re is one part purer or more akin to knowledge
than the other. There is an element of guess-work and an element
of number and measure in them. In music, for example, especially in
flute-playing, the conjectural element prevails; while in carpentering
there is more application of rule and measure. Of the creative arts,
then, we may make two classes--the less exact and the more exact. And
the exacter part of all of them is really arithmetic and mensuration.
But arithmetic and mensuration again may be subdivided with reference
either to their use in the concrete, or to their nature in the
abstract--as they are regarded popularly in building and binding, or
theoretically by philosophers. And, borrowing the analogy of pleasure,
we may say that the philosophical use of them is purer than the other.
Thus we have two arts of arithmetic, and two of mensuration. And truest
of all in the estimation of every rational man is dialectic, or the
science of being, which will forget and disown us, if we forget and
disown her.

'But, Socrates, I have heard Gorgias say that rhetoric is the greatest
and usefullest of arts; and I should not like to quarrel either with
him or you.' Neither is there any inconsistency, Protarchus, with
his statement in what I am now saying; for I am not maintaining that
dialectic is the greatest or usefullest, but only that she is the truest
of arts; my remark is not quantitative but qualitative, and refers not
to the advantage or repetition of either, but to the degree of truth
which they attain--here Gorgias will not care to compete; this is what
we affirm to be possessed in the highest degree by dialectic. And do not
let us appeal to Gorgias or Philebus or Socrates, but ask, on behalf of
the argument, what are the highest truths which the soul has the power
of attaining. And is not this the science which has a firmer grasp
of them than any other? For the arts generally are only occupied with
matters of opinion, and with the production and action and passion of
this sensible world. But the highest truth is that which is eternal and
unchangeable. And reason and wisdom are concerned with the eternal; and
these are the very claimants, if not for the first, at least for the
second place, whom I propose as rivals to pleasure.

And now, having the materials, we may proceed to mix them--first
recapitulating the question at issue.

Philebus affirmed pleasure to be the good, and assumed them to be
one nature; I aff