17. As the reasons here advanced would seem to imply that every number
is limited, we may ask in which sense may a number be said to be
infinite? This conclusion is right, for it is against the nature of
number to be infinite. Why do people then often speak of a number as
infinite? Is it in the same sense that one calls a line infinite? A
line is said to be infinite, not that there really exists an infinite
line of this kind, but to imply the conception of a line as great as
possible, greater than any given line. Similarly with number. When
we know which is the number (of certain objects), we can double it
by thought, without, on that account, adding any other number to the
first. How indeed would it be possible to add to exterior objects the
conception of our imagination, a conception that exists in ourselves
exclusively? We shall therefore say that, among intelligible entities,
a line is infinite; otherwise, the intelligible line would be a simple
quantative expression. If however the intelligible line be not this, it
must be infinite in number; but we then understand the word "infinite"
in a sense other than that of having no limits that could not be
transcended. In what sense then is the word "infinite" here used? In
the sense that the conception of a limit is not implied in the being of
a line in itself.