significance. A common proof of the area of the circle will serve as a fair example. A regular polygon is circumscribed about the circle. Then as the number of its sides are increased its area will approach
Similarly, some statements of the infinitesimal calculus rest on the assumption that slight degrees of difference may be neglected. Though the more modern theory of limits has largely displaced this attitude in calculus and has also changed the method of proof in such geometrical problems as the area of the circle, the underlying motive seems to have been to make transitions easy, and thus to make possible a continued application of some particular method or way of dealing with things.
But granted that this is all true, what has it to do with the origin of the hypothesis? It seems likely that the hypothesis may be suggested by a few successive instances; but are these to be classed with the successive steps in proof to which we have referred? In the first place, we attempt to prove our hypothesis because we are not sure it is true; we are not satisfied that there are no other tenable hypotheses. But if we do test it, is not such test enough ? It depends upon how thorough a grasp we have of the situation; but, in general, each test case adds to its probability. The value of tests lies in the fact that they strengthen and
The question might arise why the mere repetition of conflicting tendencies would lead to a predominance of one of them. Why would they not all remain in conflict and continue to check any positive result? It is probably because there never is any absolute equilibrium. The successive instances tend to intensify and bring into prominence some tendency which is already taking a lead, so to speak. And it may be said further in this connection that only as seen from the outside, only as a mechanical view is taken, does there appear to be an excluding of definitely made out alternatives.
Welton, and logicians generally, regard analogy as an inference on the basis of partial identity. Because of certain common features we are led to infer a still greater likeness.
Both enumerative induction and analogy are explicable in terms of habit. We saw in our examination of enumerative induction that a form of reaction gains strength through a series of successful applications. Analogy marks the presence of an identical element together with the tendency to extend this "partial identity" (as it is commonly called) still farther. In other words, in analogy it is suggested that a type of reaction which is the same in certain respects may be made similar in a greater degree. In enumerative induction we lay stress on the number of instances in which the habit is applied. In analogy we emphasize the content side and take note of the partial identity. In fact, the relation between enumerative induction and analogy is of the same sort as that existing between association by contiguity and association by similarity. In association by contiguity we think of the things associated as merely standing in certain temporal or spatial relations, and disregard the fact that they were elements in a larger experience. In case of association by similarity we regard the like feature in the things associated as a basis for further correction.
In conversion of propositions we try to reverse the direction of the reaction, so to speak, and thereby to free the habit, to get a mode of response so generalized as to act with a minimum cue. For instance, we can deal with A in a way called B, or, in other words, in the same way that we did with other things called B. If we say, "Man is an animal," then to a certain extent the term " animal" signifies the way in which we regard man." Rut the question arises whether we can regard all animals as we do man. Evidently not, for the reaction which is fitting in
The subject-matter of science, says a Wundt, is constituted by that which is actually given and that which is actually to
Wundt defines a theory as a hypothesis taken together with the facts for whose elucidation it was invented. In thus establishing a connection between the facts which the hypothesis merely suggested, the theory furnishes at the
Let us look more closely at Wundt's position. We will ask, first, whether the distinction between hypotheses and expectations is as pronounced as he maintains; and, second, whether the relation between Begriindung and Bestatigung may not be closer than Wundt would have us believe.
As examples of the hypothesis Wundt mentions the Copernican hypothesis, Newton's hypothesis of gravitation, and the predictions of the astronomers which led to the discovery of Neptune. As examples of mere expectations we
If we turn to Galileo's pendulum and falling bodies, it is clear first of all that he did not have in mind the discovery of some object, as was the case in the discovery of Neptune. Did he, then, either contribute to the proof of a general law or discover further characteristics of things already known in a more general way? Wundt tells us that Galileo only determined a little more exactly what he already knew, and that he did this with but little labor or delay.
What, then, is the real difference between hypothesis and expectation? If we compare Galileo's determination of the law of falling bodies with Newton's test of his hypothesis of gravitation, we see that both expectation and hypothesis were founded on observation and took the form of mathematical formulae. Each tended to confirm the general law expressed in its formula, though there was, of course, much difference in the time and labor required. If we compare the Copernican hypothesis with Galileo's supposition concerning the pendulum, we find again that they agree in regard to general purpose and method, and differ in the difficulty of verification. If the experiment with the pendulum only substituted exactness for inexactness, did the
In the second place, we have seen that Wundt draws a sharp line between Begrundung and Bestdtigung. It is doubtless true that every hypothesis requires a certain justification, for unless other facts can be found which agree with deductions made in accordance with it, its only support would be the data from which it is drawn. Such support as this would be obtained through a process too clearly circular to be seriously entertained. The distinction which Wundt draws between Begrundung and Bestatigung is evidently due to the presence of the experimental element in the latter. For descriptive purposes this distinction is useful, but is misleading if it is understood to mean that there is mere experience in one case and mere inference in the other. The difference is rather due to the relative parts played by inference and by accepted experience in each. In Begrundung the inferential feature is the more prominent, while in Bestatigung the main emphasis is on the experiential aspect.
If the view which we have maintained is correct, the hypothesis is not to be limited to those elaborate formulations of the scientist which he seeks to confirm by crucial tests. The