[
1093a]
[1]
If all things must share in number, it
must follow that many things are the same; i.e., that the same number
belongs both to this thing and to something else. Is number, then, a
cause; i.e., is it because of number that the object exists? Or is
this not conclusive? E.g., there is a certain number of the sun's
motions, and again of the moon's,
1 and indeed
of the life and maturity of every animate thing. What reason, then, is
there why some of these numbers should not be squares and others
cubes, some equal and others double?There is no reason; all things must fall
within this range of numbers if, as was assumed, all things share in
number, and different things may fall under the same number. Hence if
certain things happened to have the same number, on the Pythagorean
view they would be the same as one another, because they would have
the same form of number; e.g., sun and moon would be the same.
2 But why
are these numbers causes? There are seven vowels,
3
seven strings to the scale,
4 seven Pleiads; most animals (though not
all
5) lose their teeth in the seventh year; and there were
seven heroes who attacked
Thebes. Is it, then, because the number 7 is such as it
is that there were seven heroes, or that the Pleiads consist of seven
stars? Surely there were seven heroes because of the seven gates, or
for some other reason, and the Pleiads are seven because we count them
so; just as we count the Bear as 12, whereas others count more stars
in both.
[20]
Indeed, they assert also that
Ξ, Ψ and
Ζ are concords,
6 and that because there are three concords, there
are three double consonants. They ignore the fact that there might be
thousands of double consonants—because there might be one
symbol for
ΓΡ. But if they say that
each of these letters is double any of the others, whereas no other
is,
7 and that the reason is
that there are three regions
8 of the mouth, and that one
consonant is combined with
ς in each
region, it is for this reason that there are only three double
consonants, and not because there are three concords—because
there are really more than three; but there cannot be more than three
double consonants.
Thus these thinkers are like the
ancient Homeric scholars, who see minor similarities but overlook
important ones.
Some say that there are
many correspondences of this kind; e.g., the middle notes
9 of the octave are respectively 8 and 9,
and the epic hexameter has seventeen syllables, which equals the sum
of these two;