Empirical law

“ An empirical law, then, is an observed uniformity, presumed to be resolvable into simpler laws, but not yet resolved into them. The ascertainment of the empirical laws of phenomena often precedes by a long interval the explanation of those laws by the Deductive Method ”

“ It is conceivable that those laws might be such, and the general circumstances of the human race such, as to determine the successive transformations of man and society to one given and unvarying order. But even if the case were so, it can not be the ultimate aim of science to discover an empirical law. ”

“ But while we are justified in extending an empirical law beyond the limits within which it has been [page 268] observed to hold good, it is a mistake to suppose that the main work of science is the collection of empirical laws, and that the only scientific inference is the inference from the observed prevalence of an empirical law to its continuance. ”

“ If, therefore, even one or two of these few instances be insufficiently known, or imperfectly analyzed into their elements, and therefore not adequately compared with other instances, nothing is more probable than that a wrong empirical law will emerge instead of the right one. ”

“ 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 [199] rightly compared to a general fact, and it is legitimate in psychology to say the law of association or the general fact of association. ”

“ If, then, it is only to cases which in point of time are adjacent (or nearly adjacent) to those which we have actually observed, that any derivative law, not of causation, can be extended with an assurance equivalent to certainty, much more is this true of a merely empirical law. Happily, for the purposes of life it is to such cases alone that we can almost ever have occasion to extend them. ”

“ In any case an approximate generalisation can never be more than an empirical law. Its authority, however, is less when it composes the whole of our knowledge of the subject, than when it is merely the most available form of our knowledge for practical guidance, and the causes, or some certain mark of the attribute predicated, being known to us as well as the effects, the proposition can be tested by our trying to deduce it from the causes or mark. ”

“ But when a generalization has been found to hold good of a very large proportion of all things whatever, it is already proved that nearly all the causes which exist in nature have no power over it; that very few changes in the combination of causes can affect it; since the greater number of possible combinations must have already existed in some one or other of the instances in which it has been found true. If, therefore, any empirical law is a result of causation, the more general it is, the more it may be depended on. ”

“ Unless we have resolved the empirical law into the laws of the causes on which it depends, and ascertained that those causes extend to the case which we have in view, there can be no reliance placed in our inferences. ”

“ A little reflection, indeed, will show that mere negations can only form the ground of the lowest and least valuable kind of empirical law. A phenomenon has never been noticed; this only proves that the conditions of that phenomenon have not yet occurred in experience, but does not prove that they may not occur hereafter. ”

“ 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. ”

“ 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. ”

“ The empirical rule is, therefore, no final law, but is capable of explaining, especially when true, e.g., the succession of a certain condition of weather from certain meteorological signs, the improvement of species through crossing, the fact that some alloys are harder than their components, and so on. ”

“ The causal law, which the critical analysis of the material scientific methods shows to be a fundamental condition of empirical thought, in its requirement that the events stand as causes and effects in necessary connection, or real dependence, comprehends these uniform contents of perception only in the way peculiar to our thought. ”

“ Still more confidently may we do so when the law is not merely empirical; when the phenomena which we find conjoined are effects of ascertained causes, from the laws of which the conjunction of their effects is deducible. ”

“ We have seen in the last chapter that there is a point of generality at which empirical laws become as certain as laws of nature, or, rather, at which there is no longer any distinction between empirical laws and laws of nature. ”

“ What we have said of empirical generalizations from times past to times still to come, holds equally true of similar generalizations from present times to times past; when persons whose acquaintance with moral and social facts is confined to their own age, take the men and the things of that age for the type of men and things in general, and apply without scruple to the interpretation of the events of history, the empirical laws which represent sufficiently for daily guidance the common phenomena of human nature at that time and in that particular state of society. ”

“ Empirical laws must indeed be found; or a general Science of Society would be impossible: for, the character of any one generation is so much the result of the characters of all prior ones, that men could not compute so long a series from the elementary laws producing it. But the empirical laws, when found (as they can be, since the series of the effects as a whole is ever growing in uniformity) , must be shown by deductions to be, if not the only possible, or even the most probable, at least possible, consequences of the laws of human nature. ”

“ It needs scarcely be observed, that,—if direct observation and collation of instances have furnished us with any empirical laws of the effect, whether true in all observed cases or only true for the most part,—the most effectual verification of which the theory could be susceptible would be, that it led deductively to those empirical laws; that the uniformities, whether complete or incomplete, which were observed to exist among the phenomena, were accounted for by the laws of the causes—were such as could not but exist if those be really the causes by which the phenomena are produced. ”

“ To constitute an empirical science is to show that the difference between different phenomena is due simply to 'circumstances.' The explanation of the facts becomes sufficient when the 'law' can be stated, as that of a unit of constant properties placed in varying positions. This corresponds to the procedure in the physical sciences, where the ultimate aim is to represent all laws as corresponding to the changes of position of uniform atoms. In social and political changes the goal is the same. ”

“ By combining, however, the exact laws of the greater causes, and of such of the minor ones as are sufficiently known, with such empirical laws or such approximate generalizations respecting the miscellaneous variations as can be obtained by specific observation, we can lay down general propositions which will be true in the main, and on which, with allowance for the degree of their probable inaccuracy, we may safely ground our expectations and our conduct. ”

“ It is no disparagement, therefore, to the science of Human Nature, that those of its general propositions which descend sufficiently into detail to serve as a foundation for predicting phenomena in the concrete, are for the most part only approximately true. But in order to give a genuinely scientific character to the study, it is indispensable that these approximate generalizations, which in themselves would amount only to the lowest kind of empirical laws, should be connected deductively with the laws of nature from which they result ”

“ As might be expected, the most imperfect part of those branches of social inquiry which have been cultivated as separate sciences, is the theory of the manner in which their conclusions are affected by ethological considerations. The omission is no defect in them as abstract or hypothetical sciences, but it vitiates them in their practical application as branches of a comprehensive social science. In political economy, for instance, empirical laws of human nature are tacitly assumed by English thinkers, which are calculated only for Great Britain and the United States. ”

“ For even the greater generalizations, which embrace comprehensive Kinds containing under them a great number and variety of infimæ species, are only empirical laws, resting on induction by simple enumeration merely, and not on any process of elimination—a process wholly inapplicable to this sort of case. ”

“ The empirical laws of those phenomena which depend on known causes, and of which a general theory can therefore be constructed, have, whatever may be their value in practice, no other function in science than that of verifying the conclusions of theory. ”

“ For completeness and comprehensiveness are essential and indispensable to the formation of a rational system. But, on the other hand, it is impossible to obtain a complete survey of all the details of experience, and where it may be attempted to approach this, the empirical conceptions embracing those details cannot form integral elements of the system itself, but can only be introduced in subordinate observations, and mainly as furnishing examples illustrative of the General Principles. ”

“ In statistics, it is evident that empirical laws may sometimes be traced; and the tracing them forms an important part of that system of indirect observation on which we must often rely for the data of the Deductive Science. The process of the science consists in inferring effects from their causes; but we have often no means of observing the causes, except through the medium of their effects. In such cases the deductive science is unable to predict the effects, for want of the necessary data ”

“ When by a severe and diligent analysis we have ascertained all the ingredients of any phenomenon, and have separated it from all that is foreign and adventitious, we know its true nature, and may deduce a general law from our experiment; for a general law is nothing more than an expression of the effect produced by the same cause operating under the same circumstances. ”

“ The Method proper to the Science of Society must be, in substance, the same as in all other sciences; the interrogation and interpretation of experience, by the twofold process of Induction and Deduction. But its mode of practising these operations has features of peculiarity. In general, Induction furnishes to science the laws of the elementary facts, from which, when known, those of the complex combinations are thought out deductively: specific observation of complex phaenomena yields no general laws, or only empirical ones ”

“ What we have said so far is that there have been hitherto certain observed causal laws, and that all the empirical evidence we possess is compatible with the view that everything, both mental and physical, so far as our observation has extended, has happened in accordance with causal laws. ”

“ If these various operations could be correctly performed, the result would be prophecy; but, as they can be performed only with a certain approximation to correctness, mankind can never predict with absolute certainty, but only with a less or greater degree of probability; according as they are better or worse apprised what the causes are,—have learnt with more or less accuracy from experience the law to which each of those causes, when acting separately, conforms,—and have summed up the aggregate effect more or less carefully. ”

“ It is worth remarking, that complex instances which would have been of no use for the discovery of the simple laws into which we ultimately analyse their phenomena, nevertheless, when they have served to verify the analysis, become additional evidence of the laws themselves. Although we could not have got at the law from complex cases, still when the law, got at otherwise, is found to be in accordance with the result of a complex case, that case becomes a new experiment on the law, and helps to confirm what it did not assist to discover. ”