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1091a]
[1]
And if he speaks of some other component, he will
be maintaining too many elements; while if some one thing is the first
principle of each kind of number, unity will be something common to
these several kinds.We
must inquire how it is that unity is these many things, when at the
same time number, according to him, cannot be derived otherwise than
from unity and an indeterminate dyad.
1All these views
are irrational; they conflict both with one another and with sound
logic, and it seems that in them we have a case of Simonides' "long
story
2"; for men
have recourse to the "long story," such as slaves tell, when they have
nothing satisfactory to say.The very elements too, the Great and Small,
seem to protest at being dragged in; for they cannot possibly generate
numbers except rising powers of 2.
3It
is absurd also, or rather it is one of the impossibilities of this
theory, to introduce generation of things which are eternal.There is no reason to doubt
whether the Pythagoreans do or do not introduce it; for they clearly
state that when the One had been constituted—whether out of
planes or superficies or seed or out of something that they cannot
explain—immediately the nearest part of the Infinite began
to be drawn in and limited by the Limit.
4 However, since they are here
explaining the construction of the universe and meaning to speak in
terms of physics, although we may somewhat criticize their physical
theories,
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it is only
fair to exempt them from the present inquiry; for it is the first
principles in unchangeable things that we are investigating, and
therefore we have to consider the generation of this kind of
numbers.
They
5 say that there is no generation of odd
numbers,
6 which clearly implies that there is generation of
even ones; and some hold that the even is constructed first out of
unequals—the Great and Small—when they are
equalized.
7 Therefore the
inequality must apply to them before they are equalized. If they had
always been equalized they would not have been unequal before; for
there is nothing prior to that which has always been.Hence evidently it is not for
the sake of a logical theory that they introduce the generation of
numbers
A difficulty, and a discredit
to those who make light of the difficulty, arises out of the question
how the elements and first principles are related to the the Good and
the Beautiful. The difficulty is this: whether any of the elements is
such as we mean when we
8 speak
of the Good or the Supreme Good, or whether on the contrary these are
later in generation than the elements.It would seem that there is an agreement
between the mythologists and some present-day thinkers,
9
who deny that there is such an element, and say that it was only after
some evolution in the natural order of things that both the Good and
the Beautiful appeared. They do this to avoid a real difficulty which
confronts those who hold, as some do, that unity is a first principle.