Chapter VII: Preface (7)

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 _n_th 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 [pi]_R_^2, since the area of the polygon is always (1/2)_R_× perimeter, and in case of the circle the circumference = 2[pi]_R_. 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

IMAGE AND IDEA IN LOGIC

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:

Not only is it indifferent whether your signal flag of today is
the same bit of cloth that you hoisted yesterday, but also, no one
knows or cares whether it is clean or dirty, thick or thin, frayed
or smooth, as long as it is distinctly legible as an element of
the signal code. Part of its content, of its attributes and
relations, is a fixed index which carries a distinct reference;
all the rest is nothing to us, and, except in a moment of idle
curiosity, we are unaware that it exists.[82]

On the other hand, the "idea" could not operate as an idea, could not be in consciousness, save as it involves some imagery, however old, dirty, thin, and frayed. Take the statement, "The angles of a triangle are equal to two right angles." If the statement means anything to a given individual, if it conveys an idea, it must necessarily involve some form of imagery, some qualitative or conscious content. But so far as the _meaning_ is concerned, it is a matter of complete indifference as to _what_ qualities are involved. These qualities may be in terms of visual, auditory, tactual, kinæsthetic, or verbal imagery. The individual may visualize a blackboard drawing of a triangle with its sides produced, or he may imagine himself to be generating a triangle while revolving through an angle of 180°. Any imagery anyone pleases may be employed, so long as there goes with it somehow the _idea_ of the relation of equality between the angles of a triangle and two right angles. But the conceptualist does not stop here. The act of judgment comes in to affirm that the "idea" is no mere idea, but is a quality of the real. "The act [of judgment] attaches the floating adjective [the idea, the logical meaning] to the nature of the world, and, at the same time, tells one it was there already."[83] The "idea," the logical meaning, begins where the "image" leaves off. Yet, somehow, the "idea" could not begin, unless there were an "image" to leave off.

An "image" is not an "idea," says the conceptualist. An "idea" is not an "image." (1) An "image" is not an "idea," because an "image" is a particular, individual fragment of consciousness. It is so bound up with its own existence that it cannot reach out to the existence of an "idea," or to anything beyond itself. Chemically speaking, it is an _avalent_ atom of consciousness, if such a thing is thinkable. Mr. Bosanquet raises the question:

Are there at all ideas which are not symbolic?... The answer is
that _(a)_ in judgment itself the idea can be distinguished _qua_
particular in time or psychical fact, and _so far_ is not
symbolic; and _(b)_ in all those human experiences from which we
draw our conjectures as to the animal intelligence, when in
languor or in ignorance image succeeds image without conscious
judgment, we feel what it is to have ideas as facts and not as
symbols.[84]

(2) An "idea" is not an "image," because an idea _is_ meaning, which consists in a part of the content of the image, cut off, and considered apart from the _existence_ of the content or sign itself.[85] This meaning, this fragment of psychical existence, lays down all claim to existence on its own account, that it may refer through an act of judgment to a reality beyond itself and beyond the act also. An "image" is not an "idea" and an "idea" is not an "image," because an "image" exists only as a quality, a sense-content, whereas an "idea" exists only as a relation, a reference to reality beyond. "On the one hand," to recall Bradley's antinomy, "no possible idea [as a psychical image] can be that which it means.... On the other hand, no idea [as logical signification] is anything but just what it means."

There is a significant point of agreement between the conceptualist and the empiricist. Both regard imagery as on the level with sense-perception. For the empiricist, as we have seen, the fact that imagery may be compelled to serve as a yoke-fellow of sense-experience constitutes its logical value. For the conceptualist, however, the association of imagery with sense-experience is of no logical consequence whatsoever, save as it may help to intensify the distinction between imagery and meaning. To quote again from Bradley:

For logical purposes the psychological distinction of idea and
sensation may be said to be irrelevant, while the distinction of
idea and fact is vital. The image, or psychological idea, is for
logic nothing but a sensible reality. It is on a level with the
mere sensations of the senses. For both are facts and neither are
meanings. Neither are cut from a mutilated presentation and fixed
as a connection. Neither are indifferent to their place in the
stream of psychical events, their time and their relations to the
presented congeries. Neither are adjectives to be referred from
their existence, to live on strange soils, under other skies, and
through changing seasons. The lives of both are so entangled with
their environment, so one with their setting of sensuous
particulars, that their character is destroyed if but one thread
is broken.[86]

This point of agreement between conceptualism and empiricism, this placing of imagery and sense-experience on a common level, serves to bring into relief fundamental differences between the two schools of thought; fundamental, because they have to do with the nature of reality itself. The conceptualist in his zealous endeavor to distinguish between imagery and logical meaning has come perilously near driving imagery into the arms of reality. It is the opportunity of empiricism to make them one. How can conceptualism prevent the union? Has it not disarmed itself? The act of judgment, which includes within itself logical meaning as predicate, refers to a reality beyond the act. Both imagery and reality, then, lie outside of the act of judgment! What alliance, or _mésalliance_, may they not form, one with the other?

The difficulties we have noted thus far in the discussion are due to a large extent, I believe, to incomplete psychological analysis of logical machinery. The empiricist has not carried the psychology of logic as far as the conceptualist, although the latter might be the loudest to disclaim the honor. I will not try to prove this statement, but simply give it as a reason why, in the interest of brevity, I shall pass with little comment over the psychological shortcomings and contributions of empirical logic, and devote what space remains to the psychology implicitly worked out by conceptual logic, and to its possible development, with special reference, of course, to the problem of the logical function of imagery.

The logical distinction, which practically amounts to a separation between imagery and meaning, is the counterpart of the psychological distinction between stimulus and response, between the two poles of sensori-motor activity, where the stimulus is defined in consciousness in the form of imagery, in the form of sense-qualities centrally excited, and where the response is directed and controlled _via_ this imagery, so as to function in bringing some end, project, purpose, or ideal, nearer to realization, some problem nearer to solution.

Psychologically, there is no break between image and response, between thought and action. The stimulus is a condition of action, in both senses of the ambiguity of the word "condition." (1) It _is_ action; it is a state or condition of action. (2) It is also an initiation of action. _If_ the appropriate stimulus, then the desired action. The response to an image is the meaning of the image. Or, the response to any stimulus _via_ an image--mediated, controlled or directed by an image--is the meaning of that image. The less imagery involved in any response, the greater the presumption in favor of the belief that the response is either an instinctive impulse or else has become a habit of mind, an adequate idea. The reduction and loss of sense-content which an image may undergo--the wearing away of an image, it is sometimes called--is not a sign that this sense-content has no logical function; but rather that it has fulfilled a logical function so well that it has made part of itself useless. The husk, to recall one of Mr. Bradley's comparisons, that useless husk, tends to fall away, to lapse from consciousness, after it has served the purpose of helping to bring the kernel of truth to fruition.

This raises again the original question as to whether the sense-content, the quality, the existential quality, of an image has a logical function. I will ask first whether it has a function from the standpoint of psychology. We will agree with the empiricist that the content of an image is representative, that it is a return, a revival, of a sense-content previously experienced through the activity of sense-organs stimulated from the periphery. What is the function, then, of the representative image? Sensation, quality, as we have implied above, is the stimulus come to consciousness. To explain how a stimulus can "come" to consciousness is a problem I will not attempt to go into here. I assume as a fact that there are times when we know what we are about; when we are conscious of the stimuli, or conditions of action, which are tending in this direction or in that, and when through this consciousness we exercise a controlling influence over action by selecting and reinforcing certain stimuli and suppressing or inhibiting others. It is true that we do not always realize to how great an extent our actions are controlled by stimuli which do not come to consciousness, by reflexes, instincts, and habits which do not rise above the threshold of imagery. And when this vast complex of hidden machinery is partly revealed to us, it may either cause the beholder to take a materialistic, mechanical, or fatalistic view of existence, to say that we are the victims of our own machinery, or else it may induce the other extreme of more or less mystic pronouncements regarding the province of the subconscious, of the subliminal self; thus out of partial views, out of half-truths, metaphysical problems arise and arm for mutual conflict. Nevertheless, there is a presumption, amounting in most minds to a conviction, that we do at times consciously control some of our actions. And it is only making this conviction a little more explicit to say that we consciously control our actions through becoming aware of the stimuli, or conditions of action, and through selecting and reinforcing them.

Is it begging the question to speak of consciousness as exercising a selective function with reference to stimuli? From the standpoint of psychology, I cannot see that it is. No characteristic of consciousness has been more clearly made out, both reflectively and experimentally, than its selective function, than its ability to pick out and intensify within certain limits the stimuli or conditions of action.

The representational image is a stimulus come to consciousness in the same way that a sensation is a stimulus come to consciousness. It is both a direct and an indirect stimulus. The terms "direct" and "indirect" are used as relative solely to the demands of the particular situation out of which they arise. By direct stimulus I mean a stimulus which initiates with almost no appreciable delay the response or attitude appropriate to the demands of a given situation, bridging the difficulties, removing the obstacles, or solving the problem with the minimum of conscious reflection. As an image becomes more and more of a working symbol, an idea, it tends to become simply a direct stimulus.

By an "indirect stimulus" is meant a stimulus initiating a response which, if not inhibited, would be irrelevant to the situation, yet which may represent stimuli which are not found in the immediate field of sense-perception, and which are essential to the carrying on of the activity. The situation is a problematic one. Acquired habits or mental adjustments break down at some point or fail to operate smoothly, either owing to the absence of customary stimuli or to the presence of new and untried conditions of action. Part of the stress of meeting such a situation as this falls on the side of discovering appropriate stimuli and part on the side of developing out of habits already acquired new methods of response.

In such a situation as this, imagery may function on the side of _stimulus_ when, taking its cue from the stimuli which are actually present, and which grow out of the strain and friction, it represents the missing conditions of action sufficiently to direct a search for them. It projects a map, so to speak, in which the fragmentary conditions immediately present to sense-perception may find their bearings, or in which in some way the missing members may be discovered. A familiar instance of this would be the experience one sometimes has in trying to recall the forgotten name of an acquaintance. The images of scenes associated with the acquaintance, of various letters and sounds of words associated with his name, which may be called to mind, do not function so much as direct stimuli as they do as intermediate or indirect stimuli. It is a case of casting about for the image that will function as a direct stimulus in bringing an acquired but temporarily lost adjustment into play.

Image functions on the side of _response_, on the side of developing new habits, new forms of adjustment, in so far as the conditions of action which it represents, or projects, are not the actual conditions of action, either because they are so inaccessible as to demand development of new habits for purposes of attaining them, or else because, though actually present, they stimulate relatively uncontrolled æsthetic or emotional responses, whose very expression, however, may be translated into a demand for more adequate, intelligent, controlled habits or adjustments. The conscious projection of the unattained, even of the unattainable, not only marks a certain degree of attainment, but is the initiation of further development. Here we see again that a stimulus is a condition of action in both senses of the ambiguity of the word "condition." It is both a state or condition of activity, and an initiation or condition of further activity.

As an indirect stimulus growing out of a problematic situation imagery necessarily brings in more or less irrelevant material. If I may be permitted the paradox, imagery would not be relevant if it did not bring in the irrelevant. The novelty of the situation makes it impossible to say in advance what will be relevant. Hence the demand for range and play of imagery. It is only the successful adjustment finally hit upon and worked out that is the test of the relevancy of the imagery which anticipated it. Even this test may be unfair, since it is likely to discount the value of imagery which is now ruled out, but which may have been indispensable in turning up the proper cues in the course of the process of reflection and experiment.

To restate the point in regard to the psychological function of imagery. Imagery functions in representing control as ideal, not as fact. It represents a possible process of reconstructing adjustments and habits; it is not an actual and complete readjustment. It arises normally in a stress, in the presence of fresh demands and new problems. It looks forward in every possible direction, because it is important and difficult to foresee consequences. But suppose the new adjustment to be made with reasonable success--reasonable, note. Suppose the ideal to be realized. With practice the adjustment becomes less problematic, more under control--that is, it comes to require less conscious attention to bring it about. The image loses some of its sensuous content. It becomes worn away, more remote, until at last it becomes respectably vague and abstract enough to be classed as a concept. Imagery is the stimulus of the reconstructive process between habit and habit, concept and concept, idea and idea.

We now return to the original question regarding the logical function of imagery. There is only one condition, I believe, on which we can accept the assumption of both empiricist and conceptualist that imagery is on the same level with sense-perception, and that is the assumption that meaning, logical meaning, is on the same level with habit, habit naming the more obvious, overt forms of response to stimuli, logical meaning naming the more internal forms of response or reference. Psychical response and logical reference thus become equivalent terms.

We have seen that imagery may exercise two functions with reference to habit, as direct and as indirect stimulus; so also with reference to logical meaning, imagery may be the stimulus to a direct reference of the idea to reality, or it may present, or mirror, conditions with regard to which some new meaning is to be worked out. The quality, the sense-content, of imagery may _per se_ suffice directly to arouse a habitual attitude, to call forth an immediate reference to reality. It may cause one to "tumble" to what is taking place, to "catch on," to apprehend (pardon these expressions for the sake of their description of the motor aspect of meaning), as when we say, for example: "It came over me like a flash what I was to do, and I did it." Our more abstract and complicated forms of judgment and reasoning, in which the imagery involved is reduced to the minimum of conscious, qualitative content, are of the same order, though at the other extreme, so far as immediate overt expression is concerned. We are working along lines of habitual activity so familiar that we can work almost in the dark. We need no elaborate imagery. Guided only by the waving of a signal flag or by the shifting gleam of a semaphore, we thread our way swiftly through the maze of tracks worn smooth by use and habit. But suppose a new line of habit is to be constructed. No signal flags or semaphores will suffice. A detailed survey of the proposed route must be had, and here is where imagery with a rich and varied yet flexible sensuous content, growing out of previous surveys, may function in projecting and anticipating the new set of conditions, and thus become the stimulus of a new line of habit, of a new and more far-reaching meaning. As this new line of habit, of meaning, gets into working order with the rest of the system, imagery tends normally to decline again to the rôle of signal flags and semaphores.

The distinction in logical theory between "image" and "idea" which we have been considering is only a half-truth from the point of view of psychology. It virtually limits the "idea" to a fixed, unalterable reference of a fragment of a desiccated image to a reality beyond. It indifferently loses the play and richness of imagery to the floating remnants of sense-content, or to an external reality. It limits itself to an examination of a final stage in thinking, a stage in which the image acts as a direct stimulus, a stage in which the sense-content of the image has little or no function _per se_, because this content now initiates directly a habitual adjustment, a worked-out and established adaptation of means to end. It overlooks the process of conscious reflection which logically precedes every such adjustment not purely instinctive or accidental, a process in which imagery as representational functions indirectly in bringing the resources of past experience, the fund of acquired habits, to bear upon the fragmentary and problematic elements of sense-experience actually present, thus maintaining the flow and continuity of experience. It fails to recognize that in the inseparable association of meaning with quality, of "idea" with "image," there goes the possibility of working out and applying new meanings from old, of developing deeper meanings, of testing and affirming more inclusive and universal meaning.

We are confronted with this alternative. Either the image has a logical function in virtue of its sense-content, or else the image functions logically merely as a symbol, the sense-content of which is a matter of complete logical indifference. According to the empiricist, the former is the case, according to the conceptualist, the latter. The empiricist would say that he needs the image to piece out the data upon which logical processes operate. Having met this need, the image is retired from active service. For the empiricist the processes of thought, observing, comparing, generalizing, etc., are as independent of the data they use as, for the conceptualist, logical meaning, reference, and "idea" are independent of the sense-content of the "image." In reality he agrees with the conceptualist in excluding the sense-content of the image from the processes of thought, and hence from the domain of logic.