Once
more, how come I by so just a notion of numbers? All numbers are
but repeated units. Every number is but a compound, or a repetition
of units. The number of two, for instance, is but two units; the
number of four is reducible to one repeated four times. Therefore
we cannot conceive any number without conceiving unity, which is the
essential foundation of any possible number; nor can we conceive any
repetition of units without conceiving unity itself, which is its
basis.
But which way can I know any real unit? I never saw, nor so much as
imagined any by the report of my senses. Let me take, for instance,
the most subtle atom; it must have a figure, length, breadth, and
depth, a top and a bottom, a left and a right side; and again the
top is not the bottom, nor one side the other. Therefore this atom
is not truly one, for it consists of parts. Now a compound is a
real number, and a multitude of beings. It is not a real unit, but
a collection of beings, one of which is not the other. I therefore
never learnt by my eyes, my ears, my hands, nor even by my
imagination, that there is in nature any real unity; on the
contrary, neither my senses nor my imagination ever presented to me
anything but what is a compound, a real number or a multitude. All
unity continually escapes me; it flies me as it were by a kind of
enchantment. Since I look for it in so many divisions of an atom, I
certainly have a distinct idea of it; and it is only by its simple
and clear idea that I arrive, by the repetition of it, at the
knowledge of so many other numbers.
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