PART II.
LAWS OF THE KNOWABLE
CHAPTER I.
LAWS IN GENERAL
§ 35. We have seen that intellectual advance has been dual – has been towards the establishment of both a positively unknown and a positively known. In making ever more certain the inaccessibility of one kind of truth, experience has made ever more certain the accessibility of another kind. The differentiation of the knowable from the unknowable, is shown as much in the reduction of the one to perfect clearness, as in the reduction of the other to impenetrable mystery. Progressing enlightenment discloses a definite limit to human intelligence; and while all which lies on the other side of the limit, is, with increasing distinctness, seen to transcend our finite faculties, it grows more and more obvious that all which lies on this side of the limit may become an indisputable possession.
To speak specifically – it has been shown that though we can never learn the nature of that which is manifested to us, we are daily learning more completely the order of its manifestations. We are conscious of effects produced in us by something separate from ourselves. The effects of which we are conscious – the changes of consciousness which make up our mental life, we ascribe to the forces of an external world. The intrinsic character of these forces – of this external world – of that which underlies all appearances, we find inscrutable; as is also the internal something whose changes constitute consciousness, but at the same time we find that among the changes of consciousness thus produced, there exist various constant relations; and we have no choice but to ascribe constancy to the relations which subsist among the inscrutable causes of these changes. Observation early discloses certain invariable connexions of coexistence and sequence among phenomena. Accumulating experiences tend continually to augment the number of invariable connexions recognized. When, as in the later stages of civilization, there arises not only a diligent gathering together of experiences but a critical comparison of them, more remote and complex connexions are added to the list. And gradually there grows up the habit of regarding these uniformities of relation as characterizing all manifestations of the Unknowable. Under the endless variety and seeming irregularity, there is ever more clearly discerned that “constant course of procedure” which we call Law.
The growing belief in the universality of Law, is so conspicuous to all cultivated minds as scarcely to need illustration. None who read these pages will ask for proof that this has been the central element of intellectual progress. But though the fact is sufficiently familiar, the philosophy of the fact is not so; and it will be desirable now to consider it. Partly because the development of our conception of Law will so be rendered more comprehensible; but chiefly because our subsequent course will thus be facilitated; I propose here to enumerate the several conditions that determine the order in which the various relations among phenomena are discovered. Seeing, as we shall, the consequent necessity of this order; and enabled, as we shall also be, to estimate the future by inference from the past; we shall perceive how inevitable is our advance towards the ultimatum that has been indicated.
§ 36. The recognition of Law, being the recognition of uniformity of relations among phenomena, it follows that the order in which different groups of phenomena are reduced to law, must depend on the frequency and distinctness with which the uniform relations they severally present, are experienced. At any given stage of progress, those uniformities will be most recognized with which men’s minds have been oftenest and most strongly impressed. In proportion partly to the number of times a relation has been presented to consciousness (not merely to the senses); and in proportion partly to the vividness with which the terms of the relation have been cognized; will be the degree in which the constancy of connexion is perceived.
The frequency and impressiveness with which different classes of relations are repeated in conscious experience, thus primarily determining the succession in which they are generalized, there result certain derivative principles to which this succession must more immediately and obviously conform. First in importance comes the directness with which personal welfare is affected. While, among surrounding things, many do not appreciably influence the body in any way, some act detrimentally and some beneficially, in various degrees; and manifestly, those things whose actions on the organism are most influential, will, cæteris paribus, be those whose laws of action are earliest observed. Second in order, is the conspicuousness of one or both the phenomena between which a relation is to be perceived. On every side are countless phenomena so concealed as to be detected only by close observation; others not obtrusive enough to attract notice; others which moderately solicit the attention; others so imposing or vivid as to force themselves upon consciousness; and supposing incidental conditions to be the same, these last will of course be among the first to have their relations generalized. In the third place, we have the absolute frequency with which the relations occur. There are coexistences and sequences of all degrees of commonness, from those which are ever present to those which are extremely rare; and it is clear that the rare coexistences and sequences, as well as the sequences which are very long in taking place, will not be reduced to law so soon as those which are familiar and rapid. Fourthly has to be added the relative frequency of occurrence. Many events and appearances are more or less limited to times and places; and as a relation which does not exist within the environment of an observer, cannot be cognized by him, however common it may be elsewhere or in another age, we have to take account of the surrounding physical circumstances, as well as the state of society, of the arts, and of the sciences – all of which affect the frequency with which certain groups of facts are exposed to observation. The fifth corollary to be noticed, is, that the succession in which different classes of phenomena are reduced to law, depends in part on their simplicity. Phenomena presenting great composition of causes or conditions, have their essential relations so masked, that it requires accumulated experiences to impress upon consciousness the true connexion of antecedents and consequents they involve. Hence, other things equal, the progress of generalization will be from the simple to the complex; and this it is which M. Comte has wrongly asserted to be the sole regulative principle of the progress. Sixth, and last, comes the degree of abstractness. Concrete relations are the earliest acquisitions. The colligation of any group of these into a general relation, which is the first step in abstraction, necessarily comes later than the discovery of the relations colligated. The union of a number of these lowest generalizations into a higher and more abstract generalization, is necessarily subsequent to the formation of such lowest generalizations. And so on continually, until the highest and most abstract generalizations have been reached.
These then are the several derivative principles. The frequency and vividness with which uniform relations are repeated in conscious experience, determining the recognition of their uniformity; and this frequency and vividness depending on the above conditions; it follows that the order in which different classes of facts are generalized, must depend on the extent to which the above conditions are fulfilled in each class. Let us mark how the facts harmonize with this conclusion: taking first a few that elucidate the general truth, and afterwards some that are illustrative of the several special truths which we here see follow from it.
§ 37. The relations earliest known as uniformities, are those subsisting between the common physical properties of matter – tangibility, visibility, cohesion, weight &c. We have no trace of an era in human history when the resistance offered by every visible object, was regarded as caused by the will of the object; or when the pressure of a body on the hand supporting it, was ascribed to the direct agency of a living being. And accordingly, we see that these are the relations oftenest repeated in consciousness; being as they are, objectively frequent, conspicuous, simple, concrete, and of immediate personal concern.
Similarly with respect to the ordinary phenomena of motion. The fall of a mass on the withdrawal of its support, is a sequence which directly affects bodily welfare, is conspicuous, simple, concrete, and very often repeated. Hence it is one of the uniformities recognized before the dawn of tradition. We know of no time when movements due to terrestrial gravitation were attributed to volition. Only when the relation is obscured – only, as in the case of an aerolite, where the antecedent of the descent is unperceived, do we find the fetishistic conception persistent. On the other hand, motions of intrinsically the same order as that of a falling stone – those of the heavenly bodies – long remain ungeneralized; and until their uniformity is seen, are construed as results of will. This difference is clearly not dependent on comparative complexity or abstractness; since the motion of a planet in an ellipse, is as simple and concrete a phenomenon as the motion of a projected arrow in a parabola. But the antecedents are not conspicuous; the sequences are of long duration; and they are infrequently repeated. Hence in a given period, there cannot be the same multiplied experiences of them. And that this is the chief cause of their slow reduction to law, we see in the fact that they are severally generalized in the order of their frequency and conspicuousness – the moon’s monthly cycle, the sun’s annual change, the periods of the inferior planets, the periods of the superior planets.
While astronomical sequences were still ascribed to volition, certain terrestrial sequences of a different kind, but some of them equally without complication, were interpreted in like manner. The solidification of water at a low temperature, is a phenomenon that is simple, concrete, and of much personal concern. But it is neither so frequent as those which we saw are earliest generalized, nor is the presence of the antecedent so uniformly conspicuous. Though in all but tropical climates, mid-winter displays the relation between cold and freezing with tolerable constancy; yet, during the spring and autumn, the occasional appearance of ice in the mornings has no very manifest connexion with coldness of the weather. Sensation being so inaccurate a measure, it is not possible for the savage to experience the definite relation between a temperature of 32° and the congealing of water; and hence the long-continued conception of personal agency. Similarly, but still more clearly, with the winds. The absence of regularity and the inconspicuousness of the antecedents, allowed the mythological explanation to survive for a great period.
During the era in which the uniformity of many quite simple inorganic relations was still unrecognized, certain classes of organic relations, intrinsically very complex and special, were generalized. The constant coexistence of feathers and a beak, of four legs with a bony internal framework, of a particular leaf with poisonous berries, are facts which were, and are, familiar to every savage. Did a savage find a bird with teeth, or a mammal clothed with feathers, he would be as much surprised as an instructed naturalist; and would probably make a fetish of the anomalous form: so showing that while the exceptional relation suggested the notion of a personal cause, the habitual relation did not. Now these uniformities of organic structure which are so early perceived, are of exactly the same class as those more numerous ones later established by biology. The constant coexistence of mammary glands with two occipital condyles in the skull, of vertebræ with teeth lodged in sockets, of frontal horns with the habit of rumination, are generalizations as purely empirical as those known to the aboriginal hunter. The vegetal physiologist cannot in the least understand the complex relation between the kind of leaf and the kind of fruit borne by a particular plant: he knows these and like connexions simply in the same manner that the barbarian knows them. But the fact that sundry of the uniform relations which chiefly make up the organic sciences, were very early recognized, is due to the high degree of vividness and frequency with which they were presented to consciousness. Though the connexion between the form of a given creature and the sound it makes, or the quality of its fur, or the nature of its flesh, is extremely involved; yet the two terms of the relation are conspicuous; are usually observed in close juxtaposition in time and space; are so observed perhaps daily, or many times a day; and above all a knowledge of their connexion has a direct and obvious bearing on personal welfare. Meanwhile, we see that innumerable other relations of exactly the same order, which are displayed with even greater frequency by surrounding plants and animals, remain for thousands of years unrecognized, if they are unobtrusive or of no apparent moment.
When, passing from this primitive stage to a more advanced stage, we trace the discovery of those less familiar uniformities which constitute what is technically distinguished as Science, we find the order of discovery to be still determined in the same manner. We shall most clearly see this in contemplating separately the influence of each derivative condition; as was proposed in the last section.
§ 38. How relations that have an immediate bearing on the maintenance of life, are, other things equal, necessarily fixed in the mind before those which have no such immediate bearing, is abundantly illustrated in the history of Science. The habits of existing uncivilized races, who fix times by moons and barter so many of one article for so many of another, show us that numeration, which is the germ of mathematical science, commenced under the immediate pressure of personal wants; and it can scarcely be doubted that those laws of numerical relations which are embodied in the rules of arithmetic, were first brought to light through the practice of mercantile exchange. Similarly with Geometry. The derivation shows us that it originally included only certain methods of partitioning ground and laying out buildings. The properties of the scales and the lever, involving the first principle in mechanics, were early generalized under the stimulus of commercial and architectural needs. To fix the times of religious festivals and agricultural operations, were the motives which led to the establishment of the simpler astronomic periods. Such small knowledge of chemical relations as was involved in ancient metallurgy, was manifestly obtained in seeking how to improve tools and weapons. In the alchemy of later times, we see how greatly an intense hope of private benefit contributed to the disclosure of a certain class of uniformities. Nor is our own age barren of illustrations. “Here,” says Humboldt when in Guiana, “as in many parts of Europe, the sciences are thought worthy to occupy the mind, only so far as they confer some immediate and practical benefit on society.” “How is it possible to believe,” said a missionary to him, “that you have left your country to come and be devoured by mosquitoes on this river, and to measure lands that are not your own.” Our coasts furnish like instances. Every sea-side naturalist knows how great is the contempt with which fishermen regard the collection of objects for the microscope or aquarium: their incredulity as to the possible value of such things, being so great, that they can scarcely be induced even by bribes to preserve the refuse of their nets. Nay, we need not go for evidence beyond daily table-talk. The demand for “practical science” – for a knowledge that can be brought to bear on the business of life; joined to the ridicule commonly vented on pursuits that have no obvious use; suffice to show that the order in which different coexistences and sequences are discovered, greatly depends on the directness with which they affect our welfare.
That, when all other conditions are the same, obtrusive relations will be generalized before unobtrusive ones, is so nearly a truism that examples appear almost superfluous. If it be admitted that by the aboriginal man, as by the child, the co-existent properties of large surrounding objects are noticed before those of minute objects; and that the external relations which bodies present are generalized before their internal ones; it must be admitted that in all subsequent stages of progress, the comparative conspicuousness of relations has greatly affected the order in which they were recognized as uniform. Hence it happened that after the establishment of those very manifest sequences constituting a lunation, and those less manifest ones marking a year, and those still less manifest ones marking the planetary periods, Astronomy occupied itself with such inconspicuous sequences as those displayed in the repeating cycle of lunar eclipses, and those which suggested the theory of epicycles and eccentrics; while modern Astronomy deals with still more inconspicuous sequences: some of which, as the planetary rotations, are nevertheless the simplest which the heavens present. In Physics, the early use of canoes implied an empirical knowledge of certain hydrostatic relations that are intrinsically more complex than sundry static relations then unknown; but these hydrostatic relations were thrust upon observation. Or if we compare the solution of the problem of specific gravity by Archimedes, with the discovery of atmospheric pressure by Torricelli, (the two involving mechanical relations of exactly the same kind,) we perceive that the much earlier occurrence of the first than the last, was determined neither by a difference in their bearings on personal welfare, nor by a difference in the frequency with which illustrations of them come under observation, nor by relative simplicity; but solely by the greater obtrusiveness of the connexion between antecedent and consequent in the one case than in the other. Similarly with Chemistry. The burning of wood, the rusting of iron, the putrefaction of dead bodies, were early known as consequents uniformly related to certain antecedents; but not until long after was there reached a like empirical knowledge of the effect produced by air in the decomposition of soil: a phenomenon of equal simplicity, equal or greater importance, and greater frequency; but one that is extremely unobtrusive. Among miscellaneous illustrations, it may be pointed out that the connexions between lightning and thunder and between rain and clouds, were established long before others of the same order; simply because they thrust themselves on the attention. Or the long-delayed discovery of the microscopic forms of life, with all the phenomena they present, may be named as very clearly showing how certain groups of relations that are not ordinarily perceptible, though in all other respects like long-familiar relations, have to wait until changed conditions render them perceptible. But, without further details, it needs only to consider the inquiries which now occupy the electrician, the chemist, the physiologist, to see that Science has advanced and is advancing from the more conspicuous phenomena to the less conspicuous ones.
How the degree of absolute frequency of a relation affects the recognition of its uniformity, we see in contrasting certain biological facts. Death and disease are near akin in most of their relations to us; while in respect of complexity, conspicuousness, and the directness with which they personally concern us, diseases in general may be put pretty nearly on a level with each other. But there are great differences in the times at which the natural sequences they severally exhibit are recognized as such. The connexion between death and bodily injury, constantly displayed not only in men but in all inferior creatures, was known as an established uniformity while yet diseases were thought supernatural. Among diseases themselves, it is observable that comparatively unusual ones were regarded as of demoniacal origin during ages when the more frequent were ascribed to ordinary causes: a truth paralleled indeed among our own peasantry, who by the use of charms show a lingering superstition with respect to rare disorders, which they do not show with respect to common ones, such as colds. Passing to physical illustrations, we may note that within the historic period, whirlpools were accounted for by the agency of water-spirits; but we do not find that within the same period the disappearance of water on exposure either to the sun or to artificial heat was interpreted in an analogous way: though a much more marvellous occurrence, and a much more complex one, its great frequency led to the early establishment of it as a natural uniformity. Rainbows and comets do not differ greatly in conspicuousness, and a rainbow is intrinsically the more involved phenomenon; but chiefly because of their far greater commonness, rainbows were perceived to have a direct dependence on sun and rain while yet comets were regarded as supernatural appearances.
That races living inland must long have remained ignorant of the daily and monthly sequences of the tides, and that intertropical races could not early have comprehended the phenomena of northern winters, are extreme illustrations of the influence which relative frequency has on the recognition of uniformities. Animals which, where they are indigenous, call forth no surprise by their structure or habits, because these are so familiar, when taken to a part of the earth where they have never been seen, are looked at with an astonishment approaching to awe – are even thought supernatural: a fact which will suggest numerous others that show how the localization of phenomena, in part controls the order in which they are reduced to law. Not only however does their localization in space affect the progression, but also their localization in time. Facts which are rarely if ever manifested during one era, are rendered very frequent in another, simply through the changes wrought by civilization. The lever, of which the properties are illustrated in the use of sticks and weapons, is vaguely understood by every savage – on applying it in a certain way he rightly anticipates certain effects; but the action of the equally simple wedge, which is not commonly displayed till tool-making has made some progress, is less early generalized; while the wheel and axle, pulley, and screw, cannot have their powers either empirically or rationally known till the advance of the arts has more or less familiarized them. Through those various means of exploration which we have inherited and are ever increasing, we have become acquainted with a vast range of chemical relations that were relatively non-existent to the primitive man: to highly developed industries we owe both the substances and the apparatus that have disclosed to us countless uniformities which our ancestors had no opportunity of seeing, and therefore could not recognize. These and sundry like instances that will occur to the reader, show that the accumulated materials, and processes, and appliances, and products, which characterize the environments of complex societies, greatly increase the accessibility of various classes of relations; and by so multiplying the experiences of them, or making them relatively frequent, facilitate their generalization. To which add, that various classes of phenomena presented by society itself, as for instance those which political economy formulates, become relatively frequent and therefore recognizable in advanced social states; while in less advanced ones they are too rarely displayed to have their relations perceived, or, as in the least advanced ones, are not displayed at all.
That, where no other circumstances interfere, the order in which different uniformities are established varies as their complexity, is manifest. The geometry of straight lines was understood before the geometry of curved lines; the properties of the circle before the properties of the ellipse, parabola and hyperbola; and the equations of curves of single curvature were ascertained before those of curves of double curvature. Plane trigonometry comes in order of time and simplicity before spherical trigonometry; and the mensuration of plane surfaces and solids before the mensuration of curved surfaces and solids. Similarly with mechanics: the laws of simple motion were generalized before those of compound motion; and those of rectilinear motion before those of curvilinear motion. The properties of equal-armed levers, or scales, were understood before those of the lever with unequal arms; and the law of the inclined plane was formulated earlier than that of the screw, which involves it. In chemistry, the progress has been from the simple inorganic compounds, to the more involved organic ones. And where, as in most of the other sciences, the conditions of the exploration are more complicated, we still may clearly trace relative complexity as one of the determining circumstances.
The progression from concrete relations to abstract ones, and from the less abstract to the more abstract, is equally obvious. Numeration, which in its primary form concerned itself only with groups of actual objects, came earlier than simple arithmetic: the rules of which deal with numbers apart from objects. Arithmetic, limited in its sphere to concrete numerical relations, is alike earlier and less abstract than Algebra, which deals with the relations of these relations. And in like manner, the Infinitesimal Calculus comes after Algebra, both in order of evolution and in order of abstractness. In Astronomy, the progress has been from special generalizations, each expressing the motions of a particular planet, to the generalizations of Kepler, expressing the motions of the planets at large; and then to Newton’s generalization, expressing the motions of all heavenly bodies whatever. Similarly with Physics, Chemistry and Biology, there has ever been an advance from the relations of particular facts and particular classes of facts, to the relations presented by still wider classes – to truths of a high generality or greater abstractness.
Brief and rude as is this sketch of a mental development that has been long and complicated, it fulfils its end if it displays the several conditions that have regulated the course of the development. I venture to think it shows inductively, what was deductively inferred, that the order in which separate groups of uniformities are recognized, depends not on one circumstance but on several circumstances. A survey of the facts makes it manifest that the various classes of relations are generalized in a certain succession, not solely because of one particular kind of difference in their natures; but also because they are variously placed with respect to time, space, other relations, and our own constitutions: our perception of them being influenced by all these conditions in endless combinations. The comparative degrees of importance, of obtrusiveness, of absolute frequency, of relative frequency, of simplicity, of concreteness, are every one of them factors; and from their union in proportions that are more or less different in every case, there results a highly complex process of mental evolution. But while it thus becomes manifest that the proximate causes of the succession in which relations are reduced to law, are numerous and involved; it also becomes manifest that there is one ultimate cause to which these proximate ones are subordinate. As the several circumstances that determine the early or late recognition of uniformities, are circumstances that determine the number and strength of the impressions which these uniformities make on the mind; it follows that the progression conforms to a certain fundamental principle of psychology. We see à posteriori, what we concluded à priori, that the order in which relations are generalized, depends on the frequency and impressiveness with which they are repeated in conscious experience.
§ 39. And now to observe the bearings of these truths on our general argument. Having roughly analyzed the progress of the past, let us take advantage of the light thus thrown on the present, and consider what is implied respecting the future.
Note first that the likelihood of the universality of Law, has been ever growing greater. Out of the countless coexistences and sequences with which mankind are environed, they have been continually transferring some from the group whose order was supposed to be arbitrary, to the group whose order is known to be uniform. Age by age, the number of recognized connexions of phenomena has been increasing; and that of unrecognized connexions decreasing. And manifestly, as fast as the class of ungeneralized relations becomes smaller, the probability that among them there may be some that do not conform to law, becomes less. To put the argument numerically – It is clear that when out of surrounding phenomena a hundred of several kinds have been found to occur in constant connexions, there arises a slight presumption that all phenomena occur in constant connexions. When uniformity has been established in a thousand cases, more varied in their kinds, the presumption gains strength. And when the established cases of uniformity mount to myriads, including many of each variety, it becomes an ordinary induction that uniformity exists everywhere. Just as from the numerous observed cases in which heavenly bodies have been found to move in harmony with the law of gravitation, it is inferred that all heavenly bodies move in harmony with the law of gravitation; so, from the innumerable observed cases in which phenomena are found to stand in invariable connexions, it is inferred that in all cases phenomena stand in invariable connexions.