Scientific men are still seeking, and may be long ere they find, a suitable definition of one of the earliest words in the vocabulary of the human race, and one of those of which the popular sense is plainest and best understood. The word I mean is Heat; and the source of the difficulty is the imperfect state of our scientific knowledge, which has shown to us multitudes of phenomena certainly connected with the same power which causes what our senses recognise as heat, but has not yet taught us the laws of those phenomena with sufficient accuracy to admit of our determining under what characteristics the whole of those phenomena shall ultimately be embodied as a class: which characteristics would of course be so many differentiæ for the definition of the power itself. We have advanced far enough to know that one of the attributes connoted must be that of operating as a repulsive force; but this is certainly not all which must ultimately be included in the scientific definition of heat.
What is true of the definition of any term of science, is of course true of the definition of a science itself: and accordingly, (as observed in the Introductory Chapter of this work,) the definition of a science must necessarily be progressive and provisional. Any extension of knowledge or alteration in the current opinions respecting the subject matter, may lead to a change more or less extensive in the particulars included in the science; and its composition being thus altered, it may easily happen that a different set of characteristics will be found better adapted as differentiæ for defining its name.
In the same manner in which a special or technical definition has for its object to expound the artificial classification out of which it grows; the Aristotelian logicians seem to have imagined that it was also the business of ordinary definition to expound the ordinary, and what they deemed the natural, classification of things, namely, the division of them into Kinds; and to show the place which each Kind occupies, as superior, collateral, or subordinate among other Kinds. This notion would account for the rule that all definition must necessarily be _per genus et differentiam_, and would also explain why any one differentia was deemed sufficient. But to expound, or express in words, a distinction of Kind, has already been shown to be an impossibility: the very meaning of a Kind is, that the properties which distinguish it do not grow out of one another, and cannot therefore be set forth in words, even by implication, otherwise than by enumerating them all: and all are not known, nor ever will be so. It is idle, therefore, to look to this as one of the purposes of a definition: while, if it be only required that the definition of a Kind should indicate what Kinds include it or are included by it, any definitions which expound the connotation of the names will do this: for the name of each class must necessarily connote enough of its properties to fix the boundaries of the class. If the definition, therefore, be a full statement of the connotation, it is all that a definition can be required to be.