7. Why children number not earlier.
Thus children, either for want of names to mark the several progressions of
numbers, or not having yet the faculty to collect 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.
