g. one might say that animals are
composed of animals, if there are Ideas of them.
In general, to differentiate the units in any way is an
absurdity and a fiction; and by a fiction I mean a forced statement
made to suit a hypothesis. For neither in quantity nor in quality do
we see unit differing from unit, and number must be either equal or
unequal-all number but especially that which consists of abstract
units-so that if one number is neither greater nor less than
another, it is equal to it; but things that are equal and in no wise
differentiated we take to be the same when we are speaking of numbers.
If not, not even the 2 in the 10-itself will be undifferentiated,
though they are equal; for what reason will the man who alleges that
they are not differentiated be able to give?
Again, if every unit + another unit makes two, a unit from the
2-itself and one from the 3-itself will make a 2. Now (a) this will
consist of differentiated units; and will it be prior to the 3 or
posterior? It rather seems that it must be prior; for one of the units
is simultaneous with the 3 and the other is simultaneous with the 2.
And we, for our part, suppose that in general 1 and 1, whether the
things are equal or unequal, is 2, e.g. the good and the bad, or a man
and a horse; but those who hold these views say that not even two
units are 2.
If the number of the 3-itself is not greater than that of the 2,
this is surprising; and if it is greater, clearly there is also a
number in it equal to the 2, so that this is not different from the
2-itself.
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