I will here take them in a body, and endeavour by a short and decisive
reason to prove at once, that it is utterly impossible they can have any
just foundation.

It is an established maxim in metaphysics, That whatever the mind
clearly conceives, includes the idea of possible existence, or in other
words, that nothing we imagine is absolutely impossible. We can form the
idea of a golden mountain, and from thence conclude that such a mountain
may actually exist. We can form no idea of a mountain without a valley,
and therefore regard it as impossible.

Now it is certain we have an idea of extension; for otherwise why do we
talk and reason concerning it? It is likewise certain that this idea,
as conceived by the imagination, though divisible into parts or inferior
ideas, is not infinitely divisible, nor consists of an infinite number
of parts: For that exceeds the comprehension of our limited capacities.
Here then is an idea of extension, which consists of parts or inferior
ideas, that are perfectly, indivisible: consequently this idea implies
no contradiction: consequently it is possible for extension really to
exist conformable to it: and consequently all the arguments employed
against the possibility of mathematical points are mere scholastick
quibbles, and unworthy of our attention.

These consequences we may carry one step farther, and conclude that all
the pretended demonstrations for the infinite divisibility of extension
are equally sophistical; since it is certain these demonstrations cannot
be just without proving the impossibility of mathematical points; which
it is an evident absurdity to pretend to.

SECT. III. OF THE OTHER QUALITIES OF OUR IDEA OF SPACE AND TIME.

No discovery coued have been made more happily for deciding all
controversies concerning ideas, than that abovementioned, that
impressions always take the precedency of them, and that every idea,
with which the imagination is furnished, first makes its appearance in a
correspondent impression. These latter perceptions are all so clear and
evident, that they admit of no controversy; though many of our ideas are
so obscure, that it is almost impossible even for the mind, which forms
them, to tell exactly their nature and composition. Let us apply this
principle, in order to discover farther the nature of our ideas of space
and time.

Upon opening my eyes, and turning them to the surrounding objects,
I perceive many visible bodies; and