Note note 22 — ANALYSIS OF THE PHENOMENA OF THE HUMAN MIND James Mill

22 The vague manner in which the author uses the phrase “to be a name of” (a vagueness common to almost all thinkers who have not precise terms expressing the two modes of signification which I call denotation and connotation, and employed for nothing else) has led him, in the present case, into a serious misuse of terms. Numbers are, in the strictest propriety, names of objects. Two is surely a name of the things which are two, the two balls, the two fingers, &c. The process of adding one to one which forms two is connoted, not denoted, by the name two. Numerals, in short, are concrete, not abstract names: they denote the actual collections of things, and connote the mental process of counting them. It is not twoness and threeness that are fiveness: the twoness of my two hands and the threeness of the feet of the table cannot be added together to form another abstraction. It is two balls added to three balls that make, in the concrete, five balls. Numerals are a class of concrete general names predicable of all things whatever, but connoting, in each case, the quantitative relation of the thing to some fixed standard, as previously explained by the author.—Ed.