and therefore the quantity or proportion of any
the least excess cannot be discovered; which is clear otherwise in
number, where, as has been said, 91 is as distinguishable from 90 as
from 9000, though 91 be the next immediate excess to 90. But it is not
so in extension, where, whatsoever is more than just a foot or an inch,
is not distinguishable from the standard of a foot or an inch; and in
lines which appear of an equal length, one may be longer than the other
by innumerable parts: nor can any one assign an angle, which shall be
the next biggest to a right one.

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.

6. Another reason for the necessity of names to numbers.

This I think to be the reason why some Americans I have spoken with,
(wh