Let us reflect that there are two kinds of knowledge--the one creative or
productive, and the other educational and philosophical. Of the creative
arts, there 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