indefinite and incomplete-which is what leads this thinker to say that
this is also true of the first principles of reality, so that the
One itself is not even an existing thing. This is incorrect, for
even in this world of animals and plants the principles from which
these come are complete; for it is a man that produces a man, and
the seed is not first.
It is out of place, also, to generate place simultaneously with
the mathematical solids (for place is peculiar to the individual
things, and hence they are separate in place; but mathematical objects
are nowhere), and to say that they must be somewhere, but not say what
kind of thing their place is.
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. Again, why in the world do the
other things that come from contraries, or that have contraries,
perish (even when all of the contrary is used to produce them),
while number does not? Nothing is said about this. Yet whether present
or not present in the compound the contrary destroys it, e.g. 'strife'
destroys the 'mixture' (yet it should not; for it is not to that
that is contrary).
Once more, it has not been determined at all in which way
numbers are the causes of substances and of being-whether (1) as
boundaries (as points are of spatial magnitudes). This is how
Eurytus decided what was the number of what (e.g. one of man and
another of horse), viz. by imitating the figures of living things with
pebbles, as some people bring numbers into the forms of triangle and
square. Or (2) is it because harmony is a ratio of numbers, and so
is man and everything else? But how are the attributes-white and sweet
and hot-numbers? Evidently it is not the numbers that are the
essence or the causes of the form; for the ratio is the essence, while
the number the causes of the form; for the ratio is the essence, while
the number is the matter. E.g. the essence of flesh or bone is
number only in this way, 'three parts of fire and two of earth'. And a
number, whatever number it is, is always a number of certain things,
either of parts of fire or earth or of units; but the essence is
that there is so much of one thing to so much of another in the
mixture; and this is no longer a number but a ratio of mixture of
numbers, whether these are corporeal or of any other kind.
Number, then, whether it be number in general or the number
which consists of abstract units, is neither the cause as agent, nor
the matter, nor the ratio and form of things. Nor, of course, is it
the final cause.