We may hence discover the error of the common opinion, that the capacity of the mind is limited on both sides, and that 'tis 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 according to that of indivisible parts or atoms, is extremely difficult, by reason of the vast number and multiplicity of these parts.
[SECTION 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 stopped 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 an 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.[1]
I may subjoin another argument proposed by a noted author,[2] which seems to me very strong and beautiful. 'Tis evident, that existence in itself belongs only to unity, and is never applicable to number, but on account of the unites of which the number is composed. Twenty men may be said to exist; but 'tis only because one, two, three, four, &c. are existent; and if you deny the existence of the latter, that of the former falls of course. 'Tis therefore utterly absurd to suppose any number to exist, and yet deny the existence of unites; and as extension is always a number, according to the common sentiment of metaphysicians, and never resolves itself into any unite or indivisible quantity, it follows that extension can never at all exist. 'Tis in vain to reply, that any determinate quantity of extension is an unite; but such a one as admits of an infinite number of fractions, and is inexhaustible in its subdivisions. For by the same rule, these twenty men may be considered as an unite. The whole globe of the earth, nay, the whole universe may be considered as an unite. That term of unity is merely a fictitious denomination, which the mind may apply to any quantity of objects it collects together; nor can such an unity any more exist alone than number can, as being in reality a true number. But the unity, which can exist alone, and whose existence is necessary to that of all number, is of another kind, and must be perfectly indivisible, and incapable of being resolved into any lesser unity.
All this reasoning takes place with regard to time; along with an additional argument, which it may be proper to take notice of. 'Tis 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 coexistent. 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. 'Tis 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.