Chapter V · EVOLUTION OF THE PRINCIPAL CONCEPTS. (continued 2)

I. Empirical laws correspond, broadly speaking, with the intermediate forms of abstraction and of generalisation. They consist in the reduction of a large number of facts to a single formula, but without any rational explanation. In the course of events we discover a constant relation of co-existence or of succession between two or several facts; we mentally detach this regular relation from the total which includes it, and extend it to other cases. Constancy is not even necessary for empirical laws, frequency suffices: at least one often has to be content with it. These laws abound in the half-sciences, and in embryo science: they are useful, they give order and simplification.

Their first characteristic is that they are identical with fact. Laws and facts are only two aspects of the same thing. To pass from facts to their empirical law, is merely replacing simple and homogeneous cognition by abstraction, multiple and heterogeneous cognition by perception. Hence the empirical law is rightly compared to a general fact, and it is legitimate in psychology to say the law of association or the general fact of association. On the other hand (in virtue of the natural tendency to anthropomorphism) vulgarisms such as “laws govern facts,” and the like, encourage in many minds the illusion of an ideal world of law superposed upon the world of facts, external to experience, and acting upon it like a government.

A second characteristic, which though frequent is not universal, is complexity. Necessarily objective, since it is a simple notation of observed facts, the empirical law does not always succeed in embracing the results of abstraction in one short and simple formula. Sometimes it does so; sometimes it is confronted with a multiplicity that cannot be reduced to a single proportion; in many cases it has to distribute itself, and resignedly to employ a long formula. Ex.: in physiology, Pflüger’s law (or the laws of reflexes), in linguistics, the laws of Grimm, etc. Here there is a summary description, reduced to the principal facts. It often has to cover a great number of details, as in Listing’s law (of the rotation of the ocular globe). Plenty of examples are to be found in the sciences that are in process of formation, and ill-constituted: psychology,[128] ethics, sociology, etc. Empirical law could only be further simplified by changing its nature, namely by transforming it into theoretical law.

Empirical law is thus the type of law that is immanent, contained in the facts, invoking their representation directly and indirectly by means of intermediate abstraction, involving ascending degrees of abstraction, that, at their highest level, bring it insensibly very near to ideal law.

II. Theoretical, or ideal, law corresponds with the higher forms of abstraction. It exhibits increasingly approximative constructions of the mind, in proportion as these ascend, and are farther removed from experience. Empirical laws are the material whence they are derived, and the transformation is accomplished at the moment, and in the degree, in which description gives place to explanation. To minds accustomed to the discipline of the strict sciences, this conception of law alone is valid, and they are prone to treat with disdain or defiance the formulæ that are a simple summing-up of the results of experience, judging them unworthy of the name of laws. To the psychologist, the position is quite other: empirical concept and theoretical concept are two forms, two aspects of the same intellectual process: there is no constitutional difference between them. Nevertheless, in its higher form, the concept of law has its proper and special characteristics which must be noted.

1. Simplicity, as contrasted with the complexity of empirical laws; this is the necessary corollary of the operation that gives rise to it, since it is an abstraction of abstractions, the final result of a long series of eliminations. Compare with the long, vague, entangled formulæ, charged with details, of which examples were given above, the enunciation of the higher laws, which are usually short and invariably precise. And, it may be added, invariably lucid, at least to the scientist who is in the habit of dealing with them, because he knows exactly what they cover. In this connexion a saying of D’Alembert deserves to be recalled and considered, because it discloses, better than any commentary, the psychology of abstract minds: “The most abstract notions, such as the majority of mankind regard as the most inaccessible, are often those which carry with them the greatest elucidating power: our ideas seem to be blotted out by obscurity in proportion as, in any object, we examine into its sensible properties.”

2. Quantitative determination. The higher laws alone can assume a numerical form, and it is a truism to say that the perfection of any science is measured by the quantity of mathematics which it involves. Not that mathematical formulæ imply or confer any magical virtue, but they are the sign of reduction to clear and simple relations, and are frequently an instrument of further progress. It is true that in the domain of empirical law, there are many processes which attempt to imitate quantitative determination: graphic records, curves, statistics, percentages, etc. Yet these are often a very poor substitute for the equation, or worse—for they offer an illusory preciseness, and are fallacious.

3. It is well to insist upon the ideal character of these laws, because one is apt to forget that, in virtue of their very abstraction, they can be approximate only; and can but be applied, and reduced from theory to practice, by means of rectifications and additions. It has been said that “physical laws are general truths that are invariably more or less falsified for each particular case.” All scientific men, and there are many, who have reflected on the subject, bring out this character of approximation.[129]

Thus—it is not absolutely true that a movement is uniform and rectilinear. The theoretic law of the oscillation of a pendulum is unrealisable, because there is no non-resisting medium, no totally rigid and inextensible bar, no suspending apparatus capable of turning without friction. A planet could only describe an exact ellipse if it alone were turning round the sun: but as, in point of fact, there are several which act and react upon one another, Kepler’s law remains ideal. It is known by very accurate researches that Mariotte’s law of the relations between the density of a gas, and the pressure which it bears, is not strictly accurate for either; but the differences between theory and reality are so slight that, in ordinary cases, they are negligible. The laws of thermodynamics (conservation of energy, correlation of forces) which are so much used in the present day because of their character of generality, and are held by some to be the ultimate principle of phenomena, have no absolute value. It is not, e. g., correct to say that all change generates a change which can be re-transformed without loss or addition. The first moment of enthusiasm passed, there was no lack of criticism and of reservation on this point. And so in other instances, ad infinitum.

In brief, the concept of law, whenever it is more than a vague term in the mind, corresponds either to a direct condensation of facts (empirical laws), or to an ideal simplification (theoretical laws); but, imperfect or perfect, the mental process is the same in the two cases. They differ only in the degree of simplification attainable by analysis for any given material or datum. If empirical law, which is in strict relation with experience, has not been idolised, this distinction and misfortune has frequently befallen the other categories. It has been forgotten that, in the sciences as in the arts, the ideal is only an ideal, although it is here attained by different means, viz., elimination, voluntary omission for the sake of preciseness, a more or less artificial reduction to unity. Consequently many have fallen into the strange illusion of believing that, in manipulating experience by the labor of an ever-growing abstraction, the absolute can be brought out.[130]

SECTION VI. CONCEPT OF SPECIES.

In departing from phenomena by successive abstractions and generalisations, we rise to laws that are more and more extensive: so in setting out from the individual, species, genera, orders, branches, and the like, are formed by a succession of abstractions and generalisations. We have already followed this labor of the intellect in its primitive attempts to introduce order into the multiplicity and variety of living beings (Ch. III.). We saw its start in the period of generic images, its passage through the various degrees of the concrete-abstract period, and its final outcome by diverse paths into a unitary conception. We must now take up the subject from the point at which we left it, and consider the nature of the classificatory concepts at the final term of their development, the moment of their highest scientific determination. If the geometers were the first who abstracted from extension the essential data of Space; if the astronomers accomplished an analogous operation for Time; the naturalists for their part had by abstraction to disengage from among the numerous characteristics of living beings, those which, as fundamental, enable them to reduce individuals to species, species to genera, and so on. They are the inventors of the concepts which govern this province of experience.

The notion of the individual, which is the basis, and preliminary material, of biological classification, is sufficiently clear so long as we confine ourselves to the higher creatures; it becomes obscure and equivocal in descending to the lower grades, where life multiplies by budding, or by division. Hence it has been a great stumbling-block to the naturalists. For our purpose, the point is negligible. We can without inconvenience omit the debates on this subject, and presume that individuality always has its fixed characteristics. The work of abstraction and of generalisation alone concern us.

Among all others, the Concept of Species is certainly the one which—more especially in our own day—has been the most studied and disputed. Many efforts have been made to determine its essential characters, to which some attribute, and others refuse, an objective value. In effect, and broadly speaking—two contrary theories obtain in this connexion:

1. That of fixity of species, the oldest, and long paramount: still perhaps finding its partisans. If we accept this, we admit at the same time that the naturalist in determining species, reveals a mystery of nature, and partially discovers the plan of creation.

2. The complete antithesis of the foregoing, which maintains that only individuals exist. In its absolute and radical form, this assertion seems rarely to have been brought forward. It has, however, been said that “the idea of species is not given to us by nature itself.”[131] In point of fact, the contention of the transformists is different. They do not refuse to recognise the grouping of living beings, according to their degrees of similarity, into varieties and species; but they grant to species only a momentary fixedness in time and space. It does not exist, it is not a natural type, it is transitionally a stable variation; the individual is the reality. From our point of view, this signifies that the specific characters isolated by abstraction are of value only as practical means of simplification in no way helping us to penetrate into the nature of things.

However this may be,—and without for the moment inquiring whether the work of abstraction in this province gives objective or subjective results, whether it limits itself to simplification in relation to man, or discovers in relation to nature,—let us follow it in its ascending progress. Once again, we can distinguish two principal stages: that of species corresponding to empirical and concrete law; that of genera, and the still higher forms, corresponding to theoretical and ideal laws.

I.

The nature of a concept is fixed by the determination of its constituent elements; these are determined by abstraction. Abstraction that is not vulgar and arbitrary, but scientific, should disclose characteristics that are the substitutes for a group (here living beings in general), taking its place, and enabling us to think it. These constituent elements of the concept of species are met with in nearly all the naturalists’ definitions.[132] They are two in number; species is determined by two essential characteristics: similarity (morphological criterion), filiation (physiological criterion).

1. Similarity seems at first sight easy to determine—as though we had only to open our eyes; yet by this elementary procedure we hardly pass beyond the level of generic images, and there is risk of falling into many errors. It is necessary to penetrate into resemblances deeper than the superficial; and here is the first degree of complexity. Buffon observed that “the horse and the donkey, which are distinct species, resemble each other more than the water spaniel and the harrier, which are of the same species.” The facts which our contemporaries denote by the name of polymorphism, entirely baffle the criterion of similarity. Not to speak of the obvious difference between the larva and the perfect insect, the caterpillar and the butterfly, or between the males, females, and neuters of bees, ants, and termites; there are cases in which the disparity between the two sexes is so great that the male and the female, taken respectively as two different creatures, have been classified in distinct genera, and even orders: e. g., the lampyris or glow-worm, Lernea, and many others. The character of the resemblance is thus too often vague, sometimes deceptive, nearly always inadequate: it follows that we must resort to the other, to filiation.

2. This, the physiological criterion, again appears to leave no opening for equivocation, since it can be materially stated. Generally speaking, one is imbued with the notion that children resemble their parents, that the immediate product is the reproduction of the type of the progenitors. But the alternating generations (metagenesis, geneagenesis) discovered in the course of the present century, show that this conception is too simple, and often fallacious. This mode of reproduction is by no means rare; we meet with it among a great number of the lower plants, infusoria, worms, and even insects. “The dominating fact in the reproduction of all these creatures, is that a sexual being, of definite form, gives birth to a-sexual beings which do not resemble it, but which in their turn produce by a sort of budding, or by fission of their bodies, the sexual creatures similar to those from which they issued.” Vogt, accordingly, in his definition of species, is forced to include the case of alternate generation by saying: “Species is the reunion of all the individuals that originate from the same parents, and are in themselves, or in their descendants, similar to their primordial ancestors.”

In brief, the general notion of species depends upon two ideas, complex notwithstanding their apparent simplicity, fluctuating in spite of their apparent precision.

Till now, we have spoken of species as if it were directly superposed upon individuals, as if it resulted from immediate generalisation. This is not the naturalists’ position. Their classification descends from the species to the individual by decreasing generalisations of the race and the variation. Thus the human species comprises several races (white, yellow, etc.), the white race comprises several variations (English, Arab type, etc.). To the partisan of fixedness of species, these three general notions have not the same value: species alone has peculiar and irreducible characters, which are deduced from the function of reproduction and the facts of cross-breeding.

Couple two individuals of distinct species: the union is generally sterile. If otherwise, the hybrids which result from it are unfruitful. If, as rarely happens, they propagate themselves, the offspring rapidly return to the type of one of the ancestral species.

Couple two individuals of distinct races or variations, the union will be fruitful; the resulting cross-breeds are again fertile; the progenitors are able to create and fix varieties, and even races.

Hence, it is concluded, species must be a thing that exists, that protects itself, does not let itself be encroached upon.

Evidently the debated question is one of facts: and both the parties in dispute adduce experimental evidence. Few in number as they may be, there are fertile hybrids, which perpetuate themselves. They are found among birds and mammals, e. g., the alpaca and the vicuna, the bull and the zebu, the goat and the sheep—which have for issue the ovicaprinæ,—the hare and the rabbit—whose offspring is the leporide, (their perpetuity has been contested). On the other hand, if certain species have thus been formed by a durable blend, there exist races that have been refractory to all attempts at cross-breeding: i. e., the domestic and Brazilian guinea-pig, different races of rats, of rabbits, etc.

We need not enter into the discussion, nor enumerate the observations and experiments invoked on either side: they are to be found in special works. Our aim was to discover the constituent elements of the notion of species in its scientific aspect. Now, neither the morphological element nor the physiological element has any distinguishing mark of permanence and universality. The concept of species is possessed of no absolute value; neither is it a simple replica in the mind of the “plan of nature.” The result of abstraction and of generalisation, it corresponds to something which is fixed for a certain time in certain conditions; it has temporary and provisional objectivity.[133]

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.