NUMERICAL DIFFERENCE. (Logic.) Down to our own time, logicians have distinguished one individual as differing numerically from another, when both belong to the same species : thus one horse is said to differ numerically from another. The idiom has never found its way into common language, though given in our old dictionaries. Nor is this to be wondered at, for number in English is multitude ; and two regiments may differ numerically, but two men cannot.
The wrong use of the English adjective arises from the Greek word Itis0a4r, which is used for the result of counting, being supposed to signify the multitude counted. This it did only in the sense in which summa (sum) came to signify multitude in English : thus 10 is a sum, of which the unites summa is unites decima. The difference is, that the word sum never had any other sense in English : while in Greek it never lost its first meaning, that of the item of enumeration. Thus
of tcptOyol TOFI aceiyaror meant the limits of the body : Herodotus cannot tell what multitude (witS,Oor) each nation furnished to the enumeration (?s apa94v). And Aristotle distinctly lays it down that pords and Itpt0/44r differ neither in quantity nor in quality : meaning that the thing which is pords when it stands alone becomes ainOpacr when it stands in an enumeration as one of the items. Hence the Greek logicians could properly say that though a horse and a sheep differ ef3ct (in species), one horse and another only differ apiel.S, (as different items of one species). The word monadic would be better than numerical, for logical use. See more details in the Transactions of the Philological Society.'