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 supreme mind?
Thirdly, the nature of the fourth class. Fourthly, the meaning of the
allusion to a sixth class, which is not further investigated.

(I) Plato seems to proceed in his table of goods, from the more abstract to
the less abstract; from the subjective to the objective; until at the lower
end of the scale we fairly descend into the region of human action and
feeling. To him, the greater the abstraction the greater the truth, and he
is always tending to see abstractions within abstractions; which, like the
ideas in the Parmenides, are always appearing one behind another. Hence we