Welcome to my course on Plato's Theaetetus. My name is Richard Polt. I've been teaching philosophy at Xavier University for over thirty years, and this is a Platonic dialogue that I've taught almost every year without growing tired of it. I keep returning to it because it is not only conceptually fascinating, with some genuinely deep arguments, but also a piece of drama that is entertaining and fun. Every time I teach it, I encounter unexpected insights and questions, and it proves to be a great conversation starter.
I've designed this course as an introduction to the Theaetetus, to Plato, or indeed to philosophy in general, because the question of the nature of philosophy arises at several points directly in the dialogue and is always implicitly present as well. For that reason, I think it makes a great first text in philosophy. I should say that I am not a Plato specialist or scholar, so please challenge me with a clear conscience: "You missed this," or "You didn't realize that." I genuinely hope to learn from you.
My main area of specialization is actually Martin Heidegger, a twentieth-century German philosopher. My engagement with Plato comes not as a scholar but as a devoted and loving reader of several favorite dialogues over many years. With that in mind, we're going to have a spontaneous dialogue, improvising, surprising one another, and we'll see where it goes.
This course is, above all, food for thought. That is what I take to be the real purpose of Plato's dialogues: food for thought for an individual reader, or for a group of readers such as those who would have gathered in Plato's school, the Academy, and who would have had, I think, lively conversations inspired by his writings.
The real Plato is thousands of miles away from us, and more importantly, thousands of years away. There is another problem as well: he never actually says anything directly in this dialogue, or in any of his dialogues. Before we get to page one, I want to talk a little about how to read such an unusual writer.
What we have from Plato is a set of letters, but mostly dialogues, philosophical plays in which Plato himself is hardly ever even mentioned. In The Apology, the dialogue representing Socrates' trial, Socrates does refer to Plato by name. And in the Phaedo, which concerns Socrates' death, the narrator mentions that Plato could not be there because he was sick, which is remarkable. How could he miss the death of Socrates? Plato is deliberately removing himself from his own dialogues.
In his place, the main speaker and hero of these works is Socrates. Socrates was Plato's mentor, teacher, and hero, and he died when Plato was in his twenties, not a natural death. He was put on trial, charged with impiety and corrupting the youth, which are perennially useful charges against philosophers. In fact, a professor was recently banned from teaching Plato's Symposium in Texas on the grounds that it espoused radical gender ideology. Plato is still corrupting the youth, I am happy to say.
Socrates is the central figure, the hero if you will, of most of these dialogues. But you should not necessarily believe what he says or assume that his arguments are sound. I think we are often meant to see that his arguments are not sound. He is ironic, he is playful, he is deliberately unsettling people's assumptions, and for that reason you cannot take anything he says at face value. I do not think you are meant to.
How should we read these texts? I want to run through a few things that Plato says about writing. In the Seventh Letter, the most interesting, important, and lengthy letter we have from Plato, he says, "I have never put my thoughts into writing and I never will. I would never be so foolish as to do such a thing." His reasoning is that writing is at many removes from reality. Take the geometer's concept of a circle: there is the real thing itself, and then there are various levels beneath it, the definition of a circle, an image of a circle, a physical approximation of a circle, the words we use to describe these things, and finally writing, which fixes those words into a text. If you believe that reality itself is contained in a book, you are deeply confused.
There is also a dialogue called the Phaedrus, in which Socrates discusses writing. He recounts that writing was invented in Egypt by a god named Theuth, who brought this wonderful new invention to Thamus, the king of the gods, saying, "Look, I have discovered a potion for wisdom and memory." Thamus replies, "No, you have discovered a potion for foolishness and oblivion." Why would he say such a thing? Consider what writing does to memory: we are far less inclined to put in the work of memorizing texts when we know the material is already accessible on the page.
This has been empirically demonstrated. Certain noble families of Rajas in India, for instance, kept oral bards who composed and recited epics about the family's exploits entirely from memory. These bards were traditionally illiterate. When someone had the idea of teaching them to read and write in order to preserve these epics, the bards soon lost the ability to recite from memory. They no longer knew the texts by heart; they had to consult the written page. There is genuine truth in Plato's concern.
Socrates goes on in the Phaedrus to identify further liabilities of writing as opposed to oral speech. If a reader has a question that the book does not directly answer, the book simply sits there. It cannot defend itself, it cannot respond to a particular challenge, it just keeps repeating the same thing. Writing also cannot speak differently to different people, whereas a skilled rhetorician tailors speech to the individual listener. The book says the same thing to everyone. Socrates therefore concludes that no serious person would take writing very seriously.
Of course, Plato then went on to write some two thousand pages of dialogues, so is he simply confused, or is something else going on? Why would such a great writer compose so extensively on the futility of writing?
Could this be deliberately ironic on Plato's part? After all, Socrates is not there to defend himself, and do we even know whether he really said what Plato attributes to him? We cannot know anything for certain about what Socrates actually said. We have three original sources: Plato; Xenophon, a similar writer whom most scholars consider less philosophically deep; and Aristophanes, who is quite different. Aristophanes was a writer of comedies who produced The Clouds during Socrates' lifetime, and it offers a very different portrayal, a comic attack on the man. Most scholars would say these works are imitations of the way Socrates used to operate, but we should not take any of them too literally.
Socrates himself wrote nothing, which goes hand-in-hand with his frequent claim that he knew nothing, for why would you commit ignorance to a text? This raises the question of whether Plato is writing in a way that tries, at least partially, to get around these limitations. One cannot perfectly circumvent them; they apply to all kinds of recording. This very session, for instance, will be filmed and posted online, and we have no control over who watches it, what they make of it, or whether they will think we are talking nonsense. We cannot defend ourselves or speak to them directly. These are real limitations.
How might a writer partially get around them? You cannot anticipate in advance every psychological type of reader who will pick up your book over thousands of years, but you might at least differentiate between surface readers and critical readers. I believe Plato tries to do exactly that. I cannot read the man's mind, but I do notice that when you question and criticize what is in the text, you often make genuinely interesting discoveries that connect very nicely to other parts of it. He seems to be sending different messages to what we might call the philosophical and the non-philosophical reader.
On some theories of how to read Plato, this distinction is absolutely crucial. One must differentiate between exoteric and esoteric teachings, between what the text says on its surface and what it communicates to the careful, critical reader who is willing to press beyond that surface.
Let's begin with a few assumptions. First, we'll assume that Plato is a genius, whether or not he is in total control of every detail, and that every word counts. There is a reason why everything was included, and everything can and should be questioned. The text begins with a brief prologue. We are using the translation by M. J. Levitt, revised by Miles Burnyeat, published by Hackett, though those following along may use any translation. We will refer to the text by the marginal numbers and letters known as Stephanus numbers, named after an early printed edition of Plato.
The dialogue opens with a couple of pages of prologue featuring two characters, Euclides and Terpsion. It emerges that Euclides possesses a written text, and the bulk of the dialogue proceeds to recount its contents. What do these first two pages give us? Assuming Plato had good reason to include them, what purpose do they serve?
Audience: They talk a little about Theaetetus himself, giving, if not foreshadowing, at least a preview of who this young man might be.
Exactly. So what are his characteristics? I'll abbreviate him as THT. The prologue mentions that he was a soldier involved in some battle, that he behaved bravely and well, and that the speakers were not surprised to hear it. Apparently they had expected as much from him.
Audience: He has made a reputation for himself as a courageous man, not as a mathematician. He is not mentioned in his capacity as a mathematician.
Precisely. His courage is what defines him in the prologue, not his mathematical ability.
What about Socrates? What did we learn about him? Socrates had a conversation with Theaetetus, but unsurprisingly, he had not written it down. Socrates must have had a great memory, however, because he was able to recount the entire conversation from memory to Euclides, who then tried to get it all down on papyrus.
What other strengths does Socrates display? He is called a prophet, because he had a sense even then of what a fine person Theaetetus would become. He is a good judge of character. He prophesies that they would hear more about Theaetetus once he grew up, adding, significantly, "if he lives."
Death seems to hang over these first few pages rather darkly. Theaetetus appears to be on the verge of death, Socrates is long dead, and the conversation itself apparently took place shortly before Socrates' own death. There is a great deal of doom here, which makes one wonder whether this will be a tragic dialogue, though we will see soon enough that it is actually quite funny.
One more thing worth noting about the opening pages: this is a dialogue about the nature of knowledge, and Plato typically tries to show that philosophical questions arise out of real life rather than being dreamed up in an armchair. The characters illustrate how we are concerned with knowledge in an everyday way. The simple opening question, "Are you only just in from the country, Terpsion, or have you been here for some time?", is a perfectly natural inquiry. The characters are seeking knowledge about where someone came from, working out a chronology, looking into causes, and exercising their memory. All of this will be taken up again on a more theoretical level as the dialogue proceeds.
In the opening of the main dialogue, Socrates runs into Theodorus, apparently in a gymnasium, and here we discover that this could be a comic dialogue. It is, in fact, quite funny. Socrates says that the one kind of knowledge he is always trying to acquire is knowledge of which particular young men in Athens show promise. Theodorus replies that there is one boy he has been teaching who is absolutely fantastic, so fantastic, in fact, that people might think Theodorus was in love with him, were it not that the boy looks rather like Socrates, though not quite as ugly. This is perhaps the sort of remark one can make to a close friend without giving offense, but it is not the most gracious opening.
The comment is valuable, though, because it gives us a sense of what Plato's contemporaries said Socrates actually looked like. Descriptions of Socrates' physical appearance are not common in Plato or elsewhere, but this passage mentions his snub nose, and he is generally portrayed as very unattractive by Greek standards, yet fascinating, even erotically fascinating. In the Symposium, Alcibiades, that charismatic, handsome, and captivating figure, confesses that he is obsessed with Socrates and desperately wants to be with him despite his ugliness, because inwardly Socrates is wonderful. Alcibiades even recounts that they spent an entire night together and Socrates never touched him, which drove Alcibiades to distraction.
Theodorus goes on to describe the personality of Theaetetus, and it amounts to a fine account of what it takes to be a good learner. One needs to be both sharply intelligent and deeply dedicated and steady, a combination that Theodorus says is genuinely rare.
At 144b, Socrates asks whose son Theaetetus is. Theodorus replies that he has heard the name but cannot remember it, a detail that will prove relevant later, since Theodorus is somewhat oblivious to the concrete particulars of people's lives. Socrates, by contrast, knows immediately: Theaetetus is the son of Euphronius of Sunium. He may not recall the boy's name, but he knows all about his family, bearing out his earlier claim that he is always interested in the particular promising individuals of Athens.
The question of knowledge arises naturally from the situation, grounded as it is in real life: Theodorus is a teacher trying to convey knowledge, and Theaetetus is a student trying to acquire it. What, then, is this thing they are both engaged in? Why are they here, and what are they aiming at? At 145d–e, Socrates quickly touches on wisdom and identifies it with knowledge, and implicitly philosophy is present as well, since the word philosophia means love of wisdom. What is ultimately at stake is what we are even trying to achieve when we philosophize.
At 145e, Socrates argues: "Isn't it the things which they know that men are wise about?" And from this he concludes that knowledge and wisdom must be the same thing. But does this actually follow logically? Consider a parallel: it is the things you hear that you can listen to, therefore hearing and listening are the same thing. Clearly they are not. Something can go in one ear and out the other, so listening involves an additional level beyond mere hearing. Similarly, I might know a few facts about Manhattan without being an expert on it; wisdom seems to require something more than the mere possession of knowledge.
When apparent slips like this arise, I am always reluctant to assume that Socrates, or Plato, is simply confused. If we can work this out in a few minutes of reflection, Plato certainly could have. What he is doing instead is addressing different audiences simultaneously. For a less reflective reader, the identification of knowledge and wisdom washes over without friction. For a more reflective one, it prompts deeper thought about what wisdom really is, and therefore about what philosophy is, and that inquiry leads somewhere far more interesting.
Socrates then turns to the question of defining knowledge, putting it into words. Theaetetus offers an answer at 146C: "I think that the things Theodorus teaches are knowledge — geometry and the subjects you enumerated just now. Then again, there are the crafts, such as cobbling, whether you take them together or separately." He is giving examples instead of a general definition. This same move appears in other dialogues as well: when asked "What is virtue?" a character will respond, "There is women's virtue, men's virtue, children's virtue" — but that is not yet an answer to what virtue is altogether.
This is a move that could be questioned. Some philosophers call it the Socratic fallacy: why must these things share some single, identical feature? Why can they not belong together in a rough, family-resemblant way without a common essence? Perhaps they do share such a feature, perhaps they do not. The question is genuinely open. It is also worth noting that Theaetetus does begin to make an interesting distinction between theoretical sciences and practical skills, between knowing-that and knowing-how, which could itself be explored further. Socrates, however, chooses not to pursue it.
Another point worth considering at this juncture is the comparison Socrates draws to clay at 147A–B, the clay of the potters.
Socrates offers the example of clay: clay is the stuff of which bricks and stoves are made. But if a person doesn't know what the word clay means, that definition is not going to help. As Socrates puts it, no one can understand the name of a thing when he doesn't know what the thing is. The question, though, is whether this analogy really applies to knowledge. Someone learning Greek might never have encountered the word for clay before, but these interlocutors all speak Greek. This is not a question of a foreign language. Are they really so ignorant of what knowledge is?
This is where the argument becomes somewhat strained. At 147B, Socrates says, "A man who is ignorant of what knowledge is will not understand what cobbling is, or any other craft." Imagine going to a shoe shop and asking the cobbler for a working definition that encompasses all knowledge. He would likely throw you out. But does that mean he cannot fix your shoes? The cobbler can certainly repair shoes without being able to define knowledge, or even define cobbling. Socrates, however, is not asking for a practical result; he is asking for conceptual clarity.
Heidegger speaks to this tension directly. In everyday life, he argues, we do not form theoretical abstractions or objective statements; we simply use things, and a certain clarity and know-how accompanies that practical engagement. The insistence on objectifying what we already use fluently may itself be a kind of error. This is worth keeping in mind as we follow Socrates down the path of definition.
There is also a curious self-referential moment in the argument. Socrates says that a man ignorant of what knowledge is will not know what cobbling is, and notice that he uses the word know in the very act of discussing our ignorance of knowledge. Later in the dialogue, Socrates will call this sort of thing shameless: how can we shamelessly use the word know when we do not yet know what knowledge is? But can we really avoid it? Is it possible to start entirely from scratch, without relying on concepts that have not yet been defined?
There is a circle here, but it may not be a vicious one. It may in fact be a virtuous circle. We have to begin with what is familiar, with what we already "know," and then work to deepen and clarify it. We may never fully finish that process, but the circularity itself is instructive. In some sense, the answer to the question "what is knowledge?" must already be within the interlocutors, because they use the word and it means something to them. At least some answer, perhaps not the right one, is already present, and they are, as it were, pregnant with it.
Theaetetus now understands what kind of answer Socrates is looking for: a general answer. We learn that he is rather good at mathematics, because Theodorus had demonstrated a point about certain quantities, and Theaetetus and his friend, confusingly also named Socrates, generalized this into a universal rule. Consider three squares defined by their areas: one square foot, three square feet, and five square feet. The question is whether the sides of these squares are commensurable with one another.
The side of the one-square-foot figure is obviously one. The side of the three-square-foot figure is the square root of three, but what does that mean? Is it commensurable with one? To be commensurable means that you can express it as a ratio of two whole numbers, making it a rational number. Is the square root of three, say, seven-eighths? Eight-thirteenths? One hundred forty-three two-hundred-sixty-eighths? It is none of these, and one of the great achievements of Greek mathematics was to demonstrate that irrational numbers exist, quantities that cannot be expressed as a ratio of two whole numbers.
Crucially, they cannot be expressed in a logos, a word that will become very important later in the dialogue. Logos is a fundamental Greek term meaning language, reason, and also ratio. It is worth noting that the Latin word ratio likewise means reason. An irrational number, then, is one that eludes rational articulation entirely. The existence of such quantities was rather mind-blowing for the Greeks, who generally wanted things to come down to something that can be precisely articulated and defined.
This may be a hint of what is to come: knowledge itself may turn out to be irrational in the sense that one cannot fully give a logos of it, a complete account.
Theaetetus was able to give a general mathematical account, essentially arguing that any number is either the square of some natural number or has an irrational square root. And yet, as he says at 148B, "I shouldn't be able to answer your question about knowledge in the same way." Theodorus, then, turns out to be a false witness.
Socrates responds by urging Theaetetus to put his heart into it: this is no small matter, and the very fact that he has been wondering and worrying about it is an excellent sign. Those are labor pains; he is pregnant. This introduces a wonderful extended metaphor in which Socrates compares himself to his mother, who was apparently a midwife with the fitting name Phainorete, meaning "she who brings virtue to light," a name that resonates with his frequent claim that he himself knows nothing. Just as midwives are older women past the age of childbearing, Socrates says he can no longer give birth to theories. He has had some in the past, but none of them have worked out, and so he possesses no wisdom of his own.
What he does seem to possess is a kind of psychological knowledge, a knowledge of character. This fits with what he said at the beginning of the dialogue about always seeking out particularly promising individuals. As the prologue suggests, he has genuine insight into particular human beings and human situations, even if he cannot supply general, abstract answers to questions such as what is virtue, what is knowledge, or what is being.
Another striking detail in the metaphor is that Socrates claims midwives are also good matchmakers, something that seems to surprise everyone, and may well be his own invention. He adds, in a comic moment, that he too is a good matchmaker: sometimes he meets people who simply do not seem to be pregnant, and so he must send them off to someone like Prodicus to get them philosophically fertilized. Prodicus was one of the sophists, and since another sophist will appear shortly, it is worth noting the distinction. If "philosopher" means lover of wisdom, "sophist" means wise guy. These figures traveled throughout Greece teaching on many subjects, but especially rhetoric, the art of persuasive oratory, which could bring considerable power in a democracy like Athens where every citizen had the right to address the assembly.
Audience: Isn't there another issue there? He talks about the distinction between being a matchmaker and being a procurer, and then he just leaves it alone without saying which one he is, leaving open the possibility that he might be a kind of sophist himself.
That is exactly right. He will make sophistical arguments at times. We just saw him make one: "You cannot be wise without knowing something; therefore, knowledge is wisdom." That is sophistry. Both the sophist and Socrates can make bad arguments, though one might ask whether they differ in their intentions, and whether the sophists are more driven by greed or self-interest. In any case, one can see why Socrates was accused, not entirely without reason, of corrupting the youth and undermining sound, healthy opinions through verbal trickery.
The overall effect of the midwife metaphor, however, is to encourage Theaetetus: there is an answer within him, and Socrates will help him bring it to birth. And so, at last, we get a proper answer.
At 151E, Theaetetus says: "It seems to me that a man who knows something perceives what he knows, and the way it appears at present, at any rate, is that knowledge is simply perception." Notice that he uses the same word in various ways within that very statement. "It seems to me" is itself a perception; "a man who knows something perceives what he knows" invokes perception again; and "the way it appears at present is that knowledge is simply perception" is yet another form of it. He is doing exactly what Socrates did earlier, using the same word to define itself.
Audience: His definition is illustrating itself in the way he expresses it.
Precisely. Appearance goes hand-in-hand with perception, and Theaetetus is enacting that connection as he speaks. The Greek words, for anyone curious, are: episteme for knowledge, the root of epistemology, the theory of knowledge; aisthesis for perception, related to aesthetics, insofar as beauty and art concern how we feel and perceive things; and phainetai for "it seems" or "it appears." All three concepts are bound together, and Theaetetus illustrates that bond in the very act of stating his thesis.
There is also something worth noting about appearance and time. Appearance is always in the present: something appears now, then disappears, and something else appears in its place. When Theaetetus says "the way it appears at present," he is telling us that this is how he perceives knowledge at this moment, without being entirely certain. And is that not almost a self-refutation? He is saying, in effect, "Right now I perceive knowledge to be the same as perception, but I am not sure," which means he does not really know where he stands. He is already hedging, already ready to be corrected.
He did offer a miniature argument for his view, however: a man who knows something perceives what he knows, therefore knowledge is perception. This should sound familiar. It mirrors the earlier move in which Socrates argued that if you have wisdom you have knowledge, therefore wisdom and knowledge are the same thing, a plainly invalid inference. Now Theaetetus is reproducing the same logical error: if you know something, you perceive it, therefore knowledge just is perception. Socrates seems to have set a very bad example, perhaps deliberately, and Theaetetus has followed it. Notably, Socrates does not tear the argument down.
Socrates praises this answer because it is exactly what he wanted. He wanted Theaetetus to give birth to something like this. The birth process, however, is not quite complete: the baby is crowning but not yet delivered. We do not really know what it means to say that knowledge is perception until we examine some of its implications, consider how it would be applied in various situations, and see how it answers some rather obvious objections. It will take a while before Socrates declares, "Now your firstborn is here: now we will truly test it and see whether it is true or false."
We should remember one important difference between Socrates and a midwife: a baby is a baby. Even a stillbirth is real. But a theoretical baby, an idea, may be what Socrates calls a wind egg, an infertile egg, a nothing. With that caveat in mind, Socrates praises the answer and immediately connects it to the view of Protagoras.
Protagoras was a Sophist, perhaps the most famous of all the Sophists. It was said that he had no fixed fee for his teachings, but would ask his students to go to a temple and swear to the god that the instruction was worth a certain amount of gold, which they would then deposit there. In this way, Protagoras became very wealthy, because people judged his teachings to be enormously valuable. The direct statements we have from Protagoras come almost exclusively through Plato, and the most famous of them is this: "Man" (meaning the human being) "is the measure of all things: of the things which are, that they are, and of the things which are not, that they are not."
This statement can be read in many ways. How does Socrates interpret it? He reads it as grounding everything in each individual's experience, in this case, sense experience. On this reading, "my experience as one human being is the measure of all things, at least in my own mind." Each individual human being is thus the measure of his or her own reality, and there is no reality in itself. Is the wind warm or cold in itself? The question does not even make sense. There is no warmth or cold except in relation to a perceiver, no temperature of the wind in itself, and, in fact, no wind in itself.
One can quickly see that this is going to become rather strange. At first, it seems initially plausible to say that knowledge is perception, that what you know is how things seem and are perceived by you. That seems fair enough. But very soon the implication emerges that there is no absolute reality, no being in itself of anything. If a tree falls in the forest and no one is listening, the tree does not even fall in the forest. There is no tree, there is no forest, unless some human being, or perhaps some animal, is perceiving it.
When I first read the Theaetetus, it was taught by Paul Feyerabend, a brilliant philosopher of science at UC Berkeley, and the main thing he focused on was some uncanny parallels between this ancient notion and quantum mechanics.
There are some fascinating issues at the quantum level, and I am by no means an expert, but consider wave-particle duality. Does light consist of photons, discrete particles of light, or does it consist of waves propagating through some medium? The answer depends entirely on which experiment you perform. Some experiments compel the conclusion that light is a stream of particles; others compel the conclusion that it is a wave. So which is it?
Protagoras would love this. He would say: "What do you mean, which is it? It is nothing in itself. It depends on what the observer perceives and how they perceive it." The reality that emerges is the reality to that perceiver, to that experimenter, in that moment. The ancient relativist's formula maps surprisingly well onto the situation modern physics has placed us in.
The uncertainty principle raises a similar point. On some interpretations, there simply is no such thing as the simultaneous position, velocity, and mass of a subatomic particle. Certain properties are not merely unknown; they are undefined, indeterminate, nonexistent, precisely because they are not what the experiment is testing for. Reality, on this view, does not pre-exist the measurement; it emerges only in the act of observation itself.
Are we clear on why Socrates immediately drags in Protagoras? If you say knowledge is perception, why does it follow that everything is relative to a perceiver, and that there is no absolute knowledge or absolute objective being of things? I think it is implicit in the statement itself. If I perceive something and take that perception as knowledge, and if perception is the standard of knowledge, then any perception can be claimed as knowledge, which means there is no absolute reality, only what things appear to be to each perceiver.
We also assume, and this will be taken for granted throughout the dialogue, that knowledge is by definition true. It does not make sense to speak of incorrect knowledge; we would speak instead of incorrect opinion. Now, if knowledge is simply perception, there can be no things-in-themselves. Consider a pen: if there were a pen existing in itself, apart from my perception of it, then my perception could deviate from that reality and could be incorrect. But if there is no pen in itself, if there is only what appears to me, then I cannot be wrong.
That brings us through Theaetetus 152c. In our next session, we will look at further developments in which Socrates connects the claim that knowledge is perception to additional theories, until the intellectual baby is fully born and ready to be tested.