rmed
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 numbers, and is due to their abstract nature;--although we admit of
course what Plato seems to feel in his distinctions between pure and
impure knowledge, that the imperfection of matter enters into the
applications of them.

Above the other sciences, as in the Republic, towers dialectic, which is
the science of eternal Being, apprehended by the purest mind and reason.
The lower sciences, including the mathematical, are akin to opinion
rather than to reason, and are placed together in the fourth class of
goods. The relation in which they stand to dialectic is obscure in the
Republic, and is not cleared up in the Philebus.

V. Thus far we have only attained to the vestibule or ante-chamber of
the good; for there is a good exceeding knowledge, exceeding
essence, which, like Glaucon in the Republic, we find a difficulty
in apprehending. This good is now to be exhibited to us under various
aspects and gradations. The relative dignity of pleasure and knowledge
has been determined; but they have not yet received their exact position
in the scale of goods. Some difficulties occur to us in the enumeration:
First, how are we to distinguish the first from the second class of
goods, or the second from the third? Secondly, why is there no mention
of the s