Form and Good in Plato's Eleatic Dialogues Chapter Two The Theaetetus
Author: Unknown
Date: 0101-01-01T00:00:00+00:00

Form and Good in Plato’s Eleatic DialoguesHome | Show Table of Contents Search this book all books for Customize |

Help

Kenneth Dorter

Form and Good in Plato’s Eleatic Dialogues The Parmenides, Theaetetus, Sophist, and Statesman

Chapter Two The Theaetetus

Chapter Two

The Theaetetus

1. Knowledge and Virtue (142a-153e)

Near the beginning of the dialogue Socrates asks Theaetetus whether knowledge and wisdom are the same thing (145e). Theaetetus answers in the affirmative, and Socrates responds noncommittally: “Now it is this very thing that perplexes me, and I am not sufficiently capable of grasping by myself what knowledge is.” There matters are allowed to rest. After Republic 4’s analysis of human wisdom as knowledge together with self-mastery (the subordination of appetite and competitiveness to reason in the tripartite soul, 442c), this uncritical identification of wisdom with knowledge is provocative, and leads us to wonder whether the aporetic ending of the dialogue is in any way connected with this oversimplified beginning. Plato’s readers would hardly have forgotten the doctrine of the tripartite soul so quickly, and there seems to be a deliberate reminder of it in the names of the initial speakers, Eucleides (“Renown”) and Terpsion (“Delight”), which correspond to the two lower motivations of the soul, “love of honor” and “love of pleasure.”

Later, in the long, central digression that recalls the Republic and Phaedo ,[1] where Socrates speaks not as a midwife but from his own ― 69 ―
conviction, he says that we must seek to escape the evils of the corporeal world, and that “to escape means assimilation to god, and assimilation means to become just and pious, with wisdom” (176b). The word for wisdom here is phronêsis (sophia is used in the earlier passage and in the Republic ), but the point is the same, that the highest rational attainment goes beyond intellectual knowledge alone (which may be in the service of our irrational passions) and involves the subordination of “corporeal evils” to the “divine.” Accordingly, Socrates goes on to say that “knowledge of this [how to assimilate ourselves to god] is true wisdom [sophia this time] and virtue” (176c).

There are more direct reminders of the Republic doctrine. Before Socrates meets Theaetetus, Theodorus describes him as being quick to learn, gentle, and courageous, and remarks that this is a combination which otherwise I would not have supposed to exist, nor do I see it. Rather, those who are as sharp as he is, and quick and with retentive memories, are also for the most part quick-tempered, … manic rather than courageous.

Those on the other hand who are more sedate are also somewhat sluggish when they come up against their studies, and are forgetful.

(144a-b)

We can restate this passage, which recalls the qualities sought for in the guardian class of the Republic (2.375b-376c), in terms of the categories of that dialogue: intelligent people are almost always dominated by their spirited nature, and those who are not spirited tend to be lazy or sluggish, that is, more interested in comfort than in effort. Most people are thus dominated by love of honor or love of pleasure, and it is only Theaetetus’s nature that makes Theodorus realize that it is possible to be intellectual without being dominated by spiritedness: that is, that love of reason is distinct from love of honor, and that there are three types of persons rather than two (this classification will become important again at the end of the trilogy, in the contusion of the Statesman ).

The lazy, forgetful type was exemplified by the two characters with whom the dialogue opens.[2] When Terpsion asks Eucleides if he can repeat the conversation that Theaetetus had with Socrates, he replies, ― 70 ―

“No, by Zeus! Not by heart” (142e). But Socrates has recited it for him verbatim and refreshed his memory every time Eucleides went to Athens, until by now Eucleides has almost all of it written down (143a). Not only is Eucleides’ memory not impressive, but he has gone about this task in a lazy, piecemeal fashion. Terpsion too is unimpressive for his memory or energy: he has “always intended” to ask Eucleides to read the account of the conversation between Socrates and Theaetetus, but has not actually done so until now—whether out of forgetfulness or lazy procrastination, he does not say. He wants to hear it now, however, because he is tired and needs to rest (143a). Eucleides, too, is tired and would like a rest, so he decides to have his slave read the conversation to them while they are resting (143b). He also mentions that he put the conversation in the form of direct discourse rather than narrative because it would be too much trouble (

[Full Size]

) to put in Socrates’ narrative asides, such as, “And I said,” between all the speeches (143c).

This combination of poor memory and lazy lack of spirit becomes immediately evident within the conversation in the character of Theodorus, who cannot remember who Theaetetus’ father is (although Socrates, who has never met him, knows his father and native city as soon as he sees Theaetetus),[3] and who fearfully resists every attempt to draw him into the discussion.[4]

The significance of memory, which Plato foreshadows by these dramaturgic means, will emerge in due course; but some preliminary remarks may be made about courage (which is here opposed both to laziness and to fearfulness).

Throughout the ensuing discussion the need for courage and boldness is continually emphasized.[5] A clue to the reason for this may be found in a passage of the Meno . There, after introducing the doctrine of recollection, Socrates concludes that this refutes Meno’s paradox by showing that learning is possible
if one is courageous and does not desist from seeking; for seeking and learning are the whole of recollection. One must not be convinced by that conten-

― 71 ―
tious doctrine [Meno’s paradox]; that doctrine will make us lazy and is pleasant for soft people to hear. This one, however, makes people energetic and searching.

(81d, emphasis added)

The Theaetetus , in fact, recalls the Meno at almost every turn. For example: (1) at 146c-d Theaetetus is rebuked for giving a list of examples in answer to the question, “What is knowledge?” as Meno had been for “What is virtue?” (72a). (2) At 148c Socrates offers a definitional example of day as earth mixed with water, as he had offered Meno the example of shape defined as what always accompanies color (75b). (3) The Meno took as its model the knowledge that the square root of an area of eight is not expressible as a whole number but may be expressed as a diagonal (82b-85b); the Theaetetus proceeds to take as an example of knowledge the distinction between areas whose roots are expressible as whole numbers (squares) and those whose are not (oblongs; 147d-148b).[6] (4) Socrates’

remark that some people think he is a most strange person who reduces others to an impasse (149a) precisely echoes Meno’s complaint at 79e-80b.

(5) The Theaetetus (187b ff.), like the Meno (97a ff.), discusses knowledge by comparison with true opinion. (6) The Theaetetus more than once (198c-d; cf. 196d-e, 209e) alludes to Meno’s paradox (80d). (7) After Anytus warns Socrates that he may find himself in serious trouble for critical remarks he has just made (94e), the Meno ends with Socrates saying, “Convince your friend Anytus of these things of which you are now convinced, so that he may become more calm. If you convince him you may also benefit the Athenians,” a pointed anticipation of Socrates’ trial and execution; the Theaetetus ends with Socrates going off to answer the indictment of Meletus, of which Anytus was coauthor. (8) F. M. Cornford, who notes several of the above as well, suggests also that Socrates’

midwifery corresponds to the Meno’s doctrine of recollection.[7] His suggestion is often rejected on the grounds that the answers elicited by midwifery are frequently wrong,[8] but we might say the same about the answers elicited by Socrates from Meno’s slave (82e, 83e).

― 72 ―

Nevertheless midwifery, unlike recollection, cannot be considered a necessary condition for attaining knowledge, so the correspondence is only approximate.

Whether or not Plato deliberately plays out the Theaetetus against the backdrop of the Meno’s doctrine of recollection, the Theaetetus reaffirms the latter’s claim that, whatever theoretical knowledge may be, it is not something easily acquired. It requires the courage to persist amid difficulties and frustrations, and the boldness to pursue hypotheses that may fly in the face of common sense. According to the digression in the middle of the dialogue, what is called for ultimately is nothing less than the courage to change our way of life. This is not the kind of knowledge that Theaetetus will take as his model, however. Urged on by Socrates’

promise to act as the midwife of his conceptions (a metaphor that will function in a number of ways in the dialogue), Theaetetus brings forth the idea that knowledge is sense perception.

2. The Heracleitean-Protagorean Problematic (151e-160e) That Plato should assign to a mathematician the role of defining knowledge as sense perception is not surprising when we consider that for the Greeks mathematics centered on geometry, whose proofs were illustrated by diagrams. The Meno , however, reminded us that what one learns only by looking at the diagrams is not knowledge at all. Socrates says there about the slave: “At present these opinions, having just been stirred up in him, are like a dream. If, however, one were to ask him the same things many times and in many ways, you know that finally he would have knowledge of them that is no less accurate than anyone’s” (85c-d). The slave’s opinions will not be transformed into knowledge until he frees himself from dependence on particular diagrams or formulations.

In the Theaetetus Socrates pursues the opposite path, moving within the realm of sense perception rather than abstracting from it. To begin with, Theaetetus’s model of surds and roots bears only a superficial resemblance to the diagram of the Meno . Whereas Socrates used that diagram as a means of discovery, Theaetetus uses his model only as a means of classifying what is already known. It is a preliminary application of the method of collection and division (“we tried to collect them [the roots] into a unity,” 147d; “we divided all number into two,” 147e). Moreover, when Theaetetus uses this mathematical example as ― 73 ―
an instance of knowledge, Socrates does not proceed to make a connection between the nature of mathematics and the nature of knowledge generally, and to use this as an impetus to lead his partner in the direction of the intelligible, as in previous dialogues. Socrates instead pushes him in the contrary direction, to the most phenomenalistic way of conceiving knowledge. The world is just as it seems to each observer. Plato begins the dialogue with the most elementary conception of knowledge, that is, the lowest grade of information, mere sense experience. From this he will generate under the pressure of criticism progressively more complete models, in accordance with the method of hypothesis.[9]

By beginning in this way Plato is able to respond to the attack on stability launched by Heracleitus, who insisted that conceptual distinctions are always arbitrary, regardless of whether they refer to values such as beauty, or factual demarcations such as up and down, day and night, or alive and dead. The world of thought, like the world of beings, is pure becoming or flux, and conceptual knowledge is therefore delusory. The next generation took the next step and wondered how, if Heracleitus is right, it is possible for him to say so without inconsistency. Accordingly, his disciple Cratylus rejected his teacher’s claim that we cannot step into the same river twice, for we cannot step into it even once. And to make his point with greater consistency Cratylus abandoned speech altogether and limited himself to pointing with his finger.[10]

It is against this background that the Theaetetus takes place, a dialogue explicitly concerned with the Heracleitean foundations of fifth-century sophistry. Today’s “postmodernists” have advanced worldviews that are parallel in some ways to that of the Ephesians. Like their Presocratic counterparts, they attempt to break down the perceived structures of experience into negativity and flow—the problematic of the Theaetetus is of interest today not only for historical reasons. It is no accident that the reaction of the analytic-minded mathematician Theodorus to the school of Heracleitus is evocative of the reaction of contemporary analysts and traditionalists to Deconstructionists:

It is no more possible, Socrates, to discuss these doctrines [with their adherents] … than with maniacs. For they are, in accordance with their trea-

― 74 ―
tises, completely in motion; and as for keeping to an argument or a question and calmly answering and asking in turn, there is less than nothing of that in them … . If you ask one of them something, he pulls an enigmatic little phrase out of his quiver and shoots it off.

And if you try to get an account of what be said, you will be hit anew by another turn of phrase. You will never reach any conclusion with any of them; nor, indeed, do they themselves with one another; but they take very good care to let nothing be stable, either in an argument or in their own souls.

(179e-180b)

Socrates’ rejoinder, that the Heracleiteans probably exaggerate these qualifies to Theodorus because of his hostility, reminds us that Plato himself shows considerable respect for Heracleitus’s doctrines, and in the Timaeus describes the cosmos as partly grounded in chaos. The degree of his endorsement of Heracleitean destructuring is obscured by his concern about the propriety of disseminating such views even if they are true.

Half a page after Theodorus’s remarks, Socrates says, Have we not heard from the ancients, who concealed it from the many by means of poetry, that the origin of all things, Oceanus and Tethys, are flowing streams, and that nothing stands still? And also from the modems who, because they are wiser, reveal these things openly so that even the cobblers may hear them and learn their wisdom and cease from their foolish belief that some things stand still while others are in motion, and, once they have learned that all things are in motion, may honor these teachers?

(180c-d)

In view of his belief that we do ordinary people no favor by convincing them that stability is an illusion, we must expect that whatever affinity Plato has for the views of Heracleitus will not be straightforwardly acknowledged. Nevertheless, these doctrines are taken very seriously in the Theaetetus . We need to consider how receptive Plato is to the objections against natural stability and to what extent his own philosophy of form justifies itself against the considerations that lead to the destabilizing of what appears to be stable. In the Parmenides Plato threw the theory of forms into uncertainty. And even though Parmenides reaffirmed the need for forms if thinking and discourse are to be possible, the forms are missing from the Theaetetus , at least on the surface. We would expect them to make an appearance when Socrates discusses the problem of quantitative relativity: it seems unproblematic to assert that six dice are more than four by a half and less than twelve by a half (154c), but, he says (in a dear echo of the method of hypothesis), we need “to observe our thoughts in relation to themselves, whichever ones we think, to see whether for us they are consonant with one another or

― 75 ―
not at all” (154e; cf. Phaedo 100a, 101d). In the present case, three such beliefs produce tension with the statement about the relative size of numbers:

Nothing can ever become more or less, either in size or number, as long as it is equal to itself.

And second, that to which nothing is added and from which nothing is subtracted, is neither increased nor decreased, but is always equal.

Third, that something previously was not, but later is, without becoming, is impossible.

(155a-b)

“These three admissions fight with themselves in our minds when we talk about the dice,” or when we say that if Theaetetus grows taller, then Socrates goes from being taller to being shorter without changing size (155b-c). Their “fight with themselves” presumably consists of the fact that each of them seems clearly true when taken just by itself, but clearly false when applied to the relative largeness and smallness Of numbers (the dice) and sizes (Socrates and Theaetetus).[11] It is important to keep in mind that the fight must be a tension within each statement, rather than a tension among them, for the examples of the dice and Theaetetus falsify either all three of the admissions together or none at all. (It is misleading therefore to translate [Full Size]

as “contend with one another, ” which implies that if we got rid of two of them the remaining one would be unproblematic.) In the Phaedo (100e-103a) such problems are resolved by means of the theory of forms: relations like larger and smaller are not corporeal properties of individuals. They are therefore not subject to the three admissions mentioned above, which apply only to nonrelational subjects.

They are conceived instead as relational essences, which are distinct from any corporeal individual, but which may be participated in by individuals in certain circumstances. Accordingly, we would not say, in violation of the first principle (“admission”), that Socrates, while remaining equal to himself, has gone from being taller to being shorter, but only that in one comparison he participates in the relation “taller” and in another “shorter.” Nor would we say, in violation of the second principle, that Socrates has decreased without anything having been ― 76 ―
subtracted from him, but only that he participates in a different relation because the size of the other referent (Theaetetus) has changed. Nor again, in violation of the third principle, that Socrates has gone from not-short to short without a process of becoming, but only that he participates in one relational form rather than the other because of a becoming that attached to the other referent.

Unlike the Phaedo , the Theaetetus makes no mention of the theory of forms and offers no solution. Theaetetus himself is left in a state of perplexity by the puzzles, and Socrates remarks, “This feeling—wonder—very much pertains to philosophy. For there is no other beginning of philosophy than this, and it seems that the one who said that Iris is the child of Wonder did not genealogize badly” (155d). This metaphor of “parent and child” pervades the Theaetetus . It was implicit at the beginning of this passage as well. If Socrates only wanted to illustrate the simple “paradox” that six dice could be both more (than a smaller quantity) and less (than a greater one) without changing, why did he needlessly complicate the example by making the larger and smaller quantities, not five and seven as we would expect, but four and twelve—the extremes of which six is the harmonic mean? He even goes to the trouble of pointing out, for no apparent reason, that six is not only more than four and less than twelve, but more than four by a half and less than twelve by a half (154c). The only purpose this would seem to serve is to make us think of six as a kind of product or “offspring” of four and twelve, as the mean that unifies them.[12] The parent-child relation is in fact the dominant leitmotiv of the dialogue. The Theaetetus contains at least six explicit references to parentage, and at least seven references to the relation for which parental procreation is a metaphor, that is, the explanation of something as a product of the intercourse of two prior elements.

The explicit references begin (1) when Socrates, after being told about Theaetetus by Theodorus, immediately asks who Theaetetus’s father is (144c). (2) Later he speaks of his own mother, Phaenarete (149a)—the only time in any dialogue that he does so.[13] (3) He then goes on to compare the formulating of opinions to giving birth (151, 157c-d), and (4) subsequently refers to the deceased Protagoras’s theory as an orphan (164e). In between were (5) the reference to Wonder as ― 77 ―
the father of philosophy (155d), and (6) the forthcoming discussion of perception as the “twin offspring” of objective and subjective becoming (136a-157c).

The same phenomenon—the explanation of an existent as the product of two progenitors—is operative without the parentage metaphor in (1) Socrates’

definition of day as the mixture of earth and water (147c), which is to serve as a model for Theaetetus in his search for a definition of knowledge. (2) In response to Socrates’ example of clay, Theaetetus recounts his and his young friend Socrates’ idea of classifying all numbers into those that are the product of two equal roots (squares) and those that are the product of two unequal roots (oblongs). (3) Socrates himself is presented as a mixture of Theaetetus’s looks (143e) and young Socrates’ name (147d; cf. Statesman 257d). (4) In the present passage we have seen that relations like bigger and smaller can be explained only as the product of two referents, not as the property of one. (5)The analysis of syllables at 203 shows that they are normally the product of mixing vowels and consonants. (6) At 209d Socrates refers to the skytalê “a staff about which a strip of leather was rolled, on which dispatches were so written that when unrolled they were illegible until rolled again upon another staff of the same size and shape” (Fowler). It too is therefore a model of intelligibility based on the intercourse between two elements.

(7) The dialogue as a whole, that is, the account of the conversation between Socrates and Theaetetus, is a product of the joint efforts of Eucleides and Socrates (143a).

The significance of all this emphasis on parentage will be considered later on. At this point, after the implicit demonstration that relations must be a product of (at least) two terms, and the reference to Wonder and Iris as father and child, we are given a biparental model of sense perception. If none of the uninitiated is listening—by whom Socrates means coarse materialists who deny the existence of anything nonperceptible, including change—Socrates will introduce Theaetetus to the mysteries of much cleverer people. These are evidently the Heracleiteans. No criticism is offered of this doctrine, and the presumption seems to be that it is a view that Plato accepts,[14] but Socrates is noncommittal when Theaetetus tries to find out whether he subscribes to this theory (157c).

― 78 ―

Within Heracleitean flux changing things may be described as gradual processes or “slow motions,” some of which are capable of acting upon or being acted upon by others, in such a way that perception results (156a).

Perception is accordingly like the offspring of two parents. The progeny is always twins. When the slow motion that is a gradually changing object comes within range of the slow motion that is a gradually changing eye, they produce the twins, perception and the perceived thing—for example, the perception of whiteness and the representation of a white object (156d). These progeny of the slow motions—that is, of the gradual motions of changing things—are quicker because they move from place to place: from their mutual birthplace between the eye and the object, the perception moves to the eye, and the perceived object moves to its perceived location. Accordingly, “nothing is one , itself by itself, but it always comes to be for someone” (157a). Any perceived thing is only phenomenal, in something like Kant’s sense: it is the product of the intercourse between a thing in itself and our organs of perception. The physical world is therefore only a construction; the world in itself is pure flux or motion. The world of discrete and self-identical things is “objective”

only in the sense that the phenomenal world is so for Kant: it is the world that is “given” in normal experience. The doctrine applies not only to individual things but also to “universals.” “It is necessary to speak in this way both with regard to individuals and about multitudes collected together [

[Full Size]

[Full Size]

]. It is to such collections that they apply the terms ‘human’ and ‘stone,’ and every animal and form” (157b-c). A little later Socrates includes “good” and “beautiful” (157d).

One of the reasons that Plato is usually held to subscribe to the flux theory of perception is that it fits in with his view of the physical world as “becoming” rather than “being.” But all the evidence of the previous dialogues indicates that this further extension of the theory, by which “multitudes collected together,” or universals, are relativized in the same way as sensibles, is one to which he does not subscribe. On the Heracleitean hypothesis, however—which is being explored here—the natural interpretation of universals is that they are artificial constructs abstracted (not “recollected”) from particular experiences.

It might seem, Socrates points out, that we can dispute this doctrine by pointing to the fact that in dreams, madness, and other illnesses, perceptions of reality contradict those of normal, waking perceivers, and are objectively false (157e-158a). If we recognize that some opinions are false, then we must be able to recognize a standard of correct-

― 79 ―
ness, in which case, pace Protagoras, not everyone is the measure of truth. This objection proves to be without substance, for according to the theory our judgments do not have the same referents as those of anyone else—sick people and dreamers included—and therefore do not contradict one another and cannot be considered false. If wine that everyone judges to be sweet is judged by me to be bitter because I am sick, there is no contradiction. When I say “this wine” I am referring not to the “wine in itself” but to one of the twin offsprings of both the wine and my organs of perception. This offspring is numerically different from the offspring that anyone else intends by the phrase “this wine,” and that is the partial offspring of their organs of perception. The doctrine is thus compatible with the principle of noncontradiction[15] and not falsifiable on any obvious grounds. Accordingly, Socrates proceeds to explore more subtle problems to which the hypothesis leads.

3. Perception and Understanding (160e-168c) Socrates’ immediate concern will not be the theoretical model of perception underlying Theaetetus’s definition of knowledge as equivalent to perception, but the consequences of that equivalence. If the hypothetical equivalence is discredited through its consequences, then the model from which it follows cannot be accepted in its entirety either.

Socrates interprets the equivalence of knowledge and perception as a denial of the possibility that knowledge can be falsified. When Protagoras says that a person is the measure of all things, this means that there is nothing outside our individual perceptions by which they might be rendered false. Socrates launches an initial attack of this conception in four stages.

1 (161b-163a). Protagoras might as well have said that the measure of all things is not a person but a pig or baboon. Then he could laugh at us for thinking him as wise as a god when in fact he is no wiser than a tadpole.

In that case it would make no sense for anyone to pay to be his student, or to practice Socratic midwifery or dialectic, since truth is already to be found in mere perception (161c-e).

Neither Theodorus nor Theaetetus can find anything wrong with this ― 80 ―
refutation, but Socrates points out that it is an example of demagoguery (162d), and that Protagoras would accuse them of accepting appeals to mere likelihood (162e). We are not to be deterred by the seeming absurdity of saying that a pig or baboon is the measure of all things. On the basis of the foregoing theory of perception, which asserted that the object of perception is always relative to the perceiver, it is plausible and even necessary to conclude that pigs and baboons are the measures of all things (i.e., all that they perceive).

But a residue of Socrates’ objection survives this reply. His second point still stands. On Protagoras’s account it makes no sense to consider one person to be wiser than another or for one person to presume to teach or criticize another. In fact, however, Protagoras charged for teaching, and Socrates’ midwifery and dialectics were considered valuable by his students. Protagoras’s claims are not invalidated by this point only because he is really talking about a different level of knowledge. The objection speaks of interpretive knowledge—understanding— rather than perceptual information. But although this implicit distinction does not refute Protagoras at present, it will eventually become a wedge with which to dislodge Protagorean relativism. Accordingly, while the argument seems at first inconsequential, on closer inspection it implies a distinction between two levels of knowledge, a distinction that will turn out to be important. The implications of the next three objections will progressively specify what is involved in the implicit distinction between perception and understanding, and they will do so in terms of concepts that seem to recall the doctrine of recollection: recognition, memory, and intelligibility.

2 (163a-c) . What about hearing a foreign language, Socrates asks, or even seeing written words in our own language when we cannot read? How can it be maintained that perception is knowledge when we perceive these sounds and symbols but do not understand them? Theaetetus replies: We shall say that we know about them just what we see and hear. In the one case we both see and know the shape and color, and in the other case we hear and at the same time know the higher and lower sounds. However, those things that the grammarian and the interpreter teach about them, we neither perceive by sight or hearing, nor know.

(163b-c)

Socrates praises this answer but adds, “I had better not disagree with you about this, so that you will grow.”

― 81 ―

Coming after the last objection, the basis on which Socrates might have disagreed is not hard to discern. Once again the two levels of knowledge are visible, sensory information and understanding, but here the latter is made evident rather than merely implicit. At the first level— sounds and shapes—everyone’s knowledge is coextensive with the information supplied by their senses, and none is any better than any other. But at the second level it is undeniable that some people (especially grammarians) recognize the meaning of these phenomena better than other people, and this second kind of knowledge is not coextensive with sense perception. Once again a portion of Socrates’ objection remains untouched by the reply. There is an interpretive, recognitive, as well as a sensory kind of knowledge, and the former is not reducible to the latter.

3 (163c-165b) . On the hypothesis that knowledge is perception, if we see something we must know it. But if we dose our eyes, then, even if we still remember the object, we must be said no longer to know it. This would be a “monstrous” conclusion (163c-164b).

No reply is made to this objection, but Socrates remarks that their conclusion was derived from a contentious rather than philosophical style of argument (164c) and that if Protagoras were here he would have much to say in reply (164e). The fallacy of the argument may be expressed as a collapsing of the distinction between memory of knowledge and memory as knowledge. I can look at a book and say that I perceive and therefore know that a book is on my desk. I can then dose my eyes and say that I remember perceiving and knowing that a book was on my desk. But it does not follow that I still know that there is a book on my desk. There is no contradiction or monstrous conclusion. Nevertheless memory is a kind of knowledge, although of a different order than perception. And as Aristotle mentions at the beginning of the Metaphysics (A.1.980b 29-981a 1), a plurality of memories constitutes experience, which is an important kind of knowing different from sense perception. Memory is in fact a necessary condition for interpretive knowledge, and thus a precondition for the distinction implied by the previous examples.

4 (165b-e) . The final objection in this series, introduced indeed as “the most formidable,” is that if we look at something with one eye dosed, then we both see and do not see, and accordingly both know and do not know the object. This is said to reduce Theaetetus’s hypothe-

― 82 ―
sis, that perceiving is knowing, to absurdity (165d). Theaetetus is dearly not persuaded by the argument, but lacks the weapons with which to fight it. With some encouragement he might have hit upon the distinctions made in the definition of contradiction in the Republic ,[16] which stipulates that a genuine contradiction must refer to the same time, the same part of the subject, and the same object (in fact, the converse of that definition appeared above at 158e: see n. 15). In the present case we are speaking of different parts (eyes) of the subject, and so there is no contradiction.

Socrates, however, does not give Theaetetus encouragement, but the reverse.

What is the point of this “most formidable” but most transparently fallacious argument? Might the two different eyes, one open and one dosed, be meant metaphorically? The previous three objections have reminded us of the difference between perceptual and interpretive knowledge, and the difference between perception and the precondition for interpretive knowledge, memory. In other dialogues, especially the Meno —the dialogue most often alluded to in the Theaetetus —memory was used as a metaphor for a latent component of knowledge, furnished not by the senses but by the mind itself, the analogue of Aristotle’s “active intellect.” Activated by perception, this latency may be “recollected,” making possible judgments of attribution (“this is beautiful”) and understanding (“justice is the harmony of the tripartite soul”). In the dialogues after the Meno , recollection is pictured as an intellectual “seeing” of the forms.[17] And shortly hereafter in the Theaetetus we will be told that there are two kinds of seeing and two kinds of failure to see.[18] The philosopher sees what lies “above” although he may be blind to what lies at his feet or in front of his eyes (174a-c), while others see what is at their feet and before their eyes but cannot see the whole nor what is “above” them (174e-175d, 176e). The “higher” realm of the philosopher is that of divinity and goodness, while the other is that of the mortal and evil (176a).

Are these two kinds of seeing prefigured in the argument about the open and closed eye, an argument that is announced as “the most formidable” but that is a joke if taken literally? Socrates goes on to say that similar problems would arise if someone were to ask whether we can know the same thing sharply and dimly, close by but not at a dis-

― 83 ―
tance, intensely and quietly (165d). According to the doctrine of recollection, one might say that sensibles are perceived sharply, dose by, and intensely, while intelligibles are perceived dimly, at a distance, and quietly. Perhaps there is some prefiguration of this fundamental distinction in the opening words of the dialogue: “Just now, Terpsion, or long ago … ?” In a dialogue devoted to discovering the sources of knowledge, it would not be beyond Plato’s dramaturgy to give these words a double meaning. On the literal level they ask when Terpsion arrived from the country, but they are also appropriate to the fundamental epistemological alternatives of empiricism and rationalism: on the empirical model knowledge begins just now when we perceive something; on the rational model what we perceive now calls into play something acquired long ago. We need not try to decide whether Plato intended these connections or not. The only important question will be whether the doctrine of the direct apprehension of forms may in fact be brought usefully to bear on the problems of the Theaetetus . That question, which is much debated in the literature, will be answered affirmatively in the course of this study, and it may be that the present passage is meant to anticipate that answer.

The distinction between perception and understanding becomes all but explicit in what follows. Socrates, speaking in the persona of Protagoras, defends Protagoras’s theory against the preceding refutations by means of a distinction between knowledge and wisdom (a distinction that Theaetetus had collapsed at the beginning of the dialogue). He reaffirms that each of us is the measure of all things because “what is” cannot mean anything other than what appears to a perceiver. But although in this sense everyone is equally knowledgeable, wisdom may be distinguished from such knowledge as the ability, “when bad things appear and are for someone, to implement a change and make good things appear and be to him” (166d).

Thus, understanding (wisdom) exists in addition to perceptual knowledge, but it is of a pragmatic rather than factual nature. It does not tell us what exists but only what is desirable and how to achieve it. It is in this sense that doctors, educators, and sophists are wiser than ordinary people. They replace the worse with the better, but not the false with the true. There is no such thing as falsity, “because it is impossible to think [

[Full Size]

] what is not” (167a).

“Protagoras” doses with a Socratic appeal for fairness and seriousness in argument so that “your partners will blame themselves for their confusion and aporia, rather than you, and they will follow and love ― 84 ―
you, and hate and flee from themselves to philosophy in order that, by becoming different, they may be liberated from their former selves”

(168a). The sentiment is obviously Socratic rather than Protagorean, and points up the difference between them, which will soon be elaborated in Socrates’ digression. For Protagoras wisdom means the ability to eliminate unpleasant perceptions in favor of pleasant ones; for Socrates it means overcoming one kind of life in favor of another.[19]

4. Understanding and Value: Beginning (168c-172b) The first set of four objections was aimed at the Protagorean definition of knowledge as perception. Insofar as the arguments succeeded in forcing a distinction between perceptual and interpretive knowledge (understanding), that definition has been seriously compromised. The next set, also of four objections, will focus on interpretive knowledge alone.

Here Socrates finally succeeds in pressuring Theodorus to replace Theaetetus as his partner.

1 (170a-171d) . The first refutation of this series is the famous palintrope or self-refutation argument: “Shall we say that people always believe[20] truly, or sometimes truly and sometimes falsely? In both cases it follows that they don’t always believe what is true but both [what is true and what is false]” (170c). The conclusion obviously follows from the second alternative, of which it is a restatement. The subsequent argument is designed to show that the conclusion must follow from the first alternative as well.

The argument may initially be simplified as follows. The minor premise is that people generally disagree with Protagoras’s claim that each person is the only judge of what is true for him. They think that different people have different degrees of wisdom about different things, and that wisdom is true thought and that ignorance is false opinion (170c; cf. 170a-b).

The major premise is that Protagoras claims that what people believe is true (171c). The conclusion follows, that Protagoras must concede the general opinion to be true, that not everything we ― 85 ―
believe is true. Since this contradicts his own position the latter must be false.

The actual course of the argument is more complicated because of Protagoras’s insistence that truth is always relative to some believer. An opinion is not true simply, but true for someone. Accordingly, the way the argument puts it is that Protagoras’s theory may be true for him but false for tens of thousands of others (170e). Moreover, if the theory were right, then if no one believed it, it would ex hypothesi be false for everyone and therefore false. And if no one believed it but Protagoras, then:

First, by as much as those who believe it outnumber those who do not, it is that much more not true than true…. Second comes a most elegant point: he accepts that the tenet of those who believe in opposition to him about his own tenet—in that they believe it is false—must somehow be true, since he agrees that what anyone believes really is.

(171a)

The validity of this argument has been much debated.[21] It is sometimes felt that the reasoning depends on an illicit transition from “true for someone” to “true” simply: Protagoras would accept that his theory is not true for most people, but it would still be true for him and no contradiction would arise. Such a defense, although technically valid, would be disingenuous. Protagoras wants to persuade us that his theory is true for everyone, otherwise his arguing for it, publishing it, and teaching it would be inexplicable. It would be damaging for Protagoras to be forced to admit that his theory is true only for himself (and perhaps a few others), but false for everyone else. Moreover, having admitted that, it would be difficult for him to deny that the theory is false in general .[22]

What this argument demands of Protagoras is that he acknowledge that at the level of interpretation or understanding not all judgments are equally valid. He was willing to acknowledge that at this level we can distinguish opinions that are pragmatically superior from those that are pragmatically inferior, but not opinions that are true from those that ― 86 ―
are false. The present argument makes the point that, on the contrary, Protagoras does regard his interpretations as truer than those of nonrelativists, and that unless he acknowledges that his perceptual relativism ceases to be relativistic at the level of interpretation or theory, he cannot help but undermine his entire position. He must concede that no one “is the measure of any single thing that he does not understand [

[Full Size]

]” (171c). Perception may be relativized, but understanding may not.

2 (171d-172b) . The next refutation is interrupted by Socrates’

digression. Socrates begins the argument by recapitulating the claim made earlier in Protagoras’s defense: although sensible qualities are just as they appear to each of us, one person may be wiser (i.e., “more effective”) than another in pragmatic pursuits such as medicine (171e).

The same dichotomy now appears in the larger context of the state.

According to the theory, values are relative to the state, as sensa are to the individual:

In political affairs, with regard to what is noble and shameful, just and unjust, pious and not: however each state legislates these in accordance with its opinions, that is how they in truth are for it. And in these matters no one is wiser—neither one individual than another, nor one state than another…. None of these has by nature an essence [ ] of its own, but rather the common opinion becomes true when it is believed, and for as long a time as it is believed.

(172a, b)

But here, too, Socrates replies, when it comes to what is advantageous or disadvantageous to the state, Protagoras would not deny that one adviser differs from another, and one state from another, with respect to truth.

He would not dare to say that whatever a state believes to be in its advantage necessarily is so (172a-b). The escape from relativism, made possible by the distinguishing of understanding from perception, extends to value as well. Not everyone understands equally well what is good, and if in many cases there is no way of adjudicating disputes about what is beneficial, there are at least some occasions, especially in politics, when someone may proven right or wrong.

5. Socrates’ Digression (172c-177b)

It is significant that the digression begins just at the point where values are ascribed to convention rather than nature, for one of the functions of the digression is to repudiate the claim that justice and piety are arbitrary values without essence in nature. Rather, they are precisely the

― 87 ―
natural essences that the philosopher strives to know (175c, 176b). It is acquisition of this type of knowledge that requires the courage spoken of in the dialogue’s opening passages. Knowledge of this kind would be different both from the perceptual and interpretive knowledge of the corporeal world that were distinguished above. The latter two correspond to the lowest levels of the Divided Line, eikasia and pistis. Eikasia , as portrayed in the Cave, is the uncritical awareness and memory of passing perceptions, and pistis , which is by contrast the highest awareness of the corporeal world, is therefore our interpretation of the former experiences.[23] The kind of knowledge referred to in the digression, on the other hand, would correspond to the Republic’s category of noêsis .

The remaining kind of knowledge (according to the Divided Line), dianoia —the drawing-out of the implications of our initial postulates— has been illustrated throughout the dialogue by the deductive aspect of the method of hypothesis, and will be illustrated more generally in the “aviary”

modal of knowledge.

The digression is reminiscent of the middle books of the Republic (especially the Divided Line and the Allegory of the Cave) because of its placement as well as because of its content: like the central books of the Republic , it occurs in the very center of the dialogue and breaks into the beginning of the discussion of a political question, which is subsequently resumed as if the digression had never taken place.[24] The substance of the digression, again like the middle books of the Republic , deals with the difference between a life devoted to corporeal, mortal values, and one devoted to intelligible, divine values. It is a sustained comparison of the life of the philosopher with the life of those who devote themselves to law and politics. Where the denizens of the Cave were described in the Republic as prisoners, here politicians and orators are described as slaves, inasmuch as their success depends on their adherence to arbitrary rules and on the approval of their audience (172d-172e). As in the Republic , the philosopher who enters their world will appear to be ignorant and unable to see what is in front of him (174b), but “when he drags the other upward … then the situation is reversed” (175c, d) and the political person will then betray his own inability to see (174e-175a, 176e). There are also important differences between this account and that of the Republic , especially that the pres-

― 88 ―
ent account focuses on political life in particular, rather than on the ordinary generality of people depicted in the Cave. In that respect the digression is a contrast between knowledge pursued for its own sake and knowledge pursued for the sake of social rewards and honors (a theme that was present in the Cave but in a subordinate way: 516c-d), that is, a contrast between reason as an end in itself and reason as a servant of spiritedness.[25] But here, as in the Republic , the fundamental contrast is between the corporeal world and the intelligible world. For the philosopher, “in reality only his body occupies and dwells in the city, while his mind, considering all such things as of little or no importance, is contemptuous of them” (173e).

The contrast is drawn to such an extreme degree that even Socrates may not qualify as a philosopher, for the pure type represented here has no knowledge of where the marketplace is, or the law courts, nor does he know anything about parties with flute girls. In fact—in further contrast to Socrates—he is so oblivious to these things, and to himself (174b), that “all these things he doesn’t even know that he doesn’t know” (173e).

Ordinary people think they know things when they do not; Socrates has risen so far above their vanity that he knows that he is ignorant; but the true philosopher has risen so far above even this self-consciousness that he no longer knows even that he is ignorant. Socrates does not fit the description of the philosopher here, for it is a conception, like that in the Phaedo , or in the Republic’s Islands of the Blessed (519c), of the most extreme transcendence of the corporeal realm imaginable, in favor of the intelligible. The transcendence is not for the sake of abstract intellectual knowledge, but for the sake of goodness. As in the Phaedo , the corporeal world of mortals is the abode of evil, while among the gods exists goodness alone (176a). The goal of life, therefore, is to become as godlike as possible, which means “to become just and pious together with wisdom” (176b). For,

Two patterns, my friend, are set up in reality, one divine and most blessed, the other godless and most miserable. Unjust people do not see that this holds true, and because of their foolishness and complete lack of understanding they are unaware that they become more like one of them, due to their unjust behavior, and less like the other. For this they pay the penalty of living the life that is an image of what they resemble.

(176e-177a)

― 89 ―

In view of Plato’s continuing interest in politics and social justice, however, we may assume that the reason why Socrates’ own character fails to conform to the conception of the philosopher here is not because he has not yet reached that stage, but rather because, like the philosopher who returns to the Cave from the Islands of the Blessed, his experience of transcendence enables him to return to the corporeal world, in a transformed way.

6. Understanding and Value: Conclusion (177c-187a) 2 (continued, 177c-179d) . After the digression Socrates reiterates the beginning of the previous argument: people like Protagoras may claim that justice is only a matter of what is legislated by the state, but no one would say that whatever a state thinks is good or “advantageous to itself really is so” (177d). Whether it is so or not can be determined only in the future, and Protagoras can hardly maintain that each of us is the measure of what is going to happen. Rather, the ability to make predictions is what sets experts apart from ordinary people in such matters as medicine, food, and music, and what sets Protagoras apart in matters of law (178a-e). It follows that some of us are wiser than others, and that it is they who are the measure, not ordinary people (179b).[26]

“Protagoras” had already agreed that some people are wiser than others in that they are able to replace worse sensations with better ones, but he denied that this had anything to do with truth or falsity (166d). Socrates here counters that denial by pointing out that the ability to make such replacements successfully is the ability to predict what will happen, and predictions are indeed qualifiable as true or false. At this point Socrates makes fully explicit the difference between the (infallible) perceptual and (fallible) interpretive levels of knowledge that has been implicit throughout the earlier discussions: There are also many other ways to establish that not every opinion of everyone is true. However, with regard to the passing impressions from which our sense perceptions and the corresponding opinions come to be, it is harder to

― 90 ―
confirm that they are not true…. It may be that they are unassailable, and that those who say they are fully dear and instances of knowledge are perhaps saying what is really so.

(179c)

I have been referring to understanding as “interpretive knowledge,” but it is not dear what makes such interpretation and understanding possible.

According to the flux theory, even such concepts as human, stone, and “every animal and form,” including the good and the beautiful, arise in the same way as perceptions (157b-d). In that case the concepts, by which we understand our perceptions, must be said to arise out of those perceptions themselves. Those who have superior understanding of goodness can be said only to have extracted or generalized instances of them more effectively.

There are two problems with this account. First, if nonrelativistic knowledge is impossible at the perceptual level, how can relativity be overcome at the level of understanding merely by abstraction? Second, there would be a circularity not unlike that of Meno’s paradox (which is often recalled in this dialogue): in order to extract concepts from the flux of experience we must be in possession of the interpretive principles that already presuppose those concepts. The Platonic answer to both these problems has been that interpretive knowledge has its source not only in the senses’ relation to the corporeal world, but also in reason’s relation to the intelligible world. In the remaining two arguments of this section Socrates will reaffirm this answer both negatively and positively: negatively, by showing that if we try to account for knowledge only in terms of the flux model, we will be reduced to silence (like Cratylus); positively, by showing that at least some of the concepts by which we interpret experience have their source in something other than sensory experience.

3 (180c-184a) . If everything is in flux, then all that exists is the transitory impressions of the perceiver (152d)—this was the point of the theory of perception developed earlier (156a-157c) and repeated here (182a-b). There can be no other knowledge than this. The flux theory is that everything is in motion, not only in the sense of movement in space, but also in the sense of alteration (181c-e). It follows that the sensuous qualities that we perceive are changing at the very moment we perceive them, and the act of perception itself is always changing into nonperception. Moreover, since perception is knowledge, knowledge too ultimately collapses into an identity with nonknowledge: each is ― 91 ―
continuously changing into the other (182c-e). Consequently, “if everything is in motion, every answer about anything one is asked will be equally right,” and language itself will break down (183a-b).

Parmenides had told Socrates that
if anyone does not admit the existence of forms of things, or mark off a form under which each individual thing is classed, he will not have anything on which to fix his thoughts, as long as he does not admit that the Idea of each thing is always the same, and in this way he will utterly destroy the power of discourse.

(Parmenides 135b-c)

Is the present argument meant to remind us of this warning, and thereby of the theory of forms? (Socrates’ remark that “I met him when I was quite young and he quite old” [183e] seems clearly meant to remind us of that dialogue.) If so, it would explain the puzzling fact that Parmenides is mentioned immediately before and after the present passage but to no obvious purpose. Beforehand Socrates says that he “nearly forgot that others declare the opposite” of the flux theory. These others are Melissus and Parmenides, whose views Socrates proposes to examine after they examine the proponents of flux (180d-181a). Afterwards, Theaetetus reminds Socrates of this next task, but Socrates declines to pursue it, on the grounds that they could not do justice to Parmenides’ views except at great length (183c-184a).

4 (184b-187a) . If this was an indirect reminder of the theory of forms, the next section is a direct reminder of it. Socrates raises the question whether there is some one form within us (which we might call the soul) with which we perceive together whatever each of the senses perceives only separately—something that perceives sounds and sights, and the like, each of which alone is proper to a specific sense (l84d-e). The test is whether there is anything we can think about that involves more than one sense. If there is, this common factor cannot be reduced to what the individual senses give us and must somehow be provided by or through the mind or soul itself.

In fact there are several such common qualities. We can think that the objects of seeing and hearing both are , and that each is different from the other and the same as itself (185a). Socrates thus generates three of the five “greatest kinds” of the Sophist , existence, sameness, and difference (the other two, motion and rest, are already evident in the Heracleitean model and its rejection by the Eleatics). Socrates further establishes that the mind will discern that each of these objects is ― 92 ―
one , and both together are two , and that it can also ask whether they are similar or dissimilar (185b). To these qualities Theaetetus adds odd and even (185d), two of the traditional Platonic forms. And Socrates, remarking that Theaetetus has shown himself to be not ugly, as Theodorus had claimed, but beautiful and good, proceeds to add to the list the forms beautiful and ugly , and good and bad (186a), which had earlier been assimilated to the flux model of perception (157d). What all these qualities have in common is that the soul somehow perceives them through itself rather than through the body’s sensory faculties (185e).

Now, conceptions about being (

[Full Size]

) and value (

[Full Size]

) can be attained, if at all, only through a long and difficult education, and truth and knowledge are inaccessible unless we can discern being.

Accordingly, knowledge can be found only through the qualities that the soul finds by itself, rather than those that it received from the bodily senses. Knowledge cannot therefore be the same as sense perception (186c-e).

This argument is put to the epistemological purpose of refuting Theaetetus’s claim that knowledge is perception. But it also has consequences for the ontological foundation on which, according to Socrates, Theaetetus’s position rests—that all is flux. Clearly, the intended inference is that all these forms, which are not themselves in flux, are real and imply some kind of stability within Heracleitean flux.

Are these qualities in fact the Platonic forms?[27] Like the forms of the Republic they are apprehended only as the result of a long and difficult education,[28] but whether they may be regarded as “separate” forms or not cannot be answered on the strength of this passage. At the very least they correspond to the forms’ aspect as “universals,” although even this is not entirely explicit. Unlike the characterization of forms in Republic 10, they are not said to be posited for “each multiplicity to which we give the same name” (596a). Instead, we have a plurality of senses (sight, hearing, etc.) to which we can apply the same intepretive categories. But it comes to the same thing. To say that we both see and hear ― 93 ―
something beautiful is to say that “beautiful” is not a unique name, but rather one that can be applied to a plurality of sensory experiences; that is, it is a universal. The present passage affirms the need for universals, and further affirms that these universals are not reducible to sensory information, “but rather the soul, itself by itself, discerns what is common to all” (185d-e).

Let us consider what is implied ontologically by each example, and to what extent each may indeed be considered necessarily given in our experience.

“Being” is the first example because it has the greatest generality, but for that same reason it indicates nothing more than the bare need for such concepts.[29] The example of “different” and “same” does, however, imply a differentiation within reality, and is moreover a contrast that is almost universally employed: even for modern neo-Heracleiteans like Nietzsche and Derrida there are identifiable selves as well as differentiation (however uncompletable). Cratylus might perhaps reject such a concept, in view of his insistence that we cannot step into the same river even once. Yet insofar as he continued to point his finger he continued to differentiate, and to imply the relative integrity of what he indicated.

The examples of “one” and “two” suggest that we are intrinsically capable of distinguishing unity from multiplicity, and thus that we are by nature capable of discriminating between part and whole. This follows from the previous dichotomy, for, as Socrates shows, if we can distinguish one thing from another, we can distinguish between the unity of the pair and the particularity of its members. If Cratylus, pointing, distinguishes one thing from another, he distinguishes them also as parts within a complex.

The next pair, the similar and dissimilar, has more radical implications.

If we discern similarity and dissimilarity, then we discern common features; and if there are common features, then something like the existence of forms is indicated. It is not necessary to assign an ontological status to these forms, as Plato or Aristotle did—they may so far be interpreted merely epistemologically, as in Descartes and Kant, or linguistically as in contemporary thought—but there is no reason in the present passage to suppose that Plato’s Views are any different here from those expressed in the Phaedo and Republic . In any case, we may at least grant to Plato that with our mind’s eye we see resemblances, ― 94 ―
common properties, universals, in the world. There is then at least a prima facie case for an underlying ontological structure.

With the concepts of odd and even, Theaetetus explicitly introduces mathematics, which was only implicit in the earlier example of one and two. One of Plato’s favorite arguments for the ontological significance of a priori forms of knowledge is the efficacy of mathematics. If the principles of mathematics are known to us by nature, as the Meno argues, and if they also turn out to be the principles by which external nature operates, as astronomy and Pythagorean science suggest, then we are by nature attuned to understanding the structure of reality. This would suggest not only that reality is comprehensible for practical purposes, but also that it is inherently rational, and even that it has value, since the rational is the good.

The rational, value-laden aspect of the forms is made explicit by the last two examples, the beautiful and the good, and with them the entire theory of forms is present by implication. This is clearly the direction to which Plato points us in the attempt to answer the extreme Heracleiteans.

7. The Parentage of Knowledge

If the Theaetetus is hinting that the Heracleitean problematic can be answered by means of the theory of forms, such an answer seems open to the following objection. In sense perception, according to the preceding model, the thing qua perceived is not the same as the thing in itself (the affective slow motion). The offspring is not the same as the parent. If the same model is to be used now for knowledge, it would follow that the act of knowing also requires two parents—the perceived object and our interpretive concepts—and that it too produces twins, knowledge and the thing qua known. The latter is not identical either with the thing qua perceived or with the thing as it is in itself. Knowledge would then be possible only in an equivocal sense. There are three levels: (1) the thing in itself, that is, the objective slow motion; (2) the perception of that thing, which is not identical with it, but is one of its twin offspring; and now (3) knowledge of that offspring, which is a new twin offspring.

The thing qua known, therefore, is the grandchild of the thing in itself; and knowledge, rather than bringing us closer to reality than perception did, takes us a step farther away. In this respect Kant and Heracleitus are ultimately allies. But Plato would not disagree either. In fact such considerations form the basis of his claim that knowledge of ― 95 ―
the empirical world is not possible. However, the forms, which are the objects Of true knowledge for Plato, cannot be radically discontinuous from the physical world, or else the doctrine of recollection would make no sense. How then would Plato be able to find formal structure in a destructured reality of pure flux—assuming that he accepts that view of the physical world?

His argument that flux cannot be the whole story is the counterpart of the Parmenides ‘ claim, quoted above, that unless there are forms all discourse becomes impossible. Here the argument is that if there is only flux, then the referents of words are constantly changing, and words will have no stable meanings and will be ultimately self-contradictory and incoherent (181b-183b). Even if Protagoras were to reply that words need only refer to perceptual, not noumenal, reality, Socrates would press the point that, in a world of pure flux, words cannot refer to anything individuated, whether objective or subjective. Socrates’ previous remark to Theodorus (who is the respondent here) that “they are no friends of yours” (180b) suggests that mathematics too gives us reason to reject the extreme form of Heracleiteanism.

Since the subjective, relativistic aspect of the perceptual object must be passed along to its offspring, the object of empirical knowledge, such knowledge does not reach as far as physical reality itself, which is pure becoming. That is why Socrates had said that we must search for knowledge “in whatever name the soul has when, itself by itself, it is occupied with what is” (157a). In other words, if it is impossible to have knowledge of the offspring (the empirical world), or of one of its parents (the perceived quality), it is nevertheless possible in the case of the other parent, the forms. The forms must be known, no longer in their children but in themselves. Like light (one of Plato’s favorite metaphors), their presence is detected initially by their illumination of empirical objects, but they can be known in themselves only if we abstract from the objects illuminated.

The importance of this way of looking at the problems of knowledge and perception explains Plato’s persistent use of the parent-child theme as a dramatic leitmotiv in the early part of the dialogue—it appears in at least thirteen direct or indirect instances (see above, section 2). In one of those instances, Socrates turned out to be a mixture of Theaetetus’s looks and young Socrates’ name. Our looks or appearance reflect our changing nature, the slow motion of our flux. Our name, on the other hand, reflects our constant identity; and when we turn from individuals to common natures, the name reflects the eternal form. Theaetetus turns ― 96 ―
out to be the representative of appearance both in terms of what he shares with Socrates and in terms of the way he attempts to define knowledge.[30]

In fact his attempt to give an account of knowledge will fail because he sees knowledge only in terms of one of its parents, and is blind to the other.[31]

8. Five Models of Knowledge (187a-201c) The above discussions show, Socrates says, “that we should not seek [knowledge] in perception at all, but in whatever the name is, when the soul, itself by itself, is engaged with what is real” (187a). Theaetetus’s response to this is minimal: he revises his definition of knowledge to “true opinion” (

[Full Size]

). But Socrates, in return, wonders how an opinion could ever be otherwise (187b-d). In an attempt to answer this he develops five models of knowledge, which, like the earlier refutations, may be construed as progressively more adequate hypotheses.

1 (188a-c) . The first model is the simplest, deliberately abstracting from learning and forgetting, and concentrating only on knowing and not knowing. On this model false opinion can mean only that we think that (1) something we know is either (a) something else that we know or (b) something that we do not know; or else that (2) something we do not know is either (a) something else that we do not know or (b) something that we know. All these are interpreted as judgments of identity, as if we said, (1a) “Socrates, whom I know, is Theaetetus, whom I also know,” (1b) “Socrates, whom I know, is someone whom I do not know,” (2a) “Socrates, whom I don’t know, is Theaetetus, whom I also don’t know,” or (2b) “Socrates, whom I don’t know, is Theaetetus, whom I know.” Consequently they are dismissed as implausible accounts. Nevertheless, in cases of mistaken identity any one of these kinds of judgments might arise. In bad light or from a distance (1a) I

― 97 ―
might mistake Socrates for his younger look-alike, Theaetetus; or (1b) I might fail to recognize him and think he is someone I do not know; or, (2a) never having seen either Leukippus or Democritus, I might hear the former lecture and think he is the latter; or, (2b) if there were some resemblance between them, I might see Leukippus and think at first that it was Socrates. But this model abstracts from sense perception as well as from learning and forgetting. It is concerned only with the logical relationship between the concepts of something known and something not known. It is meant to be inadequate, as a way of forcing us into more sophisticated formulations. The paradox on which it is based is elegantly formulated by Burnyeat: “A necessary condition for mistaking X for Y is also a sufficient condition for not mistaking X for Y . The necessary condition is that one know X and Y . But this, it is claimed, is a sufficient condition for knowing that X is not Y .”[32]

2 (188c-189b) . The second model is ontological rather than epistemological. It substitutes “being” for “knowing,” so that to have a false opinion means to believe “what is not” about something (188d). Here the “is” of judging is interpreted as existential rather than identificatory, but the revision does not resolve the difficulty. Earlier Protagoras had insisted that there is no such thing as falsity “because it is impossible to think what is not” (167a). And here too Socrates concludes that “thinking what is not” means “thinking nothing,” which means “not thinking” (189a). Once again important distinctions have been suppressed, in particular the distinction between the two senses of “not being” that we will encounter in the Sophist : “nonexistence” and “difference.” Presumably this is done to enable us to perceive the inadequacy of the most simplistic models of explanation, and thus make us better able to appreciate the need for the progressively increasing complexity that will follow.

3 (189b-190e) . In the next model Socrates combines the first two. Now false opinion is “other-believing” (

[Full Size]

), which means that we “always have an opinion about something that is, but of one thing instead of another” (189b-c). The first clause of that description is existential (“opinion about something that is”) like the previous model, the second identificatory (“one thing instead of another”) like the first one. Theaetetus approves of this model, “for when someone thinks beautiful instead of ugly, or ugly instead of beautiful, then, most truly, his opinion is false” (159c). After rebuking him for the oxymoronic

― 98 ―
phrase “truly his opinion is false,”[33] Socrates demurs, saying that we would never say that “the beautiful is ugly” or “the unjust is just” or “the odd is even” (190b).

Socrates has perverted Theaetetus’s meaning. Clearly, Theaetetus was thinking of predication: my opinion is false if I believe that a beautiful thing is ugly (something unfamiliar may seem ugly to me at first, but beautiful on further acquaintance). But Socrates misrepresents the judgment as one of identity, as in the first modal. Plato gives with one hand and takes back with the other. He has Theaetetus remind us that the function of judgment may be predication (which would go a long way toward solving the present aporia), but he then has Socrates suppress the concept.[34] In fact this is the closest that the Theaetetus ever comes to exploring predication, even though it is dear from other dialogues (both those considered to be earlier and those considered to be later) that that is where the models for true and false opinion must be sought.

4 The Wax Block (191c-196d) . At this point learning and memory are added to the model (191c-d), after having been expressly excluded since the beginning. Learning is compared to the impression made by a shape in a block of wax, and memory is the retention of that shape. Socrates now goes through an odd, selectively exhaustive, list of types of judgment, in order to discover cases where false opinion is possible ― 99 ―

(192a-c).[35] It is not possible to make false judgments of the following kinds. (K = something Known, R = something Remembered, P = something Perceived, C = something whose imprint we place in Correspondence with what we are perceiving [

[Full Size]

[Full Size]

]. Letters within square brackets indicate terms that seem to be presupposed but are not mentioned. The subscripts indicate cases where the text explicitly speaks of mistaking one such thing [x] for a different one [y ] [although that condition is presumably implicit in the other cases as well]. Thus 1a translates as, “One thing that we know and remember but do not perceive is something else that we know and remember but do not perceive.”)

1.a. (KR~P)xis(KR~P),
b. Kis~K~R
c. KxisKy
d. ~KisK

2.a. PxisPy
b. Pis~P
c. PxisPy
d. ~PisP

3.a. (KPC)xis(KPC)y
b. (KPC)xisKy [~P]

c. (KPC)xisPy [~K]

4.a. (~K~P)xis(~K~P)y
b. (~K~P)xis~K, [P]

c. (~K~P)xis~Py [K]

5.“It remains in the following cases, if indeed anywhere, that [false
judgment] will come about” (192c-d): a. Kxis(KP)y
b. Kxis(~KP)y
c. (KP)xis(KP)y

6.“False judgment remains in the following case(s)”: a. (KP~C)xis(KP~C)y (193b-c, 194a) b. KPisK~P~C (193d)

According to 5, false judgment occurs when something we know (and possibly but not necessarily perceive) is mistaken for something ― 100 ―
else that we perceive (and possibly but not necessarily know). The mistake can happen only because we have failed to put the wax imprint of the thing we know (x ) together with the present perception (y ) well enough to see that they do not fit.[36] This becomes explicit in 6, where false judgment is said to occur when something we know and perceive (but whose imprint we may not place in correspondence with the perception) is mistaken for something else that we know (and possibly but not necessarily perceive) and whose imprint we do not place in correspondence with the perception.

In other words, in the case of at least one of the things that we are confusing with each other, we fail to compare adequately our knowledge (imprint) of a thing with our perception of it. The general conclusion that follows from all this (although it is not clear why Socrates chooses just the examples that he does) is that false judgment occurs because we sometimes fail to compare present perceptions with past imprints properly.

The wax model is thus successful in accounting for error in at least some cases of sense perception, but Socrates now proceeds to show that it fails when we attempt to apply it to intelligible rather than visible things; for in that case we can no longer speak of error as having to do with the fitting-together of knowledge with perception. For example, when we mentally add five and seven, and think the answer is eleven, we then think that eleven, which we know, is twelve, which we also know. But this would mean that we think that one thing that we know (but do not perceive) is another that we know (and do not perceive)—a scenario that has been declared impossible according to the previous survey of permutations (1a), so the model on which that survey was based must be discarded (196a-b).

Now that this hypothesis has been discredited, a fifth one is proposed, but before we turn to that I would like to raise a question about the elaborate classification that we have just reviewed: What happens to the category of memory (R)? Although memory is presented as the distinctive feature of the wax model (191d, 194d-e), it is mentioned in almost none of the cases specified.[37] It is present on both sides of 1a, then on only one side of 1b, and then not at all in the rest of the classification.

Moreover, when 1a, 1b, and 1c are restated between steps 5

― 101 ―
and 6, R is left out altogether even though P is now specified more explicitly (193a-b). It is left out again when Socrates reduces all the examples to a general statement: “I could never have false opinions about you and Theodorus either when I know both of you or when I know one but not the other; and the same applies to perceiving, if you follow me”

(193b). And it is left out of the two summaries as well: at 194a-b Socrates says that false opinion turned out to be impossible about things that we do not know and have never perceived, but possible about things that we both know and perceive; at 195c-d he summarizes their findings as, “false opinion exists neither in the relation of perceptions to one another nor in thoughts but in the fitting-together of perception with thought.” Thus, in case 6a we were told that the reason for the mismatch between the two objects is that the perception is indistinct (193b-c), but nothing was said about the obvious possibility that one’s memory of one of them might be indistinct, although the possibility is explicitly built into the model (194e).

The reason that memory disappears from consideration seems to be that it is conceived in a way that equates it with active knowledge. This can be seen from the fact that, in the three places where it does appear, its truth value is identical with that of knowledge. On this model, to know is to remember and to remember is to know. Memory remains implicitly present in terms of C (which was introduced after R was dropped), for the ability to match the imprint to the perception implies having a correct memory of our former perception, but to substitute C for R is to leave out what is distinctive about memory, that is, the fact that it may become partially but not wholly lost, that it may exist in a state of latency. That will be remedied by the “having/possessing” distinction made in the next model, the aviary. If all this is meant to make us aware of the inadequacy of the wax-block model of memory, the elaborateness of the device would seem to be an indication of the importance of memory to the dialogue’s concerns.

5 The Aviary (196d-200c) . The fact that memory can be latent rather than actualized is illustrated at the very beginning of the aviary model.

Socrates asks Theaetetus, “Have you heard what people now say that knowing is?” and Theaetetus replies, “Perhaps, but I do not remember at present”

(197a). Appropriately, Socrates goes on to distinguish “having” knowledge, which implies awareness, from “possessing” it, which does not. When we learn something, we possess it; but if like Theaetetus we cannot recall it, then we cannot be said to have it at ― 102 ―
that moment. It is as if our mind were an aviary containing “all kinds of birds, some in flocks apart from the others, others in small groups, and some alone flying randomly through them all” (197d).

It is far from dear what these last details refer to. Plato may have in mind the sort of progression that Aristotle writes of at the beginning of the Metaphysics : from individual perceptions (random individuals), to the experience that results from a multiplicity of similar perceptions (small groups), to the science that discerns the principle common to all such perceptions (distinct flocks). Alternatively, the picture may be a reference to the method of collection (which was alluded to at 147d). The single birds may be individual knowledges that have not yet been related to others, as when we do not yet see that our knowledge of Socrates and our knowledge of Theaetetus belong together within a knowledge of the species of human beings. The small groups may represent various knowledges of species that have not yet been discerned as embraced within a genus, as when we recognize the species of human beings but do not yet see its relationship to other animals. And the flocks may represent our knowledge of genera. On either explanation the aviary appears to illustrate the progression of knowledge from individual perceptions to universal kinds.[38]

The aviary is empty at our birth, and the knowledges that we acquire through learning are birds that we capture for the aviary. When we first catch one and imprison it, we may be said to “possess” it, but we do not actually “have” it until we catch hold of it again (197c-e), that is, make use of it. The modal has the advantage over the wax block that it can account for knowledge that is latent rather than actual. But it has the disadvantage that it is no longer possible to match knowledge against perception—the birds do not seem to refer to anything outside the aviary.

This does not seem at first to be a disadvantage, however, for Socrates’

examples are no longer concerned with perceptual knowledge but only with mathematics. It is as if we have now moved beyond pistis to dianoia on the Divided Line. But the model cannot be assimilated to the doctrine of recollection, because it posits a mind empty at birth and filled entirely by empirical means. In fact the suggestion that we learn mathematics by having it handed over from teacher to student (198a-b) flies in the face of the Meno .

― 103 ―

By distinguishing between possessing knowledge (latently) and having it (actively) the aviary model enables us to avoid the paradoxical conclusion that false opinion is simply not knowing what one knows (199c). We can now say that it may be not having what one possesses. But two other difficulties arise. If false opinion is the mistaking of one bird for another—grasping the knowledge of eleven, for example, when we ought to be grasping that of twelve—then we make a mistake precisely by grasping a knowledge , which is a very strange conclusion. Thus, first, for a person having knowledge of something, to be ignorant of this very thing, not through his ignorance but through his knowledge; second, to have the opinion that this is something else and something else is this; how can it not be very absurd for the soul, when knowledge has come to it, to know nothing and be ignorant of everything?

(199d)

Theaetetus suggests circumventing the problem by supposing that the aviary contains ignorances as well as knowledges (199e), but Socrates replies that in that case the problem that the aviary was meant to solve—“How can we mistake one thing for another?”—reappears within it. We must ask how we can mistake an ignorance for a knowledge, and any attempt to answer the question would involve either an aporia or an infinite regress (200a-c).

But in a sense Theaetetus is right, and we do have ignorance within the aviary: that was precisely the point of distinguishing between the (latent) possession and (active) having of knowledge. When we cannot grasp a knowledge that we possess, we are at that moment not in a state of knowing. Possessing, as distinguished from having, is a mixture of knowledge and ignorance. Let us consider the model more closely. Socrates says that mistaking eleven for twelve would be like mistaking a pigeon for a dove (199b). The analogy becomes clearer when later, in a different context, Socrates says that we have the same number in mind “when we say one, two, three, four, five, six; or twice three; or three times two; or four plus two; or three plus two plus one” (204b-c). This means, if we apply it to the present case, that our knowledge of eleven must include 5

+ 6 and 4 + 7, while our knowledge of twelve would include 5 + 7, which sufficiently resembles the other two that it is readily mistaken for them, as a pigeon is for a dove.[39] When we first make such a mistake, we place into our

― 104 ―
aviary an “ignorance,” that 7 +5 = 11, which we may continue to find there.

How then would we answer Socrates’ question as to how we can think that something we know is something we do not know? On the wax model such false opinions were explained as a mismatching of perception to knowledge (because, for example, of the former’s indistinctness). But the aviary model cannot provide such an explanation, because the birds, unlike the wax impressions, do not refer to anything beyond themselves. It often happens in Platonic dialectic that if two hypotheses are rejected a third is proposed that combines the positive features of each while avoiding their weaknesses, as number 3 in this section combined numbers 1 and 2.[40] No sixth model is proposed here to follow the wax and aviary hypotheses, but if we try to imagine what such a model would have to be like, it would be one that combined the “recognition” factor of the wax modal with the “latency” factor of the aviary model.[41] In view of the emphasis on memory both in the last two sections and in the dramatic byplay of the opening of the dialogue, and in view of the frequent allusions to the Meno , it may be significant that the doctrine of recollection does in fact incorporate both the features of latency and recognition.

That we are meant to come away with something positive from these discussions is suggested by the fact that Socrates could have refuted the “knowledge is true opinion” definition at the very outset if he had chosen to. After the aviary model is dismissed, Theaetetus reiterates this definition as still the best he can devise, and Socrates replies that true opinion cannot be the same as knowledge, because jurors can be persuaded to have a true opinion about something they have not witnessed, whereas only eyewitnesses have knowledge (201b-c).[42] Since Socrates ― 105 ―
does not offer this simple but crushing refutation at the outset, but chooses first to develop the abortive models in detail, it is worth trying to see the value of their implications.

Socrates’ remark that we can only know what we have seen (201b) is reminiscent (at a different level) of the claim that lies at the basis of the doctrine of recollection. As the Meno puts it, knowledge is possible because in some sense we have already “seen” reality.[43] We can extend the aviary model in this direction. In some sense we have latent knowledge of reality a priori , and we can add this kind of bird to the latent memories of a posteriori knowledge with which Socrates stocked the aviary.

Because the former is only latent we cannot always grasp it, just as we cannot always grasp the correct bird in the original aviary. When we perceive something (whether with the senses or the mind), it reminds us of one of these birds; and if we can grasp the correct bird, we then have knowledge of the thing perceived. But because many of the birds resemble one another, and because they are (as latent) indistinct,[44] we can mismatch a perception with a latent knowledge. This model (even in cases that do not require an a priori factor) avoids the paradoxes of the other one because when we make a mistake we are not in active possession of knowledge. Active knowledge arises only from the correct match (i.e., recognition) between latent knowledge and perception.

Even the revised aviary model, however, would leave us with the problem of how we can tell when we are matching correctly. How can we distinguish in practice between the true matching of 5 + 7 = 12 and the false matching of 5 + 7 = 11, or, more recalcitrantly, between “Justice is an arbitrary convention” and “Justice is a natural value”? If the wax block provided us with a correspondence model of truth, the aviary, which makes no reference to anything outside us, implicitly provides us with something more like a coherence model. Five and seven do not “correspond” to the twelve-bird in the same sense that our remembered knowledge of Theaetetus corresponds to the Theaetetus whom we now perceive; rather, the proposition 5 + 7 = 12 is internally coherent.

In the case of the arithmetical examples that Socrates gives through-

― 106 ―
out the aviary discussion, we can see how the truth of the propositions might be tested by counting,[45] but no method is given to us by which we might test the truth of our opinions generally . That seems to be the function of the concept of logos , which will now be introduced, and which plays a similar role in the Meno (98a). If the wax and aviary models are related to each other as the correspondence and coherence models of truth, then in the Theaetetus correspondence leads to coherence, which in turn leads to the need for some kind of methodology or logos. A central problem of the correspondence model of truth has always been that of validation: How can we tell whether our thoughts correspond to something outside them, since we cannot get outside our thoughts to compare the two? Accordingly, proponents of a correspondence theory of truth tend in general to make use of a coherence model in order to validate correspondence. Since no other validation is possible, if we can assume that reality is logically coherent, the degree of coherence Within our thoughts will be a good test of the degree to which they correspond with reality. This was certainly Plato’s view, and together with the correspondence model implicit in the theories of recollection and purification, a coherentism is implicit in the methods of hypothesis and division.[46] Thus in the Meno Socrates defends the dianoetic (coherence) approach to noetic (evidentness and correspondence) knowledge by saying, “Since all nature is akin, and since the soul has learned all things [“prenatally,” but has since “forgotten”

them], then if it recollects even one thing—which people call learning it—nothing prevents it from discovering all other things if one is courageous and does not stop searching” (81d).

We saw earlier (n. 42) that Socrates gives two apparently conflicting accounts, in close proximity with each other, of how empirical knowledge may be acquired. At 201a he says,

― 107 ―

Or do you think there are any teachers so clever that, in cases of robbery or other violence where there were no witnesses, they are able to teach, within the short time allowed by the water clock, the truth about what happened?

But at 201b-c he goes on to say,

When jurors are justly persuaded about matters that can be known only by an eyewitness and not otherwise, if then they decide these things from hearsay, acquiring a true opinion, don’t they decide without knowledge, being rightly persuaded if they passed judgment well?

The first statement appears to accept that, if more time were available, teaching could take the place of witnessing; the second insists that that is not possible. We could escape from the tension by interpreting the first remark in the sense of “especially within the short time allowed by the water clock,” which would remove the tension but would not explain why Socrates bothers to mention the clock at all, a reference that only confuses the issue. Rather than trying in this way to eliminate the tension, between the direct knowing of the witness and the indirect knowing of those to whom the facts are demonstrated by argument, we will do better to notice that this tension, which is operative with respect to knowledge of the physical world, drops away at the level of noetic knowledge. As the Meno’s slave demonstration showed, at this level rational argument may indeed bring us to the point where we are capable of seeing for ourselves, where persuasion and witnessing, coherence and correspondence, coincide (85c-d).[47]

9. The Logos of Knowledge (201c-210d)

In response to Socrates’ counterexample about juries, Theaetetus suddenly recalls something that he had forgotten (at 148e he said that he had never heard a definition of knowledge): he once heard someone say that knowledge is true opinion with a logos (201c). In an inadvertent illustration of the phenomenon of recollection, he does not think that he can explicate this claim himself, but thinks that he could follow someone else who did.

Socrates replies, ‘“Listen, then, to a dream in ― 108 ―
exchange for a dream, for I seemed to hear it from certain people”

(201d-e).

The puzzling description of this theory as a dream has given rise to several explanations.[48] It is reminiscent of the use of that term in a previously cited passage of the Meno : “At present these opinions, having just been stirred up in him, are like a dream. If, however, one were to ask him the same things many times and in many ways, you know that finally he would have knowledge of them that is no less accurate than anyone’s”

(85c-d). Perhaps the use of the term “dream” here in the Theaetetus is meant to suggest that the theory that follows is one that we should be able to recognize as true, but only indistinctly—as Meno’s slave recognized the truth of the mathematical demonstration. It is a not-yet-adequate “recollection” of the nature of knowledge. But because of its lack of distinctness, Theaetetus, who like the slave can follow it but not exhibit it himself,[49] will never successfully formulate it in this dialogue.

Earlier, Socrates described the soul’s thinking as “nothing other than a talk [

[Full Size]

] with itself, in which it asks itself questions and answers them, and affirms and denies” (189e-190a). According to Meno’s paradox, if we need to ask the questions in the first place, how can we answer them by ourselves? Conversely, if we can answer them, why did we need to ask them?

On the theory of recollection this kind of dialogue ― 109 ―
is possible because we know the answers latently but not overtly, and our self-questioning is designed to bring the “dream” into clearer focus. The same is true of Socrates’ maieutic questioning. Socrates says that he is like a midwife in that he is sterile (with regard to wisdom), and that he has always been so (150b). But he said earlier that although midwives must be past childbearing, they must also have previously given birth, “because human nature is too weak to acquire an art concerning things with which it is not experienced” (149b-c). It does not seem possible, then, that Socrates was always sterile—or, at least, if he can be a midwife to wisdom, he must have something like a “memory” or “recollection” of wisdom, even if he never actually had wisdom.

With Socrates as his midwife, Theaetetus produces three versions of the dream theory, the third of which itself has three divisions. The theory is “that the primary elements from which we and everything else are composed have no logos.” They can only be named; we cannot even say that an element is or is not, or we would be adding being or not-being to it. But we can give a logos of composite things by naming the elements of which they are composed (201e-202c). Theaetetus recognizes this as the theory he has heard. The paradigms that this theory has in mind, Socrates says, are “the elemental letters and composite syllables of writing [

[Full Size]

means both “elements” and “letters”]. Or do you think that the one who said the things we have mentioned was looking somewhere else?” (202e).

Theaetetus answers in the negative, but others have not always been so sure.[50]

1 (203a-d) . Socrates first points out that it makes no sense to say that the syllable can be known only on the basis of its elements, its component letters. For since the letters are elements, they are not reducible to a further logos; but since knowledge ex hypothesi requires a logos, the letters must be unknowable. In that case they can hardly confer knowability Upon the syllable. For example, if knowing the first syllable of “Socrates” means that we can give an account (

[Full Size]

) of it by analyzing it into the letters S and o , we will be unable to know these

― 110 ―
elements themselves because they are not further analyzable into something more elemental still. It is thus problematic how a complex can be known in terms of elements that are themselves not known.

2 (203e-206c) . Socrates then distinguishes a “whole” (

[Full Size]

) from a “sum” (

[Full Size]

).

SOCRATES: Perhaps we should have proposed, not that the syllable is its elements, but that from these a single form [

[Full Size]

] arises, which itself has a single Idea [

[Full Size]

] of its own, different from the elements.

THEAETETUS: Absolutely. And perhaps it will even be better this way than the other.

SOCRATES: Let it be then as we are now saying, the syllable is a single Idea [ ] arising from the several conjoined elements, and it is the same in writings and in all other things.

THEAETETUS: Absolutely.

But Socrates quickly cuts off this route of escape: SOCRATES: Isn’t it the case that there must not be parts of it?

THEAETETUS: How so?

SOCRATES: Because if something has parts, the whole is necessarily the sum of parts. Or do you also say that the whole that arises from the parts must be some single form [

[Full Size]

] that is different from the sum of the parts? (203e-204a) This new hypothesis is attacked with a dilemma, the first horn of which immediately collapses the new distinction between whole and sum. “A whole is … that from which nothing is missing, and that from which something is missing is neither a whole nor a sum, which together become the same for the same reason” (205a). Socrates’ objection begs the question by assuming that no account of a “whole” can be given that would satisfy the original stipulation that it is “without parts” and “different from the parts.”[51]

Can such an account be given? If a whole is without parts, how can we speak of it in terms of “the parts” at all? It is this oddity that makes Socrates’ refutation plausible. The answer would seem to lie in estab-

― 111 ―
lishing that a whole is correlated to a sum, so that one can speak of the parts of the sum in relation to the whole, but not as parts of the whole.

There are various examples that can illustrate such a relation.

a. A species can be thought of as a whole, and in a sense we can think of its members as parts of the species; but they are not parts in the strict sense, because the species retains its integrity when individual members cease to exist or come into being. Correlated with the species is the totality of its present members, which stands to the species as a sum to a whole. The totality is affected by addition and subtraction of parts, but the species is not.

b. In the case of a syllable, since historically speech preceded writing, the whole sound was given first—as a unity that was only subsequently analyzed into letters by later grammarians. Consequently, in different languages the same sound is frequently represented by different collections of elements. The long o, in the first syllable of “Socrates,”

can be regarded as a single sound, as represented by the omega in Greek; or as a combination of two sounds, a short o (o ) followed by a long u , as represented by “ou” in the Wade-Giles and pinyin systems of transcribing Chinese; or, for that matter, “oh” in English, which does not have separate vowels corresponding to the Greek omega (long o ) and omicron (short o ), and therefore adds the h to indicate that the sound must be lengthened. Even to the extent that a syllable can be analyzed unproblematically into elements, the sum of the elements is not the same as the syllable unless they are properly united with regard to sequence, relative duration, emphasis, and so on. Thus, although in one sense we can speak of the syllable as the sum of its constituent letters, in another sense it is a pregiven whole to which we must look, as a paradigm, in order to put the right elements together in the right way. Wholeness implies an organization of the parts, whereas a sum is a simple aggregation. In terms of Socrates’ later example of the parts of a wagon: when a wagon has been dismantled, or wrongly put together, the parts constitute a mere sum. The sum does not imply wholeness until the parts have been put together in a uniquely correct way.

c. According to the theory of forms, as well, the essential character of a thing precedes it as a paradigm, rather than following upon it as a consequence.[52] The importance of the sum/whole distinction to the ― 112 ―
theory of forms was already visible in the first argument of the Parmenides, the argument from participation (Chapter 1, section 4). An analogous distinction was visible in relation to that dialogue’s treatment of the One, in the distinctions implicit in the differences between the first and second hypotheses, and explicit in the third (Chapter 1, section 10).

d. In the Phaedo Socrates rejects Simmias’s conception of the soul as an epiphenomenon of bodily parts (a sum). The soul is rather what makes possible the organization of the bodily elements into a unity in the first place.

How the two present hypotheses (that a syllable is its elements, and that a syllable is a whole that is not identical with its parts) may be integrated to achieve the model of a whole that is related to its parts but is not identical with them will become evident in the third hypothesis, below.[53]

The second horn of the dilemma is that if the syllable is a whole that ― 113 ―
is not composed Of parts, then it is as irreducible as the letters, and equally unknowable (by logos): “The syllable falls into the same form [

[Full Size]

] [as the elements] if it has no parts and is a single Idea [

[Full Size]

[Full Size]

]” (205d).

Socrates adds a more general objection to the dream theory. Our experience in the learning of writing and music has taught us that it is easier to know the elements than the composites, which is the opposite of what the theory claims.[54] He adds that this can be demonstrated in other ways as well (206c). In view of the way that the language in the above quotations irresistibly reminds us of the theory of forms, it would not be surprising if the primacy of knowing “uniform” forms over multiform individuals may be what is meant .[55]

3a (206c-e) . Socrates leaves aside the sum/part/whole question and turns to the question of what is meant by logos. The first hypothesis is that it means the mirroring in words of one’s opinions. The hypothesis is dismissed because logos in this sense is natural to all normal people, so nothing would be gained by adding “with logos” to the definition of knowledge as right opinion. The image ‘with which the hypothesis was presented is nevertheless a striking one: “the making dear of one’s own thought [

[Full Size]

] through the voice with verbs and nouns, as in a mirror or water, imaging the opinion in the stream through the mouth” (206d). Here words are viewed from the other side, as primary elements of meaning rather than as derivative complexes of elemental letters. Nouns and verbs are the regularities that make it possible to give meaningful form to the otherwise undifferentiated stream of voice through the mouth. In the same way the forms always were for Plato the regularities that made it possible for a meaningful world to arise out of the undifferentiated stream of Heracleitean flux. Here the analogy between nouns and verbs, on one hand, and forms, on the other, is never made explicit, but in the Sophist nouns and verbs will function as the signs of individual forms (259e-264b).

There the Eleatic stranger will echo Socrates, saying that speech (

[Full Size]

) manifests our thought (

[Full Size]

) in “a stream proceeding from the soul through the mouth with voice”

(263e);

― 114 ―
but he adds that speech is possible only “because of the interweaving of forms with one another” (259e).

3b (207a-208b) . The second hypothesis is that logos means an account of something in terms of its elements, such as listing the parts of a wagon.

This is refuted by the observation that one may be able to enumerate elements without having knowledge in the normal sense. Someone might say, for example, that the first syllable of “Theaetetus” is spelled “The” (Q +
e ), but incorrectly think that the first syllable of “Theodoros” is spelled “Te” (T + e ). In this case he does not know how to spell the syllable, but gets it right in the first case by right opinion. Therefore, on this understanding of logos, we can satisfy the definition without having knowledge (207d-208b).

Although this hypothesis does not further the investigation directly, the examples used have implications that further it indirectly. In the Theaetetus Socrates refutes the “dream” theory in terms of the way we learn to read. Syllables are wholes, and all knowledge is of a whole in terms of its parts, such as the syllable in terms of its letters; but on that definition of knowledge the ultimate elements or letters will be unknowable since they have no parts (e.g., S and o in the first syllable of “Socrates”), and knowledge of the syllable will be indistinguishable from right opinion (e.g., “The” in the names “Theaetetus” and “Theodorus”). But when we think about this example of reading, we find that Socrates has inverted it. We noted above that historically it was speech that preceded writing, rather than the reverse, and it is even more obvious that as individuals we learn to read only after we learn speech.

Therefore we learn letters in terms of syllables, and syllables in terms of words, instead of the other way around. In fact the Statesman will make this point explicitly. In a passage that recalls Socrates’ example here of the child who can spell the syllable “The” in “Theaetetus” but cannot spell the same syllable in “Theodorus,” the Eleatic stranger says that children learn letters by seeing at first how they constitute the simplest syllables, and then using this knowledge as a paradigm for recognizing the same letters in more difficult syllables. The letters are then known in terms of their sameness with and difference from the letters in other syllables (277e-278c). Thus we come to know parts by noticing the similarities and differences among wholes, and seeing how these are reflected in the parts. Knowledge of the whole precedes that of the parts.

This point follows even more dearly from the example of knowing the wagon by listing its parts. Socrates adds that it would not, on this ― 115 ―
definition, count as knowing the wagon if we could name the wheels, axle, body, rails, and yoke, but not the “hundred pieces of wood” from which they are built (207a); nor as knowing the name “Theaetetus” if one could list the syllables but not the letters (207b). The reference to knowing the name by knowing the syllables reminds us that the present discussion of whole and parts had altogether abstracted from the name or word as a whole, and asked only about the relationship between letter and syllable.

But the meaning of the syllable comes from two directions: from the letters, which furnish its materials, and from the word itself—the nouns and verbs mentioned at 206d—which gives the syllables their purpose and meaning. Similarly, the basic parts of the wagon can be explicated either in terms of the hundred pieces of wood from which they are constructed, or in terms of the unity of the wagon, which is their reason for being. The hundred pieces of wood are not a wagon until they are properly unified.[56]

Implicit in the previous discussion was a conception of a “whole” that is not reducible to its parts. Implicit in this one is the conception of a unifying form that can explain the parts of a sum from above instead of from below. The sixth of the fifteen aporiae that Aristotle raised in Book B of the Metaphysics is,[57]

whether it is the genera that should be taken as elements and principles, or rather the primary constituents of a thing … . To judge from these arguments, then, the principles of things would not be the genera; but if we know each thing by its definition, and the genera are the principles or starting-points of definitions, the genera must also be the principles of definable things … . And some also of those who say unity or being, or the great and the small, are elements of things, seem to treat them as genera.

Essentially the same question underlies the present discussion of the Theaetetus . In response to this, Plato, like Aristotle, turns to a consideration of the nature of definition—a course subsequently pursued more intensively in the Sophist . There the “primary elements” will not be the minutest particulars but the most universal genera. The Sophist accordingly furthers the inconclusive inquiry of the Theaetetus in at least three ways. (i) The Dream paradox, that complexes are knowable in terms of their demerits but elements are ultimately unknowable, is, if not re-

― 116 ―
futed, at least undercut. The reciprocity of collection and division means that the whole and part are somehow implicit in each other: through collection (which appears only rarely in the Sophist ) we understand the whole in terms of the parts, but through division we understand the part in terms of the whole. (ii) Even though the whole may be known in terms of its parts, this knowledge is not reducible to its parts (as in 2, above), for we can know what “production” or “acquisition” is without knowing every kind of production or acquisition. (iii) Because parts can be known in terms of the whole, the logos of a thing need not be understood as the additive sum of the constitutive elements of the thing. Rather, the correct “method of logoi” (Sophist 227a) is to determine the essence of something by dividing the pregiven whole into derivative species. The method of division always takes precedence over the method of collection.[58]

The way that the Sophist goes beyond the Theaetetus can also be seen in its handling of the same illustrations. We have already seen that in the first model of “logos” (3a) the regularity inherent in the paradigm of “nouns and verbs” implied the combinability of universal forms, and that this conception becomes explicit in the Sophist . The same is true of the present paradigm of “letters.” Letters in their own way represent regularities that limit the otherwise unlimited stream of vocal sound (cf.

Philebus 17b), and as such provide illustrations of the stability and combinability of forms. The Eleatic stranger makes use of this paradigm too, in the Sophist , to illustrate the properties of forms: “Since some forms will combine and others not, they are in virtually the same condition as written letters; for some of these do not fit each other, but others do” (252e-253a). The Statesman takes the comparison farther still: not only do letters provide an image of the stability and selective combinability of the forms, but our ability to read language becomes a paradigm of our ability to understand incorporeal reality. The fact that we can transfer our reading proficiency from easy syllables to difficult ones, because of the regularity of letters, is a paradigm of our ability to discover in corporeal paradigms the regularities that enable us to “read” the highest things, “the long and difficult syllables of actuality [

[Full Size]

]” (278c-d). Because the highest forms are of qualities (good-

― 117 ―
ness, beauty, justice, and even sameness and difference) rather than species (human being, bird, pig) there are no obvious visible examples of them: “Of the greatest and most valuable [

[Full Size]

] things there is no image made clear for human beings, by the exhibition of which someone wishing to satisfy the soul of the inquirer can, by applying it to one of his senses, sufficiently satisfy it … . For the incorporeal, being finest and greatest, can be dearly exhibited only by reason and not by anything else” (285e-286a). However, we can use the visible world as a paradigm of the intelligible in an indirect way.

Learning to read, by using the combinations of letters in easy syllables as paradigms of those in difficult ones, is offered as a paradigm of this kind of paradigm (277d).

3c (208c-210b) . The final hypothesis is what hoipolloi would say—that logos is the ability to name the sign by which one thing is distinguished from everything else, that is, the definition. But this hypothesis too must fail, because we must already know the difference between one thing and another in order to have an opinion about it in the first place, and so nothing new is gained by the addition (209a f.). This definition of knowledge will be either absurd or circular, depending on whether the logos about a thing’s distinctness is itself regarded as opinion or knowledge. If it is an opinion, then we are told to add an opinion (logos) about something to the right opinion we already have about it; and “to command us to acquire the very things that we have, so that we may learn the things that we already believe to be so, greatly resembles someone completely in the dark” (209e). If, on the other hand, it is knowledge, then knowledge is defined in terms of itself, and the definition is circular (210a).

In the evaluation of this hypothesis the only example considered is the definition of “Theaetetus” (209a-c). Consequently, definition is conceived only in terms of an individual thing rather than a form or kind. But as a preliminary model Socrates had defined the sun as “the brightest of the heavenly bodies that revolve around the earth” (208d). This example is ambiguous. Although the sun is, like Theaetetus, an individual, it is a unique individual of its kind and therefore, like universals, admits of a definition by species and differentia. It is not made dear here whether a definition of an individual within a many-membered infima species is possible at all (209b-c); it is at least much easier to define a universal (208d). Nevertheless, even if Theaetetus cannot be defined, he can be known in the sense that enabled Theodorus and Soc-

― 118 ―
rates to recognize him at the beginning. This knowing is not dependent on a single specifiable mark, but on his overall “look,” which makes him easily distinguishable from Socrates, despite the similarity of individual features or “elements.”[59] Even if a definition of Theaetetus is not possible, the example shows in an analogous way the importance, for knowledge, of the unifying “form.” Nor should we forget that the other example, the sun, tends to be associated in Plato with the theory of forms.[60]

The definition of the sun is a counterinstance to the present argument’s conclusion that definition is not possible. How are we able to define the sun in spite of Socrates’ reductio? The reductio is a restatement of Meno’s paradox, but there is no question in this case of recollection, since we are asking about a visible object. Nevertheless the answer is analogous: the explicit definition can be sought and recognized because we already know it implicitly. We have all the information necessary to conclude that the sun is the brightest heavenly object, even if the unification of the information into that description has never explicitly occurred to us. If we ask in turn how definitions are possible of the common properties that Socrates speaks of at 208d (unity, goodness, etc.), we will be led to an analogous conception of latency, this time regarding nonempirical knowledge. Such a conception is to be found in the theory of recollection. In the case of latent empirical knowledge the data are given, but the principle of unification is not; in the theory of recollection’s conception of latent a priori knowledge the unity itself is given, but only in an elusive way.

10. Knowledge and Wisdom

We have seen that the Theaetetus’s examination of knowledge goes through a progression of several different kinds of knowledge, a progression that reflects in a general way that of the Divided Line. It passes from perceptual (

[Full Size]

) to interpretive (

[Full Size]

) to mathematical (

[Full Size]

) knowledge, before ending in aporia after a discussion that con-

― 119 ―
stantly evokes (but never invokes) the theory of forms and doctrine of recollection. The next step would be to return to the suggestions made by Socrates in the digression (and previously suggested by the dramatic byplay at the beginning of the dialogue), but never incorporated into the dialogue proper: in particular, the suggestion that the pursuit of wisdom is not ultimately satisfied even by adequate definitions, but eventually entails a change from one kind of life to another, like the “turning around of the soul” in the Allegory of the Cave (Republic 7.518c f.).

To the modem ear it sounds strange that our way of life should have anything to do with our intellectual ability to know things. There seems no obvious reason why thoroughgoing hedonists who pursue philosophy as a profession because they are clever and can make money at it should not be able to have a purely intellectual grasp of the nature of things without reforming their values and way of life. Even Plato’s own doctrine of the tripartite soul seems to countenance this view, for it makes clear that even if we know the truth about things, we may not have the self-mastery necessary to act on it in opposition to the demands of appetite and ambition. Thus we may have knowledge without being good. Although this is true of ordinary knowledge, at the highest level of knowledge it is no longer true (accordingly, Socrates repeatedly insists on the inadequacy of his definitions of the virtues and the good in the Republic ).[61] Here, what we know and what we are coincide. The consummation of the Divided Line coincides with the consummation of the tripartite soul. This is the doctrine of “purification,” which Plato advances in the language of the mysteries.[62] The highest, “moral” forms can be adequately grasped only to the extent that we are capable of experiencing moral truth within ourselves, and we will be capable of this only to the extent that we are free of attachment to the pleasures of appetite and ambition.

Perhaps the dearest illustration of this is to be had in Aristotle’s Nicomachean Ethics , where we find that no adequate conceptual definition of goodness is possible, although we can define it merely formally as “that at which all things aim” or the “mean between the extremes of excess and deficiency.” Only good individuals themselves can give content to these formulas; only they infallibly recognize goodness in concrete situations. The wisdom of the good person is not propositional, ― 120 ―
but is closer to what we earlier called “understanding.”[63] This is Plato’s point as well, that knowledge of the highest things requires an inner recognition that is inseparable from our devotion to those things.[64] And like Plato, Aristotle affirms that the difference between philosophy and sophistry is a difference in the kind of life that one chooses (

[Full Size]

[Full Size]

, Metaphysics F.2.1004622-25).

We have seen numerous reminders of the theory of forms throughout the Theaetetus , and have suggested that the aporetic nature of this dialogue may be a consequence of the overt absence of the forms. Nevertheless, it is best not to short-circuit Plato’s enterprise in these dialogues by too hastily supplying “solutions” from other dialogues. There are certainly, to be sure, numerous reminders within the Theaetetus of those earlier ways of resolving some of the present questions; but nevertheless the Sophist and Statesman are clearly intended to be sequels to the Theaetetus , and it would be premature to interpose the earlier doctrines in their original form before we have followed the trilogy’s own line of inquiry to its conclusion. In our discussion of 3b (above) we saw that the Sophist furthers the inquiry of the Theaetetus by showing that the part may be known in terms of the whole, as well as the other way around; that knowledge of the whole is not reducible to knowledge of the parts; and that a logos (definition) can succeed by beginning with the whole and dividing it progressively into species, rather than trying to proceed by aggregation from unknowable elements. Subsequently, in our discussion of 3c we saw that the Theaetetus’s project of definition failed because, as is the case throughout the dialogue, the focus was on (unknowable) individuals rather than genera or kinds. This too will be remedied in the Sophist .

Chapter Two The Theaetetus

Table of Contents

- Chapter Two The Theaetetus

- Chapter Two The Theaetetus