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 'tis 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. 'Tis not in demonstrations, as in probabilities, that difficulties can take place, and one argument counterbalance another, and diminish its authority. A demonstration, if just, admits of no opposite difficulty; and if not just, 'tis a mere sophism, and consequently can never be a difficulty. 'Tis either irresistible, or has no manner of force. To talk therefore of objections and replies, and balancing 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 the abstractedness of the subject; but can never have any such difficulties as will weaken their authority, when once they are comprehended. 'Tis 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, I will here take them in a body, and endeavour, by a short and decisive reason, to prove, at once, that 'tis utterly impossible they can have any just foundation. 'Tis 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 'tis certain we have an idea of extension; for otherwise, why do we talk and reason concerning it? 'Tis 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 'tis possible for extension really to exist conformable to it: and consequently, all the arguments employed against the possibility of mathematical points are mere scholastic quibbles, and unworthy of our attention.