| 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, 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 upon shutting them again, and considering the distance betwixt these bodies, I acquire the idea of extension. |
| As every idea is derived from some impression, which is exactly similar to it, the impressions similar to this idea of extension, must either be some sensations derived from the sight, or some internal impressions arising from these sensations. |
| Our internal impressions are our passions, emotions, desires and aversions; none of which, I believe, will ever be asserted to be the model, from which the idea of space is derived. |
| There remains therefore nothing but the senses, which can convey to us this original impression. |