Theaetetus

Overview

A hundred and ten pages, the longest of the dialogues devoted to a single question, and the first work in Western philosophy that is entirely about knowledge.

The frame is unusual and moving. Euclides of Megara meets Terpsion outside the city and tells him he has just seen Theaetetus carried back from the army at Corinth, dying of dysentery and wounds. They go indoors and have a slave read out a conversation Euclides wrote down from Socrates’ own account, of a discussion with Theaetetus as a boy, years before, shortly before Socrates’ trial. So the brilliant young man we are about to watch is, as we watch him, dying.

Theaetetus was a real mathematician who worked on irrationals and the construction of the regular solids, and Book X and Book XIII of Euclid’s Elements are largely his. Plato introduces him as ugly, snub-nosed like Socrates, and unusually gifted, and the affection in the portrait is not disguised.

The dialogue is aporetic: it ends without an answer. What it has done by then is close off three routes and invent the subject.

The argument

The midwife. Theaetetus, asked what knowledge is, first lists examples, geometry, cobbling, and Socrates says he asked for one thing, not many. Theaetetus then reports a piece of his own mathematics, a classification of incommensurable lines, and Socrates says that is exactly the form an answer should take.

Then the image. Socrates’ mother was a midwife, and his own art is the same for souls: he is barren himself, delivers other men’s thoughts, and his skill is in judging whether the newborn is a real child or a wind-egg. Young men sometimes hate him when he takes their offspring away. It is the most complete account anywhere of the Socratic method as its practitioner understood it.

First answer: knowledge is perception. Theaetetus offers it and Socrates immediately connects it to two other doctrines. Protagoras’ man is the measure of all things, so that the wind is cold for the one who feels cold and warm for the one who does not, with no fact beyond. And the Heraclitean claim that everything is in flux, which Socrates develops into an elaborate theory in which perceiver and perceived come into being together at the moment of perception and neither exists beforehand.

He constructs this position with enormous care, even making a speech in Protagoras’ defence after Protagoras has been knocked down too easily, before taking it apart.

The objections accumulate. If each person’s perception is knowledge, no one is wiser than anyone else and Protagoras has nothing to teach. If all appearances are true, then the many who think Protagoras is wrong are right, and by his own doctrine his truth is true for no one. Predictions show that expertise is real: the doctor knows better than the patient what the fever will do tomorrow, and the many are not the measure of what has not yet happened. Perception cannot reach being, sameness, difference or number, which the soul considers by itself and without any organ. And if everything is in flux in every respect, language collapses, since nothing can be called this rather than that, and one may as well say not thus as thus.

Knowledge is not perception.

Second answer: knowledge is true judgement. Theaetetus offers it, and Socrates immediately interposes the problem that swallows the middle of the dialogue: how is false judgement possible at all?

If you know something you cannot think it is something else. If you do not know it, you cannot be thinking about it to be wrong about. Trying to judge what is not seems to be judging nothing, which is not judging.

Two models are built. The wax tablet: memory is an impression in wax of varying quality, and error occurs when a present perception is fitted to the wrong stored imprint, as when you see a man at a distance and match him to the wrong memory. This explains some errors but not the arithmetical ones, since nobody misidentifies eleven by a faulty impression.

The aviary: knowledge pieces are birds in a cage, and having them is not the same as holding one, so error is grabbing the wrong bird, reaching for eleven and catching twelve. But this requires a piece of knowledge to be the instrument of a mistake, which is odd, and patching it with ignorance-birds in the same cage makes it worse.

The problem is not solved here. It is solved in the Sophist, the following morning.

Setting it aside, Socrates disposes of the definition briskly. A jury persuaded by a skilful speaker may reach a true verdict about an event nobody present witnessed. Their judgement is true, and it is not knowledge, because persuasion is not the same as knowing.

Third answer: true judgement with an account. Theaetetus recalls a theory he has heard: the primary elements of things are unknowable and can only be named, while the complexes made of them are knowable, because an account is the weaving together of names.

Socrates attacks the premise with the example of syllables and letters. If knowing SO means knowing S and O, the elements are not unknowable after all; if the syllable is a single form over and above its letters, it has no parts and is as unknowable as they are. And anyone who has taught a child to read knows that learning the letters is precisely how the syllables become known.

Then he tries three senses of account. Speaking your thought aloud: everyone with a true belief can do that, so it adds nothing. Enumerating the elements: a child who spells Theaetetus correctly today and wrongly tomorrow had the parts without the knowledge. Naming the differentia, the mark that distinguishes this thing from everything else: but to have a true judgement about Theaetetus at all you must already be picking him out by what distinguishes him, so the addition is empty, or else it says knowledge is true judgement plus knowledge of the difference, which is circular.

The ending. All three fail. Socrates says the wind-eggs have been taken away, that Theaetetus will be less overbearing for knowing he does not know, and that if he conceives again he will be the better for this. Then he says he must go to the King Archon’s porch to meet the indictment Meletus has brought, and will see Theaetetus in the morning.

How to read it

Read the midwife passage at 148e to 151d first and return to it at the end. It tells you what kind of success the dialogue’s failure is meant to be.

Slow right down for 170a to 179b, the refutation of Protagoras. The self-refutation argument is subtler than its summary, and the objection about future predictions is the one relativists still have the most trouble with.

Read the digression at 172c to 177c as a separate essay. The philosopher who cannot find his way to the marketplace, who does not know whether his neighbour is a man, who is helpless in court and laughed at by a servant girl, is being praised and mocked at once. Decide which Plato means and the reading changes.

Expect the false-judgement section to be frustrating. It is meant to be. Read the Sophist immediately afterwards, where the visitor solves it by redefining not-being as difference, and the two dialogues become one argument.

Notice that the third definition is still live. Justified true belief was the standard analysis of knowledge until Edmund Gettier published three pages in 1963 producing cases where all three conditions hold and we would not say the person knows. Plato’s own objection at 209d anticipates the difficulty about how the third condition connects to the first two.

And keep the frame in mind. A dying soldier’s boyhood conversation, read aloud from a notebook, with a man who is about to be killed by his city. Plato put that around an argument about definitions for a reason.

Questions it raises

• Is there any version of man is the measure that survives the self-refutation argument?
• Perception cannot grasp being, sameness or number. What does the soul use instead, and how does it get it?
• How can anyone judge what is false, if to think of a thing at all is to have it in mind?
• A jury may reach a true verdict by persuasion. What does knowledge have that their belief lacks?
• Every proposed account either repeats the true judgement or presupposes knowledge. Can the circle be broken?
• The philosopher in the digression cannot function in the city. Is that a cost of the theoretical life or a sign of it?