scattered ideas
into complex ones, and range them in a regular order, and so retain them
in their memories, as is necessary to reckoning, do not begin to number
very early, nor proceed in it very far or steadily, till a good while
after they are well furnished with good store of other ideas: and one
may often observe them discourse and reason pretty well, and have very
clear conceptions of several other things, before they can tell twenty.
And some, through the default of their memories, who cannot retain the
several combinations of numbers, with their names, annexed in their
distinct orders, and the dependence of so long a train of numeral
progressions, and their relation one to another, are not able all their
lifetime to reckon, or regularly go over any moderate series of numbers.
For he that will count twenty, or have any idea of that number, must
know that nineteen went before, with the distinct name or sign of every
one of them, as they stand marked in their order; for wherever this
fails, a gap is made, the chain breaks, and the progress in numbering
can go no further. So that to reckon right, it is required, (1) That
the mind distinguish carefully two ideas, which are different one from
another only by the addition or subtraction of ONE unit: (2) That it
retain in memory the names or marks of the several combinations, from an
unit to that number; and that not confusedly, and at random, but in that
exact order that the numbers follow one another. In either of which, if
it trips, the whole business of numbering will be disturbed, and there
will remain only the confused idea of multitude, but the ideas necessary
to distinct numeration will not be attained to.

8. Number measures all Measurables.

This further is observable in number, that it is that which the mind
makes use of in measuring all things that by us are measurable, which
principally are EXPANSION and DURATION; and our idea of infinity, even
when applied to those, seems to be nothing but the infinity of number.
For what else are our ideas of Eternity and Immensity, but the repeated
additions of certain ideas of imagined parts of duration and expansion,
with the infinity of number; in which we can come to no end of addition?
For such an inexhaustible stock, number (of all other our ideas) most
clearly furnishes us with, as is obvious to every one. For let a man
collect into one sum as great a number as he pleases, this multitude how
great soever, lessen