| 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.]. |
| [Footnote 3. It has been objected to me, that infinite divisibility supposes only an infinite number of PROPORTIONAL not of ALIQIOT parts, and that an infinite number of proportional parts does not form an infinite extension. |
| But this distinction is entirely frivolous. |
| Whether these parts be calld ALIQUOT or PROPORTIONAL, they cannot be inferior to those minute parts we conceive; and therefore cannot form a less extension by their conjunction.] |
| I may subjoin another argument proposed by a noted author [Mons.MALEZIEU], which seems to me very strong and beautiful. |
| It is 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 it is 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. |
| It is 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. |
| It is 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 sub-divisions. |
| For by the same rule these twenty men may be considered as a unit. |
| The whole globe of the earth, nay the whole universe, may be considered as a unit. |
| 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. |
| It is 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 co-existent. |
| 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. |
| It is 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. |