Chapter V Evolution of the Principal Concepts
After this general study of the nature of the most elevated forms of abstraction, we must take the principal concepts one by one, and retrace their evolution in outline. Let us once more note that we are concerned with pure psychology, and are to eliminate all that depends on the theory of knowledge and other transcendental speculations. As regards the first origin of our notions of time, space, cause, etc., each may adopt the opinion that pleases him. Whether we admit the hypothesis of à priori forms of the mind (Kant), or that of an innate sense acquired by repetition of experience in the species, and fixed by heredity in the course of centuries (Herbert Spencer), or any other whatsoever—it is clear that the appearance of these concepts, and the data of their evolution, depend on experimental conditions, and consequently fall within our province. Accordingly it is with their empirical genesis, and development through experience, that we are concerned—and with that alone.
Section I. Concept of Number
The lower phases of this concept are already known to us. We have traversed them in considering numeration, in brutes, children, and aborigines. And here we return to it finally under its higher aspects.
At the outset, counting was, as we found, merely the perception of a plurality; abstraction being practically at zero. Later on a rudiment of numeration appeared, under a practical concrete form: we have perception plus the word—a poor auxiliary, whose part is so insignificant as to be mostly negligible. We noted the different stages of this concrete abstract period, marked by the increasing importance of the word. Finally we arrived at the point at which it is the prime and almost the only factor. Number under its abstract form, as it results, from a long elaboration, consists in a collection of unities that are, or are reputed, similar. We have therefore first to examine how the idea of unity is formed. Next by what mental operation the sequence of numbers is constituted, lastly what is the part played by the sign.
I. To common sense nothing appears more easy than to explain how the idea of unity is formed. I see a man, a tree, a house; I hear a sound; I touch an object; I smell an odor, and so on: and I distinguish this single state from a plurality of sensations. John Stuart Mill seems to admit that number (at least in its simplest forms) is a quality of things that we perceive, as white, black, roundness, hardness: there is a distinct and special state of consciousness corresponding to one, two, three, etc.
Even if we admit this very doubtful thesis, we should arrive at last only at perceived numbers, with which consistent and extended numeration is impossible. It can only be carried on with homogeneous terms, i. e., such as are given by abstraction.
The notion of unity must however find its point of departure in experience, at first under a concrete form; Although it may enter consciousness by several doors, some psychologists, with no legitimate reason, have attributed its origin to one definite mode of external, or even internal, perception which they have chosen to the exclusion of all others.
For some, it is the primordial sense, the sense par excellence; touch. The child regards as a unity the object which it can hold in its hand (a ball, a glass), or follow uninterruptedly in all its boundaries. Wherever his operations are interrupted, where there are breaks of surface continuity, he perceives plurality. In other terms unity is the continuous, plurality is the discontinuous. Numerous observations prove that children actually have a far more exact and precocious notion of continuous quantity (extension), than of discontinuous, discrete quantity (number).91
For others, it is sight, for which all that was said above may obviously be repeated. The retina replaces the cutaneous surface: an image clearly perceived without discontinuity is the unity; the perception of simultaneous images leaving intermediate lacunæ in the field of vision, gives plurality.
The same may be said of the acoustic sensations. Preyer, in a work on “Arithmogenesis,” claims that “hearing takes first rank in the acquisition of the concept of number.” Number must be felt before it is thought. Ideas of number and of addition have to be acquired, and this, according to him, takes place in the child when it hears and compares sounds. Subsequently, touch and sight complete this first outline. It is known that Leibnitz assimilated music to an unconscious arithmetic. Preyer reverses the proposition and says: Arithmetica est exercitium musicum occultum nescientis se sonos comparare animi.92
As against those who seek the origin of the idea of unity in external events, others attribute it to internal experience.
Thus it has been maintained that consciousness of the ego as a monad which knows itself, is the prototype of arithmetical unity. Obviously this assertion is open to numerous objections. To wit, the late formation of the notion of the ego, the fruit of reflexion; its instability,—still more, this unity, like all the preceding, is concrete, complex; it is a composite unity.
The thesis of W. James is very superior: “Number seems to signify primarily the strokes of our attention in discriminating things. These strokes remain in the memory in groups, large or small, and the groups can be compared. The discrimination is, as we know, psychologically facilitated by the mobility of the thing as a total.... A globe is one if undivided; two, if composed of hemispheres. A sand heap is one thing, or twenty thousand things, as we may choose to count it.”93 This reduction to acts of attention brings us back definitely to the essential and fundamental conditions of abstraction.
Save this last, the hypotheses enumerated (and internal sensation might also have been invoked; e. g., a localised pain as compared with several scattered pains) give only percepts or images, i. e., the raw material of abstract unity. This is itself a subjective notion. We said above (Chapter II) that the question whether consciousness starts from the general or the particular is a misstatement, because it applies to the mind which is in process of formation, categories valid only for the adult intelligence. So here. At the outset there is no clear perception of primary unity and subsequent plurality, or vice versa: neither observation nor reasoning justifies an affirmation. There is a confused, indefinite state, whence issues the antithesis of continuous and discontinuous, the primitive equivalents of unity and plurality. It took centuries to arrive at the precise notion of abstract unity as it exists in the minds of the first mathematicians, and this notion is the result of a decomposition, not of any direct and immediate act of postulation. It was necessary to decompose an object or group into its constituent parts, which are or appear to be irreducible. Then a new synthesis of these parts was required to reconstitute the whole, in order that the notion of relation between unity and plurality should be perceived clearly. It cannot be doubted that for the lesser numbers two, three, four, the successive perception of each separate object, and then of the objects apprehended together at a single glance, has aided the work of the mind in the conception of this relation. We have seen that many human races never passed beyond this phase. The abstract notion of unity is that of the indivisible (provisory). It is this abstract quality of the indivisible, fixed by a word, that gives us the scientific idea of unity as opposed to the vulgar notion. Perceived unity is a concrete, conceived unity is a quality, an abstract; and in one sense it may be said that unity, and consequently all abstract number, is a creation of the mind. It results like all abstraction from analysis—dissociation. Like all abstraction, it has an ideal existence; yet this in no way prevents it from being an instrument of marvellous utility.
II. It is owing to this that the sequence of numbers, homogeneous in material, can be constituted; for the identity of unities is the sole condition in virtue of which they can be counted, and the scant numerations of the concrete-abstract period transcended. The sequence is constituted by an invariable process of construction, which may be reduced to addition or subtraction. “Thus the number 2, simplest of all numbers, is a construction in virtue of which unity is added to itself; the number 3 is a construction in virtue of which unity is added to the number 2, and so on in order. If numbers are composed by successively adding unity to itself, or to other numbers already formed by the same process, they are decomposed by withdrawing unity from the previously constructed sums; and thus, to decompose is again to compose other numbers. For example, if 3 is 2 + 1, it is also 4 - 1. Addition and subtraction are two inverse operations whose results are mutually exclusive: they are the sole primitive numerical functions.”94
The simplicity and solidity of this process result from its being always identical with itself, and although the series of numbers is unlimited, some one term of the sequence is rigorously determined, because it can always be brought back to its point of departure, unity. In this labor of construction by continuous repetition, two psychological facts are to be noted:
1. No sooner is unity passed, in the elaboration of numbers, than intuition fails altogether. Directly we reach 5, 6, 7, etc, (the limit varies with the individual), objects can no longer be perceived or represented together: there is now no more in consciousness than the sign, the substitute for the absent intuition: each number becomes a sum of unities fixed by a name.
2. For our unity-type we substitute higher unities, which admit of simplification. Thus in the predominating decimal system, ten and a hundred are unities ten and a hundred times larger than unity, properly so called. They may be of any given magnitude: the Hindus, whose exuberant imagination is well known, invented the koti, equivalent to four billions three hundred and twenty-eight millions of years, for calculating the life of their gods; each koti represents a single day of the divine life.95
Inversely, we may consider the unity-type as a sum of identical parts, and represent 1 = 10/10 or 100/100, etc. A tenth, a hundredth, are unities ten times, a hundred times, smaller than unity properly so called, but they obey the same laws in the formation of fractional numbers.
It is well for the psychologist to note the privileged position of what we term the unity-type, or simply 1. It originates in experience, because unity, even when concrete, and apprehended by gross perception, appears as a primitive element, special and irreducible. So long as the mind confines itself to perceiving or imagining, there is in the passage from one object to two, three, or four objects, or inversely in the passage from four objects to three, two, or only one, an augmentation or diminution. But below unity in the first case, and above unity in the second, there is no longer any mental representation; unity seems to border on nonentity and to be an absolute beginning.
From this privileged point the mind can follow two opposite directions, by an identical movement: the one towards the infinitely great, with constant augmentation; the other towards the infinitely small, with constant diminution—but in one sense or the other, infinity is a never exhausted possibility. Here we reach the much disputed question of infinite number: psychology is not concerned with this. For some, infinite number has an actual existence. For others, it only exists potentially, i. e., as an intellectual operation which may, as was said above, add or subtract, without end or intermission.96
III. The importance of signs, as the instruments of abstraction and generalisation, is nowhere so well shown as in their multiple applications to discrete or continuous quantity. The history of the mathematical sciences is in part that of the invention, and use of symbols of increasing complexity, whose efficacy is clearly manifested in their theoretical or practical results. In the first place, words were substituted for the things that were held to be numerable; next, particular signs, or figures; later still, with the invention of algebra, letters took the place of figures, or at any rate assumed their function and part in the problem to be solved; later still, the consideration of geometrical figures was replaced by that of their equations; finally, the use of new symbols corresponded with calculations for infinitesimal quantities, negative quantities, and imaginary numbers.
These symbols are such a powerful auxiliary to the labor of the mathematicians that those among them who affect philosophy have gladly discoursed upon their nature and intrinsic value. They seem to be divided into two camps.
One faction attribute reality to the symbols, or at least incline that way. It is the introduction of the nomina numina into mathematics. They maintain that these pretended conventions are only the expression of necessary relations which the mind is obliged, on account of their ideal nature, to represent by arbitrary signs, but which are not invented by caprice, or by the necessity of the individual mind—since this contents itself with laying hold of that which is offered by the nature of the things. Do we not see moreover that the labor accomplished by their aid is, with necessary modifications, applicable to reality?
To the other, symbols are but means, instruments, stratagems. They mock at those who “look upon relations once symbolised as things which have in themselves an à priori scientific content, as idols, which we supplicate to reveal themselves” (Renouvier). Signs, whatever they may be, are nothing more than conventions: negative quantities represent a change in the direction of thought. Imaginary numbers “represent important relations under a simple and abridged form.” Symbols are an aid in surmounting difficulties, as, empirically, the lever and its developments serve for the lifting of weights. “It is not calculation,” said Poinsot, “that is the secret of this art which teaches us to discover; but the attentive consideration of things, wherein the intellect seeks above all to form an idea of them, endeavoring by analysis properly so called to decompose them into other more simple ideas, and to review them again subsequently as if they had been formed by the union of those simpler things of which it had full knowledge.”97
In sum: numbers consist in a series of acts of intellectual apprehension, susceptible of different directions, and of almost unlimited applications. They serve for comparison, for measurement, for putting order into a variety of things. If we compare now the two extremes,—viz., the first attempt at infantine numeration and the highest numerical inventions of the mathematician,—we must recognise the notion of number to be a fine example of the complete evolution of the faculty of abstraction, as applied to a particular case, the principal stages of which we have been able to note in bringing out the ever-increasing importance of signs.
Section II. The Concept of Space
The idea of space has given rise to so many theories that it is difficult to restrain ourselves within the strict limits of psychology, and of our particular subject. Whether or no this concept be innate, given à priori or derived from our cerebral constitution, we have here—setting aside all question of origin—only to inquire by what ways and means we attain full consciousness of it and determine it to be a fundamental concept.
In order to follow its development we must necessarily set out from experience; since space, like number or time, is perceived before it is conceived. For the sake of clearness and precision, let us designate the primitive concrete data, the result of perception, as extension, and the concept, the result of abstraction, as space—properly so called.
I. At the outset what is given us by intuition is extension under a concrete form. What first becomes known to us is not space but a limited and determined extension—what the child can hold in its hand, reach by a movement of its arms, later on the room which it crosses with uncertain steps; it is a street, a square traversed, a journey made by carriage or by train, the horizon which the eye embraces, the nebulæ vaguely seen in the nocturnal sky, etc. All this is concrete and measurable, and can be reduced to a measure, i. e., to a concrete extension such as the metre and its fractions.
These different extensions, although given by the senses, and therefore concrete, are already abstract; since they co-exist with other qualities (resistance, color, cold, heat, etc.) from which a spontaneous analysis separates them, in order to consider them individually. This analysis is translated by the common terms, long, short, high, deep, near, far, to the right, to the left, in front, behind, etc.
By a simplification which occurred much later (for it implies the foundation of geometry) this somewhat confused and incoherent list is replaced by a more rational analysis: height, breadth, depth, distance, position. It marks the transition from the concrete-abstract to the abstract period. It is in fact certain that before constituting itself as a science founded upon reasoning, geometry traversed a semi-empirical stage, it was born of practical needs—the necessity of measuring fields, building houses, and the rest. Moreover certain great mathematicians have by no means disdained to admit its relations with experience: Gauss called it the “science of the eye,” and Sylvester declared “that most if not all the chief ideas of modern mathematics originated in observation.”
Let us, without insisting further, recollect that extension is given us by touch and sight. Touch is par excellence the sense of extension: thus geometry reduces the problems of equality or inequality to superpositions, and all measure of extension is finally reducible to tactile and muscular sensations. The terms touch and vision ought in fact to be completely co-extensive, representing not merely a passive impression upon the cutaneous surface, or the retina, but an active reaction of the motor elements proper to the sensorial organs.
The term acoustic space has recently come into use. Much work has been done on the semi-circular canals, leaving no doubt as to the part they play in the sense of bodily equilibrium;98 some authors have even localised a “space-sense” in them. Münsterberg relates from his personal experience that while the vestibule and the cochlea receive excitations whence result the purely qualitative sensations of sound (height, intensity, etc.), the semi-circular canals receive others which depend upon the position of the source of the sound: these excitations would produce reflexes, probably in the cerebellum, the purpose of which would be to bring the head into the position best adapted for clear audition. The synthesis of sounds, of the modifications perceived in the canals, and of the aforesaid movements (or images of movement) would constitute the elements of an acoustic space. Wundt, who opposes this theory, sees nothing more in the semi-circular canals than internal tactile organs, auxiliary to external touch.99
Leaving this hypothesis of acoustic space (which is by no means well-established), we know from numerous observations that the different modalities of tactile and visual extension, notably that of distance, are only known with precision after much groping and long apprenticeship.100
Extension under all its aspects, whether perceived or imagined, presents according to constitution, age, or circumstances, a character of variability which is in complete contrast with the stability and fixity of the concept of space. The conditions of this relativity have been exposed at length by Herbert Spencer. “A creature without eyes cannot have the same conception of space as one that has eyes; and it is the same with the congenitally blind as compared with those who are in full possession of their eyesight; and for the creature whose locomotion is rapid and powerful as compared with the creature which moves slowly and painfully.” Our bodily bulk and organic dimensions also affect conceptions of space; distances which seemed great to the boy seem moderate to the man, and buildings once thought imposing in height and mass dwindle into insignificance. Without speaking of nervous subjects, who illusively imagine their bodies enormously large or infinitely small, there are also transient and momentary states of the organism which considerably modify the consciousness of space; thus, De Quincy, describing some of his opium dreams, says that “buildings and landscapes were exhibited in proportions so vast as the bodily eye is not fitted to receive. Space swelled, and was amplified to an extent of unutterable infinity.”101 “Deliberate analysis of their movements,” says Lotze, “is so little practised by women that it can be asserted without fear of error that such expressions as ‘to the right,’ ‘to the left,’ ‘forwards,’ ‘backwards,’ etc., express in their language no mathematical relations whatever, but merely certain particular feelings which they experience when during work they perform movements in these directions.”102 In fine, the consciousness of concrete extension varies in quantity and quality with the structure, position, age, and momentary condition of the feeling subject.
II. Starting from these concrete data—extension as included in our perceptions—how does the intellect arrive at the abstract notion of space?
The immense majority of men left to their own resources do not rise above a confused notion, half-concrete, half-abstract, of the properties of extension, and what Lotze says (supra) applies even better to their total idea of space-relations. The fundamental conception in such minds is simply the possibility of going very far in all directions, or of placing a succession of bodies one behind the other. As to limit, this operation remains vaguely undetermined. It is however translated into current parlance, e. g., “bodies are in space,” and other analogues. Space is conceived, or rather imagined, as an immense sphere which encloses everything, as the receptacle of all extension. It contains bodies, as a barrel holds wine. The primitive cosmologies which yet demand a certain development of reflexion and of abstraction reveal the nature of this conception to us when they speak of the circle of the horizon, the vault of heaven, the firmament (a kind of firm enclosure), and other expressions which denote belief in an insurmountable limit. This conception, which is wholly imaginative at bottom, is a fine example of abstraction elevated into an entity, and the phantom thus created becomes in its turn the source of idle or badly-stated problems such as the following.
‘We have never,’ contends J. S. Mill, ‘perceived an object, or a portion of space, without there being space beyond it, and from the moment of our birth we have always perceived objects or parts of space. It follows from this that the idea of an object or part of space must be inseparably associated with the notion of a further space beyond it. Each moment of our life tends to rivet this association, no experience has ever interrupted it. Under the actual conditions of existence, this association is indissoluble.... Yet we can conceive that, given other conditions of existence, it might be possible to transport ourselves to the limits of space, and that after there receiving impressions of a kind totally unknown to our present state, we might instantly become capable of conceiving the fact and of stating the truth of it. After some experience of the new conception, the fact would seem as natural to us as the revelations of sight to the blind man whose cure is of long standing.’
This argument is founded upon an equivocation. Mill appears to admit as the basis of his discussion the semi-concrete, semi-abstract notion of space, described above; namely, that of common sense. Consequently he confounds and mixes up two perfectly distinct questions; that of Extension, the concrete fact perceived or imagined, and Space, abstract and conceived. In the case of the former, the problem is cosmological and objective, and we are not concerned with it; it is, under another form, the repetition of the discussion on infinite number,—are we, or are we not, to admit a continuous, real magnitude? In the latter, the problem is psychological, subjective, relative to abstraction alone, and will be answered later on.
Up to this point, in fact, the concept of Space corresponds to the state of evolution that we have so frequently denoted as concrete-abstract. The true concept of space—of purely abstract space—was only constituted when the geometricians (Greek and otherwise) disengaged from different extensions those essential features which they termed dimensions, showing by their science that elements thus abstracted and considered separately can be substituted for all the rest. Stallo justly observes that the geometrical elements are neither real, nor ideal, nor hypothetical; they are conceptual, the result of abstraction. “In the processes of discursive thought the intellect never has before it either sensible objects or the whole complement of relations which make up their mental images or representations, but only some single relation or class of relations. It operates along lines of abstraction, the final synthesis of whose result never yields anything more than outlines of the objects represented. During all its operations the intellect is fully aware that neither any one link in the chain of abstraction nor the group of abstract results which we call a concept (in the narrower sense of a collection of attributes representing an object of intuition or sensation) is a copy or an exact counterpart of the object represented. It is always conscious that to bring about true conformity between concepts or any of their constituent attributes with forms of objective reality, the group of relations embodied in these concepts would have to be supplemented with an indeterminate number of other relations which have not been apprehended and possibly are insusceptible of apprehension....”103
No one imagines that there are in Nature points, surfaces, lines, volumes, such as geometry proposes them, nor that its concepts are copies of these, but it is not therefore necessary to take refuge in the à priori: abstraction suffices, the act, i. e., by which fundamental qualities are abstracted, to be subsequently fixed by definition. It is strange that Stuart Mill in his long and untoward discussion of this subject should content himself with saying that “we have a power, when a perception is present to our senses, or a conception to our intellect, of attending to a part only of that perception or conception.”104 In this remark upon attention he is very near recognising the rôle of abstraction (which for the rest he fails to name), but instead of insisting upon it he returns to his thesis, that “the foundation of all sciences, even deductive and demonstrative sciences, is induction....”
The concept of space such as the geometers have made it, namely at its highest degree of abstraction, is thus the result of association. It is extension emptied of all its constitutive qualities, save the necessary conventions which determine it. This schema (apart from all transcendental considerations) appears to us as the total of the conditions of bodily existence in so far as they are endowed with extension. Thus constituted, with the marks which are proper to it, and distinguish it from all others, this concept, like that of number, is susceptible of multiple application, while moreover it has no assignable limits in any direction (i. e., according to the time-honored expression, it is infinite).
Just as concrete number represents real unities or collections, while abstract number detached from discontinuous realities admits of infinite numeration; so concrete space (extension) corresponds to the intuition of certain bodies, while abstract space, by an unrepresentable concept, if not by words, implies an unlimited extension.
If, hypothetically, it were possible to count all the leaves of all the trees in the world, this prodigious number corresponding to concrete unities would be as nothing to the mind that can count for ever beyond that. So for the extension determined by the movement of our arms or legs, by days of railway travelling or sailing, by balloon ascensions, and finally by the most powerful telescopes that can scrutinise the infinity of the heavens,—in all these concrete, fixed, measured extensions we can always imagine a beyond, because the end of one extension is the beginning of the next. All that, however, is but the work of the imagination manipulating abstraction. The law of construction for infinite space is the same as for infinite number: this infinity is only in the operation of our mind, it is a pure psychological process; we believe we are dealing with real magnitudes, and we are only acting upon our own judgment: we are but adding states of consciousness one upon another. Space is only potentially infinite, and this potentiality is in us, and in nothing but ourselves; it is a virtuality which can neither be exhausted nor achieved. To erect it into an entity is to reify an abstraction, to attribute an undue objective value to an entirely subjective concept. The journey to the end of space as suggested by Stuart Mill in the passage above cited (if by space he means the simple possibility of containing extended bodies) would really be a journey to the end of our minds: if he means a journey to the end of the real world, i. e., determinable and measurable extension—which has no limits beyond the imperfection of our instruments—then he admits implicitly that the universe has bounds, he takes sides in a debate in which experimental psychology (we repeat) sees nothing, and which it is even totally incompetent to decide.
During this century certain illustrious mathematicians,—Gauss, 1792, in an unpublished work, Lobachévski in 1829, Riemann, Beltrami, Helmholtz and many others after them, constructed a new geometry known under various names: astral, imaginary, pangeometric, metageometric, and lastly non-Euclidean geometry. Its fundamental principle is that our Euclidean space is only one particular case among several possible cases, and our Euclidean geometry one species of which pangeometry is the genus—that the sole determining reason in its favor is that Euclidean geometry alone is practically applicable to, and verified by, experience. These essays, beyond their direct interest to mathematicians, have already given rise to a considerable number of philosophical considerations. While they have only very distant relations with psychology, they deserve notice, because they enable us the better to understand the genesis of the concepts of space, and are moreover a striking proof of the constructive power of the mind, emancipated from experimental data, and subject only to the rules of logic.
Our space being of three dimensions, the neo-geometers speculated in the first place as to the hypothesis of a space of 4, 5, or n-dimensions; later on they chose as their base of operations a space of three dimensions, considered no longer as plane (Euclidean space) but as spherical or pseudo-spherical, having, i. e., instead of a zero curvature, either a positive (spherical space) or a negative curvature (pseudo-spherical space). Their point of departure is the rejection of Euclid’s postulate—they do not admit that it is impossible to draw through a point more than one parallel to a given straight line. In spherical space there is nothing analogous to the Euclidean axiom of parallels; in pseudo-spherical space two parallels to a line can be drawn through any point. In the first hypothesis, the sum of the three angles of a triangle is greater than two right angles; in the second it is smaller. Thus by deduction after deduction, the neo-geometers constructed an edifice very different from ordinary geometry, subject to no other conditions than that of being free from internal contradiction.
In our connexion, the sole utility of the invention of imaginary geometries is to have reinforced, as if by a magnifying process, the distinction between space perceived and conceived; this assumes various forms according to the process of abstraction employed and fixed in definitions. “Euclidean” space has only one advantage, that it is the simplest, the most practical, the best adapted to facts: in short, that which involves the least disparity between the ideal and our experience, and consequently the most useful. “Certain neo-geometers have in fact maintained that it is uncertain whether space can, or cannot, have the same properties throughout the whole universe... and that it is possible that in the rapid march of the solar system across space we might gradually pass into regions in which space has not the same properties as those we know”; yet this thesis, which, fundamentally, reifies an entity, does not seem to have gained many partisans. Stallo criticises it at length (op. cit., Chap. XIII).
There is no agreement as to the measure in which the new concepts agree or disagree with the theory of space, “the à priori form of sensibility.” Some hold them to be indifferent, others to be unfavorable to Kantism: this discussion which, for the rest, does not concern us is still in progress.
In conclusion, extension is a primary datum of perception and cannot be further reduced: it is multiple, full, heterogeneous, continuous (at least in appearance), variable, perhaps finite; while space (concept) is void, unified, homogeneous, continuous, and without limits.
Many men and races never get beyond this stage of concrete representation, which corresponds with the first moment of evolution in the individual and in the species. The first step towards the concept of space (concrete-abstract period) consists in representing it to oneself as the place, the receptacle of all bodies. This is the direct result of primitive reflexion: image rather than concept, to which the mind attributes an illusive reality.
The true concept, resultant of abstraction, has been the elaboration of geometricians. It is actually constituted by a synthesis of abstracts or extracts which are, according to Riemann, size, continuity, dimension, simplicity, distance, measure. This synthesis or association of abstracts has nothing necessary about it; its elements may be combined in several ways; hence the possibility of different concepts of space (Euclidean, non-Euclidean). Space conceived as infinity reduces itself to the power that the human mind has of forming sequences, and it forms them thanks to abstraction, which admits of its seizing the law of their formation.
Intuition is the common basis of all concepts of space. Euclidean space rests directly upon this, and upon definitions. Non-Euclidean space rests directly upon it, but more particularly upon definitions.
Although inapplicable to the real world, these last—which are constructions in which the mind is submitted to no other laws than agreement with itself—are brilliant examples of the power of abstraction, when it attains its highest degree of development.
Section III. The Concept of Time
In evolving the idea of time, as in that of space, we must first examine the concrete fact which is its starting-point, i. e., real duration; next the concept which is extracted from it, time in abstracto—and this must be followed in the successive stages of its development.
I
Real, concrete duration is a quality known by itself, included among internal and external sensations, as later on in the representations which psychology, in what concerns it, must accept as an ultimate datum.
What is this concrete duration, furnished by experience? It might strictly be said to be the present; yet this answer is somewhat theoretical, for it must be admitted that what we term “the present” has vague and fluctuating limits. Moreover, its clear and precise distinction from what has preceded and what is to follow it—the past and the future—is a somewhat late production. Of this we have objective witness (see Ch. II.) in primitive languages, during the period in which the value of the verbs was undetermined. Take again the fact, as frequently observed, that children even at the age of three, or older, having vague notions of past and future, make a general confusion, and do not distinguish between “yesterday” and last week, between “to-morrow” and next week (Sully).
Still, we must admit that the present has the privilege of appearing in consciousness as the typical duration, the standard, the measure to which everything must be referred. Nor can this be otherwise, seeing that (as is too often forgotten) we live only in the present; that the past and the future have no existence for us, are only known to us under the condition of becoming present, of occupying actual consciousness. The present is the only psychical element, which, consciously or unconsciously, gives a content and reality to duration.
It is essential to rid ourselves of the opinion accredited by many authors, that the present is only an elusive moment, a transition, a passage, a flash, a mathematical point, a zero, a nullity; on the contrary—it alone has duration, is now long, now short. It is even possible, to some extent, to determine its limits, and to transcend this vague description. Here we are aided by the labors of the psycho-physicists. We may say that this study, long restricted to metaphysical dissertations, entered upon a positive phase with Czermak, who (in 1857) opened out a new line, in which he has been followed by many others. The numerous researches and experiments made upon the “sense of time” may be omitted without prejudice to our subject, while the discussion of them would deter us from our principal aims. We must, however, give a rapid summary of those which relate either to the actual perception of duration, or to the reproduction in memory of past duration.105
1. This present, declared to be inapprehensible, has however been determined as regards its minimum duration. For the discrimination period between two different sensations (taken as the type of the briefest and simplest psychical act), Kries and Auerbach found durations varying between 0·01 and 0·07 second with an average of 0·03 second. At a later period, Exner, experimenting with Savart’s wheel, stated that the interval at which two successive taps can be perceived separately may be reduced to 0·05 second: as also for the sound produced by two electric sparks. For the eye, the minimum perceptible interval between two impressions falling on the yellow spot, is 0·044 second. Below this, one of the conditions necessary to consciousness—an adequate duration—is wanting.
Certain experiments contributed by Wundt and his pupils throw light also upon the maximum duration that can be apprehended by consciousness. They made use, almost exclusively, of auditory sensations, which are more closely allied than any others to the sense of time. Wundt finds that twelve impressions equivalent to a duration varying from 3·6 to 6 seconds can be clearly perceived to form a group. Dietze admits the continuous perception of 40 beats of the metronome, provided the mind arranges them spontaneously in 5 sub groups of 8, or 8 sub-groups of 5. Total duration: 12 seconds. Others vary in their conclusions from 6 to 12 seconds and even more.106 James is inclined to think that the actual present may extend to a minute.
Of course these figures, of which we can only give a few, vary with the subjects, quality of the impressions received, conditions of experience, exercise, etc. Nor must we forget that these laboratory researches are somewhat artificial, and concerned with the perception of “the present” under studied conditions of simplicity which are not precisely those of spontaneous consciousness. Still it is plain that “the present” is by no means an abstraction, a nothing, and we may conclude, in the words of James, “by saying that we are constantly conscious of a certain duration—the specious, present—varying in length from a few seconds to probably not more than a minute, and that this duration (with its content perceived as having one part earlier and the other part later) is the original intuition of time. Longer times are conceived by adding, shorter ones by dividing, portions of this vaguely broached unit, and are habitually thought by us symbolically.”107
2. Experiments relating, not to consciousness of actual duration, but to the reproduction of durations, and determination of the errors involved, are numerous, and contradictory. I refer to them in passing only because they are eminently suited to show the very relative and precarious character of our concrete notions of duration.
Through all divergencies, the formula enunciated by Vierordt, the principal initiator of these researches, remains stable; our consciousness of time comes, not from a sensation, but from a judgment, and in our retrospective appreciation of duration, we diminish intervals that are long, and increase those that are short. The debates and disagreements of the experimenters relate above all to the determination of the “indifferent point.” Vierordt denoted by this term the interval of time which we appreciate the most exactly, which we have no tendency to lengthen or abridge, so that if we are required to repeat it experimentally, the error is nil, or very rare. This duration, reproduced according to reality, is 0·35 sec. (according to Vierordt and Mach); 0·4 sec. (Buccola); 0·72 sec. (Wundt); 0·75 sec. (Kollert); 0·71 sec.; etc. According to another author, Glass, there is a series of points at which we find maximum relative accuracy; 1·5 sec., 2·5 sec., 3·75 sec., 5 sec., 6·25 sec., etc. Münsterberg again criticises the entire series of figures and experiments, for reasons that will be given below.
Independent of these experiments, which are restricted to very simple events, the facts of our daily life show to superabundance that our memory of duration is almost always inexact. Thus it has often been remarked that the years seem to be shorter with advancing age: which is again an instance of abbreviation of the longer intervals.108 It is hardly necessary to say that our appreciation of duration (concrete), like that of extension (concrete), depends upon multiple conditions, and varies with these. Such are pre-eminently constitution and temperament: compare a phlegmatic with a nervous individual; an Oriental for whom time is not, with an Occidental, agitated by a feverish existence. Add to these, age, number, and vivacity of impressions received, certain pathological states, etc., and we find here, as for space, that the variability of concrete knowledge is opposed to the fixity of the concept.
This consciousness of duration, fluctuating, variable, and unstable as it may be, is nevertheless the source whence our abstract notion of time is derived: but whence comes it, itself? Where does it originate? “Time has been called an act of mind, of reason, of perception, of intuition, of sense, of memory, of will, of all possible compounds and compositions to be made up from all of them. It has been deemed a General Sense accompanying all mental content in a manner similar to that conceived of pain and pleasure.”109
Here are many answers. We may add that among these supposed origins some authors admit only one, to the exclusion of the rest, though nothing justifies them in such arbitrary selection.
Some prefer external sensations, inasmuch as they give us the consciousness of a sequence. Hearing has been termed the sense of time par excellence. This thesis has notably been sustained by Mach:110 since in a melody we can separate the rhythm from the sounds which compose it, he concludes that rhythm forms a distinct sequence, and that there must be in the ear, as in the eye, a mechanism of accommodation which is perhaps the organ of the “time-sense.” Others decide in favor of the general sense, touch, capable in all animals of receiving a succession of impressions at once distinct and forming a series. Sight, with its fine and rapid perception of movements and changes, is an organ admirably adapted to the formation of relations of sequence, the constitutive elements of time. Were not, moreover, the first essays at determining time (succession of days and nights, seasons, etc.) founded upon visual perceptions?
The majority of contemporary psychologists are, however, inclined with reason to seek the principal origin of the notion of duration in internal sensations; and these derive their prerogative from the primordial and rhythmical nature which pertains to the principal functions of life.
“A stationary creature,” says Herbert Spencer, “without eyes, receiving distinct sensations from external objects only by contacts which happen at long and irregular intervals, cannot have in its consciousness any compound relations of sequence save those arising from the slow rhythm of its functions. Even in ourselves, the respiratory intervals, joined sometimes with the intervals between the heart’s pulses, furnish part of the materials from which our consciousness of duration is derived; and had we no continuous perceptions of external changes, and consequently no ideas of them, these rhythmical organic actions would obviously yield important data for our consciousness of Time: indeed, in the absence of locomotive rhythms, our sole data.”111
“Rhythm,” to quote Horwicz, “is the measure, and the sole measure, of time; a being incapable of regular periodic intervals could not attain to any conception of time. All the rhythmic functions of the body subserve this end: respiration, pulse, locomotor movements, hunger, sleep, work, habits and needs of whatever kind.”—Guyau maintains essentially the same thesis, under a more metaphysical aspect: “Time is embryonically in primitive consciousness; under the form of force and effort; succession is an abstraction of motor effort, exerted in space. The past is the active become passive.”112
More recently, Münsterberg113 has attributed a preponderant and almost exclusive part to respiration. Although he affirms that the origin of our notions of duration must be sought in our consciousness of muscular effort in general, and that its primitive measure lies in the rhythm of the bodily processes; yet the gradual rise and fall of the sense of effort which accompanies the two phases of the respiratory function (inspiration, expiration) seem to him the principal source of our appreciation of duration. After a rather sharp criticism of the attempts of his predecessors (which we have already reviewed) to determine the “indifferent point,” he maintains that their disagreements were caused by incomplete comprehension of the psychical events produced in the course of experience. In the perception of the successive beats of a metronome, or taps of Wundt’s electric hammer, only the auditory impressions are attended to; this is a mistake. It is supposed that the sensation-limits form the entire content of consciousness, and that the intervals between them are empty. On the contrary, they are filled by an act of attention. We are conscious of a process of variable tension which, from the initial moment, goes decreasingly towards zero, and then rises again, to adapt itself to the sonorous impression that should follow it. In other words, there are, in the perception of three successive taps, not three, but five states of consciousness: three external and two internal sensations. We must reckon thus if we are rigorously to determine the psychological conditions of experience. As evidence, Münsterberg brings forward the following results, which are from his own experiments.
The “normal time” is first determined, i. e., the standard of duration that should be reproduced by the experimenter as exactly as possible (“time of comparison”).
In one case, different durations were given, such as 15, 7, 22, 18 secs., etc., without attending to the respiration (expiration or inspiration) of the subject, who reacted independently of it. In the reproduction of normal time, the mean error was 10·7 per cent.
In the second case, the same numbers were given again, but care was taken that the subject began his estimation at precisely that respiratory period which coincided with the beginning of the normal time. The mean error did not now exceed 2·9 per cent.
In the two cases cited, there was no interruption between the determination of the normal time and its reproduction; the two operations succeeded each other immediately. If, on the contrary, a short pause, or arrest, was introduced between the two, varying from 1 to 60 seconds, the results are—proceeding at random as in the first case—a mean error of 24 per cent.; as in the second, a mean error of 5·3 per cent.
Münsterberg has been not unreasonably reproached for attributing to respiration, among all the other internal sensations, the exclusive privilege of measuring time. A less justifiable criticism asserts that his thesis is devoid of value because we can appreciate the variations in duration in the beats of a clock more readily than the changes in the rhythm of respiration. This is confounding two distinct factors in the genesis of the idea of duration: its period of formation and its period of constitution; that which occurs at the commencement, and that which takes place in the adult. Our measure is at first subjective, variable; progress consists in the substitution of a fixed, objective measure. Doubtless, the latter is superior in clearness and in precision; yet this is no proof, not even presumption, that it is first in order: we shall return to this point later on.
In short, our consciousness of duration is a complex state, more exactly, a process—since it is less a state than a becoming. The rhythmical visceral sensations are its core; it is an internal chronometer, fixed in the depths of our organisation. Around this subjective element, other objective elements are added and co-ordinated—the regular sequences which are caused by external sensations. They form the sheath of the core, and constitute the sensible portion of our consciousness of duration, not, however, its totality.
II
Until now we have considered time under its concrete form alone, whether given as an actual event in consciousness, or revived as a past event in memory. We have now to follow the complete development of this idea to its extreme limit. In this study we may conveniently distinguish two stages:
The first, which depends on memory and imagination, consists in thinking a certain extension of duration, that may be more or less vaguely represented: a day, a week, a year, etc.
The second, which depends on abstraction alone, gives time in general, the pure concept, which cannot be represented, and is determined by signs alone.
First Stage.—Certain minds never get beyond this first stage. In respect of time, this corresponds to the lower forms of abstraction which we have so often designated by the terms, generic image and, at a higher degree, concrete-abstract notions (intermediate abstracts).
The lowest form, which is just higher than the recognition of concrete duration, results like the generic image from the repetition of a sequence of events that recur constantly, and are approximately uniform. They are series of which the terms are variable, but which begin and end always in the same manner. Such are the appearance and disappearance of the sun, lying down to sleep and waking up again, and similar facts of common life. The points of departure, the start and finish, are always the same, whatever the variations in the intermediate states. These generic images are met with among the higher brutes, children, and primitive races.
To what extent are the higher animals capable of having a certain representation of time, constructed from their experience of real duration? This is an obscure problem which has been little studied. We are not of course referring to time in abstracto, to the concept, but to the recognition of certain often repeated cycles. Many animals are known to have an approximate appreciation of sufficiently protracted periods, supplied by the periodicity of their needs (hours at which they get food, are taken out, etc., etc.). Prejudice apart, we know of others which, in addition to this subjective physiological knowledge, possess a fairly exact notion of certain regular and objectively caused periods, determined by the progress of natural phenomena, especially by the path of the sun.114
In all these instances we may assign as cause, the incontestable preponderance (in animal life) of automatism and of routine: which is equivalent to saying that the notion of these durations is formed by a passive assimilation, and this—as we have seen—is the creative process of generic images.
According to some authors, there are instances of exact appreciation of much less simple periods. Brehm says that during a long passage an ourang-outang visited the sailors every Wednesday and Friday at 8 o’clock, because on those days sago, sugar, and cinnamon were served out, of which he got his share. An anecdote has often been cited after Romanes, of “the geese who came regularly every fortnight, from afar, the morning after the market, in a small English town, to pick up the corn scattered on the marketplace. One year the market was postponed for a day of national humiliation, but the geese came as usual.”115
These and other analogous facts seem scarcely sufficient in number, nor strictly enough observed, to warrant any scientific conclusion.
We have previously remarked that, up to the age of three years or more, children who already have an approximate knowledge of space relations, (distance, proximity, within, without, upper, lower, etc.) have a very confused notion of periods as short as three to four days, a week, etc. It has been hypothetically suggested that the extension of the notion of duration must for them arise in expectation rather than in memory, in an orientation towards the future rather than the past.
The concrete-abstract period with its different degrees, limited on the one extreme by generic images, on the other by the pure concept, is met with among savage races, and in rising civilisations. It is a stage that has to be traversed by every human race; many now existing have not got beyond it. Days (solar revolution), months (lunar revolution), and seasons, the round of the changing aspects of nature, give the primitive and simplest notions of time in extension. No tribe is so low in the scale as not to have reached this level. The determination of the (solar) year, even when only approximate, marks a decisive progress.
The peculiar feature of this period, in its lowest degrees, is that the notion of time cannot as yet be separated, or extracted, from the sequence of events. We have already given many examples of this state of intelligence. It is not poetical feeling that makes the savage reckon the age of his children by the flowering of certain plants (and other analogous locutions abound among primitive races,)—nor any innate taste for metaphor: it is merely that he requires concrete marks to determine duration. He cannot think the longer periods in abstracto; they must be imagined, represented in virtue of a more or less arbitrary choice, imprisoned in a concrete mould. Moreover, in the absence of any extended, coherent, systematic numeration, the mind loses itself after the first step. It lacks the necessary vehicle for movement in front and behind, knowing whither it is tending. The natural phenomena which it takes as its starting-point are poor substitutes for the absent sign, and moreover rivet it invincibly to the concrete.
In my opinion, the culminating point of this period is arrived at in the popular conception of time—considered as a vague entity which unrolls itself, as it gives birth to events. This is the notion that is general among most men of medium culture, who are ignorant of philosophical speculation on the subject. It is the final term of common, spontaneous reflexion, left to its own resources. Thus it is said of time that it brings the unexpected, consoles sorrow, extinguishes passion, changes tastes, solves difficulties, and the like; it seems to be an active power, a thing in itself. In fact, no other abstraction has perhaps been so often reified. We may further remark that time has often been personified and even deified in several religions. Such an honor has never been conceded to space. The cause of this difference is that time has an internal, human character: above all, that it is opposed to space as dynamic to static. It is an entity manifested in movement and change, and thereby essentially acting and living. While, in the popular conception, space is the passive receptacle of bodies, time is the active spring by which the whole is set in motion.
Second Stage.—The generic images of duration, and later, the semi-concrete, semi-schematic representation of more prolonged lapses of time, provide the material whence we obtain the purely abstract concept of time. It was stated above (p. 153) that the true concept of space was constituted on the day when the ancient geometers disengaged from the different extensions, the essential features which they termed dimensions. So must the first astronomers, without knowing or seeking for what they did, have laboriously disengaged the essential characteristics of time conceived in abstracto. First, they purified the notion of duration from all anthropomorphic features, studying it objectively, in the course of the regular phenomena of nature. Moreover, they introduced measure. The Chaldæans of Alexander’s time, who possessed a series of astronomical observations embracing a period of 1,900 years, who made an error of only two minutes in their computation of the sidereal year, who determined a cycle of 6,585 days by which they were able to calculate eclipses;116 who were later on the inventors of the clepsydra, hour-glass, and other more or less imperfect instruments for measuring the subdivisions of the day; all these counted for more than metaphysical speculation in ridding our subject of popular conceptions—or at least to a large extent prepared the way. Accustomed as we are in civilised life to a convenient and exact knowledge of the flow of time, measuring it off at any moment by clocks and watches, we forget how widely different must be the state of mind in the man whose only guides are approximations: such, e. g., as the varying height of the sun in different seasons, with other natural changes apt to be misinforming. The one life is precise, the other vague, or at least mysterious. That our measure of time (as of aught else) is relative, matters little, and the vexed problems of this subject do not concern us. By measure, the notion of time acquires a quantitative mark; it no longer appears as an entity, but as a possibility of successive events, as a divisible and subdivisible process; as an extract or abstract, set apart from the events, dissociated from them by an intellectual operation: in short—time is a thing no longer real or imaginary, but conceptual.
It is wasted labor to repeat for time what has already been said for space, and is applicable to both concepts. Time, like space and number, can be conceived as illimitable; but here again the infinity is only in our mental operation. We can add century to century, million upon million of years. This infinite time is potential only—constituted by a two-fold process: either as a sequence of numbers, which is the ordinary, simplest, and most abstract proceeding; or by filling it with fictitious events, with arbitrary constructions, for the future; by evoking the image of vanished states, when we go back to the first geological ages of our globe, to the nebulous period, and so on. This conception of infinite time is however quite subjective, and in itself reveals nothing as to the nature of things: we do but add one state of consciousness to another; it is an inexhaustible possibility of progression and retrogression; and it is nothing more.
It is a common illusion to transform this conceived infinity into a real infinity; we forget that the mind is only working upon the abstract, i. e., upon a fiction, useful no doubt, but created by ourselves alone, according to our intellectual nature.
Let us suppose that, in consequence of gradual cooling, the disappearance of the sea, or any other cause, man and all animals capable of appreciating duration were to disappear from the surface of the earth; time would disappear with them. Doubtless the earth would continue to turn round its axis, the moon round our planet, the sun to take its course; yet nothing would exist beyond the movements. Just as—if every eye were to disappear—there would be neither light nor color; if every ear failed, there would be neither sounds nor noises, but only the bare potentiality of luminous and auditory sensations if the appropriate organs were to appear again: so, on our hypothesis, there could only be a potentiality of time.
Consciousness is the necessary condition of any notion whatever of the time which appears and disappears with it.
It is no part of our subject to discuss the various theories that have been advanced as to the nature of the psychological process by which the primitive notion of time is constituted in consciousness. This question is, on the one hand, distinct from the history of its development as an abstract idea, which we have been endeavoring to follow, and, on the other, from all hypotheses as to its ultimate origin (Kant’s à priori form, Renouvier’s law of the mind, Spencer’s cerebral innateness) which explains neither its appearance as a fact, nor its genesis in experience. We may, however, complete our account by summarising the latest psychological opinions.117
It is clear that a simple sequence of impressions will not suffice to constitute the idea of time; the series must be cognised as such, felt or thought as a sequence. How is it to be cognised? Contemporary opinion upon this point appears to be capable of reduction into two principal types.
1. Some admit, as adequate conditions, sensations and their consecutive images, strong states and weak states; provided, however, that the latter arise before the former have disappeared from consciousness.
Wundt supposes that similar beats of a clock succeed each other at regular intervals in a vacant consciousness. When the first has disappeared its image remains until the second succeeds it. This reproduces the first, in virtue of the law of association by similarity, but at the same time encounters the still persisting image. Hence the simple repetition of the sound contains all the elements of time-perception. The first sound (recalled by association), gives the commencement, the second the end, and the persistent image represents the length of the interval. At the moment of the second impression, the entire perception of time exists simultaneously, since all the elements are presented together: the second sound and the image directly, and the first impression by reproduction.
“The phenomena of ‘summation of stimuli’ in the nervous system prove,” says James, “that each stimulus leaves some latent activity behind it which only gradually passes away. Psychological proof of the same fact is afforded by those ‘after-images’ which we perceive when the sensorial stimulus is gone.... With the feeling of the present thing there must at all times mingle the fading echo of all those other things which the previous few seconds have supplied. Or, to state it in neural terms, there is at every moment a cumulation of brain-processes overlapping each other, of which the fainter ones are the dying phases of processes which but shortly previous were active in a maximal degree. The amount of the overlapping determines the feeling of the duration occupied.... Why such an intuition should result from such a combination of brain-processes, I do not pretend to say. All I aim at is to state the most elemental form of the psycho-physical conjunction.” James is careful to repeat in several places that he makes no attempt at explanation.
2. Others admit sensations and intervals; sensations that are no longer images, but internal sensations of tension, of effort; more properly a subconscious element, which consciousness is able to apprehend by observation or induction. This theory has a more active character than that first discussed.
The cleanest and most complete form of this interpretation is that of Münsterberg,—as set forth above.
Fouillée supports the same thesis as a particular case of his general theory of idées-forces. The apparent present is a synthesis of real presents. Our primitive perception is of change, not of stability; we are conscious of transition. The static point of view must be completed by the dynamic.
The complete separation of present and past is a mathematical fiction. The sum of transition which is a factor in appetite aids in forming the series. Time is a form of appetite; beneath the floating image there is a tendency to movement. A non-volitional being would have no representation of time: time is a form of appetition.118
“It is probable,” says Mach, “that time sensation is connected with the organic consumption necessarily associated with consciousness,—that we feel the work of attention as time.... The fatiguing of the organ of consciousness goes on continually in waking hours, and the labor of attention increases just as continually. These sensations connected with greater expenditure of attention appear to us to happen later.”119
Others again (Waitz, Guyau, and more particularly Ward) admit temporal signs in imitation of Lotze’s “local signs.” Our successive acts of attention leave a series of residua, variable in intensity and precision; these “temporal signs” permit the conception of representations as successive, and no longer as simultaneous. “What is this distance that separates A from B, B from C, and so on?... It is probably that the residuum of which I have called a temporal sign; or, in other words, it is the movement of attention from A to B.”120
These extracts will suffice to show the character of the second theory, which seems to me the more acceptable. It is the more complete, inasmuch as it takes into consideration, not only the clear states, existing in consciousness, but the subconscious states also; it is not confined to intellectual elements alone (sensations and images), but recognises the necessary rôle of the active, motor elements.
Moreover, it seems more apt than the other to explain certain facts of current experience. It is a matter of common observation that time seems long to us, under two contrary conditions: (1) when it is very long; (2) when it is very empty. Here we have an apparent psychological contradiction. The two cases, however, are equally explained by the quantity of the states of consciousness: the first is filled with events, the second, with efforts. After three or four days of a journey fertile in incident, one seems to have left home a long time, because (in comparison with three or four days of ordinary life) the quantity of adventures held in mind, each implying a quantum of duration, appears to us in sum as an enormous duration. On the other hand, to the prisoner incarcerated in a cell, to the traveller at a deserted station waiting for a train; briefly, to all who are in the state known by the name of expectant attention, time seems to be of immeasurable extension. This is because there is a constant expenditure of effort, a tension incessantly renewed, incessantly frustrated; consciousness is nearly void of representations, while it is filled with acts of attention constantly repeated. This instance of time prolonged, while apparently empty, is difficult to explain, if only the intellectual elements are taken into consideration, omitting the consciousness of motor states. It should be noticed that “full” time seems longer in the past; “empty” time, in the present and immediate past; perhaps because the former rests principally upon intellectual memory, which is stable; the latter, upon motor memory, which is vague and fragile.
Section IV. Concept of Cause
The idea of cause has for centuries been the subject of so many speculations, that our first care must be to confine ourselves scrupulously to our subject, i. e., to retrace its evolution simply, marking the principal phases of its development in the individual and the species, while as far as possible eliminating whatever lies outside this one question.
It has been remarked that the word cause signifies sometimes an antecedent, sometimes a process, sometimes antecedent, process, and effect produced, taken all three together.121 This last sense alone is complete. For, if the primitive, popular conception tends to restrict the cause to the antecedent, to that which acts, a little reflexion will show us that the cause is only determined as such by its effect, that the two terms are correlative, the one not existing without the other. Finally, with more profound reflexion, the process itself, the transition, the passage, the nexus between antecedent and consequent, appears as the vital point, the proprium quid of causality. As psychical fact, as state of consciousness, therefore, this notion is complex, and among the elements which compose it, now one and now the other, according to the epoch, has been considered the most important.
In what follows, we shall have to consider: I. the origin of the idea of cause in experience; II. its generalisation, and passage from the individual subjective, to the objective form; III. its transformation as resulting from the work performed in the various sciences, its scission into two fundamental ideas: on the one hand, that of force, energy, active and effective power, cause in the true sense (vera causa), which tends more and more to become a postulate, an x, a metaphysical residuum; on the other, that of a constant and invariable succession, a fixed relation, which becomes the scientific form of the concept of cause, equivalent in all respects to the concept of law.
I. Every one seems agreed, fundamentally at least, upon the empirical origin of the idea of cause. It is of internal, subjective origin; suggested to us by our motor activity. A being who was hypothetically perfectly passive, while seeing or feeling constant external sequences, would have no idea of causality. It would be superfluous to show, by multiplying our quotations, that spiritualists like Maine de Biran, empiricists like Mill, critics like Renouvier, all the schools in short, with varying formulæ, agree upon this point. At the same time it must not be overlooked that some writers attribute an exclusive privilege to the “will,” maintaining it to be the type of causality; whereas the assertion that “our own voluntary action is the exclusive source whence this idea is derived” is unjustifiable. If, with some authors, the word “will” is used in a large and vague sense, as designating all mental activity that is translated by movements, no objection can be raised. But if it be used in the proper, restricted sense, as meaning a fully conscious, deliberate act, resulting from motive, the statement cannot be accepted.122 Volition is a state that makes its appearance somewhat tardily. It is preceded by a period of appetites, of needs, instincts, desires, passions; and all these facts of internal activity, translated into movements; are as apt as the “will” to engender the empirical notion of cause, i. e., transitive action, i. e., change produced: they have moreover the advantage of being anterior in chronological order.
Contemporary psychology has studied the rôle of movements, far more than any of its predecessors. It attributes to them a capital importance; it shows that motor elements are included in every intellectual state without exception, in percepts, in images, and even in concepts. Hence it feels no repugnance in accepting the common thesis. We must however remember that the psychology of motion is centred in the consciousness of muscular effort, which moreover represents the type of primitive causality. The nature of this sense of effort has given rise to long and animated debate. For some, it is of central origin: It is anterior to, or at least concomitant with, the movement produced; it goes from within outwards—it is efferent. For others, it is of peripheral origin, posterior to the movement produced; it goes from without, inwards—is afferent. It is an aggregate of the sensations coming from the articulations, tendons, muscles, from the rhythm of respiration, etc.: so that the sense of effort is no more than the consciousness of energy that has been expended, of movements that have been effectuated: it is a resultant. This second theory, without so far being decisively and incontestably established, is daily gaining more adherents, and remains the most probable. So that, since consciousness of effort is essentially that of effect produced, it follows that in considering the act as the source of the idea of cause, we know much less of antecedent than of consequent. Yet this consciousness of effort produced is not the whole, whatever people may say, of what is in the primitive conception of a proper, personal causality. Something more remains: this is the confused idea, illusory or not, of a creation that proceeds from us. We shall return to this point.
To conclude: at the outset, the two terms antecedent and consequent, form almost the exclusive elements in the notion of cause. At any rate, they preponderate in consciousness, to the exclusion of the third, relation. The idea of a constant invariable sequence, which was, later on, to be the intrinsic mark of the causal process, cannot yet be distinguished.
II. The idea of cause—at first strictly individual—soon commences its movement of extension.
1. During the first period, this extension is the work of the imagination, rather than of generalisation properly so called. By an instinctive tendency, well-known, though not explained, man concludes for intentions, a will, and a causality analogous to his own, in the medium that acts and reacts around him: his fellows, all living things, and whatever else by their movements simulate life (clouds, rivers, etc.). This is the period of primitive fetishism that is fixed in mythologies and languages. It may actually be observed in children, in savage races, in brutes (as in the dog that bites the stone by which it is hit), even in rational man, when—becoming again for the moment a creature of instinct—he falls into a passion at the table that has hurt him.
This period corresponds fairly well with that of generic images, because the idea of cause thus generalised results from gross, external, partial, accidental resemblances, which the mind perceives almost passively. It cannot be doubted that the higher brutes have a generic image of causality; i. e., they are capable—given an antecedent—of invariably representing to themselves the consequence. This mental state, which has been termed “empirical consecution,” and which is not infrequent even among men who may never rise beyond it, resolves itself into a permanent association of ideas, the result of repetition and of habit.123
All this, however, is merely an external conception of causality, of its form, and not its nature; it is an outside view, an approximation. The proper characteristic of this period is that it remains subjective, anthropomorphic, representing cause as an intentional activity, which produces movements only in view of an end.
2. The second period begins with philosophic reflection, and proceeds by the slow constitution of the sciences. Its development may thus be summarised: little by little it deprives the notion of cause of its subjective, human character, without however completely attaining this ideal end; it reduces the essentials of the concept to a fixed, constant, and invariable relation between a determined antecedent and consequent; hence it sees in cause and effect only the two moments, or aspects of one and the same process, which is fundamentally the affirmation of an identity.
Here imagination recedes, to make way for abstraction and generalisation,—for abstraction since it is less a question of terms than of a certain relation between the terms, for generalisation because the natural tendency of the mind is to extend causality to the whole of experience.
It must, however, be remarked that the transition from particular cases to generalisation, and finally to the universalisation of the concept of cause, in a strict sense, has only been effected little by little. An opinion that has gained much credit, on the authority of the apriorists, is that every man has an intuitive, innate idea of the law of causality, as universal. This thesis is equivocal. If it means that all change suggests to every normal man who witnesses it an invincible belief in a known or unknown agent of its production, then the assertion is incontestable: but this, as we have seen, is only the popular, practical, and external notion of causality. If the true concept (that of the solidly constituted sciences), which is reducible to an inflexible, invariable determination, is implied, then it is a fallacy to pretend that the human mind acquired it at the outset. The belief in a universal law of causality is no gratuitous gift of nature: it is a conquest. The fallacy persists, because for at least three centuries this idea has been propagated by the writings of philosophers and scientists who have made it familiar enough. None the less, it is a late conception, unknown to the great mass of the human species. Scientific research began by establishing laws, (i. e., invariable relations of cause and effect) between certain groups of phenomena, began by establishing a law of causality that was valid for these and these only; and the transfer of this law to all that is known and unknown has only been effected little by little, and is even yet incomplete. In a word, the law of universal causality is the generalisation of particular laws, and remains a postulate.
In support of the above (without entering into historical detail) we may note the existence in human consciousness of two ideas, which from time to time, each after its own fashion, give check to the universality of the principle. Although, from the development of scientific thought, their influence has been a decreasing factor, they are still very active. These two ideas are those of miracle and chance.
Miracle, taking this word not in the restricted, religious sense, but in its etymological acceptance (mirari), is a rare and unexpected event, produced extrinsically to, or against, the ordinary course of events. The miracle gives no denial to cause, in the popular sense, because it assumes an antecedent: God, an unknown power. It does deny it, in the scientific sense, since it is an abrogation of determinism among phenomena. Miracle is cause without law. Now, for a long period, no belief could have appeared more natural. In the physical world, the appearance of a comet, eclipses, and many other things were regarded as prodigies and warnings. Many races are still imbued with weird fancies on this subject (monsters that would swallow up the sun or moon, etc.), and even among civilised men these phenomena produce in many minds a certain uneasiness. In the biological world, this belief has been much more tenacious: enlightened spirits in the seventeenth century still admitted the errores or lusus naturæ, held the birth of monstrosities to be a bad augury, and so on. In the psychological world it has been even worse. Not to speak of the widely-spread (and not yet extinct) prejudices of antiquity as to prophetic dreams, auguries of the future; of the mystery which so long surrounded natural or induced somnambulism, and analogous contemporary speculations on the occult sciences; of those who regard liberty as an absolute beginning, etc.: there is, even in the limited circle of scientific psychology, so little well-determined relation between cause and effect, that the partisans of contingency may comfortably imagine anything. Useless to insist upon sociology. We need only recall the fact that Utopians abound who, while rejecting miracle in the religious order, admit it freely in the social; believing all to be possible, and reconstructing human society from top to bottom according to their dreams. If, finally, we consider that this very dry and incomplete enumeration covers millions of cases, past and present, we must recognise that the human mind in its spontaneous and self-governed progress, experiences no reluctance to admit causes without law.
The idea of chance is more obscure. We might almost say that, for the majority of people who make no attempt to clear it up, it is an event that supposes neither cause nor law; it is sheer indetermination, a cast of the die arriving no one knows how, by means of no one knows what. It is very evident that chance excludes neither cause nor law, but evident to those alone who have reflected upon its nature, and have analysed the notion. To others, it is a mysterious, impenetrable entity, a Tyche whose acts cannot be foreseen. Hume says that “chance is only our ignorance of true causes.” Cournot rightly observes that this is incorrect, that chance involves something real and positive: the conjunction, the crossing of several sequences of cause and effect, which are independent of one another by origin, and not naturally intended to exert any reciprocal influence. Thus one series of causes and effects lead a traveller to take a particular train: on the other hand a totally distinct set produces at a given place or time an accident which kills the man.124 There is, in short, in chance, no contravention of the laws of universal mechanism. Why then does it seem to the vulgar mind to be an exception, indeterminate by nature? First, because the problem set by the unexpected is insufficiently analysed; but also in my opinion, because the primitive idea of cause is nearly always that of a single antecedent, whereas here the unique antecedent is not present, and cannot be discovered. The conception of a complex causation, constituted by a sum of concurrent conditions, of equal necessity, is the fruit of advanced reflexion.
Accordingly, while the man who is formed by scientific discipline refuses when confronted with these so-called prodigious or fortuitous facts, to concede that they are exceptions to the law of universal causality, others are quite ready to admit that the wall that surrounds phenomena may give way at certain points, with resulting breaches.
From the point of view of pure psychology, it is impossible not to affirm that the idea of universal causality, of uniformity in the course of nature, of rigorous determinism (and other analogous formulæ), is acquired—superposed. Whether this notion be applicable to the whole of experience, although experience is not yet exhausted, or whether it is simply a guide to research, a stratagem for introducing order into things, is a question which psychology has no capacity for discussing, still less power to resolve.
III. We return to the work of transformation, which, starting with the notion of cause as it is given in experience—i. e., a force, a power, that acts and produces—culminates finally in its last term, the law of causality.
Just as the plurality of objects perceived in nature, forms the material of the concept of number; as the diverse durations present in our consciousness are the material of the concept of time; so our consciousness of acting, of modifying our self and our environment (a power which we attribute freely to everything that surrounds us) is the prime material of the concept of cause. But in order that this concept may be constituted as such—fixed and determined—a work of abstraction is needed to isolate and bring into relief its distinctive, essential characteristic from among all the different elements that compose the primitive and complex notion of empirical cause (antecedent, consequent, action or reaction, change, transformation, etc.). This distinctive characteristic is an invariable relation of sequence (the conditions being supposed the same); and the establishment of it has been, almost exclusively, the result of scientific research.
A history of the secular fluctuations in the idea of cause, as affected by the various philosophical theories and changes of method in the sciences, would be the best review of the phases of its evolution. Impossible here to attempt such a task. We may only note the two extreme points: the speculations of antiquity, and the contemporaneous aspect of the question.125
The ancient philosophers who (at least during the great eras) were at once metaphysicians and scientists, constructed systems of cosmogony and assumed “first causes,” which were conceived either as forces, principles of action, motive elements of nature (water, air, fire, atoms), or as rational types (numbers, ideas). On the other hand they invented mathematics, and laid the foundations of astronomy and physics. Now, as regards causality, these essays at the scientific investigation of nature involved consequences which were not plainly disclosed until a much later period. They exacted another position,—a passage from subjective to objective: whether in relation to the fall of bodies, or to a law of hydrostatics (such as that to which Archimedes gave his name), any one who studies the physical world necessarily sees its changes from without. He considers cause no longer as an internal factor revealed by consciousness, but as a sequence given by the senses. Antecedents, consequents, invariable succession, are for him the only useful data. Conditions equal cause; and the important determination is that not of an operating entity, but of a constant relation. This—the only scientific conception of cause—it is which is covered by Stuart Mill’s definition: “Cause is the sum of the positive and negative conditions, which, when given, are followed by an invariable consequent.”
This external aspect, old as science itself, was big with consequences that have only been clearly revealed in our own day, and which may be summed up in a word as identity of cause and effect. There is no separation between the two; the antecedent is not one thing and the consequent another; they are two manifestations, different in time, of a fundamental unity. It has rightly been observed that the mechanical theory of the universe (correlation of forces, conservation and transformation of energy, etc.) is the contemporaneous form of the concept of natural causality. Expressed from earliest antiquity in the form of a metaphysical anticipation (ex nihilo nihil), it enters in the seventeenth century upon its scientific phase, and is completed in our own day. The physicists who have established it upon experience and by calculation, saw plainly the consequences it involved. To cite only one instance, R. Mayer in his Mechanik der Wärme says, “If the cause c produces the effect e, then c = e; if e is the cause of another effect f, then e = f, and so on. Since c becomes e, e = f, etc., we must consider these magnitudes as the different phenomenal forms of one and the same object. Just as the first property of cause is its indestructibility, so the second property is convertibility, i. e., capacity for assuming different forms. And this capacity must not be regarded as a metamorphosis; each cause is invariable, but the combination of its relations is variable. There is quantitative indestructibility and qualitative convertibility.”
It must not be forgotten that the general principles of thermodynamics—the latest form of the concept of natural causality—are not absolute, but are proposed as ideal. We know, e. g., that heat can never give rise again to all the work from which it was produced, that no physical event is exactly reversible, i. e. it cannot be reproduced identically at the opposite end of the process, because in its first appearance it had to overcome resistance, and thus lost part of its energy. All this, however, is outside our scope. As much as the doctrine of the conservation of energy is valid, so much is the actual concept of natural causality worth. We merely undertook to follow the evolution of this concept down to the present day, to point out its transformations, without in any way prejudging the future, or still less attributing to it any absolute value.126
What now becomes of the idea of causality taken in the other sense, no longer as an invariable relation of antecedent to consequent, but as a thing that acts, creates, modifies, or persists under all transformations and clothes all masks? The scientific method, as soon as it penetrates into any order of phenomena, tends to exclude cause, to reduce it to the strictest limits, to make the least possible use of it. Cause then becomes the synonym of force. But physical science defines force only by its effects:—movement, or work done. So, too, the biologist rejects the notion of “vital force”; non-metaphysical psychology will have none of the “faculties,” intervention of “the soul,” and the like. Is the notion thus discarded, totally suppressed? Nay,—for even in mechanics and physics it cannot be entirely eliminated. It is there as a postulate, a residuum, an unknown factor covering lacunæ. Yet, do what we will, force or energy, in order to be more than an empty word and to become intelligible, can only be represented and imagined under the form of the muscular effort whence it originates, and which is its type; and despite all the elaborations to which it is submitted in order to rid it of its anthropomorphical character, and dehumanise it, it remains rather a fact of internal experience than a concept. Is it destined to undergo other transformations, by reason of more profound apprehension, or some new aspect of the problem? Is there—along with mechanical causality and rigorous determinism—room for any other mode of causality, proper to psychology, to linguistics, to history, in short to the positive sciences of the mind, as is maintained by Wundt and others? The secret remains for the future.
The natural tendency of the mind (which is but one aspect of the instinct of conservation) to seek and investigate in face of the unknown and unexpected, its clear or confused need of explanation for better or worse, at the outset concluded for an acting entity. The idea still survives under a naïve or transcendental form; it reappears in every unexplained contingency, whether in regard to the first origin of things, or (for the partisans of liberty) to freedom of action. In this sense, “causality is an altar to the Unknown God, an empty pedestal that awaits its statue.”127
In its other sense, which is widely different and even contrary, which has been slowly fixed, and more slowly extended to the whole of experience, cause is a true concept: the resultant namely of abstraction, summarised in the characters exclusively proper to it. Under this form it is equivalent to the concept of law.
Section V. Concept of Law
Our general ideas, from those immediately bordering on the concrete to those which attain pure symbolism, constitute a hierarchy of ever-increasing simplicity. What value must be assigned to this thinking by concepts, in proportion as it ascends higher in the scale? We are all familiar with the debates upon this question, bearing, as it does, fundamentally upon the objective value of abstraction and generalisation. Psychology, as the science of facts, is able to ignore this point, since it is concerned only with the nature of the two intellectual processes, their variations, and adaptations to multiple cases. Still, it is reasonable enough that it should assume a position, at any rate provisionally, and for convenience of discussion.
To recall only the two extreme opinions: On the one side we have those who maintain that the particular alone exists—for event or individual—that our general ideas are but a means of maintaining order, while they teach us nothing as to the nature of things. They are comparable to a catalogue, or to the card-index of a library which are an easy indicator to the millions of books, leaving us totally ignorant as to their contents and value. Hence, the higher we ascend, the farther we penetrate into the region of the fictitious and the vacant.
On the other hand, there are those who assert that nature has general and fixed characteristics; in discovering them, we penetrate into the essence of things. Events and individuals have but a borrowed existence; under their fleeting appearances, we must seek the enduring; and thus, the greater the generalisation, the higher we rise in reality and in dignity.
The psychologist can only take up the position of relativity. To him, general ideas are approximations: they have an objective value, but it is provisional and momentary, dependent on the variability of phenomena and on the state of our knowledge.
On the one hand, the similarities that are the substrata of generalisation are not fictitious. Since, moreover, knowledge of the laws of nature has a practical value, by enabling us to act upon things, and since we fail, in ignorance of them,—we are fain, objections notwithstanding, to attribute to them at least a certain measure of objective value.
On the other, if there is evolution in nature, there must also be evolution in our ideas, and the pretension to laws or types that are fixed unalterably, becomes chimerical. There is no longer the sharp distinction, as formerly admitted, between “essential” and “accidental,” i. e., permanent and variable characters. The Primary epoch of our globe may have obeyed laws which no longer hold for our Quaternary age: all changes in the course of development. We shall return to this point in the concluding section.
Without insisting further upon a debate that is of secondary interest for the psychologist, we may remark that three principal periods can be distinguished in the development of the Concept of Law: viz., the periods of generic images, of concrete or empirical laws, and of theoretical or ideal laws.
It is useless to study the first phase in detail, since it interests us only as an embryonic form, a germ, or essay. It consists in the mechanical conception of regularity for a very restricted number of events. Resulting from the constant or frequent repetition of certain cycles (the course of the sun, moon, seasons, etc.) it is organised in the mind by a process of semi-passive assimilation, that of generic images. Many men have had, and still have, only this shadow, this simulacrum of law, resting upon pure association, upon practical habit, upon the unreflecting expectation of an often-perceived recurrence. Humble as it is, this notion was nevertheless useful in the education of humanity, for it checked the exuberant tendency of the imagination to people the world with capricious causes, obedient to no law. It prevented the establishment of a rule of universal contingency; it was the first affirmation of a faith in regular order. The progress of reflexion, and methodical research, have done the rest.
We owe to Wundt (Philosophische Studien, 1886, III., p. 195 et seq.) an observation of great interest to any one concerned in the development of the idea of law. To-day this word is current in all the sciences; indeed its most rigorous acceptance is in mathematics and chemical physics. This was not always the case. In antiquity, the word was employed almost exclusively in a social, juristic, moral sense. The concept of natural law, regarded as a sort of order, a police-force, was only very slowly formed and established. Copernicus and Kepler employed the word “hypothesis.” Galileo calls the fundamental laws of nature “axioms,” and those derived from them “theorems,” following the terminology of the mathematicians. Descartes begins his Philosophy of Nature by laying down certain Regulæ sive leges naturales. Newton says: Axiomata sive leges motus. The extension of the word law is due apparently to the need of establishing a clear distinction between the purely abstract axioms of mathematics, and the principles to which we attribute an objective value, an existence in nature. Montesquieu’s celebrated definition, “Laws are the necessary relations derived from the nature of things,” exhibits this concept in its highest degree of generalisation. We may note, in passing, that in the enquiry referred to above (ch. IV.), nearly all the answers indicate that images of the social juristic order were evoked, although the scientific acceptance of the word was perfectly familiar to a large number of the subjects: showing that the primitive signification preponderates in the vulgar conscience.
In another article, entitled Wer ist der Gesetzgeber der Naturgesetze? (loc. cit., pp. 493 et seq.), the same author maintains an opinion, which, notwithstanding its paradoxical appearance, seems to me perfectly valid. Descartes called the laws of nature “rules,” inasmuch as they explain phenomena to us; “laws,” inasmuch as God constituted them ab initio as properties of matter. At a later period, nature takes the place of God, which is still the survival of a pantheistic conception of the world. Still later, the preponderating tendency is to call laws by the names of their inventors: Mariotte, Gay-Lussac, Dulong and Petit, Avogadro, Ohm, Weber, etc. “In the seventeenth century it was God who established the laws of nature; in the eighteenth it was Nature herself; in the nineteenth it is the affair of the scientists.” This thesis agrees with what was said above, of the approximate character of laws, of the mixture of objective and subjective elements that obtain in their formulæ, and it is no paradox to assert that the state of mind of a Mariotte, a Gay-Lussac, a Weber, etc., when they discover their law, represents this approximation at a given moment.
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.