e.g. the first or
indivisible line, then the 2, and so on; these too extending up to
10.The "indivisible line"
or point was connected with 1, the line with 2, the plane with 3
and the solid with 4 (Aristot. Met. 14.3.9);
and 1+2+3+4=10.Again, if
number is separable, the question might be raised whether Unity is
prior, or 3 or 2.Now if
we regard number as composite, Unity is prior; but if we regard the
universal or form as prior, number is prior, because each unit is a
material part of number, while number is the form of the units. And
there is a sense in which the right angle is prior to the acute
angle—since it is definite and is involved in the definition
of the acute angle—and another sense in which the acute
angle is prior, because it is a part of the other, i.e., the right
angle is divided into acute angles.Thus regarded as matter the acute angle and
element and unit are prior; but with respect to form and substance in
the sense of formula, the right angle, and the whole composed of
matter and form, is prior. For the concrete whole is nearer to the
form or subject of the definition, although in generation it is
posterior.Cf. Aristot. Met. 7.10, 11.In what sense, then, is the One a first principle?
Because, they say, it is indivisible.But the universal and the part or element are
also indivisible. Yes, but they are prior in a different sense; the
one in formula and the other in time. In which sense, then, is the One
a first principle? for, as we have just said, both the right angle
seems to be prior to the acute angle, and the latter prior to the
former; and each of them is one.Accordingly the Platonists make the One a
first principle in both senses. But this is impossible; for in one
sense it is the One qua form or
essence,and in the
other the One qua part or matter, that is
primary. There is a sense in which both number and unit are one; they
are so in truth potentially—that is, if a number is not an
aggregate but a unity consisting of units distinct from those of other
numbers, as the Platonists hold— but each of the twoAristotle takes the number two as an example, but
the principle is of course universal. In a sense both number and
unit are one; but if the number exists as an actual unity, the
unit can only exist potentially. units is not one in
complete reality. The cause of the error which befell the Platonists
was that they were pursuing their inquiry from two points of
view—that of mathematics and that of general
definition—at the same time. Hence as a result of the former
they conceived of the One or first principle as a point, for the unit
is a point without position. (Thus they too, just like certain
others,represented
existing things as composed of that which is smallest.)Perhaps the Atomists; but cf.
Aristot. Met. 1.8.3, 4. We get,
then, that the unit is the material element of numbers, and at the
same time is prior to the number 2; and again we get that it is
posterior to 2 regarded as a whole or unity or form. On the other
hand, through looking for the universal, they were led to speak of the
unity predicated of a given number as a part in the formal sense also.
But these two characteristics cannot belong simultaneously to the same
thing. And if Unity itself must only be without
positionIf the text is
sound (and no convincing emendation has been suggested), it
seems best to understand ἄθετον in a rather wider sense than the
semi-technical one put forward by
Ross. "Without position"=not localized, i.e.
abstract. Unity as a principle has no concrete
instance.(for it differs only in that it is a principle) and 2
is divisible whereas the unit is not, the unit will be more nearly
akin to Unity itself; and if this is so, Unity itself will also be
more nearly akin to the unit than to 2. Hence each of the units in 2
will be prior to 2. But this they deny; at least they make out that 2
is generated first.Cf. Aristot. Met. 13.7.5.