Studies in Logical Theory

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:

In the next section of the same chapter he goes on to state that, having discriminated the various antecedents and consequents, we then "are to inquire which is connected with which." This requires a still further resolution of the complex and of the confused. To effect this we must vary the circumstances; we must modify the experience as given with reference to accomplishing our purpose. To accomplish this purpose we have recourse either to observation or to experiment: "We may either find an instance in nature suited to our purposes, or, by an artificial arrangement of circumstances, make one" (the italics in "suited to our purpose" are mine; the others are Mill's). He then goes on to say that there is no real logical distinction between observation and experimentation. The four methods of experimental inquiry are expressly discussed by Mill in terms of their worth in singling out and connecting the antecedents and consequents which actually belong together, from the chaos and confusion of direct experience.

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."[64]

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 Whewell, it will put the discussion in better perspective if we turn first to Whewell's views.[65] The latter began by stating a distinction which easily might have been developed into a theory of the relation of fact and idea which is in line with that advanced in this chapter, and indeed in this volume as a whole. He questions (chap. 2) the fixity of the distinction between theory and practice. He points out that what we term facts are in effect simply accepted inferences; and that what we call theories are describable as facts, in proportion as they become thoroughly established. A true theory is a fact. "All the great theories which have successively been established in the world are now thought of as facts." "The most recondite theories when firmly established are accepted as facts; the simplest facts seem to involve something of the nature of theory."

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 are transferred into the class of theories and even of mere opinions.

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, "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 would have been that residuum of familiarity and certainty which cannot be eliminated, however much else of an experience is dissolved in the inner conflict. Idea as hypothesis or theory would have been the corresponding element in experience which is necessary to redintegrate this residuum into a coherent and significant experience.

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.[66]

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" one idea or hypothesis, rather than any other, upon any particular set of data.

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:

Even here Mill's sense for the positive side of scientific inquiry suffices to reveal to him that the "facts" are somehow inadequate and defective, and are in need of assistance from ideas—and yet the ideas which are to help out the facts are to be the impress of the unsure facts! The contradiction comes out very clearly when Mill says: "The really difficult cases are those in which the conception destined to create light and order out of darkness and confusion has to be sought for among the very phenomena which it afterward serves to arrange."[68]

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 have in view."[69] 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."[70]

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 that ideas are mere re-registrations of such facts. It is perfectly just to say that the hypothesis is impressed upon the mind (in the sense that any notion which occurs to the mind is impressed) in the course of an experience. It is well enough, if one define what he means, to say that the hypothesis is impressed (that is to say, occurs or is suggested) through the medium of given facts, or even of sensations. But it is equally true that the facts are presented and that sensations occur within the course of an experience which is larger than the bare facts, because involving the conflicts among them and the corresponding intention to treat them in some fashion which will secure a unified experience. Facts get power to suggest ideas to the mind—to "impress"—only through their position in an entire experience which is in process of disintegration and of reconstruction—their "fringe" or feeling of tendency is quite as factual as they are. The fact that "the conception we have obtained is the one we want can be known only when we have done the work for the sake of which we wanted it," is enough to show that it is not bare facts, but facts in relation to want and purpose and purpose in relation to facts, which originate the hypothesis.

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 fact so intimate that the idea develops only by being "compared" with facts (that is, used in construing them), and facts get to be known only as they are "connected" through the idea—and we find that what is a maze of paradoxes and inconsistencies from an absolute, from a non-historic standpoint, is a matter of course the moment it is looked at from the standpoint of experience engaged in self-transformation of meaning through conflict and reconstitution.

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.[71] He states expressly:

Venn, however, does not attempt a thoroughgoing statement of logical distinctions, relations, and operations, as parts "of the act of passing from the unknown to the known." He recognizes the relation of reflection to a historic process, which we have here termed "reconstruction," and the origin and worth of hypothesis as a tool in the movement, but does not carry his analysis to a systematic form.

III

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[73] 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 cases 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 characteristic feature which determines classification among the concrete particulars our first step will be an inference by analogy. In analogy attention is turned from the number of observed instances to their character, and, because particulars have some feature in common, they are supposed to be the same in still other respects. While the best we can reach in analogy is probability, the arguments may be such as to result in a high degree of certainty. The form of the argument is valuable in so far as we are able to distinguish between essential and nonessential characteristics on which to base our analogy. What is essential and what nonessential depends upon the particular end we have in view.

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 hold for, say, the second power. Then it must be true for the third, and hence for the fourth, and so on. Whether this law, though discovered by inductive processes, depends on deduction for the conclusiveness of its proof, as Jevons holds;[74] whether, as Erdmann[75] contends, the proof is thoroughly deductive; or whether Wundt[76] is right in maintaining that it is based on an exact analogy, while the fundamental axioms of mathematics are inductive, it is clear that in such proofs a few instances are employed to give the learner a start in the right direction. Something suggests itself, and is found true in this case, in the next, and again in the next, and so on. It may be questioned whether there is usually a very clear notion of what is involved in the "so on." To many it appears to mark the point where, after having been taken a few steps, the learner is carried on by the acquired momentum somewhat after the fashion of one of Newton's laws of motion. Whether the few successive steps are an integral part of the proof or merely serve as illustration, they are very generally resorted to. In fact, they are often employed where there is no attempt to introduce a general term such as n, or k, or l, but the few individual instances are deemed quite sufficient. Such, for instance, is the custom in arithmetical processes. We call attention to these facts in order to show that successive cases are utilized in the course of explanation as an aid in establishing the generality of a law.

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 that of the circle, as its perimeter approaches the circumference of the circle. The area of the circle is thus inferred to be πR², since the area of the polygon is always ½R× perimeter, and in case of the circle the circumference =2πR. Here again we get under such headway by means of the polygon that we arrive at the circle with but little difficulty. Had we attempted the transition at once, say, from a circumscribed square, we should doubtless have experienced some uncertainty and might have recoiled from what would seem a rash attempt; but as the number of the sides of our polygon approach infinity—that mysterious realm where many paradoxical things become possible—the transition becomes so easy that our polygon is often said to have truly become a circle.

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 tend to confirm our hypothesis by checking the force of alternatives. One instance is not sufficient because there are other possible incipient hypotheses, or more properly tendencies, and the enumeration serves to bring one of these tendencies into prominence in that it diminishes other vague and perhaps subconscious tendencies and strengthens the one which suddenly appears as the mysterious product of genius.

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.

In explanation of the part played by analogy in the origin of hypotheses, Welton points out that a mere number of instances do not take us very far, and that there must be some "specification of the instances as well as numbering of them," and goes on to show that the argument by enumerative induction passes readily into one from analogy, as soon as attention is turned from the number of the observed instances to their character. It is not necessary, however, to pass to analogy through enumerative induction. "When the instances presented to observation offer immediately the characteristic marks on which we base the inference to the connection of S and P, we can proceed at once to an inference from analogy, without any preliminary enumeration of the instances."[77]

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." But the question arises whether we can regard all animals as we do man. Evidently not, for the reaction which is fitting in case of animals would be only partially applicable to man. With the animals that are also men we have the beginning of a habit which, if unchecked, would lead to a similar reaction toward all animals, i. e., we would say: "All animals are men." Man may be said to be the richer concept, in that only a part of the reaction which determines an object to be a man is required to designate it as an animal. On the other hand, if we start with animal, then (except in case of the animals which are men) there is lacking the subject-matter which would permit the fuller concept to be applied. By supplying the conditions under which animal=man we get a reversible habit. The equation of technical science has just this character. It represents the maximum freeing or abstraction of a predicate qua predicate, and thereby multiplies the possible applications of it to subjects of future judgments, and lessens the amount of shearing away of irrelevancies and of re-adaptation necessary when so used in any particular case.

Formation and test of the hypothesis.—The formation of the hypothesis is commonly regarded as essentially different from the process of testing, which it subsequently undergoes. We are said to observe facts, invent hypotheses, and then test them. The hypothesis is not required for our preliminary observations; and some writers, regarding the hypothesis as a formulation which requires a difficult and elaborate test, decline to admit as hypotheses those more simple suppositions, which are readily confirmed or rejected. A very good illustration of this point of view is met with in Wundt's discussion of the hypothesis, by an examination of which we hope to show that such distinctions are rather artificial than real.

The subject-matter of science, says Wundt,[78] is constituted by that which is actually given and that which is actually to be expected. The whole content is not limited to this, however, for these facts must be supplemented by certain presuppositions, which are not given in a factual sense. Such presuppositions are called hypotheses and are justified by our fundamental demand for unity. However valuable the hypothesis may be when rightly used, there is constant danger of illegitimately extending it by additions that spring from mere inclinations of fancy. Furthermore, the hypothesis in this proper scientific sense must be carefully distinguished from the various inaccurate uses, which are prevalent. For instance, hypotheses must not be confused with expectations of fact. As cases in point Wundt mentions Galileo's suppositions that small vibrations of the pendulum are isochronous, and that the space traversed by a falling body is proportional to the square of the time it has been falling. It is true that such anticipations play an important part in science, but so long as they relate to the facts themselves or to their connections, and can be confirmed or rejected any moment through observation, they should not be classed with those added presuppositions which are used to co-ordinate facts. Hence not all suppositions are hypotheses. On the other hand, not every hypothesis can be actually experienced. For example, one employs in physics the hypothesis of electric fluid, but does not expect actually to meet with it. In many cases, however, the hypothesis becomes proved as an experienced fact. Such was the course of the Copernican theory, which was at first only a hypothesis, but was transformed into fact through the evidence afforded by subsequent astronomical observation.

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 same time partly the foundation (Begründung) and partly the confirmation (Bestätigung) of the hypothesis.[79] These aspects, Wundt insists, must be sharply distinguished. Every hypothesis must have its Begründung, but there can be Bestätigung only in so far as the hypothesis contains elements which are accessible to actual processes of verification. In most cases verification is attainable in only certain elements of the hypothesis. For example, Newton was obliged to limit himself to one instance in the verification of his theory of gravitation, viz., the movements of the moon. The other heavenly bodies afforded nothing better than a foundation in that the supposition that gravity decreases as the square of the distance increases enabled him to deduce the movements of the planets. The main object of his theory, however, lay in the deduction of these movements and not in the proof of universal gravity. With the Darwinian theory, on the contrary, the main interest is in seeking its verification through examination of actual cases of development. Thus, while the Newtonian and the greater part of the other physical theories lead to a deduction of the facts from the hypotheses, which can be verified only in individual instances, the Darwinian theory is concerned in evolving as far as possible the hypothesis out of the facts.

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 Begründung and Bestätigung 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 are referred to Galileo's experiments with falling bodies and pendulums. In case of Newton's hypothesis there was the assumption of a general law, which was verified after much labor and delay. The heliocentric hypothesis of Copernicus, which was invented for the purpose of bringing system and unity into the movements of the planets, has also been fairly well substantiated. In the discovery of Neptune we have, apparently, not the proof of a general law or the discovery of further peculiarities of previously known data, but rather the discovery of a new object or agent by means of its observed effects. In each of these instances we admit that the hypothesis was not readily suggested or easily and directly tested.

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 formulæ. 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 Copernican theory do anything different in kind? It is true that the more exact statement of the swing of the pendulum was expressed in quantitative form, but quantitative statement is no criterion of either the presence or the absence of the hypothesis.

Again, we may compare the pendulum with Kepler's laws. What was Kepler's hypothesis, that the square of the periodic times of the several planets are proportional to the cubes of their mean distances from the sun, except a more exact formulation of facts which were already known in a more general way? Wundt's position seems to be this: whenever a supposition or suggestion can be tested readily, it should not be classed as a hypothesis. This would make the distinction one of degree rather than kind, and it does not appear how much labor we must expend, or how long our supposition must evade our efforts to test it, before it can win the title of hypothesis.

In the second place, we have seen that Wundt draws a sharp line between Begründung and Bestätigung. 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 Begründung and Bestätigung 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 Begründung the inferential feature is the more prominent, while in Bestätigung the main emphasis is on the experiential aspect. It must not be supposed, however, that either of these aspects can be wholly absent. It is difficult to understand how any hypothesis can be entertained at all unless it meets in some measure the demand with reference to which it was invented, viz., a unification of conflicts in experience. And, in so far, it is confirmed. The motive which casts doubt upon its adequacy is the same that leads to its re-forming as a hypothesis, as a mental concept.

The difficulties in Wundt's position are thus due to a failure to take account of the reconstructive nature of the judgment. The predicate, supposition, or hypothesis, whatever we may choose to call it, is formed because of the check of a former habit. The judgment is an ideal application of a new habit, and its test is the attempt to act in accordance with this ideal reconstruction. It must not be thought, however, that our supposition is first fully developed and then tried and accepted or rejected without modification. On the contrary, its growth is the result of successive minor tests and corresponding minor modifications in its form. Formation and test are merely convenient distinctions in a larger process in which forming, testing, and re-forming go on together. The activity of experimental verification is not only a testing, a confirming or weakening of the validity of a hypothesis, but it is equally well an evolution of the meaning of the hypothesis through bringing it into closer relations with specific data not previously included in defining its import. Per contra, a purely reflective and deductive consideration which develops the idea as hypothesis, in so far as it introduces the determinateness of previously accepted facts within the scope, comprehension, or intension of the idea, is in so far forth, a verification.

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 hypothesis of the investigator differs from the comparatively rough conjecture of the plain man only in its greater precision. Indeed, as we have attempted to show, the hypothesis is not a method which we may employ or not as we choose; on the contrary, as predicate of the judgment it is present in a more or less explicit form if we judge at all. Whether the time and labor required for its confirmation or rejection is a matter of a lifetime or a moment, its nature remains the same. Its function is identical with that of the predicate. In short, the hypothesis is the predicate so brought to consciousness and defined that those features which are not noticed in the ordinary judgment are brought into prominence. We then recognize the hypothesis to be what in fact the predicate always is, viz., a method of organization and control.

VIII

The logic of sense-impressions and of ideas as copies of sense-impressions has had its day. It engaged in a conflict with dogmatism, and scored a decisive victory. It overthrew the dynasty of prescribed formulæ and innate ideas, of ideas derived ready-made from custom and social usage, ancient enough to be lost in the remote obscurity of divine sources; and enthroned in their place ideas derived from, and representative of, the sense-experiences of a very real and present world. It marked a reaction from dogma back to the original meaning of dogma, back to the seeming, the appearance, of things. So thoroughly did Bacon and Hobbes, Locke and Hume, to mention only these four, do their work, that many of the problems growing out of the conflict itself, to say nothing of the scholastic traditions that were combated, have come to have merely a historical rather than a logical interest. Logic no longer concerns itself very eagerly with the content or sensuous qualities of ideas, with their derivation from sense-impressions, or with questions as to the relation of copy to original, of representative to that which is presented. It is concerned rather with the constructive operations of thought, with meaning, reference to reality, inference—with intellectual processes. Perhaps in no respect is this shifting of logical standpoint indicated more clearly than in the unregretful way with which the old logical interest in the sense-qualities of ideas is now made over to psychology. States of consciousness as such, we are told, are the proper study of psychology; whereas logic concerns itself with the relation of thought to its object. True, these states of consciousness include thought-states, as well as sense-impressions; ideas and concepts, as well as feelings and fancies; and the business of psychology is to observe, compare and classify, describe and chronicle, these states and whatever else is carried along in the stream of consciousness. But logic is concerned, not with these states of consciousness per se, least of all with the flotsam and jetsam of the stream, but with its reference to reality; not with the true, but with truth; not even with what consciousness does, but with how consciousness is to outdo itself, transcend itself, in a rational and universal whole. Even an empirical logic has to arrange somehow the way to get from one sense-impression to another.

In drawing this distinction between logic and psychology—a distinction which virtually amounts to a separation—two things are overlooked: first, that the distinction itself is a logical distinction, and may properly constitute a problem falling under the province of logical inquiry and theory; and, second, that the rather arbitrary and official setting apart of psychology to look after the task of studying states of consciousness does not carry with it the guarantee that psychology will confine itself exclusively to that task. This last point in particular must be my excuse for discussing the question of image and idea from the psychological rather than from the logical standpoint. The logic of ideas derived from sense-impressions has had its day. But even the very leavings of the past may have been gathered up and reconstructed by psychology in such a way as to anticipate some of the newer developments of logical theory and meet some of its difficulties. One can hardly hope to justify in advance a discussion based on such a sheer possibility. Let us begin, rather, by noting down from the standpoint of logic some of the distinctions between image and idea, and the estimate of the logical function and value of mental imagery, and see in what direction they take us and whether they suggest a resort to an analysis from the standpoint of psychology.

Proceeding from the standpoint of logic to inquire into the logical function of mental imagery and into the distinction between image and idea, we shall come upon two opposed but characteristic answers. If the inquiry be directed to a member of the empirical school of logic, he would be bound to answer in the affirmative, so far as the question regarding the function of mental imagery is concerned. He would be likely to say, if he were loyal to the traditions of his school, that mental imagery is the counterpart of sense-perception, and is thus the representative of the data with which empirical logic is concerned. Mental imagery, he would continue, is a representative in a literal sense, a copy, a reflection, of what comes to us through the avenues of sensation. True, it is not the perfect twin of sense-experience; else we could not tell them apart; indeed, there are times when the copy becomes so much like the original that we are deceived by it, as in dreams or in hallucinations. Ordinarily, however, we are able to distinguish one from the other. Two criteria are usually present; (1) imagery is fainter, more fleeting, than the corresponding sense-experience; and (2), save in the case of accurate memory-images, it is subject to a more or less arbitrary rearrangement of its parts, as when, for example, we make over the images of scenes we have actually experienced, to furnish forth the setting of some remote historical event.

Barring, or controlling and rectifying, its tendencies toward both arbitrary and constructive variations from the original, mental imagery is on the same level as sense-experience, and serves the same logical purpose. That is to say, it contributes to the data which constitute the foundations of empirical logic. It furnishes materials for the operations of observing, comparing, abstracting and generalizing. Mental imagery helps to piece out the fragments that may be presented to sense-experience. It supplies the entire anatomy when only a single bone, say, is actually given. Yet, however useful as a servant of truth, it has to be carefully watched, lest its spontaneous tendency to vary the actual order and coexistence of data lead the investigator astray. The copy it presents is, after all, a temporary makeshift, until it can be shown to correspond point for point to the now absent reality. Mental imagery furnishes one with an illustrated edition of the book of nature, but the illustrations await the confirmation of comparison with the originals.

Mental imagery functions logically when it extends the area of data beyond the range of the immediate sense-perceptions of any given time, and thus makes possible a more comprehensive application of the empirical methods of observation, comparison, abstraction, and generalization. It functions logically when it acts as a feeder of logical machinery, though it is not indispensable to this machinery and does not modify its principles. The logical mill could grind up in the same way the pure grain of sense-perceptions, unmixed with mental images, but it would have to grind more slowly for lack of material. In other words, empirical logic could carry on its operations of observing, comparing, abstracting, and generalizing, solely on the basis of objects or data present to the senses, and with no extension of this basis in terms of imagery, or copies of objects not immediately present; but it would take more time for it to apply and carry through its operations. The logical machinery is the same in each case. The materials fed and the product issuing are the same in each case. Imagery simply fulfils the function of providing a more copious grist.

The empiricist's answer to our question regarding the logical function of mental imagery leaves that function in an uncertain and parlous state. Imagery lacks the security of sense-perception on the one hand, and it has no part in the operation of thought on the other. It is a sort of hod-carrier, whose function it is to convey the raw materials of sense-perception to a more exalted position where someone else does all the work. I suppose this could be called a functional interpretation of a logical element. The question, then, would be whether an element so functioning is in any sense logical. As an element lying outside of the thought-process it owes no responsibility to logic; it is not amenable to its regulations. Thought simply finds it expedient to operate with an agent over which it has no intrinsic control. The case might be allowed to rest here. Yet were this extra-logical element of imagery to abandon thought, all conscious thinking as opposed to sense-perception would cease. A false alarm, perhaps. Imagery may be so constituted that it is inseparably subordinated to thought and can never abandon it. Thought may simply exude imagery. But imagery somehow has to represent sense-perception, also. It can hardly be a secretion of thought and a copy of sense-perceptions at one and the same time, unless the empiricist is willing to turn absolute idealist! Before taking such a desperate plunge as this, it might be desirable to see whether there is any other recourse.

There is another and a very different answer to the question regarding the logical function of mental imagery. To distinguish this answer from that of the associationist or empiricist, I will call it the answer of the conceptualist. I am not at all positive that this label would stick even to those to whom it might be applied with considerable justification. The terms "rationalistic" and "transcendental" might be preferred in opposition to the term "empirical." And we have the term "apperceptionist" in opposition to the term "associationist." If the term "conceptualist" is admissible, it should be brought down to date, perhaps, by making it "neo-conceptualist." The present difficulties regarding terminology would be eased considerably if we only had a convenient set of derivatives made from the word "meaning." Since we have not, I will use derivatives made from the word "concept" to denote views opposite to those held by the empirical school.

The conceptualist could be depended upon to answer our question in the negative. Logical functions begin where the image leaves off. They begin with the idea, with meaning. The conceptualist distinguishes sharply between the image as a psychical existence and the idea, or concept, as logical meaning. On the one hand, you have the "image," not only as a mere psychical existence, but a mocking existence at that, fleeting, inconstant, shifting, never perhaps twice alike; yet, mind you, an existence, a fact—that must be admitted. On the other hand, you have the "idea," with "a fixed content or logical meaning,"[80] which is referred by an act of judgment to a reality beyond the act.[81]

The "idea," the logical meaning, begins where the "image" leaves off. Does this mean that the "idea" is wholly independent of the "image"? Yes and no. The "idea" is independent of that which is ordinarily regarded as the special characteristic of an "image," namely, its quality, its sense-content. That is to say, the "idea" is independent of any particular "image," any special embodiment of sense-content. Any image will do. As Mr. Bosanquet remarks in comparing the psychical images that pass through our minds to a store of signal flags: