| In rejecting the infinite capacity of the mind, we suppose it may arrive at an end in the division of its ideas; nor are there any possible means of evading the evidence of this conclusion. |
| It is therefore certain, that the imagination reaches a minimum, and may raise up to itself an idea, of which it cannot conceive any sub-division, and which cannot be diminished without a total annihilation. |
| When you tell me of the thousandth and ten thousandth part of a grain of sand, I have a, distinct idea of these numbers and of their different proportions; but the images, which I form in my mind to represent the things themselves, are nothing different from each other, nor inferior to that image, by which I represent the grain of sand itself, which is supposed so vastly to exceed them. |
| What consists of parts is distinguishable into them, and what is distinguishable is separable. |
| But whatever we may imagine of the thing, the idea of a grain of sand is not distinguishable, nor separable into twenty, much less into a thousand, ten thousand, or an infinite number of different ideas. |
| It is the same case with the impressions of the senses as with the ideas of the imagination. |
| Put a spot of ink upon paper, fix your eye upon that spot, and retire to such a distance, that, at last you lose sight of it; it is plain, that the moment before it vanished the image or impression was perfectly indivisible. |
| It is not for want of rays of light striking on our eyes, that the minute parts of distant bodies convey not any sensible impression; but because they are removed beyond that distance, at which their impressions were reduced to a minimum, and were incapable of any farther diminution. |
| A microscope or telescope, which renders them visible, produces not any new rays of light, but only spreads those, which always flowed from them; and by that means both gives parts to impressions, which to the naked eye appear simple and uncompounded, and advances to a minimum, what was formerly imperceptible. |
| We may hence discover the error of the common opinion, that the capacity of the mind is limited on both sides, and that it is impossible for the imagination to form an adequate idea, of what goes beyond a certain degree of minuteness as well as of greatness. |
| Nothing can be more minute, than some ideas, which we form in the fancy; and images, which appear to the senses; since there are ideas and images perfectly simple and indivisible. |
| The only defect of our senses is, that they give us disproportioned images of things, and represent as minute and uncompounded what is really great and composed of a vast number of parts. |
| This mistake we are not sensible of: but taking the impressions of those minute objects, which appear to the senses, to be equal or nearly equal to the objects, and finding by reason, that there are other objects vastly more minute, we too hastily conclude, that these are inferior to any idea of our imagination or impression of our senses. |
| This however is certain, that we can form ideas, which shall be no greater than the smallest atom of the animal spirits of an insect a thousand times less than a mite: And we ought rather to conclude, that the difficulty lies in enlarging our conceptions so much as to form a just notion of a mite, or even of an insect a thousand times less than a mite. |
| For in order to form a just notion of these animals, we must have a distinct idea representing every part of them, which, according to the system of infinite divisibility, is utterly impossible, and, recording to that of indivisible parts or atoms, is extremely difficult, by reason of the vast number and multiplicity of these parts. |
| SECT. II. OF THE INFINITE DIVISIBILITY OF SPACE AND TIME. |
| Wherever ideas are adequate representations of objects, the relations, contradictions and agreements of the ideas are all applicable to the objects; and this we may in general observe to be the foundation of all human knowledge. |
| But our ideas are adequate representations of the most minute parts of extension; and through whatever divisions and subdivisions we may suppose these parts to be arrived at, they can never become inferior to some ideas, which we form. |
| The plain consequence is, that whatever appears impossible and contradictory upon the comparison of these ideas, must be really impossible and contradictory, without any farther excuse or evasion. |
| Every thing capable of being infinitely divided contains an infinite number of parts; otherwise the division would be stopt short by the indivisible parts, which we should immediately arrive at. |
| If therefore any finite extension be infinitely divisible, it can be no contradiction to suppose, that a finite extension contains an infinite number of parts: And vice versa, if it be a contradiction to suppose, that a finite extension contains an infinite number of parts, no finite extension can be infinitely divisible. |