rd matter to
further speculation.

CHAPTER XVI.

IDEA OF NUMBER.

1. Number the simplest and most universal Idea.

Amongst all the ideas we have, as there is none suggested to the mind by
more ways, so there is none more simple, than that of UNITY, or one: it
has no shadow of variety or composition in it: every object our senses
are employed about; every idea in our understandings; every thought of
our minds, brings this idea along with it. And therefore it is the most
intimate to our thoughts, as well as it is, in its agreement to all
other things, the most universal idea we have. For number applies itself
to men, angels, actions, thoughts; everything that either doth exist or
can be imagined.

2. Its Modes made by Addition.

By repeating this idea in our minds, and adding the repetitions
together, we come by the COMPLEX ideas of the MODES of it. Thus, by
adding one to one, we have the complex idea of a couple; by putting
twelve units together we have the complex idea of a dozen; and so of a
score or a million, or any other number.

3. Each Mode distinct.

The SIMPLE MODES of NUMBER are of all other the most distinct; every the
least variation, which is an unit, making each combination as clearly
different from that which approacheth nearest to it, as the most remote;
two being as distinct from one, as two hundred; and the idea of two as
distinct from the idea of three, as the magnitude of the whole earth is
from that of a mite. This is not so in other simple modes, in which it
is not so easy, nor perhaps possible for us to distinguish betwixt
two approaching ideas, which yet are really different. For who will
undertake to find a difference between the white of this paper and that
of the next degree to it: or can form distinct ideas of every the least
excess in extension?

4. Therefore Demonstrations in Numbers the most precise.

The clearness and distinctness of each mode of number from all
others, even those that approach nearest, makes me apt to think that
demonstrations in numbers, if they are not more evident and exact
than in extension, yet they are more general in their use, and more
determinate in their application. Because the ideas of numbers are more
precise and distinguishable than in extension; where every equality and
excess are not so easy to be observed or measured; because our thoughts
cannot in space arrive at any determined smallness beyond which it
cannot go, as an unit;