A philosopher and mathematician (c. 417 - 369 BCE) that lived in ancient Athens. According to the Suda Lexicon, 1 there are two references to an ancient scholar that both have the name of Theaeteus, and experts debate over whether or not they are the same individual. Most of the knowledge of Theaetetus comes from Plato's writing about him. Plato wrote two dialogues in which he is a central participant, the Theaetetus and the Sophist.

Theaetetus made significant contributions to the field of mathematics. None of his writing has survived to the present day, but it is thought that Books X and XIII of Euclid's work Elements are descriptions of Theaetetus' work. From Pappus' commentary on Book X:

"The aim of Book X of Euclid's treatise on the "Elements" is to investigate the commensurable and the incommensurable, the rational and irrational continuous quantities. This science has its origin in the school of Pythagoras, but underwent an important development in the hands of the Athenian, Theaetetus, who is justly admired for his natural aptitude in this as in other branches of mathematics. One of the most gifted of men, he patiently pursued the investigation of truth contained in these branches of science ... and was in my opinion the chief means of establishing exact distinctions and irrefutable proofs with respect to the above mentioned quantities." 2

Theaetetus was heavily influenced in his mathematical work by his teacher Theodorus who is also a participant in the Socratic dialogue Theaetetus. From the Elements:

" ... was considerably developed by Theaetetus the Athenian, who gave proof, in this part of mathematics as in others, of ability which has been justly admired. ... As for the exact distinctions of the above-named magnitudes and the rigorous demonstrations of the propositions to which this theory gives rise, I believe that they were chiefly established by this mathematician. For Theaetetus had distinguished square roots commensurable in length from those which are incommensurable, and who divided the more generally known irrational lines according to the different means, assigning the medial line to geometry, the binomial to arithmetic and the apotome to harmony, as stated by Eudemus ... " 2

Theatetus is also said to have been the first to work with the dodecahedron and the octahedron, two of the five "Platonic" figures, the other three of which were initially worked with by Pythagoras. He is also often credited with developing the Theory of Proportion which appears in the work of Exodus.

Theaetetus is also the name of a Socratic dialogue written by Plato. Partcipants in the dialogue include:

The central particpants are Socrates, Theaetetus and Theodorus. Knowledge is the most important issue explored in the dialogue, as Plato inititally presents the idea that knowledge is comprised of seeing and doing, as in learning a craft. Plato's theory of knowledge is looked at in a more advanced manner in The Republic and the Meno, but here it is first understood as being the mastery of a skill 3. This definition is also looked at in The Apology. 4

At the beginning of the Theaetetus, Socrates prompts Theodorus to talk about his young student, Theaetetus:

"I speak without any qualms; and I assure you that among all the people I have ever met - and I have got to know a good many in my time - I have never yet seen anyone so amazingly gifted. Along with a quickness beyond the capacity of most people he has an unusually gentle temper ... People as acute and keen and retentive as he is are apt to be very unbalanced. They get swept along with a rush, like ships without ballast ... But this boy approaches his studies in a smooth, sure, effective way ... " 5

Socrates goes on to ask Theaetetus to defend this praise that Theodorus has given him by describing his work and what he has studied. Theaetetus does in the following manner:

"We defined under the term 'length' any line which produces in square an equilateral plane number; while any line which produces in square an oblong number we defined under the term 'power', for the reason that although it is incommensurable with the former in length, it is commensurable in the plane figures which they respectively have the power to produce." 6

Later in the dialogue, Socrates asks Theaetetus to give a definition of "knowledge". Theatetus attempts to give three explanations:

  • Knowledge is Perception 7 Socrates dismisses this definition because he thinks knowledge presupposes being and truth, which perception cannot access. We perceive, he thinks, not by sensory organs, but via the soul.
  • Knowledge is True Judgment 8 Socrates rejects this explanation using the example of Athenian jurors. In their case, they can have true judgment without knowledge as lawyers can pursuade them without teaching them anything (causing them to actually know anything). Instead, they are convinced to hold a certain belief - whichever belief the lawyer wants.
  • Knowledge is True Judgment with an Account 9 No definitive conclusion is reached by Socrates on this account, as he attempts to define what giving an "account" entails, and their conclusion is that more inquiry is needed when they gather to discuss the matter again the next day. 10 Socrates is pleased that Theaetetus has become more adept at philosophical inquiry and criticism.

1 The Suda Project's website is at: http://www.stoa.org/sol/
2 http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Theaetetus.html
3 gk. technê
4 Plato. The Apology. tr. G. M. A. Grube. Stephanus pp. 19 e - 20 c.
5 Plato. Theaetetus. tr. M. J. Levett, rev. Myles Burnyeat. Stephanus pp. 144 a-b.
6 Stephanus p. 148 b.
7 gk. aisthêsis. Stephanus p. 151 e.
8 Stephanus p. 187 b.
9 gk. logos. Stephanus p. 201 d.
10 The Theaetetus leads directly into the next dialogue, the Sophist, where similar issues are discussed at length.


In the Platonic dialogue, Theaetetus, Socrates tackles the thorny issue of the unreliability of the senses. What we perceive seems to makes sense on the surface; it feels like the sense data is enough to deliver us the world in a clear and a reliable way. That's what Theaetetus, Socrates's dialogue partner, seems to initially believe. However, Socrates prods him with dilemmas and puzzles to get him to see that appearances are not so straightforward and that the more you think about how perceiving works, the more confusing and difficult it seems to get the senses to acquire knowledge and put together a coherent, logical picture of the world. The process of the dialogue is just as important as the content. Socrates gets Theaetetus to confront the difficulties of perception and propose solutions. He places a premium on making the young man reflect upon various alternatives and make choices as to what seems right or wrong. Despite giving him lots of direction and plenty of hints, he makes Theaetetus struggle to come up with answers because he has faith in the inherent intelligence and power of the mind to discover truths. In the paragraphs to come, I will first explain why Socrates believes that Theaetetus's mind is capable of penetrating the truth about the way perception can become knowledge. I will then delve into the arguments he uses to convince Theaetetus that acquiring knowledge requires not just perception but various capacities of the mind. Lastly, I will illustrate Socrates's vision of the necessity of the mind for coherent perception with examples taken from everyday situations.

Giving Birth to Ideas

In explaining how Theaetetus is supposed to learn about perception and knowledge, Socrates embeds the process of the generation of ideas within the mind in a mythological foundation. You see, as Socrates would have it, ideas are born to men like children are to women. Men's confusion and anxiety concerning their lack of knowledge and inability to answer questions is the equivalent to women's birth pangs that will eventually, after much pain, produce the desired ideas. These ideas, born much like children, won't always survive in the world as miscarriages happen. Socrates takes it upon himself to tell his conversation partner that the idea he has given birth to is not viable.

In this dialogue, Socrates thus positions himself as a midwife to men's souls pregnant with ideas not only as a way of making the painful process of arguing more palatable but also in order to distance himself from the ideas towards which he pushes his conversation partners. Since he says that the goddess Artemis favors midwives that cannot give birth themselves, his own mind is supposedly barren. The ideas that his interlocutors end up articulating were born in their mind and not his. In a way, this assertion of Socrates is quite disingenuous. Most of the time, it is he who advances arguments and Theaetetus only assents or dissents to them. To say that Theaetetus was the one that generated the ideas but that his own role was merely that of assistance gives the young man far more credit than he deserves. But then again, this assertion is in accord with Plato's theory of recollection that postulates that learning is the recollection of the soul's lost knowledge from its previous lives. Citing glorious priests (a vague reference as they aren't named) in the dialogue Meno, Socrates says: “The soul, then, as being immortal, and having been born again many times, and having seen all things that exist, whether in this world or in the world below, has knowledge of them all; and it is no wonder that she should be able to call to remembrance all that she ever knew about virtue, and about everything.”

Knowledge is Subjective Because We Perceive Differently

So, as Socrates accompanies Theaetetus on a journey of rediscovering the hidden knowledge within his soul, he is constantly rejecting those ideas of Theaetetus that he perceives as miscarriages. Theaetetus initially equates knowledge with perception. Socrates, who will later challenge this theory in not only critical but disparaging terms, initially humors it, probably for the sake of intellectual honesty. (After all, Socrates is all for letting young men give birth to bad ideas; he wants them to struggle before getting answers.) Now, in conceding the plausibility of the equation of knowledge with perception, Socrates draws on the theories of Protagoras and Heraclitus. Echoing the legacy of Heraclitus, he proposes that the whole world is in a flux – everything is in motion. No object is ever stuck at any position, it or its elements are always moving from one position to another. (Think of a moist object becoming dry and brittle – that is “motion” that leads to change within the object.) In a world of flux, perceptions are created when a causing object acts upon the senses of a perceiver so that a sensation is produced. The motion of light rays combine with the capturing action of the retina to create the sensations of light. Whether red, purple, or gray, colors are never stable “objects” at rest; they are a product of both the motion of the sense of sight and the light affecting that sense, neither of which will remain in the same position for long. All this is cited by Socrates to support Protagoras's idea that the world is what one perceives it to be. The senses and the unstable, ever-fluctuating elements in motion acting upon them are caught up in endless variation and cannot be pinned down or defined. Hence, perception results in unique perceptions and experiences for every perceiving agent. The varied background configurations that produce each perception make the search for absolute knowledge that applies to all untenable. (The belief in the subjectivity of perception explains Protagoras's famous quote: “Man is the measure of all things.”) The truth of wine and wind are to be found in the perception of those experiencing them. Wine is neither sweet nor bitter in an absolute sense and neither is wind cold or warm in an absolute sense. Wind is cold for him who feels it be cold and warm for him who feels it to be warm. For a healthy person, sweet-tasting wine is sweet but not absolutely for everyone, since that same person in a sick state experiences it as bitter.

Perception Needs Mind to Avoid Confusion

However, if initially it seems that Socrates allowed the theory of flux and motion to lead him to accept that the perception of things in motion makes knowledge subjective, he goes on to challenge this notion to show Theaetetus that his first-born idea must be smothered in the womb. If perception is constantly in flux and sensations always fluctuate, then perception will be overwhelmed and confused. White can bleed into yellow, yellow into red, and red into purple. It suffices to look at a detailed painting to see how the surface is divided into a variety of tiny, diverse shades of color. Or perhaps to stand in the sunlight and watch how leaves, water, and grass have various different colors in various spots depending on the way the light touches them. Even if one tried to note every little pixel and its coloration, it wouldn't be possible since the colors would change quickly, both based on the rays of the sun and the position of the observer.

With all this in mind, Socrates argues that the constant changes in the field of perception make perception an unreliable candidate for knowledge. Based on pure perception, things can't be identified and assigned properties. A windbreaker on a hanger illuminated by a tall lamp seems beige at the top but seems more dark and grayish towards the bottom away from the light. Socrates asserts that perception by itself, without any assistance, would be mired in this chaos of different sensations and wouldn't be able to abstract them away to fix on one single object with a continuous set of properties. (The varying colors of the windbreaker could make it seem a set of various objects, each with its own color.) The production of fixed objects and properties out of the chaos of sensation, Socrates insists, would need the referral of these perceptions to an entity that wouldn't only perceive but would also be able to reflect upon the similarities and differences, the unity and separateness within sense data. Cornered by Socrates to consider how chaotic perception needs to be structured in order to become coherent, Theaetetus concedes that “the mind, by a power of her own, contemplates the universals in all things,” thereby agreeing with Socrates's assertion that ”knowledge does not consist in impressions of sense, but in reasoning about them; in that only, and not in the mere impression, truth and being can be attained.”

Real Life Examples of Confused Perception

There is no better example to illustrate Socrates's point than the way babies perceive adults. When an adult dresses up in a costume that's very different from his normal appearance, let's say a man that attaches a fake mustache, puts on makeup, and wears clothes that are unusual for him such as a toga or a dress, a baby may not be able to identify this person despite knowing him well. An older child or an adult, however, would not experience similar confusion and would still be able to recognize the man. That is because, in addition to pure perception, the adult and the older child are able to draw upon the resources of his mind to compare the new appearance of the person to his previous one and find the common features that would enable them to equate the past and the present versions of the same man despite their differences.

So what happens in order to make this act of recognition possible? First of all, Socrates envisions the mind as a block of wax on which we imprint our impressions. After seeing objects and meeting people for the first time, we are able to identify these objects and people instantaneously by matching our perceptions with the images impressed in the mind. Imagine the case of woman who caught the eye of a certain man at a party who later changed into a ski mask and a different set of clothes to follow her on her way home and rape her. She has already met the rapist at the party but will she be able to recognize him in disguise? That depends on the image that was imprinted on her mind. If she had paid sufficiently close attention to him while at the party to be able to remember a whole set of details about him, then it is more likely she will recognize him. The clothes may be different and the face concealed, but the body itself, as well as the voice and gestures have remained the same.

Knowledge Based on Constitutive Elements and Distinguishing Characteristics.

For this very reason, Socrates insists on the quality of the image imprinted on the waxen block of the mind. He stipulates that in order to have true knowledge you have to have not only a vague image of an object or person but in fact be able to list the elements that he or it are composed of. However, the key point that Socrates makes is that in order to truly know and be able to identify an object or a person, the elements that constitute it must be retained with their distinguishing characteristics that would enable the perceiver to exclude all similar objects of persons. That is why upon finding a stolen car, the supposed owner of the car is asked to list specific features of his car that could only belong to his car and no other. Perhaps there is a special dent somewhere, a stain from a hot drink or a marker. These distinguishing characteristics are especially important in the recognition of objects or beings that have changed over time. A set of puppies all born at the same time may all be given separate names, but unless the owner looks them over and finds that special little patch of color, or the shape of a muzzle, he won't be able to remember which puppy is which once they have grown. In all of these cases, it is not enough to just recognize based on a vague or instinctive memory. That kind of identification/recognition is only “true opinion.” True opinion becomes knowledge only with an explanation that cites the constitutive elements of the object/person as well as the distinguishing characteristics. Thus for the woman above, to have knowledge of the rapist, she will have to provide a set of his characteristics, physical and otherwise, with one or several of them specific enough that others would be unlikely to share it. For as Socrates says, how can one know/identify Theaetetus by his snub nose when there are others who also have a snub nose? Hence, the need for the distinguishing characteristic.

The Mind's Mistakes in the Quest for Knowledge

While Socrates spends a lot of time talking about how the mind's attention to the elements and distinguishing characteristics of things and people is what enables it to successfully gain knowledge of objects, that is to identify and recognize them, he also gives equal attention to how the mind either fails to attain these objectives or experiences delays or impediments in acquiring knowledge. And this failure happens at the stage where we try to match the mental images in the waxen block of our mind to the chaos of perception that invades our senses. For example, distance may obscure or distort the appearance of someone to the point that we match them up with wrong impression in our mind. Or we fail to distinguish between two very similar items or beings, when only one is present to our perception. Thus, if we happen to hear the voices of two sisters that sound alike, when they are both there, we may be reminded of the subtle difference between the two and identify them correctly. When only one of the sisters is there, sister A, we grasp onto to the aspects of her voice that are like the other sister's and believe ourselves to be in the presence of sister B. The failure to recognize something or someone we know may happen for a simpler reason. Socrates conceives of the knowledge we possess as an aviary of birds. The mental impressions that we have collected throughout our life are flying around in our mind like birds but we can't actively use them until we catch the bird. Hence when meeting someone we haven't seen in many years, we are aware that the memory of who they are is within us, but we have to roam around in the aviary of our mind to get a hold of it. So we chase after that bird and once we grasp it, we experience an aha moment of recovering lost knowledge.


The goal of the dialogue is therefore to establish knowledge on a secure basis and protect it against the unreliability of perception. At the beginning, Socrates concedes to chaotic conceptions of perception advanced by Heraclitus. He does not fight the notion that the very same objects give rise to different experiences of taste and color. Even shape and size of objects are not secure as they can both change with time. He does believe, however, that through the mind's power to contrast and compare, we can penetrate different appearances and identify them with the history of the same objects/beings that underlie them. A table can be traced to its history as chopped wood and a tree. Milk can curdle, wine can become acidic and bitter with time, but we can still identify the curdled milk with fresh milk, the acidic wine with sweet wine. Socrates is therefore contesting Protagoras's theory that appearances dictate truth and therefore truth is subjective based on individual perception. He postulating that out of diversity of appearances, a steady set of absolute traits and features can be derived that do not depend on subjective perceptions. (Hence “man is not a measure of all things” like Protagoras would have it, but things are as they are regardless of how man measures them.) Socrates also manages to refute Heraclitus's view that everything is ever-changing and therefore nothing is ever the same. Whereas Heraclitus would say that you can't step in the same river twice because it's completely different from what it used to be at a previous moment, Socrates would say that despite the various changes in the river, it has a set of constituve elements and distinguishing characteristics that make it the same river as it was before. Just like there is something about a person as a child that endures into his adulthood, even though there are great differences between the younger and the older version of the same person. Socrates would agree with Wordsworth that “the child is the father of the man.”


Note: I am not sure if the assertions about wine and milk in my conclusion are factually valid. If you have any modifications to propose, send me a message.

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