53. Definitions, according to the ordinary meaning of the word, are nothing but explanations of words which denote universal ideas. They are then meant to state what is comprehended in these general ideas. The old rules are familiar, that this must be done by combining the genus with the specific difference, and its corollary: that the definition must not be too wide, nor yet too narrow, hence that it must exactly cover that which the word really means. The investigation of the meanings actually accepted, i.e., almost always in customary language or in some particular branch of customary language, is in itself an important scientific problem; but it has nothing to do with pure scientific thought. In this application the problem is generally confused with the quite different one which supposes that the person defining is to state in what sense he wills to use the general name. We say the problems are confused, for in the first place we are far from being always conscious of the difference, and in the second place it is expected that the scientific subject shall not behave as if he were sovereign; i.e., that he should keep as closely as possible to customary usage. It is even assumed that the person defining apprehends his problem best when he really only unfolds the customary usage, in other words, when he thinks what every one thinks. If now it happens that a fluid and manifold usage is brought into a fixed and uniform form, then indeed such a limitation of the meaning may suffice for many ends. It is in this sense that laws determine the meaning of words; but then the theory breaks down that we are dealing with the explication of usage; it is manifest that we are aiming at establishing indisputable limits within which the law shall hold. Quite analogous is the end to which scientific definition must always refer; the fixing of a meaning within a train of thought, hence within a book, a system, etc. In coining a scientific concept therefore, we do it upon our own responsibility and with complete freedom in respect of customary usage. This is what Pascal means when he says: “nothing is more free than definitions”. And so the more acute logicians have always seen that scientific definitions are propositions, the truth of which rests upon the will of the person advancing them. Even if a name already denotes a concept in some (e.g.) scientific usage (i.e. denotes a definitely limited universal idea), still the person defining must appropriate this concept and the name, if the definition is to hold in his mental context also, i.e. is to be true for him. But free definition is completely necessary when we are operating with those works of thought of the individual
