ed in trading with exact calculation, shall we say of either of the
pairs that it is one or two?

PROTARCHUS: On the analogy of what has preceded, I should be of opinion
that they were severally two.

SOCRATES: Right; but do you understand why I have discussed the subject?

PROTARCHUS: I think so, but I should like to be told by you.

SOCRATES: The argument has all along been seeking a parallel to
pleasure, and true to that original design, has gone on to ask whether
one sort of knowledge is purer than another, as one pleasure is purer
than another.

PROTARCHUS: Clearly; that was the intention.

SOCRATES: And has not the argument in what has preceded, already shown
that the arts have different provinces, and vary in their degrees of
certainty?

PROTARCHUS: Very true.

SOCRATES: And just now did not the argument first designate a particular
art by a common term, thus making us believe in the unity of that art;
and then again, as if speaking of two different things, proceed to
enquire whether the art as pursed by philosophers, or as pursued by
non-philosophers, has more of certainty and purity?

PROTARCHUS: That is the very question which the argument is asking.

SOCRATES: And how, Protarchus, shall we answer the enquiry?

PROTARCHUS: O Socrates, we have reached a point at which the difference
of clearness in different kinds of knowledge is enormous.

SOCRATES: Then the answer will be the easier.

PROTARCHUS: Certainly; and let us say in reply, that those arts into
which arithmetic and mensuration enter, far surpass all others; and that
of these the arts or sciences which are animated by the pure philosophic
impulse are infinitely superior in accuracy and truth.

SOCRATES: Then this is your judgment; and this is the answer which,
upon your authority, we will give to all masters of the art of
misinterpretation?

PROTARCHUS: What answer?

SOCRATES: That there are two arts of arithmetic, and two of mensuration;
and also several other arts which in like manner have this double
nature, and yet only one name.

PROTARCHUS: Let us boldly return this answer to the masters of whom you
speak, Socrates, and hope for good luck.

SOCRATES: We have explained what we term the most exact arts or
sciences.

PROTARCHUS: Very good.

SOCRATES: And yet, Protarchus, dialectic will refuse to acknowledge us,
if we do not award to her the first place.

PROTARCHUS: And pray, what is dialectic?

SOCRATES: Clearly the sci