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Metaphysics   


In a sense, however, they make it plain that goodness belongs to
numbers, and that the odd, the straight, the square, the potencies
of certain numbers, are in the column of the beautiful. For the
seasons and a particular kind of number go together; and the other
agreements that they collect from the theorems of mathematics all have
this meaning. Hence they are like coincidences. For they are
accidents, but the things that agree are all appropriate to one
another, and one by analogy. For in each category of being an
analogous term is found-as the straight is in length, so is the
level in surface, perhaps the odd in number, and the white in colour.
Again, it is not the ideal numbers that are the causes of
musical phenomena and the like (for equal ideal numbers differ from
one another in form; for even the units do); so that we need not
assume Ideas for this reason at least.
These, then, are the results of the theory, and yet more might
be brought together. The fact that our opponnts have much trouble with
the generation of numbers and can in no way make a system of them,
seems to indicate that the objects of mathematics are not separable
from sensible things, as some say, and that they are not the first
principles.


-THE END-

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