1. Simplicity, as contrasted with the complexity of empirical laws; this is the necessary corollary of the operation that gives rise to it, since it is an abstraction of abstractions, the final result of a long series of eliminations. Compare with the long, vague, entangled formulæ, charged with details, of which examples were given above, the enunciation of the higher laws, which are usually short and invariably precise. And, it may be added, invariably lucid, at least to the scientist who is in the habit of dealing with them, because he knows exactly what they cover. In this connexion a saying of D’Alembert deserves to be recalled and considered, because it discloses, better than any commentary, the psychology of abstract minds: “The most abstract notions, such as the majority of mankind regard as the most inaccessible, are often those which carry with them the greatest elucidating power: our ideas seem to be blotted out by obscurity in proportion as, in any object, we examine into its sensible properties.”
2. Quantitative determination. 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. Yet these are often a very poor substitute for the equation, or worse—for they offer an illusory preciseness, and are fallacious.
3. It is well to insist upon the ideal character of these laws, because one is apt to forget that, in virtue of their very abstraction, they can be approximate only; and can but be applied, and reduced from theory to practice, by means of rectifications and additions. It has been said that “physical laws are general truths that are invariably more or less falsified for each particular case.” All scientific men, and there are many, who have reflected on the subject, bring out this character of approximation.[129]
Thus—it is not absolutely true that a movement is uniform and rectilinear. The theoretic law of the oscillation of a pendulum is unrealisable, because there is no non-resisting medium, no totally rigid and inextensible bar, no suspending apparatus capable of turning without friction. A planet could only describe an exact ellipse if it alone were turning round the sun: but as, in point of fact, there are several which act and react upon one another, Kepler’s law remains ideal. It is known by very accurate researches that Mariotte’s law of the relations between the density of a gas, and the pressure which it bears, is not strictly accurate for either; but the differences between theory and reality are so slight that, in ordinary cases, they are negligible. The laws of thermodynamics (conservation of energy, correlation of forces) which are so much used in the present day because of their character of generality, and are held by some to be the ultimate principle of phenomena, have no absolute value. It is not, e. g., correct to say that all change generates a change which can be re-transformed without loss or addition. The first moment of enthusiasm passed, there was no lack of criticism and of reservation on this point. And so in other instances, ad infinitum.
In brief, the concept of law, whenever it is more than a vague term in the mind, corresponds either to a direct condensation of facts (empirical laws), or to an ideal simplification (theoretical laws); but, imperfect or perfect, the mental process is the same in the two cases. They differ only in the degree of simplification attainable by analysis for any given material or datum. If empirical law, which is in strict relation with experience, has not been idolised, this distinction and misfortune has frequently befallen the other categories. It has been forgotten that, in the sciences as in the arts, the ideal is only an ideal, although it is here attained by different means, viz., elimination, voluntary omission for the sake of preciseness, a more or less artificial reduction to unity. Consequently many have fallen into the strange illusion of believing that, in manipulating experience by the labor of an ever-growing abstraction, the absolute can be brought out.[130]
SECTION VI. CONCEPT OF SPECIES.
In departing from phenomena by successive abstractions and generalisations, we rise to laws that are more and more extensive: so in setting out from the individual, species, genera, orders, branches, and the like, are formed by a succession of abstractions and generalisations. We have already followed this labor of the intellect in its primitive attempts to introduce order into the multiplicity and variety of living beings ([Ch. III.]). We saw its start in the period of generic images, its passage through the various degrees of the concrete-abstract period, and its final outcome by diverse paths into a unitary conception. We must now take up the subject from the point at which we left it, and consider the nature of the classificatory concepts at the final term of their development, the moment of their highest scientific determination. If the geometers were the first who abstracted from extension the essential data of Space; if the astronomers accomplished an analogous operation for Time; the naturalists for their part had by abstraction to disengage from among the numerous characteristics of living beings, those which, as fundamental, enable them to reduce individuals to species, species to genera, and so on. They are the inventors of the concepts which govern this province of experience.
The notion of the individual, which is the basis, and preliminary material, of biological classification, is sufficiently clear so long as we confine ourselves to the higher creatures; it becomes obscure and equivocal in descending to the lower grades, where life multiplies by budding, or by division. Hence it has been a great stumbling-block to the naturalists. For our purpose, the point is negligible. We can without inconvenience omit the debates on this subject, and presume that individuality always has its fixed characteristics. The work of abstraction and of generalisation alone concern us.
Among all others, the Concept of Species is certainly the one which—more especially in our own day—has been the most studied and disputed. Many efforts have been made to determine its essential characters, to which some attribute, and others refuse, an objective value. In effect, and broadly speaking—two contrary theories obtain in this connexion:
1. That of fixity of species, the oldest, and long paramount: still perhaps finding its partisans. If we accept this, we admit at the same time that the naturalist in determining species, reveals a mystery of nature, and partially discovers the plan of creation.