h for the most part is mere guess-work. But there is
also a higher arithmetic, and a higher mensuration, which is exclusively
theoretical; and a dialectical science, which is higher still and the
truest and purest knowledge.

(7) We are now able to determine the composition of the perfect life.
First, we admit the pure pleasures and the pure sciences; secondly, the
impure sciences, but not the impure pleasures. We have next to discover
what element of goodness is contained in this mixture. There are three
criteria of goodness--beauty, symmetry, truth. These are clearly more
akin to reason than to pleasure, and will enable us to fix the places
of both of them in the scale of good. First in the scale is measure; the
second place is assigned to symmetry; the third, to reason and wisdom;
the fourth, to knowledge and true opinion; the fifth, to pure pleasures;
and here the Muse says 'Enough.'

'Bidding farewell to Philebus and Socrates,' we may now consider the
metaphysical conceptions which are presented to us. These are (I)
the paradox of unity and plurality; (II) the table of categories or
elements; (III) the kinds of pleasure; (IV) the kinds of knowledge;
(V) the conception of the good. We may then proceed to examine (VI) the
relation of the Philebus to the Republic, and to other dialogues.

I. The paradox of the one and many originated in the restless dialectic
of Zeno, who sought to prove the absolute existence of the one by
showing the contradictions that are involved in admitting the existence
of the many (compare Parm.). Zeno illustrated the contradiction by
well-known examples taken from outward objects. But Socrates seems
to intimate that the time had arrived for discarding these hackneyed
illustrations; such difficulties had long been solved by common sense
('solvitur ambulando'); the fact of the co-existence of opposites was
a sufficient answer to them. He will leave them to Cynics and Eristics;
the youth of Athens may discourse of them to their parents. To no
rational man could the circumstance that the body is one, but has many
members, be any longer a stumbling-block.

Plato's difficulty seems to begin in the region of ideas. He cannot
understand how an absolute unity, such as the Eleatic Being, can be
broken up into a number of individuals, or be in and out of them at
once. Philosophy had so deepened or intensified the nature of one or
Being, by the thoughts of successive generations, that the mind could