Respecting the whole of the phenomena implied under causation, the principle of nature's uniformity is embodied in one great and comprehensive statement, called the law of causation; the import of which is, that whatever begins to exist is uniformly preceded by something else, to which it invariably succeeds. Events do not arise of themselves, or out of nothing; and although there is such a thing as plurality of causes, everything that arises is preceded by some other thing as a cause, and always follows when that cause occurs; there being supposed no counteracting agency. The aim of the scientific inquirer, then, is to single out from the mass of circumstances that have accompanied and preceded any event, some one or more that invariably precede the occurrence of that event, which being found, are thenceforth known as its cause. This has to be accomplished by a process technically called elimination, by which is under stood a series of operations intended to separate everything that is indifferent to the production of the phenomenon, until we arrive at some one thing or more that cannot be removed without making the effect to cease.
Mr. John Stuart Mill, in his Logic, has illustrated in detail the methods to be adopted for making sure that we have singled out the true causative circumstance from among the many that may precede a.given effect. They resolve themselves mainly into two. "One is, by comparing together different instances in which the phenomenon occurs. The other is, by comparing instances in which the phenomenon does occur, with instances in other respects similar in which it does not. These two methods may be respectively denominated the method of agreement, and the method of difference." The method of agreement supposes that we make it a study to vary the circumstances under which the supposed phenomenon is produced. Either by observation of cases presented in nature. or by artificially contriving new cases, in other words, by experi ment, we do our utmost to obtain the effect in a great many different connections, whereby we ascertain what things are indifferent to it. Whatever circumstance can be excluded, the phenomenon still happening, or can be absent notwithstanding its pres ence, is not connected with it in the way of causation. The accidental or indifferent circumstances being thus eliminated, if only one remains, that is the cause; if the elimi nation does not go so far, but leaves three or four circumstances or agents, we can only say that the cause is among them. Mr. Mill enunciates the method of agreement in a formal canon, or rule of induction, to the following effect: If two or more instances of the phenomenon, under investigation have only one circumstance in common, the circumstance in which alone all the instances agree is the cause (or effect) of the given phenomenon.
If we could always obtain the of circumstances, for' the exclusion of all indifferent adjuncts, this method would fully answer the ends of inductive inquiry. But this is not always to be bad, and even when practicable, the operation is often very laborious. When the other method (difference) on be applied, the desired end is reached by a shorter route. If, instead of excluding the indifferent one. by one, we can contrive an experiment, or make an observation, that excludes072e agency or circumstance, followed by the cessation of the effect, we conclude at once that what has thus been left out is the cause, or an essential condition or part of the cause. Whenever we are so fortunate as to light upon two instances suited to tl. 4 method, we establish causation at once and beyond all question. The experimentuut eructs of Bacon was something of this nature; only it supposed that a question lay between two alternative or competing agencies, which an experiment had been hit upon for deciding; such an experiment behooved to be one of difference. This method is embodied in the following canon: If an instance in which the phenomenon under investi gation occurs, and an instance in which it does not occur, hare every circumstance, except one, en common, that one occurring only in the former, the circumstance in which alone the two instances differ is the or cause, or a necessary part of the cause, of the phenomenon.
These are the two leading methods, but there are certain cases met by a procedure somewhat different. Sometimes we have a phenomenon made up of causes partly known and partly unknown. It is then possible to subduct the effects due to the known causes, and what remains will be attributed to the remaining agencies. This is expressed by Mr. Mill in the following rule or canon: Subduct from any phenomenon such part its is known by previous induction to be the effect of certain ,antecedents, and the residue e the phenomenon is the of the remaining antecedents. The more our knowledge is extended, the more able are we to proceed upon this method, termed the method of residues. "It is by this process, in fact," says sir John Herschel, "that science in its
present advanced state is chiefly promoted." There remains a class of laws wherein the application of any of those three methods is rendered impracticable, from the circumstance that the agency in their case is irre-, movable and indestructible, so that we cannot obtain any cases where it is entirely absent. Such an agent is heat, which can never be entirely separated from any body, so as to ascertain, by comparing cases of its presence with those of its absence, what effects are due to it. So we can never get out of the sphere of the earth's attraction. The difficulty hence arising is surmounted by observing the variations of degree of the cause, and whether there be a corresponding variation in the degree of the effect. Thug, we infer that heat is the cause of the expansion of bodies, and that its total absence would lead to their maximum condensation and consolidation, by watching the effects of any additions or subtractions of a body's temperature. Solids, liquids, and gases (with certain limited and special exceptions) are found expanding steadily as they are, heated, and contracting as they are cooled; and this is to us a sufficient justification for considering that the law in question holds good. This process is termed by Mr. Mill the method of concomitant variations, and is expressed by him in the following terms: Whatever phenomenon varies in an 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, There are many problems growing out of the applications of induction to the great variety of natural phenomena, the main principles being nevertheless the same. An important extension of the means of scientific discovery and proof arises after a certain number of general laws have been discovered, and when phenomena can be shown to be results of the operation of one or more of such laws. Thus, the great induction of uni versal gravity was applied deductively to explain a great many facts besides those that enabled the induction to be made. Not merely the motions of the planets about the sun, and the satellites about the planets, but the remote and previously unexplained phe nomena of the tides, the precession of the equinoxes, etc., were found to be inferences from the general principle. This mode of determining causes is called the deductive method. When several agents unite in a compound effect, there is required a process of calculation to find from the effects of the causes acting separately the combined effect due to their concurrent action, as when the path of a projectile is deduced from the laws of gravity and of projectile force. It is the deductive stage of science that enables mathematical calculation to be brought into play wills such remarkable success as is seen in astronomy, mechanics, etc. See DEDUCTION.
The circumstance that phenomena may result from a concurrence of causes, leads to the distinction between ultimate laws and derivative or subordinate laws. Thus, gravity is an ultimate law; the movement of the planets in ellipses is but a subordinate law. These inferior laws may be perfectly true within their own limits, but not necessarily beyond certain limits, of time, place, and circumstance. A different adjustment of lb two forces that determine a planet's motion, would cause a circular or a parabolic orb;.t; and therefore it is, that when phenomena result from a combination of ultimate Is ws acting under a certain arrangement, they are not to be generalized beyond the spl.tere where that arrangement holds. These inferior laws are sometimes mere induc Lions that have not been resolved into their constituent laws, and then they go undi.r: time name of " empirical laws." Thus, in the hands of Kepler,, the elliptic orbit of the planets was only an empirical generalization, ascertained by the method of agreemeet;.
Newton converted it into a derivative law, when he showed that it resulted from the More general laws of gravity, etc. The earlier stages of induction present us with many of those empirical laws; in some subjects—as physiology, medicine, etc.—the greater number of inductions are of this character. The cure of disease is especially an example of this: hardly any medicine can have its efficacy traced to ultimate laws of the human system. Hence the uncertainty attending the application of reme - dies to new cases, and also the want of success that often attends them in circum stances where we think they ought to succeed.
Induction applies to other laws than those of causation—namely, to uniformities of co-existence. For the illustration of these, as well as the other parts of induc tion, see Mill's Logic, book iv.