Theaetetus
he has a quickness of apprehension which is almost unrivalled, and he
is exceedingly gentle, and also the most courageous of men; there is a
union of qualities in him such as I have never seen in any other, and
should scarcely have thought possible; for those who, like him, have
quick and ready and retentive wits, have generally also quick tempers;
they are ships without ballast, and go darting about, and are mad rather
than courageous; and the steadier sort, when they have to face study,
prove stupid and cannot remember. Whereas he moves surely and smoothly
and successfully in the path of knowledge and enquiry; and he is full of
gentleness, flowing on silently like a river of oil; at his age, it is
wonderful.
SOCRATES: That is good news; whose son is he?
THEODORUS: The name of his father I have forgotten, but the youth
himself is the middle one of those who are approaching us; he and his
companions have been anointing themselves in the outer court, and now
they seem to have finished, and are coming towards us. Look and see
whether you know him.
SOCRATES: I know the youth, but I do not know his name; he is the son of
Euphronius the Sunian, who was himself an eminent man, and such another
as his son is, according to your account of him; I believe that he left
a considerable fortune.
THEODORUS: Theaetetus, Socrates, is his name; but I rather think that
the property disappeared in the hands of trustees; notwithstanding which
he is wonderfully liberal.
SOCRATES: He must be a fine fellow; tell him to come and sit by me.
THEODORUS: I will. Come hither, Theaetetus, and sit by Socrates.
SOCRATES: By all means, Theaetetus, in order that I may see the
reflection of myself in your face, for Theodorus says that we are alike;
and yet if each of us held in his hands a lyre, and he said that they
were tuned alike, should we at once take his word, or should we ask
whether he who said so was or was not a musician?
THEAETETUS: We should ask.
SOCRATES: And if we found that he was, we should take his word; and if
not, not?
THEAETETUS: True.
SOCRATES: And if this supposed likeness of our faces is a matter of any
interest to us, we should enquire whether he who says that we are alike
is a painter or not?
THEAETETUS: Certainly we should.
SOCRATES: And is Theodorus a painter?
THEAETETUS: I never heard that he was.
SOCRATES: Is he a geometrician?
THEAETETUS: Of course he is, Socrates.
SOCRATES: And is he an astronomer and calculator and musician, and in
general an educated man?
THEAETETUS: I think so.
SOCRATES: If, then, he remarks on a similarity in our persons, either
by way of praise or blame, there is no particular reason why we should
attend to him.
THEAETETUS: I should say not.
SOCRATES: But if he praises the virtue or wisdom which are the mental
endowments of either of us, then he who hears the praises will naturally
desire to examine him who is praised: and he again should be willing to
exhibit himself.
THEAETETUS: Very true, Socrates.
SOCRATES: Then now is the time, my dear Theaetetus, for me to examine,
and for you to exhibit; since although Theodorus has praised many a
citizen and stranger in my hearing, never did I hear him praise any one
as he has been praising you.
THEAETETUS: I am glad to hear it, Socrates; but what if he was only in
jest?
SOCRATES: Nay, Theodorus is not given to jesting; and I cannot allow you
to retract your consent on any such pretence as that. If you do, he will
have to swear to his words; and we are perfectly sure that no one will
be found to impugn him. Do not be shy then, but stand to your word.
THEAETETUS: I suppose I must, if you wish it.
SOCRATES: In the first place, I should like to ask what you learn of
Theodorus: something of geometry, perhaps?
THEAETETUS: Yes.
SOCRATES: And astronomy and harmony and calculation?
THEAETETUS: I do my best.
SOCRATES: Yes, my boy, and so do I; and my desire is to learn of him,
or of anybody who seems to understand these things. And I get on pretty
well in general; but there is a little difficulty which I want you and
the company to aid me in investigating. Will you answer me a question:
'Is not learning growing wiser about that which you learn?'
THEAETETUS: Of course.
SOCRATES: And by wisdom the wise are wise?
THEAETETUS: Yes.
SOCRATES: And is that different in any way from knowledge?
THEAETETUS: What?
SOCRATES: Wisdom; are not men wise in that which they know?
THEAETETUS: Certainly they are.
SOCRATES: Then wisdom and knowledge are the same?
THEAETETUS: Yes.
SOCRATES: Herein lies the difficulty which I can never solve to my
satisfaction--What is knowledge? Can we answer that question? What say
you? which of us will speak first? whoever misses shall sit down, as at
a game of ball, and shall be donkey, as the boys say; he who lasts out
his competitors in the game without missing, shall be our king,
and shall have the right of putting to us any questions which he
pleases...Why is there no reply? I hope, Theodorus, that I am not
betrayed into rudeness by my love of conversation? I only want to make
us talk and be friendly and sociable.
THEODORUS: The reverse of rudeness, Socrates: but I would rather that
you would ask one of the young fellows; for the truth is, that I am
unused to your game of question and answer, and I am too old to learn;
the young will be more suitable, and they will improve more than
I shall, for youth is always able to improve. And so having made a
beginning with Theaetetus, I would advise you to go on with him and not
let him off.
SOCRATES: Do you hear, Theaetetus, what Theodorus says? The philosopher,
whom you would not like to disobey, and whose word ought to be a command
to a young man, bids me interrogate you. Take courage, then, and nobly
say what you think that knowledge is.
THEAETETUS: Well, Socrates, I will answer as you and he bid me; and if I
make a mistake, you will doubtless correct me.
SOCRATES: We will, if we can.
THEAETETUS: Then, I think that the sciences which I learn from
Theodorus--geometry, and those which you just now mentioned--are
knowledge; and I would include the art of the cobbler and other
craftsmen; these, each and all of, them, are knowledge.
SOCRATES: Too much, Theaetetus, too much; the nobility and liberality of
your nature make you give many and diverse things, when I am asking for
one simple thing.
THEAETETUS: What do you mean, Socrates?
SOCRATES: Perhaps nothing. I will endeavour, however, to explain what I
believe to be my meaning: When you speak of cobbling, you mean the art
or science of making shoes?
THEAETETUS: Just so.
SOCRATES: And when you speak of carpentering, you mean the art of making
wooden implements?
THEAETETUS: I do.
SOCRATES: In both cases you define the subject matter of each of the two
arts?
THEAETETUS: True.
SOCRATES: But that, Theaetetus, was not the point of my question: we
wanted to know not the subjects, nor yet the number of the arts or
sciences, for we were not going to count them, but we wanted to know the
nature of knowledge in the abstract. Am I not right?
THEAETETUS: Perfectly right.
SOCRATES: Let me offer an illustration: Suppose that a person were to
ask about some very trivial and obvious thing--for example, What is
clay? and we were to reply, that there is a clay of potters, there is
a clay of oven-makers, there is a clay of brick-makers; would not the
answer be ridiculous?
THEAETETUS: Truly.
SOCRATES: In the first place, there would be an absurdity in assuming
that he who asked the question would understand from our answer the
nature of 'clay,' merely because we added 'of the image-makers,' or of
any other workers. How can a man understand the name of anything, when
he does not know the nature of it?
THEAETETUS: He cannot.
SOCRATES: Then he who does not know what science or knowledge is, has no
knowledge of the art or science of making shoes?
THEAETETUS: None.
SOCRATES: Nor of any other science?
THEAETETUS: No.
SOCRATES: And when a man is asked what science or knowledge is, to
give in answer the name of some art or science is ridiculous; for the
question is, 'What is knowledge?' and he replies, 'A knowledge of this
or that.'
THEAETETUS: True.
SOCRATES: Moreover, he might answer shortly and simply, but he makes an
enormous circuit. For example, when asked about the clay, he might have
said simply, that clay is moistened earth--what sort of clay is not to
the point.
THEAETETUS: Yes, Socrates, there is no difficulty as you put the
question. You mean, if I am not mistaken, something like what occurred
to me and to my friend here, your namesake Socrates, in a recent
discussion.
SOCRATES: What was that, Theaetetus?
THEAETETUS: Theodorus was writing out for us something about roots, such
as the roots of three or five, showing that they are incommensurable by
the unit: he selected other examples up to seventeen--there he stopped.
Now as there are innumerable roots, the notion occurred to us of
attempting to include them all under one name or class.
SOCRATES: And did you find such a class?
THEAETETUS: I think that we did; but I should like to have your opinion.
SOCRATES: Let me hear.
THEAETETUS: We divided all numbers into two classes: those which are
made up of equal factors multiplying into one another, which we compared
to square figures and called square or equilateral numbers;--that was
one class.
SOCRATES: Very good.
THEAETETUS: The intermediate numbers, such as three and five, and every
other number which is made up of unequal factors, either of a greater
multiplied by a less, or of a less multiplied by a greater, and when
regarded as a figure, is contained in unequal sides;--all these we
compared to oblong figures, and called them oblong numbers.
SOCRATES: Capital; and what followed?
THEAETETUS: The lines, or sides, which have for their squares the
equilateral plane numbers, were called by us lengths or magnitudes; and
the lines which are the roots of (or whose squares are equal to) the
oblong numbers, were called powers or roots; the reason of this latter
name being, that they are commensurable with the former [i.e., with the
so-called lengths or magnitudes] not in linear measurement, but in the
value of the superficial content of their squares; and the same about
solids.
SOCRATES: Excellent, my boys; I think that you fully justify the praises
of Theodorus, and that he will not be found guilty of false witness.
THEAETETUS: But I am unable, Socrates, to give you a similar answer
about knowledge, which is what you appear to want; and therefore
Theodorus is a deceiver after all.
SOCRATES: Well, but if some one were to praise you for running, and to
say that he never met your equal among boys, and afterwards you were
beaten in a race by a grown-up man, who was a great runner--would the
praise be any the less true?
THEAETETUS: Certainly not.
SOCRATES: And is the discovery of the nature of knowledge so small a
matter, as just now said? Is it not one which would task the powers of
men perfect in every way?
THEAETETUS: By heaven, they should be the top of all perfection!
SOCRATES: Well, then, be of good cheer; do not say that Theodorus was
mistaken about you, but do your best to ascertain the true nature of
knowledge, as well as of other things.
THEAETETUS: I am eager enough, Socrates, if that would bring to light
the truth.
SOCRATES: Come, you made a good beginning just now; let your own answer
about roots be your model, and as you comprehended them all in one
class, try and bring the many sorts of knowledge under one definition.
THEAETETUS: I can assure you, Socrates, that I have tried very often,