Variable

“ But the most hopeful theory takes into account a very strange fact lately established, viz. that the variable is at its brightest not when approaching its fellow but when coming directly toward us, and at its faintest when receding directly from us. ”

“ Any attempt to reckon with these three forces, each of which is extremely variable, not only among different individuals but in the same person at different times—any attempt to analyze these elements and observe, as well, their mutual influences and combined effects, is bound to result in a complication of details that almost defies expression or comprehension. ”

“ Always there is a large variable element in the problem of our activities; and on this variable element, which we have no means of calculating, depends all that is most precious and vital in our results. Husbandry here is the great witness for, and key to, higher things. ”

“ If we examine the matter closely, we will see that all the cases considered come under the head of form—worlds, plants, animals, men. But there is another great class of cases which fall under the head of forces or principles, and these when carefully examined are found not to be variables but constants—the constants of nature. ”

“ To express, shortly, what appears to me to be the only intelligible meaning of the three most important words in physics, immediate invariable antecedence, is power,—the immediate invariable antecedent, in any sequence, is a cause,—the immediate invariable consequent is the correlative effect. ”

“ Is the fact that science is possible a proof of the principle of causation—"From like causes, like effects"—"A permanent law of things"—"Invariable order"? Because something is calculable, is it therefore on that account necessary? ”

“ Nothing can, of course, differentiate itself, nor can any two things differentiate each other, even when functionally allied. The actual coëfficient sought is the difference effected, in functional value, in one of two independent variables. ”

“ To certain facts, certain facts always do, and, as we believe, will continue to, succeed. The invariable antecedent is termed the cause; the invariable consequent, the effect. And the universality of the law of causation consists in this, that every consequent is connected in this manner with some particular antecedent, or set of antecedents. ”

“ The fewer but more fundamental the identities the greater the number of the individuals in the class; the fewer the number of variables and the less fundamental the variables, the smaller the number of individuals within the class. ”

“ Even those attributes of an object which might seem with greatest propriety to be called states of the object itself, its sensible qualities, its color, hardness, shape, and the like, are in reality (as no one has pointed out more clearly than Brown himself) phenomena of causation, in which the substance is distinctly the agent, or producing cause, the patient being our own organs, and those of other sentient beings. What we call states of objects, are always sequences into which the objects enter, generally as antecedents or causes ”

“ The mode of discovering and proving laws of nature, which we have now examined, proceeds on the following axiom: Whatever circumstances can be excluded, without prejudice to the phenomenon, or can be absent notwithstanding its presence, is not connected with it in the way of causation. [pg 280] The casual circumstances being thus eliminated, if only one remains, that one is the cause which we are in search of: if more than one, they either are, or contain among them, the cause; and so, mutatis mutandis, of the effect. ”

“ All the uniformities which exist in the succession of phenomena, and most of the uniformities in their co-existence, are either, as we have seen, themselves laws of causation, or consequences resulting from, and corollaries capable of being deduced from, such laws. If we could determine what causes are correctly assigned to what effects, and what effects to what causes, we should be virtually acquainted with the whole course of nature. ”

“ This throwing of the whole body of possible inferences from a given set of particulars, into one general expression, operates as a security for their being just inferences, in more ways than one. First, the general principle presents a larger object to the imagination than any of the singular propositions which it contains. ”

“ This last principle, which we may call the axiom of constant result, holds good throughout all our mental operations, not only when we compare, but when we add, divide, class, or infer a given matter in any conceivable way. ”

“ Thus we see that each and every condition of the phenomenon may be taken in its turn, and, with equal propriety in common parlance, but with equal impropriety in scientific discourse, may be spoken of as if it were the entire cause. And in practice, that particular condition is usually styled the cause, whose share in the matter is superficially the most conspicuous, or whose requisiteness to the production of the effect we happen to be insisting on at the moment. ”

“ When, however, we find it possible to connect many of these detached generalizations together, by discovering the more general laws of which they are cases, and to the operation of which in some particular sets of viii circumstances they are due, we gain not only a scientific, but a practical advantage ”

“ Distinguish between induction as a mode of inference and induction as a method.
(7) State and explain the law of universal causation. Illustrate fully.
(8) Make evident that a cause may involve many antecedents.
(9) State and explain by illustration the law of uniformity of nature.
(10) Verify by illustration the notion that the “fact of causation” conditions all induction.
(11) Which of the two laws is empirical, “causation” or “uniformity”? Why?
(12) Show that induction is a form of thinking.
(13) Why should the law of uniformity of nature convince man that nature is honest? ”

“ And if we carry our observation outward, we also find that light and darkness, sound and silence, motion and quiescence, equality and inequality, preceding and following, succession and simultaneousness, any positive phenomenon whatever and its negative, are distinct phenomena, pointedly contrasted, and the one always absent where the other is present. I consider the maxim in question to be a generalization from all these facts. ”

“ We require, also, that none of the circumstances which we do know shall have effects susceptible of being confounded with those of the agents whose properties we wish to study. We take the utmost pains to exclude all causes capable of composition with the given cause; or, if forced to let in any such causes, we take care to make them such that we can compute and allow for their influence, so that the effect of the given cause may, after the subduction of those other effects, be apparent as a residual phenomenon. ”

“ As has been already pointed out, this is all that art can do. To test a generalization, by showing that it either follows from, or conflicts with, some stronger induction, some generalization resting on a broader foundation of experience, is the beginning and end of the logic of Induction. ”

“ But with the enlargement of mind and its more perfect organization, there arises a new method of appraising values, and so a new type of value altogether. I mean of course the so-called absolute values. Absolute values are never absolute in the sense of absolute completeness; they are relative to two things—to external reality and to our mental powers and organization. [48] They are abstractions; we generalize the value in our minds, and at the same time raise it to the highest pitch of intensity we can. ”

“ And since it is by these laws, combined with the facts of each particular case, that the whole of the phenomena of human action and feeling are produced, it is on these that every rational attempt to construct the science of human nature in the concrete, and for practical purposes, must proceed. ”

“ But when we are studying objects not for any special practical end, but for the sake of extending our knowledge of the whole of their properties and relations, we must consider as the most important attributes those which contribute most, either by themselves or by their effects, to render the things like one another, and unlike other things; which give to the class composed of them the most marked individuality ”

“ Present Being of two sorts, namely in nature and in minds, Past and Future Being, these four types of reality we have now enumerated as types recognized by common sense and natural science. Our study of the Third Conception of Being, some time since, made us familiar with the still different sort of reality ordinarily attributed to the realm of moral and of mathematical truth. This realm of eternal validity common sense as well as science recognizes ”

“ We shall next advert to a rather more intricate operation of the same principle, namely, when the cause does not merely continue in action, but undergoes, during the same time, a progressive change in those of its circumstances which contribute to determine the effect. ”

“ Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation. ”

“ The functions of life may be divided into two classes, those which are affected by the properties of this principle alone, and those, by far the most numerous class, which result from the co-operation of these properties with those of the principles which operate in inanimate nature. ”

“ On Observation and Experiment.
§ 1. It results from the preceding exposition, that the process of ascertaining what consequents, in nature, are invariably connected with what antecedents, or in other words what phenomena are related to each other as causes and effects, is in some sort a process of analysis. That every fact which begins to exist has a cause, and that this cause must be found in some fact or concourse of facts which immediately preceded the occurrence, may be taken for certain. ”

“ Every such operation brings us a step nearer toward answering the question which was stated in a previous chapter as comprehending the whole problem of the investigation of nature, viz.: what are the fewest assumptions, which being granted, the order of nature as it exists would be the result? What are the fewest, general propositions from which all the uniformities existing in nature could be deduced? ”

“ The use of words is thus a method of substituting for two particulars which differ widely, in spite of being instances of the same universal, two other particulars which differ very little, and which are also instances of a universal, namely the name of the previous universal. Thus, so far as logic is concerned, we are entirely free to adopt any theory as to general ideas which empirical observation may recommend. ”

“ Causes are preferable, both as being the surest and most direct of marks, and as being themselves the properties on which it is of most use that our attention should be strongly fixed. But the property which is the cause of the chief peculiarities of a class, is unfortunately seldom fitted to serve also as the diagnostic of the class. Instead of the cause, we must generally select some of its more prominent effects, which may serve as marks of the other effects and of the cause. ”

“ The properties of human behaviour are taken to be relatively invariant, of the same general character but of a specifically different subject matter as the properties investigated by any natural science. ”

“ That there must be an indefinite number of such terms is obvious, on reflection; since we cannot define anything except by an analysis, which, when carried as far as it will go, refers us to something, which is simply different from anything else, and which by that ultimate difference explains the peculiarity of the whole which we are defining: for every whole contains some parts which are common to other wholes also. ”

“ To the foregoing examples from physical science, let us add another from mental. The following is one of the simple laws of mind: Ideas of a pleasurable or painful character form associations more easily and strongly than other ideas, that is, they become associated after fewer repetitions, and the association is more durable. This is an experimental law, grounded on the Method of Difference. ”

“ 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. ”

“ The combination of the two elements, the subjective or ideal, and the objective or observed, is necessary, in order to give us any insight into the laws of nature. But different persons, according to their mental habits and constitution, may be inclined to dwell by preference upon the one or the other of these two elements. ”

“ If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance, the circumstance in which alone the two sets of instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon. ”

“ When, in pursuing the method of Variations, the phenomena compared do not always correspond in their fluctuations, the irregular movements of that phenomenon which we regard as the effect may often be explained by treating them as residuary phenomena, and then seeking for exceptional causes, whose temporary interference has obscured the influence of the general cause. ”