It is quite generally recognized that imagination is indispensable in all sciences; that without it we could only copy, repeat, imitate; that it is a stimulus driving us onward and launching us into the unknown. If there does exist a very widespread prejudice to the contrary—if many hold that scientific culture throttles imagination—we must look for the explanation of this view first, in the equivocation, pointed out several times, that makes the essence of the creative imagination consist of images, which are here most often replaced by abstractions or extracts of things—whence it results that the created work does not have the living forms of religion, of art, or even of mechanical invention; and then, in the rational requirements regulating the development of the creative faculty—it may not wander at will. In either case its end is determined, and in order to exist, i.e., in order to be accepted, the invention must become subject to preËstablished rules.

This variety of imagination being, after the esthetic form, the one that psychologists have best described, we may therefore be brief. A complete study of the subject, however, remains yet to be made. Indeed, we may remark that there is no "scientific imagination" in general, that its form must vary according to the nature of the science, and that, consequently, it really resolves itself into a certain number of genera and even of species. Whence arises the need of monographs, each one of which should be the work of a competent man.

No one will question that mathematicians have a way of thinking all their own; but even this is too general. The arithmetician, the algebraist, and more generally the analyst, in whom invention obtains in the most abstract form of discontinuous functions—symbols and their relations—cannot imagine like the geometrician. One may well speak of the ideal figures of geometry—the empirical origin of which is no longer anywhere contested—but we cannot escape from representing them as somehow in space. Does anyone think that Monge, the creator of descriptive geometry, who by his work has aided builders, architects, mechanics, stone cutters in their labors, could have the same type of imagination as the mathematician who has been given up all his life to the theory of number? Here, then, are at least two well-marked varieties, to say nothing of mixed forms. The physicist's imagination is necessarily more concrete; since he is incessantly obliged to refer to the data of sense or to that totality of visual, tactile, motor, acoustic, thermic, etc., representations that we term the "properties of matter." Our eye, says Tyndall, cannot see sound waves contract and dilate, but we construct them in thought—i.e., by means of visual images. The same remarks are true of chemists. The founders of the atomic theory certainly saw atoms, and pictured them in the mind's eye, and their arrangement in compound bodies. The complexity of the imagination increases still more in the geologist, the botanist, the zoologist; it approaches more and more, with its increasing details, to the level of perception. The physician, in whom science becomes also an art, has need of visual representations of the exterior and interior, microscopic and macroscopic, of the various forms of diseased conditions; auditory representations (auscultation); tactile representations (touch, reverberation, etc.); and let us also add that we are not speaking merely of diagnosis of diseases, which is a matter of reproductive imagination, but of the discovery of a new pathologic "entity," proven and made certain from the symptoms. Lastly, if we do not hesitate to give a very broad extension to the term "scientific," and apply it also to invention in social matters, we shall see that the latter is still more exacting, for one must represent to oneself not only the elements of the past and of the present, but in addition construct a picture of the future according to probable inductions and deductions.

It might be objected that the foregoing enumeration proves a great variety in the content of creative imagination but not in the imagination itself, and that nothing has proven that, under all these various aspects, there does not exist a so-called scientific imagination, that always remains identical. This position is untenable. For we have seen above[109] that there exists no creative instinct in general, no one mere indeterminate "creative power," but only wants that, in certain cases, excite novel combinations of images. The nature of the separable materials, then, is a factor of the first importance; it is determining, and indicates to the mind the direction in which it is turned, and all treason in this regard is paid for by aborted construction, by painful labor for some petty result. Invention, separated from what gives it body and soul, is nothing but a pure abstraction.

The monographs called for above would, then, be a not unneeded work. It is only from them collectively that the rÔle of the imagination in the sciences could be completely shown, and we might by abstraction separate out the characters common to all varieties—the essential marks of this imaginative type.

Mathematics aside, all the sciences dealing with facts—from astronomy to sociology—suppose three moments, namely, observation, conjecture, verification. The first depends on external and internal sense, the second on the creative imagination, the third on rational operations, although the imagination is not entirely barred from it. In order to study its influence on scientific development, we shall study it (a) in the sciences in process of formation; (b) in the established sciences; (c) in the processes of verification.

II

It has often been said that the perfection of a science is measured by the amount of mathematics it requires; we might say, conversely, that its lack of completeness is measured by the amount of imagination that it includes. It is a psychological necessity. Where the human mind cannot explain or prove, there it invents; preferring a semblance of knowledge to its total absence.[110] Imagination fulfills the function of a substitute; it furnishes a subjective, conjectural solution in place of an objective, rational explanation. This substitution has degrees:

(1) The sway of the imagination is almost complete in the pseudo-sciences (alchemy, astrology, magic, occultism, etc.), which it would be more proper to call embryonic sciences, for they were the beginnings of more exact disciplines and their fancies have not been without use. In the history of science, this is the golden age of the creative imagination, corresponding to the myth-making period already studied.

(2) The semi-sciences, incompletely proved (certain portions of biology, psychology, sociology, etc.), although they show a regression of imaginative explanation repulsed by the hitherto absent or insufficient experimentation, nevertheless abound in hypotheses, that succeed, contradict, destroy one another. It is a commonplace truism that does not need to be dwelt on—they furnish ad libitum examples of what has been rightly termed scientific mythology.

Aside from the quantity of imagination expended, often without great profit, there is another character to be noted—the nature of the belief that accompanies imaginative creation. We have already seen repeatedly that the intensity of the imaginary conception is in direct ratio to the accompanying belief, or rather, that the two phenomena are really one—merely the two aspects of one and the same state of consciousness. But faith—i.e., the adherence of the mind to an undemonstrated assertion—is here at its maximum.

There are in the sciences hypotheses that are not believed in, that are preserved for their didactic usefulness, because they furnish a simple and convenient method of explanation. Thus the "properties of matter" (heat, electricity, magnetism, etc.), regarded by physicists as distinct qualities even in the first half of the last century; the "two electric fluids;" cohesion, affinity, etc., in chemistry—these are some of the convenient and admitted expressions to which, however, we attach no explanatory value.

There is also to be mentioned the hypothesis held as an approximation of reality—this is the truly scientific position. It is accompanied by a provisional and ever-revocable belief. This is admitted, in principle at least, by all scientists, and has been put into practice by many of them.

Lastly, there is the hypothesis regarded as the truth itself—one that is accompanied by a complete, absolute, belief. But daily observation and history show us that in the realm of embryonic and ill-proven sciences this disposition is more flourishing than anywhere else. The less proof there is, the more we believe. This attitude, however wrong from the standpoint of the logician, seems to the psychologist natural. The mind clings tenaciously to the hypothesis because the latter is its own creation, or, because in adopting it, it seems to the mind that it should have itself discovered the hypothesis, so much does the latter harmonize with its inner states. Let us take the hypothesis of evolution, for example: we need not mention its high philosophical bearing, and the immense influence that it exerts on almost all forms of human thought. Nevertheless, it still remains an hypothesis; but for many it is an indisputable and inviolable dogma, raised far above all controversy. They accept it with the uncompromising fervor of believers: a new proof of the underlying connection between imagination and belief—they increase and decrease pari passu.

III

Should we assign as belonging solely to the imagination every invention or discovery—in a word, whatever is new—in the well-organized sciences that form a body of solid, constantly-broadening doctrine? It is a hard question. That which raises scientific knowledge above popular knowledge is the use of an experimental method and rigorous reasoning processes; but, is not induction and deduction going from the known to the unknown? Without desiring to depreciate the method and its value, it must nevertheless be admitted that it is preventive, not inventive. It resembles, says Condillac, the parapets of a bridge, which do not help the traveler to walk, but keep him from falling over. It is of value especially as a habit of mind. People have wisely discoursed on the "methods" of invention. There are none; but for which fact we could manufacture inventors just as we make mechanics and watchmakers. It is the imagination that invents, that provides the rational faculties with their materials, with the position, and even the solution of their problems. Reasoning is only a means for control and proof; it transforms the work of the imagination into acceptable, logical results. If one has not imagined beforehand, the logical method is aimless and useless, for we cannot reason concerning the completely unknown. Even when a problem seems to advance towards solution wholly through the reason, the imagination ceaselessly intervenes in the form of a succession of groupings, trials, guesses, and possibilities that it proposes. The function of method is to determine its value, to accept or reject it.[111]

Let us show by a few examples that conjecture, the work of the combining imagination, is at the root of the most diverse scientific inventions.[112]

Every mathematical invention is at first only an hypothesis that must be demonstrated, i.e., must be brought under previously established general principles: prior to the decisive moment of rational verification it is only a thing imagined. "In a conversation concerning the place of imagination in scientific work," says Liebig, "a great French mathematician expressed the opinion to me that the greater part of mathematical truth is acquired not through deduction, but through the imagination. He might have said 'all the mathematical truths,' without being wrong." We know that Pascal discovered the thirty-second proposition of Euclid all by himself. It is true that it has been concluded, wrongly perhaps, that he had also discovered all the earlier ones, the order followed by the Greek geometrician not being necessary, and not excluding other arrangements. However it be, reasoning alone was not enough for that discovery. "Many people," says Naville, "of whom I am one, might have thought hard all their lives without finding out the thirty-two propositions of Euclid." This fact alone shows clearly the difference between invention and demonstration, imagination and reason.

In the sciences dealing with facts, all the best-established experimental truths have passed through a conjectural stage. History permits no doubt on this point. What makes it appear otherwise is the fact that for centuries there has gradually come to be formed a body of solid belief, making a whole, stored away in classic treatises from which we learn from childhood, and in which they seem to be arranged of themselves. We are not told of the series of checks and failures through which[113] they have passed. Innumerable are the inventions that remained for a long time in a state of conjecture, matters of pure imagination, because various circumstances did not permit them to take shape, to be demonstrated and verified. Thus, in the thirteenth century, Roger Bacon had a very clear idea of a construction on rails similar to our railroads; of optical instruments that would permit, as does the telescope, to see very far, and to discover the invisible. It is even claimed that he must have foreseen the phenomena of interferences, the demonstration of which had to be awaited ten centuries.

On the other hand, there are guesses that have met success without much delay, but in which the imaginative phase—that of the invention preceding all demonstration—is easy to locate. We know that Tycho-BrahÉ, lacking inventive genius but rich in capacity for exact observation, met Kepler, an adventurous spirit: together, the two made a complete scientist. We have seen how Kepler, guided by a preconceived notion of the "harmony of the spheres," after many trials and corrections, ended by discovering his laws. Copernicus recognized expressly that his theory was suggested to him by an hypothesis of Pythagoras—that of a revolution of the earth about a central fire, assumed to be in a fixed position. Newton imagined his hypothesis of gravitation from the year 1666 on, then abandoned it, the result of his calculations disagreeing with observation; finally he took it up again after a lapse of a few years, having obtained from Paris the new measure of the terrestrial meridian that permitted him to prove his guess. In relating his discoveries, Lavoisier is lavish in expressions that leave no doubt as to their originally conjectural character. "He suspects that the air of the atmosphere is not a simple thing, but is composed of two very different substances." "He presumes that the permanent alkalies (potash, soda) and the earths (lime, magnesia) should not be considered simple substances." And he adds: "What I present here is at the most no more than a mere conjecture." We have mentioned above the case of Darwin. Besides, the history of scientific discoveries is full of facts of this sort.

The passage from the imaginative to the rational phase may be slow or sudden. "For eight months," says Kepler, "I have seen a first glimmer; for three months, daylight; for the last week I see the sunlight of the most wonderful contemplation." On the other hand, HaÜy drops a bit of crystallized calcium spar, and, looking at one of the broken prisms, cries out, "All is found!" and immediately verifies his quick intuition in regard to the true nature of crystallization. We have already indicated[114] the psychological reasons for these differences.

Underneath all the reasoning, inductions, deductions, calculations, demonstrations, methods, and logical apparatus of every sort, there is something animating them that is not understood, that is the work of that complex operation—the constructive imagination.

To conclude: The hypothesis is a creation of the mind, invested with a provisional reality that may, after verification, become permanent. False hypotheses are characterized as imaginary, by which designation is meant that they have not become freed from the first state. But for psychology they are different neither in their origin nor in their nature from those scientific hypotheses that, subjected to the power of reason or of experiment, have come out victorious. Besides, in addition to abortive hypotheses, there are dethroned ones. What theory was more clinging, more fascinating in its applications, than that of phlogiston? Kant[115] praised it as one of the greatest discoveries of the eighteenth century. The development of the sciences is replete with these downfalls. They are psychological regressions: the invention, considered for a time as adequate to reality, decays, returns to the imaginative phase whence it seems to have emerged, and remains pure imagination.

IV

Imagination is not absent from the third stage of scientific research, in demonstration and experimentation, but here we must be brief, (1) because it passes to a minor place, yielding its rank to other modes of investigation, and (2) because this study would have to become doubly employed with the practical and mechanical imagination, which will occupy our attention later. The imagination is here only an auxiliary, a useful instrument, serving:

(1) In the sciences of reasoning, to discover ingenious methods of demonstration, stratagems for avoiding or overcoming difficulties.

(2) In the experimental sciences for inventing methods of research or of control—whence its analogy, above mentioned, to the practical imagination. Furthermore, the reciprocal influence of these two forms of imagination is a matter of common observation: a scientific discovery permits the invention of new instruments; the invention of new instruments makes possible experiments that are increasingly more complicated and delicate.

One remark further: This constructive imagination at the third stage is the only one met with in many scientists. They lack genius for invention, but discover details, additions, corrections, improvements. A recent author distinguishes (a) those who have created the hypothesis, prepared the experiments, and imagined the appropriate apparatus; (b) those who have imagined the hypothesis and the experiment, but use means already invented; and (c) those who, having found the hypothesis made and demonstrated, have thought out a new method of verification.[116] The scientific imagination becomes poorer as we follow it down this scale, which, however, bears no relation to exactness of reasoning and firmness of method.

Neglecting species and varieties, we may reduce the fundamental characters of the scientific imagination to the following:

For its material, it has concepts, the degree of abstraction of which varies with the nature of the science.

It employs only those associational forms that have an objective basis, although its mission is to form new combinations, "the discoveries consisting of the relation of ideas, capable of being united, which hitherto have been isolated."[117] (Laplace.) All association with an affective basis is strictly excluded.

It aims toward objectivity: in its conjectural construction it attempts to reproduce the order and connection of things. Whence its natural affinity for realistic art, which is midway between fiction and reality.

It is unifying, and so just the opposite of the esthetic imagination, which is rather developmental. It puts forward the master idea (Claude Bernard's idÉe directrice), a center of attraction and impulse that enlivens the entire work. The principle of unity, without which no creation succeeds, is nowhere more visible than in the scientific imagination. Even when illusory, it is useful. Pasteur, scrupulous scientist that he was, did not hesitate to say: "The experimenter's illusions are a part of his power: they are the preconceived ideas serving as guides for him."

V

It does not seem to me wrong to regard the imagination of the metaphysician as a variety of the scientific imagination. Both arise from one and the same requirement. Several times before this we have emphasized this point—that the various forms of imagination are not the work of an alleged "creative instinct," but that each particular one has arisen from a special need. The scientific imagination has for its prime motive the need of partial knowledge or explanation; the metaphysical imagination has for its prime motive the need of a total or complete explanation. The latter is no longer an endeavor on a restricted group of phenomena, but a conjecture as to the totality of things, as aspiration toward completely unified knowledge, a need of final explanation that, for certain minds, is just as imperious as any other need.

This necessity is expressed by the creation of a cosmic or human hypothesis constructed after the type and methods of scientific hypotheses, but radically subjective in its origin—only apparently objective. It is a rationalized myth.

The three moments requisite for the constitution of a science are found here, but in a modified form: reflection replaces observation, the choice of the hypothesis becomes all-important, and its application to everything corresponds to scientific proof.

(1) The first moment or preparatory stage, does not belong to our subject. It requires, however, a word in passing. In all science, whether well or ill established, firm or weak, we start from facts derived from observation or experiment. Here, facts are replaced by general ideas. The terminus of every science is, then, the starting-point of philosophical speculation:—metaphysics begins where each separate science ends; and the limits of the latter are theories, hypotheses. These hypotheses become working material for metaphysics which, consequently, is an hypothesis built on hypotheses, a conjecture grafted on conjecture, a work of imagination superimposed on works of imagination. Its principal source, then, is imagination, to which reflection applies itself.

Metaphysicians, indeed, hold that the object of their researches, far from being symbolic and abstract, as in science, or fictitious and imaginary, as in art, is the very essence of things,—absolute reality. Unfortunately, they have never proven that it suffices to seek in order to find, and to wish in order to get.

(2) The second stage is critical. It is concerned with finding the principle that rules and explains everything. In the invention of his theory the metaphysician gives his measure, and permits us to value his imaginative power. But the hypothesis, which in science is always provisional and revocable, is here the supreme reality, the fixed position, the inconcussum quid.

The choice of the principle depends on several causes: The chief of these is the creator's individuality. Every metaphysician has a point of view, a personal way of contemplating and interpreting the totality of things, a belief that tends to recruit adherents.

Secondary causes are: the influence of earlier systems, the sum of acquired knowledge, the social milieu, the variable predominance of religions, sciences, morality, esthetic culture.

Without troubling ourselves with classifications, otherwise very numerous, into which we may group systems (idealism, materialism, monism, etc.) we shall, for our purpose, divide metaphysicians into the imaginative and rational, according as the imagination is superior to the reason or the reason rules the imagination. The differences between these two types of mind, already clearly shown in the choice of the hypothesis, are proven in its development.

(3) The fundamental principle, indeed, must come out of its state of involution and justify its universal validity by explaining everything. This is the third moment, when the scientific process of verification is replaced by a process of construction.

All imaginative metaphysics have a dynamic basis, e.g., the Platonic Ideas, Leibniz' Monadology, the Nature-philosophy of Schelling, Schopenhauer's Will, and Hartmann's Unconscious, the mystics, the systems that assume a world-soul, etc. Semi-abstract, semi-poetic constructions, they are permeated with imagination not only in the general conception, but also in the numberless details of its application. Such are the "fulgurations" of Leibniz, those very rich digressions of Schopenhauer, etc. They have the fascination of a work of art as much as that of science, and this is no longer questioned by metaphysicians themselves;[118] they are living things.

Rational metaphysics, on the other hand, have a chilly aspect, which brings them nearer the abstract sciences. Such are most of the mechanical conceptions, the Hegelian Dialectic, Spinoza's construction more geometrico, the Summa of the Middle Ages. These are buildings of concepts solidly cemented together with logical relations. But art is not wholly absent; it is seen in the systematic concatenation, in the beautiful ordering, in the symmetry of division, in the skill with which the generative principle is constantly brought in, in showing it ever-present, explaining everything. It has been possible to compare these systems with the architecture of the Gothic cathedrals, in which the dominant idea is incessantly repeated in the numberless details of the construction, and in the branching multiplicity of ornamentation.

Further, whatever view we adopt as to its ultimate value, it must be recognized that the imagination of the great metaphysicians, by the originality and fearlessness of its conceptions, by its skill in perfecting all parts of its work, is inferior to no other form. It is equal to the highest, if it does not indeed surpass them.

[109] See Part I, chapter II.