| 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. |
| But that this latter supposition is absurd, I easily convince myself by the consideration of my clear ideas. |
| I first take the least idea I can form of a part of extension, and being certain that there is nothing more minute than this idea, I conclude, that whatever I discover by its means must be a real quality of extension. |
| I then repeat this idea once, twice, thrice, &c., and find the compound idea of extension, arising from its repetition, always to augment, and become double, triple, quadruple, &c., till at last it swells up to a considerable bulk, greater or smaller, in proportion as I repeat more or less the same idea. |
| When I stop in the addition of parts, the idea of extension ceases to augment; and were I to carry on the addition in infinitum, I clearly perceive, that the idea of extension must also become infinite. |
| Upon the whole, I conclude, that the idea of all infinite number of parts is individually the same idea with that of an infinite extension; that no finite extension is capable of containing an infinite number of parts; and consequently that no finite extension is infinitely divisible [Footnote 3.]. |