Chapter XCII: Section III: Definitions Explain the Abstract Generating Elements

of Things

To begin with Definitions. Mill teaches that there is no definition of things, and that when you define a sphere as the solid generated by the revolution of a semicircle about its diameter, you only define a name. Doubtless you tell me by this the meaning of a name, but you also teach me a good deal more. You state that all the properties of every sphere are derived from this generating formula; you reduce an infinitely complex system of facts to two elements; you transform sensible into abstract data; you express the essence of the sphere, that is to say, the inner and primordial cause of all its properties. Such is the nature of every true definition; it is not content with explaining a name, it is not a mere description; it does not simply indicate a distinctive property; it does not limit itself to that ticketing of an object which will cause it to be distinguished from all others. There are, besides its definition, several other ways of causing the object to be recognized; there are other properties belonging to it exclusively: we might describe a sphere by saying that, of all bodies having an equal surface, it occupies the most space; or in many other ways. But such descriptions are not definitions; they lay down a characteristic and derived property, not a generating and primitive one; they do not reduce the thing to its factors, and reconstruct it before our eyes; they do not show its inner nature and its irreducible elements. A definition is a proposition which marks in an object that quality from which its others are derived, but which is not derived from others. Such a proposition is not verbal, for it teaches the quality of a thing. It is not the affirmation of an ordinary quality, for it reveals to us the quality which is the source of the rest. It is an assertion of an extraordinary kind, the most fertile and valuable of all, which sums up a whole science, and in which it is the aim of every science to be summed up. There is a definition in every science, and one for each object. We do not, in every case, possess it, but we search for it everywhere. We have arrived at defining the planetary motion by the tangential force and attraction which compose it; we can already partially define a chemical body by the notion of equivalent, and a living body by the notion of type. We are striving to transform every group of phenomena into certain laws, forces, or abstract notions. We endeavor to attain in every object the generating elements, as we do attain them in the sphere, the cylinder, the circle, the cone, and in all mathematical loci. We reduce natural bodies to two or three kinds of movement--attraction, vibration, polarization--as we reduce geometrical bodies to two or three kinds of elements--the point, the movement, the line; and we consider our science partial or complete, provisional or definite, according as this reduction is approximate or absolute, imperfect or complete.