The path of knowledge: the theaetetus by Robert Cavalier

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III. Knowledge is belief accompanied by an explanation (logos) (3309-3893)

One way of making mere belief approach the status of knowledge would be to accompany one's judgment with an explanation (or reason) of why one holds this or that belief. Such a reason (logos) would then serve to ground the belief, it would provide a foundation for the judgment, This seems to be the further buttressing that mere belief needs, and the dialogue now begins to move in this direction.

Theaetetus and Socrates approach the problem by investigating various modes of explanation The first, strangely enough, is presented through the image of a dream which Socrates had once had (3323- 3346). It seems that in Socrates' dream he had heard of a theory which held that all things are essentially complexes made up of many simple elements, For example, we can say that a broom is a complex thing made up of (the simpler elements of) a long wooden handle and straw bristles. This theory then goes on to say that the broom's handle would itself be made of simpler elements (it is, for instance, both wooden and long), and that, in fact, these elements get simpler and simpler until we reach the simplest possible elements. These primary elements would then be described as the ultimate (conceptual) building blocks of the complex entity called the broom.

Now, from within this dream image, it seems possible to give an account of knowledge. We may be said to know a thing when we are able to explain it in terms of its simple elements. Once we analyze a complex object down to its constituent parts, we may then be said to have arrived at a full explanation of the object-and we may then be said to have arrived at a knowledge of the object.

Theaetetus is at first favorably inclined to accept this view, but Socrates is uncertain. The problem is that, within the dream itself, there is the belief that these simple elements are so simple that they cannot even be described. In fact, these ultimate simples seem "unknowable" (3368), This is the theory’s fatal flaw. When we attempt to arrive at a knowledge of something (by analyzing it into its simplest elements) we eventually arrive at something unknowable. Yet how can that which is unknowable serve as a foundation for knowledge? What does it mean to make complexes knowable (for example, a word) while at the same time to make its elements (viz., the syllables) unknowable (3379-3665)? It seems as if Socrates and Theaetetus really have been dreaming. If we are going to give an explanation of a thing in terms of its elements, then these elements must at least be capable of being known.

Awake now from the dream, both Socrates and Theaetetus return to the problem of explanation. Together, they will explore three possible meanings of the phrase "to give an account."

(1) To give an account means to express one's thought in speech (3673-3684), This most obvious meaning of account viz,, the mere uttering of one s opinion, is also the most unhelpful, Anyone with "speech"' could give an account, but this could not clear up the problem of how an account can explain a belief, We wouldn't be able to distinguish those who spoke with knowledge from those who didn't, if mere speaking were all that was required in order to give an account.

(2) To give an account means to list the parts (3688-3818). This attempt is similar to the one in the dream-story, though this time the simplest elements ("parts") are assumed to be knowable. In this vein, the account of, for instance, a wagon, would simply consist of listing its various parts e.g., wheels, seat, horses, etc.

But what would a mere listing of the individual parts contribute to a knowledge of what the wagon really is? We might well know all the parts of a wagon and still not know what a wagon is (for instance, what a wagon is used for, how to ride it, etc.). To know the parts is different from knowing what the thing is; to know the parts of Theaetetus' name is not to know Theaetetus.

Plato is making us feel the need for something more in our description of things. In this case, what is missing is the "Form'' or essence of the wagon, and this is something distinct from the mere enumeration of the parts (elements). So even if one claims that the elements are knowable, one still cannot arrive at a "knowledge of X" from an "analysis (of the parts) of X," This second account fails, and Theaetetus and Socrates go on to their final attempt to arrive at an understanding of knowledge.

(3) To give an account means to know what distinguishes an object from other objects (3828-3889). In a sense, if I know what makes Theaetetus different from everyone else, then I know Theaetetus. The problem becomes one of locating distinguishing marks. For instance, what distinguishes a wagon from a tree is that the former has wheels, is drawn by a horse, etc.

But Socrates immediately sees a fatal circularity in this approach. (3882) How can I know what differentiates one object from another unless I already know precisely what that object is? One must know Theaetetus in order to say what makes him different. This final account quite simply begs the question.

The dialogue closes (3894-3940), Socrates has been unable to assist Theaetetus in the birth of an adequate account of knowledge, In the spirit of a true Socratic encounter, both men are now more aware of their ignorance in the areas discussed. Yet such an awareness separates them immeasurably from those who have never attempted such questions. Perhaps Theaetetus' embryonic thoughts will be better as a consequence of Socrates' midwifery. Be this as it may, Socrates must now go to the portico of King Archon to meet an indictment which a man named Meletus has drawn against him. He bids Theodorus and Theaetetus farewell, and entreats them to join him tomorrow, when they can again take up the problem of knowledge.

This proposed conversation makes up the dialogue called the Sophist, and it is in this dialogue that Plato will feel free to introduce his own account of the nature of knowledge. The Theaetetus has served its purpose, It has attempted to arrive at an understanding of knowledge without any appeal to the world of the Forms, and it has failed at every turn.

The attempt to arrive at knowledge through the senses (aisthesis) gave us only momentary and empty sensations--not a true knowledge of the object (not an adequate idea of what a thing really is), The attempt to describe knowledge in terms of judgment (i.e., belief/opinion--doxa) was found lacking insofar as mere belief is simply a statement without reasons, and in such judgments there can be found no criteria for distinguishing true opinions from false opinions. The attempt to buttress one's belief with an explanation (logos) likewise failed, The accounts of "explanation," when not trivial or question-begging, always sought to describe a thing in terms of its "parts." But what was really needed here was an idea of its "whole." That is to say, a true account of something must ultimately be given through a description of its essence or nature (its "Form," if you will).

The dialogue thus leaves us with a sense that something is lacking. As long as we stay "on the earth," with our sensations and our opinions, we will fail to come to an understanding of the nature of knowledge. Plato has used the Theaetetus to create a felt need within the reader's mind to move beyond the limitations imposed on these first attempts. There is a desire kindled to transcend the world of the Theaetetus. The reader is thus prepared for the movement of the Sophist-a movement which leads upward toward the realm of the Forms.

Translated by Benjamin Jowett

PERSONS OF THE DIALOGUE: Socrates, Theodorus, Theaetetus.

Euclid and Terpsion meet in front of Euclid's house in Megara; they enter

the house, and the dialogue is read to them by a servant.

EUCLID: Have you only just arrived from the country, Terpsion?
TERPSION: No, I came some time ago: and I have been in the Agora looking

for you, and wondering that I could not find you.

EUCLID: But I was not in the city.
TERPSION: Where then?
EUCLID: As I was going down to the harbour, I met Theaetetus--he was being

carried up to Athens from the army at Corinth.

TERPSION: Was he alive or dead?
EUCLID: He was scarcely alive, for he has been badly wounded; but he was

suffering even more from the sickness which has broken out in the army.

TERPSION: The dysentery, you mean?
TERPSION: Alas! what a loss he will be!
EUCLID: Yes, Terpsion, he is a noble fellow; only to-day I heard some

people highly praising his behaviour in this very battle.

TERPSION: No wonder; I should rather be surprised at hearing anything else

of him. But why did he go on, instead of stopping at Megara?

EUCLID: He wanted to get home: although I entreated and advised him to

remain, he would not listen to me; so I set him on his way, and turned

back, and then I remembered what Socrates had said of him, and thought how

remarkably this, like all his predictions, had been fulfilled. I believe

that he had seen him a little before his own death, when Theaetetus was a

youth, and he had a memorable conversation with him, which he repeated to

me when I came to Athens; he was full of admiration of his genius, and said

that he would most certainly be a great man, if he lived.

TERPSION: The prophecy has certainly been fulfilled; but what was the

conversation? can you tell me?

EUCLID: No, indeed, not offhand; but I took notes of it as soon as I got

home; these I filled up from memory, writing them out at leisure; and

whenever I went to Athens, I asked Socrates about any point which I had

forgotten, and on my return I made corrections; thus I have nearly the

whole conversation written down.
TERPSION: I remember--you told me; and I have always been intending to ask

you to show me the writing, but have put off doing so; and now, why should

we not read it through?--having just come from the country, I should

greatly like to rest.

EUCLID: I too shall be very glad of a rest, for I went with Theaetetus as

far as Erineum. Let us go in, then, and, while we are reposing, the

servant shall read to us.
TERPSION: Very good.
EUCLID: Here is the roll, Terpsion; I may observe that I have introduced

Socrates, not as narrating to me, but as actually conversing with the

persons whom he mentioned--these were, Theodorus the geometrician (of

Cyrene), and Theaetetus. I have omitted, for the sake of convenience, the

interlocutory words 'I said,' 'I remarked,' which he used when he spoke of

himself, and again, 'he agreed,' or 'disagreed,' in the answer, lest the

repetition of them should be troublesome.
TERPSION: Quite right, Euclid.
EUCLID: And now, boy, you may take the roll and read.
SOCRATES: If I cared enough about the Cyrenians, Theodorus, I would ask

you whether there are any rising geometricians or philosophers in that part

of the world. But I am more interested in our own Athenian youth, and I

would rather know who among them are likely to do well. I observe them as

far as I can myself, and I enquire of any one whom they follow, and I see

that a great many of them follow you, in which they are quite right,

considering your eminence in geometry and in other ways. Tell me then, if

you have met with any one who is good for anything.

THEODORUS: Yes, Socrates, I have become acquainted with one very

remarkable Athenian youth, whom I commend to you as well worthy of your

attention. If he had been a beauty I should have been afraid to praise

him, lest you should suppose that I was in love with him; but he is no

beauty, and you must not be offended if I say that he is very like you; for

he has a snub nose and projecting eyes, although these features are less

marked in him than in you. Seeing, then, that he has no personal

attractions, I may freely say, that in all my acquaintance, which is very

large, I never knew any one who was his equal in natural gifts: for 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

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?

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

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?

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?
SOCRATES: And is that different in any way from knowledge?
SOCRATES: Wisdom; are not men wise in that which they know?
THEAETETUS: Certainly they are.
SOCRATES: Then wisdom and knowledge are the same?
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?
SOCRATES: And when you speak of carpentering, you mean the art of making

wooden implements?

SOCRATES: In both cases you define the subject matter of each of the two


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

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?

SOCRATES: Nor of any other science?
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.'
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

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

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

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