A System of Logic, Ratiocinative and Inductive

by John Stuart Mill

Of The Limits To The Explanation Of Laws Of Nature; And Of Hypotheses.

§ 1. The preceding considerations have led us to recognize a distinction between two kinds of laws, or observed uniformities in nature: ultimate laws, and what may be termed derivative laws. Derivative laws are such as are deducible from, and may, in any of the modes which we have pointed out, be resolved into, other and more general ones. Ultimate laws are those which can not. We are not sure that any of the uniformities with which we are yet acquainted are ultimate laws; but we know that there must be ultimate laws; and that every resolution of a derivative law into more general laws brings us nearer to them.

Since we are continually discovering that uniformities, not previously known to be other than ultimate, are derivative, and resolvable into more general laws; since (in other words) we are continually discovering the explanation of some sequence which was previously known only as a fact; it becomes an interesting question whether there are any necessary limits to this philosophical operation, or whether it may proceed until all the uniform sequences in nature are resolved into some one universal law. For this seems, at first sight, to be the ultimatum toward which the progress of induction by the Deductive Method, resting on a basis of observation and experiment, is tending. Projects of this kind were universal in the infancy of philosophy; any speculations which held out a less brilliant prospect being in these early times deemed not worth pursuing. And the idea receives so much apparent countenance from the nature of the most remarkable achievements of modern science, that speculators are even now frequently appearing, who profess either to have solved the problem, or to suggest modes in which it may one day be solved. Even where pretensions [pg 346] of this magnitude are not made, the character of the solutions which are given or sought of particular classes of phenomena, often involves such conceptions of what constitutes explanation, as would render the notion of explaining all phenomena whatever by means of some one cause or law, perfectly admissible.

§ 2. It is, therefore, useful to remark that the ultimate Laws of Nature can not possibly be less numerous than the distinguishable sensations or other feelings of our nature; those, I mean, which are distinguishable from one another in quality, and not merely in quantity or degree. For example: since there is a phenomenon sui generis, called color, which our consciousness testifies to be not a particular degree of some other phenomenon, as heat or odor or motion, but intrinsically unlike all others, it follows that there are ultimate laws of color; that though the facts of color may admit of explanation, they never can be explained from laws of heat or odor alone, or of motion alone, but that, however far the explanation may be carried, there will always remain in it a law of color. I do not mean that it might not possibly be shown that some other phenomenon, some chemical or mechanical action, for example, invariably precedes, and is the cause of, every phenomenon of color. But though this, if proved, would be an important extension of our knowledge of nature, it would not explain how or why a motion, or a chemical action, can produce a sensation of color; and, however diligent might be our scrutiny of the phenomena, whatever number of hidden links we might detect in the chain of causation terminating in the color, the last link would still be a law of color, not a law of motion, nor of any other phenomenon whatever. Nor does this observation apply only to color, as compared with any other of the great classes of sensations; it applies to every particular color, as compared with others. White color can in no manner be explained exclusively by the laws of the production of red color. In any attempt to explain it, we can not but introduce, as one element of the explanation, the proposition that some antecedent or other produces the sensation of white.

The ideal limit, therefore, of the explanation of natural phenomena (toward which as toward other ideal limits we are constantly tending, without the prospect of ever completely attaining it) would be to show that each distinguishable variety of our sensations, or other states of consciousness, has only one sort of cause; that, for example, whenever we perceive a white color, there is some one condition or set of conditions which is always present, and the presence of which always produces in us that sensation. As long as there are several known modes of production of a phenomenon (several different substances, for instance, which have the property of whiteness, and between which we can not trace any other resemblance) so long it is not impossible that one of these modes of production may be resolved into another, or that all of them may be resolved into some more general mode of production not hitherto recognized. But when the modes of production are reduced to one, we can not, in point of simplification, go any further. This one may not, after all, be the ultimate mode; there may be other links to be discovered between the supposed cause and the effect; but we can only further resolve the known law, by introducing some other law hitherto unknown, which will not diminish the number of ultimate laws.

In what cases, accordingly, has science been most successful in explaining phenomena, by resolving their complex laws into laws of greater simplicity [pg 347] and generality? Hitherto chiefly in cases of the propagation of various phenomena through space; and, first and principally, the most extensive and important of all facts of that description, mechanical motion. Now this is exactly what might be expected from the principles here laid down. Not only is motion one of the most universal of all phenomena, it is also (as might be expected from that circumstance) one of those which, apparently at least, are produced in the greatest number of ways; but the phenomenon itself is always, to our sensations, the same in every respect but degree. Differences of duration or of velocity, are evidently differences in degree only; and differences of direction in space, which alone has any semblance of being a distinction in kind, entirely disappear (so far as our sensations are concerned) by a change in our own position; indeed, the very same motion appears to us, according to our position, to take place in every variety of direction, and motions in every different direction to take place in the same. And again, motion in a straight line and in a curve are no otherwise distinct than that the one is motion continuing in the same direction, the other is motion which at each instant changes its direction. There is, therefore, according to the principles I have stated, no absurdity in supposing that all motion may be produced in one and the same way, by the same kind of cause. Accordingly, the greatest achievements in physical science have consisted in resolving one observed law of the production of motion into the laws of other known modes of production, or the laws of several such modes into one more general mode; as when the fall of bodies to the earth, and the motions of the planets, were brought under the one law of the mutual attraction of all particles of matter; when the motions said to be produced by magnetism were shown to be produced by electricity; when the motions of fluids in a lateral direction, or even contrary to the direction of gravity, were shown to be produced by gravity; and the like. There is an abundance of distinct causes of motion still unresolved into one another: gravitation, heat, electricity, chemical action, nervous action, and so forth; but whether the efforts of the present generation of savants to resolve all these different modes of production into one are ultimately successful or not, the attempt so to resolve them is perfectly legitimate. For, though these various causes produce, in other respects, sensations intrinsically different, and are not, therefore, capable of being resolved into one another, yet, in so far as they all produce motion, it is quite possible that the immediate antecedent of the motion may in all these different cases be the same; nor is it impossible that these various agencies themselves may, as the new doctrines assert, all of them have for their own immediate antecedent modes of molecular motion.

We need not extend our illustration to other cases, as, for instance, to the propagation of light, sound, heat, electricity, etc., through space, or any of the other phenomena which have been found susceptible of explanation by the resolution of their observed laws into more general laws. Enough has been said to display the difference between the kind of explanation and resolution of laws which is chimerical, and that of which the accomplishment is the great aim of science; and to show into what sort of elements the resolution must be effected, if at all.[159]

§ 3. As, however, there is scarcely any one of the principles of a true method of philosophizing which does not require to be guarded against errors on both sides, I must enter a caveat against another misapprehension, of a kind directly contrary to the preceding. M. Comte, among other occasions on which he has condemned, with some asperity, any attempt to explain phenomena which are “evidently primordial” (meaning, apparently, no more than that every peculiar phenomenon must have at least one peculiar and therefore inexplicable law), has spoken of the attempt to furnish any explanation of the color belonging to each substance, “la couleur élémentaire propre à chaque substance,” as essentially illusory. “No one,” says he, “in our time attempts to explain the particular specific gravity of each substance or of each structure. Why should it be otherwise as to the specific color, the notion of which is undoubtedly no less primordial?”[160]

Now although, as he elsewhere observes, a color must always remain a different thing from a weight or a sound, varieties of color might nevertheless follow, or correspond to, given varieties of weight, or sound, or some other phenomenon as different as these are from color itself. It is one question what a thing is, and another what it depends on; and though to ascertain the conditions of an elementary phenomenon is not to obtain any new insight into the nature of the phenomenon itself, that is no reason against attempting to discover the conditions. The interdict against endeavoring to reduce distinctions of color to any common principle, would have held equally good against a like attempt on the subject of distinctions of sound; which nevertheless have been found to be immediately preceded and caused by distinguishable varieties in the vibrations of elastic bodies; though a sound, no doubt, is quite as different as a color is from any motion of particles, vibratory or otherwise. We might add, that, in the case of colors, there are strong positive indications that they are not ultimate [pg 349] properties of the different kinds of substances, but depend on conditions capable of being superinduced upon all substances; since there is no substance which can not, according to the kind of light thrown upon it, be made to assume almost any color; and since almost every change in the mode of aggregation of the particles of the same substance is attended with alterations in its color, and in its optical properties generally.

The really weak point in the attempts which have been made to account for colors by the vibrations of a fluid, is not that the attempt itself is unphilosophical, but that the existence of the fluid, and the fact of its vibratory motion, are not proved, but are assumed, on no other ground than the facility they are supposed to afford of explaining the phenomena. And this consideration leads to the important question of the proper use of scientific hypotheses, the connection of which with the subject of the explanation of the phenomena of nature, and of the necessary limits to that explanation, need not be pointed out.