5. Names necessary to numbers.
By the repeating, as has been said, the idea of an unit, and joining it to another
unit, we make thereof one collective idea, marked by the name two. And whosoever can do this, and proceed on,
still adding one more to the last collective idea which he had of any number, and gave a name to it, may count, or
have ideas, for several collections of units, distinguished one from another, as far as he hath a series of names for
following numbers, and a memory to retain that series, with their several names: all numeration being but still the
adding of one unit more, and giving to the whole together, as comprehended in one idea, a new or distinct name or
sign, whereby to know it from those before and after, and distinguish it from every smaller or greater multitude of
units. So that he that can add one to one, and so to two, and so go on with his tale, taking still with him the distinct
names belonging to every progression; and so again, by subtracting an unit from each collection, retreat and
lessen them, is capable of all the ideas of numbers within the compass of his language, or for which he hath
names, though not perhaps of more. For, the several simple modes of numbers being in our minds but so many
combinations of units, which have no variety, nor are capable of any other difference but more or less, names or
marks for each distinct combination seem more necessary than in any other sort of ideas. For, without such names
or marks, we can hardly well make use of numbers in reckoning, especially where the combination is made up of
any great multitude of units; which put together, without a name or mark to distinguish that precise collection,
will hardly be kept from being a heap in confusion.
