laws (books 7 - 12)
length, and breadth with breadth, and depth in like manner with depth?
Ath. But if some things are commensurable and others wholly
incommensurable, and you think that all things are commensurable, what
is your position in regard to them?
Cle. Clearly, far from good.
Ath. Concerning length and breadth when compared with depth, or
breadth when and length when compared with one another, are not all
the Hellenes agreed that these are commensurable with one in some way?
Cle. Quite true.
Ath. But if they are absolutely incommensurable, and yet all of us
regard them as commensurable, have we not reason to be ashamed of
our compatriots; and might we not say to them:-O ye best of
Hellenes, is not this one of the things of which we were saying that
not to know them is disgraceful, and of which to have a bare knowledge
only is no great distinction?
Ath. And there are other things akin to these, in which there spring
up other errors of the same family.
Cle. What are they?
Ath. The natures of commensurable and incommensurable quantities
in their relation to one another. A man who is good for a thing
ought to be able, when he thinks, to distinguish them; and different
persons should compete with one another in asking questions, which
will be a fair, better and more graceful way of passing their time
than the old man's game of draughts.
Cle. I dare say; and these pastimes are not so very unlike a game of
Ath. And these, as I maintain, Cleinias, are the studies which our
youth ought to learn, for they are innocent and not difficult; the
learning of them will be an amusement, and they will benefit the
state. If anyone is of another mind, let him say what he has to say.
Ath. Then if these studies are such as we maintain we will include
them; if not, they shall be excluded.
Cle. Assuredly: but may we not now, Stranger, prescribe these
studies as necessary, and so fill up the lacunae of our laws?
Ath. They shall be regarded as pledges which may be hereafter
redeemed and removed from our state, if they do not please either us
who give them, or you who accept them.
Cle. A fair condition.
Ath. Next let us see whether we are or are not willing that the
study of astronomy shall be proposed for our youth.
Ath. Here occurs a strange phenomenon, which certainly cannot in any
point of view be tolerated.
Cle. To what are you referring?
Ath. Men say that we ought not to enquire into the supreme God and
the nature of the universe, nor busy ourselves in searching out the
causes of things, and that such enquiries are impious; whereas the
very opposite is the truth.
Cle. What do you mean?
Ath. Perhaps what I am saying may seem paradoxical, and at
variance with the usual language of age. But when any one has any good
and true notion which is for the advantage of the state and in every
way acceptable to God, he cannot abstain from expressing it.
Cle. Your words are reasonable enough; but shall we find any good or
true notion about the stars?
Ath. My good friends, at this hour all of us Hellenes tell lies,
if I may use such an expression, about those great Gods, the Sun and
Cle. Lies of what nature?
Ath. We say that they and divers other stars do not keep the same
path, and we call them planets or wanderers.