their contact he can conceive them as touching in a mathematical point,
or if he must necessarily imagine them to concur for some space.
Whichever side 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, be 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