confession) the main thesis is not worth determining; the real interest
lies in the incidental discussion. We can no more separate pleasure from
knowledge in the Philebus than we can separate justice from happiness in
the Republic.

IV. An interesting account is given in the Philebus of the rank and order
of the sciences or arts, which agrees generally with the scheme of
knowledge in the Sixth Book of the Republic. The chief difference is, that
the position of the arts is more exactly defined. They are divided into an
empirical part and a scientific part, of which the first is mere guess-
work, the second is determined by rule and measure. Of the more empirical
arts, music is given as an example; this, although affirmed to be necessary
to human life, is depreciated. Music is regarded from a point of view
entirely opposite to that of the Republic, not as a sublime science,
coordinate with astronomy, but as full of doubt and conjecture. According
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
the numbers which are used in practice represent different sizes or
quantities. He does not see that this power of expressing different
quantities by the same symbol is the characteristic and not the defect of