Str. That we shall some day require this notion of a mean with a
view to the demonstration of absolute truth; meanwhile, the argument
that the very existence of the arts must be held to depend on the
possibility of measuring more or less, not only with one another,
but also with a view to the attainment of the mean, seems to afford
a grand support and satisfactory proof of the doctrine which we are
maintaining; for if there are arts, there is a standard of measure,
and if there is a standard of measure, there are arts; but if either
is wanting, there is neither.
Y. Soc. True; and what is the next step?
Str. The next step clearly is to divide the art of measurement
into two parts, all we have said already, and to place in
the one part
all the arts which measure number, length, depth, breadth, swiftness
with their opposites; and to have another part in which they are
measured with the mean, and the fit, and the opportune, and the due,
and with all those words, in short, which denote a mean or standard
removed from the extremes.
Y. Soc. Here are two vast divisions, embracing two very different
Str. There are many accomplished men, Socrates, who say, believing
themselves to speak wisely, that the art of measurement is
universal, and has to do with all things. And this means what we are
now saying; for all things which come within the province of art do
certainly in some sense partake of measure. But these
they are not accustomed to distinguish classes according to real
forms, jumble together two widely different things, relation to one
another, and to a standard, under the idea that they are the
also fall into the converse error of dividing other things not
according to their real parts. Whereas the right way is, if a man
has first seen the unity of things, to go on with the enquiry and
not desist until he has found all the differences contained in it
which form distinct classes; nor again should he be able to rest
contented with the manifold diversities which are seen in a
multitude of things until he has comprehended all of them that have
any affinity within the bounds of one similarity and embraced them
within the reality of a single kind. But we have said enough on this
head, and also of excess and defect; we have only to bear in
two divisions of the art of measurement have been discovered
concerned with them, and not forget what they are.
Y. Soc. We will not forget.
Str. And now that this discussion is completed, let us go on to
consider another question, which concerns not this argument only but
the conduct of such arguments in general.
Y. Soc. What is this new question?
Str. Take the case of a child who is engaged in learning his
letters: when he is asked what letters make up a word, should we say
that the question is intended to improve his grammatical knowledge
of that particular word, or of all words?
Y. Soc. Clearly, in order that he may have a better
knowledge of all
Str. And is our enquiry about the Statesman intended only
our knowledge of politics, or our power of reasoning generally?
Y. Soc. Clearly, as in the former example, the purpose is general.
Str. Still less would any rational man seek to analyse the
weaving for its own sake. But people seem to forget that some things
have sensible images, which are readily known, and can be easily