y be proper to take notice of. It is a
property inseparable from time, and which in a manner constitutes its
essence, that each of its parts succeeds another, and that none of them,
however contiguous, can ever be co-existent. For the same reason, that
the year 1737 cannot concur with the present year 1738 every moment must
be distinct from, and posterior or antecedent to another. It is certain
then, that time, as it exists, must be composed of indivisible moments.
For if in time we could never arrive at an end of division, and if
each moment, as it succeeds another, were not perfectly single and
indivisible, there would be an infinite number of co-existent moments,
or parts of time; which I believe will be allowed to be an arrant
contradiction.

The infinite divisibility of space implies that of time, as is evident
from the nature of motion. If the latter, therefore, be impossible, the
former must be equally so.

I doubt not but, it will readily be allowed by the most obstinate
defender of the doctrine of infinite divisibility, that these arguments
are difficulties, and that it is impossible to give any answer to them
which will be perfectly clear and satisfactory. But here we may
observe, that nothing can be more absurd, than this custom of calling a
difficulty what pretends to be a demonstration, and endeavouring by that
means to elude its force and evidence. It is not in demonstrations as
in probabilities, that difficulties can take place, and one argument
counter-ballance another, and diminish its authority. A demonstration,
if just, admits of no opposite difficulty; and if not just, it is a
mere sophism, and consequently can never be a difficulty. It is either
irresistible, or has no manner of force. To talk therefore of objections
and replies, and ballancing of arguments in such a question as this, is
to confess, either that human reason is nothing but a play of words, or
that the person himself, who talks so, has not a Capacity equal to such
subjects. Demonstrations may be difficult to be comprehended, because of
abstractedness of the subject; but can never have such difficulties as
will weaken their authority, when once they are comprehended.

It is true, mathematicians are wont to say, that there are here equally
strong arguments on the other side of the question, and that the
doctrine of indivisible points is also liable to unanswerable
objections. Before I examine these arguments and objections in detail,