If number
is an entity and its substance is nothing other than just number, as
some say, it follows that either (1) there is a first in it and a
second, each being different in species,-and either (a) this is true
of the units without exception, and any unit is inassociable with
any unit, or (b) they are all without exception successive, and any of
them are associable with any, as they say is the case with
mathematical number; for in mathematical number no one unit is in
any way different from another. Or (c) some units must be associable
and some not; e.g. suppose that 2 is first after 1, and then comes 3
and then the rest of the number series, and the units in each number
are associable, e.g. those in the first 2 are associable with one
another, and those in the first 3 with one another, and so with the
other numbers; but the units in the '2-itself' are inassociable with
those in the '3-itself'; and similarly in the case of the other
successive numbers. And so while mathematical number is counted
thus-after 1, 2 (which consists of another 1 besides the former 1),
and 3 which consists of another 1 besides these two), and the other
numbers similarly, ideal number is counted thus-after 1, a distinct
2 which does not include the first 1, and a 3 which does not include
the 2 and the rest of the number series similarly. Or (2) one kind
of number must be like the first that was named, one like that which
the mathematicians speak of, and that which we have named last must be
a third kind.
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