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 measureables. 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, lessens not one jot the power of adding
to it, or brings him any nearer the end of the inexhaustible stock
of number; where still there remains as much to be added, as if none
were taken out.
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