Those who say that existing things come from elements and that the
first of existing things are the numbers, should have first
distinguished the senses in which one thing comes from another, and
then said in which sense number comes from its first principles.
By intermixture? But (1) not everything is capable of
intermixture, and (2) that which is produced by it is different from
its elements, and on this view the one will not remain separate or a
distinct entity; but they want it to be so.
By juxtaposition, like a syllable? But then (1) the elements
must have position; and (2) he who thinks of number will be able to
think of the unity and the plurality apart; number then will be this-a
unit and plurality, or the one and the unequal.
Again, coming from certain things means in one sense that these
are still to be found in the product, and in another that they are
not; which sense does number come from these elements? Only things
that are generated can come from elements which are present in them.
Does number come, then, from its elements as from seed? But nothing
can be excreted from that which is indivisible. Does it come from
its contrary, its contrary not persisting? But all things that come in
this way come also from something else which does persist. Since,
then, one thinker places the 1 as contrary to plurality, and another
places it as contrary to the unequal, treating the 1 as equal,
number must be being treated as coming from contraries. There is,
then, something else that persists, from which and from one contrary
the compound is or has come to be.
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