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The excerpt represents the core issue or deciding factor on which you must meditate, and is drawn from Philebus by Plato: to the standard of accuracy which is here adopted, it is rightly placed
lower in the scale than carpentering, because the latter is more capable of
being reduced to measure.
The theoretical element of the arts may also become a purely abstract
science, when separated from matter, and is then said to be pure and
unmixed. The distinction which Plato here makes seems to be the same as
that between pure and applied mathematics, and may be expressed in the
modern formula--science is art theoretical, art is science practical. In
the reason which he gives for the superiority of the pure science of number
over the mixed or applied, we can only agree with him in part. He says
that the numbers which the philosopher employs are always the same, whereas
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