ion
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 ma