II.
Contemporary discussion is almost entirely centred upon species. Little is said about genera, and still less of the higher divisions. We do not, in any case, find what we require: the determination of constitutive elements, of general acceptance, which shall be for the genus, family, order, or class, the equivalent of the two denotative marks—morphological and physiological—that are attributed to species.
This has not always been the case. At the time when there was general belief in a scheme of creation, the naturalists were careful, by bringing together species, genera, families, etc., to disengage more and more general characters, which they regarded as essential, and determined by the nature of the thing. We have already said that Linnæus was the first to formulate a precise notion of genus, to which he expressly attributed a reality: “You must know,” he says, in his Philosophia botanica, “that it is not character that constitutes the genus, but genus the character; that character devolves from genus, not genus from character; that character exists not in order that genus should come about (fiat), but so that the genus should be known.” In the binary nomenclature which he adopted, the first term designates the genus, the second one of the species included. Thus the dog and the wolf have characters by which they resemble each other, and are distinguished from other animals (five fingers on the anterior limbs, four only on the posterior, twenty-two teeth in the upper and lower jaw, etc.) Linnæus classifies them as the genus Canis, of which Canis familiaris, Canis lupus, Canis vulpes, etc., are the species. Again, the genus Felis, determined by the characters common to certain animals exclusively, comprises in its species: the cat (Felis catus), the lion (Felis leo), the tiger (Felis tigris), etc.
Agassiz, the last representative of the line of naturalists who aspired at reproducing the order of nature in the hierarchy of their classificatory concepts, characterises the genera and divisions superior to them by vague formulæ. Of these we can judge from the following passage:
“Individuals are the support, at the actual moment, of the characters not merely of species, but of all other divisions. As representative of genus, they have certain details of a definite and specific structure, identical with those possessed by the representatives of other species. As representative of family, they have a definite constitution, expressive of a distinct and specific model, in forms resembling those of the representatives of other genera. As representative of order, they take definite rank, as compared with the representatives of other families. As representative of class, they manifest the structural plan of their ramifications by the aid of special means, and according to specific directions. As representative of branches the individuals are all organised on a distinct plan which differs from the plan of other branch-lines.”[134]
It was shown above ([Ch. III.]) that the contemporary classifications, which are radically embryological, transformist, and generic, proceed otherwise, and have a different aim. Their ideal is to draw up the genealogical tree of living beings, with its multiple ramifications, marking the principal moments of evolution.
But if, leaving aside the material of these (animal or vegetable) classifications, we consider only the psychological labor by which they are constituted, we find that the transformists and their adversaries have at least one common point which is of cardinal importance. The notion of fundamental types—conceived as fixed or provisory—is for the one as for the other a compass, a guide in research, a normal, by means of which deviations are appreciated. Hence, these concepts have a practical value, and it is true that we find abstraction and generalisation in their principal rôle, which is, not to discover, but to simplify, above all to be useful.
In effect, the one side, yielding to the natural tendency of the mind to reify abstractions, admit the permanence and objectivity of types: they believe firmly that they have in certain concepts the possibility of an ideal reconstruction of the entire world of living beings. This faith sustains them and urges them on to more and more exact determinations.
Their opponents, the transformists of every degree, are guided by a different ideal; they search after continuity, transition, forms of passage. Species, genera, families, etc., are but provisory starting-points, with intermediate lacunæ which they endeavor to bridge over. Although the animal order, the chain of life, is itself only a theoretical construction, a natural abstraction, many fine works could be quoted which are inspired by this faith in continuity. Such, e. g., are Huxley, Cope, and others upon the genus Equus, establishing the filiation of the four-fingered Eohippus of the old Tertiary epoch, with the Hipparion of the new Tertiary epoch, and with the Horse of the Quaternary period.
The hierarchy of concepts formed by superposition of abstractions and generalisations only facilitates the task. The sole incontestable value that can be assigned to any notion of species, and still more to genus, and other still more general concepts, is that of utility. They are successful implements in the investigation of nature. All other pretensions are open to discussion. One position more especially is untenable: that which claims for concepts, the pure results of abstraction, an absolute value. It is obvious that they can have none. They are neither reality nor fiction, but approximations.
Laws and species—two general notions which must be connected—were bound to vary in the course of evolution, because they are entirely subordinated to the conditions which govern the existence of phenomena and of living beings. Let us—merely as an illustration to fix our ideas—admit the hypothesis of a primitive nebula. Imagine (which is impossible) an intelligent being, able, at that point in the world’s history, to draw up a scheme of the existing laws. He could discover none but those which govern matter in the gaseous state,—some of which are still extant, others unknown to us, and unknowable—since, their conditions of existence having ceased, they are annihilated. When at a later time this matter, uniformly diffused and dispersed through space, became divided from one or other cause into vast nebulous spheres commencing their slow revolution, our hypothetical being might have surprised the birth of the astronomical laws. Subsequently, the constitution of the liquid state of matter, and then of the solid state in its different degrees, would give birth to new physico-chemical laws, others meantime disappearing. When, finally, life—whatever may have been its origin—appeared, other laws again loomed forth, and the possibility of classification. Yet to the hypothetical spectator, these must needs be highly singular, highly dissimilar from our own—unless we admit the hypothesis of a world created at one throw.
It is needless to enter into the details of this long evolution, as it is generally admitted to have been. Enough to remember that the matter whence abstraction deduces laws and species has varied, and may vary again in the course of ages. If, on the other hand, we consider the slow progress of human knowledge, and the incessant corrections imposed by experience and reasoning from century to century, we find ourselves confronted with two variable factors, one objective, the other subjective. No permanence can result from their union. Long as may be the stability of laws and species, nothing guarantees their perpetual duration. So that after two centuries which make a brave show in the history of the sciences, we may still advance the formula of Leibnitz: “Our determinations of physical species are provisional and proportional to our knowledge.”[135]
Many other concepts might be added to the preceding, among them, those of the moral sciences. I forbear, because the history of their fluctuations would in itself exact a volume. Till now, these have been ill-determined, badly defined. May we even speak of any regular evolution? Have they not rather suffered corsi e ricorsi, which bring them back perennially to their point of departure? Whenever—during a development of centuries—the work of abstraction has succeeded, we have seen it pass through successive phases:—generic ideas, intermediate forms, higher forms—but not by any constant process. Sometimes it has rapidly attained the period of complete simplification, as in mathematics; sometimes it is long arrested in its progress, as in the natural sciences: sometimes, again, as in the less established sciences, it is incapable even to the present day of transcending the lowest stages.
CHAPTER VI.
CONCLUSION.
We have endeavored to show how the faculty of abstracting and of generalising has been developed empirically, and to follow it in its spontaneous and natural evolution as shown in history,—not in the philosophical speculations which are only its efflorescence, and which, for the most part, ignore or despise its origins. It remains to us, in conclusion, to seek out how, and by what causes, this intellectual process has constituted and developed itself: further—what are the different directions it has followed in the course of its development.
I. To contemporary psychology, the mind is a sum of processes of dissimilar nature, whose mode of appearance and of evolution depends upon predetermined conditions. In the total of intellectual operations, abstraction is a process of secondary formation: it does not belong to the primary stratum of sensations and percepts, of appetites and tendencies, of primitive emotions. We found however that it was there in embryo. How then, instead of remaining in this rudimentary state, has it been so differentiated as to become a function proper to the intellect, and with a long development that is still in progress?
The primary condition is the existence of attention, which brings a few points into relief, amid the general confusion. We have shown elsewhere that attention itself depends originally upon the instinct of individual preservation.[136] Attention, however, can only precede and prepare for abstraction, because it is a momentary state of application to the variable aspects of events, and does not isolate anything.
We know how the first labor of separation, of dissociation, takes effect in the formation of generic images, and how the extracted quality fixed itself, for better or worse, by the aid of a visual, auditory, tactile scheme, by a movement, a gesture, which confers on it a sort of independence.
Finally, with the word—the substitute for the abstract intuition—the mental dissociation approximates to a real dissociation: the abstract character, incarnated in the word, seems, as happens only too often, to exist by itself. The process of abstraction, with its fitting instrument, is completely constituted.
During these successive phases, and afterwards, throughout the course of the historical development of human intelligence, the progress of abstraction and of generalisation, depends upon two principal causes: one general, i. e., utility; the other accidental and sporadic, the advent of inventors.
I. In his book on Darwinism (Ch. XV.) Wallace, in contesting the theory that applies the law of conservation of variations, useful in the struggle for existence, to the mental faculties, insists at length upon the mathematical faculty; he maintains that it is an inexplicable exception, a case that cannot be reduced to law. The inaptitude of inferior races for even the simplest calculations is well known; how—from such a rudimentary origin—could it develop into the genius of a Newton, a Laplace, or a Gauss? What motive power accounts for this development? The author establishes by a host of sufficiently useless historical details, that mathematical superiority played no part in the struggle of tribe with tribe, and later on of people with people (Greeks against Persians), and that the victory resulted from other causes, moral and social. For this there is abundant evidence. But since mathematical aptitude is only a particular instance of abstraction, albeit one of the most perfect, the question ought to be proposed under a more general form. Had the aptitude for abstraction, ab initio, any practical value? Yes, “the motive power that caused its development, that Wallace claims without specifying it, is utility.”
To avoid possibility of equivocation, let us remark that the development of the attitude for abstracting and generalising may be explained in a two-fold manner: by acknowledging the influence of heredity, and by omitting it.
In the former case, it is supposed that this aptitude appears as a “spontaneous variation” in the individual or race, that it fixes itself, is reciprocal, grows by slow accumulation in the course of generations. This theory postulates the heredity of acquired characters, which is accepted by some, rejected by others, more especially since the advent of Weismann. I refrain from invoking it, by reason of its hypothetical and disputed nature. The probability of any transmission would moreover be far harder to establish here than in other psychical directions, such as imagination, or feeling.
In the second case, with elimination of the hereditary factor, progress must be attributed to social causes, utility and imitation. From all time there have been minds which when face to face with practical problems knew better than others how to extract the essential, and neglect the accessory, in the complex of facts. The utility of abstraction is identical with that of attention, which does not require demonstration; it may be summed up in a single word: to simplify. As the process succeeds, it finds imitators. There is no need to admit at the outset any reflected and fully conscious abstraction: a happy instinct, guided by the needs of life, is sufficient at the commencement. Races that are poorly gifted in this respect, or little apt at imitating their betters, have never got beyond a low level. In effect, abstraction and generalisation are the nerve of all knowledge that transcends sensation. Is this mode of cognition useful? There can be no possible doubt as to the answer.
2. The rôle of inventors corresponds to the fact which, in transformist terminology, is known as spontaneous variation. By inventors, we mean those who are born with the talent or the genius for abstraction. It is superfluous to prove that such have been found, in considerable numbers. They are abstract thinkers by instinct, as others are musicians, mechanicians, designers. The biography of the great mathematicians abounds in examples: Pascal inventing geometry out of a few vague indications from his father; Newton divining Euclid’s demonstrations from the simple enunciation of the theorems; Ampère, before he could read or understand the use of figures, making long calculations by means of a few pebbles; Gauss, at five years old, rectifying the arithmetic of a workman, etc. If fewer analogous facts can be quoted from the other sciences, it is because mathematical precocity is frequent, and is more surprising. All that is the effect of innate disposition: this word serving only to recapitulate our ignorance of the causes which produce such minds. In the development of knowledge by abstraction and generalisation, the first cause—utility—may be likened to the part played by slow actions in geology; whether in the case of practical inventions, or of the constitution of an idiom, it is continuous, collective, and anonymous. The rôle of the great abstract thinkers, on the contrary, resembles the rapid and epoch-making actions.
II. If we now consider the progress of abstraction from a more general point of view (instead of following it step by step, from its lowest to its highest degree, as in the preceding chapters), i. e., according to its orientation towards a given end, we find that it has followed three principal directions during its history: practical, speculative, scientific. These are, indeed, inseparable, inasmuch as practical abstraction leads to science, scientific abstraction is profitable to practice, and speculation cannot entirely forego the other two.[137]
Abstraction and practical generalisation are necessarily the first in order, as we found in studying their first appearance in the lower animals, in children, and in savages. They serve to distinguish the qualities of things by some word, or sign; they subserve the simple adaptations of daily life. Later on, at a higher stage, they note the appearance of mixed processes, which, while more especially directed to utility, are already the prelude to scientific knowledge. Disinterested curiosity has awakened, and timidly makes for daylight. A minimum acquaintance with the history of the sciences teaches us that all were at their origin processes of applied research, and that often, in their uncertain efforts, our forbears found what they were not looking for. The numerative systems issued from the need of counting objects, and later on, from rude commercial exchanges. Elementary geometry was required, in order to measure the fields, to determine a right angle, to fix relative positions, and to furnish the indispensable parts of primitive architecture. The invention of the lever, of the balance, of rudimentary engines for the lifting of heavy masses, gave the first foundations of mechanics. Astronomy arose in the desire to regulate civil life and the religious festivals, and the wish (e. g., among the Peruvians and Mexicans) not to irritate the gods by delaying the sacrifices due to them. Metallurgy, and later on the search for the philosopher’s stone, and the elixir of life, were the prelude to scientific chemistry. The historical outset of each science would furnish a profusion of similar facts.
The two other operations issued by an internal division of labor from this—at first the only—tendency of the mind.
First come purely speculative, i. e., philosophical or metaphysical abstraction and generalisation. This new trend has clean and well defined characteristics; and it was, in antiquity, the privilege of two peoples alone, the Greeks and the Hindus. Abstraction leads immediately to the highest generalisations; from the crude and direct simplification of a few facts, the mind leaps at a bound to the final causes of things; it skips the intermediate stages: it ignores the sequence of slow and progressive evolution. This procedure where, in point of fact, abstraction and generalisation are only the servants of a particular form of imagination, found its first complete expression in Plato, and the Theory of Ideas. With Plato, the human intellect tasted for the first time the supreme pleasures of playing with the highest abstractions, and believing firmly that the universe can be summed up, constructed and explained by the help of some few entities. In this direction, notwithstanding its manifold changes of aspect, the generalising process has remained fundamentally the same, and has done no more than repeat itself. We are here concerned with statement, not with criticism. Psychologists must needs admit that this tendency to construct the world (whether or no it be illusory) is a fact inherent in the nature of the human intellect. Stallo, in the book already quoted,[138] gives an incisive critique of the fundamental concepts of the physical sciences, and their unconscious trend towards metaphysics. His appreciation of the characteristics proper to the purely speculative process of abstraction and generalisation is so apt, that we cannot do better than transcribe it:
“Whatever diversity may exist between metaphysical systems, they are all founded upon the express or implied supposition that there is a fixed correspondence between concepts and their filiations on the one hand and things and their mode of interdependence on the other. This fundamental error is in great part due to a delusory view of the function of language as an aid to the formation and fixation of concepts. Roughly stated, concepts are the meanings of words; and the circumstances that words primarily designate things, or at least objects of sensation and their sensible interactions, has given rise to certain fallacious assumptions which, unlike the ordinary infractions of the laws of logic, are in a sense natural outgrowths of the evolution of thought (not without analogy to the organic diseases incident to bodily life) and may be termed structural fallacies of the intellect. These assumptions are:
“1. That every concept is the counterpart of a distinct objective reality, and that hence there are as many things, or natural classes of things, as there are concepts or notions.
“2. That the more general or extensive concepts and the realities corresponding to them pre-exist to the less general, more comprehensive, concepts and their corresponding realities; and that the latter concepts and realities are derived from the former, either by a successive addition of attributes or properties, or by a process of evolution, the attributes or properties of the former being taken as implications of those of the latter.
“3. That the order of the genesis of concepts is identical with the order of the genesis of things.
“4. That things exist independently of and antecedently to their relations; that all relations are between absolute terms; and that therefore whatever reality belongs to the properties of things is distinct from that of the things themselves.”
The differences between this procedure and that proper to the third (or scientific) direction need hardly be enumerated.
Here the advance is step by step, without for an instant losing hold of the thread that leads back to the starting-point of experience. Even where the mind takes giant strides, or leaps across the intermediate generalisations, it pauses to verify its results and to take up the thread it had loosed for the moment. This is the typical process. Since it formed the basis of our discussion of the intermediate and higher forms of abstraction, we need not here return to it. Yet in conclusion, it is well to recall once more what makes it of sterling value.
To reduce the essentials of abstraction and generalisation to the exclusive use of the word (or sign) as is customary, is an error that can only be explained by the time-honored neglect of the function of the unconscious in psychology. The sign is no more than an instrument of simplification, an abbreviated formula. When the mind works with the aid of concepts, the co-operation of two factors, the one conscious, the other unconscious or subconscious, is required, in order that its labor may be legitimate and fruitful: on the one hand, we have words or signs, accompanied sometimes by a vague representation; on the other hand, a latent, potential, organised knowledge. We endeavored above ([Ch. IV.]) to show how this couple forms and fixes itself. The mechanism is invariably the same, without exception. Whether we keep up a trivial conversation by means of the abstract terms which compose our languages, or whether we ascend to the highest generalisations, there is in the mental state no more than a difference in degree; there is no difference in nature. Beneath the words that are the clear factors, exists the dumb travail, the vague invocation, of the organised experience that gives life to them. Without this unconscious factor which may, often does, become conscious, there is nought but illusion. When we induct, deduct, traverse a long series of abstractions to demonstrate or to discover, the useful work consists in new relations which establish themselves in our organised potential knowledge; words are no more than the instruments that commence the task, facilitate and mark its phases. When the mind is grappling with the highest abstractions, and climbs from height to height, what preserves it from catastrophe, and guarantees against error, is the quantity and quality of the unconscious material stored up beneath the words. The entomologist who at first sight, and immediately, classifies one insect among millions of species, acts in virtue of his long experience, impressed firmly in his memory with salient characteristics: he proceeds from the sensory data to the name. In the inverse operation, when he merely enunciates the name, all this acquired knowledge is the substrate. The existence of these conscious-unconscious couples is, so to speak, a rule in psychology: general ideas are but a particular case, perhaps the least well-known: hence we previously likened them ([Ch. IV.]) to mental habits.
It follows that in proportion as we ascend in generalisation we rise, not into vacuity, as has been said, but into the simple—as also, it must be confessed, into the approximate. The relatively empty concepts (there are none that are absolutely void of content) are the product of a discontinuous generalisation which prevents descent without interruption or omission into the concrete. Of course these are chiefly encountered in the world of pure speculation. They are names representing a knowledge that is incomplete, partial, inadequate, or ill-organised; they correspond not to elimination of what is useless, but to deficit of what is necessary. Having no possible contact with reality, they float in an unreal atmosphere, and are material for a fragile and quickly crumbling architecture. The aim of thinking by concepts is to substitute for complex states, simpler conditions that may be turned and re-turned in every possible sense, in order the better to discover their relations: whereas here, by the nature of things, the unconscious activity, the labor that operates silently in the lower strata, is applied to a soil that is full of faults and fissures, and can but project a false light into consciousness.
It has frequently been stated that symbolic thought is thinking by substitution. This formula is admissible only when we recognise that the substitute supposes, nay expects, the actual existence of that for which it is substituted. Substitution is valid in consciousness, but not for the total operation. To sum up in a word: the psychology of abstraction and generalisation, is in a great measure the psychology of the unconscious.
We have merely studied general ideas in so far as they have an assignable origin in experience, and do not transcend its limits. Are there, as some maintain, notions anterior to any sensory intuition—that can by no means nor effort be derived from empirical data? It is not our part to discuss this question. The thesis—whether or no it be legitimate—is a contention in favor of innate ideas, and in whatever fashion it is conceived (à priori forms, hereditary disposition, cerebral conformation), it is the problem of the ultimate constitution of human intelligence, which we have rigorously eliminated from our present subject.