By a definition I do not mean a statement conveying the exact sense of a word, although that will naturally be involved in a definition. But what I mean is the explanation of the relations of an intellectual conception to other conceptions.
A definition is the logical analysis of a predicate in general terms. It has two branches, the one asserting that the definitum is applicable to whatever there may be to which the definition is applicable; the other (which ordinarily has several clauses), that the definition is applicable to whatever there may be to which the definitum is applicable. A definition does not assert that anything exists.
As Aristotle well says (and his authority is well-nigh absolute upon a question of logical terminology), a definition asserts the existence of nothing. A definition would consist of two members, of which the first should declare that any object to which the definitum, or defined term, should be applicable would possess the characters involved in the definition; while the second should declare that to any object which should possess those characters the definitum would be applicable.
The definition and the utility of a definition require it to specify everything essential, and to omit all that is inessential, to its definitum: though it may be pardoned for calling special attention to an omission in order to show that it was not inconsiderate.