ide he chuses, he runs himself into equal
difficulties. If he affirms, that in tracing these figures in his
imagination, he can imagine them to touch only in a point, he allows
the possibility of that idea, and consequently of the thing. If he says,
that in his conception of the contact of those lines he must make
them concur, he thereby acknowledges the fallacy of geometrical
demonstrations, when carryed beyond a certain degree of minuteness;
since it is certain he has such demonstrations against the concurrence
of a circle and a right line; that is, in other words, he can prove an
idea, viz. that of concurrence, to be INCOMPATIBLE with two other
ideas, those of a circle and right line; though at the same time he
acknowledges these ideas to be inseparable.

SECT. V. THE SAME SUBJECT CONTINUED.

If the second part of my system be true, that the idea of space
or extension is nothing but the idea of visible or tangible points
distributed in a certain order; it follows, that we can form no idea
of a vacuum, or space, where there is nothing visible or tangible. This
gives rise to three objections, which I shall examine together, because
the answer I shall give to one is a consequence of that which I shall
make use of for the others.

First, It may be said, that men have disputed for many ages concerning
a vacuum and a plenum, without being able to bring the affair to a
final decision; and philosophers, even at this day, think themselves
at liberty to take part on either side, as their fancy leads them. But
whatever foundation there may be for a controversy concerning the things
themselves, it may be pretended, that the very dispute is decisive
concerning the idea, and that it is impossible men coued so long reason
about a vacuum, and either refute or defend it, without having a notion
of what they refuted or defended.

Secondly, If this argument should be contested, the reality or at least
the possibility of the idea of a vacuum may be proved by the following
reasoning. Every idea is possible, which is a necessary and infallible
consequence of such as are possible. Now though we allow the world to be
at present a plenum, we may easily conceive it to be deprived of motion;
and this idea will certainly be allowed possible. It must also be
allowed possible, to conceive the annihilation of any part of matter by
the omnipotence of the deity, while the other parts remain at rest. For
as every idea, that is distinguish